A simulation method and system for low-cycle fatigue cracks based on continuous cumulative damage.

Abstract

This invention provides a method and system for simulating low-cycle fatigue cracks based on continuous cumulative damage, belonging to the field of low-cycle fatigue crack simulation. The method includes: establishing a cyclic elastoplastic constitutive model with coupled damage; establishing a finite element model under multiaxial stress states, and calculating the stress-strain tensor for each loading cycle using the cyclic elastoplastic constitutive model; calculating the fatigue damage increment for each loading cycle based on the low-cycle fatigue damage evolution model combined with the stress-strain tensor; and using the element failure method to numerically simulate the crack initiation and propagation processes using a unified method. This invention overcomes the limitations of traditional methods that can only rely on data from fatigue crack initiation and propagation tests to analyze the crack initiation and propagation processes separately.

Description

Technical Field

[0001] This invention belongs to the field of low-cycle fatigue crack simulation, and more specifically, relates to a simulation method and system for low-cycle fatigue cracks based on continuous cumulative damage. Background Technology

[0002] During operation, nuclear reactor units experience frequent power fluctuations and temperature volatility during start-up and shutdown, causing some structural components to undergo prolonged low-cycle fatigue, which can easily lead to material fatigue failure. Although high-temperature structural components in nuclear reactor units are required to meet the highest standards of high-temperature resistance, high cleanliness, and high sealing, it is still difficult to avoid the emergence of minute defects exceeding the capabilities of current non-destructive testing techniques, which can become the origin of cracks. The initiation and propagation mechanisms of small cracks are significantly different from those of long cracks, and their propagation rates cannot be characterized using long crack prediction models. Therefore, establishing a method for accurately predicting the initiation and propagation behavior of small cracks is a pressing problem that needs to be solved for the accurate prediction of the long-life of high-temperature structural components.

[0003] Currently, most methods for predicting the propagation rate of long cracks employ fracture mechanics approaches. These models are generally derived from the Paris crack propagation formula. Using this method requires first conducting fatigue crack propagation tests to obtain the fatigue crack propagation rate, and then determining the relationship between the fatigue crack propagation rate and the stress intensity factor. However, this method cannot adequately describe the influence of cyclic plastic strain history on crack propagation in complex structures. Furthermore, studies on short cracks show that in the early stages of propagation, the crack propagation rate gradually decreases from a high value as the crack length increases. Once the crack has expanded to a certain size, the crack propagation rate gradually increases again, returning to the stable propagation state described by fracture mechanics. Therefore, directly applying the prediction methods for long cracks to structures containing short cracks can lead to a dangerously high overestimation of fatigue life. Moreover, traditional prediction methods often divide the fatigue failure process of structural components into two stages: fatigue crack initiation and crack propagation. Continuum mechanics or fracture mechanics methods are used to analyze the life of each stage separately. However, from the perspective of continuum mechanics combined with damage mechanics, the two stages belong to the same continuous fatigue failure process. Therefore, it is desirable to obtain a new method for predicting the initiation and propagation of fatigue short cracks, which couples fatigue damage with elastoplastic constitutive model, in order to better predict the initiation and propagation behavior of fatigue cracks in structural components under multiaxial stress. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a simulation method and system for low-cycle fatigue cracks based on continuous cumulative damage, thereby solving the problem that existing methods cannot effectively evaluate crack initiation and propagation behavior under complex cyclic plastic strain histories.

[0005] To achieve the above objectives, on the one hand, the present invention provides a simulation method for low-cycle fatigue cracks based on continuous cumulative damage, comprising the following steps:

[0006] S1: Under multiaxial stress, update the kinematic hardening parameters in the cyclic elastoplastic constitutive model based on the current equivalent plastic strain and memory surface size at the nodes, and calculate the yield surface size caused by isotropic hardening using the current equivalent plastic strain at the nodes.

[0007] S2: Assuming the strain tensor increment of the current increment step is the elastic strain increment, based on the current stress tensor, strain tensor, and fatigue damage value, obtain the elastic test state according to the elastic stress-strain relationship in the cyclic elastoplastic constitutive model, and calculate the test state of the yield function corresponding to the elastic test state. If the test state value of the yield function is less than 0, save the stress tensor, strain tensor, and equivalent plastic strain in the elastic test state, and go to S4; otherwise, go to S3.

[0008] S3: Update the equivalent plastic strain using the radial backtracking mapping method, and calculate whether the stress tensor increment converges based on the updated equivalent plastic strain. If it converges, update and retain the stress tensor and strain tensor, and retain the equivalent plastic strain, then proceed to S4; otherwise, proceed to S1.

[0009] S4: Determine whether the incremental step is in the loading or unloading process by increasing or decreasing the updated stress tensor. If the current incremental step is within the current loading cycle, proceed to S1 to calculate the next incremental step. If the current incremental step is not within the current loading cycle and the number of loading cycles has not reached the maximum number of cycles, update the number of loading cycles, memory surface parameters, and fatigue damage value, determine whether the element where the node is located is a crack element, and proceed to S1 to calculate the next incremental step.

[0010] The method for constructing the cyclic elastoplastic constitutive model is as follows:

[0011] A cyclic elastoplastic constitutive model for coupled damage of the test material is defined for uniaxial low-cycle fatigue tests. Damage parameters of the low-cycle fatigue damage evolution model are determined using strain-controlled uniaxial low-cycle fatigue test results. Fatigue damage values ​​are removed from the strain-controlled uniaxial low-cycle fatigue test results, and material parameters of the equivalent undamaged cyclic elastoplastic constitutive model are calculated.

[0012] More preferably, the method for determining whether the element containing the node is a crack element is as follows:

[0013] If the updated fatigue damage value is greater than the critical value, the Young's modulus of the element containing the node is reduced to a preset ratio of the initial Young's modulus. The element containing the node is determined to be a crack element, and the updated fatigue damage value is restored to the critical fatigue damage value and transferred to S1. Otherwise, the updated fatigue damage value is retained and transferred to S1.

[0014] More preferably, the cyclic elastoplastic constitutive model includes: the master governing equation of the elastoplastic constitutive model, a nonlinear kinematic hardening sub-model of the back stress tensor, a nonlinear isotropic hardening sub-model, and a strain range memory effect sub-model.

[0015] More preferably, the critical fatigue damage value is determined by the ratio of Young's modulus during the last loading cycle before crack initiation and Young's modulus during the initial loading cycle in a uniaxial fatigue test.

[0016] On the other hand, the present invention provides a simulation system for low-cycle fatigue cracks based on continuous cumulative damage, comprising:

[0017] The state variable recovery module is used to obtain the current stress tensor, strain tensor, equivalent plastic strain, loading cycle number, memory surface parameters, and fatigue damage value for each node.

[0018] The material parameter update module is used to update the corresponding kinematic hardening parameters based on the current equivalent plastic strain and memory surface size.

[0019] The isotropic hardening module is used to calculate the yield surface size caused by isotropic hardening using the current equivalent plastic strain;

[0020] The elastic prediction module assumes that the strain tensor increment of the current increment step is the elastic strain increment. Based on the current stress tensor, strain tensor and fatigue damage value of the node, it obtains the elastic test state and the corresponding yield function test state according to the elastic stress-strain relationship in the cyclic elastoplastic constitutive model. If the test state value of the yield function is less than 0, it saves the stress tensor, strain tensor and equivalent plastic strain in the elastic test state.

[0021] The plasticity correction module is used to update the equivalent plastic strain by radial backtracking mapping when the trial state value of the yield function is greater than or equal to 0.

[0022] The Consistent Tangent Modulus module is used to calculate whether the stress tensor increment converges based on the updated equivalent plastic strain. If it converges, the current stress tensor and strain tensor are updated and retained.

[0023] The loading loop module is used to determine whether the incremental step is in the loading or unloading process by the increase or decrease of the updated stress tensor. If the current incremental step is within the current loading loop, the state variable recovery module is run for the next incremental step. If the current incremental step is not within the current loading loop and the number of loading loops has not reached the maximum number of loops, the number of loading loops, memory surface parameters, and fatigue damage values ​​are updated.

[0024] The element failure module is used to determine whether the element containing the node is a cracked element based on the fatigue damage value.

[0025] More preferably, the method by which the element failure module determines whether the element containing the node is a cracked element is as follows:

[0026] If the updated fatigue damage value is greater than the critical fatigue damage value, the Young's modulus of the element containing the node is reduced to a preset proportion of the initial Young's modulus, the element containing the node is determined to be a crack element, and the updated fatigue damage value is restored to the critical fatigue damage value; otherwise, the updated fatigue damage value is retained.

[0027] More preferably, the cyclic elastoplastic constitutive model includes: the master governing equation of the elastoplastic constitutive model, the nonlinear kinematic hardening sub-model of the back stress tensor, the nonlinear isotropic hardening sub-model, and the strain range memory effect sub-model.

[0028] More preferably, the critical fatigue damage value is determined by the ratio of Young's modulus during the last loading cycle before crack initiation and Young's modulus during the initial loading cycle in a uniaxial fatigue test.

[0029] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0030] The cyclic elastoplastic constitutive model for coupled damage of test materials established in this invention can determine damage parameters using strain-controlled uniaxial low-cycle fatigue test results, and then calculate the material parameters of the cyclic elastoplastic constitutive model under undamaged conditions. Based on the obtained cyclic elastoplastic constitutive model, the continuous accumulation method can be used to predict the initiation and propagation behavior of fatigue cracks under multiaxial stress. The strain-controlled fatigue damage evolution model can solve the problem of large errors in the low-cycle fatigue region of traditional fatigue damage evolution models. Furthermore, the prediction of the initiation and propagation of fatigue short cracks under multiaxial stress conditions using uniaxial fatigue test results can avoid the tendency of traditional methods to overestimate the fatigue life prediction of structural components containing short cracks. Moreover, the combination of continuum mechanics, damage mechanics, and finite element method is used to simulate the stress-strain field considering damage coupling, organically combining the two processes of short crack initiation and propagation, thus overcoming the limitation of traditional methods that can only analyze the two processes separately. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of a simulation method for the initiation and propagation of short cracks in low-cycle fatigue provided in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of a finite element model of a unit provided in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of a finite element model under multiaxial stress state provided in an embodiment of the present invention;

[0034] Figure 4 This is a flowchart of step 4 provided in an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram of incremental steps provided in an embodiment of the present invention;

[0036] Figure 6 This is a schematic diagram of parameter fitting for the low-cycle fatigue damage evolution model provided in an embodiment of the present invention;

[0037] Figure 7 This is a schematic diagram of parameter fitting for the isotropic hardening model provided in an embodiment of the present invention;

[0038] Figure 8 This is a schematic diagram of parameter fitting for the kinematic hardening model provided in an embodiment of the present invention;

[0039] Figure 9 This is a schematic diagram of parameter fitting for the strain range memory effect model provided in an embodiment of the present invention;

[0040] Figure 10 The simulation method provided in this embodiment of the invention provides the prediction results of uniaxial fatigue tests.

[0041] Figure 11 This is a schematic diagram showing the prediction result of the crack initiation life of a short fatigue crack at the notch root under one embodiment of the simulation method provided in this invention.

[0042] Figure 12 This is a schematic diagram showing the prediction results of the propagation rate of fatigue short cracks at the notch root under one embodiment of the simulation method provided in this invention.

[0043] Figure 13 This is a schematic diagram showing the cumulative damage value at different locations at the root of the notch before crack initiation in one embodiment of the simulation method provided by the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0045] This invention provides, for example Figure 1 The simulation method for low-cycle fatigue crack initiation and propagation based on continuous cumulative damage, as shown, includes the following steps:

[0046] Step 1: As Figure 2 The diagram shows the establishment of a single-element finite element model, and the definition of a cyclic elastoplastic constitutive model for coupled damage of the test material using the subroutine UMAT. Solving the cyclic elastoplastic constitutive model requires calculating the damage values ​​using a low-cycle fatigue damage evolution model; details are as follows:

[0047] The cyclic elastoplastic constitutive model of coupled damage includes: the master governing equation of the elastoplastic constitutive model, the nonlinear kinematic hardening sub-model of the back stress tensor, the nonlinear isotropic hardening sub-model, and the strain range memory effect sub-model;

[0048] The governing equations of the elastoplastic constitutive model are:

[0049] (1)

[0050] in, , and These are the total strain tensor, elastic strain tensor, and plastic strain tensor, respectively. For stress tensor; and These are the effective deviatoric stress tensor and the effective back stress tensor of the damaged material, respectively, which can be calculated from the actual deviatoric stress tensor and back stress tensor. E The elastic tensor of the material; Let be the yield function; This refers to the yield surface dimension of the material, i.e., the elastic limit. For plastic strain rate tensor; This is the equivalent plastic strain rate;

[0051] The following formula is used to describe the nonlinear kinematic hardening submodel:

[0052] (2)

[0053] in, and These are the total back stress tensor and the first... i The back stress component tensor of the term; For the first i The evolution rate of the back stress component tensor of the term; and For the first i Material parameters corresponding to the back stress components of the term; The fatigue damage evolution rate; These are control parameters that describe the hardening / softening behavior that occurs during the cycle; p Equivalent plastic strain; kinematic hardening parameters , k and The value is determined by the size of the memory surface. q Decide, and k Used to describe the rapid change in back stress during the initial hardening stage. Used to describe the kinematic hardening law in the subsequent stable hardening stage;

[0054] The following formula is used to describe the nonlinear isotropic hardening sub-model:

[0055] (3)

[0056] in, This represents the initial yield surface size; , and B All are isotropic hardening parameters. and B Used to describe the evolution of the yield surface size during the initial hardening stage. Used to describe the evolution of the yield surface size during the subsequent stable hardening stage;

[0057] The following formula is used to describe the strain range memory effect sub-model:

[0058] (4)

[0059] in, ; ; A , B and C All are strain memory effect parameters in vector form, used to describe the evolution of kinematic hardening parameters with respect to the size of the memory surface; The index function for the memory surface; and These represent the center and size of the memory surface, respectively. This is a parameter used to represent the ratio of isotropic hardening and kinematic hardening in the memory surface;

[0060] Step 2: Determine the damage parameters required for calculating the low-cycle fatigue damage evolution model in Step 1 using the results of strain-controlled uniaxial low-cycle fatigue tests; details are as follows:

[0061] The low-cycle fatigue damage evolution model is as follows:

[0062] (5)

[0063] in, This represents the increment of fatigue damage per loading cycle; , , c and M For damage parameters; M To control the shape of damage evolution, a value of 1.5 is recommended. This represents the normal strain component in the maximum / minimum elastic strain tensor during a loading cycle; This represents the strain component in the maximum / minimum elastic / plastic strain tensor during a loading cycle. v The Poisson's ratio of the material; This represents the distortion strain amplitude; and These represent the elastic and plastic components of the distortion strain amplitude, respectively. This represents the average expansion strain over one loading cycle.

[0064] In uniaxial fatigue testing, the low-cycle fatigue damage evolution model can be simplified as follows:

[0065] (6)

[0066] The material parameters are the same as those under multiaxial stress. The strain amplitude under cyclic loading; This represents the average strain under cyclic loading.

[0067] Low-cycle fatigue damage The range of variation is 0~ This represents the continuous process of a material going from no damage to failure. The value is taken from Young's modulus during the last loading cycle before macroscopic crack initiation in uniaxial fatigue testing. Young's modulus during the initial loading process E ratio Sure;

[0068] In strain-controlled low-cycle fatigue tests, the method for determining the initiation of macroscopic cracks is as follows: the peak stress value decreases rapidly relative to the steady-state change stage, and a decrease of 10% is considered as the initiation of macroscopic cracks.

[0069] When determining the damage parameters for the low-cycle fatigue damage evolution model, the strain amplitude of the uniaxial fatigue test is greater than 0.2%;

[0070] Step 3: Using the low-cycle fatigue damage evolution model determined in Step 2, after removing the influence of fatigue damage from the strain-controlled uniaxial low-cycle fatigue test results, determine the material parameters required for the calculation of the cyclic elastoplastic constitutive model in Step 1 under the equivalent undamaged state.

[0071] Step 4: As Figure 3 The finite element model under multiaxial stress is established as shown. Using the subroutine in step 1 and the material parameters in steps 2 and 3, the stress-strain tensor for each loading cycle is calculated; more specifically, as shown... Figure 4 As shown;

[0072] In the numerical simulation of short crack initiation and propagation in a structure under multiaxial stress, the cyclic strain amplitude at the most critical location is greater than 0.2%.

[0073] A subroutine for implementing a simulation method for the initiation and propagation of short-cycle fatigue cracks based on continuous cumulative damage includes:

[0074] The state variable recovery module is used to store and transfer the stress tensor, strain tensor, equivalent plastic strain, loading cycle number, memory surface parameters and fatigue damage value of each node in the model using the user-defined subroutine USDFLD, and pass them to the subroutine UMAT at the beginning of each incremental step for the next calculation.

[0075] The material parameter update module is used to update the corresponding kinematic hardening parameters based on the values ​​of equivalent plastic strain and memory surface size.

[0076] The isotropic hardening module is used to calculate the yield surface size caused by isotropic hardening using the current equivalent plastic strain.

[0077] The elastic prediction module is used to assume, for example Figure 5 The strain tensor increment of the new increment step shown is the elastic strain increment. An elastic test state is obtained based on the elastic stress-strain relationship. Based on the stress-strain state of this elastic test state, the test state of the yield function is calculated. If the test state value of the yield function is less than 0, then this test state is the true state. The calculation equation is expressed as follows:

[0078] (7)

[0079] Among them, superscript This indicates the trial state, with the subscript n representing the nth increment step and the subscript N representing the Nth loading loop;

[0080] Figure 5The concept of load in this context is as follows: fatigue load, in contrast to static load, refers to stress / strain whose magnitude / direction is not constant but changes cyclically over time. The load level can be measured by indicators such as stress, strain, and pressure. A cycle includes a loading cycle and an unloading cycle.

[0081] The plasticity correction module is used to calculate the equivalent plastic strain using the radial backtracking mapping method if the test state value of the yield function is greater than 0, thereby obtaining the true stress-strain state. The calculation equation is as follows:

[0082] (8)

[0083] The consistent tangent modulus module, to ensure the convergence speed of the overall iteration without affecting the accuracy of the calculation, adopts the following expression, where, I It is a fourth-order unit tensor. It is a fourth-order unit partial tensor;

[0084] (9)

[0085] Step 5: Based on the low-cycle fatigue damage evolution model in Step 2 and the stress-strain tensor calculated in Step 4, calculate the fatigue damage increment for each loading cycle. Using the element failure method, numerically simulate the two processes of crack initiation and propagation using a unified method.

[0086] The subroutine also includes:

[0087] The loading loop module is used to determine whether the current increment step is a loading / unloading process by the increase / decrease of the effective stress, and updates the loading loop number, memory surface parameters and fatigue damage value at each loading loop.

[0088] Unit failure module, used when the current fatigue damage value exceeds This process ensures that the fatigue damage at the node no longer increases and reduces the Young's modulus of the element containing the node to 0.1% of the initial Young's modulus, thus simulating crack initiation and propagation behavior.

[0089] Example

[0090] like Figure 1 As shown, the present invention provides a simulation method for low-cycle fatigue short cracks under multiaxial stress, including: parameter fitting of a low-cycle fatigue loss evolution model based on uniaxial fatigue test, parameter fitting of a cyclic elastoplastic constitutive model determined based on uniaxial low-cycle fatigue test results, and simulation of low-cycle fatigue short cracks under multiaxial stress.

[0091] To better illustrate the simulation method for the initiation and propagation of short-cycle fatigue cracks based on continuous cumulative damage provided by this invention, a single-sided notched specimen will be used for verification. The material used for verification is 316H heat-resistant steel, and the high-temperature low-cycle fatigue test is carried out at 550℃. During the test, due to the influence of the geometric discontinuity of the single-sided notched specimen, the weakest part at the root of the notch is in a multiaxial stress-strain state. Before this, uniaxial fatigue tests with different strain amplitudes and average strain values ​​at 550℃ need to be carried out to determine the required material parameters for formulas (1) to (6).

[0092] S1: Based on the Young's modulus in the last loading cycle before fracture in the uniaxial fatigue test. Young's modulus during the initial loading process E ratio Determine the critical loss value of the material The average value of all test results is taken as 0.2; the evolution model formula (6) for low-cycle fatigue loss under uniaxial conditions is from 0~ / Integrating the data and using a nonlinear fitting method, fatigue test results of multiple strain amplitudes under different average strain values ​​were fitted, such as... Figure 6 As shown, the material parameters of the 316H low-cycle fatigue loss evolution model at 550℃ were obtained. , , c and M The values ​​are 890.1, 63.5, 2.741, and 1.5, respectively.

[0093]

[0094] in, The strain amplitude under cyclic loading conditions is the strain amplitude under uniaxial loading. This represents the average strain under cyclic loading conditions under uniaxial loading. , , c and M These are material parameters, the same as those in the low-cycle fatigue loss evolution model under multiaxial conditions;

[0095] S2: Based on the initial loading results of the uniaxial fatigue test, some material parameters of the 316H elastoplastic model at 550℃ were obtained, including: Young's modulus. E 200 GPa; Poisson's ratio 0.3; initial yield surface size The back stress is 70 MPa; material parameters of the back stress in each part of the kinematic hardening model ( The values ​​are (5000, 127000), (200, 7060), and (20, 1890), respectively.

[0096] S3: Based on the equivalent plastic strain and corresponding yield surface size at different cycles in the uniaxial fatigue test, a nonlinear fitting method is used, such as... Figure 7 As shown, the material parameters of the isotropic hardening model of 316H at 550℃ were obtained. H , and B The values ​​are 1.046, 72.61, and 1.282, respectively.

[0097]

[0098] in, The yield surface size is determined by taking into account the cumulative equivalent plastic strain.

[0099] S4: According to the kinematic hardening model defined by formula (2), the back stress at the same plastic strain after cyclic loading is the initial state. Therefore, based on the equivalent plastic strain, corresponding peak plastic strain, and peak back stress values ​​at different cycles in the uniaxial fatigue test, nonlinear fitting methods are applied to the kinematic hardening model parameters under different loading conditions, such as... Figure 8 As shown, some material parameters used to describe cyclic hardening / softening in the kinematic hardening model of 316H at 550℃ under different strain amplitudes are shown. , k , The strain ranges are: 0.6% (4.11, 1.602, 0.25), 0.5% (3.23, 1.696, 0.248), 0.4% (2.91, 1.953, 0.244), and 0.3% (1.93, 2.977, 0.238).

[0100]

[0101] in, To control the cyclic hardening / softening index, in relation to material parameters , k and And related to equivalent plastic strain;

[0102] S5: Using the results obtained in S4, such as Figure 9 As shown, to determine the material parameters of the strain range memory effect model, the memory surface related model in formula (4) is first simplified. Under uniaxial conditions, it can be expressed by the following formula:

[0103]

[0104] in, The index function for the memory surface; and These represent the center and size of the memory surface, respectively. Here, is a material parameter representing the ratio of isotropic hardening to kinematic hardening in the memory surface; its value is set to 0.5. Clearly, under uniaxial symmetric cyclic loading conditions, It reached stability after the first loading cycle, with a value of ; then, as Figure 9 As shown, the material parameters of 316H in vector form at 550℃ can be determined using a nonlinear fitting method. A , B and C The values ​​are (-70.71, 1.583, 0.2535), (70.58, 71.49, -0.07044), and (-18.03, 2625, 1008), respectively.

[0105] S6: Using the material parameters determined in S1~S5, numerical simulations of uniaxial fatigue are performed to verify the accuracy of the material parameters. Fine-tuning is then performed using the trial-and-error method to ensure the model's effectiveness. For low-cycle fatigue tests, peak stress data is generally used to represent the material's cyclic response characteristics, such as... Figure 10 As shown;

[0106] In one embodiment of the present invention, a peak load of 1500~3000N and a load ratio of 0.1 are selected. Multiple sets of single-sided notch fatigue tests showed that fatigue short cracks in all cases initiated at the subsurface of the notch root, consistent with numerical simulation results. Figure 11 The figure shows the fatigue short crack initiation life prediction results of the method provided by the present invention. It can be seen that the errors are all within the 1.5-fold error band. Therefore, the simulation method for low-cycle fatigue short crack initiation and propagation based on continuous cumulative damage provided by the present invention can effectively predict the fatigue short crack initiation life under multiaxial stress state.

[0107] In one embodiment of the present invention, the peak load is selected to be 2500 N, and the load ratio is 0.1,550. The single-sided notch fatigue test revealed that in the early propagation stage after fatigue crack initiation, typical short crack characteristics were observed. Specifically, the crack propagation rate was rapid when the crack size was small, and slowed down with increasing crack length, exhibiting a distinct hook-shaped curve in the early propagation stage. Figure 12 As shown, the experimental results are consistent with the fatigue short crack propagation rate prediction results provided by the present invention; therefore, the simulation method for low-cycle fatigue short crack initiation and propagation based on continuous cumulative damage provided by the present invention can effectively predict the propagation rate of fatigue short cracks under multiaxial stress.

[0108] like Figure 13As shown, the present invention provides an embodiment with a peak load of 2500 N and a load ratio of 0.1,550. The diagram shows the cumulative damage values ​​at different locations at the notch root just before crack initiation in a single-sided notch fatigue test. Due to stress concentration, there is a greater degree of fatigue damage accumulation near the notch root, while the damage is less at locations farther from the notch. This also explains the phenomenon that short cracks propagate faster in the early stages.

[0109] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is 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 within the scope of protection of the present invention.

Claims

1. A method of simulating low-cycle fatigue cracking based on continuous cumulative damage, characterized by, The method comprises the following steps: S1: in a multi-axial stress state, according to the numerical value of the current equivalent plastic strain at the node and the size of the memory surface, updating the follow-up hardening parameter in the cyclic elastoplastic constitutive model; And calculate the yield surface size caused by isotropic hardening by using the current equivalent plastic strain at the node; S2: assuming that the strain tensor increment of the current incremental step is the elastic strain increment, based on the current stress tensor, strain tensor and fatigue damage value at the node, according to the elastic stress-strain relationship in the cyclic elastoplastic constitutive model, the elastic trial state and the corresponding yield function trial state are obtained, if the numerical value of the yield function trial state is less than 0, the stress tensor, strain tensor and equivalent plastic strain in the elastic trial state are saved, and S4 is turned to; otherwise, S3 is turned to; S3: the equivalent plastic strain is updated by the radial back mapping method, and whether the stress tensor increment converges is calculated based on the updated equivalent plastic strain, if the convergence is obtained, the current stress tensor and strain tensor are updated and reserved, and S4 is turned to; otherwise, S1 is turned to; S4: whether the incremental step is in the loading or unloading process is judged by the increase or decrease of the updated stress tensor, if the current incremental step is in the current loading cycle, S1 is turned to for the calculation of the next incremental step; if the current incremental step is not in the current loading cycle, and the number of loading cycles does not reach the maximum number of cycles, the number of loading cycles, the memory surface parameter and the fatigue damage value are updated, and whether the node is in a crack element is judged according to the fatigue damage value, and S1 is turned to for the calculation of the next incremental step. The method for constructing the cyclic elastoplastic constitutive model comprises the following steps: A cyclic elastoplastic constitutive model coupled with damage of a test material is defined for a uniaxial low-cycle fatigue test; damage parameters of a low-cycle fatigue damage evolution model are determined by using the results of the strain-controlled uniaxial low-cycle fatigue test; the fatigue damage value is removed from the results of the strain-controlled uniaxial low-cycle fatigue test, and material parameters of the cyclic elastoplastic constitutive model in an equivalent undamaged state are calculated.

2. The simulation method of claim 1, wherein, The method for judging whether the node is in a crack element comprises the following steps: If the updated fatigue damage value is greater than a critical value, the Young's modulus of the node is reduced to a preset proportion of the initial Young's modulus, it is determined that the node is in a crack element, the updated fatigue damage value is restored to the critical fatigue damage value, and S1 is turned to; otherwise, the updated fatigue damage value is reserved, and S1 is turned to.

3. The simulation method of claim 2, wherein, The cyclic elastoplastic constitutive model comprises: a master equation of an elastoplastic constitutive model, a nonlinear follow-up hardening submodel of a back stress tensor, a nonlinear isotropic hardening submodel and a strain range memory effect submodel.

4. The simulation method of claim 3, wherein, The critical fatigue damage value is determined by using the ratio of the Young's modulus in the last loading cycle before crack initiation to the Young's modulus in the initial loading cycle in the uniaxial fatigue test.

5. A simulation system for low cycle fatigue crack based on continuous cumulative damage, characterized by, The method comprises the following steps: A state variable recovery module is configured to obtain the current stress tensor, strain tensor, equivalent plastic strain, loading cycle number, memory surface parameter and fatigue damage value of each node; A material parameter updating module is configured to update the corresponding follow-up hardening parameter according to the numerical value of the current equivalent plastic strain and the size of the memory surface; An isotropic hardening module is configured to calculate the yield surface size caused by isotropic hardening by using the current equivalent plastic strain; an elastic prediction module, assuming that the strain tensor increment of the current increment step is an elastic strain increment, based on the current stress tensor, strain tensor and fatigue damage value of the node, obtaining an elastic trial state and a trial state of a yield function corresponding to an elastic stress-strain relationship in a cyclic elastoplastic constitutive model, if the trial state value of the yield function is less than 0, saving the stress tensor, strain tensor and equivalent plastic strain in the elastic trial state; a plastic correction module, configured to update the equivalent plastic strain by a radial return mapping method when the trial state value of the yield function is greater than or equal to 0; a consistent tangent modulus module, configured to calculate whether the stress tensor increment converges based on the updated equivalent plastic strain, and if the stress tensor increment converges, updating and preserving the current stress tensor and strain tensor; a loading cycle module, configured to judge whether the increment step is in a loading or unloading process by increasing or decreasing the updated stress tensor, if the current increment step is in the current loading cycle, driving a state variable recovery module to run in the next increment step; if the current increment step is not in the current loading cycle, and the number of loading cycles does not reach the maximum number of cycles, updating the number of loading cycles, memory surface parameters and fatigue damage value; a unit failure module, configured to judge whether the unit where the node is located is a crack unit according to the fatigue damage value; a method for constructing the cyclic elastoplastic constitutive model comprises: defining a cyclic elastoplastic constitutive model of a coupling damage of a test material for a uniaxial low-cycle fatigue test; determining damage parameters of a low-cycle fatigue damage evolution model by using a strain-controlled uniaxial low-cycle fatigue test result; removing the fatigue damage value in the strain-controlled uniaxial low-cycle fatigue test result, and calculating material parameters of the cyclic elastoplastic constitutive model in an equivalent undamaged state.

6. The simulation system of claim 5, wherein, a method for the unit failure module to judge whether the unit where the node is located is a crack unit comprises: if the updated fatigue damage value is greater than a critical fatigue damage value, reducing the Young's modulus of the unit where the node is located to a preset proportion of the initial Young's modulus, determining that the unit where the node is located is a crack unit, and restoring the updated fatigue damage value to the critical fatigue damage value; otherwise, preserving the updated fatigue damage value.

7. The simulation system of claim 5 or 6, wherein, the cyclic elastoplastic constitutive model comprises: a master equation of an elastoplastic constitutive model, a nonlinear servo-hardening submodel of a back stress tensor, a nonlinear isotropic hardening submodel and a strain range memory effect submodel.

8. The simulation system of claim 7, wherein, the critical fatigue damage value is determined by using a ratio of the Young's modulus in the last loading cycle before crack initiation to the Young's modulus in the initial loading cycle in a uniaxial fatigue test.

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