High-temperature discontinuous structure fatigue fracture prediction method based on phase field method under variable-temperature working condition

Abstract

The invention discloses a method for predicting fatigue fracture of a high-temperature discontinuous structure based on a phase field method under a variable-temperature working condition, and belongs to the technical field of fracture behavior prediction. Acquiring a stress-strain field of a coupling temperature field of the viscous-plastic material under any cyclic load; based on a stress strain field of a coupling temperature field, a phase field residual error and a phase field stiffness matrix are obtained by obtaining a fracture phase field of a viscous-plastic material under any cyclic load, a phase field variable is obtained through iterative solution, and a corresponding UEL subprogram is compiled; and correcting and updating a stress-strain field, a temperature field and a phase field by adopting a data interaction process of a UMAT subprogram, a UMATHT subprogram and a UEL subprogram, and predicting the fracture behavior of the viscous-plastic material under the temperature gradient by identifying a phase field variable and an evolution path thereof under a cyclic load.

Description

Technical Field

[0001] The present invention belongs to the technical field of fracture behavior prediction, and in particular relates to a high-temperature discontinuous structure fatigue fracture prediction method based on a phase field method under variable temperature conditions. Background Art

[0002] In engineering fields such as high-temperature energy systems, aerospace propulsion devices, and high-end manufacturing equipment, key load-bearing structures generally serve in complex high-temperature and high-stress environments. Affected by the uneven distribution of heat sources and differences in heat dissipation conditions, significant temperature gradients are often formed inside the structure, making the thermal-mechanical coupling response of the material strongly spatially dependent. At the same time, the complex configuration and geometric characteristics lead to stress concentration in local areas, further exacerbating the nonlinear mechanical behavior under high-temperature conditions. Engineering materials represented by high-temperature metal alloys usually show obvious viscoplastic response in high-temperature service environments, and their mechanical parameters such as elastic modulus, yield stress, hardening modulus and fracture energy all vary significantly with temperature. Such materials are accompanied by energy dissipation, plastic accumulation and damage evolution during the loading process. Their fracture behavior is affected by the combined influence of temperature field and stress field, showing a complex evolution process.

[0003] Phase-field fracture theory has attracted widespread attention because it does not require a preset crack surface and can continuously describe the crack development process. However, most existing viscoplastic phase-field models have many limitations in terms of damage evolution under high-temperature gradients. They can only describe damage at a single temperature and are insufficient for describing the viscoplastic response of materials under temperature gradients and the thermal-damage multi-field coupling. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for predicting fatigue fracture of high-temperature discontinuous structures based on the phase field method under variable temperature conditions, so as to realize the damage initiation and crack propagation behavior of materials under non-uniform temperature distribution environments, and have the advantages of wide applicability in terms of materials, geometric structures, etc., and high prediction accuracy. A direct coupling mechanism between the temperature field and the phase field damage variables is introduced to characterize the influence of temperature on the inelastic response and damage evolution behavior of the material; a fully coupled solution system of the stress-strain field, the temperature field, and the fracture phase field is constructed to realize the synchronous update and iteration of the three-field information, thereby improving the simulation accuracy of the damage process; the model is applicable to complex geometric structures, and is particularly suitable for analyzing the damage initiation and crack propagation behavior of key components such as turbine disks serving under non-uniform temperature distribution environments, providing an effective numerical tool for life assessment and safety design of aviation components under high-temperature service conditions.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions: The present invention provides a method for predicting fatigue fracture of high-temperature discontinuous structures based on a phase field method under variable temperature conditions, comprising: Based on the Chaboche viscoplastic cyclic constitutive model and its corresponding UMAT subroutine and the temperature field heat conduction and its UMATHT subroutine, the stress and strain fields of the viscoplastic material coupled with the temperature field under arbitrary cyclic loading are obtained; Based on the stress-strain field coupled with the temperature field, the fracture phase field of the viscoplastic material under arbitrary cyclic loading is obtained, the phase field residual and phase field stiffness matrix are obtained, the phase field variables are obtained by iterative solution, and the corresponding UEL subroutine is compiled; The stress-strain field, temperature field, and phase field are modified and updated by using the data interaction process of the UMAT subroutine, UMATHT subroutine, and UEL subroutine. By identifying the phase field variables and their evolution path under cyclic loading, the fracture behavior of viscoplastic materials under temperature gradient is predicted.

[0006] Furthermore, the Chaboche viscoplastic cyclic constitutive model is used in combination with its corresponding UMAT subroutine to describe the mechanical behavior of the material, thereby obtaining the stress-strain field. At the same time, the temperature-related parameters are corrected in the UMAT subroutine, and the relationship between temperature and material parameters is expressed as follows using a function fitting method: ; in, represents the correction factor, is the initial temperature is the parameter at the initial temperature The temperature field is introduced through the built-in thermal-mechanical coupling solver of ABAQUS to simulate the effect of temperature on the material.

[0007] Furthermore, in the process of obtaining the historical accumulated plastic work, a temperature-dependent viscoplastic cyclic constitutive model is established based on the coupled temperature field to simulate the stress and strain fields of the material under the action of the temperature field under cyclic loads. The historical accumulated plastic work is thus obtained. In order to ensure the irreversibility of material damage, the maximum historical variable is introduced, and the formula is expressed as follows: ; in, To accumulate plastic work, is the maximum value in time t, and the inequality guarantees irreversibility.

[0008] Furthermore, in the process of obtaining the fracture energy, the critical fracture energy release rate and characteristic crack width related parameters are introduced into the UEL subroutine, and the type function, isoparametric unit and coordinate transformation are constructed. The user-defined unit is integrated according to the phase field variable to obtain the fracture energy.

[0009] Furthermore, in the process of obtaining the heat dissipation work, the UMATHT subroutine is compiled to obtain the dissipated energy due to temperature damage to the material based on the temperature difference of each incremental step and the specific heat capacity parameter affected by temperature. The formula is expressed as follows: ; in, represents the initial temperature, Indicates the current incremental step temperature, Represents the specific heat capacity of the material.

[0010] Furthermore, in the process of obtaining the phase field residual and the phase field stiffness matrix, the accumulated plastic work of the cyclic loading history, the fracture energy of the viscoplastic material, and the heat dissipation work affected by the temperature on the material are calculated based on the stress-strain field, the fracture phase field, and the temperature field to obtain the phase field residual and the phase field stiffness matrix; The temperature-dependent residual is expressed as: ; in, is the temperature B matrix, is the degradation function, is the heat conduction matrix, is the temperature interpolation function, is the heat flux vector of the internal heat source, is the current temperature.

[0011] Furthermore, during the compilation of the UMAT subroutine, the temperature-related parameters, including the elastic modulus, Poisson's ratio, and initial yield stress, are corrected based on the Chaboche viscoplastic cyclic constitutive model. At the same time, the accumulated plastic work calculated from the stress-strain field is stored in the COMMON public array.

[0012] Furthermore, in the process of compiling the UEL subroutine, the mapping from the global coordinate system to the natural coordinate system is achieved by introducing the finite element shape function to construct isoparametric units; Based on the mapping relationship, the Gauss-Legendre numerical integration method with weighted function is used to discretize the weak form of the phase field governing equation. The crack driving force expression combines the historical accumulated plastic work, the fracture energy of viscoplastic materials, and the thermal dissipation work affected by temperature on the material to calculate the phase field residual and phase field stiffness matrix in a multi-item cumulative form; The phase field residual and phase field stiffness matrix local variable data are stored and iteratively solved using the built-in Newton-Raphson nonlinear solver in ABAQUS to finally obtain the updated phase field variables and realize dynamic tracking of crack evolution.

[0013] Furthermore, in the compiled UMATHT subroutine, the temperature-related specific heat capacity and thermal conductivity parameters are modified, and the phase field variables are read from the COMMON array. The thermal conductivity matrix of the material is modified by introducing a degradation function to reflect the influence of material damage on thermal conductivity. The formula is expressed as follows: ; in, represents the degradation function, represents the temperature B matrix, represents the heat conduction matrix.

[0014] Furthermore, during the data interaction between the UMAT, UEL, and UMATHT subroutines, in the finite element calculation, one layer of elements uses the UMAT and UMATHT subroutines for thermal-mechanical coupling to solve the stress-strain and temperature fields, while another layer of user-defined elements uses the UEL subroutine to solve the phase field. Various data variables between the two layers of elements, including phase field variables, historical accumulated plastic work, and thermal dissipation work, are transferred through the COMMON public array. During the iterative solution process, the phase field variables are calculated through the stress-strain field and temperature field, the unit stress-stiffness matrix and the unit heat conduction matrix are corrected using the degradation function, the stress-strain field and the temperature field are updated, and then the phase field variables are updated through the newly calculated historical accumulated plastic work and heat dissipation energy.

[0015] Compared with the existing technology, the beneficial effects achieved by the present invention are as follows: the high-temperature discontinuous structure fatigue fracture prediction method based on the phase field method under variable temperature conditions provided by the present invention couples the temperature field with the viscoplastic fracture phase field, describes the influence of temperature on the inelastic part and phase field evolution of the viscoplastic material, realizes the damage initiation and crack propagation behavior of the material under a non-uniform temperature distribution environment, and realizes damage prediction and fracture prediction of complex structures, especially structural parts of viscoplastic materials with temperature gradients; it has wide applicability in terms of materials, geometric structures, etc., and has the advantages of high prediction accuracy.

[0016] A direct coupling mechanism of temperature field and phase field damage variables is introduced to characterize the influence of temperature on the inelastic response and damage evolution behavior of the material; a fully coupled solution system of stress-strain field, temperature field and fracture phase field is constructed to achieve synchronous updating and iteration of the three-field information, thereby improving the simulation accuracy of the damage process; the model is suitable for complex geometric structures, and is particularly suitable for analyzing the damage initiation and crack propagation behavior in key components such as turbine disks serving in non-uniform temperature distribution environments, providing an effective numerical tool for life assessment and safety design of aviation components under high-temperature service conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1This is a flow chart of a method for predicting fatigue fracture of high-temperature discontinuous structures based on a phase field method under variable temperature conditions provided by an embodiment of the present invention; Figure 2 is a diagram of a coupling mechanism provided by an embodiment of the present invention; Figure 3 It is a data transmission diagram between subroutines provided by an embodiment of the present invention; Figure 4 This is a V-shaped asymmetric notch waist specimen diagram and a gauge section grid detail diagram provided by an embodiment of the present invention.

[0018] Figure 5 Schematic diagram of displacement, temperature, and yield strength provided by an embodiment of the present invention.

[0019] Figure 6 It is a schematic diagram of deformation, stress, and damage provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0021] Example like Figure 1 As shown, an embodiment of the present invention provides a method for predicting fatigue fracture of a high-temperature discontinuous structure based on a phase field method under variable temperature conditions, comprising the following steps: Step S1: Based on the Chaboche viscoplastic cyclic constitutive model, the temperature-related parameters are modified in the UMAT subroutine to obtain the coupling of the stress-strain field and the temperature field, realize the thermomechanical coupling solution, and then simulate the influence of temperature on the material, and then enter step S2; Step S2: Calculate the historical accumulated plastic work based on the stress-strain field under the temperature field. Combine the incremental temperature difference and the temperature-dependent specific heat capacity parameter to solve for the thermal dissipation energy of the material damage. Based on the variational minimum energy principle, combined with the critical fracture energy release rate and the characteristic crack width parameter, calculate the material fracture energy and proceed to step S3. Step S3: Select the maximum historical accumulated plastic work, heat dissipation work, and fracture energy during the cyclic loading process, construct the phase field residual and phase field stiffness matrix, and use the built-in Newton-Raphson iteration method in ABAQUS to solve the nonlinear equations to obtain the phase field value, and then proceed to step S4; Step S4: Use the phase field variables calculated in the previous incremental step to construct a degradation function, and update the unit stiffness matrix in the stress-strain field and the unit heat conduction matrix in the temperature field accordingly, and then proceed to step S5; Step S5: Based on the degradation function with the phase field variable as the independent variable, the stress-strain field and the temperature field are updated to characterize the degree of material damage, and the accumulated plastic work and heat dissipation work are recalculated, and then the process proceeds to step S6; Step S6: Calculate the updated phase field variables for the nth incremental step and use them to solve for the new fracture energy. Combined with the updated historical accumulated plastic work and thermal dissipation work, derive the phase field value for the n+1th incremental step, thus achieving an alternating solution process for damage and material response.

[0022] The embodiment of the present invention provides a method for predicting fatigue fracture of high-temperature discontinuous structures based on the phase field method under variable temperature conditions. On the basis of the existing Chaboche viscoplastic cyclic constitutive model, the material parameters related to temperature are corrected, and the stress-strain field of the coupled temperature field is further given. The thermomechanical coupling unit is used to describe the cyclic stress-strain response of the complex structure. After that, the influence of the accumulated plastic strain energy and heat dissipation work on the material damage is considered, which is manifested in the phase field variables. A fully coupled alternating iterative solution method between the three physical fields of stress-strain field, temperature field and fracture phase field is developed, and finally the accurate prediction of the fracture behavior of viscoplastic materials under temperature interference is achieved. Compared with the prior art, the present invention has a wide range of applicability in terms of materials, geometric structures, etc., and can accurately predict the fracture behavior of viscoplastic materials under temperature gradient interference.

[0023] Example 1 As attached Figure 1 As shown, the method for predicting fatigue fracture of high-temperature discontinuous structures based on the phase field method under variable temperature conditions of the present invention includes the following steps: Step S1, based on the Chaboche viscoplastic cyclic constitutive model, the temperature-related parameters are corrected to obtain the main control equations (1-1)-(1-5) of the stress-strain field model coupled with the temperature field, where formula (1-1) is: represents the total strain, elastic, plastic and thermal strain tensors; in formula (1-3), represents the thermal expansion coefficient under isotropic material; Equation (1-4) represents the thermodynamic equilibrium equation that needs to be satisfied by the thermomechanical coupling constitutive model. represents the specific heat capacity of the material, Represents the heat flow tensor, following Fourier's Law (1-5). The material parameters related to temperature are modified as shown in (1-6) to (1-11), where and Indicates the current incremental step temperature and the initial incremental step temperature, and represents the elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, yield strength and thermal expansion coefficient at the initial temperature, and is the correction factor.

[0024]

[0025] Step S2: Based on the stress-variation field under the action of the temperature field, the cumulative plastic work is calculated using formula (1-12). The maximum cumulative plastic work in the time period t can be obtained by introducing the historical variable formula (1-15); the heat dissipation energy of the material damage caused by temperature is calculated using formula (1-13); and the fracture energy of the material is calculated using formula (1-14). and Represents the critical fracture energy release rate and characteristic crack width. The solution process according to the variational method is as shown in formulas (1-16)-(1-19). Formula (1-16) represents the phase field function in exponential form. Formula (1-17) is the solution of the homogeneous differential equation of formula (1-16). According to formula (1-18), the functional formula (1-19) can be obtained by inverse deduction of the Euler equation, thereby obtaining the crack area functional formula (1-20), which is the same as The product is calculated to obtain the phase field variable.

[0026]

[0027] Step S3: Select the maximum historical accumulated plastic work, heat dissipation work and fracture energy during the cyclic loading process, and construct the internal energy functional as shown in Equation (1-21) and the external energy functional as shown in Equation (1-22), where the first two terms in Equation (1-22) represent volume work and area work, and the last two terms represent surface heat and body heat; use Equation (1-24) as the degeneration function, and solve the total energy functional to obtain the phase field driving force equation of Equation (1-25).

[0028] The total energy functional composed of equations (1-21) and (1-22) is expressed in finite element discrete format. The isoparametric unit is introduced using the finite element shape function. The positional relationship in the global coordinate system is converted into an isoparametric coordinate system. The displacement, temperature and phase field variables are solved respectively to obtain the displacement field residual equation (1-25), the temperature field residual equation (1-26) and the phase field residual equation (1-27). The corresponding stiffness matrix is ​​obtained by differentiating the variables themselves. For example, the stiffness matrix of equation (1-28) is obtained by differentiating equation (1-27) with respect to the phase field value. The obtained residuals and stiffness matrices construct a nonlinear equation group, which is solved using the built-in Newton-Raphson iteration method in ABAQUS to update the phase field value.

[0029]

[0030] Step S4: Use the phase field variables calculated in the previous increment to construct the degradation function. Equation (1-29) represents the updated element stiffness matrix in the stress-strain field. Represents the material stiffness matrix represents the strain-displacement matrix; Equation (1-30) represents the unit heat conduction matrix in the updated temperature field, represents the heat transfer coefficient matrix.

[0031]

[0032] Step S5: Based on the degradation function with the phase field variable as the independent variable, the stress-strain field and the temperature field are updated to characterize the degree of material damage. Steps S2 and S3 are repeated to achieve an alternating solution process of damage and material response.

[0033] Example 2 The research object is selected as asymmetric notch specimen, such as Figure 4 The high-temperature nickel-based alloy GH4169 was studied. This material exhibits obvious viscoplastic deformation and thermal damage evolution characteristics under non-uniform temperature conditions.

[0034] To accurately describe its high-temperature mechanical behavior, this study obtained temperature-dependent material parameters (see Table 1) based on experimental data fitting within the temperature range of 300°C to 600°C. The plastic behavior was characterized using the Von Mises yield criterion for isotropic hardening, while the hardening behavior was characterized using a hybrid hardening model combining isotropic and kinematic hardening, comprehensively reflecting the material's response characteristics under complex stress states. The plastic and damage-related parameters are shown in Table 2.

[0035] Table 1 Physical performance parameters and fitting function parameters

[0036] Table 2 Plastic parameters and phase field parameters

[0037] The geometric model uses a three-dimensional tensile specimen with a waist-shaped asymmetric V-notch. The top is only allowed to move in the axial direction, and the displacement in the X and Y directions is constrained to zero; a displacement-controlled loading method is used, applying a constant rate of axial displacement such as Figure 5 (a) Temperature boundary conditions: a 600°C hot boundary is applied to one end of the sample and a 300°C cold boundary is applied to the other end, forming a stable temperature gradient as shown in Figure 5 (b) shows the temperature distribution during the service process; the mechanical properties of materials are different at different temperatures, and the initial yield strength distribution of the specimens is different, such as Figure 5 (c) shown.

[0038] A coupled thermo-viscoplastic-phase-field fracture model constructed using ABAQUS software and user subroutines enables simultaneous simulation of the temperature, stress, and phase fields. Damage evolution is simulated using the phase-field fracture model. The evolution of phase-field variables in this model is influenced by the coupled effects of temperature, stress state, and strain history. Material failure is identified when the d-value reaches 1. Output includes Von Mises equivalent stress, plastic strain, and phase-field damage variables for subsequent analysis.

[0039] From the initial yield strength distribution cloud diagram, it can be seen that the constructed temperature-dependent material model can accurately reflect the differences in material yield behavior in different regions. The simulation results show that due to the high temperature in the upper left region, the material yield strength decreases and it enters the plastic stage first, resulting in a larger overall plastic deformation. Figure 6 (a) shows that the notch in the upper left section has more obvious stress concentration, as shown in Figure 6 As shown in (b); under the action of large plastic deformation and stress concentration, the damage variable in the notch area of ​​the upper left section is significantly higher than that of the lower right section. The corresponding phase field variable distribution clearly depicts the damage evolution path, as shown in Figure 6 (c) shown.

[0040] By constructing a thermal-viscoplastic-phase-field fracture model, they successfully simulated the material damage behavior under high-temperature gradients. Comparing the results of the viscoplastic-phase-field fracture model with those of the model, the simulations show that, when unaffected by the temperature field, the two notches interfere with each other but exhibit the same damage magnitude. The evolution of notched components under temperature differential loading was systematically simulated. The simulation results are consistent with the material's actual service behavior and can provide theoretical and numerical support for life prediction and failure analysis of high-temperature structural components.

[0041] 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 flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, 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 flowcharts and / or block diagrams. 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.

[0042] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A high-temperature discontinuous structure fatigue fracture prediction method based on the phase field method under variable temperature conditions, characterized by: include: Based on the Chaboche viscoplastic cyclic constitutive model and its corresponding UMAT subroutine and the temperature field heat conduction and its UMATHT subroutine, the stress and strain fields of the viscoplastic material coupled with the temperature field under arbitrary cyclic loading are obtained; Based on the stress-strain field coupled with the temperature field, the fracture phase field of the viscoplastic material under arbitrary cyclic loading is obtained, the phase field residual and phase field stiffness matrix are obtained, the phase field variables are obtained by iterative solution, and the corresponding UEL subroutine is compiled; The stress-strain field, temperature field and phase field are corrected and updated by using the data interaction process of the UMAT subroutine, UMATHT subroutine and UEL subroutine. By identifying the phase field variables and their evolution path under cyclic loading, the fracture behavior of viscoplastic materials under temperature gradient is predicted.

2. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1 is characterized in that: The Chaboche viscoplastic cyclic constitutive model is used in combination with its corresponding UMAT subroutine to describe the mechanical behavior of the material, thereby obtaining the stress-strain field. At the same time, the temperature-related parameters are corrected in the UMAT subroutine, and the relationship between temperature and material parameters is expressed as follows using a function fitting: y(T)=x a (T-T0) 2 +x b (T-T0)+x0; Among them, x a 、x b Represents the correction coefficient, T0 is the initial temperature, x0 is the parameter at the initial temperature, and y(T) is the parameter at the current temperature. The temperature field is introduced through the built-in thermal-mechanical coupling solver of ABAQUS to simulate the effect of temperature on the material.

3. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the process of obtaining the historical accumulated plastic work, a temperature-dependent viscoplastic cyclic constitutive model is established based on the coupled temperature field to simulate the stress and strain fields of the material under the action of the temperature field under cyclic loading. The historical accumulated plastic work is thus obtained. In order to ensure the irreversibility of material damage, the maximum historical variable is introduced. The formula is expressed as follows: in, To accumulate plastic work, is the maximum value in time t, and the inequality guarantees irreversibility.

4. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the process of obtaining the fracture energy, the critical fracture energy release rate and characteristic crack width related parameters are introduced into the UEL subroutine, and the type function, isoparametric unit and coordinate transformation are constructed. The user-defined unit is integrated according to the phase field variable to obtain the fracture energy.

5. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the process of obtaining the heat dissipation work, the UMATHT subroutine is compiled to obtain the dissipated energy due to temperature damage to the material based on the temperature difference of each incremental step and the specific heat capacity parameter affected by temperature. The formula is expressed as: Where T0 represents the initial temperature, T represents the current incremental temperature, and c(T) represents the specific heat capacity of the material.

6. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the process of obtaining the phase field residual and the phase field stiffness matrix, the accumulated plastic work of the cyclic loading history, the fracture energy of the viscoplastic material, and the heat dissipation work affected by the temperature on the material are calculated based on the stress-strain field, the fracture phase field, and the temperature field to obtain the phase field residual and the phase field stiffness matrix; The temperature-dependent residual is expressed as: in, is the temperature B matrix, [(1-d) 2 +k] is the degradation function, K is the heat conduction matrix, is a temperature interpolation function, q is the heat flux vector of the internal heat source, and θ is the current temperature.

7. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: During the compilation of the UMAT subroutine, the temperature-related parameters, including the elastic modulus, Poisson's ratio, and initial yield stress, are corrected based on the Chaboche viscoplastic cyclic constitutive model. At the same time, the accumulated plastic work calculated from the stress-strain field is stored in the COMMON public array.

8. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the process of compiling the UEL subroutine, the mapping from the global coordinate system to the natural coordinate system is achieved by introducing the finite element shape function to construct the isoparametric unit; Based on the mapping relationship, the Gauss-Legendre numerical integration method with weighted function is used to discretize the weak form of the phase field governing equation. The crack driving force expression combines the historical accumulated plastic work, the fracture energy of viscoplastic materials, and the thermal dissipation work affected by temperature on the material to calculate the phase field residual and phase field stiffness matrix in a multi-item cumulative form; The phase field residual and phase field stiffness matrix local variable data are stored and iteratively solved using the built-in Newton-Raphson nonlinear solver in ABAQUS to finally obtain the updated phase field variables and realize dynamic tracking of crack evolution.

9. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: In the compiled UMATHT subroutine, the temperature-related specific heat capacity and thermal conductivity parameters are modified, and the phase field variables are read from the COMMON array. The thermal conductivity matrix of the material is modified by introducing a degradation function to reflect the influence of material damage on thermal conductivity. The formula is expressed as follows: Where g(d) represents the degradation function, [B] represents the temperature B matrix, and [κ] represents the heat conduction matrix.

10. The method for predicting fatigue fracture of high-temperature discontinuous structures based on phase field method under variable temperature conditions according to claim 1, characterized in that: During the data exchange process between the UMAT, UEL, and UMATHT subroutines, in the finite element calculation, one layer of elements uses the UMAT and UMATHT subroutines for thermal-mechanical coupling to solve the stress-strain and temperature fields, while another layer of user-defined elements uses the UEL subroutine to solve the phase field. Various data variables between the two layers of elements, including phase field variables, historical accumulated plastic work, and thermal dissipation work, are transferred through the COMMON public array. During the iterative solution process, the phase field variables are calculated through the stress-strain field and temperature field, the unit stress-stiffness matrix and the unit heat conduction matrix are corrected using the degradation function, the stress-strain field and the temperature field are updated, and then the phase field variables are updated through the newly calculated historical accumulated plastic work and heat dissipation energy.

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