A method for determining parameters of crystal plasticity model and its application

Abstract

The present invention relates to the field of metal materials technology, and more particularly to a method and application for determining parameters of a crystal plasticity model, comprising: Step 1: using electron backscatter characterization technology to select a grain region with the desired slip system characteristics; Step 2: processing a single-crystal micropillar specimen and completing a single-crystal micropillar compression experiment; Step 3: establishing a crystal plasticity finite element model for the single-crystal micropillar experiment; Step 4: inversely determining the critical shear stress parameter using the experimental displacement-load curve; and Step 5: verifying the fitted value of the critical shear stress parameter using an equivalent plastic strain distribution. Accurately determining the critical shear stress parameter for a single slip system in the crystal plasticity model through micromechanical experiments and computational inverse analysis can significantly improve the accuracy of material mechanical property predictions and material mechanical behavior response simulations, and is of great significance for the design of plastic deformation processes for actual metal components and the design of new alloys.

Description

Technical Field

[0001] The present invention relates to the technical field of metal materials, and in particular to a method for determining crystal plasticity model parameters and its application. Background Art

[0002] The Crystal Plasticity Model has been widely used in the prediction of the mechanical behavior of metal materials. The Crystal Plasticity Model is a material mechanics model based on the microscopic scale. This model no longer regards the material as homogeneous, but instead establishes the microscopic stress-strain response (material constitutive relationship) on the crystal slip system. Therefore, through the Crystal Plasticity Model, the mechanical behavior of the material can be directly linked to the microscopic structural characteristics of the material, such as the crystal structure and orientation. This model can not only predict the stress and strain distribution at the microscopic scale, but also reflect the macroscopic mechanical response through averaging. Therefore, it is widely used in the prediction of material processing behavior, strength, creep, fatigue and other mechanical properties. Since the microscopic structural characteristics can be obtained through methods such as phase field, the Crystal Plasticity Model is a key method for serial organization and performance calculations, and is an important link in the integrated calculation of materials.

[0003] Since the physical basis of the crystal plasticity model is built on the crystal slip system, all material parameters in its constitutive model are based on the slip system as a reference. The critical shear stress of the slip system is essentially a mechanical characterization of the ability of a certain crystal slip system to resist the activation of external forces, and is a set of crucial parameters in the crystal plasticity model. Most metal materials are polycrystalline materials. This parameter cannot be directly measured through experiments and can generally only be obtained through fitting and inverse analysis. Traditional macroscale material mechanics constitutive models treat materials as continuous and uniformly distributed homogeneous materials. Therefore, the load-displacement experimental curve is obtained through macroscopic uniaxial tension or compression experiments, and the constitutive model parameters can be obtained through computational fitting. However, in the crystal plasticity model, the macroscopic load-displacement curve is the result of the nonlinear superposition of the mechanical responses of multiple grains. This response not only includes the complex loading process of all slip systems, but also includes the grain boundary interaction. Therefore, using macroscopic mechanical experiments to fit and inversely determine the critical shear stress of a slip system does not actually yield the intrinsic critical shear stress of the slip system. Instead, it implicitly includes information about the interactions between the slip system and grain boundaries. This results in parameters obtained through macroscopic mechanical experiments being less applicable and portable, and their prediction accuracy under complex loading conditions is insufficient. Consequently, the lack of a precise method for determining this parameter significantly limits the application of crystal plasticity models. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for accurately obtaining the microscopic material parameter of the critical shear stress of the crystal plasticity model of metal materials, which solves the problem that this parameter in engineering alloy materials cannot be directly measured through experiments and the macroscopic experimental fitting error is large; by adopting a method of inverse analysis combining microscopic experiments and simulation calculations, the accuracy and practical value of this parameter are significantly improved.

[0005] The present invention provides a method for accurately obtaining the microscopic material parameters of the critical shear stress of a crystal plasticity model of a metal material. By designing a micromechanical experiment, it is ensured that a specific slip system participates in the activation and deformation, thereby avoiding the interaction of multiple slip systems and the influence of grain boundary effects on the mechanical response. Combined with displacement-load curves and orientation change experimental measurements, an appropriate parameter inverse optimization algorithm is used to inversely calculate the critical shear stress parameters of a specific slip system.

[0006] Specifically, the present invention adopts the following technical solutions:

[0007] A method for determining crystal plasticity model parameters, comprising the following steps:

[0008] Step 1: Use electron backscatter characterization technology to select the grain region with the slip system characteristics to be determined;

[0009] Step 2: Processing single crystal micropillar specimens on the selected grain area and completing single crystal micropillar compression tests;

[0010] Step 3: Establish a crystal plasticity finite element model for the single crystal micropillar experiment;

[0011] Step 4: Using the displacement-load curve obtained from the single crystal micropillar compression experiment, the critical shear stress parameter in the crystal plasticity finite element model is fitted and inversely calculated, and the critical shear stress value of the slip system is output;

[0012] Step 5: Use the equivalent plastic strain distribution to verify the critical shear stress parameter fitting value.

[0013] In some embodiments, in step 1, an alloy sample with typical microstructural characteristics is prepared, the slip system type is determined based on the alloy crystal structure, the crystal orientation distribution of each grain of the sample is determined using electron backscattering characterization technology, and a single grain region with a representative orientation is selected.

[0014] In some embodiments, in step 1, the grain region includes two characteristics of the slip system to be determined: (1) a complete single crystal microcolumn specimen can be cut out of the grain region; and (2) the grain orientation and the compression direction satisfy a specific orientation relationship. Specifically, according to the Schmid law, the Schmid factor 1 / m of each slip system under the uniaxial compression deformation condition of each grain is calculated separately, and the grain with the largest Schmid factor of the slip system to be determined is selected.

[0015] In some embodiments, the Schmid factor 1 / m is calculated as: in is the angle between the normal direction of the slip surface of the slip system to be determined and the external load, and θ is the angle between the slip direction of the slip system to be determined and the external load.

[0016] In some embodiments, in step 2, the grain region in step 1 is cut using micro-nano processing technology to obtain a single crystal microcolumn sample, and electron backscattering technology is used to characterize the three-dimensional EBSD orientation and precise three-dimensional size of the sample.

[0017] Furthermore, the micro-nano processing technology includes but is not limited to focused ion beam.

[0018] In some embodiments, in step 2, a single crystal microcolumn compression test is performed on the single crystal microcolumn sample to record the displacement-load curve, orientation change after deformation, and size and morphology of the single crystal microcolumn after deformation.

[0019] In some embodiments, in step 3, the crystal plasticity finite element model includes two features: (1) the geometric dimensions, initial crystal orientation, and loading conditions are consistent with the characterization results of the single crystal micropillar specimen in step 2; and (2) the critical shear stress of all slip systems is the only variable to be determined, and the material intrinsic parameters are known quantities.

[0020] Furthermore, the material intrinsic parameters include shear modulus and Burgers vector, which are generally obtained through experiments or theoretical calculations.

[0021] Furthermore, a set of preset values ​​is assigned to the critical shear stress of the slip system, and the crystal plasticity model established in step 5 is used to simulate the uniaxial compression process of the microcolumns, and the simulated displacement-load curve, orientation distribution, and stress / strain distribution are output.

[0022] Furthermore, the calculated displacement-load curve is preferentially compared with the experimentally obtained displacement-load curve. If stress concentration occurs, the curve segment before the stress concentration occurs is selected as a reference for comparison.

[0023] In some embodiments, in step 4, the simulation results of the crystal plasticity finite element model are compared with the single crystal microcolumn compression test results, and the ratio of the absolute difference between the two to the experimental results is calculated. If it is greater than a threshold, the critical shear stress of the slip system is adjusted using an inverse optimization algorithm until the ratio is less than or equal to the threshold. The calculation is stopped, and the critical shear stress value of the slip system to be determined under this condition is output.

[0024] In some embodiments, the threshold is 1%-10%.

[0025] In some embodiments, in step 5, the critical shear stress value is recalculated during the single crystal micropillar compression process to obtain the deformation orientation distribution and the local strain distribution.

[0026] Furthermore, if the statistical distribution deviation between the deformation orientation distribution and the local strain distribution is less than 10% when compared with similar experimental data, the calculated orientation and microscopic strain distribution are considered consistent with the experiment. At this point, the critical shear stress of the slip system obtained in step 5 is determined as the final fitting value.

[0027] The invention discloses an application of a parameter determination method in the micromechanics model of metal materials.

[0028] The mechanism of the present invention for obtaining the critical shear stress parameters of the slip system by combining microscopic experiments with calculations is as follows:

[0029] Crystal plasticity model parameters fall into two main categories: one is intrinsic parameters of the material's atomic structure and physical properties, such as shear modulus, Poisson's ratio, and lattice constant. These parameters can generally be accurately obtained through experimental methods or theoretical calculations; the other is micromechanical response parameters, such as critical shear stress and hardening coefficient. These parameters cannot be directly measured experimentally and are generally inversely derived through comparison with experimental results. For the second category of crystal plasticity model parameters, all parameters are established using the slip system as a reference system, resulting in a complete set of parameters for each slip system. Inversely deriving these parameters using macroscopic mechanical experiments effectively involves performing a multi-objective optimization inverse on all slip system parameters simultaneously. This approach presents a problem in that it fails to distinguish between interactions between slip systems and the influence of grain boundaries. This also means that the inversely derived parameters for a single slip system implicitly incorporate the influence of other slip systems and grain boundaries and are not true microscopic crystal plasticity parameters. This results in limited applicability of the fitted parameters, and changes in external loading conditions or the material's microstructure can lead to a decrease in calculation accuracy. Therefore, in order to minimize the influence of these factors, the present invention selects single crystal micropillar experiments to avoid the effect of grain boundaries, maximizes the activation effect of the slip system to be determined through orientation selection, and minimizes the influence of the interaction of other slip systems. At the same time, local strain response and orientation rotation changes are introduced to assist in comparative analysis and calculation reliability. The entire process minimizes the complexity of the multi-parameter fitting optimization process. The physical meaning of the critical shear stress is very clear, and its qualitative change law is completely consistent with the theoretical analysis.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. This invention accurately determines the critical shear stress parameters of a single slip system in a crystal plasticity model through micromechanical experiments and inverse calculations. Accurate and reasonable crystal plasticity parameters can significantly improve the accuracy of material mechanical property predictions and material behavior simulations, and are of great significance for the design of plastic deformation processes for actual metal components and the design of new alloys.

[0032] 2. The present invention can be applied to alloy materials with various crystal structures, including face-centered cubic austenitic stainless steel and nickel-based high-temperature alloys, body-centered cubic ferritic steel, aluminum alloy and β-phase titanium alloy, close-packed hexagonal α-phase titanium alloy, magnesium alloy, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A and B are the initial microstructure grain orientation distribution of the titanium alloy obtained in Example 1. The circled position is the grain with the largest Schmid factor in the calculated conical slip system, where A is the orientation imaging diagram obtained by EBSD and B is the anti-pole figure in the AD direction.

[0034] Figure 2 This is the SEM characterization image of the single crystal microcolumn sample obtained by FIB cutting in Example 1.

[0035] Figure 3 The displacement-load curves are obtained from the experimental measurement of the single crystal micropillar and the crystal plasticity finite element (CPFEM) simulation of Example 1.

[0036] Figure 4 This is the microscopic morphology of the single crystal microcolumn after compression deformation in Example 1.

[0037] Figure 5 This is the microscopic plastic strain distribution diagram obtained by carrying out micro-pillar compression crystal plasticity simulation using the critical shear stress value obtained by fitting in Example 1.

[0038] Figure 6 A and B are the initial microstructure orientation distribution of the titanium alloy obtained in Example 2. The position indicated by the circle is the grain with the largest Schmid factor of the calculated cylindrical slip system, where A is the orientation imaging diagram obtained by EBSD and B is the anti-pole figure in the AD direction.

[0039] Figure 7 This is the SEM characterization image of the single crystal microcolumn sample obtained by FIB cutting in Example 2.

[0040] Figure 8 This is the displacement-load curve obtained from the single crystal micropillar experimental measurement in Example 2.

[0041] Figure 9 This is the microscopic morphology of the single crystal microcolumn after compression deformation in Example 2.

[0042] Figure 10 This is the microscopic plastic strain distribution diagram obtained by carrying out micro-pillar compression crystal plasticity simulation using the critical shear stress value obtained by fitting in Example 2. DETAILED DESCRIPTION

[0043] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0044] Example 1

[0045] This embodiment provides a method for determining parameters of a crystal plasticity model. Specifically, this embodiment determines the critical shear stress of a cone slip system of an hcp phase of a near-α-type titanium alloy. The method includes the following steps:

[0046] Step 1: Use EBSD (backscattered electron diffraction technology) to select a grain region that includes two slip system features to be determined ((1) the grain region can be cut out of a complete single crystal micropillar specimen; (2) the grain orientation and compression direction meet a specific orientation relationship, so that only cone slip can be activated when the micropillar is compressed) and determine the orientation of each grain in the specimen, such as Figure 1 As shown; the Schmid factor of each grain is calculated using the Schmid law, and the calculation formula is: in is the angle between the normal direction of the slip surface of the slip system to be determined and the external load, θ is the angle between the slip direction of the slip system to be determined and the external load; through analysis, we can get Figure 1 When the grain shown in the black circle is subjected to uniaxial compression perpendicular to the normal, the Schmid factor of the conical slip system is the largest, and the orientation (Euler angle) of the grain is (31.72°, 1.49°, 30.78°).

[0047] Step 2: Use FIB (focused ion beam) to cut the grain area and obtain a single crystal microcolumn sample, such as Figure 2 As shown. Under SEM, a compression test was conducted on a single crystal microcolumn sample using a nano-in-situ mechanical test bench, and the displacement-load curve after deformation was obtained as shown in Figure 3 shown.

[0048] Step 3: A finite element model of the titanium alloy micropillar compression specimen is established using a crystal plasticity model (details of the model can be found in reference [1]). The crystal plasticity finite element model includes two features: (1) the geometric dimensions, initial crystal orientation, and loading conditions are consistent with the characterization results of the single crystal micropillar specimen in step 2; (2) the critical shear stress of all slip systems is the only variable to be determined, and the material intrinsic parameters are known. The most basic phenomenological model uses the decomposed shear stress as the material state variable and describes the change of the critical decomposed shear stress through different hardening models; the phenomenological model is as follows:

[0049]

[0050] in and n are the reference shear rate, critical decomposed shear stress and sensitivity of shear rate to shear stress of the i-th slip system, respectively. is the shear strain rate of the slip system, τ i is the shear stress of the slip system, χ i is the back stress of the slip system.

[0051] Step 4: Set the reference shear rate and sensitivity n to constant values, and set the initial critical shear stress value of the conical slip system to 500 MPa; using the genetic optimization algorithm, compare the simulation results of the crystal plasticity finite element model with the single crystal micropillar compression test results, calculate the ratio of the absolute difference between the two and the experimental results, set the fitting threshold to less than 5%, calibrate the critical shear stress in the model, and finally obtain the critical shear stress value of the conical slip to be 852 MPa.

[0052] Step 5: Substitute the critical shear stress value into the crystal plasticity simulation analysis and compare the strain distribution and morphology of the micropillars after deformation obtained by simulation ( Figure 5 ) and experimental deformation morphology ( Figure 4 ) It can be seen that the two are in good agreement, which verifies the rationality of the fitting value.

[0053] Example 2

[0054] This embodiment provides a method for determining parameters of a crystal plasticity model. Specifically, this embodiment determines the critical shear stress of the basal slip system of the hcp phase of a near-α-type titanium alloy. The method includes the following steps:

[0055] Step 1: Use EBSD (backscattered electron diffraction technology) to select a grain region that includes two slip system features to be determined ((1) the grain region can be cut out of a complete single crystal micropillar specimen; (2) the grain orientation and compression direction meet a specific orientation relationship, so that only basal slip can be activated when the micropillar is compressed) and determine the orientation of each grain in the specimen, such as Figure 6 As shown; the Schmid factor of each grain is calculated using the Schmid law, and the calculation formula is: in is the angle between the normal direction of the slip surface of the slip system to be determined and the external load, θ is the angle between the slip direction of the slip system to be determined and the external load; through analysis, we can get Figure 6 When the grain shown in the black circle is subjected to uniaxial compression perpendicular to the normal direction, the Schmid factor of the basal slip system is the largest, and the orientation (Euler angle) of the grain is (76.88°, 88.89°, 14.6°).

[0056] Step 2: Use FIB (focused ion beam) to cut the grain area and obtain a single crystal microcolumn sample, such as Figure 7 As shown. Under SEM, a compression test was conducted on a single crystal microcolumn sample using a nano-in-situ mechanical test bench, and the displacement-load curve after deformation was obtained as shown in Figure 8 shown.

[0057] Step 3: A finite element model of the titanium alloy micropillar compression specimen is established using a crystal plasticity model (details of the model can be found in reference [1]). The crystal plasticity finite element model includes two features: (1) the geometric dimensions, initial crystal orientation, and loading conditions are consistent with the characterization results of the single crystal micropillar specimen in step 2; (2) the critical shear stress of all slip systems is the only variable to be determined, and the material intrinsic parameters are known. The most basic phenomenological model uses the decomposed shear stress as the material state variable and describes the change of the critical decomposed shear stress through different hardening models; the phenomenological model is as follows:

[0058]

[0059] in and n are the reference shear rate, critical decomposed shear stress and sensitivity of shear rate to shear stress of the i-th slip system, respectively. is the shear strain rate of the slip system, τ i is the shear stress of the slip system, χ i is the back stress of the slip system.

[0060] Step 4: Set the reference shear rate and sensitivity n to constant values, and set the initial critical shear stress value of the basal slip system to 500 MPa; using the genetic optimization algorithm, compare the simulation results of the crystal plasticity finite element model with the single crystal micropillar compression test results, calculate the ratio of the absolute difference between the two and the experimental results, set the fitting threshold to less than 5%, calibrate the critical shear stress in the model, and finally obtain the critical shear stress value of basal slip as 284 MPa.

[0061] Step 5: Substitute the critical shear stress value into the crystal plasticity simulation analysis and compare the strain distribution and morphology of the micropillars after deformation obtained by simulation ( Figure 10 ) and experimental deformation morphology ( Figure 9 ) It can be seen that the two are in good agreement, which verifies the rationality of the fitting value.

[0062] References:

[0063] [1]H.Zhang,J.Liu,D.Sui,Z.Cui,MWFu,Study of microstructural grainand geometric size effects on plastic heterogeneities at grain-level by using crystal plasticity modeling with high-fidelity representativemicrostructures,International Journal of Plasticity 100(2018)69-89.

[0064] The above is 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 principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for determining crystal plasticity model parameters, characterized in that: The method comprises the following steps: Step 1: Use electron backscatter characterization technology to select the grain region with the slip system characteristics to be determined; Step 2: Processing single crystal micropillar specimens on the selected grain area and completing single crystal micropillar compression tests; Step 3: Establish a crystal plasticity finite element model for the single crystal micropillar experiment; Step 4: Using the displacement-load curve obtained from the single crystal micropillar compression experiment, the critical shear stress parameter in the crystal plasticity finite element model is fitted and inversely calculated, and the critical shear stress value of the slip system is output; Step 5: Use equivalent plastic strain distribution to verify the critical shear stress parameter fitting value; In step 1, the grain region includes two slip system features to be determined: (1) A complete single crystal microcolumn specimen can be cut out of the grain region; (2) The directional relationship between the grain orientation and the compression direction satisfies certain conditions. Specifically, according to the Schmid law, the Schmid factor 1 / m of each slip system under uniaxial compression deformation conditions of each grain in different orientation is calculated separately, and the grain with the largest Schmid factor of the slip system to be determined is selected; The Schmid factor 1 / m is calculated as follows: 1 / m=cosθcosφ; where φ is the angle between the normal direction of the slip surface of the slip system to be determined and the external load, and θ is the angle between the slip direction of the slip system to be determined and the external load. In step 3, the crystal plasticity finite element model includes two features: (1) the geometric dimensions, initial crystal orientation, and loading conditions are consistent with the characterization results of the single crystal micropillar specimen in step 2; (2) the critical shear stress of all slip systems is the only variable to be determined, and the material intrinsic parameters are known quantities; In step 4, the simulation results of the crystal plasticity finite element model are compared with the single crystal micropillar compression test results, and the ratio of the absolute difference between the two and the experimental results is calculated. If it is less than a threshold, the input critical shear stress of the slip system is accepted as the calibration value. If it is greater than the threshold, the critical shear stress of the slip system is adjusted using an inverse optimization algorithm until the ratio is less than or equal to the threshold. The calculation is stopped and the critical shear stress value of the slip system to be determined under this condition is output; The threshold is 1%-10%; In step 5, the stress value of the critical split is used to calculate the single crystal microcolumn compression process again to obtain the deformation orientation distribution and local strain distribution.

2. The parameter determination method according to claim 1, characterized in that: In step 2, the grain area in step 1 is cut using micro-nano processing technology to obtain a single crystal microcolumn sample, and the electron backscattering technology is used to characterize the three-dimensional EBSD orientation and precise three-dimensional size of the sample.

3. The parameter determination method according to claim 2, characterized in that: In step 2, a single crystal microcolumn compression test is performed on the single crystal microcolumn sample, and the displacement-load curve, orientation change after deformation, and size and morphology of the single crystal microcolumn after deformation are recorded.

4. Application of the parameter determination method according to any one of claims 1 to 3 in parameter determination in a micromechanics model of metal materials.

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