HEALING OF STRUCTURAL MATERIAL WORKPIECES

Abstract

A method of repairing a workpiece that comprises a structural material, the method comprising: applying a current to an electrolyte comprising a repair material so as to electroplate the repair material onto a fracture of the workpiece and onto a plating region proximate to the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area Ae about the fracture, the workpiece defining a cross-section area Am at the fracture, Ae/Am is in the range of from about 10 to about 150, the plating being accomplished such that the healed workpiece exhibits a tensile strength σU that is within about 20% of a corresponding tensile strength σM of a corresponding pristine workpiece, and optionally, at least one of the structural material and the repair material comprising at least one metal.

Description

TECHNICAL FIELD

The present disclosure relates to the field of self-healing and adaptive materials and to the field of electrodeposition of metals.

BACKGROUND

A variety of materials with self-healing properties have been conceived and developed. Polymers are by far the most studied class of these materials. Earlier development focused on designing polymers with embedded microscale capsules that rupture upon the fracture of the polymer and release a liquid monomer. Then, a catalyst induces the polymerization of the monomer in the crack, which leads to crack closure and self-healing. This technique, however, is not repeatable, as a second crack at the same location cannot be self-healed because the capsules in its vicinity were depleted to close the first crack. In addition, this approach is not conducive to healing metals, which can require elevated temperatures near the metal's melting point to increase metal transport and to heal cracks. Accordingly, there is a long-felt need in the art for improved self-healing materials and related methods.

SUMMARY

Materials found in nature can change their morphology and material properties to achieve an incredible range of functionalities. This ability to dynamically change morphology and composition without failure, which one can refer to as dynamic morphogenesis, enables efficient use of limited resources, minimizes weight to reduce energy consumption for walking and running, and enables effective healing when damaged. Despite these desirable functionalities, scientists and engineers have yet to develop structural materials with similar dynamic morphogenesis. Structural materials made today are fixed and designed to withstand all current and predicted future loading cases.

In natural materials, changes in morphology and composition, in general, are enabled by the transport of mass and energy (oxygen, ATP, nutrients, and cells, for example) through cellular structures to and from the areas in which morphogenesis is occurring. These cellular structures have a continuous hard phase (ceramic or cellulose, for example) and a continuous pore structure. The continuous hard phase provides a structural network for supporting mechanical loading, while the continuous pores are critically important for (1) housing functional active materials that respond to environmental stimuli and (2) allowing mass and energy transport to and from locations of morphogenesis. This strategy of morphogenesis, through mass and energy transport, is significantly different than the strategy used by engineers in synthetic self-healing materials, where the capability for self-healing is locally stored. Although these self-healing systems based on local storage have demonstrated impressive capabilities, they are largely not applicable to hard materials, like metals or ceramics, can only be healed once (which prevents continuous adaptation and morphogenesis), and are not analogous to biological morphogenesis.

The present disclosure applies mass and energy transport mediated through electrochemical reactions to affect the dynamic morphogenesis of cellular metals, and how the resulting pore structure affects the mechanical response of the material. The disclosed materials are a new class of structural materials that, like bone, improve mechanical and chemical functionality in response to the way the material is used. Similar to bone, a matrix material acts as a structural material that distributes mechanical loads and that can be chemically modified to respond to the local environment.

As one non-limiting embodiment, to take advantage of the fast transport of metal species in electrolytes, one can infiltrate an electrolyte into the pores of high strength cellular nickel and use electrochemistry to drive chemical changes. One can apply potentials to different parts of a cellular nickel foam. Areas with negative potential will plate nickel (reduction). Areas with positive potential (oxidation) will etch nickel. In addition to changing the local density and morphology of the cellular nickel, the cellular nickel can be coated with additional materials to impart unique functionality. Using this approach, one can will fuse struts in cellular nickel to enable rapid room temperature healing.

In one aspect, the present disclosure provides adaptive material systems, comprising: an electrically conductive matrix material defining a plurality of voids; and an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal.

Also provided are methods, comprising: effecting application of an electrical current to a system according to the present disclosure so as to give rise to deposition of an amount of the first metal on a cathode region of the electrically conductive matrix material, the cathode region being in fluid communication with the electrolyte.

Further provided are methods, comprising: applying a force to a system according to the present disclosure so as to give rise to a fracture of the matrix material; and effecting application of an electrical current to the system so as to give rise to deposition of an amount of the first metal on a cathode region of the electrically conductive matrix material, the cathode region being at least partially disposed along the fracture of the matrix material.

Also provided are methods, comprising: effecting application of an electrical current to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of an amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte.

Further disclosed are adaptive materials, comprising: an electrically conductive matrix material defining a plurality of voids and the matrix material defining a grain size, and an amount of a first metal deposited on the matrix material, the amount of the first metal defining a grain size that differs from the grain size of the matrix material.

Further provided are methods, comprising: effecting application of a negative potential to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of a deposited amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte, the cathode region being disposed within a fractured region of the electrically conductive matrix material; effecting application of a positive potential to an electrolyte comprising a monomer, the application being effected so as to give rise to deposition of a deposited amount of the monomer on the deposited amount of the first metal, and giving rise to a monomer-derived polymer coating on the deposited amount of the first metal. Without being bound to any particular theory, the monomer (and resulting polymer) can be attached (e.g., via Van Der Waals forces, e.g., via chelation) to the surface of the metal, but this is not a requirement. Again without being bound to any particular theory or any particular embodiment, a monomer can be selected such that the monomer is soluble in the solvent (e.g., electrolyte) in which the monomer is dispersed, while the polymer derived from that monomer is not soluble in the solvent.

Also provided are adaptive material systems, comprising: an electrically conductive matrix material defining a plurality of voids; an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal, the electrolyte further comprising an amount of a monomer that gives rise to a dielectric polymer; and a source of one or both of a positive electrical potential and a negative electrical potential.

Additionally disclosed are adaptive material systems, comprising: an electrically conductive matrix material defining a plurality of voids; an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal, the electrolyte further comprising an amount of a monomer that gives rise to a dielectric polymer; and a source of one or both of a positive electrical potential and a negative electrical potential.

Also provided are methods, comprising: effecting application of a potential to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of a deposited amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte, the cathode region being disposed within a fractured region of the electrically conductive matrix material; effecting application of a potential to an electrolyte comprising a monomer, the application being effected so as to give rise to deposition of a deposited amount of the monomer about the deposited amount of the first metal, a monomer-derived polymer coating on the deposited amount of the first metal.

Further provided are workpieces, comprising: an electrically conductive matrix material defining a plurality of voids, a dielectric coating surmounting the electrically conductive matrix material, an opening formed in the dielectric coating, the electrically material defining two edges physically separate from one another, the opening placing the two edges into fluid communication with the environment exterior to the dielectric coating.

Also provided are workpieces, comprising: an electrically conductive matrix material defining a plurality of voids, the electrically material defining two edges physically separate from one another, an amount of deposited metal connecting the two edges, and a dielectric coating surmounting the matrix material and the deposited metal.

Further provided are adaptive material systems, comprising: an electrically conductive matrix material defining a plurality of voids; a detection device configured to detect a fracture within the matrix material; and a supply of an electrolyte comprising at least an ion of a first metal, the electrolyte optionally comprising an amount of a monomer, and the system being configured to contact the matrix material with the electrolyte upon detection of a fracture within the matrix material, and the system being configured to apply a potential to the matrix material so as to effect deposition of an amount of the first metal onto a detected fracture.

Also provided are adaptive material systems, comprising: a metallic matrix material; an electrolyte sealably contained within a void within the metallic matrix material, the electrolyte comprising at least an ion of a first metal; and a source of a potential, the source being configured to effect plating of the first metal onto a fractured region of the metallic matrix material.

Further disclosed are adaptive material systems, comprising: a metallic matrix material; a solid or semisolid electrolyte disposed about the metallic matrix material, the solid or semisolid electrolyte comprising at least an ion of a first metal; and a source of a potential configured to effect plating of the first metal onto a fractured region of the metallic matrix material.

Further provided are adaptive material systems, comprising: a metallic matrix material; and an electrolyte comprising at least an ion of a first metal, the system being configured to deliver the electrolyte to a fractured region of the metallic matrix material.

Additionally provided is a method of repairing a workpiece that comprises a structural material, the method comprising: applying a current to an electrolyte comprising a repair material so as to electroplate the repair material onto a fracture of the workpiece and onto a plating region proximate to the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area Ae about the fracture, the workpiece defining a cross-section area Am at the fracture, Ae/Am is in the range of from about 10 to about 150, and the plating being accomplished such that the repaired workpiece exhibits a tensile strength σU that is within about 20% of a corresponding tensile strength σM of a corresponding pristine workpiece, and, optionally, at least one of the structural material and the repair material comprising at least one metal.

Also provided is method of repairing a workpiece that comprises a structural material, the method comprising: applying a current to an electrolyte comprising a repair material so as to electroplate the repair material onto a fracture of the workpiece and onto a plating region proximate to the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area A_e about the fracture, the workpiece defining a cross-section area A_m at the fracture, A_e/A_m is in the range of from about 10 to about 150, and the plating being accomplished such that the repaired workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of a corresponding pristine workpiece, and, optionally, at least one of the structural material and the repair material comprising at least one metal.

Further disclosed is a method of constructing a workpiece, comprising:

• • applying a current to an electrolyte comprising joint metal so as to incorporate joint metal (i) into a gap between a first metallic section comprising a first structural metal and a second metallic section comprising a second structural metal and (ii) onto a plating region proximate to the first metallic section and the second metallic section so as to give rise to a workpiece comprising joint metal connecting the first metallic section and the second metallic section, the plating region defining an exposed area A_e, the first metallic section and the second metallic section defining a cross-section area A_m at the gap between the first metallic section and the second metallic section, and A_e/A_m is in the range of from about 10 to about 150, and optionally, the plating being accomplished such that the workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of either one of the first metallic section and the second metallic section.

Also provided is a material repair system, comprising: an electrolyte comprising a repair metal; a fractured workpiece comprising structural metal; and a source of current configured to apply a current to the electrolyte, the system configured to effect application of the current to the electrolyte so as to electroplate repair metal onto a fracture of the workpiece and onto a plating region of the workpiece extending from the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area A_e about the fracture, the workpiece defining a cross-section area A_m at the fracture, and A_e/A_m is in the range of from about 10 to about 150, and the plating being accomplished such that the repaired workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of a corresponding pristine workpiece

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

In the drawings, which are not necessarily drawn to scale, like numerals may describe similar components in different views. Like numerals having different letter suffixes may represent different instances of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various aspects discussed in the present document. In the drawings:

FIG. 1 provides a geometry of a simulated electrochemical cell. Boundaries representing the anode, the cathode and a constant concentration condition are highlighted in red, blue and purple respectively. The side surfaces of the broken strut are coated with a passivating layer; hence no electrochemical reactions occur on those surfaces.

FIGS. 2A-2C provides a SEM image (FIG. 2A) and photograph (FIG. 2B) of the Ni foam used in this study (scale bar represents 5 mm). Cross-sectional SEM image of ALD alumina coating on Ni foam FIG. 2C. The coating thickness is approximately 150 nm.

FIGS. 3A-3B provides representative constitutive mechanical behavior of nickel foam with SEM insets showing cracks in regime II samples and regime III samples (scale bars represent 300 m).

FIGS. 4A-4D provides representative pre-healing and post-healing stress-strain plots of regime III samples healed using electrodeposition for 1 h (FIG. 4A), 2 h (FIG. 4B), 3.5 h (FIG. 4C) and 5 h (FIG. 4D). Pre-healing curves are plotted in line form while post-healing curves are plotted using dots.

FIGS. 5A-5C provides representative pre-healing and post-healing stress-strain plots of regime II samples healed using electrodeposition for 1 h (FIG. 5A), 3.5 h (FIG. 5B) and 5 h (FIG. 5C).

FIGS. 6A-6B provides representative healing efficiency with respect to electrical energy dispensed during healing for regime III samples (FIG. 6A) and regime II samples (FIG. 6B).

FIGS. 7A-7B provides a representative SEM image showing nanocrystalline grains in Ni electrodeposited on Ni foam (FIG. 7A) compared to micron-sized grains in uncoated Ni foam (FIG. 7B). Both scale bars represent 10 μm.

FIGS. 8A-8B provides representative current measured during nickel electrodeposition on uncoated nickel foam and nickel foam with various passivation coatings (FIG. 8A). Cracking in ALD alumina coating observed by SEM after tensile testing (FIG. 8B). Scale bar represents 50 μm.

FIG. 9 provides a representative concentration distribution close to the cathode (the two strut surfaces highlighted in blue in FIG. 1) at t=0 s, t=120 s, t=1200 s and t=2280 s. Mesh deformation allows a visualization of the nickel film profile on the two strut surfaces at each time instant.

FIG. 10 provides a representative profile of electrodeposited nickel coating on blue-colored cathode boundary at time instants incremented by 150 s. Electrodeposited nickel exhibits a non-uniform growth rate across time and position on the blue surface.

FIG. 11 provides a representative diffusive flux of nickel ions close to the cathode at t=30 s, t=300 s, t=1200 s and t=2280 s.

FIG. 12 provides a representative probability of achieving 100% stress and toughness healing efficiency in healed Ni foams subjected to micro-scale cracking (dashed lines) and large-scale cracking (full lines).

FIG. 13 provides a representative Gaussian distribution of stress healing efficiency of Ni foams subjected to micro-scale cracking and healed for varying time durations.

FIG. 14 provides representative SEM images showing the same strut in a coated Ni foam before (left panel) and after healing (right panel). The passivating coating limits nickel deposition to cracked areas.

FIG. 15 provides representative Ni foams with two different crack configurations were obtained by halting tensile testing at two distinct regimes

FIG. 16 provides representative SEM images showing nickel deposits along healed large-scale cracks in Ni foams.

FIGS. 17A-17E provide representative transport-mediated healing in cellular metals inspired by bone. FIG. 17A—Illustration of hematoma formation during bone fracture. Healing occurs by transporting cells and nutrients through the cellular bone to the fracture location. FIG. 17B—Illustration of our transport-mediated approach for healing polymer-coated cellular nickel. Healing occurs by transporting electrons through the nickel and nickel ions through the electrolyte in the pores to the healing location. The nickel ions electrochemically reduce, and new nickel is electrodeposited. FIG. 17C—SEM image of a fractured nickel strut. Exposed nickel and the plastic coating are false-colored with blue and brown, and the background brightened to highlight the strut. FIG. 17D—The same strut in (c) after healing. Electrodeposited nickel is false-colored green. FIG. 17E—Stress-strain data of a cellular nickel sample. We characterize the healing effectiveness of cellular nickel subjected to three damage types: plastic deformation at 3% strain (P), failure beyond the ultimate strain (F1), and local failure by scission (F2).

FIGS. 18A-18I provide representative healing of cellular nickel with scission damage (F2). Photograph (FIG. 18A) and SEM micrograph (FIG. 18B) of cellular nickel with F2 failure before healing. FIG. 18C—SEM micrograph of healed cellular nickel showing nickel deposits isolated to the scission vicinity. FIGS. 18D-18F—Stress-strain data of F2 cellular nickel healed with 0 J, 500 J, and 1,500 J of electrical energy. Data from a pristine cellular nickel is included in FIG. 18D for reference. FIG. 18G—Strength and toughness healing efficiency, e_σ and e_U, plotted versus electrical energy input. FIG. 18H—The probability of attaining a target strength healing efficiency plotted versus electrical energy input. Connected lines correspond to 50, 80, and 100% healing efficiency. FIG. 18F—Fraction of samples that fractured outside the healed scission (B samples) compared to samples fractured at the scission (A samples) as a function of electrical energy input.

FIGS. 19A-19I provides representative healing of cellular nickel subjected to tensile loading near failure (F1). Photograph (FIG. 19A) and SEM micrograph (FIG. 19B) of F1 nickel foam before healing. FIG. 19C—SEM micrograph of F1 foam healed with 250 J. FIGS. 19D-19G—Stress-strain data of F2 cellular nickel healed with 0 J, 250 J, 2,500 J and 3,500 J of electrical energy. Data from a pristine cellular nickel is included in FIG. 19D for reference. FIG. 19H—Toughness and strength healing efficiency plotted with respect to electrical energy input. FIG. 19I—The probability of attaining a target strength healing efficiency (50, 80 and 100%) plotted versus electrical energy input.

FIGS. 20A-20G provide representative healing of plastically-deformed cellular nickel (P). FIG. 20A—Stress-strain data for the first loading of P cellular nickel, followed by stress-strain data for the second loading after healing with 0 J (no healing) and 1,500 J of energy input. FIG. 20B—Strengthening factor plotted versus electrical energy input. FIG. 20C—The probability of attaining a target strengthening factor (0.8, 1.0 and 1.2) plotted versus electrical energy input. FIG. 20D—SEM micrograph of P cellular nickel before healing. FIG. 20E—SEM micrograph of P cellular nickel after healing. FIG. 20F—SEM micrograph of post-healed fracture in a P cellular nickel strut. FIG. 20G—Temperature during healing plotted versus healing energy input per mm crack length for our work, different reports of metal healing, and two welding methods. The numbers correspond to the references for each data range.

FIGS. 21A-21C provide (FIG. 21A) stress-strain data of F2 cellular nickel healed with 0 J, 250 J, 900 J, 1,500 J, and 2,100 J of electrical energy. (FIG. 21B) Stress-strain data of twenty pristine cellular nickel samples used to calculate the healing efficiencies of F2 samples. Average tensile strength is 2.1432 MPa and average toughness is 97,178 J/m³. c) SEM images of F2 sample before (image to the right) and after healing (scale bars: 1 mm).

FIGS. 22A-22C provide (FIG. 22A) stress-strain data of F1 cellular nickel in the pristine state (dashed lines) and after healing with 0 J, 250 J, 1,000 J, 1,500 J, 2,500 J, and 3,500 J of electrical energy (continuous lines). SEM micrographs of microscale cracks in F1 cellular nickel after tensile failure (scale bar: 100 μm) (FIG. 22B) and F1 cellular nickel healed with 2,500 J of electrical energy input (scale bar: 1 mm)*FIG. 22C).

FIGS. 23A-23C provide (FIG. 23A) stress-strain data of P cellular nickel healed with 100 J, 360 J, 900 J, 1,500 J, and 2,100 J of electrical energy. (FIG. 23B) Stress-strain data of ten non-healed P cellular nickel samples used to calculate the strengthening factors of P samples. Average tensile strength is 1.8578 MPa. (FIG. 23C) SEM image of a nickel strut in a P sample before healing (image to the left), and another strut after healing (scale bars: 100 μm).

FIGS. 24A-24D provide representative probability density functions of strength healing efficiency at each energy input for F2 samples (FIG. 24A) F1 samples (FIG. 24B), and P samples (FIG. 24C). (FIG. 24D) Fit data for the Gaussian distributions shown in FIGS. 24A, 24B, and 24C.

FIGS. 25A-25C provide (FIG. 25A) X-ray diffraction spectrum of electrodeposited nickel. SEM micrographs of electrodeposited nickel (FIG. 25B) and a pristine nickel surface in the cellular nickel (FIG. 25C) (scale bars: 10 μm).

FIG. 26 provides an exemplary 3D printed device used for healing of cellular nickel samples (dimensions are in inches).

FIG. 27 provides exemplary images of embodiments of the disclosure technology, showing (from left to right) an example setup for healing fractured nickel foam, views of fractured and healed nickel foam, and pristine, fractured, and healed dog-bones of nickel foam.

FIG. 28 provides exemplary elements (metals and metalloids) that can be electrodeposited with current technology; alloys containing two or more of these elements can be electrodeposited as well.

FIG. 29 provides a representative schematic of an example process according to the present disclosure;

FIG. 30 provides some example (non-limiting) polymers that can be used as insulating polymers for the disclosed technology;

FIG. 31 provides a polymer-coated working electrode, made according to the disclosed technology.

FIGS. 32A-32C. Limitations of welding as a repair technique in a metals circular economy. (FIG. 32A) Life cycle of structural metal parts under a linear model and a sustainable circular model with 2019 numbers for aluminum (in kilotons) from the International Aluminum Institute. (FIG. 32B) Illustration of thermal cracking resulting from welding “unweldable” alloys. (FIG. 32C) 3D rendering of an octet-truss lattice structure. Top inset shows that a conventional welding torch cannot access a fracture in an internal strut. Bottom insets show how nickel ions can easily access the fractured internal strut, where they are reduced to nickel metal during electrochemical healing. A passivating coating enables targeted electrochemical reduction at the fracture site.

FIGS. 33A-33F. Electrochemical healing of a nickel alloy. FIG. 33A—Illustrations of Ni 200 dogbone samples in the pristine, fractured, and healed state. The fractured sample is masked to leave only an area A_e exposed. FIG. 33B—Stress-strain data of a pristine Ni 200 sample, and two samples with the same exposed area, healed with different charge inputs (200 and 1000 mAh). FIG. 33C—Strength healing efficiency σ_U/σ_M as a function of exposed area ratio A_e/A_o for Ni 200 samples healed using a charge input of 200 mAh and 1000 mAh. FIG. 33D—Strength healing efficiency σ_U/σ_M as a function of charge input Q for Ni 200 samples with A_e/A_o=0.4375. FIG. 33E—Photographs showing the three types of fracture sustained by healed samples upon subsequent tensile loading. FIG. 33F—Incidence of the three types of fracture after healing as function of A_e/A_o in Ni 200 samples healed with 1000 mAh and 200 mAh of charge input. Each datapoint corresponds to between 3 and 5 samples.

FIGS. 34A-34F. Model for effective tensile strength recovery. FIG. 34A—Two plots of σ_U/σ_M as a function of A_e/A_M that include three curves corresponding to each fracture type (I, P, M). The top plot represents a hypothetical case in which only partial healing is possible (σ_U/σ_M<1), while the bottom plot represents a case in which full healing (σ_U/σ_M=1) is possible. FIG. 34B—Plot of σ_U/σ_M as a function of A_e/A_M showing the theoretical model applied to healed nickel (Ni 200) samples. The circles with standard deviation bars are experimental data, with circles colored according to the corresponding charge input. The data enclosed by the dashed line rectangle is the same data shown in FIG. 2d. FIG. 34C—SEM image of cross-section of half-dogbone Ni 200 sample. FIG. 34D—Higher magnification image of FIG. 34C showing detail of surface morphology. FIG. 34E—SEM image of cross-section of Ni 200 sample after post-healing type-P fracture. FIG. 34F—Higher magnification image of FIG. 34E showing the presence of plated nickel within the cross-sectional area.

FIGS. 35A-35F. Electrochemical healing of steel and “unweldable” aluminum alloys. FIG. 35A—Plot of σ_U/σ_M as a function of A_e/A_M showing the model applied to healed AISI 1008 steel samples. The circles with standard deviation bars represent experimental data, with circles colored according to the corresponding charge input. FIG. 35B—Plot of σ_U/σ_M as a function of A_e/A_M showing the model applied to healed Al 7075 samples. FIG. 35C—Plot of σ_U/σ_M as a function of A_e/A_M showing the model applied to healed Al 2024 samples. FIG. 35D—Incidence of the three types of fracture after healing as function of A_e/A_M for healed Al 2024 and Al 7075 samples (Al 2024 samples healed with 600 mAh are excluded). FIG. 35E—Strain-strain data of four healed Al 7075 samples with A_e/A_M=81.0 that experienced type-I and type-M fracture. FIG. 35F—Plot of toughness healing efficiency U/Um for healed Al 7075 samples with respect to A_e/A_M. Yellow data corresponds to all Al 7075 samples, while red data corresponds only to samples that experienced type-I fracture.

FIGS. 36A-36C. Electrochemical healing of a 3D printed shellular funicular structure. FIG. 36A—Rendering of the shellular structure with vertical and horizontal sections. FIG. 36B—Photographs of a 3D printed shellular structure in its pristine state, after initial tensile fracture, after healing, and after post-healing fracture. FIG. 36C—Pristine and healed stress-strain data for two shellular structures, one healed with the normal process (potentiostatic only), and another healed with the enhanced process (pulsed+potentiostatic).

FIGS. 37A-37G. Practical application of electrochemical healing at different length scales. FIG. 37A—Minimum charge input required for full healing for metals with a cross-sectional area A_M ranging from 10⁻⁸ to 1 m² assuming 1×, 5×, 10×, and 20× improvement in shear strength at the nickel-metal interface, including inset showing data for A_M ranging from 10⁻⁴ to 10⁻² m². FIG. 37B—Financial cost of healing due to the consumption of electricity and nickel, assuming 1×, 5×, 10×, and 20× improvement in shear strength at the nickel-metal interface. FIG. 37C—Time required for full healing with a current density of 10 mA/cm². FIG. 37D—Pristine and fractured chrome-coated steel wrench. FIG. 37E, 37F—Both sides of a fractured wrench after healing with 8,200 mAh. FIG. 37G—Torque applied to a pristine, fractured, and healed wrench after loading with a 10 N·m torque wrench.

FIG. 38. Drawings with dimensions of a half-dogbone and a full-dogbone.

FIGS. 39A-39E. A pair of half-dogbone Ni 200 samples (FIG. 39A) without and (FIG. 39B) with masking tape. FIG. 39C—Healed Ni 200 sample showing how the masking tape only allows nickel plating at the central exposed area. FIG. 39D—3D printed custom fixture holding a fractured sample. FIG. 39E—Photograph of the fixture during the healing process. The alligator clips are attached to the nickel anode, and both ends of the fracture sample, and connected to the Biologic SP-300 (not shown in photograph).

FIGS. 40A-40O. The process of subdividing a tetrahedron as a force diagram (FIG. 40A) corresponding to a node with anticlastic curvature as a form diagram (FIG. 40B), to a group of tetrahedrons (FIG. 40C, 40E, 40G) corresponding to a discrete anticlastic surface as a form diagram (FIG. 40D, 40F, 40H). The process of adding tetrahedrons between skew labyrinths (FIG. 40I-40M) to result in a tetrahedralized force diagram (FIG. 40O) corresponding to a two-manifold form diagram. Notice that to result in the smooth version of the form diagram (FIG. 40N), one needs to apply the anticlastic subdivision in part g to each tetrahedron in the tetrahedralized force diagram (FIG. 40O.

FIGS. 41A-41C. The shellular funicular structure designed in 3DGS (FIG. 41B), along with horizontal (FIG. 41A) and vertical (FIG. 41C) sections.

FIGS. 42A-42C. FIG. 42A—Dimensions of dogbone used for plated nickel testing. FIG. 42B Free-standing plated nickel dogbones after tensile fracture. FIG. 42C—Stress-strain data of free-standing plated nickel

FIG. 43. Photograph of the stainless-steel custom grips fabricated to facilitate the tensile testing of the 3D printed shellular structure.

FIG. 44. Stress-strain data of pristine Ni 200, Al 2024, Al 7075, and AISI 1008.

FIG. 45. Stress-strain data for healed Ni 200 dogbone samples

FIG. 46. Stress-strain data for healed AISI 1008 steel samples.

FIG. 46. Stress-strain data for healed Al 2024 dogbone samples.

FIG. 47. Stress-strain data for healed Al 7075 dogbone samples.

FIG. 48. Stress-strain data for example samples.

FIGS. 49A-49E. Finite element analysis results for a pristine 3D printed shellular structure. Structural steel with an elastic modulus of 70 MPa simulates 3D printed AlS₁₁₀Mg_0.35. FIG. 49A—Normal x-axis stress, FIG. 49B—normal z-axis stress, and FIG. 49C—normal y-axis stress with 500 N of tensile load applied along the y-axis. The funicular nature of the structure leads to the mitigation of shear or bending stresses, so local stress corresponds to the direction of general applied stress. FIG. 49D—Normal y-axis stress with 1000 N of tensile load. FIG. 49E—Von-Mises stress map showing stress concentrations at distinct sharp corners and edges in the structure.

FIGS. 50A-50C. Photographs, SEM images, and strain-strain data of 3D printed shellular structured healed with (FIG. 50A) 1200 mAh using the normal healing process, (FIG. 50B) 1200 mAh using the enhanced process, and (FIG. 50C) 1500 mAh using the enhanced process.

FIG. 51. Linear regression of the type-I fracture line for healed Ni 200, Al 2024, Al 7075, and AISI 1008 steel. The regressions determined that interfacial shear strength was 6.14 MPa for Ni 200, 6.64 MPa for Al 2024, 7.23 MPa for Al 7075, and 7.61 MPa for AISI 1008. Note the very high coefficients of determination (R²>0.9), which indicate that the model is a good fit for the experimental data.

FIG. 52. Current density data (in mA/cm²) with respect to time (in hours) collected during the healing of seven Al 2024 and Al 7075 dogbone samples with A_e/A_o=0.4375.

FIGS. 53A-53B. (FIG. 53A) 3-D plot of charge input required for full healing with respect to the width and thickness of a structural metal across multiple length scales, and (FIG. 53B) subsection of the same plot.

FIGS. 54A-54C. (FIG. 54A) EDS spectrum, (FIG. 54B) nickel and iron EDS maps with corresponding SEM image, and (FIG. 54C) XRD spectrum of plated nickel on a healed steel sample.

FIGS. 55A-55B. (FIG. 55A) Photographs of notched and fractured samples, before and after mechanical processing. (FIG. 55B) Stress-strain data of from the initial tensile test of notched steel samples (left plots) and the second tensile test after healing (right plots). Curves with the same color correspond to the same sample. Photographs to the left show healed processed and non-processed samples that exhibited type-M fracture after the second tensile test.

FIG. 56. Simplified finite element analysis results for pristine and healed metal showing the distribution of axial stress and strain.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present disclosure can be understood more readily by reference to the following detailed description taken in connection with the accompanying figures and examples, which form a part of this disclosure. It is to be understood that this invention is not limited to the specific devices, methods, applications, conditions or parameters described and/or shown herein, and that the terminology used herein is for the purpose of describing particular embodiments by way of example only and is not intended to be limiting of the claimed invention.

Also, as used in the specification including the appended claims, the singular forms “a,” “an,” and “the” include the plural, and reference to a particular numerical value includes at least that particular value, unless the context clearly dictates otherwise. The term “plurality”, as used herein, means more than one. When a range of values is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. All ranges are inclusive and combinable, and it should be understood that steps can be performed in any order.

It is to be appreciated that certain features of the invention which are, for clarity, described herein in the context of separate embodiments, can also be provided in combination in a single embodiment. Conversely, various features of the invention that are, for brevity, described in the context of a single embodiment, can also be provided separately or in any subcombination. All documents cited herein are incorporated herein in their entireties for any and all purposes.

Further, reference to values stated in ranges include each and every value within that range. In addition, the term “comprising” should be understood as having its standard, open-ended meaning, but also as encompassing “consisting” as well. For example, a device that comprises Part A and Part B can include parts in addition to Part A and Part B, but can also be formed only from Part A and Part B.

Many biological organisms and systems, such as bones and mollusks, possess regenerative or self-healing capabilities, which not only allow them to regain their mechanical strength and geometric integrity after damage or fracture, but also enable them to efficiently redistribute matter in response to dynamic deformation. In contrast, barring recently-developed self-healing materials, synthetic structural materials cannot autonomously adapt their geometries and local densities to dynamic loading scenarios. These materials also cannot self-heal to recover their mechanical properties once damaged. This inability to autonomously respond to mechanical stress and structural damage, thus, means that materials need to be repaired and monitored regularly, which translates to high costs and short lifetimes. Moreover, designers and engineers must conduct probabilistic and computational analyses (e.g. finite element analysis, topology optimization) to account for possible loading scenarios. They must also calculate safety factors to guard against brittle fracture and fatigue failure, which leads, in many cases, to heavy and bulky structures. Using self-healing materials instead can lead to significantly lighter and less voluminous designs, as well as afford designers more room for error since these materials can potentially autonomously adapt to even the most extreme loading conditions.

A variety of materials with self-healing properties have been conceived and developed. Polymers are by far the most studied class of these materials. Earlier development focused on designing polymers with embedded microscale capsules which rupture upon the fracture of the polymer and release a liquid monomer. Then, a catalyst induces the polymerization of the monomer in the crack, which leads to crack closure and self-healing. This self-healing technique, while very effective and scalable, is not repeatable: a second crack at the same location cannot be self-healed because the capsules in its vicinity were depleted to close the first crack.

To enable repeatable self-healing in polymers, supramolecular polymers held together by moderately strong, highly directional and reversible non-covalent bonds have been developed. The mechanical strength of such polymers, therefore, emanates not from covalent bonding and chain entanglement, but from molecular/atomic interactions such as hydrogen bonds, π-π bonds, ionic bonds and metallic bonds. In the event of a crack, these supramolecular bonds conserve their “stickiness” for a certain period of time and tend to recombine (autonomously or upon application of a thermal or mechanical stimulus), thus closing the crack and healing the material. The reversible character of these bonds means that the self-healing process can be repeated many times, with little to no degradation in its efficiency. Repeatable self-healing in polymers has also been shown to be possible through sunlight-induced photopolymerization.

As for metals, repeatable and efficient self-healing has remained largely elusive. Metals present significant challenges compared to other types of materials due to the non-directional character of their bonds which may prevent preservation of the original microstructure after healing, in addition to their slow mass transport at room temperature. Hence, introducing self-healing in metals cannot rely on a direct emulation of techniques developed for polymers or ceramics. Mimicking polymer healing agent encapsulation, for instance, has been attempted in metals by using solder tubes and embedded capsules. But the necessity of thermal stimuli and the weak bonding between the solder and crack surfaces meant that these attempts were largely unsuccessful at developing a self-healing meta.

New techniques and innovative paradigms are necessary. High temperature precipitation is one relatively well-studied technique for self-healing in metals. Heat treatment in a two-phase precipitation-hardened alloy results in the precipitation of the solute atoms. Since it is more energetically favorable for the precipitates to nucleate and grow in defective regions such as voids, vacancies and dislocations, small cracks can be filled with solute atoms and healed. An example of this self-healing method is a modified steel prepared by adding boron to a standard 347 stainless steel. As nanoscale cracks start forming, the boron atoms, acting as the solute healing agent, precipitate at the crack surfaces and promote crack closure. This process, however, which was initially designed to suppress creep fracture, is driven by heat at temperatures greater than 1000 K, thus limiting its applicability. An alternative method exploits stress-driven grain boundary migration in nanocrystalline metals. Using molecular dynamics simulations, this phenomenon was shown to lead to the closure of a pre-existing nanocrack in a nickel bicrystal when a shear stress is applied parallel to the crack plane. Although grain boundary migration can also lead to crack advance, especially in the case of an unstable crack, the simulations showed that it is, in fact, more likely to close them even under continuous tensile loading.

This disclosure shows that cellular metallic materials can be healed with high (e.g., 174%) efficiency by electrodeposition, so that their yield strength after healing exceeds their original strength. To demonstrate this in a non-limiting way, open-cell nickel foams coated with a passivating conformal thin film were subjected to tensile testing, healed via electrodeposition at constant voltage in a nickel sulfamate electrolyte, then tested in tension again. The mechanical constitutive behavior of samples before and after healing is compared, and the effect of electrodeposition duration on mechanical properties and healing efficiency is studied. Moreover, the morphology of the electrodeposited nickel is characterized using scanning electron microscopy to glean insights into factors such as morphology and grain size which may affect the mechanics of the healed samples. A Multiphysics finite element model can be used to simulate the kinetics and mass transport phenomena governing nickel electrodeposition to heal a representative fractured nickel foam strut.

Experimental Methods

Nickel foam (MTI Corp.), as pictured in FIG. 2A, was selected as a materials platform for this study. Samples were cut in the dog-bone configuration (FIG. 2C), immersed for 1 hour in a solution containing methanol (96%), ultrapure water (6%), hydrochloric acid (0.5%) and nitric acid (0.5%), then conformally coated with an approximately 150 nm-thick layer of alumina (FIG. 3B) using atomic layer deposition (ALD). ALD was performed in a Cambridge Nanotech Savannah 3900 reactor at 150° C. using trimethylaluminum and water as precursors. The use of alumina, which is a good electrical insulator used in passivation layers and corrosion resistant coatings, was intended to prevent nickel electrodeposition in areas other than the crack surfaces during healing. Therefore, healing can be rendered more effective since most or all nickel is deposited on the crack surfaces and broken struts in the nickel foam.

The experimental procedure of this study consisted of conducting a first tensile testing, healing the cracked samples using electrodeposition, then conducting a second tensile testing to assess the effectiveness of the healing. Tensile testing was performed using an MTS Criterion Model 43 equipped with a 50 kN load cell. The dogbone-shaped samples were loaded at a speed of 0.10 in/min (0.042 mm/s) which corresponds to a strain rate of approximately 0.001 s⁻¹. Healing was conducted via constant-voltage electrodeposition, controlled by a BioLogic SP-300 potentiostat/galvanostat. The electrolytic cell was composed of a working electrode (damaged nickel foam sample) and a reference electrode (pure nickel plate) in a commercial nickel sulfamate electrolyte (Technic, Inc.). The electrodeposition was performed at room temperature with no electrolyte agitation. Voltage was maintained at −1.8 V with respect to the reference electrode.

To characterize the ALD alumina coating and the surface morphology of the nickel foam samples before and after healing, scanning electron microscopy was performed using a Quanta 600 FEG E-SEM under high vacuum.

Computational Methods

A 2-D model of a broken nickel foam strut during healing was constructed in COMSOL Multiphysics 5.3 using the electrodeposition module. Equations governing mass transport and electrochemical reaction kinetics were solved, first, for a steady state initial case, then, for a time dependent case using the results of the first step as initial values.

Geometry and Boundary Conditions

FIG. 1 shows an exemplary geometry. The upper (red) surface is the anode (pure nickel plate) and the two lower (blue) surfaces are the cathode (two crack surfaces in a 500 μm-thick nickel foam strut). The large domain is the electrolyte, which contains Ni²⁺ ions with an initial bulk concentration of 1.4 M. This concentration is approximately the same as in commercial nickel sulfamate solutions, though this is not a requirement. NH₂SO₃ ions are used as a second species in the solution to enforce electroneutrality. The presence of boric acid, hydronium ions and chloride ions is neglected because their concentrations is significantly smaller than the concentrations of nickel and sulfamate ions.

A constant potential of −0.9 V is set at the two cathode surfaces, and the potential is set as 0.9 V on the anode surface. A constant concentration is set at the boundaries highlighted in purple, as shown in FIG. 1, to simulate a large electrolyte volume and avoid rapid nickel ion depletion during the time-dependent study. Furthermore, to account for corrosion at the anode and electrodeposition at the cathode, mesh deformation is allowed on both electrode surfaces.

Physics and Governing Equations

In the electrolyte, the net current density can be described as the sum of ionic fluxes (Eq. 1), with i_l the current density vector, F Faraday's constant, and N_i and z_i corresponding to the flux and charge number of species i.

$\begin{array}{cc}{i}_l=F\sum _i{z}_i{N}_i& \left(1\right)❘\end{array}$

The flux of ions in the electrolyte is described using the Nernst-Planck equation (Eq. 2) which combines the contributions of concentration-driven diffusion and charge-driven migration (convection is not relevant in this case). c_i represents the concentration of the ion i, D_i the diffusion coefficient, u_i its mobility, ϕ_i the electrolyte potential.

$\begin{array}{cc}{N}_i=-D_i\nabla c_i-z_i{u}_i{c}_{i}F\nabla {\varphi }_l& \left(2\right)\end{array}$

Combining Eq. 1 and Eq. 2 yields an expression for the current density in the electrolyte.

$\begin{array}{cc}{i}_l=-F\left(\nabla \sum _i{z}_i{D}_i{c}_i\right)-F^2\nabla {\varphi }_l\sum _i{z}_i^2{u}_i{c}_i& \left(3\right)\end{array}$

The Nernst-Einstein equation relates the mobility u_i to the diffusion coefficient, which simplifies Eq. 3 by requiring less inputs.

$\begin{array}{cc}{u}_i=\frac{D_i}{\mathrm{RT}}& \left(4\right)\end{array}$

The tertiary current distribution, as defined in the COMSOL electrodeposition module, solves Eq. 3 explicitly for all species in the electrolyte to obtain the current density distribution. The concentration distribution is computed, first, by enforcing electroneutrality in the bulk of the electrolyte according to

$\begin{array}{cc}\sum _i{z}_i{c}_i=0& \left(5\right)\end{array}$

Electroneutrality breaks down in the electric boundary layer close to the electrode surface, but the electric boundary layer is not described or studied in detail in this simulation because it exists at a length scale much smaller compared to the characteristic length scale of the electrodes.

The red-ox reaction rate at the anode and cathode also affects the concentration distribution. This rate is governed by the charge transfer current density in which on can model using Butler-Volmer kinetics, according to

$\begin{array}{cc}{i}_n=i_0\left[\exp \left(\frac{{\alpha }_{a}F}{\mathrm{RT}}\eta \right)-\exp \left(-\frac{{\alpha }_{c}F}{\mathrm{RT}}\eta \right)\right],& \left(6\right)\end{array}$

The variables in Eq. 6 are defined below:

• • i₀ is the exchange current density and is set at 0.6 A/m².
  • a_a and a_c are the apparent transfer coefficients at the cathode and anode respectively. Their values are usually between 0.2 and 2, and are set at 0.5 and 1.5 respectively.
  • R is the ideal gas constant (8.314 J/mol·K)
  • T is the operating temperature, which is set at room temperature (298 K).
  • F is Faraday's constant (˜96485 C/mol)
  • η is the overpotential measured by subtracting the electrolyte potential and the equilibrium potential from the electrode potential (Eq. 7). Here, the electrolyte potential is initially set to zero and the equilibrium potential is assumed to be zero because the two electrodes are made of the same material, nickel.

$\begin{array}{cc}\eta ={\varphi }_s-{\varphi }_l-E_{\mathrm{eq}}& \left(7\right)\end{array}$

Mesh deformation is allowed at the cathode and anode surfaces shown in FIG. 1 to describe both nickel deposition at the cathode and corrosion at the anode. The kinetics of the electrochemical reaction, combined with the density and molar mass of nickel, allow the computation of the rate of mesh deformation, and, as a result, the rate of nickel film growth along the cathode surface.

Table 1 below contains values of the parameters used in this simulation.

TABLE 1
Parameters used in the computational study.
Variable	Value	Unit
Diffusivity (nickel ions)	1.0E−9	m2/s
Diffusivity (sulfamate ions)	1.0E−9	m2/s
Charge number (nickel ions)	2
Charge number (nickel ions)	1
Exchange current density	0.6	A/m2
Transfer coef. (anode)	0.5
Transfer coef. (cathode)	1.5
Equilibrium potential	0	V
Cathode potential	−0.9	V
Anode potential	0.9	V
Initial concentration (nickel ions)	1400	mol/m3

Results and Discussion

Mechanical Behavior Before and After Healing

Nickel foams were tested in tension, healed then tested again. The change in mechanical properties after healing relative to the original properties is studied by healing samples at different stages of plastic deformation for various durations.

A typical constitutive behavior of a ductile material, such as nickel foam, can be divided into three regimes: the elastic regime (I), and the plastic deformation regime which is composed of the hardening regime (II) and the failure regime (III), as shown in FIG. 3. As such two types of tensile tests were conducted. In the first type, tests were stopped at a strain of 0.020, which corresponds to a point right at the end of regime II when maximum stress is reached and results in microscale cracks, as shown in FIG. 3A. In the second type, the test is left to continue until the end of regime III when the material loses all its load-carrying capability, resulting in the complete rupture of the sample or large cracks similar to the one shown in FIG. 3B.

Regime III samples healed for 5 and 3.5 hours are for the most part able to recover their tensile strength, despite a clear decrease in ductility (FIG. 4C, FIG. 4D)). Except for one sample healed for 3.5 hours, the tensile strength of samples healed for 3.5 and 5 hours exceeded their original tensile strength, which (without being bound to any theory) may be due to both the bulking of the foam struts and the nanocrystalline structure of the electrodeposited nickel. Reduced recovery of both tensile strength and toughness is observed in regime III samples healed for 1 hour and 2 hours (FIG. 5C, FIG. 5D), likely (again without being bound to any particular theory) because insufficient amounts of electrodeposited nickel were available to heal all broken struts.

Regime II samples exhibited a markedly different post-healing mechanical behavior as the healing duration had little effect on the tensile strength of the healed samples. FIG. 5 shows the tensile strength of most healed samples exceeded their original tensile strength by 20 to 70 percent, and the difference was more pronounced for samples healed for 5 hours (FIG. 5D). The ductility of regime II samples degraded after healing, but not as significantly as the ductility of regime III samples.

Healing Efficiency

To quantify the recoverability of tensile strength and toughness, one can create two parameters: the stress healing efficiency, e_σ, which characterizes the tensile strength recovery, and the toughness healing efficiency, e_T, which characterizes the toughness recovery. One can calculate e_σ and e_T using

$\begin{array}{cc}{e}_{\sigma }=\frac{{\sigma }_{\mathrm{TS},h}}{{\sigma }_{\mathrm{TS},o}}\mathrm{and}& \left(8\right)\end{array}$ $\begin{array}{cc}{e}_T=\frac{W_{\epsilon ,h}}{W_{\epsilon ,o}},& \left(9\right)\end{array}$

Where W is the strain energy,

$\begin{array}{cc}{W}_s=\int \sigma d\epsilon .& \left(10\right)\end{array}$

For healed regime II samples, strain energy was calculated between zero strain and the strain at maximum stress. This approximation equates the calculated strain energy for the second and first tensile tests, as the first tensile test was stopped at or very close to the point of maximum stress. Healed samples have a subscript h and original samples have a subscript o.

FIG. 6A shows that regime III samples exhibited an increase in both measures of efficiency as the amount of energy dispensed during healing increased. A cut-off point between low and high efficiency appears to occur around 1 kJ, as the stress efficiency increases beyond 100% after this point while the toughness efficiency also increases but never exceeds 100%. The maximum stress efficiency, at 173%, is associated with a sample healed for 3.5 h. FIG. 6B shows that the toughness and stress healing efficiencies of regime II samples followed different trends. The toughness efficiency increased rapidly until about 0.5 kJ then reached a steady state at around 130%. On the other hand, the stress efficiency increased at two distinct rates: a rapid rate until about 0.5 kJ followed by a slower rate. The maximum stress efficiency reached 174%.

The behavior of both measures of efficiency can be ascribed to both the bulking of the foam's struts due to excess electrodeposited nickel, and the higher strength of electrodeposited nickel compared to the nickel originally available in the foam due to its nanocrystalline structure (explained in the next section).

Effect of Morphology on Mechanical Behavior

Pristine nickel foam and electrodeposited nickel show different microstructure and surface characteristics, as evidenced by FIG. 7. Electrodeposited nickel shows crystalline grains of nanoscale dimensions, while nickel foam possesses grains that range from a few micrometers to 20 μm in size. A grain size between 10 and 20 nm has been reported to maximize strength in metals as the microscopic deformation mechanism shifts from dislocation-mediated plasticity in a coarse-grained material to grain-boundary sliding in a nanocrystalline material. A study on nanocrystalline nickel fabricated by electrodeposition shows that its yield strength increases linearly with respect to the inverse square root of grain size, in good agreement with the Hall-Petch model. Therefore, and without being bound to any particular theory, electrodeposited nickel likely possesses greater strength than the coarse-grained nickel foam. This fact, combined with the increased density of the foams due to strut bulking from excessive nickel deposition, may explain the higher tensile strengths measure after healing, and, thus, the high stress healing efficiencies which exceeded 100% in many cases. The nanocrystalline structure of electrodeposited nickel can also explain the limited toughness efficiency, as nanostructured metals are known to exhibit low toughness due to a lack of work hardening. Further characterization using x-ray diffraction, electron backscatter diffraction and transmission electron microscopy is needed to improve our understanding of the relationship between the morphology of electrodeposited nickel and the mechanics of healed samples.

Passivation Coating

To understand the role of the passivation layer on the healing process, the electrochemical behavior of ALD alumina was studied. Using a passivating coating with a maximum strain equivalent to nickel can help remediate this issue. It should be understood that the use of alumina in this example is non-limiting, as a passivating coating can be polymeric, ceramic, or of other nature. Parylene-D is one exemplary such coating.

Other insulating conformal coatings on nickel foam samples (100 nm of hafnia on 10 nm of alumina, 150 nm of parylene), performed slightly better than the alumina coatings in a test consisting of nickel electrodeposition on a 1.5×1.5 cm² sample area for one hour at a constant −1.8 V vs. a reference nickel plate. FIG. 8A shows that coating nickel foam with any of three coating compositions significantly limited the measured current.

Computational Study

A simulation of nickel electrodeposition was conducted to heal a broken nickel strut in a nickel sulfamate electrolyte at constant voltage. The concentration distribution showed a significant increase in nickel ion concentration close to the cathode (FIG. 9). The concentration was highest around the upper parts of the two cathode surfaces, which resulted in faster nickel growth on the upper parts than on the lower parts. The non-uniformity in nickel growth rate is evidenced by the evolution of the shape of curves representing the surface of the nickel coating on one of the strut's surfaces at different time instants (FIG. 10). Instead of remaining flat, as the curve at t=0, the curve at t=150 s shows a faster growth rate on the upper part of the cathode surface (closer to the anode) than on the lower part. In addition to this local non-uniformity, the increasing proximity of the curves as time passes shows a slowdown in nickel growth rate, as the diffusion of ions becomes more and more restricted as the two nickel films growing from the two cathode surfaces become closer together.

An examination of the diffusive flux elucidates the reason for non-uniformity in nickel coating growth rate. The diffusive flux, as shown in FIG. 11, is initially highest at the upper part of the cathode as nickel ion diffuse and adsorb to the nearest surface with available electrons. But diffusion subsequently dominates, and the diffusive flux becomes highest at the top and bottom of the two cathode surfaces, with a low diffusive flux region located in the middle. Diffusion in this middle region is low likely because the rate at which nickel ions are depleted is much higher than their diffusivity.

The presence of this low diffusive flux region can lead to the formation of a void once the two nickel coatings meet and coalesce to heal the broken strut. Reducing the strut size in the simulation from 500 to 1 μm, which can be achieved empirically by using nanostructured or hierarchical materials, led to a reduction in the time needed for healing but no significant improvement in nickel film uniformity on the strut's surfaces.

FIG. 12 provides example probability of achieving 100% stress and toughness healing efficiency in healed Ni foams subjected to micro-scale cracking (dashed lines) and large-scale cracking (full lines).

FIG. 13 provides an exemplary Gaussian distribution of stress healing efficiency of Ni foams subjected to micro-scale cracking and healed for varying time durations.

FIG. 14 provides exemplary SEM images showing the same strut in a coated Ni foam before (left panel) and after healing (right panel). The passivating coating limits nickel deposition to cracked areas.

FIG. 15 provides an illustration of Ni foams with two different crack configurations were obtained by halting tensile testing at two distinct regimes

FIG. 16 provides SEM images showing nickel deposits along healed large-scale cracks in Ni foams.

Additional Disclosure

Although metallic bonds are strong, room-temperature healing of metals is difficult because metal atoms have low room-temperature diffusivities in solid phases (10⁻⁴ to 10⁻³⁵ m²/s). Metals, therefore, are healed at temperatures near or above their melting points which requires high temperatures and large amounts of energy (10⁷ J to 10⁹ J per 1 mm crack length for solute precipitation, for example).

Strategies using low melting temperature alloys (10² to 10³ J/mm), highly-localized joule heating (10² to 10⁴ J/mm), and combined solute diffusion and phase transformation (10⁶ to 10⁷ J/mm) have been developed to reduce the healing energy input, but none have demonstrated effective room-temperature healing.

To achieve effective healing at or near room temperature, biological structural materials, such as bone, transport mass and energy (oxygen, nutrients, and cells, for example) to and from areas where healing is needed. This transport-mediated approach is dramatically different from the local storage of healing matter used by most synthetic healing strategies.

FIG. 17A shows the cellular structure and healing response of bone. The cellular structure plays a critical role in realizing transport-mediated healing. The continuous hard phase (mineralized collagen) provides a structural network to support mechanical loads while the open-cell pores, where open cell means the pore volume is a continuous phase, house functional materials (cells and blood vessels) that sense where fracture occurs and allow mass and energy transport to and from fracture locations. Matter transported to the fracture site forms a cartilaginous callus and reconstructs blood vessels leading to full bone remodeling and healing, which typically takes one month to a few years at 37° C.

In this work, we show electrochemical transport of nickel in polymer-coated cellular nickel materials to demonstrate rapid, effective, and low-energy healing of metal at room temperature. We chose cellular nickel because of its wide use, electrochemical reversibility, and demonstrated light weight and high strength, but it should be understood that nickel is illustrative only and does not limit the scope of the present disclosure.

The polymer coating enabled selective healing only at fractured locations. The combination of ion migration, fast ion diffusion (10⁻⁹ m²/s), and the cellular structure enabled 100% strength recovery of 1.6 mm thick fractured samples after as little as 1500 J and four hours of potentiostatic healing at room temperature. Healed samples fully recovered their strength after being loaded to within 1% strain of total failure, which corresponded to a 350% increase in the fractured nickel strength.

By choosing a polymer coating with a lower failure strain than the underlying metal, plastically-deformed samples were electrochemically strengthened by up to 55% of their original strength, thus preventing fracture in areas exposed to high stress. Also provided is a method to quantify the stochastic healing process and predict healing success based on energy input.

FIG. 17B illustrates an exemplary approach for healing cellular nickel at room temperature. First, we conformally coated 5 to 9 μm-thick films of Parylene D (an insulating polymer with excellent barrier properties and chemical stability) onto cellular nickel. The cellular nickel had 250 μm average diameter pores and 3% relative density. FIG. 17C shows a fractured nickel strut after straining the cellular nickel in tension. The 10% failure strain of Parylene D was large enough so that only severely damaged nickel was exposed, but lower than the 23% failure strain of the nickel so that fractured nickel was not covered by polymer.

Applying a negative potential (−1.8 V) to the fractured cellular nickel, relative to a nickel counter electrode, healed the sample by driving electrons through the conductive nickel to the fracture location and reducing nickel ions in the electrolyte to solid nickel. The open-cell pores enabled rapid ion transport to the fracture site, as previously demonstrated in battery electrodes.

Nickel electrodeposited on both sides of the fractured strut grew until the growth fronts merged, forming a continuous strut (FIG. 17D). The strength of two electrochemically merged interfaces were comparable to bulk nickel. FIG. 17E shows the typical stress-strain data of Parylene-coated cellular nickel. To characterize the healing effectiveness, we healed cellular nickel samples after three types of damage: plastic deformation at 3% strain (P), tensile failure beyond the ultimate strain su (F1), and local failure by scission (F2) (FIG. 17E).

We first characterized the healing of 8 mm-wide dog-bone shaped samples with a 4 mm scission cut at the center (F2 damage). FIG. 18A and FIG. 18B show a photograph and scanning electron microscopy image of cellular nickel after fracture. Damage was limited to the immediate vicinity of the scission. FIG. 18C shows the sample after healing. Nickel electrodeposited on the exposed nickel at the scission merged and formed a dense nickel deposit.

As the scission was applied, stress was imparted on the surrounding cellular nickel, which fractured local segments of the Parylene coating and allowed spherical nickel deposits to form during electrodeposition. The Parylene coating remained pristine and prevented nickel deposition beyond 1 to 3 mm from the scission (FIG. 18C). After healing, we subjected samples to tensile loading until failure. FIG. 18D—FIG. 18F shows the stress-strain behavior of F2 samples healed with 0 J (non-healed), 500 J, and 1,500 J of electrical energy (additional data can be found in FIG. 21). Pristine sample data is shown in FIG. 18D for reference.

The tensile strength σ_U (maximum stress) and toughness UT (area under the stress-strain curve) increased with increasing electrical energy input. The tensile strength and toughness were measured from the average of ten healed samples at each energy and normalized by the average strength and toughness of twenty pristine samples to quantify the strength healing efficiency, e_σ=σ_u,healed/σ_u,pristine, and the toughness healing efficiency, e_U=U_T,healed/U_T,pristine. FIG. 18D shows e_σ and e_U versus energy input.

Strength and toughness healing efficiencies increased linearly with energy input from 51% and 20% at 0 J until they plateaued near 100% and 84% at 1,500 J which corresponds to a minimum of four hours of healing. The strength healing efficiency fit normal Gaussian distributions for samples healed at each energy (FIG. 24A). We used the statistical healing efficiency data to predict the likelihood that healed cellular nickel samples achieved a target strength healing efficiency for a given energy input.

FIG. 18H shows the resulting healing curves for 50, 80, and 100% target healing efficiencies. For a sample healed at 1,500 J, there is a 100, 96, and 69% chance of achieving 50, 80, and 100% strength healing efficiencies. Samples loaded after healing fractured either at the healed scission (A samples) or in the cellular nickel outside the scission (B samples). FIG. 18I shows how the fraction of B samples increased with healing energy. This trend suggests that the stagnation of strength healing efficiency after 1,500 J in FIG. 18G is due to the strength of the healed region surpassing the material strength, which forced failure in the surrounding cellular nickel.

We also tested the ability of this healing technique to recover electrical conductivity by cutting the samples in half (complete scission) and comparing the electrical resistance in the pristine state and after healing with 1500 J. The pristine resistance was 0.159±0.001Ω and the healed resistance was 0.163±0.032Ω (see Table 6 below). Thus, we are able to recover electrical resistance after complete scission to within 2.5% of the original value. This result indicates that the disclosed electrochemical healing techniques can enable full recovery of electrical conductivity in cellular metals.

Cellular nickel samples loaded to near failure in tension (F1 damage) exhibited full recovery of strength after as little as 10 hours of healing. FIG. 19A and FIG. 19B show optical and SEM images of cellular nickel subjected to F1 failure. Typically, a single large macroscopic crack (>1 mm) emerged along with numerous microscale cracks (<100 μm) throughout the sample due to the uniform loading (FIG. 21B and FIG. 21C). FIG. 19D-FIG. 19G show stress-strain data of F1 samples strained in tension after 0, 250, 2,500, and 3,500 J of healing (additional data in FIG. 22).

In general, the cellular nickel strength and toughness increased as the input energy increased. The strength and toughness healing efficiencies were the strength and toughness of each healed sample normalized by the same sample's strength and toughness during the first loading. FIG. 19H shows the average strength and toughness healing efficiency of ten samples for each energy.

The average strength healing efficiency increased linearly, starting at 23% for non-healed samples and rising to 104% for 3,500 J, representing a 4.5× increase in the fractured sample strength. The average toughness healing efficiency increased from 4.5% for non-healed samples to 36% after 3,500 J.

We fit healing efficiency data to Gaussian distributions (FIG. 24B), using the same method used for F2 samples, to predict the likelihood that healed F1 samples achieved a target healing efficiency for a given energy input. FIG. 119I shows the healing design curves for 50, 80, and 100% target strength healing efficiencies. The probability of achieving a strength healing efficiency of 50, 80 and 100% is 95, 77, and 56% respectively for a 3,500 J energy input. The high strength healing efficiency was due to the electrodeposited nickel mending cracks and increasing the relative density of the cellular nickel. Without being bound to any particular theory, the limited toughness recovery was likely due to the low ductility of electrodeposited nickel (27 nm average grain size) compared to the pristine cellular nickel with 5-15 m wide grains (see Experimental Section for an extended discussion). Without being bound to any particular theory, the slight decline in toughness healing efficiency from 42% at 2500 J to 36% at 3500 J (FIG. 19H) is likely due to the brittle nature of the nanocrystalline electrodeposited nickel, compared to the pristine nickel, as well as the electrodeposited nickel locally restricting the bending of nickel struts, which decreased the failure strain.

Electrochemical healing of plastically deformed cellular nickel increased the cellular nickel strength and resistance to future failure. To characterize this strengthening effect, we loaded cellular nickel samples in tension until 3% strain (P damage), unloaded the samples, healed them with 0-2,100 J, and then loaded the samples again until failure. FIG. 20A shows the resulting stress-strain data of a healed (pink) and non-healed (blue) sample (additional data in FIG. 23). The tensile strength of the healed sample was noticeably larger than the non-healed sample.

We defined the strengthening factor, f_σ, as the ratio of the healed to non-healed strength. Under this definition, f_σ=1 for non-healed samples. The strengthening factor represents the extent to which a healed P sample can resist future damage compared to a non-healed sample.

FIG. 20B shows the strengthening factor of cellular nickel samples subjected to 100-2,100 J of healing energy. The average strengthening factor increased from 0.98 to 1.26 until 1,500 J, after which it plateaus. FIG. 20C shows the probability of achieving 0.8, 1.0, and 1.2 strengthening factors with increased energy input. Scanning electron microscopy images provided insight into the strengthening mechanism.

During plastic deformation, local regions of the cellular nickel were subjected to large stress concentrations which cracked the Parylene coating and exposed the underlying nickel when the local strain exceeded the Parylene failure strain (FIG. 20D). Nickel was then electrodeposited on exposed nickel during healing (FIG. 20E), which selectively strengthened the nickel in areas subjected to the highest stress concentrations. Fracture in healed struts during the second loading occurred between nickel deposits (FIG. 20F), which confirms that the deposited nickel increased the strut strength.

Transport-mediated electrochemical healing of cellular nickel at room temperature requires lower energy input than many metal healing techniques. FIG. 20G compares the healing temperature and energy input per mm of crack length for several metal healing techniques. Electrochemical healing of cellular nickel required 200 to 700 J/mm at room temperature, about 0.6 to 2.2% of the energy available in a 5,000 mAh smartphone battery. This energy input is 10⁴ to 10⁶ times lower than solute precipitation, 0-10⁴ times lower than electron beam welding, 10² times lower than prior electrochemical healing, 1-10 times lower than arc welding, and comparable to crack-localized joule heating and phase transition in low melting temperature alloys. The low energy requirements of the disclosed healing approach can be especially advantageous to energy-constrained systems, e.g., as autonomous vehicles and battery-powered robots.

The disclosed technology also comprises autonomous healing of fractures in metal. Cracking can be detected using several methods.

In one method, one can apply a short pulse at a negative potential and measuring current. If the current exceeds a threshold value, healing is initiated.

In another method, one can perform a cyclic voltammetry scan and measure the maximum current.

In other methods, one can measure resistance between the metal to be healed and the counter electrode, using a multimeter or electrochemical impedance spectroscopy. When a crack forms, the resistance drops below a threshold value, and healing can be initiated.

In other approaches, when the metal to be healed is different from the metal that is electrodeposited, we can use the difference between their equilibrium redox potentials to initiate healing. In other words, when a crack occurs, the equilibrium potential difference leads to an increase in current, which can be used as a signal to initiate healing by applying a higher current or potential.

Additionally, one can use a strain sensor (capacitive, resistive or piezoelectric) to measure local strain/stress, and initiating healing once a predesignated high strain/stress is reached.

This work demonstrates rapid, effective, and low-energy healing of polymer-coated cellular nickel at room temperature using electrochemistry. Immersing the cellular nickel into an external electrolyte allowed nickel transport from an anode to fractured nickel struts. The polymer coating reduced the required healing energy by restricting nickel plating to only fractured locations.

As described herein, we also provide repeated healing and encapsulating electrolyte into the cellular material for a fully integrated and healable structural material. The disclosed transport-mediated approach can be applied to increase lifetime, reduce weight, and prevent premature failure of cellular metals, which are widely used in structural materials with high strength, high stiffness, and low weight. Additionally, this work presents a new approach to heal electrically and thermally conductive materials.

Additional disclosure is provided below, with reference to certain appended figures.

FIG. 27 provides exemplary images of embodiments of the disclosed technology, showing (from left to right) an example setup for healing fractured nickel foam, views of fractured and healed nickel foam, and pristine, fractured, and healed dog-bones of nickel foam.

As shown in the left-hand panel, nickel foam (e.g., fractured nickel foam) is placed in an electrolyte, along with a source of nickel (e.g., nickel plate). A potential is then applied to effect nickel deposition onto the metal foam. The middle panel shows a fractured metal foam, with nickel being exposed through a fracture in an insulating coating disposed on the nickel foam. Following deposition of nickel onto the fracture, the metal foam is healed. The right-hand image shows a dog-bone of nickel in pristine, fractured, and healed (post fracture) conditions.

FIG. 28 provides exemplary elements (metals and metalloids) that can be electrodeposited with current technology. Alloys containing two or more of these elements can be electrodeposited as well.

FIG. 29 provides a schematic of an example process according to the present disclosure. As shown, a metal strut (or other metal shape) can be electrochemically coated with an insulating polymer; the polymer's monomer can be disposed in an electrolyte. The coated strut is then fractured, the fracture exposing metal where the coating (and underlying metal) are cracked. A metal ion-containing electrolyte is then contacted to the fractured metal strut, and metal electrodeposition is then performed to deposit metal at the fracture, thereby healing the crack. As shown, the deposited metal is thus exposed to the exterior environment, as the deposited metal is not (yet) covered by a polymeric coating. In a further step, the exposed metal on the healed crack is electrochemically coated with an insulating polymer. As shown, subsequent cracks can be healed without metal deposition on the first healed crack.

Thus, to enable repeatable healing, one can extend the healing technique by electrochemically depositing an insulating polymer on exposed metal after the first healing, then after each subsequent healing step. Because the polymer is deposited electrochemically, polymer is deposited only where metal is exposed and no polymer is deposited in areas where insulating polymer is already present. This repeatable healing technique (shown in FIG. 29) can enable healing of the same metallic part several times with no loss of healing efficiency.

Repeatable healing can proceed in a batch-like manner (e.g., fracture, dip in metal electrolyte, dip in polymer electrolyte, repeat). But one can also create a dual-function electrolyte, as there are polymers that can be deposited from an acidic aqueous medium containing metal ions. In this case, a positive potential is applied to initiate polymer formation, while a negative potential is needed for metal deposition.

Polymers can be deposited electrochemically using a solution that contains a monomer, a salt or some suitable organic compound and a solvent or mixture of solvents. As one example, we deposited polyphenol using a solution containing phenol and allylamine both dissolved in a mixture of water, 2-methoxyethanol and methanol. We used nickel as both the working electrode and the counter electrode. Silver/silver chloride was used as a reference electrode.

After cycling between 0 and 3V 200 times, we obtained a thick coating on the working electrode as shown in FIG. 31. After drying the polyphenol-coated nickel, we immersed it in a nickel sulfamate electrolyte with a nickel counter electrode, then applied a constant potential of −1.8 V vs. Ni for one hour. The polyphenol coating remained pristine with no signs of nickel growth. One can obtain such barrier properties with other polymers and copolymers.

FIG. 30 provides a non-limiting listing of polymers that can be used as insulating polymers for the disclosed technology.

Additional Experimental Disclosure

Materials: We purchased cellular nickel (nickel foam) with 3% relative density from MTI Corporation, and cut it into dog-bone shaped samples. The samples were 75 mm in length, 15 mm in width and 1.6 mm in thickness, which corresponds to ˜6.4 times the pore size and ˜32 times the strut width. The gauge section for each sample was approximately 45 mm in length and 8 mm in width. Immersing samples for one to two hours in a mixture of methanol (˜93 vol %), hydrochloric acid (˜0.5 vol %), nitric acid (˜0.5 vol %) and ultrapure water (˜6 vol %) removed organic contaminants and etched the native nickel oxide.

A Specialty Coating Systems PD39010, then, conformally coated samples with Parylene D (poly(dichloro-p-xylylene)) by vapor deposition. We set the dimer vaporizer at 175° C., the pyrolysis furnace at 700° C., and the deposition chamber was kept at room temperature (˜25° C.). Detailed information on the deposition process of Parylene D and its polymerization is available in other articles. We chose Parylene D as a passivating coating because of its chemical stability, high dielectric strength, and superior barrier properties, as well as its failure strain (10%).

To measure the thickness of the Parylene coating, we cleaned ˜2 cm² glass slides by oxygen plasma (100 W and 80 sccm) for 15 mins in an Anatech SCE 106 plasma system, then placed them in the coating chamber with the cellular nickel samples. Parylene thickness ranged from 5 to 9 μm, as determined from step height measurements using a KLA Tencor P7 stylus profilometer.

Mechanical testing: We conducted tensile testing using an Instron 5564 equipped with a 100 N load cell. We set the testing speed at 2.54 mm/min which corresponds to a strain rate of about 0.001 s⁻¹.

Electrical measurements: We performed electrical resistance measurements using a Keithley DMM6500 digital multimeter.

Materials characterization: We performed scanning electron microscopy (SEM) under high-vacuum mode in a FEI Quanta 600 Environmental SEM. Using a Rigaku D/Max-B x-ray diffractometer with a Cu K-α source, we performed x-ray diffraction, then plotted and analyzed the resulting data using X'Pert Highscore Plus by Malvern Panalytical.

Electrochemical healing: We healed cellular nickel, ten samples at each energy, using an electrochemical cell with the sample as the working electrode and a pure nickel plate as the counter/reference electrode.

The non-limiting liquid electrolyte was nickel sulfamate RTU (Technic Inc.), which is composed mainly of nickel sulfamate (26%), nickel bromide (0.7%) and boric acid (2.3%). Immersing the samples briefly in isopropyl alcohol or methanol immediately before healing improved electrolyte wetting. A 3D printed device served both as electrolyte vessel and sample holder during the electrochemical healing process (FIG. 26). The healing of all samples was conducted at room temperature, 21.1±0.3° C.

A BioLogic SP-300 potentiostat/galvanostat controlled the electrochemical cell, supplying a constant voltage (−1.8 V vs. Ni), measuring the current i(t), and stopping when the target total charge output Q was reached. We obtained energy E by multiplying the total charge Q by the voltage V as follows,

$\begin{array}{cc}E=V·Q=V\int i\left(t\right)\mathrm{dt}.& \left(1\right)\end{array}$

Scherrer analysis of XRD data: We performed x-ray diffraction on a thick layer of electrodeposited nickel coated on the same cellular nickel used in this work (FIG. 25A). The electrodeposition occurred in the same conditions described above (−1.8 V vs. Ni reference, Ni sulfamate RTU electrolyte, and room temperature). We used the Scherrer equation to estimate grain size,

$\begin{array}{cc}D=\frac{K\lambda }{\mathrm{\beta cos\theta }},& \left(2\right)\end{array}$

where D is the crystalline grain size, K is a dimensionless shape factor (K˜1), λ is the x-ray wavelength (here, λ=0.154 nm), β is the peak broadening (defined as the peak width at half the maximum intensity), and θ is the Bragg angle. By applying Eq. 2, we obtained an average grain size of 27 nm in electrodeposited nickel. This grain size was qualitatively confirmed by SEM (FIG. 25B). In comparison, the pristine cellular nickel had grains ranging in size from 5 to 15 μm (FIG. 25C). Since nickel follows the Hall-Petch model, we concluded that the electrodeposited nickel had higher strength and lower ductility than the pristine nickel.

Probabilistic analysis of healing success: The cellular nickel samples showed a stochastic healing performance (Tables 2-4). In other words, healing with a high energy input did not guarantee a high healing efficiency. Therefore, we developed a probabilistic approach based on Gaussian statistics to analyze and predict the evolution of mechanical properties due to healing.

We calculated the probability of achieving a target strength healing efficiency (for F1 and F2 samples) or strengthening factor (for P samples) for each healing energy. Ten samples were processed, tested and healed as described above for each value of energy input. We then calculated the relevant figure of merit (strength healing efficiency e_σ or strengthening factor f_σ) for each sample depending on its damage type (P, F1 or F2). Using Matlab, we produced a Gaussian (normal) probability distribution that fits each set of ten data points for a given energy. The result is a probability density function (pdf) for each set of ten samples (FIG. 24). The probability density function φ(x) of a statistical variable x is described by

$\begin{array}{cc}\phi \left(x\right)=\frac{1}{\sqrt{2\pi v^{{ }_{}2}}}{e}^{-{\left(x-\mu \right)}^2/2v^{{ }_{}2}},& \left(\mathrm{Equation}38\right)\end{array}$

where v is the standard deviation and μ is the arithmetic mean. In practical terms, the Matlab fitting process consisted of finding the values of μ and v for each set of ten samples.

To calculate the probability of x=a, we integrate φ(x) as follows:

$\begin{array}{cc}p\left(x=a\right)={\int }_a^{\infty }\phi \left(x\right)\mathrm{dx}.& \left(\mathrm{Equation}39\right)\end{array}$

The lower bound of integration was the target figure of merit and the upper bound was set to e=250% (or f_σ=2.50). Using this method, we plotted design figures (FIGS. 18H, 19I and 20B) that enabled the targeting of expected healing performance based on a specific energy input.

Estimation of Healing Energy and Temperature from the Literature:

We resorted to different means to estimate the healing energy and temperature ranges for our work, different metal healing methods, and two metal welding methods (arc welding and electron beam welding).

For arc welding, we obtained a voltage range of 17-45 V and a current range of 190-590 A which encompasses the most common arc welding techniques (gas metal arc welding, flux-cored arc welding, and shielded metal arc welding, for example). The current and voltage ranges yielded a power range of 3,230-26,550 W. The travel speed ranged from 2 to 10 mm/s. Dividing the power by the travel distance in a second provides the energy input per mm crack length: 323 to 13,275 J/mm.

The temperature of the plasma arc at the metal surface was reported to be between 3,000 and 20,000° C. For electron beam welding, the energy input ranges from 6,000 to 3,000,000 J/mm. A study of the temperature distribution on the surfaces of different metals and metallic alloys during electron beam welding revealed that peak temperatures range from 1,100 to 2,300° C.

For the various reports of metal healing, we calculated energy input based on available information such as healing time, temperature, current, and voltage. In cases where information on the furnaces used for heating could not be obtained, we used the electric power of commercial lab furnaces by Thermo Scientific rated for the temperature range in the study to calculate total energy consumption (1,000 W for ˜1,200° C., 700 W for ˜750° C., 190 W for ˜200° C., and 170 W for ˜150° C.). For the electrochemical healing study, we calculated energy input based on 500 ml of electrolyte with the same specific heat capacity as water and determined convective heat losses to be negligible.

Temperature ranges were all reported in their respective studies except for one study on crack-localized joule heating which we assumed to have roughly the same temperature range as the other study that used the same healing method. For each study, the calculated energy was normalized by the healed crack length. Whenever the sizes of healed cracks were not explicitly reported, we relied on scanning electron micrographs to estimate crack size. We summarize the data estimated or directly retrieved from other metal healing reports in Table 5.

For our work, we estimated the lower bound of healing energy per unit crack length based on a F2 sample with a 4 mm scission healed with 900 J. The upper bound was estimated based on a F1 sample with a 5 mm macroscopic crack healed with 3,500 J.

Possible Empirical Explanations for the Variation in Post-Healing Stress-Strain Data:

For identical conditions, many cellular nickel samples exhibited great variation in their stress-strain behavior after healing. Without being bound to any particular theory, this variation may be due to two reasons.

The first reason is the significant variation in relative density resulting from the variation in parylene coating thickness. Since the cellular nickel struts are hollow with ˜10 μm-thick walls, the volume fraction of the Parylene coating (5 to 9 μm in thickness) varies between 41% and 57%, which is representative of most of the variation in strength that we measure experimentally.

The second reason is that when the foam is fractured, the individual struts that make up the foam are split into two parts and there is a natural variation in the distance between the two parts of a fractured strut. If the spacing between fractured struts is larger, more energy is required to heal those struts. The stochastic distribution of spacings between fractured struts means that samples healed at the same energy can exhibit varying levels of strength and toughness as only a certain fraction of the fractured struts are close enough to heal effectively.

TABLE 2
Strength healing efficiency eσ and toughness
healing efficiency eU for all F2 samples.
0 J	250 J	500 J
eσ	eU	eσ	eU	eσ	eU
44.8738	15.9935	58.2133	30.2323	89.1772	76.1944
44.6317	14.9267	74.6148	35.5187	70.1961	38.4706
38.0732	14.6607	81.7306	41.2253	75.1629	43.0954
46.0657	20.4104	60.8511	32.9445	117.0358	84.52
48.1259	15.7461	57.3192	25.7382	120.5706	116.732
58.6377	21.296	56.8274	19.6087	34.6966	12.0655
59.2263	26.1214	48.6316	22.4507	66.3764	28.345
53.2709	27.6469	39.9978	19.3036	36.4651	14.0729
49.9348	16.0855	48.7349	24.7125	43.7843	2.8569
62.3922	27.4423	41.9449	19.2681	62.5122	27.0546
900 J	1,500 J	2,100 J
eσ	eU	eσ	eU	eσ	eU
108.1753	97.0712	93.9784	65.8805	95.2939	52.0583
83.1004	52.4603	85.4738	64.2525	100.6287	74.5683
85.1732	63.8496	90.5907	71.394	94.8645	56.0464
123.7154	93.5784	99.9121	83.3149	104.2474	66.5609
117.2572	100.7517	94.0625	91.2723	106.4991	88.7265
87.8115	52.5474	118.3926	96.0715	102.6186	68.7005
101.7359	87.7235	130.5875	95.8774	130.0777	113.407
70.1591	22.1144	110.7877	90.2446	118.627	124.8568
86.1892	42.06	119.7367	103.4487	112.2841	89.2017
73.4091	29.0506	126.5708	76.4666	119.5524	105.4429

TABLE 3
Strength healing efficiency eσ and toughness
healing efficiency eU for all F1 samples.
0 J	250 J	1,000 J
eσ	eU	eσ	eU	eσ	eU
21.0943	2.9985	35.0746	14.3804	33.0123	13.6124
23.6453	3.5352	35.1792	8.4700	64.5745	9.9222
16.7393	1.5321	25.3237	8.5484	36.2600	5.5118
19.0665	1.5606	40.7039	10.2332	25.6704	2.9258
27.7569	13.1454	40.1619	5.1628	58.0123	6.3404
15.0923	1.1752	36.8715	8.5879	24.4865	5.1419
30.1459	11.4526	16.5049	5.8940	41.5218	8.2369
24.6799	3.9063	12.4887	3.5789	94.6802	29.9663
23.1653	2.5836	20.3087	3.1602	41.3786	7.4766
31.6532	3.2104	16.1541	1.4037	67.0186	14.7414
1,500 J	2,500 J	3,500 J
eσ	eU	eσ	eU	eσ	eU
95.6751	18.8274	48.9879	6.8230	130.2697	69.7569
111.9315	31.5815	131.4432	64.6084	114.4421	39.9882
87.9601	34.1084	59.9733	16.9451	91.7985	12.2286
29.4396	10.0856	131.5648	100.7711	49.7342	10.8695
30.6392	5.8910	66.7634	9.3828	51.4856	14.9047
41.6183	5.9003	135.1484	82.1517	97.0847	17.8115
28.7275	10.1522	35.9451	3.2211	130.4396	48.8561
46.8527	6.8506	101.6827	130.5233	116.8388	16.7466
67.1198	6.9835	61.9500	8.0510	156.4824	104.1017
71.0493	23.5992	21.0992	3.0180	102.2734	21.8186

TABLE 4
Strengthening factor fσ values for all P samples.
100 J	360 J	900 J	1,500 J	2,100 J
1.0751	1.0885	1.1195	1.2201	1.3691
0.9796	1.0578	1.1821	1.2739	1.2821
1.0515	1.0618	1.1826	1.3213	1.2098
0.8546	1.0055	1.2130	1.3158	1.1162
1.1619	1.1531	1.0669	1.3250	1.2065
0.9993	0.9988	0.9671	1.5475	1.0942
0.9111	1.0295	1.0834	1.0736	1.0059
0.7433	0.9553	1.0614	1.1446	1.3563
0.9926	1.1235	1.0966	1.2138	1.1696
0.9763	1.0226	1.1971	1.1504	1.2445

TABLE 5
Healing energy, temperature and crack length in different studies of metal healing.
Reference	Healing method	Energy (J)	Temperature (° C.)	Crack length (mm)
15 (K. W. Gao, et	Heat-driven	2.80E5	700 to 750	0.002
al. Scr. Mater.	precipitation
2001, 44, 1055.)
16 (C. Chen, Appl.	Heat-driven	6.84E7	200	0.100
Phys. Lett. 2016,	precipitation
109, DOI
10.1063/1.4962333
17 (H. Yu, Metall.	Heat-driven	1.20E6	1050 to 1200	0.050
Mater. Trans. A	precipitation
Phys. Metall.
Mater. Sci. 2014,
45, 1001)
18 (I. M. Van	Phase transition	5.0E3	70	15.000
Meerbeek, Adv.
Mater. 2016, 28,
2801)
19 (H. Song, Sci.	Joule heating	−200	600	0.020
Rep. 2017, 7, 1)
20 (A. Hosoi,	Joule heating	−35	600	0.250
Mater. Sci. Eng. A
2012, 533, 38)
21 (J. T. Kim, Sci.	Heat-driven	2.25E5	150	0.050
Rep. 2018, 8, 2)	precipitation +
	Phase transition
24 (X. G. Zheng,	Electrochemistry	4.0E4 to 2.0E5	40 to 55	1.500
Y. N. Shi, K. Lu,
Mater. Sci. Eng. A
2013, 561, 52)

Table 6. Electrical resistance for three pristine cellular nickel samples and the same samples after healing from complete scission with 1500 J of energy input.

TABLE 6
Electrical resistance for three pristine cellular
nickel samples and the same samples after healing
from complete scission with 1500 J of energy input.
		Pristine	After healing
	Average (Ω)	0.159	0.163
	Standard deviation (Ω)	0.001	0.032

Summary

Using electrodeposition enabled the recovery of tensile strength and toughness in fractured or plastically deformed nickel foams. Regime II samples showed good recovery of mechanical properties with high healing efficiencies regardless of healing time. On the other hand, regime III samples, which had large cracks, depended strongly on healing time in their ability to recover their mechanical properties. Those samples healed for 5 and 3.5 hours exhibited, for the most part, high healing efficiencies, while samples healed for less time showed both low toughness and low tensile strength. The improved mechanical properties of samples after healing was attributed to the bulking of the struts with excess nickel and to the high strength of electrodeposited nickel due to its nanocrystalline structure.

A simulation of nickel electrodeposition to heal a broken foam strut showed that spatial and time-dependent variations in the diffusive flux of nickel ions led to non-uniform deposition. This non-uniformity means that the formation of small voids is possible, albeit at a smaller scale than in bulk metals. Future iterations of this simulation will use the level set method, instead of the deformed mesh method, to analyze the geometry and size of these voids since it allows topological changes. The simulation can, therefore, be continued beyond the point when the nickel films growing from the two strut surfaces meet and form one continuous domain.

Additional Disclosure

Repairing fractured metals to extend their useful lifetimes advances sustainability and mitigates greenhouse gas emissions from metal mining and processing. While high-temperature techniques have long been used to repair metals, the increasing ubiquity of digital manufacturing and “unweldable” alloys, as well as the integration of metals with polymers and electronics, call for radically different repair approaches. This disclosure presents a framework for effective room temperature repair of fractured metals using an area-selective nickel electrodeposition process we refer to as electrochemical healing. Based on a theoretical model that links geometric, mechanical, and electrochemical parameters to the recovery of tensile strength, this framework enables 100% recovery of tensile strength in nickel, low-carbon steel, two “unweldable” aluminum alloys, and a 3D-printed difficult-to-weld shellular structure while using a single common electrolyte chemistry.

Through a distinct energy dissipation mechanism, this framework also enables recovery—up to 136%, in some example, non-limiting instances—recovery of toughness in an aluminum alloy. To facilitate practical adoption, this work reveals scaling laws for the energetic, financial, and time costs of healing, and demonstrates the restoration of a functional level of strength in a fractured standard steel wrench. Empowered with this framework, room-temperature electrochemical healing provides effective, scalable repair of workpieces—including those that include metals—in diverse applications.

Annually, the mining, refining, and processing of structural metals result in over 3 billion tons of CO₂-equivalent emissions, and the mining and refining of aluminum, alone, produces over 14,000 tons of largely toxic byproducts^[1-4]. Improving the sustainability of structural metals, through a circular economic model based on recycling, refurbishing, repair, and reuse^[5], plays a role in mitigating greenhouse gas emissions and addressing many detrimental ecological effects^[1,4,6] (FIG. 32A). Repair, in particular, not only extends the operational lifetime of metal structures, thus reducing waste from end-of-life disposal and byproducts of mining and refining^[4,7,8] (FIG. 32A), but also complements recycling, which is limited by the difficulty of removing elemental contaminants from alloys and multi-metal parts^[9].

For the past 6,000 years, high-temperature techniques, such as brazing and welding^[10-12] have enabled metal repair without the high resource costs of melting and recasting fractured parts. Recent innovations in repairable and self-healing metals have exploited joule heating^[13,14], phase transitions^[15-17], solute precipitation^[18,19], combined phase transitions and precipitation^[20], and exothermic reactions^[21]. These innovative techniques, along with the established techniques of welding and brazing, remain limited by the need for high temperature to make metal atoms mobile and the resulting high energy input, as well as by either the low strength of healed metals, the small size of repairable cracks, or the constrained microstructure and chemical composition of healed metals.

Notably, welding suffers from distinct limitations that are accentuated by recent advances in digital manufacturing and material integration, which calls for radically different approaches to repair metals. Several metallic alloys, including aluminum alloys of the 2000, 6000, and 7000 series^[22,23] and nickel superalloys with Al and Ti concentrations in excess of 4 wt. %^[24], are considered “unweldable” as they are vulnerable to cracking due to extreme thermal gradients and solute segregation^[25,26] (FIG. 32B. Approaches have been developed to mitigate these limitations^{[22,25,27,28]}, however, high levels of operator skill, experience, and precision are required, which limit the wide adoption of welding in a decentralized circular economy. Posing further challenges to welding are recent advances in design^[29,30] and additive manufacturing^[31-34] which have enabled metal structures with high levels of geometric complexity. The octet-truss lattice shown in FIG. 32C is an example of a complex geometry where a fracture in an internal strut cannot be readily accessed by a welding torch (or beam). Moreover, the high temperatures induced by welding can cause damage to nearby non-metallic materials, as metals are increasingly integrated with polymers^[35,36] or electronics^[37-39] in various aerospace, robotic, and sensing applications.

By enabling fast room-temperature diffusion of metal ions in an aqueous medium (10⁻⁹ m² s⁻¹), electrochemical healing represents a fundamentally different approach to repair fractured structural metals^[40-42]. Coating a metal structure with a passivating coating ensures that metal ions are only reduced at fracture sites, thus resulting in efficient targeted healing (Bottom insets of FIG. 32C). Using this approach, electrochemical plating of nickel has shown promise, by enabling 100% recovery of tensile strength in fractured cellular nickel (or nickel foam), with minimal energy use (˜10² J per mm of crack length) compared to many high-temperature healing techniques (up to 10⁹ J/mm)^[40]. However, prior attempts to repair bulk metals using nickel plating failed to recover 100% of pristine tensile strength due to poor nickel-metal adhesion or defects caused by diffusion-limited plating^[41-44]. Electrochemical healing can employ a simple process with a single electrolyte chemistry to effectively repair a wide variety of structural metals beyond nickel (including complex 3D printed structures and “unweldable” alloys) within a quantitative predictive framework. Prior work on the electrochemical joining of metal parts achieved high adhesion of plated nickel to other metals, but required multi-step processes with acid pre-treatments and plating in different electrolyte chemistries, and did not present a model that predicted or provided understanding of how to achieve optimal mechanical properties of the joined parts^[45-49].

Here, we provide a framework for electrochemical healing, based on an experimentally validated theoretical model that elucidates the geometric, electrochemical, and mechanical parameters needed for 100% recovery of tensile strength in fully fractured structural metals. This framework enables the full restoration of tensile strength in nickel, low-carbon steel, two “unweldable” aluminum alloys, and a difficult-to-weld 3D printed funicular shellular structure. This framework shows the possibility of over 100% recovery of toughness (or work of fracture) in fractured metals subject to tensile loading. To facilitate practical adoption, we demonstrate the effective repair of a fully fractured steel wrench, and propose scaling laws for the energetic, financial, and time costs of repairing metals from the microscale to the meter-scale.

Results and Discussion

FIG. 33A illustrates the disclosed approach to electrochemically heal structural metals. One can describe this process as electrochemical healing because of its similarity to bone healing, where healing matter is transported to the fracture site through an immersed electrolyte and strength is restored through the growth and connection of matter from opposite fracture surfaces^[40].

As an improvement over earlier approaches in which metal was only plated at the cross-section of a fractured strut^[40,41] we exposed the non-fractured surface of the metal to plating (FIG. 33A). A pair of Ni 200 (>99% nickel alloy) half-dogbone samples prepared by waterjet cutting simulated a fractured dogbone sample (FIGS. 33A, 39A). Insulating electric tape masked the fractured sample so that only a fraction, A_e/2, of the total available area, A_o/2, in each half-dogbone was exposed (FIGS. 39A, 39B). A custom fixture (FIG. 39D) held the fractured sample in a nickel sulfamate aqueous electrolyte in alignment and with no gap at the fracture. Prior work showed that minimizing the fracture gap is essential to achieving effective healing with minimal time and charge input^[41]. Applying a constant potential of −1.8 V vs. Ni to the fractured sample resulted in nickel deposition over the entire exposed area A_e, with the amount of plating controlled by the charge input Q (FIGS. 2A, 39C).

After removing the masking tape, healed Ni 200 samples were tested in tension until fracture. FIG. 33Bb shows the resulting stress-strain data for two samples healed with 200 mAh and 1000 mAh, alongside the stress-strain data of a pristine sample for reference. To assess the effectiveness of the healing process, we compared the tensile strength of each healed sample, σ_U, with the average tensile strength of five pristine samples, σ_M (Table 9). Samples healed with Q=1000 mAh exhibited an increase in strength healing efficiency σ_U/σ_M as A_e increased, eventually reaching a plateau at σ_U/σ_M=1, or full restoration of pristine tensile strength (FIG. 33C). In contrast, samples healed with Q=200 mAh exhibited an increase in σ_U/σ_M reaching a maximum of σ_U/σ_M=0.8395 at A_e/A_o=0.3125, before subsequently declining down to σ_U/σ_M=0.4817 at A_e/A_o=0.5625 (FIG. 33C). We also examined the impact of varying the charge input Q at a fixed A_e/A_o=0.4375, and observed that, at a low charge input, Q=200 mAh, σ_U/σ_M=0.6244 but as Q is increased to 400 mAh and beyond, σ_U/σ_M reached and remained around 1.0 (FIG. 33D.

To develop a quantitative model of these experiments, we first differentiated samples by the type of fracture experienced upon post-healing tensile testing. Three types of fracture were observed: I, P, and M (FIG. 33E). In type I, de-bonding occurred at the interface between the plated nickel and the structural metal, with the metal sliding out of the plated nickel sleeve that surrounds it. In type P, the plated nickel fractured at the same location as the initial fracture. In type M, the metal dogbone fractured in a new location, indicating that the tensile strength of the healed sample was approximately equal to the tensile strength of a pristine sample. The incidence of these three types of fracture varied with changes in A_e (FIG. 33F). Samples healed with Q=1000 mAh all experienced type-I fracture at low A_e/A_o, but as A_e increased, the incidence of type-M fracture increased at the expense of type-I fracture. Samples healed with Q=200 mAh experienced the same high incidence of type-I fracture at low A_e, though unlike 1000 mAh samples, the incidence of type-P fracture increased with larger A_e. Comparing the data in FIG. 33C and FIG. 33F reveals that type-I fracture was always dominant at low A_e/A_o, type-M fracture was prevalent when σ_U/σ_M˜1, while an increasing prevalence of type-P fracture was associated with declining σ_U/σ_M.

Informed by these experimental insights, we developed a model—not necessarily bound to any particular theory or embodiment—that predicts the tensile strength of healed samples for each type of fracture. Assuming force continuity and using Faraday's law, we related σ_U (the tensile strength of the healed sample) to τ_Ni-M (the interfacial shear strength, for type-I fracture), σ_M (the tensile strength of the structural metal, for type-M fracture), and σ_Ni (the tensile strength of plated nickel, for type-P fracture) through a single independent variable X=A_e/A_M, where A_M is the cross-sectional area of the structural metal. The three governing equations of the model are

$\begin{array}{cc}{\sigma }_U={\sigma }_{\mathrm{Ni}}\frac{A_{\mathrm{Ni}}}{A_M}=2{\sigma }_{\mathrm{Ni}}{\left(\frac{1}{A_M}\right)}^3\left(\frac{\epsilon \mathrm{QM}}{2F_{\rho }}\right)\left(2\left(\frac{\epsilon \mathrm{QM}}{2F_{\rho }}\right)X^{{ }_{}-2}+A_M\left(L_M+W_M\right)X^{{ }_{}-1}\right)& \left(1\right)\end{array}$

for type-P fracture,

$\begin{array}{cc}{\sigma }_U={\tau }_{\mathrm{Ni}-M}X+{\sigma }_{\mathrm{Ni}-M,o}& \left(2\right)\end{array}$

for type-I fracture, and

$\begin{array}{cc}{\sigma }_U={\sigma }_M& \left(3\right)\end{array}$

for type-M fracture, where A_Ni is the cross-sectional area of plated nickel, E is the cathodic efficiency of nickel plating (Table 7), M is the molar mass of nickel (58.69 g/mol), F is Faraday's constant (96,485 C/mol), and ρ is the mass density of nickel (8,900 kg/m³), L_M and W_M are the thickness and width of the structural metal such that A_M=L_MW_M, and σ_Ni-M,o is an added stress term.

FIG. 34A shows σ_U/σ_M as a function of A_e/A_M for each fracture type using expressions (1), (2), and (3). For a given value of A_e/A_M, the lowest curve determines the type of fracture that occurs and the achievable strength healing efficiency σ_U/σ_M. There are two hypothetical healing cases. In case 1, the type-I line intersects the type-P curve below the sample's pristine strength (type-M horizontal line), which means that σ_U/σ_M=1 cannot be achieved and full recovery of tensile strength is not possible. In case 2, the intersection point moves above the type-M line, either due to the use of plated metal with a higher tensile strength, an increase in the charge input, or an increase in the interfacial shear strength. This opens a window in which σ_U/σ_M=1, or full healing, is physically possible.

This model showed good agreement with the healed Ni 200 samples (FIG. 34B, Table 10). A linear regression of the type-I fracture line showed that τ_Ni-M=6.14 MPa and σ_Ni-M,o=158.97 MPa (FIG. 34B, red line; FIG. 51). Because we used no chemical or electrochemical treatment before nickel plating to maintain a simple healing process, the Ni-metal interface shear strength, τ_Ni-M, was lower than values reported from ring shear tests of nickel plated on different metals, including nickel itself^[45,47] Type-P fracture curves were plotted for charge inputs from 200 to 1000 mAh, with the tensile strength of plated nickel at σ_Ni=358 MPa (FIG. 42). Experimental data and type-P fracture curves are colored in shades of green according to the charge input used (FIG. 34B). The type-P fracture curve for 200 mAh is slightly above, but closely follows experimental data for samples healed with 200 mAh and A_e/A_M values of 41.36, 57.91, and 74.45. The experimental data from FIG. 33D is also shown in FIG. 34B, with a cluster of datapoints at σ_U/σ_M˜1.0 and A_e/A_M=57.91. FIG. 34B demonstrates that to guarantee full healing, or σ_U/σ_M˜1.0, two conditions need to be met: a sufficiently high exposed area so that A_e/A_M>45, and a charge input higher than 200 mAh.

Interestingly, the samples retained significant strength, σ_U/σ_M˜0.4, when there was no exposed metal on which nickel could be plated, A_e/A_M=0. To explain this, we compared the surface morphologies of the cross-sections of a pristine sample (FIG. 34C, 34D) and a healed sample after type-P fracture (FIG. 34E, 34F). The pristine sample cross-section shows plastic damage resulting from waterjet cutting, while the healed sample cross-section shows clear morphological evidence of plated nickel suggesting that there was a microscale gap which allowed nickel ion transport, and thus, nickel deposition and adhesion at the cross-sectional areas. As a result, one might expect a non-zero tensile strength in healed samples even if A_e=0, which we accounted for in the model with the σ_Ni-M,o stress term (equation 2).

Extending our framework to various types of structural metals demonstrated the viability of electrochemical healing as an alternative to conventional welding. With the same experimental approach used with Ni 200 samples, we electrochemically healed low-carbon steel (AISI 1008), and two “unweldable” aluminum alloys (Al 2024 and Al 7075). In FIG. 35A, we applied the theoretical model to AISI 1008 samples healed with 400 and 800 mAh of charge input. Linear regression of the type-I fracture line showed that τ_Ni-M=7.61 MPa (FIG. 4A, red line; FIG. 51). Fitting the type-P curve to experimental data revealed that σ_Ni=213.4 MPa, which is lower than expected likely due to the presence of iron within plated nickel (FIG. 54). Using 800 mAh of charge input, healing at A_e/A_M=74.45 and A_e/A_M=91.00 resulted in full restoration of tensile strength, with strength healing efficiencies σ_U/σ_M of 1.010 and 1.022 respectively. In FIG. 35B, we applied our theoretical model to Al 7075 samples healed with 200 and 400 mAh.

Linear regression of the type-I fracture line showed that τ_Ni-M=7.23 MPa and σ_Ni-M,o=97.10 MPa (FIG. 4B, red line; FIG. 51). Fitting the type-P curve to experimental data revealed that σ_Ni=387.42 MPa, which is close to the measured value of 358.2 MPa (FIG. 42). Using 400 mAh of charge input, full healing of tensile strength was achieved at A_e/A_M=63.00 and A_e/A_M=81.00, indicated by strength healing efficiencies au u of 1.022 and 1.021 (FIG. 35B, Table 12). In FIG. 35C, we applied the theoretical model to Al 2024 samples healed with 400 and 600 mAh. Linear regression showed that τ_Ni-M=6.65 MPa and σ_Ni-M,o=4.44 MPa (FIG. 4C, red line; FIG. 51).

Fitting the type-P curve to experimental data revealed that σ_Ni=330.88 MPa, which is close to the measured value of 358.2 MPa (FIG. 42). As a charge input of 400 mAh was insufficient to enable full healing, we healed Al 2024 samples with 600 mAh of charge input at A_e/A_M=81.00 and A_e/A_M=99.00, achieving near-full healing with σ_U/σ_M at 0.9532 and 0.9574 respectively (FIG. 35C, Table 13). Occasional stress concentration at the junction between the plated area and the non-plated area led to a substantial reduction in strength recovery at A_e/A_M=99.00, from σ_U/σ_M=0.9574 to σ_U/σ_M=0.7153 (downward arrow in FIG. 35C).

Remarkably, the ability of this electrochemical healing framework to fully restore tensile strength in fractured metals was insensitive to nickel-metal adhesion. Shear strengths at the interface between plated nickel and the four healed metals (Ni 200, AISI 1008, Al 2024, and Al 7075) ranged between 6.1 and 7.6 MPa (FIG. 51). These values are very low compared to 10× to 70× higher interfacial shear strength values measured via ring shear testing of nickel plated on a range of metallic alloys, which underwent multi-step processes that included chemical or electrochemical pre-treatment in acidic solutions, followed in some cases by plating in a low-pH nickel solution (e.g., Woods strike), before plating in a standard nickel sulfamate solution^[45,47,51] Our framework obviates the need for these multi-step processes because it removes interfacial adhesion as the limiting factor of healing performance, replacing it instead with factors that can more easily be controlled such as exposed area and charge input.

Healing waterjet-cut metal samples validated the theoretical model and demonstrated effective restoration of tensile strength. However, our framework could also heal metals that were plastically deformed and fractured under tensile loading. AISI 1008 steel dogbone samples were fully fractured in tension, then healed to recover ˜100% of pristine tensile strength. Mechanical polishing of the fracture surface reduced the requirements of full healing in terms of charge input (from 1600 mAh to 1000 mAh) and time (from 50 hours to 16 hours) (see FIG. 55).

Though our framework targets tensile strength recovery in fractured metals, it presents full recovery of both toughness and tensile strength under specific conditions. Here, toughness, which is also known as “work of fracture”, refers to the area under the stress-strain curve. Similar to Ni 200 samples, type-I fracture dominated initially in Al 2024 and Al 7075, before declining in favor of type-P and type-M fractures (FIG. 35D). For Al 2024, the incidence of type-I fracture decreased to 0% at A_e/A_M=81, as the incidences of type-M and type-P fractures increased to 40% and 60%, respectively. Incidence of type-P fracture then increased further in line with our theoretical prediction that type-P fracture dominates for large A_e/A_M. For Al 7075, type-M and type-I fractures co-existed while A_e/A_M was between 45 and 81, but as A_e/A_M increased to 99, type-P fracture dominated. The co-existence of type-M and type-I fracture within this intermediate range of A_e/A_M values occurred along with high toughness recovery, in addition to full recovery of tensile strength. FIG. 35E shows the stress-strain data of four Al 7075 samples healed with Q=400 mAh and A_e/A_M=81, with two experiencing type-I fracture and the two others experiencing type-M fracture. While all four samples exhibited similar tensile strength with σ_U/σ_M˜1, the samples that experienced type-I fracture showed remarkably high toughness (area under the stress-strain curve) as the plated nickel slid across the Al 7075 surface during loading. Toughness healing efficiency σ_U/σ_M, the ratio of healed to pristine toughness, for all Al 7075 samples rose with increasing A_e/A_M, peaked at σ_U/σ_M=1.00 for A_e/A_M=63, then decreased to σ_U/σ_M=0.258 for A_e/A_M=99 (FIG. 35F, yellow data). Toughness healing efficiency was highest for samples that experienced type-I fracture, peaking at σ_U/σ_M=1.364 for A_e/A_M=81 (FIG. 35F, red data; Table 14). In summary, healed Al 7075 samples with A_e/A_M values equal to or slightly higher than the A_e/A_M at which the type-I and type-M fracture lines intersect (red and yellow lines in FIG. 35B) were likely to experience type-I fracture, and as a result, to exhibit up to 136% recovery of toughness (or work of fracture). This insight provides improved toughness recovery in healed metals under tensile loading.

In addition to repairing “unweldable” alloys, electrochemical healing enabled tensile strength recovery in 3D printed metal structures with complex geometries, which would be impossible to repair using conventional welding. Using 3D/polyhedral graphic statics as a design method and selective laser melting of AlSi10Mg for 3D printing, we fabricated a funicular shellular structure that carries internal forces axially (no transverse stress) (FIG. 48) and is designed to fail at its central section, which includes three outer struts and a middle strut that is difficult to access (FIGS. 36A, 41). This structure is a type of funicular polyhedral frame designed using a technique of topological subdivision which generates two-manifold anticlastic surface-based structures with cross-sections normal to the direction of the internal force flow for any given loading condition^[52-55]. Owing to its geometric complexity and the inaccessibility of the middle strut, this structure could not be repaired by conventional welding and would need to be re-printed or replaced. We loaded the structure in tension until the four struts fractured, healed it via selective nickel plating, then fractured it in tension again to assess the recovery of tensile strength (FIG. 36B). In addition to the healing process which we have used thus far (potentiostatic plating at −1.8V vs. Ni), we used an enhanced process in which we apply 1000 cycles of pulsed plating (one cycle includes plating at −1.8V vs. Ni for 5 seconds followed by −0.2V vs. Ni for 3 seconds) before proceeding with potentiostatic plating at −1.8V vs. Ni (FIG. 49). Pulsed plating mitigated diffusion-limited electrodeposition, which improves nickel adhesion to the healed metals and prevents void formation at the fracture gaps^[41]. The normal healing process (potentiostatic only) with Q=1200 mAh resulted a low 38.5% recovery of tensile strength (top plot in FIG. 36C, FIG. 49A), while the enhanced healing process (pulsed+potentiostatic) with Q=1200 mAh enabled a 110.1% recovery of tensile strength (bottom plot in FIG. 36CFIG. 49B). We observed that the normal healing process resulted in type-P fracture of all four struts, while the enhanced process resulted in type-P fracture at the central strut, with limited or no type-I fracture at the three outer struts (FIG. 36B, 49). By maximizing nickel density at the fracture gap, this enhanced process is useful in cases where there are constraints either on energy (e.g., battery-powered robot) or on metal area available for plating.

Using electrochemical healing to repair metals in practical applications requires careful consideration of its energetic, financial, and time requirements across length scales. We used our model (with properties for Al 7075) to estimate the charge input, Q (FIG. 37A), financial cost, C (FIG. 37B), and time, T (FIG. 37C) required for full healing in fractured metals with a cross-sectional area ranging from 10⁻⁸ to 1 m². For metals similar in size to the dogbone samples in this study (A_M=2.0 mm²), full healing would require 335 mAh, 30 hours, and $0.01. Q and C are low, if not negligible, for small length scales, but rise at an increasing rate as length scale increases. On the other hand, T rises with a declining rate as length scale increases but may become prohibitively high at large length scales.

Improving the adhesion between the plated nickel and structural metal, as measured by the interfacial shear strength τ_Ni-M, using proven chemical and electrochemical processes^[41,45,47] can decrease the energetic and financial costs of electrochemical healing. For a structural metal with A_M=2.0 mm², required charge input decreases by 80% to 67.1 mAh due to a 5× improvement in τ_Ni-M, by 90% to 33.5 mAh due to a 10× improvement, and by 95% to 16.8 mAh due to a 20× improvement. Thus, the marginal benefit of improving τ_Ni-M declines rapidly, which suggests that common electrochemical pretreatments^[41] might be the optimal choice. Though we focused our cost-reduction analysis on increasing interfacial shear strength, τ_Ni-M, using plated metal with higher tensile strength or increasing the average current density during plating would also lower the costs of full healing.

According to the scaling relationships that govern Q, C, and T (FIGS. 37A37C), with τ_Ni-M=7.23 MPa, healing a standard concrete-reinforcing steel bar or a metal part of similar size (A_M˜104 m²), would require $4.0, 224 hours (or 9.3 days), and 123 Ah (or 0.3% of the capacity of a Tesla Model 3 battery at 1.8 V)^[56]. A 100 mA/cm² current density would reduce the healing time tenfold, to 22.4 hours. Costs increase dramatically for a large metal part (A_M˜0.1 m²): $125,892, 7079 hours (or 9.7 months), and 3,890,451 Ah (or 93× the capacity of a Tesla Model 3 battery at 1.8 V)^[56], where financial cost is dominated by nickel. In summary, without the implementation of cost reduction measures, electrochemical healing is attractive for metal fractures from the micrometer to the centimeter-scale, but can be prohibitively expensive and slow at or near the meter-scale.

With these scaling relationships in mind, we used electrochemical healing to repair a fully fractured ¼-inch chrome-coated steel wrench, with cross-sectional area A_M˜30 mm² (FIG. 37D). We applied a total charge input of 8,230 mAh over 138 hours in an unstirred room temperature bath (FIG. 37E, 37F). The wrench recovered a functional level of bending strength and withstood multiple loadings at torques up to 10 N·m, with no discernable damage (FIG. 37Gg). Therefore, the healed wrench could readily meet the 3.6 N·m minimum tightening torque for ¼ inch ASTM A307 bolts and 8.5 N·m minimum tightening torque for ¼ inch SAE J429 Grade 5 bolts, which are used in a range of industrial applications^[57]. Healing a wrench demonstrated the recovery of functionality after full fracture of a common metallic part. With further electrolyte and process optimization^[41], faster and stronger electrochemical healing could be deployed as an effective approach to repair many high-value metallic parts.

Conclusion

Room-temperature electrochemical healing represents a radical shift from the current high temperature approaches to repair metals, including welding. We present here a framework for the effective electrochemical healing of fractured metals based on a model that relates the recovery of tensile strength to relevant geometric (e.g., exposed area, cross-sectional area), electrochemical (e.g., charge input, cathodic efficiency), and mechanical parameters. We experimentally validated this model and demonstrated full recovery of tensile strength in a nickel alloy, low-carbon steel, and two “unweldable” aluminum alloys. We also showed that fully recovering both toughness and tensile strength is possible under specific conditions. Informed by this framework and using a healing process that combined pulsed and potentiostatic plating, we enabled full restoration of tensile strength in a 3D printed difficult-to-weld shellular structure. Repairing 3D printed parts mitigates the high energy and cost associated with the current approach of recycling and reprinting fractured parts. To facilitate the adoption of electrochemical healing, we revealed the scaling relationships that govern the charge input, financial cost, and time required for full healing at different length scales, as well as demonstrated the restoration of a functional level of strength in a fractured wrench.

In short, this work enables 100% recovery of tensile strength in a diverse range of metallic materials using a simple nickel sulfamate electrolyte; a well-studied, widely-used, and relatively inexpensive electrolyte chemistry, which could potentially enable a universal and scalable approach to repair fractured metals at various length scales. Electrochemical healing also provides electrically-controlled autonomous and preemptive repair^[40], as well as 3D-printed metal structures optimized for repair through funicularity and designed failure characteristics. Electrochemical healing may reduce demand for metal mining and refining, thus mitigating the emissions intensity of structural metals by up to 400 kg of CO₂ per ton of metal^[9], and moving toward sustainability and net-zero emissions.

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• [55] M. Akbari, A. Mirabolghasemi, M. Bolhassani, A. Akbarzadeh, M. Akbarzadeh, Adv. Funct. Mater. 2022, 2109725, 1.
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Supplementary Text

Cathodic Efficiency

The cathodic efficiency, E, (also known as coulombic efficiency) represents the efficiency by which electrons are used to reduce nickel ions to nickel atoms. ε<100% signifies that some side reactions, such as hydrogen evolution, have occurred. We calculate the cathodic efficiency using the following expression:

$\begin{array}{cc}\epsilon =\frac{m_{\exp }}{m_{\mathrm{theo}}}=m_{\exp }\times \frac{2F}{\mathrm{QM}},& \left(S1\right)\end{array}$

where m_exp and m_theo are the experimental and theoretical masses of electrodeposited nickel, Q is the charge input (in coulombs), M is the molar mass of nickel (58.69 g/mol), and F is Faraday's constant (96,485 C/mol). We set Q 91.332 mAh, so that m_theo=0.1000 g.

We measure the cathodic efficiency of nickel electrodeposition at −1.8V vs. Ni in our lab-made nickel sulfamate electrolyte. The measured values for each metal substrate (Ni 200, A12024, and A17075) are listed in the table below. We observe that the substrate has no discernable influence on cathodic efficiency.

TABLE 7
Cathodic efficiency of nickel sulfamate electrolyte
at −1.8V vs. Ni using Ni 200, Al 2024, and Al 7075 as substrates.
	Cathodic Efficiency (%)
	Ni 200	A1 7075	A1 2024
	96.0	97.5	97.9
	96.4	98.0	96.0
	98.0	99.5	97.7
Average	96.8	98.3	97.2

Mechanical Properties of Pristine and Healed Dogbone Samples

TABLE 8
Dimensions of healed and pristine dogbone samples
Unit:	Ni 200	AISI 1008	Al 2024 & Al 7075
mm	Pristine	Healed	Pristine	Healed	Pristine	Healed
WM	4.0	4.0	4.0	4.0	4.0	4.0
LM	0.55	0.55	0.77	0.75	0.52	0.50
lo	24	32	24	32	24	32

TABLE 9
Tensile strength and toughness of pristine Ni 200, Al 7075, Al
2024, and AISI 1008. Averages and standard deviations
obtained from testing of five to six samples.
	Tensile strength,	Toughness,	Engineering
	σM (MPa)	UM (MJ/m3)	strain at fracture
		Standard		Standard		Standard
	Average	deviation	Average	deviation	Average	deviation
Ni 200	406.91	0.65	117.91	1.49	0.3338	0.0055
Al 7075	493.55	1.96	47.66	2.54	0.1139	0.0047
Al 2024	441.27	6.70	69.71	3.25	0.1638	0.0244
AISI	342.59	1.30	101.40	3.03	0.3170	0.0185
1008

TABLE 10
Strength and toughness healing efficiency and plated nickel
thickness data for healed Ni 200. Calculated values of Ni thickness are used, except in cases
where calculated and measured values differ significantly. These differences arise from non-
uniform growth or overplating outside the edges of the exposed metal area.
			Plated Ni	σU/σM (%)	U/UM (%)
			thickness		standard		standard
Q (mAh)	Ae/Ao	Ae/ Am	(mm)	average	deviation	average	deviation
1000	0.0625	8.27	2.23	50.402	10.043	2.9028	1.5115
	0.1875	24.82	1.50	81.679	5.520	25.0294	10.5320
	0.3125	41.36	1.31	97.128	2.899	62.7701	14.4213
	0.4375	57.91	0.94	99.576	2.336	57.9791	10.9101
800	0.4375	57.91	0.75	99.282	1.573	62.6933	14.1411
600	0.4375	57.91	0.56	99.878	1.120	63.9173	6.4803
400	0.2500	33.09	0.66	85.854	4.035	34.1124	7.2929
	0.4375	57.91	0.37	98.963	0.652	57.0185	4.3869
	0.5625	74.45	0.29	93.990	4.282	41.0139	15.8421
200	0.125	16.55	0.66	63.185	6.125	6.0036	2.3608
	0.3125	41.36	0.26	83.954	10.804	29.6942	17.1423
	0.4375	57.91	0.19	62.442	5.774	3.1415	1.2056
	0.5625	74.45	0.15	48.169	18.520	1.7920	0.8766

TABLE 11
Strength and toughness healing efficiency and plated nickel thickness data for healed AISI 1008 steel.
			Plated Ni	σU/σM (%)	U/UM (%)
Q			thickness		standard		standard
(mAh)	Ae/Ao	Ae/Am	(mm)	average	deviation	average	deviation
400	0.1250	16.5455	1.26	28.4609	9.5485	0.6903	0.3284
	0.1875	24.8182	0.84	30.9356	9.7253	0.7754	0.3968
	0.2500	33.0909	0.63	50.6914	36.0135	16.5584	31.8044
	0.3125	41.3636	0.50	74.9803	30.4697	23.0904	35.4469
	0.4375	57.9091	0.36	75.0790	9.3252	4.9303	4.1550
	0.5625	74.454	0.28	70.6354	22.9460	4.8458	4.2244
	0.6875	91.0000	0.23	29.6043	6.7812	0.7576	0.5390
800	0.5625	74.4545	0.56	100.9986	8.1437	43.7810	27.7567
	0.6875	91.0000	0.46	102.1750	7.9079	31.1115	16.0599

TABLE 12
Strength healing efficiency and plated
nickel thickness data for healed Al 7075
			Plated Ni	σU/σM (%)
			thickness		standard
Q (mAh)	Ae/Ao	Ae/Am	(mm)	average	deviation
200	0.0625	9.00	1.33	22.6984	3.4450
	0.1250	18.00	0.66	47.6614	3.1367
400	0.1875	27.00	0.88	67.3824	6.6348
	0.3125	45.00	0.53	95.7485	6.2821
	0.4375	63.00	0.38	102.2264	2.6517
	0.5625	81.00	0.29	102.1014	1.6978
	0.6875	99.00	0.24	95.3457	5.5365

TABLE 13
Strength and toughness healing efficiencies data for healed Al 2024
			Plated	σU/σM (%)	U/UM (%)
			Ni		stand-		stand-
			thick-		ard		ard
Q		Ae/	ness	aver-	devia-	aver-	devia-
(mAh)	Ae/Ao	Am	(mm)	age	tion	age	tion
400	0.0625	9.00	2.22	7.1370	2.5450	0.3124	0.0946
	0.1875	27.00	0.88	48.7567	5.5487	4.5559	1.3645
	0.3125	45.00	0.53	76.9385	4.0118	19.4727	1.2578
	0.4375	63.00	0.38	88.1369	1.2253	46.2178	6.0145
	0.5625	81.00	0.29	74.6869	10.6147	8.9057	3.1343
	0.6875	99.00	0.24	66.3348	25.7801	9.5204	10.0838
600	0.5625	81.00	0.44	95.3189	2.2743	31.7080	5.4292
	0.6875	99.00	0.36	95.7429	5.2930	30.8278	11.5422
	*0.6875	99.00	0.36	71.5284	10.1290	7.7185	4.2031
(* = samples with stress concentration fracture in Al 2024 metal at junction between Ni plated and non-plated areas)

TABLE 14
Toughness healing efficiency data for healed Al 7075
		U /UM (%)	U/UM (%)
		[all fracture types]	[only type-I fracture]
			standard		standard
Q (mAh)	Ae/Am	average	deviation	average	deviation
200	9.00	2.0495	0.9620	2.0495	0.9620
	18.00	6.5978	1.9001	6.5978	1.9001
400	27.00	19.0599	3.4440	19.0599	3.4440
	45.00	56.8241	36.1670	81.2986	18.2094
	63.00	100.0539	51.5519	136.3731	2.2290
	81.00	79.9109	41.2675	123.0536	2.0586
	99.00	25.7858	9.7595	—	—

Mechanical Behavior of Pristine and Healed 3D Printed Shellular Structures

TABLE 15
Dimensions of 3D printed shellular structure
Length of central four-strut section, lo (mm) 11
Cross-sectional area of central strut, Acent (mm2) 0.88
Cross-sectional area of outer strut, Aout (mm2) 1.47
Total cross-sectional area, AM (mm2) 5.29

Theoretical Model

In this research article, we described a model that relates the strength healing efficiency of healed metals to influential parameters of a geometric (e.g., exposed metal area, metal cross-sectional area), electrochemical (e.g., charge input, cathodic efficiency), and mechanical nature (e.g., tensile strength of structural metal, shear strength at Ni-metal interface). This model offers a systematic approach to understand and predict the post-healing mechanical behavior of electrochemically healed structural metals under tensile loading, as well as enables the targeting of parameters and empirical conditions that enable full recovery of tensile strength. As shown in FIG. 4E. 4F, this model also hints at the possibility of full recovery of toughness after electrochemical healing. We briefly described the model in the main text, but we describe it below with elaborate detail.

We consider each of the three types of fracture separately. For all cases, force F is considered to be uniform across the healed metal. First, here is a description of all the parameters and variables used:

• • L_M=Thickness of structural metal (in case of rectangular cross-section)
  • W_M=Width of structural metal (in case of rectangular cross-section)
  • R_M=Radius of structural metal (in case of circular cross-section)
  • A_M=cross-sectional area of metal
  • t=thickness of plated nickel
  • A_e=exposed area of metal
  • A_Ni=cross-sectional area of plated nickel
  • ε=cathodic efficiency
  • Q=charge input
  • M=molar mass of plated nickel
  • F=Faraday's constant
  • ρ=mass density of plated nickel
  • z=valence number (2 for nickel)
  • σ_U=tensile strength of healed metal
  • τ_Ni-M=shear strength at the interface between structural metal and plated nickel
  • σ_M=tensile strength of structural metal
  • σ_Ni=tensile strength of plated nickel

For structural metal with a rectangular cross-section of thickness L_M and width W_M

For Type-I Fracture:

$\begin{array}{cc}F={\tau }_{\mathrm{Ni}-M}{A}_e\mathrm{and}& \left(S2\right)\end{array}$ $\begin{array}{cc}{\sigma }_U={\tau }_{\mathrm{Ni}-M}\frac{A_e}{A_M}.& \left(S3\right)\end{array}$

To account for stress due to adhesion at the cross-sectional area, we add a term σ_Ni-M,o

$\begin{array}{cc}{\sigma }_U={\tau }_{\mathrm{Ni}-M}\frac{A_e}{A_M}+{\sigma }_{\mathrm{Ni}-M,o}.& \left(S4\right)\end{array}$

This model uses a single independent variable

$X=\frac{A_e}{A_M},$

which captures the geometry of the healed metal. Therefore,

$\begin{array}{cc}{\sigma }_U={\tau }_{\mathrm{Ni}-M}X+{\sigma }_{\mathrm{Ni}-M,o}& \left(S5\right)\end{array}$

For Type-M Fracture:

$\begin{array}{cc}F={\sigma }_M{A}_M\mathrm{and}& \left(S6\right)\end{array}$ $\begin{array}{cc}{\sigma }_U={\sigma }_M.& \left(S7\right)\end{array}$

Thus, type-M fracture guarantees full healing, or full recovery of tensile strength, since

$\frac{{\sigma }_U}{{\sigma }_M}=1.$

For Type-P Fracture,

$\begin{array}{cc}F={\sigma }_{\mathrm{Ni}}{A}_{\mathrm{Ni}}\mathrm{and}& \left(S8\right)\end{array}$ $\begin{array}{cc}{\sigma }_U=\frac{F}{A_M}={\sigma }_{\mathrm{Ni}}\frac{A_{\mathrm{Ni}}}{A_M}.& \left(S9\right)\end{array}$

To retain a single independent variable

$\left(X=\frac{A_e}{A_M}\right),$

we have to eliminate A_Ni. We relate the exposed area A_e to plated nickel thickness t using Faraday's law:

$\begin{array}{cc}{A}_e=\frac{\epsilon \mathrm{QM}}{{\mathrm{zF}}_{\rho }}\left(\frac{1}{t}\right).& \left(S10\right)\end{array}$

Then, since the structural metal has a rectangular cross-section, A_Ni can be written in terms of t:

$A_{\mathrm{Ni}}=4t^2+2t\left(L_M+W_M\right)·\left(S11\right)$

Using both (S10) and (S11) to eliminate t, we obtain:

$A_{\mathrm{Ni}}=\left(\frac{2}{A_M}\right)\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)\left(\left(\frac{2}{A_M}\right)\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)X^{-2}+\left(L_M+W_M\right)X^{-1}\right)·\left(S12\right)$

We use (S12) to substitute A_Ni in (S9):

${\sigma }_U=2{{\sigma }_{\mathrm{Ni}}\left(\frac{1}{A_M}\right)}^3\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)\left(2\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)X^{-2}+A_M\left(L_M+W_M\right)X^{-1}\right)·\left(S13\right)$

For structural metal with circular cross-section of radius R_M

Though we used for our study metal samples with a rectangular cross-section, the model can be extended to other cross-section geometries. For instance, for a circular cross-section, expressions (S5) and (S7) will remain applicable for type-I and type-M fracture, respectively. Expression (S11) has to be modified to account for the circular geometry:

$A_{\mathrm{Ni}}=\pi \left(t^2+2R_{M}t\right)·\left(S14\right)$

Thus, to obtain an expression for type-P fracture, we use (S10) and (S14) to modify (S9):

${\sigma }_U=\pi {{\sigma }_{\mathrm{Ni}}\left(\frac{1}{A_M}\right)}^3\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)\left(\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)X^{-2}+2R_M{A}_M{X}^{-1}\right)·\left(S15\right)$

Estimating Charge Input, Financial Cost, and Time Required for Full Healing

The condition for full healing (of 100% recovery of tensile strength) is expression (S7). Therefore, we can determine the minimum charge input needed for full healing by substituting (S7) into (S13):

${\sigma }_M=2{{\sigma }_{\mathrm{Ni}}\left(\frac{1}{A_M}\right)}^3\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right)\left(2\left(\frac{\epsilon QM}{\mathrm{zF}\rho }\right){\left(\frac{A_e}{A_M}\right)}^{-2}+A_M\left(L_M+W_M\right){\left(\frac{A_e}{A_M}\right)}^{-1}\right)·\left(S16\right)$

We perform some algebraic manipulation to obtain the following:

$\left(\frac{4{\sigma }_{\mathrm{Ni}}{K}^2}{A_M{A}_e^2}\right)Q^2+\left(\frac{2{\sigma }_{\mathrm{Ni}}K\left(L_M+W_M\right)}{A_M{A}_e}\right)Q-{\sigma }_M=0,\left(S17\right)$

where

$K=\frac{\epsilon M}{\mathrm{zF}\rho }$

and A_M=L_MW_M. To solve this quadratic equation, we first determine A_e by substituting S7 into S5,

$A_e=\frac{\left({\sigma }_M-{\sigma }_{\mathrm{Ni}}\right)A_M}{{\tau }_{\mathrm{Ni}-M}}·\left(S18\right)$

A_e is determined by the intersection point of the type-I fracture line and the type-M fracture line, showing that a higher τ_Ni-M, or adhesion at the nickel-metal interface, leads to lower A_e. We solve the quadratic equation (54), and the positive solution is the minimum charge input required to achieve full healing.

From the charge input, we can derive the time required for healing. Knowing that Q=∫i(t)dt≈IΔt, where i(t) is the instantaneous current at time t, and I is the mean current over time period Δt, we can obtain the following expression:

$T=\Delta t=\frac{Q}{j{A}_e},\left(S19\right)$

where j is the current density which we approximate to be 10 mA/cm² based on experimental data (FIG. 52). Commercial electrolytes with chemical additives can achieve significantly higher current densities, which reduces T proportionally.

Our estimate of financial cost, in 2022 US dollars, includes the cost p_e of electricity to power the electroplating process and the cost p_Ni of nickel that is removed from the nickel anode and deposited on the fractured metal. Electricity cost $0.0746/kWh in February 2022 for the average U.S. industrial customer according to the U.S. Energy Information Administration^[25], and nickel cost around $30/kg in the period between mid-March and mid-May 2022 according to the London Metal Exchange^[26]. Our cost estimate does not include the costs of “non-consumables” such as the nickel electrolyte and any required equipment (e.g., potentiostat, battery), which can be used over a long period of time, likely making their usage cost for each healing process negligible. Therefore, the financial cost of full healing can be expressed as follow:

$C=\left(p_e\left|u\right|+p_{\mathrm{Ni}}\rho K\right)Q,\left(S20\right)$

where u is the applied overpotential (here, −1.8 V) and

$K=\frac{\epsilon M}{\mathrm{zF}\rho }.$

For values of L_M and W_M ranging from 0.1 to 1000 mm, we calculated Q using four different values of τ_Ni-M and visualized the results in FIG. 53A, with FIG. 53B showing a subset of the data. To facilitate the visualization of these estimates on a 2-D plot in the main text (FIG. 5), we plotted Q, C, and T with respect to A_M for the special case where L_M=W_M.

Our model reveals scaling laws that govern changes in the charge input, financial cost, and time requirements for full healing. For charge input,

$Q\sim {10}^b{A}_M^{1.5},\left(S20\right)$

where b is equal to 8.09, 7.39, 7.09, and 6.79 when τ_Ni-M is equal to 7.23, 36.15, 72.30, and 144.60 MPa, respectively. For financial cost,

$C\sim {10}^b{A}_M^{1.5},\left(S21\right)$

where b is equal to 6.60, 5.90, 5.60, and 5.30 for the same four values of τ_Ni-M. For time,

$T\sim {10}^b{A}_M^{0.5},\left(S22\right)$

where b is equal to 4.35 and 3.35 when current density, j, is equal to 10 and 100 mA/cm², respectively.

Generalized Prediction and Limitations of the Theoretical Model

Through equations (54) and (55), the theoretical model provides a predictive tool to determine the minimal exposed area and charge input needed to heal a given structural metal with plated nickel (or any other metal than can be plated^[27]). This predictive tool can only be applied to metals under tensile loading. The inputs that need to be quantified a priori are σ_M, σ_Ni, A_M, and τ_Ni-M. The first two, σ_M and σ_Ni, can be readily measured via tensile testing or obtained from extensive data available in the scientific literature and in industry publications. The third, A_M, is, for the most part, a deliberate design choice but can also be readily measured using other dimensions (for example, L_M and W_M).

The fourth, τ_Ni-M, or the shear strength at the Ni-metal interface, can be more difficult to quantify because it depends on a myriad of factors: the chemical composition of the plated metal and structural metal, the chemical and morphological conditions of the structural metal surface (which is affected by surface cleaning, or any chemical or electrochemical pre-treatment), and the chemical, structural, and morphological conditions of the plated metal (which depend on the electrolyte and the electrochemical process parameters). Ring shear testing has enabled the collection of substantial data on the shear strength at the interface between plated nickel and a diverse array of metals that were cleaned and processed under different conditions^[28]. Thus, τ_Ni-M can be quantified using this data if the same metals and process conditions are replicated. Moreover, our study showed that τ_Ni-M was close to 7 MPa for all the four metallic alloys that we tested. This approximate value might remain consistent for a broad range of metallic materials if the same process conditions used in this work are replicated, though this necessitates further experimental and computational investigation.

Elemental and Crystallographic Characterization of Nickel Plated on AISI 1008 Steel

Fitting our theoretical model to the strength healing efficiency data of healed low-carbon steel (AISI 1008) samples showed that the average strength of the Ni—Ni interface in these samples (216.3 MPa) was significantly lower than the tensile strength of bulk plated nickel (358.2 MPa). We hypothesize that this low strength is likely due to iron (Fe) contamination of the plated nickel, which might have led to the formation of intermetallic Ni—Fe phases. Energy-dispersive x-ray spectroscopy (EDS) characterization of nickel plated on a healed steel sample showed the presence of iron throughout the plated nickel (FIGS. 54A, B). X-ray diffraction (XRD) showed the dominance of the (200) peak of FCC Ni, though minor (110), (111), and (211) peaks revealed the possible presence of Fe either as BCC Fe or in an FCC Ni—Fe phase^[29,30] (FIG. 54C).

The formation of this Ni—Fe phase may be due to the co-deposition of Ni and Fe during the healing process. Likely, iron in the steel samples oxidized and became Fe²⁺ ions dissolved in the acidic aqueous nickel electrolyte. As the reduction potentials of Fe²⁺/Fe (−0.44 V vs. SHE) and Ni²⁺/Ni (−0.25 V vs. SHE) are close, and the electrochemical healing occurs at a potential of −1.8 V vs. Ni, Fe²⁺ ions present in the electrolyte likely reduced simultaneously with the Ni²⁺ ions, leading to a co-deposition of nickel and iron.

Healing of AISI 1008 Steel after Tensile Fracture

In the main text, we used half-dogbone samples to simulate fractured dogbone samples, which ensured dimensional consistency and good experimental controls for the purpose of validating the theoretical model. However, in many applications, metals experience plastic deformation and fracture under tensile loading. Here, we show that electrochemical healing can enable full restoration of tensile strength in AISI 1008 steel samples after tensile fracture.

We sanded full-dogbone steel samples using ultrafine silicon carbide abrasive paper, while applying WD-40 solution, to remove rust. After sonication for 10 min in isopropanol and 10 min in methanol, samples were rinsed with isopropanol then dried thoroughly under nitrogen flow. Steel samples were tested in tension until fracture, with two ˜1 mm-long notches ensuring that fracture occurred at the center of the dogbone during tensile testing (FIG. 55A). One set of samples was mechanically processed to reduce the energy and time required for healing^[1], while the rest of the samples were not processed beyond sonication in isopropanol to remove surface contaminants. Mechanical processing involved polishing both fracture surfaces of a given sample using a Dremel tool with a rotating abrasive head until the “neck” which formed due to plastic deformation was rendered flat and smooth (FIG. 55A). Flat fracture surfaces reduced the maximum gap between the two halves of the fractured sample from close to 1000 μm to under 10 μm.

We conducted healing in a commercial nickel sulfamate electrolyte with a potential of −1.8 V vs. Ni. The processed samples were healed under potentiostatic plating until reaching 1000 mAh of charge input, while the non-processed samples required an initial 24 hours of pulsed plating (1 sec at −1.8 V, 1 sec at OCV) before continuing with potentiostatic plating until reaching 1600 mAh. After healing, the steel samples were subjected to tensile testing until fracture.

FIG. 55B shows stress-strain data from the initial tensile test of notched samples and from the tensile testing of the same samples after healing. For processed and non-processed samples, electrochemical healing recovered, on average, 103.0% and 102.3% of pristine tensile strength (342.59 MPa) respectively. However, pre-healing mechanical processing significantly reduced the costs of healing in terms of charge input (from 1600 mAh to 1000 mAh) and time (from 50 hours to 16 hours).

Why is failure strain lower in healed samples compared to pristine samples?

Healed dogbone samples (FIGS. 45-48) exhibited lower failure strain than pristine samples (FIG. 44), even in instances of type-M fracture and full recovery of tensile strength. A simple finite element model of a healed metal showed that, due to the high stiffness of plated nickel (˜58 GPa), axial strain was significantly lower in the plated region than in the non-plated metal (FIG. 56). This reduced the overall strain of the healed metal compared to the pristine metal. In other words, plated nickel constrained the elongation of the healed sample in samples that experienced type-M fracture. Strain tended to be even lower in healed samples that exhibited type-P fracture due to the low failure strain of plated nickel (˜4%) (FIG. 42C).

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Exemplary Embodiments

The following embodiments are exemplary only and do not serve the limit the scope of the present disclosure or the attached claims. Any one or more parts of any one or more embodiments can be combined with any one or more parts of any one or more other embodiments.

Embodiment 1. An adaptive material system, comprising: an electrically conductive matrix material defining a plurality of voids; and an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal, the electrolyte optionally comprising an amount of a monomer. The system can also optionally include a device configured to detect a fracture within the matrix material. Such devices include, e.g., a current-measuring device, a resistance-measuring device, a device configured to measure equilibrium potentials, a strain sensor, a cyclic voltammeter, or any combination thereof.

Essentially any monomer can be used with the disclosed technology; monomers that include a vinyl group (e.g., a C═C) are considered especially suitable, as are cyclic monomers, e.g., those monomers that include a carbon-containing ring structure, such as styrene. Exemplary vinyl monomers include, e.g., acrylonitrile, acrylic acid, N-methylolacrylamide, methyl methacrylate, styrene, maleic anhydride, methacrylic acid-acrylamide, methacrylic acid-N,N′-methylenebisacrylamide, glycidyl methacrylate, and the like.

B. K. Garg, R. A. V. Raff, R. V. Subramanian, Electropolymerization Of Monomers On Metal Electrodes, J Appl. Polym. Sci. 22, 65-87 (1978) (incorporated herein by reference in its entirety) provides example monomers and electrolytes/solvents for use in electrodeposition. Such monomers include, without limitation, phenyl glycidyl ether, N-methylolacrylamide, azirdine, and the like.

An electrolyte can include, e.g., water, an organic solvent, an ionic liquid, and the like. Polar and non-polar solvents can be used. Example solvents (that can be used as electrolytes) include, e.g., propylene carbonate, acetonitrile, ethylene carbonate, dimethyl carbonate, THF, DMSO, and methanol. Any of the foregoing can be used as the solvent in which the first metal ion is disposed.

A monomer can be disposed in any of the foregoing. Monomers can be dispersed in water, organic solvent, and the like.

Example metals include, e.g., nickel, zinc, tin, iron, copper, cobalt, tungsten, gold, silver, brass, palladium, cadmium, rhenium, tungsten, lithium, titanium, chromium, platinum, and aluminum. The foregoing list is exemplary only and is not limiting.

Embodiment 2. The system according to Embodiment 1, further comprising a source of electrical current capable of electronic communication with the electrolyte. Exemplary such sources include, e.g., potentiostats, electronic voltage sources, electronic current sources, photovoltaics, flexoelectrics, photoelectrics, batteries, supercapacitors, capacitors, piezoelectrics, thermoelectrics, pyroelectrics, photoelectrics, triboelectrics, photoelectrochemicals, magnetoelectrics, microbial, and thermogalvanic.

As an exemplary embodiment of the thermogalvanic effect, one part of the matrix is brought from equilibrium to a different temperature than another part of the matrix. This temperature difference results in a difference in the Gibbs free energy of the electrochemical reactions between the matrix and electrolyte. The Gibbs free energy difference between the hot and cold areas drives electrochemical oxidation (or reduction depending on the reaction) at the hot location, and vice versa at the cooler locations.

Embodiment 3. The system according to any of Embodiments 1-2, further comprising a region of conformal coating disposed on a coated region of the matrix material, the region of conformal coating being disposed so as to interrupt fluid communication between the coated region of matrix material and the electrolyte. The conformal coating can be non-conductive. The conformal coating can also be non-reactive with the electrolyte and/or with the matrix material. (The conformal coating can also be termed a passivation coating or a passivation layer.)

Embodiment 4. The system according to Embodiment 3, wherein the conformal coating is characterized as a dielectric.

Embodiment 5. The system according to any one of Embodiments 1-4, wherein the matrix material defines an elongation at break of unit length/length (m/m).

Embodiment 6. The system according to Embodiment 5, wherein the conformal coating defines an elongation at break that is within about 5% of the elongation at break of the matrix material.

Embodiment 7. The system according to Embodiment 5, where in the conformal coating is configured such that a mechanical stress that fractures the coated region of matrix material does not fracture the region of conformal coating.

In such embodiments, the matrix material breaks before the coating breaks. This can be used in embodiments where small fractures in the matrix material are acceptable to the user; by the time fractures form in the coating (so as to allow electrolyte contact with the underlying matrix material), relatively large fractures are present in the matrix material.

Embodiment 8. The system according to Embodiment 5, wherein the conformal coating is configured such that a mechanical stress that fractures the coated region of matrix material fractures the region of conformal coating. In such embodiments, the coating and the underlying matrix material break together such that cracks in the matrix material contact the electrolyte at the same time that such cracks are formed, as cracks form in the coating at the same time as cracks in the matrix material.

Embodiment 9. The system according to Embodiment 5, wherein the conformal coating is configured such that a mechanical stress that fractures the region of conformal coating does not fracture the coated region of matrix material. In such embodiments, the coating breaks before the underlying matrix material. In such a way, areas of the matrix material that are likely to fracture are contacted with electrolyte (by way of the already-cracked coating) before those areas fracture, and the electrolyte acts to pre-heal and/or strengthen those regions of the matrix material before fractures form.

Embodiment 10. The system according to any one of Embodiments 3-9, wherein the conformal coating comprises silica, parylene, an acrylic, ceramic/metal oxide (e.g., alumina, hafnia, titania), a polymer (e.g., polytetrafluoroethylene, polypropylene, polyethylene), an elastomer (e.g., silicone, polyeurethane, and poly (ethylene-vinyl acetate)).

Embodiment 11. The system according to any one of Embodiments 1-10, wherein the matrix material comprises a matrix metal. Example metals include, e.g., Nickel, Zinc, Tin, Iron, Copper, Cobalt, Tungsten, Gold, Silver, Brass, titanium, chromium, platinum, tungsten, aluminum, magnesium and combinations (including alloys) thereof. A matrix material can also include carbon foam, carbon fiber, conductive polymers including: polyacetylene, polypyrrole, polyindole and polyaniline.

Embodiment 12. The system according to Embodiment 11, wherein the matrix metal is the same as the first metal.

Embodiment 13. The system according to any one of Embodiments 1-12, further comprising a source of the first metal. The source can be present as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Embodiment 14. The system according to any one of Embodiments 1-13, wherein at least some of the plurality of voids are in fluid communication with one another.

Embodiment 15. The system according to any one of Embodiments 1-14, wherein the plurality of voids are present in a periodic structure.

Embodiment 16. The system according to any one of Embodiments 1-15, wherein the electrolyte is characterized as a hydrogel electrolyte or as a solid electrolyte.

Embodiment 17. The system according to any one of Embodiments 1-16, further comprising a fluid-impervious enclosure disposed about the matrix material. Without being bound to any particular theory, such an enclosure can prevent leakage of electrolyte.

Embodiment 18. The system according to any one of Embodiments 1-17, wherein the system is comprised in a weight-bearing structural member.

Embodiment 19. The system according to any one of Embodiments 1-18, wherein the system is comprised in an impact shield, an electrode, a prosthesis, a medical implant, a flexible electrode, a contained, a protective coating, a lubricated surface, a prosthetic device, a sound absorber, a heat exchanger, a mechanical damper, a buoyant article, sporting equipment, a sandwich panel, or any combination thereof.

Embodiment 20. A method, comprising: effecting application of an electrical current to a system according to any one of Embodiments 1-19 so as to give rise to deposition of an amount of the first metal on a cathode region of the electrically conductive matrix material, the cathode region being in fluid communication with the electrolyte. Without being bound to any particular theory, the disclosed methods can be applied to, e.g., heal a fractured material, to strengthen a material before or during stress application, to add material to a region of an article (e.g., to transfer material from the right side of an article to the left side), or any combination of the foregoing.

The methods can include detection of a fracture in the matrix material. Detection of a fracture can then be used to initiate a healing process, as described herein. Suitable methods of detecting a fracture are described elsewhere herein.

Systems according to the present disclosure can be configured for autonomous fracture detection and repair. As an example, a system can be configured to detect a fracture in a matrix material; when a fracture is detected, the system can execute a healing process as described herein. A system can include one or more supplies of metal ion-containing electrolyte and/or one or more supplies of monomer-containing electrolyte. (As mentioned herein, an electrolyte can include both monomer and metal ion.) In this way, a system can be configured to detect and repair cracks, thus allowing for autonomous operation and maintenance by the system.

Embodiment 21. The method according to Embodiment 20, wherein the amount of the first metal is disposed within an opening in a conformal coating disposed on the matrix material.

Embodiment 22. A method, comprising: applying a force to a system according to any one of Embodiments 1-19 so as to give rise to a fracture of the matrix material; and effecting application of an electrical current to the system so as to give rise to deposition of an amount of the first metal on a cathode region of the electrically conductive matrix material, the cathode region being at least partially disposed along the fracture of the matrix material.

Embodiment 23. A method, comprising: effecting application of an electrical current to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of an amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte. As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Embodiment 24. The method according to Embodiment 23, wherein the cathode region is at least partially disposed along a fracture of the matrix. As an example, the cathode region can be an edge of the matrix, which edge at least partially defines the fracture.

Embodiment 25. The method according to Embodiment 23, wherein the cathode region of the matrix material is in fluid communication with the electrolyte by way of an opening in a conformal coating disposed on the matrix material.

Embodiment 26. The method according to Embodiment 25, further comprising forming the opening in the conformal coating.

Embodiment 27. The method according to Embodiment 26, wherein the forming comprises application of a force to the conformal coating.

Embodiment 28. The method according to Embodiment 27, wherein the force fractures the matrix material.

Embodiment 29. The method according to Embodiment 27, wherein the force fractures the matrix material before forming the opening in the conformal coating.

Embodiment 30. The method according to Embodiment 27, wherein the force fractures the conformal coating before the matrix material.

Embodiment 31. The method according to Embodiment 27, wherein the force fractures the matrix material concurrent with forming the opening in the conformal coating.

Embodiment 32. The method according to any one of Embodiments 23-31, wherein the matrix material provides the amount of the first metal deposited on the cathode region.

Embodiment 33. The method according to any one of Embodiments 23-32, wherein a source of first metal provides at least some of the amount of the first metal deposited on the cathode region.

Embodiment 34. An adaptive material, comprising: an electrically conductive matrix material defining a plurality of voids and the matrix material defining a grain size, and an amount of a first metal deposited on the matrix material, the amount of the first metal defining a grain size that differs from the grain size of the matrix material. Without being bound to any particular theory, a “healed” article according to the present disclosure comprises an amount of metal at the “healed” region that has a grain size that differs from the grain size of the matrix material.

Embodiment 35. The adaptive material according to Embodiment 34, wherein the matrix material comprises a matrix metal.

Embodiment 36. The adaptive material according to Embodiment 35, wherein (a) the matrix material defines a grain size in the range of from about 1 nanometers to about 1 millimeter, (b) wherein the amount of the first metal defines a grain in the range of from about 1 nanometer to about 100 micrometers, or any combination of (a) and (b).

Embodiment 37. The adaptive material according to any one of Embodiments 34-36, further comprising an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal.

Embodiment 38. The adaptive material according to any one of Embodiments 34-37, further comprising a region of conformal coating disposed on a coated region of the matrix material, the region of conformal coating being disposed so as to interrupt fluid communication between the coated region of matrix material and the electrolyte.

Embodiment 39. The adaptive material according to Embodiment 38, wherein the amount of the first metal is disposed within an opening in the conformal coating.

Embodiment 40. The adaptive material according to any one of Embodiments 34-39, wherein the amount of the first metal is disposed along a fracture of the matrix material.

Embodiment 41. A method, comprising: effecting application of a negative potential to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of a deposited amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte, the cathode region being disposed within a fractured region of the electrically conductive matrix material; effecting application of a positive potential to an electrolyte comprising a monomer, the application being effected so as to give rise to deposition of a deposited amount of the monomer on the deposited amount of the first metal, and polymerizing the deposited amount of the monomer so as to give rise to a polymer coating on the deposited amount of the first metal.

As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Suitable matrix materials are described elsewhere herein and can include metals, metalloids, and alloys. The metal ion can be of a metal that is present in the matrix material, but this is not a requirement. As an example, the metal ion and the matrix material can both comprise nickel. As another example, the metal ion can comprise nickel, and the matrix material can comprise zinc.

Embodiment 42. The method of Embodiment 41, wherein the first metal ion and the monomer are disposed in the same electrolyte. In such an embodiment, the matrix material can be contacted with a single electrolyte, which single electrolyte comprises both the first metal ion and the monomer.

Embodiment 43. The method of Embodiment 41, wherein the first metal ion and the monomer are disposed in different electrolytes. In this way, the matrix material can be contacted with the electrolyte that comprises the first metal ion, metal can be disposed on the matrix material to as to heal or close a fracture on the matrix material, and then the healed matrix material can be contacted with a second electrolyte, which second electrolyte comprises the monomer. The monomer can then be deposited on the metal that was disposed on the matrix material.

Embodiment 44. The method of any one of Embodiments 41-43, wherein the deposited amount of the first metal physically connects two portions of the electrically conductive matrix material. An example of this is shown in FIG. 29, which figure shows the deposited metal connecting the portions of the matrix material that were previously disconnected by a fracture.

Embodiment 45. The method of any one of Embodiments 41-44, wherein the first metal ion comprises Li, Be, Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Cs, Ba, Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Ti, Pb, Bi, Po, La, Nd, Sm, Eu, Gd, Dy, Yb, or U.

Embodiment 46. The method of any one of Embodiments 41-45, wherein the monomer is polymerized to give rise to a dielectric polymer.

Embodiment 47. The method of any one of Embodiments 41-46, wherein the deposition of a deposited amount of the first metal is characterized as deposition on two or more growth fronts until the growth fronts merge.

Embodiment 48. The method of any one of Embodiments 41-47, wherein the electrically conductive matrix material comprises a region having a cross-sectional dimension in the range of from about 0.1 to about 100 μm. As but one example, such a material can be a metal foam whereby the ligaments have diameters of from about 0.1 to about 100 μm, or from about 0.5 to about 50 μm, or from about 1 to about 25 μm, or from about 10 to about 30 μm.

For this reason, the disclosed technology is especially suitable for repairing metal materials that were prepared via metal additive manufacturing, as such materials are characterized as having fine details, often in the range of 100 to about 1000 or even 5000 nm.

It is now possible to 3D print metal structures with highly complex topologies and at a resolution as low as 100 nm. For this reason, using traditional arc welding to repair cracks within these structures becomes difficult, if not impossible. Not only would a welding torch not be able to access the area of interest (especially if it is located inside a high-tortuosity complex structure), but it also would likely melt metal in areas other than the targeted crack. Thus, the disclosed electrochemical healing technique is a substitute for traditional arc welding to access cracks in the most complex and minuscule of 3D printed metal structures. Electrochemical healing also offers greater control and accuracy during the healing process.

Embodiment 49. An adaptive material system, comprising: an electrically conductive matrix material defining a plurality of voids; an electrolyte disposed in at least some of the voids, the electrolyte comprising at least an ion of a first metal, the electrolyte further comprising an amount of a monomer that, when polymerized, gives rise to a dielectric polymer; and a source of one or both of a positive electrical potential and a negative electrical potential.

Embodiment 50. A method, comprising: effecting application of a potential to an electrolyte comprising a first metal ion, the application being effected so as to give rise to deposition of a deposited amount of the first metal on a cathode region of an electrically conductive matrix material defining a plurality of voids, the cathode region being in fluid communication with the electrolyte, the cathode region being disposed within a fractured region of the electrically conductive matrix material; effecting application of a potential to an electrolyte comprising a monomer, the application being effected so as to give rise to deposition of a deposited amount of the monomer on the deposited amount of the first metal, and polymerizing the deposited amount of the monomer so as to give rise to a polymer coating on the deposited amount of the first metal.

As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Embodiment 51. A workpiece, comprising: an electrically conductive matrix material defining a plurality of voids, a dielectric coating surmounting the electrically conductive matrix material, an opening formed in the dielectric coating, the electrically material defining two edges physically separate from one another, the opening placing the two edges into fluid communication with the environment exterior to the dielectric coating.

An example is shown in the left-middle panel of FIG. 29, which illustrates an electrically conductive matrix material (i.e., the metal strut) defining a plurality of voids, a dielectric coating surmounting the electrically conductive matrix material, an opening formed in the dielectric coating, the electrically material defining two edges physically separate from one another, the opening placing the two edges into fluid communication with the environment exterior to the dielectric coating.

Embodiment 52. A workpiece, comprising: an electrically conductive matrix material defining a plurality of voids, the electrically material defining two edges physically separate from one another, an amount of deposited metal connecting the two edges, and a dielectric coating surmounting the matrix material and the deposited metal. Such a workpiece is shown in, e.g., the lower left panel of FIG. 29, which illustrates a strut (e.g., in a electrically conductive matrix material) having two edges separate from one another (i.e., the edges of the now-healed crack), an amount of deposited metal connecting the two edges, and a dielectric coating surmounting the strut and the metal that was used to heal the crack in the strut.

Embodiment 53. An adaptive material system, comprising: an electrically conductive matrix material defining a plurality of voids; a detection device configured to detect a fracture within the matrix material; and a supply of an electrolyte comprising at least an ion of a first metal, the electrolyte optionally comprising an amount of a monomer, and the system being configured to contact the matrix material with the electrolyte upon detection of a fracture within the matrix material, and the system being configured to apply a potential to the matrix material so as to effect deposition of an amount of the first metal onto a detected fracture. As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Embodiment 54. The adaptive material system of Embodiment 53, further comprising a supply of an electrolyte that comprises a monomer.

Embodiment 55. The adaptive material system of any one of Embodiments 53-54, wherein the electrolyte that comprises a monomer is the electrolyte that comprises the ion of the first metal.

Embodiment 56. The adaptive material system of any one of Embodiments 53-55, wherein the system is configured to apply a potential so as to effect deposition, onto the amount of the first metal, of a polymer derived from the monomer.

Embodiment 57. An adaptive material system, comprising: a metallic matrix material; an electrolyte sealably contained within a void within the metallic matrix material, the electrolyte comprising at least an ion of a first metal; and a source of a potential, the source being configured to effect plating of the first metal onto a fractured region of the metallic matrix material.

It should be understood that in this embodiment (and in any other embodiment herein), a metal source (e.g., a nickel bar, iron particles, and the like) can be present. Without being bound to any particular theory, the metal source can act as a reference electrode.

In some embodiments, the metal ion (of the electrode) is the same metal as the metal of of the reference electrode, though this is not always a requirement. The metal ion can be the same as the metal of the metallic matrix material, though this is not a requirement. The metal of the metallic matrix material can be the same as the metal of the reference electrode, although this too is not a requirement.

As an illustrative embodiment, one can fill the voids of a metallic foam material with the metal ion-containing electrolyte, and then seal the electrolyte within the voids, e.g., via silicone or other sealant. In this manner, the electrolyte (and metal ion) are already on-site in the event of a fracture of the matrix material, and application of potential can then effect deposition of metal (from the electrolyte) onto the fractured region and heal the fracture.

Embodiment 58. The adaptive material system of Embodiment 57, further comprising a source of monomer disposed in an electrolyte, the source of monomer being in fluid communication with the fractured region of the metallic matrix material. The monomer-containing electrolyte can be introduced to the matrix material after a fracture of the matrix material is healed (via the techniques disclosed herein), and a potential can then be applied to place a passivating coating of the polymer onto the metal that has been deposited to heal the fracture in the matrix material.

Embodiment 59. An adaptive material system, comprising: a metallic matrix material; a solid or semisolid electrolyte disposed about the metallic matrix material, the solid or semisolid electrolyte comprising at least an ion of a first metal; and a source of a potential configured to effect plating of the first metal onto a fractured region of the metallic matrix material.

As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Without being bound to any particular theory or embodiment, in this manner, the electrolyte (and metal ion) are already on-site in the event of a fracture of the matrix material, and application of potential can then effect deposition of metal (from the electrolyte) onto the fractured region and heal the fracture. The electrolyte can be, e.g., a hydrogel electrolyte, a polymer electrolyte, and the like. The electrolyte can be one that clings, attaches, adheres to, or otherwise persists at the metallic matrix material's surface. Again, in this manner, the electrolyte (and metal ion) are already on-site in the event of a fracture of the matrix material, and application of potential can then effect deposition of metal (from the electrolyte) onto the fractured region and heal the fracture.

Embodiment 60. The adaptive material system of Embodiment 59, wherein the electrolyte comprises a polymer electrolyte.

Embodiment 61. The adaptive material system of any one of Embodiments 59-60, further comprising a source of monomer disposed in an electrolyte, the source of monomer being in fluid communication with the fractured region of the metallic matrix material. The monomer-containing electrolyte can be one that clings, attaches, adheres to, or otherwise persists at the metallic matrix material's surface. Again, in this manner, the electrolyte (and monomer ion) are already on-site in the event of a fracture of the matrix material, and application of potential can then effect deposition of monomer (from the electrolyte) to coat the metal that has been deposited to heal the fracture, as well as to replace any other coating that may have been displaced from elsewhere on the matrix material so as to leave some of the matrix material exposed.

As described elsewhere, a source of the first metal can be present, e.g., as a bar, a particle, a flake, a wire, or in other form. As an example, when the electrolyte comprises nickel ions, a source of nickel (e.g., a nickel bar) can be present. The metal source is suitably in contact with the electrolyte.

Embodiment 62. An adaptive material system, comprising: a metallic matrix material; and an electrolyte comprising at least an ion of a first metal, the system being configured to deliver the electrolyte to a fractured region of the metallic matrix material.

As one non-limiting embodiment, a system can include a detector configured to detect the presence of a fracture or crack in a matrix material. Upon detection of this fracture or crack, the system can deliver (e.g., via pumping, spraying, dripping) the metal ion-containing electrolyte to the location of the fracture, where an appropriate potential can be applied so as to effect healing of the fracture or crack. Excess (or unconsumed or unused) electrolyte can be returned to its original location (e.g., a primary reservoir) or to another location (e.g., a secondary reservoir). The electrolyte can be a static source (e.g., a stationary reservoir), but can also be a mobile source, e.g., a movable tank or sprayer.

Embodiment 63. The adaptive material system of Embodiment 62, further comprising a source of a potential configured to effect plating of the first metal onto the fractured region of the metallic matrix material. The source of potential can be static in location (e.g., located by the location of the fracture or crack), but can also be moveable, e.g., a movable battery or other moveable source of potential.

Embodiment 64. The adaptive material system of any one of Embodiments 62-63, wherein the system comprises a reservoir configured to contain the electrolyte, and wherein the system is configured to deliver the electrolyte from the reservoir to the fractured region of the metallic matrix material. Delivery can be accomplished by, e.g., pumps, sprayers, and the like. Delivery can also be accomplished by mobile reservoirs, e.g., via drones or other mobile entities that can deliver electrolyte to a given location.

Embodiment 65. The adaptive material system of any one of Embodiments 62-64, wherein the electrolyte is a flowable electrolyte.

Embodiment 66. The adaptive material system of any one of Embodiments 62-65, wherein the system is configured to return to the reservoir electrolyte (e.g., excess electrolyte) that is delivered to the fractured region of the metallic matrix material.

Embodiment 67. The adaptive material system of any one of Embodiments 62-66, wherein the system further comprises an electrolyte comprising at least a first monomer. Suitable monomers and electrolytes are described elsewhere herein.

Embodiment 68. The adaptive material system of Embodiment 67, wherein the electrolyte comprises a polymer electrolyte.

Embodiment 69. A method of repairing a workpiece that comprises a structural material, the method comprising: applying a current to an electrolyte comprising a repair material so as to electroplate the repair material onto a fracture of the workpiece and onto a plating region proximate to the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area A_e about the fracture, the workpiece defining a cross-section area A_m at the fracture, A_e/A_m is in the range of from about 10 to about 150, and the plating being accomplished such that the repaired workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of a corresponding pristine workpiece, and, optionally, at least one of the structural material and the repair material comprising at least one metal.

Either or both of the structural material and the repair material can comprise carbon or a composite thereof. Either or both of the structural material and the repair material can comprise a metal; the structural material and the repair material can comprise different metals. Either or both of the structural material and the repair material can comprise carbon and one or more metals.

Embodiment 70. The method of Embodiment 69, wherein the current is constant.

Embodiment 71. The method of Embodiment 69, wherein the current is intermittent.

Embodiment 72. The method of anyone of Embodiments 69-71, wherein the current is in the range of from about 1 mA to about 10 A. The current can be, for example, from about 1 mA to about 10 A, from about 2 mA to about 1 A, from about 5 mA to about 500 mA, from about 10 mA to about 100 mA, and all intermediate values and sub-ranges.

Embodiment 73. The method of any one of Embodiments 69-72, wherein the plating is performed such that the repaired workpiece exhibits a tensile strength σ_U that is within about 5% of a corresponding tensile strength σ_M of a corresponding pristine workpiece.

Embodiment 74. The method of Embodiment 73, wherein the plating is performed such that the repaired workpiece exhibits a tensile strength σ_U that is within about 0.1% of the corresponding tensile strength σ_M of a corresponding pristine workpiece.

Embodiment 75. The method of any one of Embodiments 69-74, wherein the repair material and the structural material differ from one another.

Example metals that can be used as one or both of a repair metal and a structural metal include, for example, iron and steel alloys, aluminum and its alloys, nickel and its alloys, bismuth and its alloys, tin and its alloys, zinc and its alloys, gold and its alloys, lead and its alloys, copper and its alloys including brass and bronze, titanium and its alloys, multi-principal element alloys, molybdenum and its alloys, magnesium and its alloys, tungsten and its alloys.

A structural metal can include any one or more of iron and steel alloys, aluminum and its alloys, nickel and its alloys, bismuth and its alloys, tin and its alloys, zinc and its alloys, gold and its alloys, lead and its alloys, copper and its alloys including brass and bronze, titanium and its alloys, multi-principal element alloys, molybdenum and its alloys, magnesium and its alloys, tungsten and its alloys. A repair metal can include any one or more of iron and steel alloys, aluminum and its alloys, nickel and its alloys, bismuth and its alloys, tin and its alloys, zinc and its alloys, gold and its alloys, lead and its alloys, copper and its alloys including brass and bronze, titanium and its alloys, multi-principal element alloys, molybdenum and its alloys, magnesium and its alloys, tungsten and its alloys.

Embodiment 76. The method of any one of Embodiments 68-75, wherein the repair metal comprises a plurality of different metals. As but some examples, a repair metal can include any two or more of iron and its alloys, steel and its alloys, aluminum and its alloys, nickel and its alloys, bismuth and its alloys, tin and its alloys, zinc and its alloys, gold and its alloys, lead and its alloys, copper and its alloys including brass and bronze, titanium and its alloys, multi-principal element alloys, molybdenum and its alloys, magnesium and its alloys, tungsten and its alloys

Embodiment 77. The method of any one of Embodiments 68-76, wherein at least one of the repair metal and the structural metal is characterized as resistant to welding. Such a metal can be difficult to weld or even unweldable. Some such materials are, for example, aluminum alloys of the 2xxx, 6xxx, and 7xxx series. Other such materials are nickel alloys, such as Inconel 738 and Inconel 100. Other such materials are those nickel alloys having a relatively high content (more than 4% by weight) of either or both aluminum and titanium.

Embodiment 78. The method of any one of Embodiments 68-77, wherein A_e/A_m is in the range of from about 10 to about 100. For example, the range can be from about 10 to about 100, from about 20 to 90, from about 25-75, or even from about 35 to about 55.

Embodiment 79. The method of any one of Embodiments 69-78, wherein (i) the workpiece defines a shellular structure, (ii) the fracture resides in a strut of the workpiece, or both (i) and (ii). As an example, a fracture may reside in a strut of the workpiece that might otherwise be inaccessible to welding or soldering.

Embodiment 80. The method of any one of Embodiments 68-79, wherein the method is performed at ambient temperature.

Embodiment 81. The method of any one of Embodiments 68-80, wherein at least a portion of the workpiece is masked so as to expose the exposed area A_e of the workpiece to the electrolyte. Such masking can be accomplished by, for example, application of a tape. A coating can also be used to expose the exposed area A_e of the workpiece to the electrolyte. As shown in, for example, FIG. 33A illustrates masking a workpiece so as to expose defined area A_e to the electrolyte.

Embodiment 82. The method of Embodiment 81, further comprising application of a mask to the at least a portion of the workpiece so to expose the exposed area A_e of the workpiece to the electrolyte. A mask can comprise, for example, photoresist, a photocurable polymer, a wax, a ow melting temperature polymer, vapor-deposited polymer, metal oxides, nitrides, or other ceramics, adhesive backed polymer—such as a tape, and the like.

Embodiment 83. The method of any one of Embodiments 68-82, wherein the electrolyte is disposed in an enclosure having the fracture contained therein. Such an enclosure can be a capsule or other enclosure that maintains an amount of the electrolyte in position about the fracture. Thus, a user can place an electrolyte-containing capsule about a fracture and an associated exposed area A_e. In this way, a user can place electrolyte where needed and avoid use of excess electrolyte. It should be understood, however, that the disclosed technology can be carried out by immersing the workpiece in electrolyte.

Embodiment 84. A method of constructing a workpiece, comprising: applying a current to an electrolyte comprising joint metal so as to incorporate joint metal (i) into a gap between a first metallic section comprising a first structural metal and a second metallic section comprising a second structural metal and (ii) onto a plating region proximate to the first metallic section and the second metallic section so as to give rise to a workpiece comprising joint metal connecting the first metallic section and the second metallic section, the plating region defining an exposed area A_e, the first metallic section and the second metallic section defining a cross-section area A_m at the gap between the first metallic section and the second metallic section, and A_e/A_m is in the range of from about 10 to about 150, and optionally, the plating being accomplished such that the workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of either one of the first metallic section and the second metallic section. Thus—and without being bound to any particular theory or embodiment—one can use the disclosed technology to join two metallic sections to one another. As but one example of this, one can use the disclosed technology to join two 3D-printed sections that might otherwise be difficult or even impossible to join using other methods. The disclosed approach thus also allows one to join two intricate parts together so as to create single part that could not otherwise be printed on its own.

Embodiment 85. A material repair system, comprising: an electrolyte comprising a repair metal; a fractured workpiece comprising structural metal; and a source of current configured to apply a current to the electrolyte, the system configured to effect application of the current to the electrolyte so as to electroplate repair metal onto a fracture of the workpiece and onto a plating region of the workpiece extending from the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area A_e about the fracture, the workpiece defining a cross-section area A_m at the fracture, and A_e/A_m is in the range of from about 10 to about 150, and the plating being accomplished such that the repaired workpiece exhibits a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of a corresponding pristine workpiece. Without being bound to any particular theory or embodiment, such a system can be used to perform the disclosed methods, for example a method according to any one of Embodiments 68-84.

Embodiment 86. The material repairing system of Embodiment 85, wherein the repair metal comprises a plurality of different metals. Example repair metals are described elsewhere herein.

Embodiment 87. The material repairing system of any one of Embodiments 85-86, further comprising a mask disposed on the workpiece so as to expose the exposed area A_e of the workpiece to the source of repair metal. Example masks are described elsewhere herein.

Embodiment 88. The material repairing system of any one of Embodiments 85-87, wherein the source of current is configured to apply any one or more of (i) a constant current and (ii) an intermittent current.

Embodiment 89. A repaired workpiece, comprising: a first portion comprising a first structural metal; a second portion comprising a second structural metal; and a joint region, the joint region comprising (i) repair metal bridging a gap between the first portion and the second portion and (ii) repair metal disposed on a plating region that extends from the gap along the first portion and the second portion, the plating region defining an exposed area A_e, the workpiece defining a cross-section area A_m at the gap, A_e/A_m being in the range of from about 10 to about 100, and the repaired workpiece having a tensile strength σ_U that is within about 20% of a corresponding tensile strength σ_M of a corresponding pristine workpiece. Such a workpiece can, for example, be a workpiece repaired using the technology disclosed herein.

Embodiment 90. The repaired workpiece of Embodiment 89, wherein the first structural metal and the second structural metal comprise the same metal.

Embodiment 91. The repaired workpiece of Embodiment 89, wherein the first structural metal and the second structural metal comprise different metals.

Embodiment 92. The repaired workpiece of any one of Embodiments 89-91, wherein the repair metal differs from one or more of the first structural metal and the second structural metal. Example repair and structural metals are described elsewhere herein.

Embodiment 93. The repaired workpiece of any one of Embodiments 89-92, wherein any one or more of the first structural metal, the second structural metal, and the repair metal is an unweldable metal. Example unweldable metals are described elsewhere herein.

Embodiment 94. The repaired workpiece of any one of Embodiments 89-93, wherein the repaired workpiece has a tensile strength σ_U that is within about 5% of a corresponding tensile strength σ_M of a corresponding pristine workpiece.

Embodiment 95. The repaired workpiece of Embodiment 94, wherein the repaired workpiece has a tensile strength σ_U that is within about 0.1% of a corresponding tensile strength σ_M of a corresponding pristine workpiece.

Embodiment 96. The repaired workpiece of any one of Embodiments 89-95, wherein (i) the workpiece defines a shellular structure, (ii) the gap resides in a strut of the workpiece, or both (i) and (ii).

Embodiment 97. The repaired workpiece of any one of Embodiments 89-96, wherein further comprising a mask disposed on the workpiece so to expose the exposed area A_e of the workpiece.

Embodiment 98. The repaired workpiece of any one of Embodiments 89-97, wherein A_e/A_m is in the range of from about 25 to about 75.

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Claims

1. A method of repairing a workpiece that comprises a structural material, the method comprising: applying a current to an electrolyte comprising a repair material so as to electroplate the repair material onto a fracture of the workpiece and onto a plating region proximate to the fracture of the workpiece so as to give rise to a repaired workpiece, the plating region defining an exposed area Ae about the fracture,the workpiece defining a cross-section area Am at the fracture,Ae/Am is in the range of from about 10 to about 150,the plating being accomplished such that the repaired workpiece exhibits a tensile strength σU that is within about 20% of a corresponding tensile strength σM of a corresponding pristine workpiece, andoptionally, at least one of the structural material and the repair material comprising at least one metal.

2. The method of claim 1, wherein the current is constant.

3. The method of claim 1, wherein the current is intermittent.

4. The method of claim 1, wherein the current is in the range of from about 1 mA to about 10 A.

5. The method of claim 1, wherein the plating is performed such that the repaired workpiece exhibits a tensile strength σU that is within about 5% of a corresponding tensile strength σM of a corresponding pristine workpiece.

6. The method of claim 5, wherein the plating is performed such that the repaired workpiece exhibits a tensile strength σU that is within about 0.10% of the corresponding tensile strength σM of a corresponding pristine workpiece.

7. The method of claim 1, wherein the repair material and the structural material differ from one another.

8. The method of claim 1, wherein the repair material comprises a plurality of different metals.

9. The method of claim 1, wherein at least one of the repair material and the structural material is characterized as unweldable or difficult to weld.

10. The method of claim 1, wherein Ae/Am is in the range of from about 10 to about 100.

11. The method of claim 1, wherein (i) the workpiece defines a shellular structure, (ii) the fracture resides in a strut of the workpiece, or both (i) and (ii).

12. The method of claim 1, wherein the method is performed at ambient temperature.

13. The method of claim 1, wherein at least a portion of the workpiece is masked so as to expose the exposed area Ae of the workpiece to the electrolyte.

14. The method of claim 13, further comprising application of a mask to the at least a portion of the workpiece so to expose the exposed area Ae of the workpiece to the electrolyte.

15. The method of claim 1, wherein the electrolyte is disposed in an enclosure having the fracture contained therein.

16. A method of constructing a workpiece, comprising: applying a current to an electrolyte comprising joint metal so as to incorporate joint metal (i) into a gap between a first metallic section comprising a first structural metal and a second metallic section comprising a second structural metal and (ii) onto a plating region proximate to the first metallic section and the second metallic section so as to give rise to a workpiece comprising joint metal connecting the first metallic section and the second metallic section, the plating region defining an exposed area Ae,the first metallic section and the second metallic section defining a cross-section area Am at the gap between the first metallic section and the second metallic section, andAe/Am is in the range of from about 10 to about 150, andoptionally, the plating being accomplished such that the workpiece exhibits a tensile strength σU that is within about 20% of a corresponding tensile strength σM of either one of the first metallic section and the second metallic section.

17. A material repair system, comprising: an electrolyte comprising a repair metal;a fractured workpiece comprising structural metal; anda source of current configured to apply a current to the electrolyte, the system configured to effect application of the current to the electrolyte so as to electroplate repair metal onto a fracture of the workpiece and onto a plating region of the workpiece extending from the fracture of the workpiece so as to give rise to a repaired workpiece,the plating region defining an exposed area Ae about the fracture,the workpiece defining a cross-section area Am at the fracture, andAe/Am is in the range of from about 10 to about 150, andthe plating being accomplished such that the repaired workpiece exhibits a tensile strength σU that is within about 20% of a corresponding tensile strength σM of a corresponding pristine workpiece.

18. The material repairing system of claim 17, wherein the repair metal comprises a plurality of different metals.

19. The material repairing system of claim 17, further comprising a mask disposed on the workpiece so as to expose the exposed area Ae of the workpiece to the source of repair metal.

20. The material repairing system of claim 17, wherein the source of current is configured to apply any one or more of (i) a constant current and (ii) an intermittent current.

21. A repaired workpiece, comprising: a first portion comprising a first structural metal;a second portion comprising a second structural metal; anda joint region, the joint region comprising (i) repair metal bridging a gap between the first portion and the second portion and (ii) repair metal disposed on a plating region that extends from the gap along the first portion and the second portion, the plating region defining an exposed area Ae,the workpiece defining a cross-section area Am at the gap,Ae/Am being in the range of from about 10 to about 100, andthe repaired workpiece having a tensile strength σU that is within about 20% of a corresponding tensile strength σM of a corresponding pristine workpiece.

22. The repaired workpiece of claim 21, wherein the first structural metal and the second structural metal comprise the same metal.

23. The repaired workpiece of claim 21, wherein the first structural metal and the second structural metal comprise different metals.

24. The repaired workpiece of claim 21, wherein the repair metal differs from one or more of the first structural metal and the second structural metal.

25. The repaired workpiece of claim 21, wherein any one or more of the first structural metal, the second structural metal, and the repair metal is an unweldable metal.

26. The repaired workpiece of claim 21, wherein the repaired workpiece has a tensile strength σU that is within about 5% of a corresponding tensile strength σM of a corresponding pristine workpiece.

27. The repaired workpiece of claim 26, wherein the repaired workpiece has a tensile strength σU that is within about 0.10% of a corresponding tensile strength σM of a corresponding pristine workpiece.

28. The repaired workpiece of claim 21, wherein (i) the workpiece defines a shellular structure, (ii) the gap resides in a strut of the workpiece, or both (i) and (ii).

29. The repaired workpiece of claim 21, wherein further comprising a mask disposed on the workpiece so to expose the exposed area Ae of the workpiece.

30. The repaired workpiece of claim 21, wherein Ae/Am is in the range of from about 25 to about 75.