Method for Measuring Residual Stress in Thin Plate

Abstract

Provided is a method for measuring residual stress in a thin plate. The method includes: S1: prearranging and cutting a plurality of fins, computing x-direction strain εi0 and x-direction residual stress σi0 in the length direction of the thin plate borne by each fin, and obtaining distribution of x-direction residual stress in the width direction of the thin plate according to all σi0; S2: repeatedly cutting the fixed ends in a thickness direction of the thin plate, computing a total cutting depth Zij and x-direction residual stress σij of each fin after each cutting, and obtaining distribution of x-direction residual stress in the thickness direction of the thin plate borne by an ith fin according to all σij; and S3: computing distribution σx, σx=σi0+σij, of x-direction residual stress on a yz cross section of the thin plate according to σi0 obtained in S1 and corresponding σij in S2.

Description

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present disclosure claims priority to patent application No. 202211212028.2, filed to the China National Intellectual Property Administration on Sep. 30, 2022 and entitled “Method for Measuring Residual Stress in Thin Plate”.

TECHNICAL FIELD

The disclosure relates to the technical field of measuring of residual stress in thin plates, and particularly to a method for measuring residual stress in a thin plate.

BACKGROUND

High-performance thin plates are extensively applied to the fields of aerospace, electrical and electronic engineering, chip package, etc., for example, aircraft skin, chip lead frame processing, transformers and so on. In processes of processing and manufacturing the aircraft skin and chip lead frames by the thin plates, a removed surface area accounts for 80% of a total area, and a removed thickness accounts for 60% or above of a total thickness. The thin plates have low bending stiffness on account of thinness, and will largely deform even under low residual stress during a removal process. The premise of deformation control of the thin plate during the removal process is quantitative characterization of residual stress distribution of the thin plate in a thickness.

In a related art, internal residual stress of the thin plate is generally evaluated through a single-side corrosion method. In this method, one side of the thin plate is required to be protected by pasting a film, the other side of the thin plate is required to be corroded by a corrosive liquid, and after a corrosion depth reaches 50% of the thickness of the thin plate, a warpage deformation quantity is compared. This method can only qualitatively determine magnitude of the residual stress according to a deformation degree, but cannot quantitatively characterize a distribution rule of the residual stress in the thickness of thin plate.

Since the thin plate is not uniformly cooled during solution quenching, residual stress on a surface and at a center of the thin plate have different tensile and compressive states. Therefore, it is difficult to quickly guide optimization of thin plate manufacturing technique according to a deformation law obtained through the single-side corrosion method. With mass supply requirements of civil airliners and high-performance chip packaging materials, a breakthrough on quantitative characterization technique for residual stress of a thin plate is urgently required. Therefore, a method capable of rapidly and quantitatively characterizing residual stress distribution in a thin plate is required to effectively control processing deformation of the thin plate.

SUMMARY

Some embodiments of the disclosure provide a method for measuring residual stress in a thin plate, which is used for quantitatively characterizing a distribution rule of the residual stress on a thickness of the thin plate.

In order to realize the above objective, some embodiments of the disclosure provide a method for measuring residual stress in a thin plate. The method includes: S1: prearranging and cutting a plurality of fins that are parallel to a length direction of the thin plate at equal intervals along a width direction of the thin plate, where a length of each fin is the same as each other and less than a width of the thin plate, and the fins have fixed ends and movable ends that are opposite each other, computing x-direction strain ε_i0 and x-direction residual stress σ_i0 in the length direction of the thin plate borne by each fin according to lengths of each fin before and after cutting, and obtaining distribution of x-direction residual stress in the width direction of the thin plate according to σ_i0 of all the fins; S2: repeatedly cutting the fixed end of the each fin in a thickness direction of the thin plate, recording a cutting parameter, and a warpage condition and a bending parameter of the each fin after each cutting, computing a total cutting depth Z_ij and x-direction residual stress σ_ij of the each fin after each cutting, and obtaining distribution of x-direction residual stress in the thickness direction of the thin plate borne by an ith fin according to all σ_ij; and S3: computing distribution σ_x, σ_x=σ_i0+σ_ij, of x-direction residual stress on a yz cross section of the thin plate according to σ_i0 of the ith fin computed in S1 and corresponding σ_ij of the ith fin after jth cutting in S2.

In some embodiments, S1 includes: S1.1: arranging cutting marks at equal intervals in the width direction of the thin plate, where an extension direction of each cutting mark is the same as each other and parallel to the length direction of the thin plate and extends to an end of the thin plate, an extension length of each cutting mark is less than a length of the thin plate, and a region between any two cutting marks forms one fin, and recording an initial length L₀ of the ith fin before cutting; and S1.2: cutting the cutting marks through the thin plate in the thickness direction of the thin plate, and recording a deformation length L_i0 of the each fin after deformation in the length direction of the thin plate.

In some embodiments, S1 further includes: S1.3: computing the x-direction strain ε_i0 and the x-direction residual stress σ_i0, ε_i0=(L₀−L_i0)/L₀ and σ_i0=Eε_i0, in the length direction of the thin plate borne by each fin according to the recorded initial length L₀ of the fin and the deformation length L_i0 of the fin, where E is an elastic modulus of the thin plate.

In some embodiments, S2 includes: constraining two ends of the thin plate in the length direction before each cutting, so as to make an extension direction of each fin parallel to the width direction of the thin plate, and releasing the thin plate on one side of the movable end of the fin after each cutting, so as to compute and record the bending parameter of the ith fin after jth cutting.

In some embodiments, the total cutting depth Z_ij and the x-direction residual stress σ_ij of each fin after each cutting are expressed as:

$S>Z_{\mathrm{ij}}=j\Delta z;L_{\mathrm{ij}}=L_{i0}-t$ $\mathrm{and}{\sigma }_{\mathrm{ij}}=\frac{E\pi }{90m·\Delta z·\left[S-\left(j-1\right)\right]\Delta z}\left(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}^{\prime }}{L_{\mathrm{ij}}}\right);$

where Δz is a cutting depth of each cutting, t is a cutting width, I_ij is inertia moment of an uncut portion of the ith fin after jth cutting, E is a Young's elastic modulus of the thin plate, h_ij′ is a warpage quantity of the ith fin after jth cutting minus a warpage quantity of a cut portion, h_ij is a bending height of the ith fin after jth cutting, L_ij is a remaining length of the ith fin after jth cutting, S is a thickness of the thin plate, m is an equivalent arc length of residual stress release of the ith fin after jth cutting, and under the condition that t is infinitely close to 0, a computational formula for σ_ij is expressed as:

${\sigma }_{\mathrm{ii}}=\frac{E\pi }{90m·\Delta z·\left[S-\left(j-1\right)\right]\Delta z}\left(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}}{L_{i\left(j-1\right)}}\right).$

In some embodiments, m is approximately expressed as: m=t+0.75S; after jth cutting of the ith fin, a notch is formed, and the ith fin is bent to form a first bent surface and a second bent surface that are spaced apart from each other in the thickness direction of the thin plate; on an xz cross section of the thin plate, the first bent surface and the second bent surface are two arcs that have the same curvature but different arc lengths, the equivalent arc length m is a length of an arc formed between two ends of an opening of the notch on the cross section, and curvature of the equivalent arc length m is the same as curvature of the two arcs; and h_ij′ is a height between a warping end of the opening of the notch on the cross section and a top end of the fin after warping, and h_ij is a height between a non-warping end of the opening of the notch on the cross section and the top end of the fin after warping.

In some embodiments, σ_ij is obtained according to formulas as follows

$d\left(\sum M_{\mathrm{ij}}\right)={\sigma }_{\mathrm{𝔦j}}·\mathrm{\Delta z}·m\frac{\left[S-\left(j-1\right)\Delta z\right]}{2};$ $\mathrm{and}d\left(\sum M_{\mathrm{ij}}\right)=\frac{E\pi }{180}\left(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}^{\prime }}{L_{\mathrm{ij}}}\right);$

where ΣM_ij is total bending moment of the ith fin after jth cutting, and d(ΣM_ij) is a bending moment increment of the ith fin after jth cutting.

In some embodiments, a computational method for ΣM_ij is as follows: ΣM_ij=ω_ijM_ij; where ω_ij is an average arc length, and M_ij is average bending moment of the residual stress of the ith fin after jth cutting on an arc length of any unit; and after jth cutting, the i-th fin is bent to form a first bent surface and a second bent surface that are spaced apart from each other in the thickness direction of the thin plate, on an xz cross section of the thin plate, the first bent surface and the second bent surface are two arcs that have the same curvature but different arc lengths, the average arc length is between the two arcs, curvature of the average arc length is the same as curvature of the two arcs, and distances between the average arc length and the arcs on two sides are the same.

In some embodiments, a computational method for M_ij is as follows:

$M_{\mathrm{ij}}=\frac{E{I}_{\mathrm{ij}}\pi }{180{\omega }_{\mathrm{ij}}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}.$

In some embodiments, computational methods for ω_ij, θ_ij and I_ij are as follows:

${\theta }_{\mathrm{ij}}=\frac{{\omega }_{\mathrm{ij}}}{{\rho }_{\mathrm{ij}}}·\frac{180}{\pi };{\theta }_{\mathrm{ij}}=\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}\mathrm{and}\frac{1}{{\rho }_{\mathrm{ij}}}=\frac{M_{\mathrm{ij}}}{{\mathrm{EI}}_{\mathrm{ij}}};$

where ρ_ij is a curvature radius of the ith fin after jth cutting, and θ_ij is a bending angle of the ith fin after jth cutting.

In some embodiments, S2 further includes: correcting the residual stress;

$\Delta \left({\sigma }_{\mathrm{ij}}\right)=\frac{{\sigma }_{\mathrm{ij}}·\Delta z}{S-j\Delta z};$ $\mathrm{and}{\sigma }_{\mathrm{ij}}^{\prime }={\sigma }_{\mathrm{ij}}-{\sum }_1^{j-1}\Delta {\sigma }_{\mathrm{ij}};$

where Δ(σ_ij) is an effect of residual stress of layer Δz on residual stress of the uncut portion, and σ_ij′ is a residual stress correction value of the ith fin during jth cutting.

A technical solution of the disclosure provides a method for measuring residual stress in a thin plate. The method includes: S1: prearranging and cutting a plurality of fins that are parallel to a length direction of the thin plate at equal intervals in a width direction of the thin plate, where a length of each fin is the same as each other and less than a width of the thin plate, and the fins have fixed ends and movable ends that are opposite each other, computing x-direction strain ε_i0 and x-direction residual stress σ_i0 in the length direction of the thin plate borne by each fin according to lengths of each fin before and after cutting, and obtaining distribution of x-direction residual stress in the width direction of the thin plate according to σ_i0 of all the fins; S2: repeatedly cutting the fixed ends of the fins in a thickness direction of the thin plate, recording a cutting parameter, and a warpage condition and a bending parameter of each fin after each cutting, computing a total cutting depth Z_ij and x-direction residual stress σ_ij of each fin after each cutting, and obtaining distribution of x-direction residual stress in the thickness direction of the thin plate borne by an ith fin according to all σ_ij; and S3: computing distribution σ_x, σ_x=σ_i0+σ_ij, of x-direction residual stress on a yz cross section of the thin plate according to σ_i0 of the ith fin computed in S1 and corresponding σ_ij of the ith fin after jth cutting in S2. According to this solution, according to distribution of a plurality of x-direction residual stress in the width direction (y direction) and the thickness direction (z direction) of the thin plate, distribution of the residual stress in the thin plate on the yz cross section is obtained, and the situation that a method for evaluating residual stress in a thin plate through a single-side corrosion method in the prior art can only qualitatively determine the residual stress, but cannot quantitatively characterize distribution of the residual stress in a thickness of the thin plate is avoided. Through computation of the solution, the residual stress and the distribution thereof in the thin plate are obtained, and characterization is accurate and reliable.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings of the description constitute part of the disclosure and serve to provide further understanding of the disclosure, and illustrative examples of the disclosure and the description of the illustrative examples serve to explain the disclosure and are not to be construed as unduly limiting the disclosure. In the accompanying drawings:

FIG. 1 shows a flow diagram of a method for measuring residual stress in a thin plate according to an example of the disclosure;

FIG. 2 shows a schematic structural diagram of a thin plate suitable for the method in FIG. 1;

FIG. 3 shows a schematic structural diagram of a thin plate after step S1.1;

FIG. 4 shows a schematic structural diagram of a thin plate after step S1.2;

FIG. 5 shows a schematic diagram of constraint a thin plate in step S2;

FIG. 6 shows a schematic diagram of cutting a thin plate in step S2;

FIG. 7 shows a schematic diagram of bending a thin plate in step S2; and

FIG. 8 shows a schematic diagram of an xz section of a thin plate in step S2.

The above figures include reference numerals as follows:

• • 11. notch; 12. first bent surface; and 13. second bent surface.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Technical solutions in examples of the disclosure will be clearly and completely described below in combination with accompanying drawings in the examples of the disclosure. Apparently, the examples described are merely some examples rather than all examples of the disclosure. The following description of at least one illustrative example is merely illustrative in nature and in no way serves as any limitation of the disclosure and its application or use. On the basis of examples of the disclosure, all other examples obtained by those of ordinary skill in the art without making creative efforts all fall within the scope of protection of the disclosure.

As shown in FIG. 1, an embodiment of the disclosure provides a method for measuring residual stress in a thin plate. The method includes: S1: prearrange and cut a plurality of fins that are parallel to a length direction of the thin plate at equal intervals along a width direction of the thin plate, where a length of each fin is the same as each other and less than a width of the thin plate, and the fins have fixed ends and movable ends that are opposite each other, compute x-direction strain ε_i0 and x-direction residual stress σ_i0 in the length direction of the thin plate borne by each fin according to lengths of each fin before and after cutting, and obtain distribution of x-direction residual stress in the width direction of the thin plate according to σ_i0 of all the fins; S2: repeatedly cut the fixed ends of the fins in a thickness direction of the thin plate, record a cutting parameter, and a warpage condition and a bending parameter of the each fin after each cutting, compute a total cutting depth Z_ij and an x-direction residual stress σ_ij of the each fin after each cutting, and obtain distribution of x-direction residual stress in the thickness direction of the thin plate borne by an ith fin according to all σ_ij; and S3: compute distribution σ_x=, σ_x=σ_i0+σ_ij, of x-direction residual stress on a yz cross section of the thin plate according to σ_i0 of the ith fin computed in S1 and corresponding σ_ij of the ith fin after jth cutting in S2.

In the embodiment, according to distribution of the plurality of x-direction residual stress in the width direction (y direction) and the thickness direction (z direction) of the thin plate, distribution of the residual stress in the thin plate on the yz cross section is obtained, and the situation that a method for evaluating residual stress in a thin plate through a single-side corrosion method in the prior art can only qualitatively determine magnitude of the residual stress, but cannot quantitatively characterize distribution of the residual stress in a thickness of the thin plate is avoided. Through computation of the solution, the residual stress magnitude and the distribution thereof in the thin plate are obtained, and characterization is accurate and reliable.

As shown in FIGS. 2-4 and 8, S1 includes: S1.1: arrange cutting marks at equal intervals in the width direction of the thin plate, where an extension direction of each cutting mark is the same as each other and parallel to the length direction of the thin plate and extends to an end of the thin plate, an extension length of the each cutting mark is less than a length of the thin plate, and a region between any two cutting marks forms one fin, and record an initial length L₀ of the ith fin before cutting; and S1.2: cut the cutting marks through the thin plate in the thickness direction of the thin plate, and record a deformation length L_i0 of the each fin after deformation in the length direction of the thin plate.

Specifically, as shown in FIGS. 2 and 8, an x-direction is defined as a length direction of the thin plate and a residual stress measurement direction, a y-direction is a width direction of the thin plate, and a z-direction is a thickness direction of the thin plate. The thin plate is initially in a static balance state, and resultant force of x-direction residual stress of the thin plate is zero in the width direction (y direction) of the thin plate. In the embodiment, i=1, 2, 3, . . . , 10, and specific operation processes of S1.1 and S1.2 are as follows: 11 cutting marks that extend in the length direction (x direction) of the thin plate are arranged at intervals in the width direction (y direction) of the thin plate, the plurality of cutting marks are parallel to each other and have the same length, one end of each cutting mark extends to one end of the thin plate in the length direction (x direction) of the thin plate, and the other end is located on a plane of the thin plate. A region between any two cutting marks forms one fin, and there are 10 fins in total, which are fin 1, fin 2, fin 3, fin 4, . . . , fins 10 in the width direction (y direction) of the thin plate. The length L₀ of the cutting mark is recorded, and serves as initial lengths of the 10 fins not cut. Each cutting mark is sequentially cut through the thin plate through a linear cutting method, a cutting direction is parallel to the thickness direction (z direction) of the thin plate, and 10 fins (fin 1 to fin 10, that is, 1, 2, 3, . . . , i in figures) are obtained. After cutting, each of the 10 fins is of a strip-shaped structure with one end fixed and the other end movable. After all the above fins are obtained through the linear cutting method, the resultant force of the residual stress borne by the fins in the thickness direction (z direction) of the thin plate is released, the 10 fins deform under the influence of the x-direction residual stress in the thin plate, and a length L_i0 of each fin after deformation is recorded. L₀ is less than the length of the thin plate, deformation of the fin includes elongation or shortening of the fin in the length direction of the thin plate, and L_i0 is an overall length of the ith fin after deformation, for example, L₁₀ is a length of the fin 1 after deformation. In the embodiment, lengths of each fin before and after cutting are generally measured by a laser displacement sensor. Specifically, before the cutting marks are cut, initial position coordinates (that is, coordinates of positions P₁, P₂, P₃ . . . , P_i in FIG. 3) of an end of the fin located on a side of an end of the thin plate are measured by the laser displacement sensor. After the cutting marks are cut, deformation position coordinates (that is, coordinates of positions P₁′, P₂′, P₃′ . . . , P_i′ in FIG. 4) of the movable end (which is the same end as the end of the above fin) of the fin after deformation are measured by the laser displacement sensor. According to coordinates of P_i′ and P_i, a deformation length of each fin in the length direction (x direction) of the thin plate may be obtained, and an overall length L_i0 of each fin after deformation in the length direction (x direction) of the thin plate may be obtained.

In some embodiments, S1 further includes: S1.3: compute the x-direction strain ε_i0 and the x-direction residual stress σ_i0, ε_i0=(L₀−L_i0)/L₀ and σ_i0−Eε_i0, in the length direction of the thin plate borne by the each fin according to the recorded initial length L₀ of the fin and the deformation length L_i0 of the fin, where E is an elastic modulus of the thin plate. As shown in FIG. 8, in the embodiment, x-direction strain ε_i0, ε_i0=(L₀−L_i0)/L₀, of each fin is computed according to the obtained L_i0 of each fin after deformation and initial lengths L₀ of all fins before cutting. With fin 1 as an example, ε₁₀=(L₀−L₁₀)/L₀, and ε_i0 of other fins are similar. According to the obtained ε₁₀, ε₂₀, ε₃₀ . . . , ε₁₀₀, a distribution difference of residual stress in the width direction (y direction) of the thin plate is obtained.

As shown in FIGS. 5-8, S2 includes: constrain two ends of the thin plate in the length direction before each cutting, so as to make an extension direction of each fin parallel to the width direction of the thin plate, and release the constraint on the thin plate on one side of the movable end of the fin after each cutting, so as to compute and record the bending parameter of the ith fin after jth cutting. In the embodiment, end A and end B of the thin plate after the step S1 are fixed, so as to ensure that an initial state of each fin is the same as each other. End B is released after each cutting, so as to break balance of the residual stress in the thickness direction (z direction) of the thin plate, such that a different degree of warping deformation occurs on each fin. Bending conditions of the 10 fins in the same initial state in the case of the same cutting depth are observed, and a bending parameter of each fin after each cutting is recorded.

As shown in FIG. 8, the total cutting depth Z_ij and the x-direction residual stress σ_ij of each fin after each cutting is expressed as:

$S>Z_{\mathrm{ij}}=j\Delta z;L_{\mathrm{ij}}=L_{i0}-t$ $\mathrm{and}{\sigma }_{\mathrm{ij}}=\frac{E\pi }{90m·\Delta z·\left[S-\left(j-1\right)\right]\Delta z}\left(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}^{\prime }}{L_{\mathrm{ij}}}\right);$

where Δz is a cutting depth of each cutting, t is a cutting width, I_ij is an inertia moment of an uncut portion of the ith fin after jth cutting, E is a Young's elastic modulus of the thin plate, h_ij′ is a warpage quantity of the ith fin after jth cutting minus a warpage quantity of a cut portion, h_ij is a bending height of the ith fin after jth cutting, L_ij is a remaining length of the ith fin after jth cutting, S is a thickness of the thin plate, m is an equivalent arc length of residual stress release of the ith fin after jth cutting, and under the condition that t is infinitely close to 0, a computational formula for σ_ij is expressed as

${\sigma }_{\mathrm{ii}}=\frac{E\pi }{90m·\Delta z·\left[S-\left(j-1\right)\right]\Delta z}\left(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}}{L_{i\left(j-1\right)}}\right).$

In the embodiment, cutting is carried out through an electric spark electrode discharge cutting method, a cutting direction is perpendicular to a surface of the thin plate, and ends of the fixed ends of all fins are simultaneously cut. In the cases of L_ij and the number of times of cutting j=0, L_ij=L_i0. Since a cutting width t of any fin does not change, a plurality of L_ij of an ith fin are the same as each other. For example, L₁₁ of a first fin (fin 1) after first cutting is the same as L₁₂ of the first fin (fin 1) after second cutting. In the cases of h_ij and j=0, h_i0=h_ij. Since a total cutting depth Z_ij of any fin progressively increases, a plurality of h_ij of the ith fin are different from each other. For example, h₁₁ of the first fin (fin 1) after first cutting is different from h₁₂ of the first fin (fin 1) after second cutting, and h_ij′ is similar.

With fin 1 after two-time cutting as an example, a total cutting depth after second cutting is Z₁₂=2Δz, and residual stress of fin 1 after second cutting is

${\sigma }_{12}-\frac{E\pi }{90m·\Delta z·\left[S-\left(2-1\right)\right]\Delta z}\left(I_{12}\arcsin \frac{h_{12}^{\prime }}{L_{12}}-I_{11}\arcsin \frac{h_{11}^{\prime }}{L_{11}}\right).$

Therefore, the residual stress of each fin after each cutting may be computed, and distribution of x-direction residual stress in the thickness direction of the thin plate borne by each fin may be obtained according to all the obtained σ_ij. Under the condition that t is infinitely close to 0, residual stress release is small, a bending degree is low, #^hij approximately equals to h_ij′, and thus

${\sigma }_{12}=\frac{E\pi }{90m·\Delta z·\left[S-\left(2-1\right)\right]\Delta z}\left(I_{12}\arcsin \frac{h_{12}^{\prime }}{L_{12}}-I_{11}\arcsin \frac{h_{11}}{L_{11}}\right).$

Specifically, j in the embodiment is an integer greater than 0.

In some embodiments, m is approximately expressed as: m=t+0.75S; alter jth cutting of the ith fin, a notch 11 is formed, and the ith fin is bent to form a first bent surface 12 and a second bent surface 13 that are spaced apart from each other in the thickness direction of the thin plate; on an xz cross section of the thin plate, the first bent surface 12 and the second bent surface 13 are two arcs that have the same curvature but different arc lengths, the equivalent arc length m is a length of an arc formed between two ends of an opening of the notch 11 on the cross section, and curvature of the equivalent arc length m is the same as curvature of the two arcs; and h_ij′ is a height between a warping end of the opening of the notch 11 on the cross section and a top end of the fin ater warping, and h_ij is a height between a non-warping end of the opening of the notch 11 on the cross section and the top end of the fin after warping.

In the embodiment, h_ij may be also obtained by a laser displacement sensor. Specifically, coordinates of positions P₁′, P₂′, P₃′ . . . , P_i′ in FIG. 4 serve as the standard, and the movable ends of all the fins are re-measured after each cutting. With one-time cutting as an example (that is, in the case of j=1), coordinates of positions P₁₁′, P₂₁′, P₃₁′ . . . , P_i1′ are obtained. Similarly, in the case of two-time cutting (j=2), coordinates of positions P₁₂′, P₂₂′, P₃₂′ . . . , P_i2′ are obtained. By comparing coordinates of P_i′ and P_ij′ before and after cutting, h_ij and other relevant parameters may be obtained. Alternatively, h_ij′ may be obtained by a laser displacement sensor, and a measurement method is the same as that for h_ij.

In the embodiment, the σ_ij is obtained according to formulas as follows:

$d\left(\sum M_{\mathrm{ij}}\right)={\sigma }_{\mathrm{ij}}·\Delta z·m\frac{\left[S-\left(j-1\right)\Delta z\right]}{2};$ $\mathrm{and}d\left(\sum M_{\mathrm{ij}}\right)=\frac{E\pi }{180}(I_{\mathrm{ij}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}-I_{i\left(j-1\right)}\arcsin \frac{h_{i\left(j-1\right)}^{\prime }}{L_{\mathrm{ij}}});$

where ΣM_ij is a total bending moment of the ith fin after jth cutting, and d(ΣM_ij) is a bending moment increment of the ith fin after jth cutting. d(ΣM_ij)=ΣM_ij−ΣM_i(j-1).

Specifically, a computational method for ΣM_ij is as follows: ΣM_ij=ω_ijM_ij; wherein ω_ij# an average arc length, and M_ij# an average bending moment of the residual stress of the ith fin after jth cutting on an arc length of any unit; and after j-th cutting, the i-th fin is bent to form a first bent surface 12 and a second bent surface 13 that are spaced apart from each other in the thickness direction of the thin plate, on an xz cross section of the thin plate, the first bent surface 12 and the second bent surface 13 are two arcs that have the same curvature but different arc lengths, the average arc length is between the two arcs, curvature of the average arc length is the same as curvature of the two arcs, and distances between the average arc length and the arcs on two sides are the same.

Wherein, a computational method for M_ij is as follows

$\#M_{\mathrm{ij}}=\frac{{\mathrm{EI}}_{\mathrm{ij}}\pi }{180{\omega }_{\mathrm{ij}}}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}.$

With fin 1 after two-time cutting as an example M_12# as follows:

$M_{12}=\frac{{\mathrm{EI}}_{12}\pi }{180{\omega }_{12}}\arcsin \frac{h_{12}^{\prime }}{L_{12}}.$

According to ΣM_ij=ω_ijM_ij, it can be inferred that

$\sum M_{\mathrm{ij}}=\frac{E{I}_{\mathrm{ij}}\pi }{180}\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}.$

With fin 1 after two-time cutting as an example, ΣM_ij is as follows:

$\sum M_{12}=\frac{E{I}_{12}\pi }{180}\arcsin \frac{h_{12}^{\prime }}{L_{12}}.$

Further, a computational method for ω_ij is as follows:

$\#{\theta }_{\mathrm{ij}}=\frac{{\omega }_{\mathrm{ij}}}{{\rho }_{\mathrm{ij}}}·\frac{180}{\pi };$

wherein ρ_ij is a curvature radius of the ith fin after jth cutting, and θ_ij is a bending angle of the ith fin after jth cutting.

In the embodiment, with fin 1 after two-time cutting as an example,

${\theta }_{12}=\frac{{\omega }_{12}}{{\rho }_{12}}·\frac{180}{\pi }.$

Alternatively, ρ_ij may be also obtained by a laser displacement sensor, and a measurement method is the same as that for h_ij.

A computational method for θ_ij is as follows:

${\theta }_{\mathrm{ij}}=\arcsin \frac{h_{\mathrm{ij}}^{\prime }}{L_{\mathrm{ij}}}.$

With fin 1 after two-time cutting as an example,

${\theta }_{12}=\arcsin \frac{h_{12}^{\prime }}{L_{12}}.$

Further, a computational method for I_ij is as follows:

$\frac{1}{{\rho }_{\mathrm{ij}}}=\frac{M_{\mathrm{ij}}}{{\mathrm{EI}}_{\mathrm{ij}}};$

wherein ρ_ij is a curvature radius of the ith fin after jth cutting, and M_ij is a bending moment of the ith fin after jth cutting. With fin 1 after two-time cutting as an example,

$\frac{1}{{\rho }_{12}}=\frac{M_{12}}{{\mathrm{EI}}_{12}}.$

In the embodiment, S2 further includes: correct the residual stress;

$\Delta \left({\sigma }_{\mathrm{ij}}\right)=\frac{{\sigma }_{\mathrm{ij}}·\Delta z}{S-j\Delta z};\mathrm{and}{\sigma }_{\mathrm{ij}}^{\prime }={\sigma }_{\mathrm{ij}}-{\sum }_1^{j-1}\Delta {\sigma }_{\mathrm{ij}};$

wherein Δ(σ_ij) is an effect of residual stress of layer Δz on residual stress of the uncut portion, and σ_ij′ is a residual stress correction value of the ith fin during jth cutting. Through such arrangement, distribution reliability of residual stress σ_ij on the thin plate and characterization accuracy are ensured.

What are described above are merely some embodiments of the disclosure and are not intended to limit the disclosure, and for those skilled in the art, the disclosure can be variously modified and changed. Any modification, equivalent substitution, improvement, etc. within the spirit and principles of the disclosure shall fall within the scope of protection of the disclosure.

Claims

1. A method for measuring residual stress in a thin plate, comprising: S1: prearranging and cutting a plurality of fins that are parallel to a length direction of the thin plate at equal intervals along a width direction of the thin plate, wherein a length of each fin is the same as each other and less than a width of the thin plate, and the each fin has a fixed end and a movable end that are opposite each other, computing x-direction strain εi0 and x-direction residual stress σi0 in the length direction of the thin plate borne by the each fin according to lengths of the each fin before and after cutting, and obtaining distribution of x-direction residual stress in the width direction of the thin plate according to σi0 of all the fins;S2: repeatedly cutting the fixed end of the each fin in a thickness direction of the thin plate, recording a cutting parameter, and a warpage condition and a bending parameter of the each fin after each cutting, computing a total cutting depth Zij and x-direction residual stress σij of the each fin after each cutting, and obtaining distribution of x-direction residual stress in the thickness direction of the thin plate borne by an ith fin according to all σij; andS3: computing distribution σx, σx=σi0+σij, of x-direction residual stress on a yz cross section of the thin plate according to σi0 of the ith fin computed in S1 and corresponding σij of the ith fin after jth cutting in S2.

2. The method for measuring residual stress in the thin plate according to claim 1, wherein S1 comprises: S1.1: arranging cutting marks at equal intervals in the width direction of the thin plate, wherein an extension direction of each cutting mark is the same as each other and parallel to the length direction of the thin plate and extends to an end of the thin plate, an extension length of the each cutting mark is less than a length of the thin plate, and a region between any two cutting marks forms one fin, and recording an initial length L0 of the ith fin before cutting; and S1.2: cutting the cutting marks through the thin plate in a thickness direction of the thin plate, and recording a deformation length Li0 of the each fin after deformation in the length direction of the thin plate.

3. The method for measuring residual stress in the thin plate according to claim 2, wherein S1 further comprises: S1.3: computing the x-direction strain εi0 and the x-direction residual stress σi0, εi0=(L0−Li0)/L0 and σi0=Eεi0, in the length direction of the thin plate borne by the each fin according to the recorded initial length L0 of the each fin and the deformation length Li0 of the fin, wherein E is an elastic modulus of the thin plate.

4. The method for measuring residual stress in the thin plate according to claim 1, wherein S2 comprises: constraining two ends of the thin plate in the length direction before each cutting, so as to make an extension direction of the each fin parallel to the width direction of the thin plate, and releasing the thin plate on a side of the movable end of the each fin after each cutting, so as to compute and record the bending parameter of the ith fin after jth cutting.

5. The method for measuring residual stress in the thin plate according to claim 4, wherein the total cutting depth Zij and the x-direction residual stress σij of the each fin after each cutting are expressed as:

6. The method for measuring residual stress in the thin plate according to claim 5, wherein m is approximately expressed as: #m=t+0.75S; after jth cutting of the ith fin, a notch is formed, and the ith fin is bent to form a first bent surface and a second bent surface that are spaced apart from each other in the thickness direction of the thin plate; on an xz cross section of the thin plate, the first bent surface and the second bent surface are two arcs that have the same curvature but different arc lengths, the equivalent arc length m is a length of an arc formed between two ends of an opening of the notch on the cross section, and curvature of the equivalent arc length m is the same as curvature of the two arcs; and hij′ is a height between a warping end of the opening of the notch on the cross section and a top end of a corresponding fin after warping, and hij is a height between a non-warping end of the opening of the notch on the cross section and the top end of the fin after warping.

7. The method for measuring residual stress in the thin plate according to claim 5, wherein σij is obtained according to formulas as follows:

8. The method for measuring residual stress in the thin plate according to claim 7, wherein a computational method for ΣMij is as follows:

9. The method for measuring residual stress in the thin plate according to claim 8, wherein a computational method for Mij is as follows:

10. The method for measuring residual stress in the thin plate according to claim 9, wherein computational methods for ωij, θij and Iij are as follows:

11. The method for measuring residual stress in the thin plate according to claim 10, wherein S2 further comprises: correcting the residual stress;