High temperature notch fracture phase field life prediction method based on cyclic plastic zone calibration

Abstract

The present application relates to the field of structural fatigue fracture prediction and computational fracture mechanics, and particularly relates to a high-temperature notched fracture phase field life prediction method based on cyclic plastic zone calibration. In view of the fact that significant viscoplastic flow occurs at the root of the notch under high-temperature cyclic loading, and the fact that the value of the characteristic scale parameter in the existing fatigue phase field model lacks physical basis, leading to high sensitivity of life prediction to parameters, the method obtains the local stress-strain response at the root of the notch based on a unified viscoplastic cyclic constitutive model, quantifies the characteristic size of the inelastic process zone at the root of the notch by using the cyclic plastic zone theory, and establishes a quantitative mapping between the characteristic size and the regularization length of the fracture phase field to determine the characteristic scale of the phase field; in the finite element framework, the alternating iterative solution of the displacement field and the phase field variables is realized by coupling the UMAT and UEL user subroutines, so that the crack initiation, propagation and branching can be simulated without presetting the crack path, and the crack evolution process and fatigue life prediction results of the notched component under high-temperature working conditions are output.

Description

Technical Field

[0001] This invention relates to the field of structural fatigue fracture prediction and computational fracture mechanics, specifically to a high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic region calibration, which is based on the coupling of unified viscoplastic constitutive model and fracture phase field method under high-temperature cyclic loading conditions. Background Technology

[0002] High-temperature critical load-bearing components, such as turbine disk tenons and groove roots, are subjected to repeated cyclic loads during start-up, shutdown and operating condition fluctuations. The notch roots have high stress gradients and strong constraint effects, which can easily induce local viscoplastic flow, stress redistribution and damage accumulation, and fatigue cracks often initiate and propagate from this.

[0003] The phase-field method, a dispersion fracture model based on variational principles, has made groundbreaking progress in fracture mechanics in recent years. It characterizes the damage state of materials by introducing continuous scalar field variables, regularizing sharp crack interfaces into dispersion damage bands with finite widths, thus naturally capturing crack initiation and complex evolution within a unified energy framework. However, a core bottleneck exists when applying the phase-field method to predict high-temperature viscoplastic fatigue: the ambiguity in the definition of characteristic scale parameters. In brittle fracture theory, these parameters are usually considered material constants, related to the elastic modulus and fracture strength. However, in viscoplastic materials, the flow stress dynamically evolves with strain rate and cycle count, and there is no constant critical strength, causing classical formulas to fail. Existing research typically... This is simplified to a fixed numerical regularization parameter. This approach ignores... Essentially, it represents the non-local extent of damage. In notch fatigue problems, the size of the damage process zone is highly sensitive to the geometry of the notch. (The last phrase, "fixed," appears to be an unrelated fragment and is omitted from the translation.) The inability to reflect this size effect leads to inconsistent lifetime prediction accuracy for specimens with notches of different sizes, lacking universality. To address this issue, a coupled model is established that can uniformly describe the high-temperature viscoplastic rheological behavior and fatigue damage evolution, and the phase field characteristic scale parameters are given clear physical meanings to achieve high-precision prediction of fatigue lifetime for discontinuous structures with different geometric dimensions. Summary of the Invention

[0004] To overcome the problem that the phase field characteristic scale parameter values ​​in the existing technology lack physical basis and lead to unstable prediction of high temperature notch fatigue life, this invention proposes a high temperature notch fracture phase field life prediction method based on cyclic plastic zone calibration.

[0005] The present invention adopts the following technical solution: The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic region calibration described in this invention includes the following steps: S1. Establish a finite element model of the notched or multi-notched component to be analyzed based on the finite element platform, and apply cyclic load boundary conditions. S2. A unified viscoplastic cyclic constitutive model is constructed in UMAT. This model characterizes the high-temperature cyclic response of the material, and stress updates and state variable evolution are implemented through the user material subroutine UMAT to obtain the inelastic strain and inelastic work increment during cyclic loading. Specifically, the unified viscoplastic cyclic constitutive model is implemented in UMAT to obtain the stress at each increment step. Inelastic strain increment And accumulate inelastic work according to the work conjugate relationship. ; S3. Calculate the characteristic size of the cyclic plastic zone at the root of the notch based on the theory of cyclic plastic zone. The characteristic size of the cyclic plastic zone is determined by the nominal stress range, geometric correction function, and equivalent crack length to define the characteristic scale parameters of the fracture phase field model. S4. The cumulative inelastic work increment yields the historical cumulative inelastic work. A fatigue fracture phase field evolution model with historical cumulative inelastic work as the dominant driving force is constructed. Displacement field-phase field alternating iterative coupling solution is implemented on finite element platforms such as Abaqus using UMAT and UEL. The phase field control equations are discretized and solved using the user element subroutine UEL to obtain the phase field variable field. The phase field control equations are established in UEL, with the driving force using the maximum historical variable. Depend on To ensure invertibility, Gaussian integrals are used to discretize and assemble the phase field residuals and tangent matrices, and the phase field variables are solved. ; S5. Constructing a degenerate function based on phase field variables. The material stiffness is continuously degraded and fed back to the displacement field equilibrium equation; an alternating iterative strategy is adopted to iterate within the same increment step until convergence is achieved. S6. Using the phase field variable reaching a preset threshold and the crack length criterion as the failure criteria, when Formation of penetrating damage zone or reaching the threshold Failure is determined when the load-bearing capacity degrades to a threshold, and the crack path and fatigue life are output.

[0006] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic region calibration described in this invention uses a unified viscoplastic cyclic constitutive model, which is the Chaboche viscoplastic model or its equivalent extended form. It includes elastic strain and inelastic strain decomposition, flow rules based on the von Mises yield criterion, and a combined evolution equation of kinematic hardening and isotropic hardening.

[0007] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plasticity zone calibration described in this invention uses the characteristic size of the cyclic plasticity zone calculated based on the local crack driving force parameters at the notch root and the material yield strength. The local crack driving force parameters are characterized by a stress intensity factor range, allowing the inelastic process regions under different notch sizes and stress concentration levels to be measured under a unified mechanical dimension. The characteristic size of the cyclic plasticity zone is... The expression is as follows:

[0008] in, The yield strength of the material; The range of stress intensity factors; to characterize the crack tip driving force of specimens with different notch sizes under stress-controlled fatigue test conditions; The range of stress intensity factor in the above formula From the nominal stress range With geometric correction function Sure:

[0009] in The equivalent crack length is... This represents the effective width of the sample.

[0010] The present invention is based on a sample with a circular arc notch. The root of the circular arc notch is not an ideal sharp crack. The physical crack length is directly substituted into the standard. The solution is not applicable; equivalent crack length Through the radius of curvature at the root of the notch Sure: .

[0011] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic zone calibration described in this invention establishes a one-to-one mapping relationship between the characteristic scale parameters in the fatigue fracture phase field evolution model and the characteristic dimensions of the cyclic plastic zone. The mapped fracture phase field characteristic scale parameters... Characteristic dimensions of the cyclic plastic zone satisfy:

[0012] Used to map the scale of inelastic process regions to the phase field regularization length.

[0013] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic zone calibration described in this invention calculates the corresponding cyclic plastic zone characteristic dimensions for components with different notch radii, different notch depths, different stress concentration factors, or different notch combinations, and determines their respective phase field characteristic scale parameters accordingly, thereby achieving a unified characterization of notch size effect and geometric discontinuity effect by characteristic scale parameters.

[0014] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic zone calibration described in this invention, in step S4, the historical accumulated inelastic work is gradually accumulated by the stress tensor and the inelastic strain increment according to the work conjugate relationship, and further historical variables are constructed to ensure that the crack driving force evolves monotonically during cyclic loading, so that the fracture phase field variables satisfy the damage irreversibility condition. Historical accumulated inelastic work Obtained by cumulative work conjugate:

[0015] In the elastic phase ,so After entering the viscoplastic stage, according to the dissipation inequality... This ensures the monotonous accumulation of energy.

[0016] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic zone calibration described in this invention comprises the following modules: a constitutive calculation module for executing the UMAT subroutine and outputting stress, inelastic strain, and inelastic work; a scale determination module for calculating the characteristic dimensions of the cyclic plastic zone and determining the characteristic scale parameters of the phase field; a phase field solution module for executing the UEL subroutine and solving for the phase field variables; a coupled iteration module for iteratively updating the displacement field and phase field in incremental steps and determining failure; and a result output module for outputting the crack evolution path and fatigue lifetime prediction results.

[0017] The high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic zone calibration described in this invention includes, in step S6, a failure criterion comprising one or a combination of the following: phase field variables. A damage zone forms at the root of the notch; the crack propagates to a predetermined length or the load-bearing section loses its load-bearing capacity; stiffness degradation reaches a predetermined threshold, when... Formation of penetrating damage zone or reaching the threshold Failure is determined when the load-bearing capacity degrades to a threshold, and the crack path and fatigue life are output. Beneficial effects

[0018] This invention uses the characteristic dimensions of the cyclic plastic zone at the notch root as the calibration basis for the characteristic scale parameters of the fracture phase field. It transforms the characteristic length parameters, traditionally determined through experience or trial and error, into physical quantities related to notch geometry, load levels, and the material's high-temperature cyclic response. This allows the characteristic scale parameters to adaptively change with different notch conditions, overcoming the problems of high parameter arbitrariness and poor applicability across specimens and notch geometries in existing methods. This improves the model's uniformity and transferability across different structural forms.

[0019] This invention couples the local viscoplastic response, inelastic work accumulation, and fracture phase field evolution at the notch root under high-temperature cyclic loading, enabling a continuous description of the entire process from local damage initiation and accumulation to macroscopic crack propagation. Compared to traditional methods that rely solely on nominal stress, strain, or empirical life formulas, this invention more accurately reflects the fatigue failure mechanism dominated by the inelastic region at the notch root under high-temperature conditions, thereby improving the consistency between experimental and predicted life and enhancing the reliability of engineering life assessment.

[0020] This invention utilizes the fracture phase-field method to solve crack evolution within a fixed mesh, simulating the spontaneous initiation, propagation, and localized evolution of cracks at the notch root without pre-specifying the crack initiation location and propagation path. This method is particularly suitable for fatigue fracture analysis of high-temperature discontinuous structures, multi-notch components, and complex stress concentration regions. It reduces the subjectivity and modeling difficulty caused by pre-specified path in traditional crack propagation simulations, enhancing the method's practicality in life prediction of critical engineering components such as hot-end parts of aero-engines. Attached Figure Description

[0021] Figure 1 This is a flowchart of the prediction process of the present invention; Figure 2 This is a schematic diagram illustrating the mapping relationship between the characteristic dimensions of the cyclic plastic region and the characteristic scale parameters of the phase field in this invention; Figure 3 This is a schematic diagram of the data transfer and alternating iterative coupling framework between UMAT and UEL in this invention; Figure 4 This is a diagram of a symmetrical notched sample from Embodiment 2 of the present invention, wherein (a) is... Notched specimen, (b) is Notched specimen, (c) is Notched specimen; Figure 5 This refers to the geometric model, boundary conditions, and loading method in Embodiment 2 of the present invention; Figure 6 These are the values ​​of the feature scale parameters under different notch sizes in Embodiment 2 of the present invention; Figure 7 This is a cloud map showing the phase field damage distribution at different cycles in Embodiment 2 of the present invention; Figure 8 This is a comparison chart of fatigue life predictions for different notch types in Embodiment 2 of the present invention. Detailed Implementation

[0022] To make the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0023] The overall scheme of the high-temperature notch fracture phase field lifetime prediction method based on cyclic plastic region calibration provided by this invention is as follows: A finite element model of the notched or multi-notched component to be analyzed is established. A unified viscoplastic cyclic constitutive model is built in UMAT, and the high-temperature cyclic response of the material is characterized by the unified viscoplastic cyclic constitutive model. The stress update and state variable evolution are realized through the user material subroutine UMAT to obtain the inelastic strain and inelastic work increment during cyclic loading. Based on the cyclic plastic zone theory, the characteristic size of the cyclic plastic zone at the notch root is calculated. The characteristic size of the cyclic plastic zone is determined by the nominal stress range, geometric correction function, and equivalent crack length to determine the characteristic scale parameters of the fracture phase field model. A fatigue fracture phase field evolution model with historical cumulative inelastic work as the dominant driving force is constructed, and the phase field control equation is solved by discretization through the user element subroutine UEL to obtain the phase field variables. Based on the phase field variables, a degradation function is constructed to continuously degrade the material stiffness and feed it back to the displacement field equilibrium equation. An alternating iteration strategy is used to cycle within the same increment step until convergence. The failure criteria are the phase field variables reaching a preset threshold and the crack length criterion, and the crack and fatigue life prediction results are output.

[0024] Example 1

[0025] The specific implementation process of the present invention based on the above scheme is as follows: As attached Figure 1 As shown, the method for predicting the fracture phase field lifetime of a high-temperature notched component based on the characteristic length of the cyclic plastic zone according to the present invention includes the following steps: Step S1, based on the Chaboche viscoplastic cyclic constitutive model, the main governing equations are expressed as (1-5), where the total strain tensor is... Decomposed into elastic strain With inelastic strain ; For stress tensor, The elastic stiffness tensors follow the generalized Hooke's law; a yield function based on the von Mises criterion is introduced in equation (3). tensor Represents the back stress of kinematic hardening, a scalar. This represents the increment of the yield surface area in isotropic hardening. This represents the initial yield stress; Equation (4) Poisson's ratio, Young's modulus; in equation (5), inelastic strain rate The evolution follows the associated Perzyna-type flow law, with the flow direction along the normal to the yield surface. The flow rate is controlled by the overstress function. The Macaulay brackets introduced in the equation... This ensures that irreversible inelastic deformation only occurs when the stress state is outside the yield surface. These are material parameters.

[0026]

[0027] Step S2: Based on the stress-variable field of the viscoplastic constitutive model, Equation (6) is used to calculate the cumulative plastic work. Introducing the historical variable, Equation (7) yields the maximum cumulative plastic work over time period t. Equation (8) is used to calculate the material fracture energy. and The critical fracture energy release rate and characteristic crack width are represented by the phase field variables, which are calculated.

[0028]

[0029] Step S3: Select the maximum historical cumulative plastic work and fracture energy during cyclic loading to construct the total energy functional. Use equation (9) as the degenerate function to solve the total energy functional to obtain equation (10) of the phase field driving force equation; express the total energy functional using the finite element discretization scheme, introduce isoparametric elements using finite element shape functions, convert the positional relationship in the global coordinate system to the isoparametric coordinate system, solve the displacement field residual and phase field residual respectively with respect to the displacement and phase field variables, and obtain the corresponding stiffness matrix by differentiating with respect to the self-variable. Construct a nonlinear equation system with the obtained residuals and stiffness matrix, solve it using the ABAQUS built-in Newton-Raphson iteration method, and update the phase field value.

[0030]

[0031] Step S4: The physical dimensions of the inelastic process region characterized by the cyclic plastic zone formed at the notch root under cyclic loading are determined, thereby making the width of the phase field dispersed crack zone consistent with the actual inelastic zone scale, improving the repeatability and numerical stability of the cross-notch geometry and load level.

[0032]

[0033] Step S5: Based on the degenerate function with the phase field variable as the independent variable, update the stress-strain field to characterize the degree of material damage. Repeat steps S2 and S3 to realize the alternating solution process of damage and material response.

[0034] Example 2

[0035] The research subjects were selected as three types of symmetrical notched specimens, such as Figure 4 Taking the high-temperature nickel-based alloy GH4169 as the research object, this material exhibits obvious viscoplastic deformation and damage evolution characteristics at a temperature of 650℃.

[0036] To accurately describe its high-temperature mechanical behavior, the material parameters of the Chaboche constitutive model were obtained based on tensile fatigue test data at 650℃, as shown in Table 2-1. The plastic behavior was characterized by the isotropic strengthening Von Mises yield criterion, while the hardening behavior was characterized by a hybrid strengthening model combining isotropic strengthening and kinematic strengthening, comprehensively reflecting the material's response characteristics under complex stress states.

[0037] Table 2-1 Physical performance parameters and fitting function parameters

[0038] The geometric model uses one-quarter of the specimen. The top is only allowed to move axially, with zero displacement constraint in the X direction and symmetrical boundary conditions. A displacement-controlled loading method is used, applying a constant rate of axial displacement. Figure 5 As shown.

[0039] A viscoplastic phase-field fracture coupling model was constructed using ABAQUS software in conjunction with user subroutines to achieve simultaneous calculation of the stress field and phase field. Damage evolution was simulated using the phase-field fracture model. In the model, the evolution of phase field variables was coupled with temperature, stress state, and strain history, and a d-value reaching 0.95 was identified as material failure. The output includes Von Mises equivalent stress, plastic strain, and phase-field damage variables for subsequent analysis.

[0040] like Figure 5 As shown, different notch geometries correspond to different elastic stress concentration factors. And it manifests as characteristic scale parameters of the fracture phase field. Significant differences: with Enlarged, and the notch became sharper. It exhibits a monotonically decreasing trend. This pattern stems from the physical definition of the characteristic scale in this method, which uses the characteristic size of the cyclic plastic zone at the notch root as the control quantity for the phase field regularization length.

[0041] Characteristic scale parameters are obtained based on the size of the plastic cyclic region, and the critical fracture energy of the phase field-dependent material is defined. Numerical calculations were performed using a viscoplastic fracture phase-field coupling model. The simulation results show that... Figure 7 The fracture phase field variable d is given as an isopleth map of the local region at the root of the notch during the middle and end of the lifespan. The column at the root of the notch during the middle and end of the lifespan is used to determine the material failure when the length of the region reaches a certain value, thus obtaining the lifespan.

[0042] from Figure 8 The fatigue life predictions show good overall consistency, with the scatter plots generally following the trend. The main diagonal distribution indicates that the model maintains good correlation and scale consistency across different lifespan levels, with data points for each symmetrically notched specimen falling within the ±1.5 error range. This demonstrates that the proposed fracture phase field fatigue prediction method, which controls the characteristic scale of the cyclic plastic zone, can achieve stable and engineering-usable lifespan prediction accuracy under different notch conditions.

[0043] This invention is illustrated by flowcharts and descriptions of methods, apparatus (systems), and computer program products according to embodiments of the invention. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0044] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the lifespan of a high-temperature notched fracture phase field based on cyclic plasticity calibration, characterized in that, Includes the following steps: S1. Establish a finite element model of the notched or multi-notched component to be analyzed based on the finite element platform, and apply cyclic load boundary conditions. S2. Build a unified viscoplastic cyclic constitutive model in UMAT, use the unified viscoplastic cyclic constitutive model to characterize the high-temperature cyclic response of the material, and realize stress update and state variable evolution through the user material subroutine UMAT to obtain the inelastic strain and inelastic work increment during cyclic loading. S3. Calculate the characteristic size of the cyclic plastic zone at the root of the notch based on the theory of cyclic plastic zone. The characteristic size of the cyclic plastic zone is determined by the nominal stress range, geometric correction function, and equivalent crack length to define the characteristic scale parameters of the fracture phase field model. The incremental inelastic work in steps S4 and S2 is used to obtain the historical cumulative inelastic work. A fatigue fracture phase field evolution model with historical cumulative inelastic work as the dominant driving force is constructed. The phase field control equations are then solved by the user unit subroutine UEL to obtain the phase field variables. S5. Construct a degradation function based on the phase field variables, continuously degrade the material stiffness and feed it back to the displacement field equilibrium equation; use an alternating iterative strategy to loop within the same increment step until convergence; S6. Using the phase field variable reaching a preset threshold and the crack length criterion as failure criteria, output the crack and fatigue life prediction results.

2. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic region calibration according to claim 1, characterized in that: The unified viscoplastic cyclic constitutive model is the Chaboche viscoplastic model or its equivalent extension, which includes elastic and inelastic strain decomposition, flow rules based on the von Mises yield criterion, and a combined evolution equation of kinematic hardening and isotropic hardening.

3. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic zone calibration according to claim 2, characterized in that: The characteristic size of the cyclic plastic zone in step S3 is: The expression is as follows: ； in, The yield strength of the material; The range of stress intensity factors; to characterize the crack tip driving force of specimens with different notch sizes under stress-controlled fatigue test conditions; The range of stress intensity factor in the above formula From the nominal stress range With geometric correction function Sure: ； in The equivalent crack length is... The effective width of the sample; Equivalent crack length in the above formula Through the radius of curvature at the root of the notch Sure: .

4. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic zone calibration according to claim 1 or 3, characterized in that: The characteristic scale parameters in the fatigue fracture phase field evolution model satisfy a one-to-one mapping relationship with the characteristic dimensions of the cyclic plastic region, and the mapped fracture phase field characteristic scale parameters... Characteristic dimensions of the cyclic plastic zone satisfy: ； Used to map the scale of inelastic process regions to the phase field regularization length.

5. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic region calibration according to claim 1, characterized in that: In step S4, the historical cumulative inelastic work is obtained stepwise by accumulating the stress tensor and the inelastic strain increment according to the work conjugate relationship; historical cumulative inelastic work Obtained by cumulative work conjugate: ； In the elastic phase ,so ; After entering the viscoplastic stage, according to the dissipation inequality This ensures the monotonous accumulation of energy.

6. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic zone calibration according to claim 1, characterized in that, The degenerate function for the phase field variables is constructed as follows: .

7. The method for predicting the high-temperature notch fracture phase field lifetime based on cyclic plastic region calibration according to claim 1, characterized in that: The failure criteria in step S6 include one or a combination of the following: phase field variables. A damage zone forms at the root of the notch; the crack propagates to a predetermined length or the load-bearing section loses its load-bearing capacity; stiffness degradation reaches a predetermined threshold, when... Formation of penetrating damage zone or reaching the threshold Failure is determined when the load-bearing capacity degrades to a threshold, and the crack path and fatigue life are output.

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