A residual stress distribution reconstruction method based on influence function

Abstract

The application discloses a residual stress distribution prediction method based on an influence function, and reconstructs the residual stress distribution based on intrinsic strain solution of the influence function. Taking a ring core method as an example, firstly, the quantitative constitutive relationship between the intrinsic strain and surface strain release is deduced by taking the intrinsic strain as an invariant; then, the specific expression of the influence function in the constitutive relationship is solved; finally, the method for reconstructing the residual stress by inversely calculating the residual stress through the surface strain release and the influence function is proposed, which has the advantages of wide application range, high precision and the like, can overcome the defects of the existing residual stress measurement methods, and meets the high-accuracy residual stress measurement demand under a high stress gradient. Through experimental verification, the reconstruction result obtained by adopting the method provided by the application is highly consistent with the experiment, the method provided by the application realizes the micron-level spatial residual stress distribution prediction, and has a micron-level resolution.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of residual stress measurement, and more particularly relates to a residual stress distribution reconstruction method based on influence functions. BACKGROUND

[0002] In the process of manufacturing materials, the materials will be deformed unevenly due to elastic mismatch, temperature change or phase change, etc. external influences, thereby generating residual stress. Residual stress will significantly affect the properties and process quality of materials, and plays a decisive role in the processing design of materials. At the same time, in the fatigue life prediction of components, tensile residual stress will increase the probability of crack initiation and reduce the fatigue life, while compressive residual stress can effectively improve the performance of components, so it is very important to accurately predict and evaluate the residual stress.

[0003] The evaluation method of residual stress is mainly to measure the specific parts of the component through experiment, and to evaluate by measuring the physical quantity related to residual stress. Experimental methods include methods based on material physical properties, such as acoustic elasticity effect (ultrasonic method), magnetic permeability (magnetic measurement method), crystal plane spacing (XRD diffraction), and methods based on surface strain relief caused by different milling shapes (drilling, ring core, slit, center drilling, etc.). Among them, the physical method based on strain relief has become an indispensable test means in engineering due to its high cost performance. However, the material-related release coefficient matrix in this method is directly related to the resolution, and the new release coefficient matrix needs to be calibrated by finite element simulation after the working condition changes, and the method of calculating residual stress by matrix inversion will cause the results to be coupled, so it is difficult to accurately obtain the residual stress distribution of the component. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a residual stress distribution reconstruction method based on influence functions, which solves the technical problem of low measurement accuracy of the existing residual stress measurement method.

[0005] To achieve the above purpose, according to the first aspect of the present application, a residual stress distribution reconstruction method based on influence functions is provided, characterized by comprising:

[0006] S1, establishing a finite element model of a component to be measured, setting a thermal expansion coefficient to make the stress state of the finite element model introduced subsequently exhibit equi-biaxial characteristics; respectively introducing temperature distribution T A , T B along the hole depth direction to respectively introduce equi-biaxial eigenstrain distribution A, B along the hole depth direction, and respectively performing ring core milling simulation to obtain the surface strain of the component to be measured under the equi-biaxial eigenstrain distribution A, B; in the same way, the surface strain of the component to be measured under the non-equi-biaxial eigenstrain distribution is obtained in the same way;

[0007] S2, solving the influence function of the workpiece under the equal biaxial eigenstrain and the unequal biaxial eigenstrain according to the surface strain of the finite element model of the component to be measured wherein D is the inner hole diameter, h is the drilling depth, and z is the position coordinate of the eigenstrain along the depth direction;

[0008] S3, measuring the radial strain of the circumferential points in three directions spaced by 45 degrees in sequence, and solving the residual stress field of the component to be measured based on the influence function; wherein the circumference takes the ring core center as the center and the radius is r.

[0009] According to the second aspect of the present application, a residual stress distribution reconstruction system based on an influence function is provided, comprising: a computer readable storage medium and a processor;

[0010] The computer readable storage medium is used to store executable instructions;

[0011] The processor is used to read the executable instructions stored in the computer readable storage medium, and execute the method as described in the first aspect.

[0012] Overall, compared with the prior art, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0013] 1. The residual stress distribution reconstruction method based on the influence function provided by the present application reconstructs the residual stress distribution based on the eigenstrain to solve the influence function. Taking the ring core method as an example, first, the eigenstrain is taken as an invariant, and the quantitative constitutive relationship between the eigenstrain and the surface strain release is derived; then the specific expression of the influence function in the constitutive relationship is solved; finally, the method of residual stress inversion reconstruction by surface strain release and influence function is proposed, which has the advantages of wide application range, high precision, etc., and can overcome the shortcomings of the existing residual stress measurement method, and meet the demand of residual stress measurement under high stress gradient.

[0014] 2. The residual stress distribution reconstruction method based on the influence function provided by the present application derives the relationship between the eigenstrain and the surface strain release in the milling process, and reveals the physical process of the evolution of the influence function; the influence function of isotropic materials under two representative eigenstrain distributions (equal biaxial and unequal biaxial) is successfully solved by separating parameters, and a specific method of using the influence function for residual stress reconstruction is proposed based on the ring core method, including the discrimination of the principal direction.

[0015] 3. It is verified by experiment that the reconstruction result obtained by using the method provided by the present application is highly consistent with the experiment, the method provided by the present application realizes the prediction of the spatial residual stress distribution at the micron level, and has a micron-level resolution. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 A finite element numerical model diagram provided for an embodiment of the present application;

[0017] Figure 2 A diagram showing the change of three different applied eigenstrains with depth provided for an embodiment of the present application;

[0018] Figure 3 A diagram showing the surface strain release curve and influence function (area fraction of 80%) under different eigenstrains provided for an embodiment of the present application;

[0019] Figure 4 An influence function g H provided for an embodiment of the present application D , f H , f D and a main influence function F H (area fraction of 80%) diagram provided for an embodiment of the present application;

[0020] Figure 5 A diagram showing the reconstructed surface strain release curve and reconstruction result comparison under a parabolic type provided for an embodiment of the present application;

[0021] Figure 6 A diagram showing the reconstructed surface strain release according to the diffraction result using the influence function and the experimental measurement result comparison provided for an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and implementation cases. It should be understood that the specific implementation cases described herein are only used to explain the present application and are not used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0023] An influence function based residual stress distribution reconstruction method is provided in an embodiment of the present application, as shown in Figure 1 , which comprises:

[0024] S1, a finite element model of a to-be-measured component is established, and the stress state of the finite element model is made to have an equi-biaxial characteristic by setting a thermal expansion coefficient; temperature distributions T A , T B along the hole depth direction are respectively introduced to respectively introduce equi-biaxial eigenstrain distributions A and B along the hole depth direction, and ring core milling simulation is respectively performed to obtain the surface strain of the to-be-measured component under the equi-biaxial eigenstrain distributions A and B; in the same way, the surface strain of the to-be-measured component under a non-equi-biaxial eigenstrain distribution is obtained in the same way.

[0025] Specifically, a finite element model of the component to be tested is established, and the finite element model is made to have an equi-biaxial property by setting a thermal expansion coefficient; temperature distributions t(z1), t(z2), …, t(zn) along the hole depth direction are respectively introduced to introduce equi-biaxial eigenstrains along the hole depth direction A = t A (z1), t A (z2), …, t A (z N ) along the hole depth direction are respectively introduced to introduce equi-biaxial eigenstrains along the hole depth direction and a ring core milling simulation is performed to obtain surface strains of the component to be tested under the equi-biaxial eigenstrains Similarly, temperature distributions t(z1), t(z2), …, t(zn) along the hole depth direction are respectively introduced to introduce equi-biaxial eigenstrains along the hole depth direction B = t B (z1), t B (z2), …, t N (z A ) along the hole depth direction are respectively introduced to introduce equi-biaxial eigenstrains along the hole depth direction and a ring core milling simulation is performed to obtain surface strains of the component to be tested under the equi-biaxial eigenstrains

[0026] Similarly, the finite element model is made to have a non-equibiaxial property by setting a thermal expansion coefficient, temperature distributions t(z1), t(z2), …, t(zn) along the hole depth direction are respectively introduced to introduce non-equibiaxial eigenstrains along the hole depth direction A = t A (z1), t A (z2), …, t N (z B ) along the hole depth direction are respectively introduced to introduce non-equibiaxial eigenstrains along the hole depth direction and a ring core milling simulation is performed to obtain surface strains of the component to be tested under the non-equibiaxial eigenstrains Similarly, temperature distributions t(z1), t(z2), …, t(zn) along the hole depth direction are respectively introduced to introduce non-equibiaxial eigenstrains along the hole depth direction B = t B (z1), t B (z2), …, t B (z N ) along the hole depth direction are respectively introduced to introduce non-equibiaxial eigenstrains along the hole depth direction and a ring core milling simulation is performed to obtain surface strains of the component to be tested under the non-equibiaxial eigenstrains

[0027] S2, according to the surface strains of the component to be tested, the influence functions of the workpiece to be tested under equi-biaxial eigenstrains and non-equibiaxial eigenstrains are solved wherein D is an inner hole diameter, h is a drilling depth, and z is a position coordinate of the eigenstrain along the depth direction.

[0028] wherein The function is fitted to to obtain The function is fitted to to obtain;

[0029] wherein

[0030]

[0031]

[0032]

[0033]

[0034] L = A, B;

[0035] j≤n; n = 1, 2, …, N

[0036] is an equi-biaxial eigen-strain distribution A along the hole depth direction, is another equi-biaxial eigen-strain distribution B along the hole depth direction, is the surface strain of the measured member under the equi-biaxial eigen-strain distribution A, is the surface strain of the measured member under the equi-biaxial eigen-strain distribution B;

[0037] and The calculation method is the same.

[0038] According to Solve the influence function of the measured workpiece under the equi-biaxial eigen-strain Specifically:

[0039] (1) According to to obtain

[0040] (2) According to

[0041] to obtain fit it to obtain

[0042] (3) According to

[0043] and the formula to obtain and

[0044] (4) According to

[0045] and and formula The calculation obtains Fitting it obtains

[0046] Similarly, according to

[0047]

[0048] Solving the influence function of the workpiece to be measured under non-equal biaxial eigenstrain The related calculation formula is the same as that of solving the influence function The difference is that the subscript H in each formula is replaced by S.

[0049] S3, measuring the radial strain of three circumferential points in three directions spaced 45° in turn, and solving the residual stress field of the member to be measured based on the influence function; wherein the circumference takes the ring core center as the center and the radius is r.

[0050] Specifically, taking the ring core center as the center, a circle is drawn according to a preset radius, and the radial strain of three circumferential points on the circumference spaced 45° in turn is measured.

[0051] Preferably, the residual stress field of the member to be measured

[0052] wherein,

[0053]

[0054]

[0055]

[0056]

[0057] e x (h i / D),e 45° (h i / D),e y (h i / D) is the radial strain of three circumferential points in three directions spaced 45° in turn on the surface after the i-th drilling.

[0058] Preferably, the distribution along the hole depth direction includes but is not limited to different intrinsic strain distribution forms, such as constant, linear and parabolic.

[0059] Specifically, in step S1, the distribution form of the different intrinsic strain distribution along the hole depth direction is any two of constant, linear and parabolic. For example, in step S1, if the distribution form of the different intrinsic strain distribution along the hole depth direction is linear and parabolic, then the equal biaxial intrinsic strain distribution A and the unequal biaxial intrinsic strain distribution C are linear; the equal biaxial intrinsic strain distribution B and the unequal biaxial intrinsic strain distribution D are parabolic.

[0060] Preferably, in step S1, after the finite element model of the component to be measured is established, the Young's modulus and Poisson's ratio are input.

[0061] Preferably, the finite element method is used to simulate the drilling process.

[0062] The method provided by the application will be further described below.

[0063] 1, Constitutive relationship

[0064] The relationship between intrinsic strain and surface release strain, i.e. the constitutive relationship:

[0065]

[0066] In the process of building milling, the surface strain release curve under a certain area fraction can be obtained by measurement, i.e. the left end of the equation is obtained, and in the case of known influence function, the distribution of intrinsic strain inside the component can be easily obtained.

[0067] 2, Solution method of influence function

[0068] This section describes how to solve the influence function by finite element simulation and separation of parameters. In order to improve the application range of the method before solving, the equation is normalized:

[0069]

[0070] Where the influence function contains two variables h and z. Although the expression form of the influence function is unknown, according to Taylor expansion, the influence function can always be separated into the form of product of two single-variable polynomials:

[0071]

[0072] Therefore, the replaced strain-intrinsic strain equation can be obtained:

[0073]

[0074] Taking the derivative of the above equation with respect to (h / D) gives:

[0075]

[0076] After simplifying, we get:

[0077]

[0078] Observing the above equation, we can see that the I term only contains g, so we can consider eliminating the J term by some method to solve for I. Assuming a group of materials with the same geometric appearance, there are different known eigenstrain distributions A, B, which can be obtained by finite element simulation of the milling process to release the surface strain:

[0079]

[0080] Multiply both sides of the above equation by the corresponding known eigenstrain distribution, subtract and simplify to get:

[0081]

[0082] The right side of the above equation is a known quantity, so we can solve for it. Assuming:

[0083]

[0084] The expression for the influence function g can be obtained as:

[0085]

[0086] Let:

[0087]

[0088] where ε(h / D) can be understood as the processed strain function. Taking the derivative of equation (4) after transformation, we get the expression for f:

[0089]

[0090] After obtaining the influence functions g(h / D) and f(h / D), we can obtain the influence function F according to equation (3).

[0091] 3. Method of introducing eigenstrain

[0092] In the finite element method, thermal strain is introduced, and the thermal strain expression is:

[0093] ∈ th = ΔT·α (13)

[0094] Under the small strain assumption, the total strain is the sum of the elastic strain and the eigenstrain:

[0095] ∈tol = ∈ e + ∈ * (14)

[0096] Assuming that no plastic deformation occurs during the temperature change process, and the material is homogeneous, the intrinsic strain is only related to thermal strain:

[0097] = ∈ * = ∈ th (15)

[0098] According to the simulation and experimental research, if the specimen is thick enough during the temperature change process, the total strain is almost zero. If the model boundary condition is set to symmetric boundary condition, the elastic strain and intrinsic strain are only equivalent to sign conversion:

[0099] = ∈ e = ∈ tol - ∈ * ≈ - ∈ * (16)

[0100] After the local elastic strain is obtained, the residual stress field can be calculated according to Hooke's law by reconstructing the intrinsic strain inside the component.

[0101] 4、Residual stress field inverse solution process

[0102] In the milling process, the release of plane strain in three equidistant 45° directions during milling can be monitored, which are named e x (h i / D), e 45° (h i / D), and e y (h i / D), respectively. Since the actual process is carried out in sequence, in order to facilitate data processing, the model is discretized into k layers, and the measured component is milled k times. Assuming that the size and direction of intrinsic strain in each layer are consistent, the strain increment of each layer can be obtained as Δe x,i , Δe 45°,i , and Δe y,i . According to the strain rosette theory, the principal strain increment of each layer can be obtained as Δe 1,i and Δe 2,i :

[0103] (17)

[0104] Decomposing the principal strain increment, the equal biaxial strain increment Δe H,i and the non-equal biaxial strain increment Δe S,i can be obtained:

[0105]

[0106] The intrinsic strain of the ith layer is:

[0107]

[0108] Wherein:

[0109]

[0110] The relationship between the local intrinsic strain (i.e. the intrinsic strain of the ith layer) and the elastic strain is:

[0111]

[0112] The local principal elastic strain is obtained by combining the equi-biaxial strain and the non-equibiaxial strain:

[0113]

[0114] The local residual stress of the isotropic elastic material is:

[0115]

[0116] The method provided by the present application is described below with a specific example.

[0117] 1. Process of solving the influence function based on finite elements

[0118] In order to solve the influence function, a 3D finite element model is first constructed. Considering the symmetry of the geometry and the load, only a quarter of the model needs to be built. The finite element model is shown in Figure 1 The upper part is the measurement area, and the lower part is the substrate. Three known intrinsic strain distributions are introduced through thermal strain. In order to be representative, constants, linear, and parabolic are taken respectively. The in-plane equi-biaxial intrinsic strain distribution and the non-equibiaxial intrinsic strain distribution are simulated respectively, as shown in Figure 2

[0119] Then the removal process of the material is simulated by the birth and death elements, and the surface strain elimination curve is obtained by 100 equal-step increments of milling. At this time, the area fraction δ = 80% is taken to measure the strain release. Then, according to formulas (8) and (9), the influence functions m Hij ,m Sij are calculated by two-by-two combination, where i, j respectively indicate the intrinsic strain distribution used for calculation, i.e. the introduced constant, linear, and parabolic intrinsic strain. Since the calculation of the influence function m only needs two sets of intrinsic strain distribution, in order to verify the rationality of the method provided by the present application, three sets of intrinsic strain distribution A, B, and C are introduced here, and the influence functions are calculated by two-by-two combination.

[0120] It can be seen from the difference calculation result that consistency is possessed for different intrinsic strain distribution conditions, which also verifies the objective existence of the influence function m from the side in the foregoing analysis. H ,m D The surface strain release curve and the influence function m are shown in Figure 3

[0121] In the fitting process, since the influence function is calculated according to the difference, the calculation result near the surface will approach to infinity or even appear negative. In order to ensure the accuracy and continuity of the subsequent influence function solving, therefore, the segmented approximation processing is performed on the fitting result. Subsequently, the corresponding influence function g is solved by using the fitting result. H ,g D ,f H ,f D The main influence function F is solved finally. H ,F D The specific forms of the influence functions g, f and F are shown in Figure 4

[0122] 2, reconstruction method verification process

[0123] 2.1, experimental verification

[0124] The X-ray diffraction data are taken as the intrinsic strain, and the surface strain release curve is reconstructed by using the applicable influence function expression, as shown in Figure 5 The predicted value is highly consistent with the experiment, and can reach the micron level, and has extremely high spatial resolution.

[0125] 2.2, finite element reconstruction verification

[0126] It is assumed that the distribution of the intrinsic strain of the surface layer is a sine function that does not satisfy the compatibility equation. The distribution of the intrinsic strain is constant on the surface layer, and the distribution along the thickness is assumed, and the expression is as follows:

[0127]

[0128] By this method, the corresponding residual stress distribution can be introduced on the surface of the component, the surface strain release curve can be obtained by simulating the milling process by the finite element, and the accurate reconstruction can be performed by the method proposed in the application. The surface strain release curve and the reconstruction result are shown in Figure 6

[0129] The embodiment of the application provides a residual stress distribution reconstruction system based on an influence function, which comprises a computer readable storage medium and a processor.

[0130] ​​​The computer readable storage medium is configured to store executable instructions.

[0131] The processor is configured to read the executable instructions stored in the computer readable storage medium, and execute the method according to any one of the above embodiments.

[0132] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for reconstructing residual stress distribution based on influence functions, characterized in that, include: S1. Establish a finite element model of the component to be tested, and make the finite element model have iso-biaxial characteristics by setting the coefficient of thermal expansion. Temperature distribution along the depth of the hole is introduced separately. , To introduce an equibiaxial intrinsic strain distribution along the depth of the hole. A , B And perform ring core milling simulation respectively to obtain the equibiaxial intrinsic strain distribution. A, B The surface strain of the component under test is measured below. Similarly, the surface strain of the component under test is obtained under a non-uniform biaxial intrinsic strain distribution; S2, based on the surface strain of the component under test, solve for the influence function of the component under test under equibiaxial intrinsic strain and non-equibiaxial intrinsic strain. , ;in, D Inner diameter, h The drilling depth, z The position coordinates of the intrinsic strain along the depth direction; S3, Measure the radial strain at three circumferential points at 45° intervals in three directions, and solve the residual stress field of the component under test based on the influence function; wherein, the circumference is centered at the center of the ring core and has a radius of r; To The results were obtained through fitting. To The results were obtained through fitting. in, ； ； ； ; ， L = A,B ； N is a positive integer greater than 1; The equibiaxial intrinsic strain distribution along the depth of the hole A , The equibiaxial intrinsic strain distribution along the depth of the hole B , For the isobiaxial intrinsic strain distribution A The surface strain of the component to be measured is described below. For the isobiaxial intrinsic strain distribution B The surface strain of the component to be measured is described below; and The calculation method is the same.

2. The method as described in claim 1, characterized in that, The residual stress field of the component under test ; in, , ; ； ； ； ； Let be the radial strain at three circumferential points on the surface, spaced 45° apart, after the i-th drilling.

3. The method as described in claim 1, characterized in that, Importing different intrinsic strain distributions along the hole depth direction, including but not limited to those shown.

4. The method as described in claim 1, characterized in that, In step S1, after establishing the finite element model of the component to be tested, input Young's modulus and Poisson's ratio.

5. The method as described in claim 1, characterized in that, The drilling process was simulated using the finite element method, and the influence function was solved. The residual stress was then predicted by combining the actual drilling process measurement data.

6. A residual stress distribution reconstruction system based on an influence function, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-5.

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