Crack propagation prediction method and system based on dislocation net slip failure indicator factor

Abstract

The present invention discloses a crack extension prediction method and system based on a dislocation net slip failure indicator factor, which belongs to the technical field of fatigue numerical simulation, including: constructing a crystal plastic crack extension finite element model of the material according to the microstructure diagram of the material and the random orientation of each grain; constructing a crystal plastic constitutive model based on the crystal plastic crack extension finite element model, and embedding a damage indicator factor based on dislocation net slip to generate an extended finite element crack extension criterion based on the net slip damage factor; and obtaining the average value of the net slip of the crack tip unit integral point, judging whether the crack extension direction needs to be corrected according to the rotation angle between the new and old cracks, thereby predicting crack extension. The present invention can simulate the crack extension behavior related to slip in the micro short crack extension stage, and can capture the crack extension characteristics unrelated to dislocation slip in the long crack extension stage, so as to obtain the correct crack extension path.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue numerical simulation, and in particular to a method and system for predicting crack propagation based on a dislocation net slip failure indicator factor. Background Art

[0002] Research background and significance of fatigue crack growth During the use of engineering materials and structures, materials often produce fatigue cracks under cyclic loads. The formation and growth of fatigue cracks are one of the main causes of material and structural failure. Therefore, the study of fatigue crack growth has important scientific and engineering significance. A deep understanding of the growth mechanism of fatigue cracks can improve the design life of materials and structures, avoid catastrophic failure, and ensure the safety and reliability of engineering systems. Traditional fatigue crack growth research mainly focuses on the macroscopic scale, and predicts the crack growth behavior through experiments and theoretical models. However, the complexity of materials at the microscopic scale, such as grain orientation, grain boundary characteristics, and local stress concentration, is difficult to fully describe through macroscopic models. In recent years, with the development of computing technology and material characterization methods, researchers have begun to pay attention to the fatigue crack growth mechanism at the microscopic scale.

[0003] Crystal plasticity theory is a theory that describes the deformation behavior of materials at a microscopic scale (such as the grain scale). Using crystal plasticity to study microscopic crack growth can provide a detailed description of the stress and strain distribution at the crack tip, which is crucial for understanding the crack growth mechanism. Crystal plasticity can consider the effects of grain orientation, grain boundaries, and microstructural features within the grain on the crack growth path and rate. This is particularly important for the study of fatigue crack growth in polycrystalline materials. Through crystal plasticity theory, the microstructural evolution of materials under cyclic loading, such as the formation and development of slip bands, can be simulated, which is very important for the prediction of fatigue crack growth. The extended finite element method (XFEM) is an enhanced finite element method that can effectively deal with crack generation and growth problems by introducing additional degrees of freedom. Compared with the traditional finite element method, XFEM does not require re-meshing of the crack path and can simulate the crack growth process more flexibly. Therefore, crystal plasticity combined with the extended finite element method is an emerging numerical simulation method that combines crystal plasticity theory with the extended finite element method, which can more accurately simulate the fatigue crack propagation behavior of materials at the microscopic scale.

[0004] However, the current extended finite element simulation of crack propagation still has some limitations, such as there can only be one crack line in an enriched unit, and the deflection angle during crack propagation in an incremental step cannot be greater than 90°. When the above situation occurs, the finite element will give an incorrect extension path, especially in the micro crack propagation stage, because in the micro short crack propagation stage, crack propagation is mainly caused by slip systems with different active levels, so it shows a tortuous extension path at the micro scale. This undoubtedly brings certain difficulties to the simulation of micro crack propagation. Therefore, it is of great significance in theory and application to overcome the shortcomings of simulation technology, focus on the extension of micro fatigue cracks, guide the design and optimization of new materials through in-depth understanding of the micro crack propagation mechanism, and improve the fatigue resistance of materials. Summary of the invention

[0005] In order to solve the above problems, the purpose of the present invention is to provide a crack propagation prediction technology based on dislocation net slip failure indicator factor, which is intended to overcome the difficulties of existing simulation technology and thus obtain the correct crack propagation path.

[0006] In order to achieve the above technical objectives, the present application provides a crack propagation prediction method based on dislocation net slip failure indicator factor, comprising the following steps:

[0007] According to the microstructure diagram of the material and the random orientation of each grain, a finite element model of crystal plastic crack growth of the material is constructed;

[0008] Based on the crystal plastic crack growth finite element model, a crystal plastic constitutive model is constructed, and a damage indicator factor based on dislocation net slip is embedded to generate an extended finite element crack growth criterion based on the net slip damage factor.

[0009] Based on the extended finite element crack growth criterion, the crack growth prediction is performed by obtaining the average value of the net slip of the crack tip unit integration point and according to the rotation angle between the new and old cracks.

[0010] Preferably, in the process of constructing the crystal plasticity constitutive model, the crystal plasticity constitutive model is constructed according to the plastic deformation rate gradient, the plastic deformation gradient rate, the inverse of the plastic deformation gradient, the unit vector in the slip direction on the α slip system, the unit vector in the slip normal direction on the α slip system, and the shear rate on the α slip system.

[0011] Preferably, in the process of obtaining the shear rate on the α-th slip system, the shear rate is expressed as:

[0012]

[0013] in, is the reference shear rate on the αth slip system, τ αis the analytical shear stress on the αth slip system, χ α is the back stress on the αth slip system, n is the flow rate index, g α is the slip resistance on the αth slip system.

[0014] Preferably, in the process of obtaining the net slip damage factor, the net slip damage factor S is expressed as:

[0015]

[0016] In the formula, m, is the material parameter, τ α0 It is the force required for a dislocation to move at unit velocity in an α slip system.

[0017] Preferably, in the process of obtaining the extended finite element crack growth criterion based on the net slip damage factor, the extended finite element crack growth criterion includes:

[0018] When the net slip S of the crack tip unit and the critical value S critical When the ratio is less than 1, the crack does not extend; when the ratio is greater than or equal to 1, the crack tip meets the cracking criterion and the crack extends forward; the extension direction is parallel to the slip system direction with the maximum net slip damage value.

[0019] Preferably, in the process of crack propagation prediction, the average value of the net slip of the crack tip unit integral point is used to determine whether the current incremental step meets the extended finite element crack propagation criterion. If not, proceed to the next incremental step. If so, extract the crack propagation direction.

[0020] Preferably, in the process of crack propagation prediction, the rotation angle β between the new and old cracks is calculated according to the extracted crack propagation direction to determine whether the limitation of the extended finite element occurs, that is, the crack rotation angle cannot be greater than 90° in one incremental step; if β>90°, the new crack propagation direction is adjusted to make β<90°, otherwise it is determined whether the limitation of the extended finite element occurs, that is, a unit is divided by more than one crack line. If the restriction condition is met, the new crack maintains the original propagation direction unchanged, otherwise the crack expands in the predicted direction.

[0021] The present invention also discloses a crack extension prediction system based on dislocation net slip failure indicator factor, which is used to implement a crack extension prediction method, including:

[0022] A model building module is used to build a finite element model of crystal plastic crack growth of the material based on the microstructure map of the material and the random orientation of each grain;

[0023] The criterion customization module is used to construct a crystal plastic constitutive model based on the crystal plastic crack growth finite element model, and embed the damage indicator factor based on dislocation net slip to obtain the extended finite element crack growth criterion based on the net slip damage factor;

[0024] The expansion prediction module is used to predict crack extension based on the extended finite element crack extension criterion by obtaining the average value of the net slip of the crack tip unit integration point and the rotation angle between the new and old cracks.

[0025] Preferably, the model building module is also used to construct a crystal plasticity constitutive model based on the plastic deformation rate gradient, the plastic deformation gradient rate, the inverse of the plastic deformation gradient, the unit vector in the slip direction on the α slip system, the unit vector in the slip normal direction on the α slip system, and the shear rate on the α slip system.

[0026] Preferably, the extended prediction module is also used to determine whether the current incremental step satisfies the extended finite element crack extension criterion based on the average value of the net slip of the crack tip unit integral point. If not, proceed to the next incremental step. If satisfied, extract the crack extension direction; calculate the rotation angle β between the new and old cracks based on the extracted crack extension direction to determine whether the extended finite element limitation occurs, that is, the crack rotation angle cannot be greater than 90° in one incremental step; if β>90°, adjust the new crack extension direction so that β<90°, otherwise determine whether the extended finite element limitation occurs, that is, a unit is divided by more than one crack line. If the restriction condition is met, the new crack maintains the original extension direction unchanged, otherwise the crack expands in the predicted direction.

[0027] The present invention discloses the following technical effects:

[0028] The present invention solves the inherent limitations of the simulation method when using crystal plastic expansion finite element to simulate micro fatigue crack growth. That is, in the expansion finite element simulation of crack growth, the crack angle cannot be greater than 90° in one incremental step and there can only be one crack line in one enrichment unit. The occurrence of the above two situations will lead to an incorrect crack growth path. The method described in the present invention can effectively solve the above two limitations.

[0029] The present invention can simulate the crack extension behavior related to slip in the microscopic short crack extension stage, and can also capture the crack extension characteristics unrelated to dislocation slip in the long crack extension stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 A flowchart of the present invention;

[0032] Figure 2 It is a schematic diagram of the crystal plasticity extended finite element model of the present invention;

[0033] Figure 3 A schematic diagram of the crack extension criterion based on the dislocation net slip damage indicator factor according to the present invention;

[0034] Figure 4 The stress-strain curve diagram of the welding joint test and simulation described in the present invention;

[0035] Figure 5 This is a schematic diagram of the expansion behavior of the long crack propagation stage described in the present invention that is independent of dislocation slip. DETAILED DESCRIPTION

[0036] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0037] like Figure 1-5 As shown, the present invention provides a method for predicting crack growth based on a dislocation net slip failure indicator factor, comprising the following steps:

[0038] S1. Establish a finite element model of crystal plastic crack growth based on ABAQUS software. The specific steps are as follows:

[0039] S11, generating a microstructure diagram of the simulated material and random orientation of each grain through a MATLAB program;

[0040] S12, importing the above microscopic model information into ABAQUS through a PYTHON script, generating a polycrystalline finite element model, and assigning material parameters;

[0041] S13. In the extended finite element module of ABAQUS, the model is set up to calculate the crack propagation area, and prefabricated cracks can be introduced, such as Figure 2 shown.

[0042] S2. Write the crystal plasticity constitutive model in the UMAT subroutine and embed the damage indicator factor S based on dislocation net slip;

[0043] S3. Define the extended finite element crack growth criterion based on the net slip damage factor in the UDMGINI subroutine. The specific steps are as follows:

[0044] S31, call UMAT to calculate the net slip S, when the net slip S of the crack tip unit and the critical value S critical The ratio is less than 1, that is The crack does not expand; when the ratio is greater than or equal to 1, that is, The crack tip meets the cracking criterion and the crack propagates forward;

[0045] S32, the extension direction is parallel to the direction of the slip system with the maximum net slip damage value, such as Figure 3 As shown;

[0046] S4. Write UDMGINI to extract the value of the net slip S of the unit integration point and calculate the average value of the unit net slip S;

[0047] S5. Determine whether the current incremental step meets the extension criterion according to the average value of the net slip S of the crack tip unit. If not, proceed to the next incremental step. If yes, proceed to the next step.

[0048] S6. Extract the crack propagation direction, calculate the rotation angle β between the new and old cracks, and determine whether the limit of the extended finite element occurs, that is, the crack rotation angle cannot be greater than 90° in one increment; if β>90°, adjust the new crack propagation direction to make β<90°, otherwise proceed to the next step;

[0049] S7, judging whether the limitation of the extended finite element occurs, that is, a unit is divided by more than one crack line. If such a situation occurs, the crack will expand back. If the limitation condition is met, the new crack keeps the original expansion direction unchanged, otherwise proceed to the next step;

[0050] S8, the crack is extended according to the criteria described in step S3;

[0051] The crystal plasticity constitutive equation of step S2 is:

[0052]

[0053] Among them, L p is the plastic deformation rate gradient, is the plastic deformation gradient rate, is the inverse of the plastic deformation gradient, S α is the unit vector in the slip direction of the αth slip system, n α is the unit vector in the slip normal direction of the αth slip system, is the shear rate on the αth slip system, which can be expressed as:

[0054]

[0055] in, is the reference shear rate on the αth slip system, τ α is the analytical shear stress on the αth slip system, χ α is the back stress on the αth slip system, n is the flow rate index, g α is the slip resistance on the αth slip system, and its evolution equation is:

[0056]

[0057] in, is the slip resistance increment on the αth slip system, h αα is the self-hardening modulus on the same slip system, h αβ is the potential hardening modulus between different slip systems, h0 is the initial hardening modulus, γ is the accumulated shear strain on all slip systems, τ s is the saturated slip resistance, τ0 is the initial critical analytical shear stress, q is the material constant, is the shear rate on the β slip system.

[0058] The net slip damage factor S of step S2 is:

[0059]

[0060] Among them, m, is the material parameter, τ α0 is the force required for the dislocation to move at unit speed on the α slip system, S α is the distance of dislocation movement in the α slip system.

[0061] The above method overcomes the erroneous crack propagation path caused by the simulation limitation of ABAQUS extended finite element. The crack propagation path before and after correction is compared. Figure 4 In addition, the micro fatigue crack growth prediction method based on this method can not only capture the tortuous growth behavior of micro short crack growth, but also capture the growth behavior of long crack growth stage that is not related to dislocation slip, such as Figure 5 shown.

[0062] The present invention solves the inherent limitations of the simulation method when using crystal plastic expansion finite element to simulate micro fatigue crack growth. That is, in the expansion finite element simulation of crack growth, the crack angle cannot be greater than 90° in one incremental step and there can only be one crack line in one enrichment unit. The occurrence of the above two situations will lead to an incorrect crack growth path. The method described in the present invention can effectively solve the above two limitations.

[0063] This method can not only simulate the crack growth behavior related to slip in the microscopic short crack growth stage, but also capture the crack growth characteristics independent of dislocation slip in the long crack growth stage.

[0064] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0065] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0066] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A crack propagation prediction method based on dislocation net slip failure indicator factor, characterized in that: The following steps are involved: Constructing a crystal plastic crack propagation finite element model of the material according to the microstructure diagram of the material and the random orientation of each grain; Based on the crystal plastic crack growth finite element model, a crystal plastic constitutive model is constructed, and a damage indicator factor based on dislocation net slip is embedded to generate an extended finite element crack growth criterion based on the net slip damage factor; Based on the extended finite element crack growth criterion, the crack growth prediction is performed by obtaining the average value of the net slip of the crack tip unit integration point and according to the rotation angle between the new and old cracks; In the process of constructing the crystal plastic constitutive model, the crystal plastic constitutive model is constructed according to the plastic deformation rate gradient, the plastic deformation gradient rate, the inverse of the plastic deformation gradient, the unit vector in the slip direction on the α-th slip system, the unit vector in the slip normal direction on the α-th slip system, and the shear rate on the α-th slip system; In the process of obtaining the shear rate on the αth slip system, the shear rate is expressed as: in, is the reference shear rate on the αth slip system, τ α is the analytical shear stress on the αth slip system, χ α is the back stress on the αth slip system, n is the flow rate index, g α is the slip resistance on the αth slip system; In the process of obtaining the net slip damage factor, the net slip damage factor S is expressed as: In the formula, m, is the material parameter, τ α0 is the force required for a dislocation to move at unit velocity on the α slip system; In the process of obtaining the extended finite element crack growth criterion based on the net slip damage factor, the extended finite element crack growth criterion includes: When the ratio of the net slip S of the crack tip unit to the critical value Scritical is less than 1, the crack does not extend; when the ratio is greater than or equal to 1, the crack tip meets the cracking criterion and the crack extends forward; the extension direction is parallel to the direction of the slip system with the maximum net slip damage value.

2. The crack propagation prediction method based on dislocation net slip failure indicator factor according to claim 1 is characterized in that: In the process of crack propagation prediction, the average value of the net slip of the crack tip unit integration point is used to determine whether the current incremental step meets the extended finite element crack propagation criterion. If not, the next incremental step is entered. If so, the crack propagation direction is extracted.

3. The crack propagation prediction method based on dislocation net slip failure indicator factor according to claim 2 is characterized in that: In the process of crack propagation prediction, the rotation angle β between the new and old cracks is calculated according to the extracted crack propagation direction to determine whether the limitation of the extended finite element occurs, that is, the crack rotation angle cannot be greater than 90° in one incremental step; if β>90°, the new crack propagation direction is adjusted to make β<90°, otherwise it is determined whether the limitation of the extended finite element occurs, that is, a unit is divided by more than one crack line. If the restriction condition is met, the new crack maintains the original propagation direction unchanged, otherwise the crack propagates in the predicted direction.

4. A crack growth prediction system based on dislocation net slip failure indicator factor, characterized in that: include: A model building module, for building a crystal plastic crack growth finite element model of the material according to the microstructure diagram of the material and the random orientation of each grain; A criterion customization module is used to construct a crystal plastic constitutive model based on the crystal plastic crack extension finite element model, and embed a damage indicator factor based on dislocation net slip to obtain an extended finite element crack extension criterion based on the net slip damage factor; An expansion prediction module, used for predicting crack expansion based on the extended finite element crack expansion criterion by obtaining the average value of the net slip of the crack tip unit integration point and according to the rotation angle between the new and old cracks; The model building module is further used to build the crystal plastic constitutive model according to the plastic deformation rate gradient, the plastic deformation gradient rate, the inverse of the plastic deformation gradient, the unit vector in the slip direction on the αth slip system, the unit vector in the slip normal direction on the αth slip system, and the shear rate on the αth slip system; In the process of obtaining the shear rate on the αth slip system, the shear rate is expressed as: in, is the reference shear rate on the αth slip system, τ α is the analytical shear stress on the αth slip system, χ α is the back stress on the αth slip system, n is the flow rate index, g α is the slip resistance on the αth slip system; In the process of obtaining the net slip damage factor, the net slip damage factor S is expressed as: In the formula, m, is the material parameter, τ α0 is the force required for a dislocation to move at unit velocity on the α slip system; In the process of obtaining the extended finite element crack growth criterion based on the net slip damage factor, the extended finite element crack growth criterion includes: When the ratio of the net slip S of the crack tip unit to the critical value Scritical is less than 1, the crack does not extend; when the ratio is greater than or equal to 1, the crack tip meets the cracking criterion and the crack extends forward; the extension direction is parallel to the direction of the slip system with the maximum net slip damage value.

5. The crack growth prediction system based on dislocation net slip failure indicator factor according to claim 4 is characterized in that: The expansion prediction module is also used to determine whether the current incremental step meets the extended finite element crack extension criterion based on the average value of the net slip of the crack tip unit integration point. If not, enter the next incremental step. If satisfied, extract the crack extension direction; calculate the rotation angle β between the new and old cracks based on the extracted crack extension direction to determine whether the extended finite element limitation occurs, that is, the crack rotation angle cannot be greater than 90° in one incremental step; if β>90°, adjust the new crack extension direction so that β<90°, otherwise determine whether the extended finite element limitation occurs, that is, a unit is divided by more than one crack line. If the restriction condition is met, the new crack maintains the original extension direction unchanged, otherwise the crack expands in the predicted direction.

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