A rapid calibration method for plastic constitutive parameters of polycrystalline crystals

Abstract

The invention discloses a method for rapid calibration of polycrystalline crystal plastic constitutive parameters, and the steps are: EBSD characterization of metal materials; establishment of a cubic polycrystalline geometric model, and assignment of constitutive parameters and grain orientation with the help of a Python script; writing a crystal plastic constitutive model subroutine UMAT; applying periodic boundary conditions with the help of a Python script; extracting the stress-strain relationship of the polycrystalline model, and interpolating the test data to the calculated data points; calibrating the constitutive parameters using uniaxial tension and fatigue test stress-strain / stress-time data; taking the square sum of the difference between the test and simulation data points as the optimization target, and iteratively optimizing using the Hook-Jeeves optimization algorithm; adjusting the constitutive parameters by the iterative algorithm, and updating the material parameters with the help of a Python script. The invention can reflect the mechanical properties of materials, significantly reduce the consumption of finite element calculations, shorten the optimization cycle, and improve the efficiency of parameter calibration.

Description

Technical Field

[0001] The invention relates to a method for quickly calibrating parameters of a polycrystalline plastic constitutive model, and belongs to the field of structural strength and finite element numerical simulation. Background Art

[0002] With the rapid development of advanced experimental characterization methods and computational methods, multi-scale simulations are widely used in the in-depth study of deformation and failure mechanisms of engineering materials, and further promote the design and development of high-strength and high fatigue resistance materials, as well as the establishment of high-precision structural integrity assessment methods. Grain-scale crystal plasticity finite element simulation, as a bridge connecting micro-nanoscale dislocation motion and macroscopic plastic deformation, has become a powerful tool for studying the mesoscopic deformation and failure mechanisms of metal materials.

[0003] For crystal plasticity finite element simulation, accurate calibration of constitutive parameters is a prerequisite for ensuring the validity of simulation results. For single crystal metal materials, there have been many studies on the calibration of crystal plasticity constitutive parameters, which can be achieved by fitting uniaxial tension, creep, and low-cycle fatigue test data with different grain orientations, such as patent CN 113125275 A. In addition, single crystal materials can use one finite element unit to express their macroscopic anisotropic characteristics, so the finite element iterative optimization consumption is very small. For polycrystalline finite element models, which are composed of multiple grains, their macroscopic mechanical properties are the average of each grain in the polycrystalline finite element model. Therefore, polycrystalline models usually need to contain a sufficient number of grains to make their mechanical properties representative. The more common method of calibrating polycrystalline constitutive parameters in the literature is achieved through 2D or 3D Voronoi models. For the 2D Vorinoi model, there are fewer grids and less computational cost. However, due to the introduction of the plane strain assumption, it cannot reflect the real mechanical response of the material at the macro level. For example, materials with significant texture characteristics have large differences in mechanical properties at different orientations. For the 3D Voronoi model, the distribution of grain center points can be controlled to achieve statistical consistency of grain size distribution with the real material. At the same time, by introducing the preferred orientation of the real material and considering the texture characteristics of the material, the mechanical response characteristics of the material can be better reflected. However, this results in the finite element model containing more grid units, which significantly increases the amount of calculation, resulting in huge computational cost for traditional optimization tools and a long cycle for constitutive parameter calibration. Therefore, a new efficient calibration method is needed to reduce computational cost and improve calibration efficiency. Summary of the invention

[0004] In order to solve the problems existing in the above-mentioned background technology, the present invention provides a polycrystalline crystal plastic constitutive parameter calibration method based on voxel cube equivalent representative volume unit, which can not only fully consider the microscopic properties of the material, but also significantly reduce the calculation consumption, and realize the automatic calibration of the constitutive parameters in combination with the optimization algorithm.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for calibrating polycrystalline plastic constitutive parameters comprises the following steps:

[0007] (1) Perform EBSD characterization on the metal materials under study to obtain their grain size statistical distribution and texture characteristics;

[0008] (2) Establish a cubic polycrystalline geometric model containing 512 grains, and use Python scripts to batch establish sets and assign constitutive parameters and grain orientations;

[0009] (3) Use FORTRAN77 to write the crystal plasticity constitutive model subroutine UMAT;

[0010] (4) With the help of Python scripts, the corresponding mesh nodes of the corresponding faces are automatically identified, and the Equation constraint relationship of the node degrees of freedom is established, and periodic boundary conditions are imposed;

[0011] (5) extracting the force-displacement calculation results of the control points of the polycrystalline model and converting them into stress-strain relationships, while interpolating the specimen stress-strain / stress-time data to the calculation data points;

[0012] (6) The elastic, rate-dependent, kinematic hardening and critical shear stress-related constitutive parameters were calibrated using stress-strain / stress-time data from uniaxial tension and fatigue tests. The sum of squares of the difference between the uniaxial tension and fatigue test and simulated pseudo-stress-strain / stress-time data points was used as the optimization target, and the Hook-Jeeves optimization algorithm was used for iterative optimization.

[0013] (7) The constitutive parameters are adjusted by the iterative algorithm, and the material parameters of the finite element model are updated with the help of Python scripts to optimize the objective function to the minimum within the allowed number of iterations.

[0014] In the step (1), EBSD characterization is performed on the metal material under study, and a characterization area of ​​400 μm*400 μm is selected to obtain its typical grain size distribution and texture characteristics.

[0015] In the steps (2) and (4), Python scripts are used to read the grain orientation data obtained by EBSD characterization, so as to realize batch assignment of material constitutive parameters and grain orientation and batch application of equation constraint relationships between relative nodes on relative surfaces.

[0016] In the steps (5) and (6), standard uniaxial tensile and low cycle fatigue tests are carried out on the material at the temperature under study; for materials with rate-dependent properties at 650°C, uniaxial tensile tests or tensile load holding tests are carried out at different tensile rates, and the sum of the squares of the differences between the test and simulation data points is optimized.

[0017] In the step (6), the weight coefficients of the uniaxial tensile stress-strain curve, the first week of fatigue tension-compression cycle fatigue hysteresis loop and the cyclic stress peak curve are all set to 1, and the Hook-Jeeves optimization algorithm is used for iterative optimization until the objective function is optimized to the minimum value or the maximum number of iterations is reached.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] The present invention can fully consider the texture characteristics of the material and the three-dimensional macroscopic mechanical stress-strain response characteristics, while significantly reducing the number of finite element model units and calculation consumption, shortening the optimization cycle, and realizing the rapid calibration of the plastic constitutive parameters of polycrystalline crystals. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of the implementation of the present invention;

[0021] Figure 2a is the inverse pole figure of a certain type of nickel-based high-temperature alloy along the x-axis;

[0022] Figure 2b is the statistical distribution diagram of grain size;

[0023] Figure 3a This is a cubic polycrystalline model diagram containing 512 grains;

[0024] Figure 3b is the grain orientation inverse pole figure along the x-axis;

[0025] Figure 4 Cubic polycrystalline models with different mesh densities: 1*1*1, 2*2*2, 3*3*3 and 4*4*4 meshes;

[0026] Figure 5 Representative volume unit diagram of variable grain size generated by Dream.3D;

[0027] Figure 6 The uniaxial stress-strain response diagrams are different mesh densities;

[0028] Figure 7 Compare the time consumption for different models;

[0029] Figure 8a This is the comparison diagram of stress-strain hysteresis loops in the first cycle;

[0030] Figure 8b This is the stress-time curve comparison diagram for the first cycle;

[0031] Figure 9a It is a comparison diagram of stress-strain hysteresis loops of stable cycles;

[0032] Figure 9b This is a comparison chart of the stress-time curves of stable cycles. DETAILED DESCRIPTION

[0033] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0034] Example 1

[0035] The implementation flow chart of the method for rapid calibration of polycrystalline plastic constitutive model parameters of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0036] (1) For a certain type of nickel-based alloy material, a cylindrical metallographic specimen with a diameter of 6 mm and a height of 3 mm was cut from the uniform structure in the center of the disk-shaped billet. After sandpaper grinding and SiO2 polishing liquid polishing, the grain boundary was etched out using Kailing reagent and observed using an optical microscope to preliminarily estimate the grain size. Based on the measured grain size, a scanning step size of 1 / 20 of the average grain size and a scanning area of ​​400μm*400μm were selected for EBSD characterization to include a sufficient number of grains to obtain its grain size statistical distribution and texture characteristics, such as Figure 2a and Figure 2b shown.

[0037] (2) In ABAQUS, a total of 512 cubic polycrystalline geometric models with 8*8*8 are established, such as Figure 3a As shown, a Python script is used to create a collection for each grain and number it accordingly. The orientation Euler angle data obtained by EBSD characterization is read, and the rotation transformation of the Euler angle is used to calculate two pairs of non-parallel vector groups in the global coordinate system and the crystal coordinate system to define the grain orientation. The inverse pole figures of all grain orientations along the x-axis are shown in Figure 3b As shown, the constitutive model material parameters of each slip system are defined in batches with the help of Python scripts.

[0038] (3) Use UMAT to define the crystal plasticity constitutive model. Here, the crystal plasticity constitutive model in the form of phenomenological power law is adopted:

[0039]

[0040] τ α =m *α ·τ·s *α (2)

[0041]

[0042]

[0043]

[0044] in, is the reference shear strain rate, n is the power law exponent, τ α , and χ α are the shear strain rate, partial shear stress, critical partial shear stress and back stress on the α slip system, respectively. *α and *α are the unit normal vector and the unit vector of the slip direction of the α slip system, respectively, and τ is the Kirchhoff stress. αβ is the slip hardening modulus, representing the hardening effect of the β slip system on the α slip system, h(γ) is the hardening function, q is the ratio of the self-hardening modulus to the latent hardening modulus, γ is the cumulative shear strain of each slip system, t is the slip action time, δ αβ is the Kronecker symbol. τ0, τ s and h0 are the initial value, saturation value and initial hardening modulus of the critical partial shear stress, respectively. is the back stress rate on the α slip system, C and D are the direct hardening modulus and dynamic recovery coefficient, respectively.

[0045] (4) Use Python scripts to create sets of mesh nodes on the six surfaces of the cubic voxel mesh model and define the four corner points as load control points. Use loop statements to search for corresponding nodes on the opposite surfaces and establish equation constraint relationships between the relative nodes and the load control points to ensure parallel deformation of the corresponding surfaces of the cubic voxel model.

[0046] (5) Four sets of finite element models with different mesh densities are used, such as Figure 4 As shown in the figure, the mesh sensitivity and convergence of the macroscopic mechanical response are studied. The average macroscopic response of the polycrystalline cubic voxel model is obtained by extracting the force-displacement calculation results of the polycrystalline model control points and converting them into stress-strain relationships. In order to verify the equivalence and efficiency of the cubic voxel model method, it is compared with the traditional 3D Voronoi model, as shown in the figure. Figure 5 Comparison of the computation time of four grids and the 3DVoronoi model generated by Dream.3D software Figure 6 As shown in the figure, the 3*3*3 grid division has good convergence and has an equivalent average macroscopic mechanical response compared to the traditional 3D Voronoi model. At the same time, it greatly reduces the computational cost, which is only 17.2% of the computational time of the traditional method.

[0047] (6) Based on the results of convergence analysis, the 3*3*3 model is used to calibrate the constitutive parameters. First, the elastic constant C is determined based on the linear elastic section of the uniaxial tensile test. 11 , C 12 and C 44 Secondly, the rate correlation coefficient was determined using uniaxial tensile tests or tensile load holding tests at two different tensile rates (1% / s and 0.01% / s). and n; the fatigue hysteresis loop of the first tensile-compression cycle of fatigue loading is used to calibrate the initial critical partial shear stress and back stress parameters; the cyclic soft / hardening test data is used to calibrate the critical partial shear stress saturation value and the initial hardening modulus. The uniaxial tensile and fatigue test stress-strain / stress-time data are interpolated to the calculation result data points, and the square sum of the difference between the test and simulation data points is used as the optimization target. The weight coefficients of the uniaxial tensile stress-strain curve, the first tensile-compression cycle fatigue hysteresis loop and the cyclic stress peak curve are all set to 1, and the Hook-Jeeves optimization algorithm is used for iterative optimization.

[0048] (7) The constitutive parameters are adjusted by iterative algorithm, and the material parameters of the finite element model are updated with the help of Python script, and the objective function is minimized within the allowed number of iterations. The constitutive parameters of a certain type of nickel-based alloy at 650°C after optimization are C 11 =172.44GPa, C 12 =101.28GPa,C 44 =91.45GPa, n=50,τ0=250MPa,τ s / τ0=1.2,h0 / τ0=2.16,C=55000MPa,D=300. Under the 2-2-2-2 trapezoidal wave load with a stress ratio of -1, the stress-strain curve and stress-time curve of the first cycle of the test and simulation are as follows: Figure 8a and Figure 8b As shown in the figure, the stress-strain curve and stress-time curve of the stable cycle are shown in Figure 9a and Figure 9b As shown in the figure, the final simulation and test macro stress-strain and stress-time have good fitting effect.

[0049] 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 principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calibrating plastic constitutive parameters of a polycrystalline material, characterized in that: The following steps are involved: (1) Perform EBSD characterization on the metal materials under study to obtain their grain size statistical distribution and texture characteristics; (2) Establish a cubic polycrystalline geometric model containing 512 grains, and use Python scripts to batch establish sets and assign constitutive parameters and grain orientations; (3) Use FORTRAN77 to write the crystal plasticity constitutive model subroutine UMAT; the crystal plasticity constitutive model in phenomenological power law form is used here: t α =m *α ·t·s *α (2) in, is the reference shear strain rate, n is the power law exponent, τ α , and χ α are the shear strain rate, partial shear stress, critical partial shear stress and back stress on the α slip system respectively; m *α and *α are the unit normal vector and the unit vector of the slip direction of the slip plane where the α slip system is located, τ is the Kirchhoff stress; h αβ is the slip hardening modulus, representing the hardening effect of the β slip system on the α slip system, h(γ) is the hardening function, q is the ratio of the self-hardening modulus to the latent hardening modulus, γ is the cumulative shear strain of each slip system, t is the slip action time, δ αβ is the Kronecker symbol; τ0, τ s and h0 are the initial value, saturation value and initial hardening modulus of the critical partial shear stress, respectively; is the back stress rate on the α slip system, C and D are the direct hardening modulus and dynamic recovery coefficient, respectively; (4) With the help of Python scripts, the corresponding mesh nodes of the corresponding faces are automatically identified, and the Equation constraint relationship of the node degrees of freedom is established, and periodic boundary conditions are imposed; (5) extracting the force-displacement calculation results of the control points of the polycrystalline model and converting them into stress-strain relationships, while interpolating the specimen stress-strain / stress-time data to the calculation data points; (6) The elastic, rate-dependent, kinematic hardening and critical shear stress-related constitutive parameters were calibrated using stress-strain / stress-time data from uniaxial tension and fatigue tests. The sum of squares of the difference between the uniaxial tension and fatigue test and simulated pseudo-stress-strain / stress-time data points was used as the optimization target, and the Hook-Jeeves optimization algorithm was used for iterative optimization. (7) The constitutive parameters are adjusted by the iterative algorithm, and the material parameters of the finite element model are updated with the help of Python scripts to optimize the objective function to the minimum within the allowed number of iterations.

2. The polycrystalline plastic constitutive parameter calibration method according to claim 1, characterized in that: In the step (1), EBSD characterization is performed on the metal material under study, and a characterization area of ​​400 μm*400 μm is selected to obtain its typical grain size distribution and texture characteristics.

3. The polycrystalline plastic constitutive parameter calibration method according to claim 1, characterized in that: In the steps (2) and (4), Python scripts are used to read the grain orientation data obtained by EBSD characterization, so as to realize batch assignment of material constitutive parameters and grain orientation and batch application of equation constraint relationships between relative nodes on relative surfaces.

4. The polycrystalline plastic constitutive parameter calibration method according to claim 1, characterized in that: In the steps (5) and (6), standard uniaxial tensile and low cycle fatigue tests are carried out on the material at the temperature under study; for materials with rate-dependent properties at 650°C, uniaxial tensile tests or tensile load holding tests are carried out at different tensile rates, and the sum of the squares of the differences between the test and simulation data points is optimized.

5. The polycrystalline plastic constitutive parameter calibration method according to claim 4, characterized in that: In the step (6), the weight coefficients of the uniaxial tensile stress-strain curve, the first week of fatigue tension-compression cycle fatigue hysteresis loop and the cyclic stress peak curve are all set to 1, and the Hook-Jeeves optimization algorithm is used for iterative optimization until the objective function is optimized to the minimum value or the maximum number of iterations is reached.

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