A metal microstructure evolution prediction method based on a crystal plasticity phase field model

Abstract

The application discloses a metal microstructure evolution prediction method based on a crystal plasticity phase field model and belongs to the technical field of material microstructure evolution prediction, which comprises the following steps: establishing a finite element model of a polycrystalline metal material; constructing a crystal plasticity constitutive model based on dislocation density and a multi-order parameter phase field model; introducing elastic strain energy obtained by crystal plasticity calculation and defect energy generated by dislocation accumulation into a phase field evolution equation as driving forces of grain boundary migration and grain size evolution; and obtaining stress field, dislocation density field and microstructure evolution process of the polycrystalline material under cyclic loading through full coupling solution, so as to realize the prediction of grain boundary migration, grain growth, grain refinement and stress redistribution. The application can effectively reveal the microstructure evolution law driven by non-uniform plastic deformation and provide a numerical simulation method for fatigue damage analysis, life prediction and material organization optimization.

Description

Technical Field

[0001] This invention belongs to the field of crystal plasticity mechanics and phase field simulation technology, specifically relating to a method for predicting the evolution of metal microstructures based on a crystal plasticity phase field model. Background Technology

[0002] Lightweight metallic structural materials for aerospace applications typically endure high temperatures, high stresses, and cyclic loading during service, making them prone to fatigue damage in stress / strain concentration areas. Under cyclic loading, polycrystalline materials exhibit significant stress concentration and localized plastic deformation, accompanied by microstructural evolution behaviors such as grain size changes, grain boundary migration, dislocation accumulation, and localized microstructure rearrangement. This microstructural evolution alters the material's original mechanical properties, further influencing the stress field, strain field, and subsequent mechanical behavior. Therefore, accurately predicting the microstructural evolution of polycrystalline materials is crucial for metal fatigue damage analysis and life assessment.

[0003] In existing technologies, crystal plasticity models can describe the anisotropic plastic deformation, slip system activity, and dislocation density evolution of polycrystalline materials under load, but they are generally unable to directly describe grain boundary migration, grain growth, and changes in grain morphology. Phase-field models can describe grain boundary migration, grain growth, and microstructure topological evolution, but when used alone, they are difficult to accurately reflect the influence of complex stress concentration, non-uniform plastic deformation, and dislocation accumulation on microstructure evolution in metallic materials. Therefore, existing methods cannot simultaneously describe the mechanical response, dislocation density evolution, and grain structure evolution at the mesoscale, and are particularly unable to predict the interaction between microstructure evolution and local stress-strain fields under cyclic loading, limiting their application in the analysis of metal fatigue damage mechanisms and life prediction. Summary of the Invention

[0004] Purpose of the invention: To address the problem that existing technologies cannot simultaneously predict non-uniform plastic deformation, dislocation density accumulation, grain boundary migration, and grain size evolution in metallic materials, this invention provides a method for predicting the evolution of metallic microstructures based on a crystal plastic phase-field model.

[0005] Technical Solution: To achieve the above objectives, this invention provides a method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model, comprising the following steps:

[0006] Step 1: Establish a polycrystalline geometric model of the material to be predicted, and perform finite element mesh generation on the polycrystalline geometric model to obtain a polycrystalline finite element model; the polycrystalline finite element model includes multiple finite element elements, and each finite element element is set with one or more integration points;

[0007] Step 2: Obtain the crystal orientation, grain boundary distribution, elastic parameters, crystal plasticity model parameters, phase field model parameters, and cyclic loading conditions of each grain in the polycrystalline finite element model;

[0008] Step 3: Establish a crystal plastic constitutive model based on dislocation density. According to the crystal orientation and cyclic loading conditions, calculate and update the stress, total strain, elastic strain, plastic slip variable, and dislocation density at each integration point in the polycrystalline finite element model. Calculate the elastic strain energy density from the stress and elastic strain at each integration point, and calculate the defect energy density from the dislocation density at each integration point. The elastic strain energy density and defect energy density form the elastic strain energy field and defect energy field throughout the entire calculation region.

[0009] Step 4: Establish a multi-order parameter phase-field model to describe the evolution of polycrystalline microstructures. Different grains are distinguished by multiple order parameters, and the grain boundary position and grain morphology are described by phase-field variables. The elastic strain energy field and defect energy field obtained in Step 3 are introduced into the free energy function of the multi-order parameter phase-field model as the driving force for grain boundary migration and grain size evolution.

[0010] Step 5: Under cyclic loading, perform fully coupled iterative solution of the crystal plastic constitutive model and the multi-order parameter phase field model, and update the mechanical field information and phase field variables synchronously; the mechanical field information includes stress field, dislocation density field, elastic strain energy field and defect energy field;

[0011] Step 6: Based on the updated phase field variables and mechanical field information, obtain the microstructure evolution results of the polycrystalline finite element model.

[0012] Furthermore, in step 1, the polycrystalline finite element model can be a two-dimensional polycrystalline model, a three-dimensional polycrystalline model, a Voronoi polycrystalline model, a polycrystalline model based on experimental microstructure reconstruction, or a periodic representative volume element model.

[0013] Furthermore, in step 2, the microstructure information includes crystal orientation and grain boundary distribution, which can be obtained through electron backscatter diffraction testing, orientation distribution function sampling, random orientation generation, or microstructure reconstruction methods.

[0014] Furthermore, in step 3, the crystal plastic constitutive model based on dislocation density includes slip ratio calculation and statistical storage dislocation (SSD) density evolution, the expressions for which are as follows:

[0015]

[0016]

[0017] in, For reference slip ratio, For shear stress, For slip resistance, For strain rate sensitivity parameters, For symbolic functions, and For material parameters, To calculate the density of SSDs with storage dislocations, The time derivative of the order parameter, For Macaulay brackets, denoted as the dislocation annihilation coefficient induced by grain boundary migration.

[0018] Furthermore, in step 4, the multi-order parameter phase-field model includes the total free energy, which comprises grain boundary energy, gradient energy, elastic strain energy, and defect energy, specifically expressed as follows:

[0019]

[0020] in, For the computational domain, and These are the coefficients of the double-well function. To calculate the number of phase field variables used to describe different grains within the computational domain, For the first Phase field variables corresponding to each grain For the gradient term coefficients, For interpolation functions, and The first The elastic strain energy and defect energy of each grain It is a volumetric infinitesimal element.

[0021] Furthermore, in step 4, the elastic strain energy is determined by the elastic tensor. and elastic strain tensor It is confirmed that its expression is:

[0022]

[0023] in, Represents the double dot product of tensors;

[0024] Defects can be determined by statistical storage dislocation density and shear modulus. , Burgers vector modulus and defect energy coefficient Together, we determine that its expression is:

[0025]

[0026] in, This represents the total number of crystal slip systems. For calculating time.

[0027] Furthermore, in step 5, the coupled iterative solution is a fully coupled solution, which includes: establishing a set of mechanical control equations containing mechanical equilibrium equations, dislocation density evolution equations, and constitutive update relations from the crystal plastic constitutive model; establishing phase field evolution equations from the multi-order parameter phase field model; within the same loading increment step, assembling the set of mechanical control equations and the phase field evolution equations into a unified nonlinear coupled equation set; simultaneously solving the displacement field and phase field variables through the same nonlinear solver; and simultaneously updating the stress field, dislocation density field, elastic strain energy field, defect energy field, and phase field variables.

[0028] Furthermore, in step 6, the microstructure evolution result includes at least one of the following: average grain area, grain refinement region, local plastic strain distribution, and stress distribution.

[0029] Beneficial effects: Compared with the prior art, the significant advantages of this invention are:

[0030] 1. This invention combines a crystal plasticity model based on dislocation density with a multi-order parameter phase field model, which can simultaneously describe the evolution of the mechanical field and the microstructure of metallic materials.

[0031] 2. This invention uses elastic strain energy and dislocation storage energy as driving forces for grain boundary migration and grain size evolution, which can reflect the influence of stress concentration and non-uniform plastic deformation on microstructure evolution under cyclic loading.

[0032] 3. This invention can quantitatively analyze the influence of local non-uniform deformations such as stress concentration on microstructure evolution, and predict grain boundary migration, grain growth or refinement, dislocation density accumulation and local stress redistribution.

[0033] 4. This invention can provide a simulation basis for identifying fatigue damage-sensitive areas and optimizing the microstructure design of materials. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the prediction method of the present invention.

[0035] Figure 2 This is a schematic diagram of the two-dimensional polycrystalline finite element model in this invention.

[0036] Figure 3 This is a schematic diagram of the microstructure evolution of the two-dimensional polycrystalline finite element model in this invention.

[0037] Figure 4 This is a von Mises stress distribution diagram of the two-dimensional polycrystalline finite element model in this invention.

[0038] Figure 5 This is a graph showing the change of average grain area over time in this invention. Detailed Implementation

[0039] like Figure 1 This embodiment provides a method for predicting the evolution of metallic microstructures based on a crystal plastic phase-field model, used to analyze grain boundary migration, grain size changes, and stress field redistribution behavior of metallic materials under cyclic loading. It includes the following steps:

[0040] Step 1: Establish a polycrystalline finite element model. In this embodiment, the Voronoi method is used to generate a two-dimensional polycrystalline structure. The model size is 100 μm × 100 μm, containing 36 grains, as shown below. Figure 2 As shown, a cyclic load boundary condition is applied to the polycrystalline finite element model using a sinusoidal waveform. The applied average strain is 0.2%, the strain amplitude is 0.18%, and the frequency is 0.5 Hz. By setting the load amplitude, load ratio, cycle period, and loading direction, stress concentration and localized plastic deformation are formed in the finite element model.

[0041] Step 2: Establish a crystal plastic constitutive model based on dislocation density. The crystal plastic constitutive model determines the spatial orientation of the slip system based on the crystal orientation of each grain, and calculates the slip ratio, cumulative slip, and SSD density on each slip system under cyclic loading. Through crystal plastic finite element calculations, the stress field, elastic strain field, and dislocation density field of the polycrystalline model are obtained, and the elastic strain energy and the defect energy generated by the accumulation of dislocation density are calculated. The elastic strain energy is calculated from the stress field and elastic strain field, and the defect energy is calculated from the dislocation density, shear modulus, Burgers vector, and dislocation energy coefficient. Due to the inhomogeneity of the microstructure of metallic materials, there is significant stress concentration, which can therefore serve as an important factor driving grain boundary migration and grain size evolution.

[0042] Step 3: Establish a multi-order parameter phase-field model. This model uses multiple continuously varying order parameters to represent different grains, with grain boundary regions represented by continuous transition regions between different order parameters. The free energy of the phase-field model includes grain boundary energy, gradient energy, elastic strain energy, and defect energy. Grain boundary energy and gradient energy describe grain boundary width and energy, while elastic strain energy and defect energy describe the driving effect of non-uniform deformation on grain boundary migration and grain size evolution.

[0043] Step 4: Fully couple the crystal plastic constitutive model and the multi-order parametric phase-field model for solution. Within the same loading increment step, solve the mechanical equilibrium equations and phase-field evolution equations simultaneously. Displacement and phase-field variables are updated synchronously within the same solution framework, allowing plastic deformation, dislocation accumulation, grain boundary migration, and grain size evolution in the microstructure to interact and evolve collaboratively. During the calculation, with the application of cyclic loads, the phase-field variables evolve under the drive of elastic strain energy and defect energy, causing grain boundary migration, and some grains to grow, refine, or have their morphology adjusted, such as… Figure 3 As shown, changes in grain structure alter the local mechanical properties and crystal orientation distribution, further affecting the local stress field of the microstructure, such as... Figure 4 As shown.

[0044] Step 5: Post-process the calculation results to obtain the microstructure evolution results of the polycrystalline finite element model. The post-processing results include changes in grain morphology ( Figure 3 ), stress concentration area changes ( Figure 4 ) and average grain area variation ( Figure 5 This embodiment allows for the analysis of the driving effect of non-uniform deformation, such as stress concentration, on grain boundary migration and grain structure evolution, and the evaluation of the feedback influence of microstructure evolution on the microscopic local stress-strain field. It reveals the potential mechanism of non-uniform deformation on microstructure evolution behavior, providing a basis for the analysis of metal fatigue crack propagation mechanisms and life assessment.

Claims

1. A method for predicting the evolution of metallic microstructures based on a crystal plastic phase-field model, characterized in that, Includes the following steps: Step 1: Establish a polycrystalline geometric model of the material to be predicted, and perform finite element mesh generation on the polycrystalline geometric model to obtain a polycrystalline finite element model; the polycrystalline finite element model includes multiple finite element elements, and each finite element element is set with one or more integration points; Step 2: Obtain the crystal orientation, grain boundary distribution, elastic parameters, crystal plasticity model parameters, phase field model parameters, and cyclic loading conditions of each grain in the polycrystalline finite element model; Step 3: Establish a crystal plastic constitutive model based on dislocation density. According to the crystal orientation and cyclic loading conditions, calculate and update the stress, total strain, elastic strain, plastic slip variable, and dislocation density at each integration point in the polycrystalline finite element model. Calculate the elastic strain energy density from the stress and elastic strain at each integration point, and calculate the defect energy density from the dislocation density at each integration point. The elastic strain energy density and defect energy density form the elastic strain energy field and defect energy field throughout the entire calculation region. Step 4: Establish a multi-order parameter phase-field model to describe the evolution of polycrystalline microstructures. Different grains are distinguished by multiple order parameters, and the grain boundary position and grain morphology are described by phase-field variables. The elastic strain energy field and defect energy field obtained in Step 3 are introduced into the free energy function of the multi-order parameter phase-field model as the driving force for grain boundary migration and grain growth. Step 5: Under cyclic loading, perform fully coupled iterative solution of the crystal plastic constitutive model and the multi-order parameter phase field model, and update the mechanical field information and phase field variables synchronously; the mechanical field information includes stress field, dislocation density field, elastic strain energy field and defect energy field; Step 6: Based on the updated mechanical field information and phase field variables, obtain the microstructure evolution results of the polycrystalline finite element model.

2. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The polycrystalline finite element model in step 1 can be a two-dimensional polycrystalline model, a three-dimensional polycrystalline model, a Voronoi polycrystalline model, a polycrystalline model based on experimental microstructure reconstruction, or a periodic representative volume element model.

3. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The crystal orientation in step 2 is obtained through electron backscatter diffraction testing, orientation distribution function sampling, random orientation generation, or microstructure reconstruction.

4. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The crystal plastic constitutive model in step 3 includes slip ratio calculation and statistical storage dislocation (SSD) density evolution; The expression for calculating slip ratio is: The statistical expression for the evolution of SSD density due to storage dislocation is: in, For reference slip ratio, For shear stress, For slip resistance, For strain rate sensitivity parameters, For symbolic functions, and For material parameters, To calculate the density of SSDs with storage dislocations, The time derivative of the order parameter, For Macaulay brackets, denoted as the dislocation annihilation coefficient induced by grain boundary migration.

5. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The total free energy of the multi-parameter phase-field model in step 4 includes grain boundary energy, gradient energy, elastic strain energy, and defect energy. The expression for the total free energy is: in, For the computational domain, and These are the coefficients of the double-well function. To calculate the number of phase field variables used to describe different grains within the computational domain, For the first Phase field variables corresponding to each grain For the gradient term coefficients, For interpolation functions, and The first The elastic strain energy and defect energy of each grain It is a volumetric infinitesimal element.

6. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The elastic strain energy in step 4 is determined by the elastic tensor. and elastic strain tensor It is confirmed that its expression is: in, Represents the double dot product of tensors; Defects can be determined by statistical storage dislocation density and shear modulus. , Burgers vector modulus and defect energy coefficient Together, we determine that its expression is: in, This represents the total number of crystal slip systems. For calculating time.

7. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The fully coupled iterative solution in step 5 includes: establishing a set of mechanical control equations containing mechanical equilibrium equations, dislocation density evolution equations, and constitutive update relations from the crystal plastic constitutive model; establishing phase field evolution equations from the multi-order parameter phase field model; within the same loading increment step, assembling the set of mechanical control equations and the phase field evolution equations into a unified nonlinear coupled equation set; simultaneously solving displacement and phase field variables through the same nonlinear solver; and simultaneously updating the stress field, dislocation density field, elastic strain energy field, defect energy field, and phase field variables, thereby realizing the fully coupled calculation of crystal plastic deformation, dislocation accumulation, grain boundary migration, and grain size evolution.

8. The method for predicting the evolution of metal microstructures based on a crystal plastic phase-field model according to claim 1, characterized in that, The microstructure evolution results in step 6 include at least one of the following: average grain area, grain refinement region, local plastic strain distribution, and stress distribution.

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