A method for predicting the metal elastic-plastic constitutive behavior considering laser shock peening

Abstract

The application discloses a kind of prediction methods of metal elastoplastic constitutive behavior considering laser shock peening, for the metal material after laser shock peening, residual stress field, grain size distribution field are obtained, combined with elastoplastic theory, considering the flow stress of hot and non-thermal part, the metal elastoplastic constitutive model considering laser shock peening effect is established.At the same time, the residual stress field and microstructure change caused by laser shock peening are introduced into the finite element model, and the material parameters of the corrected metal elastoplastic constitutive model are obtained by finite element model simulation calculation, so as to comprehensively consider various influencing factors of laser shock peening on metal material, calculate the tensile yield curve under different residual stress field and grain size distribution field, so that the prediction accuracy of the mechanical behavior of metal material after laser shock peening is higher.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structural strength and finite element numerical simulation, and particularly relates to a prediction method of metal elastic-plastic constitutive behavior considering laser shock peening. BACKGROUND

[0002] Laser shock peening is a new surface modification technology that uses laser-induced plasma shock waves to improve the yield strength and fatigue life of metal materials. This technology has been widely used in aerospace and other fields. Laser shock can change the microstructure of the metal surface layer, refine the surface grains, accumulate dislocations, and form residual compressive stress in a relatively thick depth, which are the main reasons for the significant changes in the mechanical properties of the material after impact. Sanchez et al. "Effects of laser shock peening on the mechanisms of fatigue short crack initiation and propagation of AA7075-T651" and Lai, Wei Jen et al. "Effect of residual stress on fatigue strength of 316L stainless steel produced by laser powder bed fusion process" studied the effects of laser shock peening and residual stress on the mechanical properties and fatigue performance of materials. The experimental study of the effects of laser shock peening on macroscopic mechanical properties and fatigue performance has become increasingly rich. At the same time, numerical simulation has also made progress. Keller et al. "Experimental and numerical investigation of residual stresses in laser shock peened AA2198" carried out numerical simulation of residual stress after laser shock peening. In the study of residual stress generated by laser shock peening, the relatively mature simulation at this stage is realized by using the finite element software ABAQUS. Among them, the patent CN 114638130 A "A fatigue life prediction method considering the effect of laser shock peening" uses ABAQUS subprograms USDFLD and HARDINI to predict the fatigue life of the material after laser shock peening, but does not predict the macroscopic mechanical properties, and does not consider the effects of laser shock peening on the microstructure changes of the material.

[0003] Therefore, it is crucial to establish a metal elastic-plastic constitutive model considering the effects of residual stress, grain size and dislocation density changes generated by laser shock peening on the study of changes in the mechanical properties of metal materials and the guidance of safe service, and the related theoretical model still needs to be developed. SUMMARY

[0004] The purpose of the present application is to provide a prediction method of metal elastic-plastic constitutive behavior considering laser shock peening, which comprehensively considers the influence of residual stress and microstructure change caused by laser shock peening, so that the prediction accuracy of the constitutive behavior of metal materials after laser shock peening is higher.

[0005] Technical scheme: The present application provides a prediction method of metal elastic-plastic constitutive behavior considering laser shock peening, comprising the following steps:

[0006] Step 1: Perform laser shock peening test on the material, and obtain the residual stress field and grain size distribution field of the material along the laser shock direction for the material after laser shock peening;

[0007] Step 2: Fit the objective function of the residual stress in the residual stress field along the laser shock direction, and the objective function of the grain size in the grain size distribution field along the laser shock direction;

[0008] Step 3: Correct the flow stress of the material based on the residual stress field and the microstructure change caused by laser shock peening, and establish a corrected metal elastic-plastic constitutive model;

[0009] Step 4: According to the grain size of the material without laser shock peening and the tensile test curve, the tensile yield behavior of the material without laser shock peening is calculated by finite element model simulation, and the stress-strain experimental data of the material without laser shock peening is fitted to obtain the optimal material parameters, which are used as the material parameters in the corrected metal elastic-plastic constitutive model;

[0010] Step 5: Use the residual stress and grain size of step 2 and the material parameters in the corrected metal elastic-plastic constitutive model obtained in step 4, and based on the metal elastic-plastic constitutive model established in step 3, calculate the tensile yield curve of different residual stress field and grain size distribution field after laser shock peening, and simulate the tensile yield behavior of the material after laser shock peening.

[0011] Further, in step 2, the least square method is used for nonlinear fitting, and the fitting function form is y=a+btanh(cx+d).

[0012] Further, in step 3, the corrected metal elastic-plastic constitutive model of the material is established, in which the flow stress is divided into thermal part and non-thermal part:

[0013] σ y =σ a +σ t

[0014] Wherein σy is the flow stress, σ a represents the non-thermal part, i.e. characterizes the long-range potential barriers and the rate-independent interaction between dislocations, σ t represents the thermal part, i.e. characterizes the short-range rate-dependent interaction, the total expression being:

[0015]

[0016] where σ0is the reference friction stress, d is the grain size, ρ is the dislocation density, k h , k ρ , β are material constants; the thermal part with the correction term is expressed as:

[0017]

[0018] σ t is the increment of the flow stress with respect to plastic strain, the empirical formula being as above, θ0is the hardening constant, α represents the linear variation of the strain hardening rate with respect to stress, the first term in brackets on the right is the correction term of the increment, ε P is the equivalent plastic strain, ε p0 is the reference equivalent plastic strain, where X is expressed as:

[0019]

[0020] where σ t0 is the stress at zero strain hardening rate.

[0021] Further, in step 4, without considering the effect of laser shock peening, there is no residual stress and the grain size is constant, the uniaxial tensile mechanical behavior of the material is calculated, and the tensile stress-strain data of the material without laser shock peening is fitted to determine the material parameters σ0, k h , k ρ , β.

[0022] Further, in step 5, the material parameters in the corrected metal elastic-plastic constitutive model, as well as the residual stress objective function and the crystal size objective function, are introduced into the input file together, and the uniaxial tensile mechanical behavior of the material after laser shock peening is calculated. When the material after laser shock peening is loaded, the residual stress is regarded as the initial stress, the initial stress σ initial = Eε eigen , ε eigen is the intrinsic strain, and E is the elastic modulus.

[0023] Beneficial effects: Compared with the prior art, the present application has the remarkable feature that a metal elastoplastic constitutive model considering the effect of laser shock peening is established by combining elastoplastic theory and considering thermal and non-thermal part flow stress. For the material after laser shock peening, the residual stress field and the grain size distribution field are obtained, the material parameters of the corrected metal elastoplastic constitutive model are obtained through finite element simulation calculation, so as to comprehensively consider various influencing factors on the material after laser shock peening, calculate the tensile yield curve under different residual stress fields and grain size distribution fields, and make the prediction accuracy of the macroscopic mechanical behavior of the laser shock peened material higher. The constitutive model is simple and effective, the model parameters are less, and it is beneficial to popularize the calculation of the mechanical behavior change of different metal materials after laser shock peening. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 is a flowchart of the present application;

[0025] Figure 2 is a distribution function of the average grain size and a fitting graph thereof in the present application;

[0026] Figure 3 is a distribution function of the residual stress field and a fitting graph thereof in the present application;

[0027] Figure 4 is a tensile stress-strain curve graph of TC4 without laser shock peening under different grain sizes;

[0028] Figure 5 is a tensile stress-strain curve graph of TC4 before and after laser shock peening when the grain size is 5 microns in the present application;

[0029] Figure 6 is a schematic diagram of the change of the yield stress along the depth under different tensile strains in the present application. DETAILED DESCRIPTION

[0030] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0031] Embodiment 1

[0032] This embodiment provides a prediction method of metal elastoplastic constitutive behavior considering laser shock peening, please refer to Figure 1 as shown, comprising the following steps:

[0033] Step 1: Perform laser shock peening test on the material, and obtain the residual stress field and the grain size distribution field of the material along the laser shock direction for the material after laser shock peening.

[0034] The residual stress field and the average grain size distribution of TC4 after laser shock peening are obtained, the residual stress field can be obtained by X-ray diffraction method, and the residual stress direction is the tensile direction; the grain size distribution field along the laser shock direction is also obtained by X-ray diffraction method.

[0035] Step 2: The residual stress in the residual stress field and the grain size in the grain size distribution field are fitted as the objective function along the laser shock direction.

[0036] The least square method is used for nonlinear fitting, and the fitting function form is y=a+btanh(cx+d).

[0037] Please refer to Figure 2 As shown in the figure, the fitting function of the average grain size along the laser shock direction after laser shock peening is d=2.9+2.3*tanh(0.022(x-66.3))μm, and x is the laser shock peening depth, that is, the vertical distance from the laser shock surface to the position.

[0038] Please refer to Figure 3 As shown in the figure, the fitting function of the residual stress along the laser shock direction after laser shock peening is σ res =-420+666.9*tanh(0.005(x-30.1))MPa.

[0039] Step 3: Based on the residual stress field and microstructure changes caused by laser shock peening, the flow stress of the material is corrected, and the corrected metal elastic-plastic constitutive model is established.

[0040] In this embodiment, TC4 is taken as the material, and the corrected metal elastic-plastic constitutive model is established, in which the flow stress is divided into thermal part and non-thermal part:

[0041] σ y =σ a +σ t

[0042] Where σ y is the flow stress, σ a represents the non-thermal part, that is, the rate-independent interaction between long-range potential barrier and dislocation, and σ t represents the thermal part, that is, the rate-dependent interaction of short-range potential barrier, and the total expression is:

[0043]

[0044] Where σ0 is the reference friction resistance, d is the grain size, ρ is the dislocation density, k h , k ρ , and β are all material constants; the thermal part with correction term is expressed as:

[0045]

[0046] σ t The increment and plastic strain are expressed as the above empirical formula, θ0 is the hardening constant, α represents the linear change of strain hardening rate with stress, the first term in the right bracket is the added correction term, ε P is the equivalent plastic strain, ε p0 is the reference equivalent plastic strain, where X is expressed as:

[0047]

[0048] where σ t0 is the stress at zero strain hardening rate.

[0049] Step 4: Based on the grain size and tensile test curve of the material that has not undergone laser shock strengthening, the tensile yield behavior of the material that has not undergone laser shock strengthening is calculated through finite element model simulation, and the stress-strain experimental data of the material that has not undergone laser shock strengthening are fitted to obtain the optimal material parameters. The optimal material parameters are used as the material parameters in the modified metal elastic-plastic constitutive model.

[0050] Without considering the laser shock strengthening effect, there is no residual stress, the grain size is constant, the uniaxial tensile mechanical behavior of the material is calculated, and the tensile stress and strain data of the material before laser shock strengthening in the experiment are fitted to determine the material parameters σ0, k h 、k ρ , β.

[0051] When calculating the mechanical properties of materials after laser shock processing, the fitted grain size distribution is written into the input file in the form of a function; the residual stress is introduced into the finite element model as the initial stress through the intrinsic strain, and σ is set. initial =σ res .

[0052] See also Figure 4 As shown in the figure, the optimal material parameters are obtained by directly fitting the experimental data before laser shock peening using the least squares method. Figure 4 As shown in Figure 1, the effect of grain size on yield behavior before laser shock processing is as follows: the smaller the grain size, the finer the grain strengthening will be due to the Hall-Petch effect, leading to an increase in yield strength. At the same time, the experimental results are completely consistent with the simulation results. The optimal material parameters are shown in Table 1.

[0053] Table 1

[0054]

[0055]

[0056] Step 5: Based on the residual stress and grain size of step 2 and the material parameters in the modified metal plastic constitutive model of step 4, the tensile yield curve of different residual stress field and grain size distribution field after laser shock peening is calculated, and the tensile yield behavior of the material after laser shock peening is simulated based on the metal plastic constitutive model established in step 3.

[0057] Please refer to Figure 5 The material parameters in the modified metal plastic constitutive model, the residual stress target function and the crystal size target function are imported into the input file as shown in the figure, and the uniaxial tensile mechanical behavior of the material after laser shock peening is calculated. When loading the material after laser shock peening, a uniaxial tensile strain of 10% is applied to the material. Laser shock peening will cause obvious early yield phenomenon and increase of yield stress, which is caused by fine grain strengthening and residual stress caused by laser shock peening.

[0058] Please refer to Figure 6 As shown in the figure, the distribution of Mises equivalent stress at different depths under different tensile strains. With the increase of tensile strain, the negative Mises equivalent stress on the surface becomes positive stress.

Claims

1. A method for predicting the elastoplastic constitutive behavior of a metal taking into account laser shock peening, characterized in that, Comprising the following steps: Step 1: laser shock peening test is performed on the metal material, and for the material after laser shock peening, the residual stress field and the grain size distribution field of the material along the laser shock direction are obtained; Step 2: a target function of the residual stress in the residual stress field along the laser shock direction and a target function of the grain size in the grain size distribution field along the laser shock direction are fitted; Step 3: the flow stress of the material is corrected based on the residual stress field and the microstructure changes caused by laser shock peening, and a corrected metal elastic-plastic constitutive model is established; wherein the flow stress is divided into a thermal part and a non-thermal part: σ y = σ a + σ t where σ y is the flow stress, σ a represents the non-thermal part, characterizing the rate-independent interaction between long-range barriers and dislocations, σ t represents the thermal part, i.e. characterizing the rate-dependent interaction with short-range barriers, the total expression being: where σ0is the reference frictional resistance, d is the grain size, p is the dislocation density, k h , k ρ , β are material constants; the thermal part with the correction term is represented as: σ t The increment of plastic strain is expressed by the above empirical formula, θ0 is a hardening constant, α represents a linear change in strain hardening rate with stress, the first term in the right-hand bracket is a correction term for the increment, ε P is the equivalent plastic strain, and ε p0 is a reference equivalent plastic strain, where X is expressed as: where σ t0 is the stress at zero strain hardening rate; Step 4: according to the grain size of the metal not subjected to laser shock peening and the tensile test curve, the tensile yield behavior of the material not subjected to laser shock peening is calculated by finite element model simulation, and the stress-strain experimental data of the material not subjected to laser shock peening is fitted to obtain optimal material parameters, which are used as material parameters in the corrected metal elastic-plastic constitutive model; Step 5: the residual stress and grain size of step 2 and the material parameters in the corrected metal elastic-plastic constitutive model obtained in step 4 are used to calculate the tensile yield curve of different residual stress fields and grain size distribution fields after laser shock peening based on the metal elastic-plastic constitutive model established in step 3, so as to simulate the tensile yield behavior of the material after laser shock peening.

2. The method for predicting the metal elastoplastic constitutive behavior taking into account the laser shock peening according to claim 1, characterized in that, In step 2, the least square method is used for nonlinear fitting, and the fitting function form is y=a+btanh(cx+d), wherein a, b, c, and d are constants, x is the laser shock peening depth, and y is the target function of the residual stress or the grain size.

3. The method for predicting the elastic-plastic constitutive behavior of metals considering laser shock processing according to claim 1, characterized in that: In Step 4, without considering the laser shock peening effect, the residual stress is not considered, the grain size is constant, the uniaxial tensile mechanical behavior of the material is calculated, and the tensile stress-strain data of the material without laser shock peening is fitted to determine the material parameters σ0, k h , β. ρ , β.

4. The method of prediction of metal elastoplastic constitutive behavior considering laser shock peening according to claim 1, characterized in that, In step 5, the material parameters in the modified metal elastic-plastic constitutive model, the residual stress objective function, and the crystal size objective function are collectively imported into an input file, and the uniaxial tensile mechanical behavior of the material after laser shock peening is calculated. When loading the material after laser shock peening, the residual stress is regarded as an initial stress, and the initial stress σ initial = Eε eigen , ε eigen is the intrinsic strain, and E is the elastic modulus.

5. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the method of any one of claims 1 to 4.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method of any one of claims 1 to 4.

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