INVERSION IDENTIFICATION METHOD OF CRYSTAL PLASTICITY MATERIAL PARAMETERS BASED ON NANOINDENTATION EXPERIMENTS

Abstract

The present disclosure provides a method for inversion of crystal plasticity material parameters based on nanoindentation experiments. The method comprises: firstly, obtaining the elastic modulus of material by Oliver-Pharr method; secondly, establishing a macroscopic parameter inversion model of nanoindentation, correcting actual nanoindentation experimental data by pile-up/sink-in parameters and calculating macroscopic constitutive parameters of indentation material in combination with a Kriging surrogate model and a genetic algorithm; and finally, establishing a polycrystalline finite element model for a tensile specimen based on crystal plasticity finite element method, and calculating the crystal plasticity material parameters according to the calculated constitutive parameters of the material in combination with the Kriging surrogate model and the genetic algorithm. Compared with the prior art, the present disclosure can improve the calculation accuracy, reduce the amount of calculation and enhance calculation convergence, and has both practical and guideline values for the inversion of crystal plasticity material parameters.

Claims

1. An inversion identification method of crystal plasticity material parameters based on nanoindentation experiments, comprising: firstly, obtaining the elastic modulus of material by using Oliver-Pharr method to simplify a macroscopic constitutive parameter inversion model; secondly, establishing a macroscopic parameter inversion model of nanoindentation by using a piecewise linear/power-law hardening material model in combination with MATLAB and ABAQUS, correcting actual nanoindentation experimental data by using pile-up/sink-in parameters and calculating macroscopic constitutive parameters of material to be tested in combination with a Kriging surrogate model and a genetic algorithm; and finally, establishing a polycrystalline finite element model of a tensile specimen by using the crystal plasticity finite element method, and calculating the crystal plasticity material parameters of experimental material in combination with the Kriging surrogate model and the genetic algorithm.

2. The inversion identification method of crystal plasticity material parameters based on nanoindentation experiments according to claim 1, specifically comprising steps of: step 1: nanoindentation experiment of a metal material to be tested; 1-1: cutting the metal material to be tested and obtaining a satisfactory nanoindentation specimen through mechanical polishing and vibration polishing; 1-2: conducting an indentation test on the indentation specimen in step 1-1 by using a nanoindentation system to obtain experimental indentation responses comprising a load-displacement curve, a maximum load, contact stiffness and contact hardness; and obtaining the elastic modulus E of the material by using the Oliver-Pharr method; step 2: establishing a conventional finite element model of nanoindentation based on the piecewise linear/power-law hardening material model in combination with MATLAB and ABAQUS, and inverting the macroscopic constitutive parameters of the material: yield stress σ.sub.y and strain hardening exponent n, wherein the constitutive description of the piecewise linear/power-law hardening material model is: $\mathrm{.Math.}=\{\begin{array}{cc}\sigma /E& \mathrm{if}\sigma <{\sigma }_y\\ {\sigma }_y^{\left(n-1\right)/n}{\sigma }^{1/n}/E& \mathrm{otherwise}\end{array}$ wherein ε is total strain and σ is stress; 2-1: establishing a two-dimensional axisymmetric finite element model of nanoindentation by using ABAQUS; calculating the contact reaction force and displacement of an indenter along a penetration direction by using displacement-controlled loading, and outputting a contact force, the contact pressure and displacement of a contact surface of the specimen, and the displacement of a lowest node of the indenter to generate an input file; 2-2: extracting the constitutive parameters of the piecewise linear/power-law hardening material model in MATLAB by using Latin hypercube sampling; modifying the material parameters in the input file in step 2-1; calculating an indentation load-displacement curve under each set of sampling parameters and an indentation pile-up/sink-in parameter s/h, wherein s is pile-up or sink-in height; s is positive when pile-up occurs, and s is negative when sink-in occurs; and h is penetration depth; calculating a mean square error between the simulated load-displacement curve and the experimental load-displacement curve; establishing the Kriging surrogate model of the constitutive parameters and the mean square error; then conducting single-target optimization by using the genetic algorithm with the target of the minimum mean square error of two sets of data; and calculating the constitutive parameters of the piecewise linear/power-law hardening material model of the experimental material; 2-3: correcting the experimental load-displacement curve by using the indentation pile-up/sink-in parameter in step 2-2 to obtain a corrected load-displacement curve; then calculating the mean square error between the simulated load-displacement curve in step 2-2 and the corrected load-displacement curve; repeating the simple-target optimization process in step 2-2; and calculating the constitutive parameters of the piecewise linear/power-law hardening material model of the material after correction; 2-4: calculating the error between the constitutive parameters of the piecewise linear/power-law hardening material model calculated in step 2-2 and the constitutive parameters corrected in step 2-3; if the error is within an allowable range, using the constitutive parameters corrected in step 2-3 as the macroscopic constitutive parameters of the material; if the error is beyond the allowable range, using the load-displacement curve corrected in step 2-3 as the experimental load-displacement curve, and repeating the steps 2-2, 2-3 and 2-4 until the error is within the allowable range; step 3: establishing the polycrystalline finite element model of a tensile specimen by using the crystal plasticity finite element method in combination with MATLAB and ABAQUS, calculating the correspondence between the crystal plasticity material parameters and the piecewise linear/power-law hardening material parameters, and then inverting the crystal plasticity material parameters of the material to be tested; 3-1: establishing a crystal plasticity finite element model of a standard tensile specimen in ABAQUS; calculating the stress-strain curve of the material by using the load-controlled loading; and generating an input file; 3-2: extracting the crystal plasticity material parameters in MATLAB by using Latin hypercube sampling; modifying the material parameters in the input file in step 3-1; calculating the stress-strain curve under each set of sampling parameters; calculating the mean square error between the simulated stress-strain curve and the stress-strain curve under the macroscopic material parameters in step 2-4; establishing the Kriging surrogate model of the crystal plasticity material parameters and the mean square error by using MATLAB; then conducting single-target optimization by using the genetic algorithm with the target of the minimum mean square error of two sets of data; and calculating the crystal plasticity material parameters of the material.

3. The inversion identification method of crystal plasticity material parameters based on nanoindentation experiments according to claim 2, wherein in the step 2, an elastic parameter and a plasticity parameter are separated in the process of material parameter inversion, the elastic parameter is solved by a mature theoretical method, and the plasticity parameter is solved by finite element inversion.

4. The inversion identification method of crystal plasticity material parameters based on nanoindentation experiments according to claim 2, wherein in the step 2-4, the allowable range of error is 0-2%.

Description

DESCRIPTION OF DRAWINGS

[0024] FIG. 1 is a flow chart of present disclosure;

[0025] FIG. 2 is a experimental load-displacement curves;

[0026] FIG. 3 is a two-dimensional axisymmetric finite element model of nanoindentation;

[0027] FIG. 4 is a finite element model of a tensile specimen; and

[0028] FIG. 5 shows a stress-strain curve of nanoindentation inversion and a stress-strain curve of a tensile test.

DETAILED DESCRIPTION

[0029] The present disclosure is further described below in combination with specific embodiments.

[0030] As shown in FIG. 1, a method for inversion calibration of microscopic constitutive parameters of metal materials based on nanoindentation and finite element modelling for crystal plasticity material parameters comprises concrete implementation steps:

[0031] Step 1: nanoindentation experiment of a metal material to be tested;

[0032] 1-1: selecting 304 stainless steel material as a specimen, cutting the material and obtaining a satisfactory nanoindentation specimen through mechanical polishing and vibration polishing;

[0033] 1-2: conducting an indentation test on the indentation specimen by using a Nano Indenter XP system; setting the penetration depth as 2 microns in the test, and obtaining experimental indentation responses comprising a load-displacement curve, a maximum load, contact stiffness and contact hardness; repeating the test for many times to obtain more than 5 effective test points, wherein the test load-displacement curve is shown in FIG. 2; meanwhile, calculating the elastic modulus E of the material as 196.08 GPa by using Oliver-Pharr method.

[0034] Step 2: establishing a conventional finite element model of nanoindentation based on a piecewise linear/power-law hardening material model in combination with MATLAB and ABAQUS, and inverting the constitutive parameters (yield stress σ.sub.y and strain hardening exponent n) of the piecewise linear/power-law hardening material model;

[0035] 2-1: By taking a conical indenter with a half cone angle of 70.3° equivalent to a Berkovich triangular pyramid indenter in step 1-2, establishing a two-dimensional axisymmetric finite element model of nanoindentation by using ABAQUS; locally refining a material grid under the indenter, with the model as shown in FIG. 3; calculating the contact reaction force and displacement of an indenter along a penetration direction by using displacement-controlled loading, and outputting a contact force, the contact pressure and displacement of a contact surface of the specimen, and the displacement of a lowest node of the indenter to generate an input file;

[0036] 2-2: extracting 60 groups of elastic moduli E (selecting near the values calculated in 1-2), yield stress σ.sub.y and strain hardening exponent n in MATLAB by using Latin hypercube sampling; calculating an indentation load-displacement curve under each set of sampling parameters and an indentation pile-up/sink-in parameter s/h; calculating a mean square error between a simulated load-displacement curve and an experimental load-displacement curve; establishing a Kriging surrogate model of the constitutive parameters and the mean square error by using MATLAB; then conducting single-target optimization by using the genetic algorithm with the target of the minimum mean square error of two sets of data; calculating the constitutive parameters (yield stress σ.sub.y and strain hardening exponent n) of the piecewise linear/power-law hardening material model of the experimental material; and recording the constitutive parameters and the elastic moduli of the material calculated by Oliver-Pharr method together as C0;

[0037] 2-3: adding the experimental displacement and the pile-up or sink-in height s to obtain a corrected contact depth and then obtain a corrected load-displacement curve; then calculating a mean square error between the simulated load-displacement curve in 2-2 and the corrected load-displacement curve; repeating the simple-target optimization process in 2-2; calculating the constitutive parameters (yield stress σ.sub.y and strain hardening exponent n) of the piecewise linear/power-law hardening material model of the material after correction, and simultaneously using the elastic modulus of the material calculated by the Oliver-Pharr method and recording as C1;

[0038] 2-4: calculating the error between the material parameter C0 calculated in 2-2 and C1 in 2-3; if the error is within 2%, using the constitutive parameter C1 calculated in 2-3 as the macroscopic constitutive parameter of the material; if the error is beyond 2%, using the load-displacement curve corrected in 2-3 as the experimental load-displacement curve, and repeating the steps 2-2, 2-3 and 2-4 until the error is less than 2%. At this moment, the elastic modulus E of 304 stainless steel is obtained as 196.12 GPa, the yield stress σ.sub.y is 196 MPa, and the strain hardening exponent n is 0.251.

[0039] Step 3: establishing a polycrystalline finite element model of the tensile specimen by using the crystal plasticity finite element method in combination with MATLAB and ABAQUS, calculating the correspondence between the crystal plasticity material parameters (initial yield stress τ.sub.0, initial hardening modulus h.sub.0 and stage I stress τ.sub.s) and the piecewise linear/power-law hardening material parameters (yield stress σ.sub.y and strain hardening exponent n), and then inverting the crystal plasticity material parameters of the material to be tested;

[0040] 3-1: establishing the finite element model of the standard tensile specimen in ABAQUS as shown in FIG. 4, providing the model with the crystal plasticity material parameters by using ABAQUS material subroutine and then establishing the crystal plasticity finite element model of the standard tensile specimen; calculating the stress-strain curve of the material by using load-controlled loading; and generating an input file;

[0041] 3-2: extracting 60 sampling points of initial hardening moduli and saturated yield stress in MATLAB by using Latin hypercube sampling; modifying the material parameters in the input file in 3-1; calculating the stress-strain curve under each set of sampling parameters; calculating the mean square error between the stress-strain curve and the stress-strain curve under the macroscopic material parameters in 2-4; establishing the Kriging surrogate model of the crystal plasticity material parameters and the mean square error by using MATLAB; then conducting single-target optimization by using the genetic algorithm with the target of the minimum mean square error of two sets of data; and calculating the initial yield stress τ.sub.0 of the material to be tested as 86.11 MPa, the initial hardening modulus h.sub.0 as 220.52 MPa and the stage I stress τ.sub.s as 256.35 MPa.

[0042] Step 4: in order to verify the material parameters obtained by inversion, conducting a tensile test on the same 304 stainless steel material, wherein the comparison between the obtained stress-strain curve and the stress-strain curve obtained in step 2 is shown in FIG. 5. The initial yield stress τ.sub.0 calculated from the curve is 85.09 MPa, the initial hardening modulus h.sub.0 is 218.77 MPa, and the stage I stress r.sub.s is 260.52 MPa. It can be seen from the comparison results that the stress-strain curves and the crystal plasticity parameters calculated by the two methods have little difference. The inversion identification method is reasonable, effective and highly accurate, and the entire inversion identification process is correct.

The above embodiments only express the implementation of the present disclosure, and shall not be interpreted as a limitation to the scope of the patent for the present disclosure. It should be noted that, for those skilled in the art, several variations and improvements can also be made without departing from the concept of the present disclosure, all of which belong to the protection scope of the present disclosure.