A coupled-damage cyclic viscoplastic constitutive model and its construction method

Abstract

The present invention discloses a cyclic viscoplastic constitutive model with coupled damage, combining viscoplastic flow laws, kinematic hardening, isotropic hardening, and damage variable evolution. Based on continuous damage mechanics, the damage variable is combined with the constitutive model to accurately simulate the cyclic deformation behavior of the entire life cycle, with high-precision life prediction capabilities. The present invention conducts strain-controlled low-cycle fatigue tests and tensile load-holding creep fatigue tests to obtain the test data required to construct the cyclic viscoplastic constitutive model, and uses a genetic algorithm to obtain a set of optimal model parameters, which can predict the cyclic deformation behavior and fatigue failure life under various cyclic loading waveforms, such as different strain amplitudes, different strain frequencies, and different load-holding times. The constitutive model ultimately obtained by the present invention has high accuracy, strong universality, and life prediction capabilities.

Description

Technical Field

[0001] The present invention relates to the technical field of material constitutive models, in particular to a coupled-damage cyclic viscoplastic constitutive model and a construction method thereof. Background Art

[0002] Critical high-temperature components in fields such as petrochemicals, power generation, and aerospace are often subjected to complex cyclic loading. Fatigue design and accurate life prediction for these high-temperature components often rely on the cyclic stress-strain response of the material. With the rapid advancement of computer technology, the use of viscoplastic constitutive models for inelastic fatigue design and life assessment of high-temperature components is becoming increasingly popular. An ideal cyclic constitutive model must accurately simulate the inelastic deformation behavior of high-temperature components under various cyclic loading conditions, such as nonlinear kinematic strengthening, cyclic hardening, stress relaxation, and strain range and time dependence.

[0003] Certain materials (such as the nickel-based superalloy Inconel 625) may undergo microstructural evolution or dynamic strain aging during high-temperature cyclic loading, resulting in negative strain rate sensitivity. However, existing cyclic viscoplastic constitutive models cannot accurately simulate this negative strain rate sensitivity. Furthermore, the accumulation of fatigue damage during cyclic loading is a factor that must be considered in fatigue design. Microdefects caused by material damage can lead to a decrease in material stiffness, thereby affecting the stress-strain response. For example, under cyclic loading with large strain amplitudes, the material's elastic modulus gradually decreases with the number of cycles. Therefore, constitutive models that ignore damage accumulation have certain limitations in simulation accuracy and physical significance. Summary of the Invention

[0004] In order to overcome the above-mentioned defects in the prior art, the present invention provides a cyclic viscoplastic constitutive model of coupled damage, which has high accuracy, strong universality, and life prediction capability.

[0005] To achieve the above object, the present invention adopts the following technical solutions, including:

[0006] A coupled-damage cyclic viscoplastic constitutive model is used to predict the cyclic deformation behavior and failure life of materials under different loading parameters, including strain amplitude, strain rate, and holding time.

[0007] The construction of the constitutive model is as follows:

[0008] The total strain rate tensor Decomposed into elastic strain rate tensor and the inelastic strain rate tensor

[0009]

[0010] Among them, i, j = 1, 2, 3, representing the three axes of the spatial coordinates;

[0011] elastic strain rate tensor and the stress rate tensor Following Hooke's law, the elastic strain rate tensor after coupling damage is The expression is:

[0012]

[0013] Where E and μ are elastic modulus and Poisson's ratio respectively, D is the damage variable, and δ ij is the identity matrix, is the stress component rate tensor;

[0014] Using viscoplastic flow laws to describe the viscoplastic or inelastic strain rate tensor and the stress tensor σ ij The corresponding relationship between the inelastic strain rate tensor after coupling damage The expression is:

[0015]

[0016]

[0017] Where, χ ij is the back stress tensor, representing kinematic hardening; R is the drag stress, representing isotropic hardening; s ij and a ij are the deviatoric stress tensors of stress and back stress, k0 is the initial yield stress, K, A and n are viscosity-related model parameters, J represents the second invariant of the effective stress deviator, σ ij is the stress tensor;

[0018] Back stress tensor χ ij It consists of three nonlinear back stress components described by the kinematic hardening rule,

[0019]

[0020] Where, is the kth back stress component tensor;

[0021] The kinematic hardening rate equation is:

[0022]

[0023]

[0024]

[0025]

[0026] The three terms on the right side of formula (6) are strain hardening term, dynamic recovery term and static recovery term respectively;

[0027] Where, is the kth back stress component velocity tensor; C k is the kth plastic modulus, γ k is the kth dynamic recovery coefficient, b is the static recovery coefficient, r is the static recovery index, is the average stress of the kth back stress component, is the evolution rate of the average stress of the kth back stress component, Y s is the average stress saturation value, b Y is the average stress rate coefficient, is the cumulative inelastic strain rate;

[0028] The cyclic hardening of back stress is achieved by the evolution of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3 with the accumulated inelastic strain p. The evolution equation is:

[0029] γ1=γ 1o (1-γ 1s (1-exp(-D1p))) (10)

[0030] C2=C 2o (1+C 2s (1-exp(-D2p))) (11)

[0031] C3=C 3o (1+C 3s (1-exp(-D3p))) (12)

[0032] Where, γ 1o 、C 2o 、C 3o They represent the initial values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3, γ 1s 、C 2s and C 3s They represent the evolution saturation values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2, and the third plastic modulus C3, respectively. D1, D2, and D3 are parameters that control the evolution rate;

[0033] Back stress-strain range correlation is obtained through γ 1s 、C 2s It is realized by the relationship with the maximum inelastic strain amplitude q:

[0034] γ 1s=a1+b1(1-exp(-c1q)) (13)

[0035] C 2s =a2+b2(1-exp(-c2q)) (14)

[0036] Where a1, b1, c1, a2, b2 and c2 are model parameters related to the back stress and strain range;

[0037] The isotropic hardening rate equation is:

[0038]

[0039] The first two terms on the right side of formula (18) are nonlinear isotropic hardening components, and the third term is the linear isotropic hardening component;

[0040] Where, is the drag stress rate, i.e., the isotropic hardening rate, Q1 and Q2 are the saturation values ​​of the two nonlinear isotropic hardening components, b R1 and b R2 are the rate parameters of the two nonlinear isotropic hardening components, and H is the linear hardening slope;

[0041] The drag stress-strain range correlation is realized by the relationship between Q1, H and the maximum inelastic strain range q:

[0042] Q1=a4+b4(1-exp(-c4q)) (19)

[0043] H=a5+b5(1-exp(-c5q)) (20)

[0044] Where a4, b4, c4, a5, b5 and c5 are model parameters related to the drag stress-strain range;

[0045] The damage variable evolution equation is:

[0046]

[0047]

[0048] Where, is the damage rate; R μ is the triaxial stress correction coefficient, σ eq is the Mises equivalent stress, σ H is the hydrostatic stress, S1, S2, g, h1, h2 and h3 are model parameters related to damage evolution; W t is the cumulative total strain energy density; N is the number of cyclic loading;

[0049] W tα N (1-α) f c -β ≥W f As the crack initiation criterion, the average total strain energy density W t / N I As a parameter, add the cycle frequency f c Correction, establish the cumulative total strain energy density W t and crack initiation life N I The relationship between:

[0050]

[0051]

[0052] Where α, β and W f are model parameters related to crack initiation criterion, H(σ ij ) is a step function, when σ ij >0, H(σ ij )=1, when σ ij ≤0, H(σ ij )=0;

[0053] According to the tensile elastic modulus at fatigue failure, the critical fatigue damage D under each strain amplitude is estimated. c , establish the strain amplitude-dependent failure criterion:

[0054] D c =a c -b c (1-exp(c c ·Δε / 2)) (26)

[0055] Where a c 、b c and c c are all model parameters related to critical fatigue damage, and Δε is the total strain range.

[0056] Preferably, the time correlation of the constitutive model includes: the time correlation of the initial tensile loading stage and the time correlation of cyclic hardening; wherein the time correlation of cyclic hardening includes: the time correlation of cyclic kinematic hardening and / or the time correlation of cyclic isotropic hardening;

[0057] Through the viscosity parameter K and strain rate The relationship between and realizes the time dependence of the initial tensile loading stage:

[0058]

[0059] Where K0 is the initial value of the viscosity parameter K, P1, P2 and m are all model parameters related to strain rate, is the strain rate;

[0060] By C 3s With the equivalent frequency f e The relationship between the time dependence of cyclic motion hardening is realized as follows:

[0061]

[0062]

[0063] Where Δε is the total strain range, t h is the load holding time, a3, b3 and c3 are the model parameters of the cyclic motion hardening response time;

[0064] Through Q2 and the equivalent frequency f e The relationship between the time dependence of cyclic isotropic hardening is achieved:

[0065]

[0066] Where a6 and b6 are model parameters related to the cyclic isotropic hardening response time.

[0067] The present invention also provides a method for constructing a coupled-damage cyclic viscoplastic constitutive model, which is characterized by comprising the following steps:

[0068] S1. Conduct strain-controlled low-cycle fatigue tests and creep fatigue tests under tensile loading at constant temperature to obtain the test data required for constructing a cyclic viscoplastic constitutive model, including stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from low-cycle fatigue tests; stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from creep fatigue tests, stress relaxation data, and mean stress data.

[0069] S2, based on the experimental data, combined with the genetic optimization algorithm to obtain the various model parameters in the cyclic viscoplastic constitutive model, and finally determine a set of optimal model parameters.

[0070] Preferably, the specific process of step S2 is as follows:

[0071] S21, based on the stress relaxation data during the creep fatigue test during the tensile load holding period, the viscous stress σ is estimated v , using the test data at the maximum strain rate, according to the viscosity equation Preliminary estimation of viscosity-related model parameters A, K0, and n;

[0072] Assuming that no cyclic hardening and fatigue damage occur during the initial tensile loading, the elastic parameters, namely the initial elastic modulus E0 and the initial yield stress k0, are obtained using the linear regression method based on the initial tensile stress-strain hysteresis loop;

[0073] According to ε in =ε–σ / E0 to calculate the inelastic strain ε in , establish (σ–σ v –k0) and ε in The corresponding relationship is used to estimate the model parameters C related to kinematic hardening. 1o 、C 2o 、C 3o , γ 1o , γ 2o and γ 3o ;ε is the total strain, σ is the stress;

[0074] The model parameters C related to kinematic hardening are analyzed by genetic algorithm. 1o 、C 2o 、C 3o , γ 1o , γ 2o , γ 3o Optimize

[0075] S22, based on the initial tensile stress-strain hysteresis loops of low-cycle fatigue tests at different strain amplitudes, the strain rate-related model parameters P1, P2, and m2 were optimized using a genetic algorithm;

[0076] S23, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the γ corresponding to each strain amplitude. 1s 、C 2s and C 3s , then the model parameters a1, b1, c1, a2, b2 and c2 related to the back stress and strain range are obtained by formulas (13) and (14), and the model parameters a3, b3 and c3 related to the cyclic motion hardening response time are estimated by formulas (16) and (17); then the genetic algorithm is used to optimize the model parameters a1, b1, c1, a2, b2, c2 related to the back stress and strain range and the model parameters a3, b3, c3 related to the cyclic motion hardening response time;

[0077] S24, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the Q1, Q2, H, and b corresponding to each strain amplitude. R1 and b R2, then the model parameters a4, b4, c4, a5, b5 and c5 related to the drag force strain range are obtained by formulas (19) and (20), and the model parameters a6 and b6 related to the cyclic isotropic hardening response time are obtained by formula (21); then the genetic algorithm is used to optimize the model parameters a4, b4, c4, a5, b5, c5 related to the drag force strain range and the model parameters a6 and b6 related to the cyclic isotropic hardening response time;

[0078] S25, based on the experimental data of creep fatigue test, including stress-strain hysteresis loop, cyclic stress amplitude evolution data, stress relaxation data, and mean stress data, a genetic algorithm is used to obtain the static recovery related model parameters b and r, as well as the mean stress evolution related model parameter Y s and b Y ;

[0079] At this point, the constitutive model ignoring fatigue damage is obtained;

[0080] S26, calculate the cumulative total strain energy density W at crack initiation using the above constitutive model ignoring fatigue damage t According to formula (24), the model parameters α, β and W related to the crack initiation criterion are obtained f ;

[0081] S27, when identifying the model parameters related to damage evolution, multiple groups of low-cycle fatigue tests and multiple groups of creep fatigue tests are carried out under different loading parameters. The loading parameters of the low-cycle fatigue test include strain amplitude and strain rate, and the loading parameters of the creep fatigue test include strain amplitude, strain rate and holding time. First, the model parameters S1, S2 and g of each group of tests are determined separately, and then the maximum inelastic strain amplitude q and cycle frequency f are used to determine the damage evolution model parameters. c The initial values ​​of the damage evolution-related model parameters S1, S2, g, h1, h2 and h3 are obtained by correction, and the genetic algorithm is used to optimize the damage evolution-related model parameters S1, S2, g, h1, h2, h3; finally, according to the damage value at fatigue failure under different strain amplitudes, the nonlinear regression method is used to fit formula (26) to obtain the critical fatigue damage-related model parameter a c 、b c and c c ;

[0082] S28, further optimizing all model parameters using a genetic algorithm to obtain a set of optimal model parameters.

[0083] Preferably, in step S1, the low cycle fatigue test involves at least three different strain amplitudes and at least three different strain rates.

[0084] Preferably, 1 / 4 cycle stretching is selected as the initial stretching load.

[0085] Preferably, in step 27, the model parameters S1, S2 and g are determined as follows:

[0086] Before crack initiation, the damage variable D is linearly related to the inelastic deformation p, and the slope k is obtained by numerical method. D =dD / dp;

[0087] The model parameter S1 is calculated by formula (27):

[0088]

[0089] Where σ aI and D I are the stress amplitude and cumulative damage at crack initiation, respectively;

[0090] The model parameters S2 and g are calculated by formula (28):

[0091]

[0092] Where N I and N f are the crack initiation life and failure life, and N I and N f Stress amplitude and inelastic strain amplitude of the intermediate life hysteresis loop.

[0093] The advantages of the present invention are:

[0094] (1) The constitutive model of the present invention combines viscoplastic flow laws, kinematic hardening, isotropic hardening, and damage variable evolution, and has high prediction accuracy and strong universality. It can predict cyclic deformation behavior and has life prediction capabilities.

[0095] (2) Based on continuous damage mechanics, the present invention combines damage variables with constitutive models, which can accurately simulate the cyclic deformation behavior of the entire life cycle and has a high-precision life prediction capability.

[0096] (3) The constitutive model constructed by the present invention using a set of optimal model parameters can accurately predict the cyclic deformation behavior and fatigue failure life under various cyclic loading waveforms, such as different strain amplitudes, different strain frequencies, and different holding times.

[0097] (4) Since the cyclic hardening of some materials is manifested as the change of drag stress with the number of cyclic loading, that is, isotropic hardening; some materials also show the cyclic evolution of back stress, which is usually achieved by the evolution of plastic modulus and / or dynamic recovery coefficient with accumulated plastic strain; in order to enhance the universality of the constitutive model, the present invention takes into account the cyclic evolution of drag stress and back stress at the same time, and which method to use can be determined based on material test data.

[0098] (5) The present invention can simulate the behavior of the elastic modulus gradually decreasing with cyclic loading, thereby greatly improving the simulation accuracy of the hysteresis loop.

[0099] (6) The crack initiation criterion proposed in this invention can accurately predict the crack initiation life.

[0100] (7) The segmented damage evolution equation proposed in this invention can accurately predict fatigue damage accumulation and fatigue failure life. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 The figure is a flow chart of constitutive model construction and prediction in an embodiment of the present invention.

[0102] Figure 2 These are the predicted results of the stress-strain hysteresis loops of the low-cycle fatigue test at different strain amplitudes in the embodiment of the present invention: 2a corresponds to a strain amplitude of 0.25%, 2b corresponds to a strain amplitude of 0.4%, and 2c corresponds to a strain amplitude of 0.5%.

[0103] Figure 3 These are the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue tests with different strain amplitudes in the embodiments of the present invention. 3a corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue test with a strain amplitude of 0.25%, 3b corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue test with a strain amplitude of 0.4%, and 3c corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue test with a strain amplitude of 0.5%.

[0104] Figure 4 These are the predicted results of the cyclic stress amplitude of the low-cycle fatigue test at different strain rates in the embodiment of the present invention.

[0105] Figure 5 5a is the predicted result of the creep fatigue test in the embodiment of the present invention: 5b is the half-life cyclic stress relaxation, and 5c is the cyclic stress response.

[0106] Figure 6 This is the life prediction result of the viscoplastic constitutive model with coupled damage in an embodiment of the present invention. DETAILED DESCRIPTION

[0107] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0108] A coupled damage cyclic viscoplastic constitutive model of the present invention, wherein the input of the constitutive model is total strain and the output is stress;

[0109] The construction of the constitutive model is as follows:

[0110] The total strain rate tensor Decomposed into elastic strain rate tensor and the inelastic strain rate tensor

[0111]

[0112] Among them, i, j = 1, 2, 3, representing the three axes of the spatial coordinates;

[0113] elastic strain rate tensor and the stress rate tensor Following Hooke's law, the elastic strain rate tensor after coupling damage is The expression is:

[0114]

[0115] Where E and μ are elastic modulus and Poisson's ratio respectively, D is the damage variable, and δ ij is the identity matrix, is the stress component rate tensor; E=E0(1-D); E0 is the initial elastic modulus;

[0116] Using viscoplastic flow laws to describe the viscoplastic or inelastic strain rate tensor and the stress tensor σ ij The corresponding relationship between the viscoplastic flow law uses the exponential equation modified by hyperbolic sine, and the inelastic strain rate tensor after coupling damage The expression is:

[0117]

[0118]

[0119] Where, χ ij is the back stress tensor, representing kinematic hardening; R is the drag stress, representing isotropic hardening; s ij and a ijare the deviatoric stress tensors of stress and back stress, k0 is the initial yield stress, K, A and n are viscosity-related model parameters, J represents the second invariant of the effective stress deviator, σ ij is the stress tensor;

[0120] In order to characterize the short-range, medium-range, and long-range interactions between grains or between dislocations and precipitates during plastic deformation, the back stress χ ij It consists of three nonlinear back stress components described by the nonlinear kinematic hardening rule.

[0121]

[0122] Where, is the kth back stress component tensor;

[0123] The kinematic hardening rate equation is:

[0124]

[0125]

[0126]

[0127]

[0128] The three terms on the right side of formula (6) are strain hardening term, dynamic recovery term and static recovery term respectively;

[0129] Where, is the kth back stress component velocity tensor; C k is the kth plastic modulus, γ k is the kth dynamic recovery coefficient, b is the static recovery coefficient, r is the static recovery index, is the average stress of the kth back stress component, is the evolution rate of the average stress of the kth back stress component, Y s is the average stress saturation value, b Y is the average stress rate coefficient, is the cumulative inelastic strain rate;

[0130] The cyclic hardening of back stress is achieved by the evolution of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3 with the accumulated inelastic deformation p. The evolution equation is:

[0131] γ1=γ 1o (1-γ 1s (1-exp(-D1p))) (10)

[0132] C2=C 2o (1+C2s (1-exp(-D2p))) (11)

[0133] C3=C 3o (1+C 3s (1-exp(-D3p))) (12)

[0134] Where, γ 1o 、C 2o 、C 3o They represent the initial values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3, γ 1s 、C 2s and C 3s They represent the evolution saturation values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2, and the third plastic modulus C3, respectively. D1, D2, and D3 are parameters that control the evolution rate;

[0135] Back stress-strain range correlation is obtained through γ 1s 、C 2s It is realized by the relationship with the maximum inelastic strain amplitude q:

[0136] γ 1s =a1+b1(1-exp(-c1q)) (13)

[0137] C 2s =a2+b2(1-exp(-c2q)) (14)

[0138] Where a1, b1, c1, a2, b2 and c2 are model parameters related to the back stress and strain range;

[0139] The time dependence of the constitutive model includes: the time dependence of the initial tensile loading stage and the time dependence of cyclic hardening; wherein the time dependence of cyclic hardening includes: the time dependence of cyclic kinematic hardening and / or the time dependence of cyclic isotropic hardening;

[0140] Among them, the viscosity parameter K and the strain rate The relationship between and realizes the time dependence of the initial tensile loading stage:

[0141]

[0142] Where K0 is the initial value of the viscosity parameter K, P1, P2 and m are all model parameters related to strain rate, is the strain rate;

[0143] By C 3s With the equivalent frequency f e The relationship between the time dependence of cyclic motion hardening is realized as follows:

[0144]

[0145]

[0146] Where Δε is the total strain range, t h is the load holding time, a3, b3 and c3 are the model parameters of the cyclic motion hardening response time;

[0147] The isotropic hardening rate equation is:

[0148]

[0149] The first two terms on the right side of formula (18) are nonlinear isotropic hardening components, and the third term is the linear isotropic hardening component;

[0150] Where, is the drag stress rate, i.e., the isotropic hardening rate, Q1 and Q2 are the saturation values ​​of the two nonlinear isotropic hardening components, b R1 and b R2 are the rate parameters of the two nonlinear isotropic hardening components, and H is the linear hardening slope;

[0151] The drag stress-strain range correlation is realized by the relationship between Q1, H and the maximum inelastic strain range q:

[0152] Q1=a4+b4(1-exp(-c4q)) (19)

[0153] H=a5+b5(1-exp(-c5q)) (20)

[0154] Where a4, b4, c5, a5, b5 and c5 are model parameters related to the drag stress-strain range;

[0155] Through Q2 and the equivalent frequency f e The relationship between the time dependence of cyclic isotropic hardening is achieved:

[0156]

[0157] Where a6 and b6 are model parameters related to the cyclic isotropic hardening response time.

[0158] Equivalent frequency f e Calculated by formula (17);

[0159] The damage variable evolution equation is:

[0160]

[0161]

[0162] Where R μ is the triaxial stress correction coefficient, σ eq is the Mises equivalent stress, σ H is the hydrostatic stress, S1, S2, g, h1, h2 and h3 are model parameters related to damage evolution; W t is the cumulative total strain energy density; N is the number of cyclic loading; is the damage rate;

[0163] W t α N (1-α) f c -β ≥W f As the crack initiation criterion, the average total strain energy density W t / N I As a parameter, add the cycle frequency f c Correction, establish the cumulative total strain energy density W t and crack initiation life N I The relationship between:

[0164]

[0165]

[0166] Where α, β and W f are model parameters related to crack initiation criterion, H(σ ij ) is a step function, when σ ij >0, H(σ ij )=1, when σ ij ≤0, H(σ ij )=0;

[0167] According to the tensile elastic modulus at fatigue failure, the critical fatigue damage D under each strain amplitude is estimated. c , establish the strain amplitude-dependent failure criterion:

[0168] D c =a c -b c (1-exp(c c ·Δε / 2)) (26)

[0169] Where a c 、b c and c c These are all model parameters related to critical fatigue damage.

[0170] A method for constructing a coupled-damage cyclic viscoplastic constitutive model of the present invention comprises the following steps:

[0171] S1. Conduct strain-controlled low-cycle fatigue tests and creep fatigue tests under tensile loading at constant temperature to obtain the test data required for constructing a cyclic viscoplastic constitutive model, including stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from low-cycle fatigue tests; stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from creep fatigue tests, stress relaxation data, and mean stress data.

[0172] Tensile loading refers to the process of holding a certain amount of deformation after tensile loading. Stress relaxation is the phenomenon of stress gradually decreasing during the tensile loading period. Stress relaxation data refers to the corresponding relationship between stress and time during the tensile loading period.

[0173] Among them, the low-cycle fatigue test involves at least three different strain amplitudes and at least three different strain frequencies;

[0174] S2, based on the experimental data, combined with the genetic optimization algorithm to obtain the various model parameters in the cyclic viscoplastic constitutive model, and finally determine a set of optimal model parameters;

[0175] The specific process of step S2 is as follows:

[0176] S21, based on the stress relaxation data during the creep fatigue test during the tensile load holding period, the viscous stress σ is estimated v , using the test data at the maximum strain rate, according to the viscosity equation Preliminary estimation of viscosity-related model parameters A, K0, and n;

[0177] Assuming that no cyclic hardening and fatigue damage occur during the initial tensile loading, the elastic parameters, namely the initial elastic modulus E0 and the initial yield stress k0, are obtained using the linear regression method based on the initial tensile stress-strain hysteresis loop;

[0178] According to ε in =ε–σ / E0 to calculate the inelastic strain ε in , establish (σ–σ v –k0) and ε in The corresponding relationship is used to estimate the model parameters C related to kinematic hardening. 1o 、C 2o 、C 3o , γ 1o , γ 2o and γ 3o ;ε is the total strain, σ is the stress;

[0179] The model parameters C related to kinematic hardening are analyzed by genetic algorithm. 1o 、C 2o 、C 3o , γ 1o , γ 2o , γ3o Optimize

[0180] S22, based on the initial tensile stress-strain hysteresis loops of low-cycle fatigue tests at different strain amplitudes, the strain rate-related model parameters P1, P2, and m2 were optimized using a genetic algorithm;

[0181] S23, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the γ corresponding to each strain amplitude. 1s 、C 2s and C 3s , then the model parameters a1, b1, c1, a2, b2 and c2 related to the back stress and strain range are obtained by formulas (13) and (14), and the model parameters a3, b3 and c3 related to the cyclic motion hardening response time are estimated by formulas (16) and (17); then the genetic algorithm is used to optimize the model parameters a1, b1, c1, a2, b2, c2 related to the back stress and strain range and the model parameters a3, b3, c3 related to the cyclic motion hardening response time;

[0182] S24, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the Q1, Q2, H, and b corresponding to each strain amplitude. R1 and b R2 , then the model parameters a4, b4, c4, a5, b5 and c5 related to the drag force strain range are obtained by formulas (19) and (20), and the model parameters a6 and b6 related to the cyclic isotropic hardening response time are obtained by formula (21); then the genetic algorithm is used to optimize the model parameters a4, b4, c4, a5, b5, c5 related to the drag force strain range and the model parameters a6 and b6 related to the cyclic isotropic hardening response time;

[0183] S25, based on the experimental data of creep fatigue test, including stress-strain hysteresis loop, cyclic stress amplitude evolution data, stress relaxation data, and mean stress data, a genetic algorithm is used to obtain the static recovery related model parameters b and r, as well as the mean stress evolution related model parameter Y s and b Y ;

[0184] At this point, the constitutive model ignoring fatigue damage is obtained;

[0185] S26, calculate the cumulative total strain energy density W at crack initiation using the above constitutive model ignoring fatigue damage t According to formula (24), the model parameters α, β and W related to the crack initiation criterion are obtained f ;

[0186] S27, when identifying the model parameters related to damage evolution, multiple groups of low-cycle fatigue tests and multiple groups of creep fatigue tests are carried out under different loading parameters. The loading parameters of the low-cycle fatigue test include strain amplitude and strain rate, and the loading parameters of the creep fatigue test include strain amplitude, strain rate and holding time. First, the model parameters S1, S2 and g of each group of tests are determined separately, and then the maximum inelastic strain amplitude q and cycle frequency f are used to determine the damage evolution model parameters. c The initial values ​​of the damage evolution-related model parameters S1, S2, g, h1, h2 and h3 are obtained by correction, and the genetic algorithm is used to optimize the damage evolution-related model parameters S1, S2, g, h1, h2, h3; finally, according to the damage value at fatigue failure under different strain amplitudes, the nonlinear regression method is used to fit formula (26) to obtain the critical fatigue damage-related model parameter a c 、b c and c c ;

[0187] The model parameters S1, S2 and g are determined as follows:

[0188] Before crack initiation, the damage variable D is linearly related to the inelastic deformation p, and the slope k is obtained by numerical method. D =dD / dp;

[0189] The model parameter S1 is calculated by formula (27):

[0190]

[0191] Where σ aI and D I are the stress amplitude and cumulative damage at crack initiation, respectively;

[0192] The model parameters S2 and g are calculated by formula (28):

[0193]

[0194] Where N I and N f are the crack initiation life and failure life, and N I and N f stress amplitude and inelastic strain amplitude of the intermediate life hysteresis loop;

[0195] S28, further optimizing all model parameters using a genetic algorithm to obtain a set of optimal model parameters.

[0196] Example

[0197] The research material in this embodiment is Inconel 625 nickel-based high-temperature alloy.

[0198] Depend on Figure 1 As shown in Figure 2, the construction and prediction process of a cyclic viscoplastic constitutive model with coupled damage is as follows:

[0199] S11, this embodiment carried out low cycle fatigue and creep fatigue tests under strain control mode at 800 ° C, including 2×10 -3 s -1 Low cycle fatigue tests were conducted at five different strain amplitudes (0.2%, 0.25%, 0.3%, 0.4%, and 0.5%). -4 s -1 and 1.6×10 -4 s -1 Conduct slow strain rate low-cycle fatigue tests; conduct creep fatigue tests at a strain amplitude of 0.4% with tensile holding times of 60s and 120s to obtain the experimental data required for constructing a cyclic viscoplastic constitutive model, including: stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from low-cycle fatigue tests; stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from creep fatigue tests, stress relaxation data, and mean stress data;

[0200] S12, according to the test results in S11, Inconel 625 alloy shows cyclic hardening and negative strain rate sensitivity at 800℃, and the cyclic hardening is only related to kinematic hardening, so isotropic hardening can be ignored;

[0201] The cyclic viscoplastic constitutive model of coupled damage constructed in this embodiment only includes kinematic hardening. The steps for constructing the constitutive model are as follows:

[0202] S121, total strain rate tensor Decomposed into elastic strain rate tensor and the inelastic strain rate tensor

[0203]

[0204] Elastic strain rate tensor and stress rate tensor Following Hooke's law, the elastic strain rate tensor after coupling damage is The expression is:

[0205]

[0206] Where E and μ are elastic modulus and Poisson's ratio respectively, D is the damage variable, and δ ij is the identity matrix, is the stress component rate tensor;

[0207] S122, using viscoplastic flow laws to describe viscoplastic or inelastic strain rate tensors and the stress tensor σ ij The corresponding relationship between the inelastic strain rate tensor after coupling damage The expression is:

[0208]

[0209] f=J(σ ij -χ ij )-R-k0

[0210]

[0211] Where, χ ij is the back stress tensor, representing kinematic hardening, s ij and a ij are the deviatoric stress tensors of stress and back stress, k0 is the initial yield stress, K, A and n are viscosity-related model parameters, J represents the second invariant of the effective stress deviator, σ ij is the stress tensor;

[0212] S123, back stress tensor χ ij It consists of three nonlinear back stress components described by the kinematic hardening rule,

[0213]

[0214] Where, is the kth back stress component tensor;

[0215] The kinematic hardening rate equation is:

[0216]

[0217]

[0218]

[0219]

[0220] The three terms on the right side of the formula are strain hardening term, dynamic recovery term and static recovery term respectively;

[0221] Where, is the kth back stress component velocity tensor; C k is the kth plastic modulus, γ k is the kth dynamic recovery coefficient, b is the static recovery coefficient, r is the static recovery index, is the average stress of the kth back stress component, is the evolution rate of the average stress of the kth back stress component, Y s is the average stress saturation value, b Y is the average stress rate coefficient, is the cumulative inelastic strain rate;

[0222] S124, cyclic hardening of back stress is achieved by evolving the first dynamic recovery coefficient γ1, the second plastic modulus C2, and the third plastic modulus C3 with the accumulated inelastic deformation p. The evolution equation is:

[0223] γ1=γ 1o (1-γ 1s (1-exp(-D1p)))

[0224] C2=C 2o (1+C 2s (1-exp(-D2p)))

[0225] C3=C 3o (1+C 3s (1-exp(-D3p)))

[0226] Where, γ 1o 、C 2o 、C 3o They represent the initial values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3, γ 1s 、C 2s and C 3s They represent the evolution saturation values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2, and the third plastic modulus C3, respectively. D1, D2, and D3 are parameters that control the evolution rate;

[0227] Back stress-strain range correlation is obtained through γ 1s and C 2s This is achieved by the relationship between the maximum inelastic strain range q:

[0228] γ 1s =a1+b1(1-exp(-c1q))

[0229] C 2s =a2+b2(1-exp(-c2q))

[0230] Where a1, b1, c1, a2, b2 and c2 are model parameters related to the back stress and strain range;

[0231] The time correlation of the constitutive model includes: the time correlation of the initial tensile loading stage and the time correlation of cyclic hardening. In this embodiment, the time correlation of cyclic hardening only includes the time correlation of cyclic motion hardening.

[0232] Through the viscosity parameter K and strain rate The relationship between and realizes the time dependence of the initial tensile loading stage:

[0233]

[0234] Where K0 is the initial value of the viscosity parameter K, P1, P2 and m are all model parameters related to strain rate, is the strain rate;

[0235] By C 3s With the equivalent frequency f e The relationship between the time dependence of cyclic motion hardening is realized as follows:

[0236]

[0237]

[0238] Where Δε is the total strain range, t h is the load holding time, a3, b3 and c3 are the model parameters of the cyclic motion hardening response time;

[0239] S125, the damage variable evolution equation is:

[0240]

[0241]

[0242] Where, is the damage rate; R μ is the triaxial stress correction coefficient, σ eq is the Mises equivalent stress, σ H is the hydrostatic stress, S1, S2, g, h1, h2 and h3 are model parameters related to damage evolution; W t is the cumulative total strain energy density; N is the number of cyclic loading;

[0243] W t α N (1-α) f c -β ≥W f As the crack initiation criterion, the average total strain energy density W t / N I As a parameter, add the cycle frequency f c Correction, establish the cumulative total strain energy density W t and crack initiation life N I The relationship between:

[0244]

[0245]

[0246] Where α, β and W f are model parameters related to crack initiation criterion, H(σ ij ) is a step function, when σ ij >0, H(σ ij )=1, when σ ij ≤0, H(σ ij )=0;

[0247] According to the tensile elastic modulus of the fatigue specimen at failure, the critical fatigue damage D under each strain amplitude is estimated. c , establish the strain amplitude-dependent failure criterion:

[0248] D c =a c -b c (1-exp(c c ·Δε / 2))

[0249] Where a c 、b c and c c is the model parameter related to critical fatigue damage, Δε is the total strain range;

[0250] S13, based on the experimental data in S11, combined with the genetic optimization algorithm, gradually obtains the model parameters in S2, and finally determines a set of optimal model parameters. The specific steps are as follows:

[0251] S131, based on the stress relaxation data during the tensile load holding period of the creep fatigue test, the viscous stress σ is estimated v , using the test data at the maximum strain rate, according to the viscosity equation Preliminary estimation of viscosity-related model parameters A, K0, and n;

[0252] Assuming that no cyclic hardening and fatigue damage occurs during the 1 / 4 cycle stretching, i.e., the initial tensile loading, the elastic parameters, i.e., the initial elastic modulus E0 and the initial yield stress k0, are obtained using the linear regression method according to the initial tensile stress-strain hysteresis loop; according to ε in =ε–σ / E0 to calculate the inelastic strain ε in , establish (σ–σ v –k0) and ε in The corresponding relationship is used to estimate the model parameters C related to kinematic hardening. 1o 、C 2o 、C 3o , γ 1o , γ 2o and γ 3o; ε is the total strain, σ is the stress; the model parameters C related to kinematic hardening are calculated by genetic algorithm. 1o 、C 2o 、C 3o , γ 1o , γ 2o , γ 3o Optimize

[0253] S132, based on the initial tensile stress-strain hysteresis loops of low-cycle fatigue tests at different strain amplitudes, the strain rate-related model parameters P1, P2, and m2 were optimized using a genetic algorithm;

[0254] S133, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the γ corresponding to each strain amplitude. 1s 、C 2s and C 3s , then obtain the model parameters a1, b1, c1, a2, b2 and c2 related to the back stress and strain range, and the correlation model parameters a3, b3 and c3 for estimating the cyclic motion hardening response time; then use the genetic algorithm to optimize the model parameters a1, b1, c1, a2, b2, c2 related to the back stress and strain range and the model parameters a3, b3, c3 related to the cyclic motion hardening response time;

[0255] S134, based on the experimental data of creep fatigue test, including stress-strain hysteresis loop, cyclic stress amplitude evolution data, stress relaxation data, and mean stress data, a genetic algorithm is used to obtain the model parameters b and r related to static recovery, as well as the model parameter Y related to mean stress evolution. s and b Y ;

[0256] At this point, the constitutive model parameters ignoring fatigue damage are completely obtained;

[0257] S135, calculate the cumulative total strain energy density W at crack initiation using the above constitutive model ignoring fatigue damage t , get the parameters α, β and W f ;

[0258] S136, when identifying damage evolution parameters, multiple groups of low-cycle fatigue tests and multiple groups of creep fatigue tests are carried out under different loading parameters. The model parameters S1, S2 and g of the single group of tests are first determined, and then the maximum inelastic strain amplitude q and the cycle frequency f are used to determine the damage evolution parameters. c The initial values ​​of the damage evolution-related model parameters S1, S2, g, h1, h2 and h3 are obtained by correction, and the genetic algorithm is used to optimize the damage evolution-related model parameters S1, S2, g, h1, h2 and h3;

[0259] Before crack initiation, the damage variable D is linearly related to the inelastic deformation p, and the slope k is obtained by numerical method. D =dD / dp, then the model parameter S1 can be calculated as follows:

[0260]

[0261] Where σ aI and D I are the stress amplitude and cumulative damage at crack initiation, respectively.

[0262] The model parameters S2 and g can be calculated as follows:

[0263]

[0264] Where N I and N f are the crack initiation life and failure life, and N I and N f stress amplitude and inelastic strain amplitude of the intermediate life hysteresis loop;

[0265] Then, according to the damage value at fatigue failure under different strain amplitudes, the model parameter a related to critical fatigue damage is obtained by fitting through nonlinear regression method. c 、b c and c c ;

[0266] S137, finally, the genetic algorithm is used to further optimize all model parameters to obtain a set of optimal parameters;

[0267] S14, using the optimal model parameters obtained in S13, the constitutive model constructed in S12 is used to predict the cyclic deformation behavior and failure life of the material under various loading conditions. The model verification is as follows Figure 2-Figure 6 As shown, Figure 2 The predicted results of the hysteresis loops of the low-cycle fatigue tests with different strain amplitudes in the embodiment of the present invention are as follows: 2a corresponds to a strain amplitude of 0.25%, 2b corresponds to a strain amplitude of 0.4%, and 2c corresponds to a strain amplitude of 0.5%. Figure 3 Figure 3a shows the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue tests with different strain amplitudes in the embodiment of the present invention. Figure 3a corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue tests with a strain amplitude of 0.25%, Figure 3b corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue tests with a strain amplitude of 0.4%, and Figure 3c corresponds to the prediction results of cyclic stress amplitude and fatigue damage under low-cycle fatigue tests with a strain amplitude of 0.5%. Figure 4 The predicted results of cyclic stress amplitudes of low-cycle fatigue tests at different strain rates in the embodiment of the present invention are as follows; Figure 5 The predicted results of the creep fatigue test in the embodiment of the present invention are shown in Figure 5a: hysteresis loop, 5b: half-life cyclic stress relaxation, and 5c: cyclic stress response. Figure 6 The figure shows the life prediction result of the viscoplastic constitutive model with coupled damage in the embodiment of the present invention. It can be seen that the present invention can well predict the low cycle fatigue and creep fatigue cyclic deformation behavior and fatigue failure life of materials under different test parameters.

[0268] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a cyclic viscoplastic constitutive model with coupled damage, characterized in that: The constitutive model is used to predict the cyclic deformation behavior and failure life of materials under different loading parameters, including strain amplitude, strain rate, and holding time. The construction of the constitutive model is as follows: The total strain rate tensor Decomposed into elastic strain rate tensor and the inelastic strain rate tensor Among them, i, j = 1, 2, 3, representing the three axes of the spatial coordinates; elastic strain rate tensor and the stress rate tensor Following Hooke's law, the elastic strain rate tensor after coupling damage is The expression is: Where E and μ are elastic modulus and Poisson's ratio respectively, D is the damage variable, and δ ij is the identity matrix, is the stress component rate tensor; Using viscoplastic flow laws to describe the viscoplastic or inelastic strain rate tensor and the stress tensor σ ij The corresponding relationship between the inelastic strain rate tensor after coupling damage The expression is: Where, χ ij is the back stress tensor, representing kinematic hardening; R is the drag stress, representing isotropic hardening; s ij and a ij are the deviatoric stress tensors of stress and back stress, k0 is the initial yield stress, K, A and n are viscosity-related model parameters, J represents the second invariant of the effective stress deviator, σ ij is the stress tensor; Back stress tensor χ ij It consists of three nonlinear back stress components described by the kinematic hardening rule, Where, is the kth back stress component tensor; The kinematic hardening rate equation is: The three terms on the right side of formula (6) are strain hardening term, dynamic recovery term and static recovery term respectively; Where, is the kth back stress component velocity tensor; C k is the kth plastic modulus, γ k is the kth dynamic recovery coefficient, b is the static recovery coefficient, r is the static recovery index, is the average stress of the kth back stress component, is the evolution rate of the average stress of the kth back stress component, Y s is the average stress saturation value, b Y is the average stress rate coefficient, is the cumulative inelastic strain rate; The cyclic hardening of back stress is achieved by the evolution of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3 with the accumulated inelastic strain p. The evolution equation is: γ1=γ 1o (1-c 1s (1-exp(-D1p))) (10) C2=C 2o (1+C 2s (1-exp(-D2p))) (11) C3=C 3o (1+C 3s (1-exp(-D3p))) (12) Where, γ 1o 、C 2o 、C 3o They represent the initial values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2 and the third plastic modulus C3, γ 1s 、C 2s and C 3s They represent the evolution saturation values ​​of the first dynamic recovery coefficient γ1, the second plastic modulus C2, and the third plastic modulus C3, respectively. D1, D2, and D3 are all parameters that control the evolution rate; Back stress strain range correlation is obtained through γ 1s 、C 2s It is realized by the relationship with the maximum inelastic strain amplitude q: γ 1s =a1+b1(1-exp(-c1q)) (13) C 2s =a2+b2(1-exp(-c2q)) (14) Where a1, b1, c1, a2, b2 and c2 are model parameters related to the back stress and strain range; The isotropic hardening rate equation is: The first two terms on the right side of formula (18) are nonlinear isotropic hardening components, and the third term is the linear isotropic hardening component; Where, is the drag stress rate, i.e., the isotropic hardening rate, Q1 and Q2 are the saturation values ​​of the two nonlinear isotropic hardening components, b R1 and b R2 are the rate parameters of the two nonlinear isotropic hardening components, and H is the linear hardening slope; The drag stress-strain range correlation is realized by the relationship between Q1, H and the maximum inelastic strain range q: Q1=a4+b4(1-exp(-c4q)) (19) H=a5+b5(1-exp(-c5q)) (20) Where a4, b4, c4, a5, b5 and c5 are model parameters related to the drag stress-strain range; The damage variable evolution equation is: Where, is the damage rate; R μ is the triaxial stress correction coefficient, σ eq is the Mises equivalent stress, σ H is the hydrostatic stress, S1, S2, g, h1, h2 and h3 are model parameters related to damage evolution; W t is the cumulative total strain energy density; N is the number of cyclic loading; As the crack initiation criterion, the average total strain energy density W t / N I As a parameter, add the cycle frequency f c Correction, establish the cumulative total strain energy density W t and crack initiation life N I The relationship between: Where α, β and W f are model parameters related to crack initiation criterion, H(σ ij ) is a step function, when σ ij >0, H(σ ij )=1, when σ ij ≤0, H(σ ij )=0; According to the tensile elastic modulus at fatigue failure, the critical fatigue damage D under each strain amplitude is estimated. c , establish the strain amplitude-dependent failure criterion: D c =a c -b c (1-exp(c c ·Δε / 2)) (26) Where a c 、b c and c c are all model parameters related to critical fatigue damage, and Δε is the total strain range.

2. The method for constructing a coupled-damage cyclic viscoplastic constitutive model according to claim 1, characterized in that: The time dependence of the constitutive model includes: the time dependence of the initial tensile loading stage and the time dependence of cyclic hardening; wherein the time dependence of cyclic hardening includes: the time dependence of cyclic kinematic hardening and / or the time dependence of cyclic isotropic hardening; Through the viscosity parameter K and strain rate The relationship between and realizes the time dependence of the initial tensile loading stage: Where K0 is the initial value of the viscosity parameter K, P1, P2 and m are all model parameters related to strain rate, is the strain rate; By C 3s With the equivalent frequency f e The relationship between the time dependence of cyclic motion hardening is realized as follows: Where Δε is the total strain range, t h is the load holding time, a3, b3 and c3 are the model parameters of the cyclic motion hardening response time; Through Q2 and the equivalent frequency f e The relationship between the time dependence of cyclic isotropic hardening is achieved: Where a6 and b6 are model parameters related to the cyclic isotropic hardening response time.

3. A method for determining model parameters of the cyclic viscoplastic constitutive model of coupled damage according to claim 2, characterized in that: The following steps are involved: S1. Conduct strain-controlled low-cycle fatigue tests and creep fatigue tests under tensile loading at constant temperature to obtain the test data required for constructing a cyclic viscoplastic constitutive model, including stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from low-cycle fatigue tests; stress-strain hysteresis loops and cyclic stress amplitude evolution data obtained from creep fatigue tests, stress relaxation data, and mean stress data. S2, based on the experimental data, combined with the genetic optimization algorithm to obtain the various model parameters in the cyclic viscoplastic constitutive model, and finally determine a set of optimal model parameters.

4. The method for determining model parameters according to claim 3, wherein: The specific process of step S2 is as follows: S21, based on the stress relaxation data during the creep fatigue test during the tensile load holding period, the viscous stress σ is estimated v , using the test data at the maximum strain rate, according to the viscosity equation Preliminary estimation of viscosity-related model parameters A, K0, and n; Assuming that no cyclic hardening and fatigue damage occur during the initial tensile loading, the elastic parameters, namely the initial elastic modulus E0 and the initial yield stress k0, are obtained using the linear regression method based on the initial tensile stress-strain hysteresis loop; According to ε in =ε–σ / E0 to calculate the inelastic strain ε in , establish (σ–σ v –k0) and ε in The corresponding relationship is used to estimate the model parameters C related to kinematic hardening. 1o 、C 2o 、C 3o , γ 1o , γ 2o and γ 3o ;ε is the total strain, σ is the stress; The model parameters C related to kinematic hardening are analyzed by genetic algorithm. 1o 、C 2o 、C 3o , γ 1o , γ 2o , γ 3o Optimize S22, based on the initial tensile stress-strain hysteresis loops of low-cycle fatigue tests at different strain amplitudes, the strain rate-related model parameters P1, P2, and m2 were optimized using a genetic algorithm; S23, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the γ corresponding to each strain amplitude. 1s 、C 2s and C 3s , then the model parameters a1, b1, c1, a2, b2 and c2 related to the back stress and strain range are obtained by formulas (13) and (14), and the model parameters a3, b3 and c3 related to the cyclic motion hardening response time are estimated by formulas (16) and (17); then the genetic algorithm is used to optimize the model parameters a1, b1, c1, a2, b2, c2 related to the back stress and strain range and the model parameters a3, b3, c3 related to the cyclic motion hardening response time; S24, based on the cyclic stress amplitude evolution data of low-cycle fatigue tests under different strain amplitudes, first estimate the Q1, Q2, H, and b corresponding to each strain amplitude. R1 and b R2 , then the model parameters a4, b4, c4, a5, b5 and c5 related to the drag force strain range are obtained by formulas (19) and (20), and the model parameters a6 and b6 related to the cyclic isotropic hardening response time are obtained by formula (21); then the genetic algorithm is used to optimize the model parameters a4, b4, c4, a5, b5, c5 related to the drag force strain range and the model parameters a6 and b6 related to the cyclic isotropic hardening response time; S25, based on the experimental data of creep fatigue test, including stress-strain hysteresis loop, cyclic stress amplitude evolution data, stress relaxation data, and mean stress data, a genetic algorithm is used to obtain the static recovery related model parameters b and r, as well as the mean stress evolution related model parameter Y s and b Y ; At this point, the constitutive model ignoring fatigue damage is obtained; S26, calculate the cumulative total strain energy density W at crack initiation using the above constitutive model ignoring fatigue damage t , according to formula (24), the model parameters α, β and W related to the crack initiation criterion are obtained f ; S27, when identifying the model parameters related to damage evolution, multiple groups of low-cycle fatigue tests and multiple groups of creep fatigue tests are carried out under different loading parameters. The loading parameters of the low-cycle fatigue test include strain amplitude and strain rate, and the loading parameters of the creep fatigue test include strain amplitude, strain rate and holding time. First, the model parameters S1, S2 and g of each group of tests are determined separately, and then the maximum inelastic strain amplitude q and cycle frequency f are used to determine the damage evolution model parameters. c The initial values ​​of the damage evolution-related model parameters S1, S2, g, h1, h2 and h3 are obtained by correction, and the genetic algorithm is used to optimize the damage evolution-related model parameters S1, S2, g, h1, h2, h3; finally, according to the damage value at fatigue failure under different strain amplitudes, the nonlinear regression method is used to fit formula (26) to obtain the critical fatigue damage-related model parameter a c 、b c and c c ; S28, further optimizing all model parameters using a genetic algorithm to obtain a set of optimal model parameters.

5. The method for determining model parameters according to claim 4, wherein: In step S1 , the low cycle fatigue test involves at least three different strain amplitudes and at least three different strain rates.

6. The method for determining model parameters according to claim 4, wherein: A 1 / 4 cycle stretch was selected as the initial tensile loading.

7. The method for determining model parameters according to claim 4, wherein: In step 27, the model parameters S1, S2 and g are determined as follows: Before crack initiation, the damage variable D is linearly related to the inelastic deformation p, and the slope k is obtained by numerical method. D =dD / dp; The model parameter S1 is calculated by formula (27): Where, σ aI and D I are the stress amplitude and cumulative damage at crack initiation, respectively; The model parameters S2 and g are calculated by formula (28): Where N I and N f are the crack initiation life and failure life, and N I and N f Stress amplitude and inelastic strain amplitude of the intermediate life hysteresis loop.

Images