Crystal plasticity fatigue accelerated calculation method based on finite element software simulation
By integrating the adaptive step-size control loop skip algorithm with ABAQUS simulation software, the problem of low computational efficiency in crystal plastic fatigue simulation was solved, and efficient and accurate fatigue simulation calculations were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-02
AI Technical Summary
Existing simulations of crystalline plastic fatigue are time-consuming and costly, and existing loop skipping algorithms cannot adapt to the differences in the evolution rate of material damage state variables, and their engineering applications have high barriers to entry.
An adaptive step-size control-based loop skip algorithm is adopted. By extrapolating the state variables through second-order Taylor expansion and combining the UMAT, UEXTERNALDB, and DISP/DLOAD subroutines of the ABAQUS simulation software, dynamic adjustment of the state variables and data interaction are realized, thereby improving computational efficiency.
It significantly improves the efficiency of fatigue simulation calculations by more than 100 times, ensures calculation accuracy, and reduces the difficulty of engineering applications.
Smart Images
Figure CN122135848A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of material fatigue simulation analysis technology, and more specifically, relates to an accelerated calculation method for crystal plastic fatigue based on finite element software simulation. Background Technology
[0002] Metallic materials are widely used in aerospace, rail transportation, and energy equipment. Key components such as turbine blades for aero-engines and axles for high-speed trains are subjected to low-amplitude, high-frequency cyclic loads during service. The Crystal Plasticity Finite Element Method (CPFEM) can explicitly consider grain morphology, orientation, and slip system characteristics by constructing a representative polycrystalline volume element model, capturing non-uniform microplastic behavior at the grain scale, and is an effective tool for studying fatigue micro-damage mechanisms. However, the computational time required for cycle-by-cycle simulation is too high.
[0003] To address this issue, researchers have proposed the basic concept of loop skipping techniques, but existing techniques still have the following shortcomings: First, existing loop skipping algorithms mostly adopt a fixed jump step size strategy, which cannot adapt to the significant differences in the evolution rate of material damage state variables at different stages, resulting in insufficient efficiency or loss of accuracy.
[0004] Second, existing loop skipping algorithms involve data interaction and coordination control between multiple user subroutines. Existing literature does not disclose enough details of the implementation of multi-subroutine collaborative work, and the threshold for engineering application is relatively high.
[0005] Therefore, there is an urgent need to develop an accelerated calculation method for crystal plastic fatigue that combines computational efficiency and numerical accuracy. Summary of the Invention
[0006] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method for accelerating the calculation of crystal plastic fatigue based on finite element software simulation, which aims to significantly improve the calculation efficiency of fatigue simulation while ensuring calculation accuracy.
[0007] To achieve the above objectives, this invention provides a method for accelerating the calculation of crystal plastic fatigue based on finite element software simulation, comprising: (1) At the beginning of the current Nth load loading cycle, determine whether the previous i consecutive loading cycles adjacent to the current Nth load loading cycle are crystal plastic fatigue simulation performed cycle by cycle. If not, execute step (2); if yes, execute step (3); where i≥2; (2) Perform crystal plastic fatigue simulation on the current Nth loading cycle to obtain the state variables at the end of the current Nth loading cycle. The state variable The damage variables of the specimen material are included, and the damage variables of the specimen material are determined based on the crystal plastic constitutive model; let N=N+1, and determine whether the target cycle number has been reached, or determine whether the failure criterion of the specimen material is met based on the current state variables; if yes, then end, and complete the crystal plastic fatigue calculation of the specimen material; if no, then return to step (1); (3) Select the allowable loading cycle step size for each state variable to jump at each integration point in the finite element software. The minimum value in the value is used as the loading cycle step size Δ to jump after the end of the current Nth loading cycle. N And update the N+Δth jump after the jump. N The state variables at the start of each loading cycle ;in, , express The second derivative of , where m represents the number of each integration point in the finite element software, and c is the accuracy control parameter; let N = N + Δ N Execute step (4); (4) Determine whether the target cycle number has been reached, or determine whether the failure criterion of the specimen material is met based on the current state variable; if not, return to step (2); if yes, end and complete the calculation of crystal plastic fatigue.
[0008] Furthermore, the N+Δth N The state variables at the start of each loading cycle for:
[0009] in, express The first derivative.
[0010] Furthermore, the allowable loading cycle step size for each state variable to jump at each integration point in the finite element software. The method for determining it is as follows: Jump Δ after the end of the current Nth loading cycle N State variables after one loading cycle step Using second-order Taylor expansion: ,in, Represents a second-order infinitesimal; based on The second-order Taylor expansion, and in Under the constraints, we obtain ;in, This indicates that it is much smaller than.
[0011] Furthermore, the damage variables of the specimen material include: plastic strain rate. and equivalent plastic strain rate ; The damage variables of the specimen material are determined based on the crystal plastic constitutive model, including: Establish the plastic velocity gradient of the specimen material in the simulation of crystalline plastic fatigue Relationship with the slip ratios of various slip systems in the crystal: ,in, The total number of slip systems in the crystal. Let be the slip ratio of the α-th slip system. Let be the unit vector of the slip direction of the α-th slip system. Let be the normal unit vector of the slip surface of the α-th slip system, with the symbol . Represents the tensor product of vectors; The slip ratio of the α-th slip system is established using a slip constitutive relation based on thermally activated dislocation motion. The functional relationship between the shear stress, microstructure parameters and current temperature T of each slip system in the simulation of crystal plastic fatigue of the specimen material; Substituting the functional relationship into the plastic velocity gradient The plastic velocity gradient is obtained from the relationship between the slip ratios of the various slip systems of the crystal. ; Based on the aforementioned plastic velocity gradient Determine the plastic strain rate and the equivalent plastic strain rate .
[0012] Furthermore, the plastic strain rate and the equivalent plastic strain rate for:
[0013]
[0014] in, express Transpose of; This represents the dot product.
[0015] Furthermore, it also includes the jump Δ N The time taken for the N+Δth loading cycle step is related to the N+Δth cycle step. N The load is balanced for each loading cycle.
[0016] Furthermore, the finite element software is ABAQUS simulation software; On the ABAQUS simulation software, the UMAT subroutine is used to construct the crystal plastic constitutive model; the UEXTERNALDB subroutine is used to determine whether the i consecutive loading cycles adjacent to the current Nth loading cycle are performing crystal plastic fatigue simulation cycle by cycle, and to determine the loading cycle step size Δ. N Calculation and the state variables Update; and use the COMMON module to bridge the UMAT subroutine and the UEXTERNALDB subroutine to achieve data transfer; use the DISP or DLOAD subroutine according to the jump Δ N The time taken for the N+Δth loading cycle step is related to the N+Δth cycle step. N The load is balanced for each loading cycle.
[0017] The present invention also provides a crystal plastic fatigue acceleration computing system, including a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the crystal plastic fatigue accelerated calculation method described above.
[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the accelerated calculation method for crystal plastic fatigue as described in any of the preceding claims.
[0019] The present invention also provides a computer program product, including a computer program that, when the computer program is run on a computer, causes the computer to execute the crystal plastic fatigue accelerated calculation method described in any of the above claims.
[0020] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) This invention establishes a loop skip acceleration algorithm with adaptive step size control. After simulating the crystal plastic fatigue of metallic materials for i consecutive loading cycles, the algorithm adjusts the state variables of the current Nth loading cycle. and its rate of change (using (Characteristics) Real-time feedback dynamically adjusts the jump loading cycle step size Δ N In order to deal with the next Δ N By skipping loading cycles, the method accelerates the calculation of crystal plastic fatigue simulation, avoiding the problem that existing fixed-step-size strategies cannot adapt to the significant differences in the evolution rate of material damage state variables at different stages. This significantly improves the computational efficiency of fatigue simulation while maintaining computational accuracy. Experiments show that, compared to the full-cycle calculation method, the computational efficiency of this invention can be improved by more than 100 times.
[0021] (2) Furthermore, the present invention provides a complete ABAQUS user subroutine integration scheme. Through the collaborative work of multiple subroutines such as UMAT, UEXTERNALDB, DLOAD / DISP, a high degree of integration between the loop skip acceleration algorithm and the crystal plastic constitutive model is achieved, which has good versatility and portability.
[0022] In general, this invention is applicable to fatigue simulation of various metallic materials, providing an effective numerical tool for revealing the mechanism of fatigue micro-damage and establishing fatigue life prediction models based on microstructure. Attached Figure Description
[0023] Figure 1 This is a detailed flowchart of the loop skip acceleration algorithm in this invention.
[0024] Figure 2 This is a schematic diagram illustrating the data interaction principle between various user subroutines in ABAQUS in this invention.
[0025] Figure 3 This is a schematic diagram of the acceleration effect of loop skipping in an embodiment of the present invention. The horizontal axis represents the ABAQUS analysis step time (in seconds), and the vertical axis represents the equivalent fatigue loading time achieved by extrapolation through loop skipping (in seconds). The slope of the curve reflects the efficiency of the accelerated calculation. Detailed Implementation
[0026] 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. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0027] In this invention, the terms "first," "second," etc., used in the invention and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.
[0028] Example 1 like Figure 1 and Figure 2 As shown, this embodiment of the invention provides an accelerated calculation method for crystal plastic fatigue based on ABAQUS (finite element analysis software) simulation, including the following steps: S1. Establish a crystal plastic constitutive model considering the temperature-dependent slip criterion to obtain the state variables of the specimen material under various load cycles in the fatigue test; wherein, the state variables include the plastic strain rate. Equivalent plastic strain rate Material damage variables included: In this embodiment of the invention, the specimen material is a metallic material.
[0029] S1.1 Establish the plastic velocity gradient of the crystals in the specimen material during the crystalline plastic fatigue process (in each load cycle of the specimen material fatigue test). Relationship with the slip ratios of various slip systems in the crystal:
[0030] in, The total number of slip systems in the crystal. Let be the slip ratio of the α-th slip system. Let be the slip direction vector of the α-th slip system. Let be the normal vector of the slip surface of the α-th slip system, with the symbol . Represents the tensor product of vectors.
[0031] S1.2 In this embodiment of the invention, the slip constitutive relation based on thermally activated dislocation motion is used to establish the slip ratio of the crystal. Functional relationship with temperature, shear stress, and microstructure parameters:
[0032] in, This represents the density of mobile dislocations in the crystal of the specimen material under various load cycles. The frequency at which dislocations in the crystal of the specimen attempt to overcome the energy barrier during various load cycles. The size of the Burgers vector. Boltzmann's constant, Here, T represents the activation energy for dislocation slip, and T represents the temperature. For the crystallization of the specimen material under various load cycles... The shear stress of a slip system This represents the critical shear stress corresponding to the slip system. This represents the dislocation pinning distance. In other embodiments, the corresponding functional relationship can also be selected based on different material properties, such as a rate-dependent power-law functional relationship.
[0033] S1.3 Under this system, the plastic strain rate of the crystals during the plastic fatigue process of the specimen material. The expression is:
[0034] in, express The transpose of .
[0035] Equivalent plastic strain rate :
[0036] in, This represents the dot product.
[0037] S2. Establish a loop skip acceleration calculation method with adaptive step size control: S2.1 Perform i (i≥2) consecutive loading cycles, and use finite element software to perform a complete and continuous numerical simulation of the crystal plastic fatigue of the specimen material. At the end of each cycle (the end of the loading cycle), obtain the state variables of the specimen material under the current loading cycle. These state variables include the plastic strain rate of the crystal. Equivalent plastic strain rate The material damage variables, including those from S1, are determined based on the bulk plastic constitutive model. The current state variables are then stored in array V; in this embodiment, i=3.
[0038] S2.2, In the current Nth loading cycle, for the N+Δth loading cycle after skipping ΔN loading cycles. N The loading cycle begins (i.e., the N+Δth loading cycle). N- State variables at the end of one loading cycle Extrapolation is performed using a second-order Taylor expansion:
[0039] in, This represents the array of state variables at the end of the Nth loading cycle. express The first derivative, express The second derivative, Represents a second-order infinitesimal. Represents the N+Δth N An array of state variables starting from the Nth loading cycle. ΔN is the number of loading cycles to jump from the current Nth loading cycle; ΔN is a variable. For example, if the current cycle is the fourth loading cycle (N=4), calculations show that two loading cycles can be jumped (ΔN=2). After jumping two loading cycles, the cycle will start at the sixth cycle, skipping the fourth and fifth loading cycles in between.
[0040] S2.3. Establish an adaptive step size determination method based on extrapolation error control, including: exist Under constraints, calculate the allowable jump time of each state variable at each integration point in the finite element software. :
[0041] in, This represents the allowable jump step size of the loading cycle at the m-th integration point of each state variable in the finite element software; c is a precision control parameter, which is selected according to actual needs; symbol This indicates that it is much smaller than.
[0042] from Choose the value with the smallest value as the jump loading cycle step size Δ N .
[0043] S2.4 Update the state variables starting from the N+ΔNth period using backward Euler linear extrapolation:
[0044] in, For the N+Δth N An array of state variables that begins at the start of each loading cycle.
[0045] Also includes based on skip Δ N The time taken for the N+Δth loading cycle step is related to the N+Δth cycle step. N The load is balanced for each loading cycle.
[0046] S2.5 After completing the extrapolation of the state variables, update the current number of fatigue loading cycles, continue to simulate i consecutive loading cycles, and then jump ΔN cycles. That is, repeat steps S2.1 to S2.4 until the target number of cycles is reached or the failure criterion of the specimen material is met.
[0047] S3. In this embodiment of the invention, multiple subroutines work collaboratively on the ABAQUS platform. Specifically, the process of establishing the crystal plastic constitutive model in step one is mounted on the UMAT subroutine, and the cyclic skip acceleration calculation method with adaptive step size control in step two is mounted on the UEXTERNALDB subroutine. By bridging the COMMON module, the state variable information on the UMAT subroutine is transferred to the UEXTERNALDB subroutine. The DISP / DLOAD subroutine is used to balance the load over time. In this way, the crystal plastic constitutive model established in step S1 is realized, as well as the cyclic skip acceleration algorithm with adaptive step size control in step S2 is integrated.
[0048] like Figure 3 The diagram illustrates the acceleration effect of loop skipping in an embodiment of the present invention. The horizontal axis represents the ABAQUS analysis step time (in seconds), and the vertical axis represents the equivalent fatigue loading time achieved through loop skipping extrapolation (in seconds). The slope of the curve reflects the efficiency of the accelerated calculation. Experiments have shown that the computational efficiency of the method of the present invention can be improved by more than 100 times.
[0049] Example 2 This invention provides a crystal plastic fatigue accelerated calculation system, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the crystal plastic fatigue accelerated calculation method in Embodiment 1 above.
[0050] The relevant technical solutions are the same as above, and will not be repeated here.
[0051] Example 3 This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the accelerated calculation method for crystal plastic fatigue in Embodiment 1 above.
[0052] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.
[0053] The relevant technical solutions are the same as above, and will not be repeated here.
[0054] Example 4 This invention provides a computer program product, including a computer program that, when run on a computer, causes the computer to execute the steps of the accelerated calculation method for crystal plastic fatigue in Embodiment 1 above.
[0055] The relevant technical solutions are the same as above, and will not be repeated here.
[0056] 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 for accelerating the calculation of crystal plastic fatigue based on finite element software simulation, characterized in that, include: (1) At the beginning of the current Nth load loading cycle, determine whether the previous i consecutive loading cycles adjacent to the current Nth load loading cycle are crystal plastic fatigue simulation performed cycle by cycle. If not, execute step (2); if yes, execute step (3); where i≥2; (2) Perform crystal plastic fatigue simulation on the current Nth loading cycle to obtain the state variables at the end of the current Nth loading cycle. The state variable The damage variables of the specimen material are included, and the damage variables of the specimen material are determined based on the crystal plastic constitutive model; let N=N+1, and determine whether the target cycle number has been reached, or determine whether the failure criterion of the specimen material is met based on the current state variables; if yes, then end, and complete the crystal plastic fatigue calculation of the specimen material; if no, then return to step (1); (3) Select the allowable loading cycle step size for each state variable to jump at each integration point in the finite element software. The minimum value in the value is used as the loading cycle step size Δ to jump after the end of the current Nth loading cycle. N And update the N+Δth jump after the jump. N The state variables at the start of each loading cycle ;in, , express The second derivative of , where m represents the number of each integration point in the finite element software, and c is the accuracy control parameter; let N = N + Δ N Execute step (4); (4) Determine whether the target cycle number has been reached, or determine whether the failure criterion of the specimen material is met based on the current state variable; if not, return to step (2); if yes, end and complete the calculation of crystal plastic fatigue.
2. The accelerated calculation method for crystal plastic fatigue according to claim 1, characterized in that, The N+Δ N The state variables at the start of each loading cycle for: in, express The first derivative.
3. The accelerated calculation method for crystal plastic fatigue according to claim 2, characterized in that, The allowable loading cycle step size for each state variable to jump at each integration point in the finite element software. The method for determining it is as follows: Jump Δ after the end of the current Nth loading cycle N State variables after one loading cycle step Using second-order Taylor expansion: ,in, Represents a second-order infinitesimal; based on The second-order Taylor expansion, and in Under the constraints, we obtain ;in, This indicates that it is much smaller than.
4. The accelerated calculation method for crystal plastic fatigue according to any one of claims 1-3, characterized in that, The damage variables of the specimen material include: plastic strain rate. and equivalent plastic strain rate ; The damage variables of the specimen material are determined based on the crystal plastic constitutive model, including: Establish the plastic velocity gradient of the specimen material in the simulation of crystalline plastic fatigue Relationship with the slip ratios of various slip systems in the crystal: ,in, This represents the total number of slip systems in the crystal. Let be the slip ratio of the α-th slip system. Let be the slip direction vector of the α-th slip system. Let be the normal vector of the slip surface of the α-th slip system, with the symbol . Represents the tensor product of vectors; The slip ratio of the α-th slip system is established using a slip constitutive relation based on thermally activated dislocation motion. The functional relationship between the shear stress, microstructure parameters and current temperature T of each slip system in the simulation of crystal plastic fatigue of the specimen material; Substituting the functional relationship into the plastic velocity gradient The plastic velocity gradient is obtained from the relationship between the slip ratios of the various slip systems of the crystal. ; Based on the aforementioned plastic velocity gradient Determine the plastic strain rate and the equivalent plastic strain rate .
5. The accelerated calculation method for crystal plastic fatigue according to claim 4, characterized in that, The plastic strain rate and the equivalent plastic strain rate for: in, express Transpose of; This represents the dot product.
6. The accelerated calculation method for crystal plastic fatigue according to claim 4, characterized in that, It also includes the Δ based on the jump. N The time taken for the N+Δth loading cycle step is related to the N+Δth cycle step. N The load is balanced for each loading cycle.
7. The accelerated calculation method for crystal plastic fatigue according to claim 6, characterized in that, The finite element software is ABAQUS simulation software; On the ABAQUS simulation software, the UMAT subroutine is used to construct the crystal plastic constitutive model; the UEXTERNALDB subroutine is used to determine whether the i consecutive loading cycles adjacent to the current Nth loading cycle are performing crystal plastic fatigue simulation cycle by cycle, and to determine the loading cycle step size Δ. N Calculation and the state variables Update; and use the COMMON module to bridge the UMAT subroutine and the UEXTERNALDB subroutine to achieve data transfer; use the DISP or DLOAD subroutine according to the jump Δ N The time taken for the N+Δth loading cycle step is related to the N+Δth cycle step. N The load is balanced for each loading cycle.
8. A crystal plastic fatigue accelerated calculation system, characterized in that, Includes computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the accelerated calculation method for crystal plastic fatigue according to any one of claims 1-7.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the accelerated calculation method for crystal plastic fatigue as described in any one of claims 1-7.
10. A computer program product, characterized in that, Includes a computer program that, when run on a computer, causes the computer to perform the accelerated calculation method for crystal plastic fatigue according to any one of claims 1-7.