This application claims benefit under 35 USC § 119 of European Application 22187862.2 filed Jul. 29, 2022, the entire contents of which are incorporated herein by reference.
The present disclosure relates to a flexible element comprising an inorganic, brittle material, as well as a method for its production. In particular, the present disclosure relates to a flexible glass element.
Inorganic material have high temperature stability and hardness. However, these materials tend to be brittle, so that in case a material for a flexible element is needed, brittle materials usually are not the material of choice.
However, in recent years, efforts have been made to use high transparency glass elements with increased flexibility for use as covers for display devices or the like. Usually, in order to increase flexibility in glass elements such as glass sheets their thickness is reduced. However, by decreasing the thickness of a glass element, its strength, such as impact strength, also decreases. This may be compensated for by using sandwich designs using polymer and glass elements and combining them, by way of example, via a lamination process. However, sandwiches are prone to delamination and further light transmission through such a sandwich laminate may be reduced as a result of refractive index steps at the interfaces. The above pros and cons also apply to other inorganic brittle materials and are not restricted to glass elements only.
Therefore it has been proposed to provide elements of an inorganic brittle material comprising at least three sections, wherein a first section is adjoined by two second sections so that the first section is arranged between the second sections. The first section is formed so as to have a higher flexibility as the second sections. This may be achieved by either slimming that portion of the element that is to become a “first section” or by introducing holes, which may be through-holes or blind holes in the element's future “first section”. For example, a first section may have an arrangement of openings that form passages through the element, i.e., between one side and the other side of the element. Slimming as well as introducing holes in a first section leads to the first section having a higher flexibility than the second sections, such that the first section may also form a hinge section for the second sections. With other words, the first section is a bending section. Commonly used structures, for example, are described in EP 3 936 485 A1, WO 2020/226939 A1 and WO 2013/123353 A1, and comprise parallel lines or groves oriented in parallel to the bending axis and that are interconnected by ridges (that may also be called interconnectors).
Quite commonly, such holes are filled with a refractive index matched filler material, for example with plastics or rubbers or adhesives. However, a 100% perfect match of refractive indices of filler material and inorganic brittle material, such as glass, is not possible, which leads to optical distortion. The roughness of the openings' walls further adds to optical distortion. This is a major drawback of the proposed parallel structures to the state of the art, as upon being used as covers for an electro-optical devices, such as a display, optical interference phenomena, such as the Moiré effect, will result.
Other patterns comprising holes shaped differently than the aforementioned elongated parallel holes have been proposed. For example, patterns may include round, square or rhomboid structures.
However, these structures still are shaped symmetrically and are not optimized for unidirectional bending of the element. In particular, the regular, periodic arrangement of the holes generally results in perceptible Moiré patterns if such a perforated glass sheet is used as a cover for a pixel display.
The object of the present disclosure therefore is to provide an inorganic brittle material element comprising a bending section that overcomes the drawbacks of the state of the art at least partially. A further object is to provide a method for producing such an element.
The disclosure therefore relates to an element of an inorganic brittle material that has two opposite sides and a circumferential edge. The element comprises at least three sections including a first section and two second sections adjoining the first section so that the first section is arranged between the second sections. The first section comprises an arrangement of openings and interconnectors so that the first section has a higher flexibility than the second sections. At least one of the openings is shaped as a fold that comprises at least limbs that intersect, thereby forming a vertex.
In the scope of the disclosure, a fold is understood as referring to a bent or curved shape of the opening that has at least two limbs that intersect, thereby forming a vertex or hinge. For example, the opening may be shaped like a chevron or generally V-shaped or U-shaped. Further, it is understood that in the sense of the disclosure, a fold is understood to any shape that shows a reversal of direction. In that sense, an arc is also understood as a fold, as well as dome-shaped openings. The vertex may in case of circular arcs also be understood as a turning point, for example a minimum or maximum, particularly in a direction along or parallel to the bending axis. The opening's boundaries may be straight lines, but it is also possible and may also be preferred that the boundaries are sinusoidally shaped or irregularly shaped. By way of example, exemplary shapes of openings shaped as folds in the sense of the disclosure are depicted schematically and not drawn to scale in
Such a shape of the opening has been found to be very advantageous by the inventors in terms of bending stress reduction. That is, as there is a reversal of direction along the pathway of the fold-like shaped opening, upon bending the element the interconnectors next to the fold-like shaped opening may be lifted. It has been shown that this significantly helps to reduce mechanical stresses in the interconnectors.
Preferably, according to an embodiment, the element comprises at least two fold-shaped openings that are adjacent to each other, and the interconnector between these openings forms a protrusion.
In that case, also the interconnector may be shaped as a fold with at least two limbs that intersect, for example, in a chevron-like shape.
It may be preferred that all openings are formed as folds.
According to a further embodiment, the first section defines a bending direction for the second sections, and an angle is drawn between the bending direction and at least one of the limbs of the fold and/or the interconnector. That is, the pattern of openings and interconnectors is tilted with regard to the bending direction, the openings being neither in parallel to the bending direction nor at a right angle. This is favourable for decreasing interference effects between the pattern of openings in the first section and an underlying pixel array in case the element is used as a cover for a display or other devices comprising pixel arrays. However, as tilted unidirectional openings would, upon bending, lead to an increase in bending stress, the present disclosure proposes to introduce first sections in elements that comprise at least one opening shaped as a fold with two intersecting limbs.
In that way, a decrease of interference effects may be combined with a decrease in bending stress in a very simple and efficient manner.
The most preferred material for the element is glass. However, it is also contemplated to fabricate the element using another brittle material such as a glass ceramics, sapphire or a semiconductor such as silicon.
Independent from the material used, the element may be easily bend and even folded at the flexible first section. Thus, it is also contemplated to provide an article comprising a flat element according to this disclosure, whereby the flat element is bent and folded at the first section so that the surfaces of the second sections of one of the sides face each other. Further, the element may be easily bent so far that the surfaces of the second sections facing each other are parallel or are at least positioned in an acute angle. However, it is also possible that second section form a “negative angle”, meaning that the outer ends of second sections may be closer to each other than the inner ends, that is, the ends next to the first section.
As well, the second sections can be brought close together, specifically if the flexible first section is sufficiently broad. The second sections can be positioned close together if the flexible first section has the freedom to bulge outwards. Thus, according to a refinement, the flat element is folded and the surfaces of the second sections facing each other are positioned so close together that the first section bulges outward so that the thickness of the folded flat element is larger at the first section than at the boundary lines between the first section and the second sections. As well, the thickness of the folded flat element in this case is larger at the first section than at a position where the second sections are opposed.
The decrease of maximum tensile strain can improve the flexibility, that is, in the scope of the present disclosure, the bendability of a given glass sheet and/or the structured section, of the structured section significantly. The minimum bending radius, and, thus the flexibility, of a glass can for example be expressed by the gap in 2 point bending test setup at breakage. According to a preferred embodiment, the flexibility of the structured part, i.e., the first section is at least 2 times, preferably at least 3 times, most preferably at least 4 times higher compared to the non-structured part, i.e., the second sections. The flexibility generally is understood as being proportional to the inverse stiffness of the element. Specifically, the flexibility f may be defined as f=α/F with F being a force applied to one of the second sections along its surface normal and α being the bending angle resulting therefrom, i.e., the angle between the two second sections. The 2 point bending is a test to measure the bending strength or bending performance of glass. The breakage bending radius is determined by using a UTM (universal testing machine) on samples at room temperature of about 20° C. and relative humidity of about 50%. The glass element is brought into a bent position and its opposite ends are positioned between two parallel plates (steel plates). Then the distance between the plates is lowered so that the bending radius of the glass element decreases wherein the loading speed is, e.g., 60 mm/min. The distance between the plates is recorded when the glass element is kinking or damaging or breaking into two or several pieces which is determined by the signal of the UTM software. From that distance, the corresponding bending radius of the glass element at the time of breakage is calculated. The flexibility is inversely proportional to the distance of the plates. Thus, if the structured part has a flexibility that is two times higher than the flexibility of the unstructured sections, the distance of the plates can be halved before breaking. This two-point bending test is adjusted and is especially suitable for ultrathin glass elements. Due to the flexibility of the elements as described herein, the method can be employed perfectly. The testing method is also described in Applicant's own application EP 3 936 485 A1, which is incorporated herein by reference.
Chemically toughening of glass can improve the flexibility further, for both structured and non-structured parts.
Typically, a molten salt is used for chemical toughening that contains Na+-or K+-ions or a mixture of these. Commonly used salts are NaNO3, KNO3, NaCl, KCl, K2SO4, Na2SO4, Na2CO3, and K2CO3. Additives like NaOH, KOH and other sodium or potassium salts may be also used for better controlling the speed of ion-exchange, CS (compressive stress) and DoL (depth of layer) during chemical toughening. Further, an Ag+-containing or Cu2+-containing salt bath could be used to add anti-microbial function to the glass. The chemical toughening is not limited to a single step process. It can also include multi steps of immersing the glass disk into salt baths with alkaline metal ions of various concentrations to reach better toughening performance.
Thus, the chemically toughened glass article according to the disclosure can be toughened in one step or in the course of several steps, e.g., two steps.
According to some embodiments, the element can be chemical toughened to reach CS (i.e., a compressive stress at the surface) higher than 100 MPa, preferably higher than 250 MPa, preferably higher than 400 MPa, more preferably higher than 500 MPa, more preferably higher than 600 MPa, or even higher than 700 MPa, or even higher than 800 MPa. However, it is preferred to limit the compressive stress so as to maintain a sufficient flexibility. Thus, in a further embodiment the CS is lower than 1500 MPa, preferably lower than 1300 MPa, more preferably lower than 1200 MPa. Further, the element can be chemical toughened to reach a DoL (DoL=“depth of layer”) higher than 1 μm, preferably higher than 3 μm, more preferable higher than 5 μm, more preferably higher than 7 μm, more preferably higher than 8 μm, more preferably higher than 10 μm, more preferably higher than 12 μm, most preferably higher than 15 μm. However, it is advantageous to limit the DoL with respect to the thickness of the glass element. According to further embodiments, therefore, the DoL is lower than 0.5·t, preferably lower than most preferable lower than 0.3·t, where t is the glass thickness. The DoL value is the depth into the surface of the glass to which compressive stress is introduced. It is defined as the distance from the physical surface to the zero stress point internal to the glass.
The structured and non-structured part may advantageously be toughened together (in a common toughening step), so the CS and DoL values are measured based on the non-structured part. In general, however, it may also be contemplated to toughen both sides of the glass sheet differently. In any case, the flexibility of the structured and non-structured parts can be improved by chemical toughening. As measured using the 2PB bending test, the bending radius of the test samples can be roughly calculated as bending radius r=d/2.4, where d is the distance between two plates in the 2 point bending test. According to some embodiments of the element, the chemically toughened structured first section can be bent with a bending radius below 500 t, preferably below 300 t, more preferably below 100 t, more preferably below 50 t, more preferably below 40 t, more preferably below 30 t, more preferably below 25 t, more preferably below 20 t, more preferably below 15 t, more preferably below 10 t, more preferably below 7.5 t, more preferably below 5 t, more preferably below 4 t, more preferably below 3 t, or even below 2 t without breakage, where t is the glass thickness.
Further, as already shown in
Here, openings 90 show a chevron- or V-like shape. Generally, without being restricted to the exemplary embodiment shown in
Further, bending direction 95 has been indicated. As can be seen an angle α is drawn between bending direction 95 and one of the limbs of the openings 90. Further, it can be seen from the depiction in
The highest point of interconnector 91 perpendicular to bending direction 95 is called the “upper ending”, whereas the lowest point is called the “lower ending”. To each lower ending of interconnector 91, two webs or bars 97, respectively are connected that are in turn connected to the upper endings of interconnectors 91 in the adjacent rows.
Reference is now made to
Webs or, respectively, bars 97, 98 may, generally, be shaped with straight boundary lines, however, it is also possible and may even be preferred that bars are formed like a zig-zag, or have a sinusoidal shape, or be shaped rather irregularly, for example in order to minimize Moiré interferences with a pixel-array in case the element is used as a cover for such an array.
Further, width and length of a web or bar 97, 98 may vary and can be optimized in order to provide for a high mechanical strength, e.g., high bending strength of first section 9 and, hence, element 1. Therefore, by way of example, it may be preferred to shape interconnectors 91 in a more platelet-like or “arrowhead-like” way, as in
The fold-like shape of at least one opening 90 is in general very advantageous in terms of providing for a high flexibility of element 1. This will be illustrated now with reference to
The inventors further found that a preferred parameter range for interconnectors' dimension may, for a given thickness d and Young's modulus E of the material of element 1 as well as the preferred minimum bending radius, may be found if at least one, preferably if both of the following relationships are satisfied:
In equation (1), hl is a component of length l of bar 97 perpendicular to bending direction as shown in
From a manufacturer's point of view, it may be preferred to produce identically shaped openings 90 and interconnectors 91 that are arranged in a periodic pattern, wherein p is the periodic length. However, it may also be contemplated to arrange openings, interconnectors and bars not in a periodic, but in an aperiodic pattern rather. This might be preferred in terms of minimizing or even totally supressing Moiré interference effects. In that case, p is understood as the average periodic length.
An example of such an aperiodic structure is shown in
It will be clear to the person skilled in the art that other shapes of openings 90 than those depicted in the figures of the disclosure are also possible, as long as the openings 90 are fold-shaped that is, comprising two limbs that intersect, thereby forming a vertex. Therefore, generally, one may also contemplate zig-zag-like openings that comprise several vertices, or else a more irregularly shaped opening. The shape of the openings 90 comprising limbs 8, 10 and a vertex 4 may also characterised in an alternative or additional way by defining a triangle that connects the ends of the limbs 8, 10 with the vertex 4. Specifically, the openings 90 are formed so that apex points 21, 22, 23 can be defined forming the edges of a triangle 20. The apex points 21, 22, 23 are defined as the points of the edge of the respective opening 90, where a parallel line to the bending axis touches the edge when shifted vertically to the bending axis 95. Specifically, the point 21 as shown in
The element 1 is preferably fabricated from glasses which can be easily structured to introduce the openings 90 and which maintain sufficient stability after the structuring.
According to a first embodiment of the composition the glass of the element comprises the following components in weight-%:
According to a second embodiment of the composition the glass of the element comprises the following components in weight-%:
According to a third embodiment of the composition, the glass of the element is essentially free from alkali oxides. The glass comprises the following components in weight-%:
Preferably, in the composition of this glass the sum of the contents of MgO, CaO and BaO is within a range from 8 to 18 weight-%.
In a fourth embodiment the glass composition comprises the following components in weight-%:
Further, the glass may contain 0 to 1 weight-%: P2O5, SrO, BaO; fining agents in an amount of 0 to 1 weight-%, preferably SnO2, CeO2 or As2O3.
According to one embodiment the element 1 is chemically toughened to increase the mechanical strength. Chemical toughening involves an ion exchange within the glass as the brittle material, wherein ions of the glass are exchanged by larger ions in a region of the glass adjacent to the surface so that the larger ions impart a compressive stress to the glass. Usually, alkali ions are exchanged to effect the toughening. Thus, the above listed glasses are suitable for chemical toughening as far as they contain a sufficient amount of alkali ions. Further, it is also possible to temper the glass to provide a compressive stress zone at the surface. Tempering or thermally toughening involves heating the glass until it softens and then rapidly cooling the glass element so that the surface contracts stronger than the glass in the bulk of the element. Thermal toughening is particular effective for thicker glass elements.
For some applications, a closed surface of the element 1 would be desirable. For this purpose, the openings 90 may be filled with organic materials, i.e., plastics, rubbers, or adhesives. Depending on the application, it may also be useful to leave some of the openings 90 open. Generally, in particular for using the element as a display cover, it may be desirable to fill the openings 90 with a transparent material. Thus, generally and without restriction to the specific example as depicted, an element 1 is provided wherein at least a subset or a part of the number of openings 90 is filled with plastic, preferably a transparent plastic. Preferably, the openings 90 are closed by the fillings. However, it would also be possible to provide fillings with one or more openings, e.g., openings that form thin channels.
According to a refinement of the embodiment with the plastics filled openings 90 it is contemplated that the plastic is chosen and adapted so that the bending force due to a deflection of the element is changed by at most 30%, preferably at most 20%, in particular at most 10%, especially preferred by at most 1%. This change is measured relative to a configuration with open openings 90, i.e., without plastic present in the openings 90. In practice, this feature can be easily verified by measuring the reaction force of the element 1 upon deflection with the openings 90 filled and then removing the plastic and repeat the measurement. Generally, without restriction to the above conditions of the reaction force, the plastics may be or at least contain an elastomer. This keeps the plastics filling sufficiently flexible to avoid a large increase in stiffness.
According to a further refinement, the plastic is transparent. In particular, the plastic may have a refractive index matching the refractive index of the brittle material of the element 1. Achieving a perfect match may be not necessary. Rather, within this disclosure a match of the refractive indexes of plastic and brittle material is understood as a refractive index difference of less than 0.3, preferably less than 0.2, more preferably less than 0.15, more preferably less than 0.1, more preferably less than 0.05, more preferably less than 0.02, or less than 0.01, or less than 0.005, or even less than 0.002.
A suitable plastic may contain silicone as a polymer. Silicone is particularly suited to bound to a silicon containing inorganic brittle material such as most of the suitable glasses. As well, silicone can be both an elastomer and a transparent plastics.
In a further embodiment, within the first section 9, the surface of the element 1 is partly formed by the plastic. Depending on the application, this may not be favorable for the application of the element 1. For example, compared to the inorganic brittle material of the element 1, the plastic may provide less adherence for components or layers which are to be applied to one of the sides 3, 5. For this purpose, an optional inorganic layer may be deposited onto at least one of the sides 3, 5. According to one embodiment, silicon oxide is deposited as the inorganic layer. For example, a layer may be deposited by chemical vapor deposition (CVD) or by flame pyrolysis. If the layer spans over both the brittle material and the plastic 33, uniform surface properties are achieved despite the different materials of the element 1.
The element 1 as described herein can be used as a part for a great variety of articles. An article comprising a flat element 1 as described herein may for example be a flexible, in particular foldable display. Typically, due to the high flexibility of the element 1 imparted by the structuring of the first section, an article comprising the element 1 has at least two sections or parts movable with respect to each other.
According to one embodiment, an article comprising an element 1 of brittle material comprises a sandwich structure wherein the element 1 forms one layer of the sandwich structure.
Generally, the sandwich structure may comprise a laminate. In a preferred embodiment, the laminate may comprise organic layers, in particular polymer or plastic layers laminated to one side of the element 1. An organic layer may also comprise or consist of a silicone. As well, organic layers, in particular plastic or polymer layers may be laminated to both sides 3, 5 of the element 1. Thus, with at least one side 3, 5 of the element 1 being laminated to an organic layer such as a polymer layer, a sandwich structure is obtained that combines a high hardness of the brittle material such as glass with a high flexibility. The polymer layer can be laminated to element 1 by adhesives, i.e., optical clear adhesive, thus forming a further organic layer, or be coated to the surface of element 1 without glue. The coating of a protective layer such as chemical vapor deposition method (CVD), dip-coating, spin-coating, ink-jet, casting, screen printing, painting and spaying. However, the disclosure is not limited to those procedures. Suitable materials are also known in the art. For example they can comprise a duroplastic reaction resin that is a polymer selected from the group consisting of phenoplasts, phenol formaldehyde resins, aminoplasts, urea formaldehyde resins, melamine formaldehyde resins, epoxide resins, unsaturated polyester resins, vinyl ester resins, phenacrylate resins, diallyl phthalate resins, silicone resins, cross-linking polyurethane resins, polymethacrylate reaction resins, and polyacrylate reaction resins.
In the case of lamimation, the polymer material can be selected for example from the group consisting of a silicone polymer, a sol-gel polymer, polycarbonate (PC), polyethersulphone, polyacrylate, polyimide (PI), an inorganic silica/polymer hybrid, a cycloolefin copolymer, a polyolefin, a silicone resin, polyethylene (PE), polypropylene, polypropylenepolyvinyl chloride, polystyrene, styrene-acrylonitrile copolymer, polymethyl methacrylate (PMMA), ethylene-vinyl acetate copolymer, polyethylene terephthalate (PET), polybutylene terephthalate, polyamide (PA), polyacetal, polyphenyleneoxide, polyphenylenesulfide, fluorinated polymer, a chlorinated polymer, ethylene-tetrafluoroethylene (ETFE), polytetrafluoroethylene (PTFE), polyvinyl chloride (PVC), polyvinylidene chloride (PVDC), polyvinylidene fluoride (PVDF), polyethylene naphthalate (PEN), a terpolymer made of tetrafluroethylene, a terpolymer made of hexafluoropropylene, and a terpolymer made of vinylidene fluoride (THV) or polyurethane, or mixtures thereof. The polymer layer can be applied onto element 1 by any known method.
Further embodiments of element 1 may also be found in Applicant's own application EP 3 936 485 A1.
The first section 9 can provide a hinge for the adjacent second sections 11, 13. The hinge may be so flexible that the element can be folded together so that the second sections 11, 13 are facing each other. Due to the folding and bulging outwards of the first section 9, generally, two concavely bent portions of the first section 9 are formed with an intermediate convexly shaped portion.
In the hitherto described embodiments the flexible first section 9 formed a continuous stripe between the second sections 11, 13 so as to provide a hinge joint between the second sections 11, 13. In another embodiment, the first section 9 is arranged between the second sections 11, 13 as well. However, according to this embodiment the first section 9 encompasses one of the second sections.
The element 1 as described herein can be produced with a method as described in DE 10 2018 100 299 A1 or PCT application PCT/CN2019/086830, which are incorporated herein by reference. A process is employed wherein a laser pre-scores the openings 90 in the element. The pre-scored element is then etched to produce the openings. Specifically, a method with the following steps can be employed: providing a plate shaped element 1 of a brittle material, directing and focusing the laser beam of a ultrashort pulsed laser onto the element 1, the laser beam having a wavelength at which the brittle material of the element 1 is transparent so that the laser beam can penetrate into the element 1, the laser beam being focused to produce an elongated focus within the element, the intensity of the laser beam being sufficient to produce a filament shaped damage zone within the element 1 along the focus, the laser beam being moved relative to the element to insert a plurality of filament shaped damage zones side by side along a multitude of ring shaped, or closed paths, etching by exposing the element to an etchant, the etchant intruding into the filament shaped damage zones so that the filament shaped damage zones are widened to form channels which combine due to the widening, so that the part of the element encompassed by the ring shaped paths detaches and openings 90 is produced so that least three sections are formed including a first section 9 and two second sections 11, 13, the second sections adjoining the first section so that the first section 9 is arranged between the second sections 11, 13, the first section 9 comprising the openings 90 so that the first section 9 has a higher flexibility than the second sections 11, 13.
According to a refinemenent, after etching, chemical toughening the element 1 may be performed.
According to a further embodiment depicted schematically and not drawn to scale in
In case of such an element 1, element 1 may be folded into an S-shape or zig-zag like, for example, as has been schematically and not drawn to scale depicted in
For example, the first section that will form, upon folding, an outfolding, that is, first section 9b in the example depicted in
Such an element 1 comprising first sections 9a, 9b being formed differently, for example, may be obtained by carefully adjusting the structuring parameters so that structures formed in sections 9a, 9b differ from each other, for example in width and/or length of structures or openings 90 (not depicted here) formed within element 9.
However, it is also possible and may even be preferred that both element 1 may be configured so that two first sections 9a, 9b result that may bend in the same direction, for example, so that two in-foldings may be obtained. Such an element 1 is depicted schematically and not drawn to scale in
However, it is also possible and may be preferred to form a first section—for example, first section 9a, in such a way that the minimum bending radius may vary within the first section. This may be achieved by arranging openings, interconnectors and bars differently throughout the section, for example, by changing the orientation and/or the shape of interconnectors and openings and/or by varying the length and/or width of interconnectors, bars and openings, such as, for example, shown in
Further, it may be contemplated to form element in such a way that a small second section 12 is formed between first sections 9a, 9b, resulting in a folding comprising a non-bent section. This is shown schematically and not drawn to scale in
According to yet a further embodiment, the element 1 may be designed to be rolled up rather than folded. Such an embodiment can be easily achieved by adapting the widths of the first section and the second sections. Generally, the first section may have a width larger that one of the second sections, or even larger than the combined width of the second sections. Further, the second sections may be reduced in width to form rigid edges to stabilize the element 1. For example, the first section may constitute more than 75% of the overall width of the element 1, or even more than 85%. According to yet a further embodiment, the second sections may even be omitted.
Also in
The structuring of the first section 9 has been so far described on the basis of the shape of the openings 90. An alternative or additional description of a suitable structuring to overcome the drawbacks of the state of the art, particularly to provide increased flexibility and/or to reduce Moiré patterns is described in the following. Reference is made again to
The path 30 describing the structuring of the first section 9 may also be described in a different, more general manner. According to a further embodiment of the disclosure, independent from whether or not at least one opening 90 is shaped as a fold that comprises at least two limbs 8, 10 that intersect, thereby forming a vertex 4, an element 1 is provided having the following features:
The element 1 of an inorganic brittle material with opposed sides 3, 5 and a circumferential edge 7 comprises at least three sections, the at least three sections including a first section 9 and two second sections 11, 13, the second sections adjoining the first section so that the first section 9 is arranged between the second sections 11, 13, the first section 9 comprises an arrangement of openings 90 and interconnectors 91 connected by webs or bars 97 so that the first section 9 has a higher flexibility than the second sections 11, 13, whereby the openings 90 are arranged and shaped so that a path can be defined, the path running along an interconnector 91, then further along a bar 97 connected thereto, then along another interconnector 91 at the end of the bar 97 and then along another bar 97 at the opposite end of the latter interconnector 91 and the path being composed of line segments, each segment starting and ending at the edge of an opening.
Preferably, the segments each start and end at an apex point 25, 26, 27, 28, 29 of either an opening 90 or a protrusion of an interconnector 91. It is preferred that adjacent line segments of this path 30 include at least one acute angle and at least one obtuse angle.
Further, according to a preferred embodiment, the sequence of line segments include two acute angles and one obtuse angle. This feature characterizes the specific structure with a plurality of interlocking and generally fold shaped openings 90 in the first section 1 of the element 1. As the path 30 starts at the edge of an opening 90 at an interconnector 91 and then follows the interconnector 91, the line segment between the points 25 and 26 typically extends along the y-direction, with the x-direction extending parallel to the bending axis. The x- and y-coordinate axes are shown in
To calculate the stresses within the first section, each point is defined by its x- and y-position in a coordinate-system. Then, for every unit-cell in the first section, maximum stresses can be calculated. In the following, for the sake of the mathematical treatment, the points 25-29 are assigned to the following symbols: Point 25 is referred to as c3, bottom, Point 26 is referred to as c3, top, Point 27 is referred to as c2, bottom, Point 28 is referred to as c2, top, and Point 29 is referred to as c1, bottom. For the sake of clarity,
Using the points 25-29 and the segments of the path, maximum stresses on the bars 97 and interconnectors 91 can be calculated. According to a preferred embodiment, the arrangement, size and shape of the openings 90 is chosen so that the following conditions are met for at least one path upon bending of the element 1:
In the formulas (i) and (ii), the variable “E” is the Young modulus. d refers to the thickness of the element 1. The variables c1, bottom,y, c2, bottom,y, c2, top,y, c3, top,y refer to the y-coordinates of the points 29, 27, 28 and 26 in this order. Similarly, the variables c1, bottom,x, c2, top,x, c2, bottom,x, and c3, top,x refer to the x-coordinates of the points 29, 28, 27 and 26 in this order. As mentioned above, the x-coordinate extends along the direction of the bending axis and the y-direction is perpendicular thereto.
Preferably, the openings and their arrangement are designed so that the maximum stress generated according to the above formulas is not only less than 10000 MPa, but even less than 5000 MPa upon bending of the element 1. More preferably, the maximum stress is less than 3000 MPa or even less than 2000 MPa.
Number | Date | Country | Kind |
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22187862.2 | Jul 2022 | EP | regional |