Elasto-plastic constitutive parameter calculation method

Abstract

The application discloses an elasto-plastic constitutive parameter calculation method, comprising the following steps: S1, performing uniaxial tension experiment, obtaining a true stress-true strain curve of the experiment, and performing intercept processing near the maximum stress to obtain an intercepted curve; S2, based on the intercepted curve, extracting data points according to an equal arc length method, and performing data compression; S3, through a selected elastic model and a plastic model, performing nonlinear analysis on each data point, obtaining the proportion of elasticity and plasticity in the strain increment at each data point, and calculating the true stress-true strain curve of the model. According to the application, data points are extracted according to the arc length, the operation speed is improved under the condition that appropriate data points are selected, the elasto-plasticity of the data points is decomposed, the rationality of the mechanical calculation is ensured, the global optimization of the elasto-viscoplastic constitutive parameter is performed by constructing an optimization objective function, the coordination of the elastic and plastic constitutive parameters is ensured, and the calculation precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical property testing of metal materials, and particularly relates to a method for calculating elastic-plastic constitutive parameters. BACKGROUND

[0002] Currently, the plastic curve of isotropic metal materials is mainly obtained through uniaxial tensile test; in engineering application, the constitutive model parameters are obtained by fitting the true stress-true strain curve before necking, and then the model and the corresponding parameters are used in numerical simulation calculation.

[0003] However, the method for obtaining the mechanical parameters of the material through uniaxial tensile test of the material has the following four shortcomings: (1) only the elastic modulus is calculated by using the quasi-linear part of the true stress-true strain curve in the initial small deformation stage, without considering the elastic component in the material deformation after the material yields; (2) after obtaining the elastic modulus, the engineering convention yield stress (σ 0.2p ) is directly calculated by the translation method, and the engineering convention yield stress is taken as the theoretical yield stress (σ0) in the numerical simulation calculation such as finite element, but the two yield stresses are not identical, which introduces calculation error; (3) the true stress-true strain curve is then truncated at the convention yield point, and it is assumed that the strain after the point is all plastic strain, however, in actuality, there are both elastic and plastic components in the strain at each point on the curve after the yield point, so this assumption introduces error; (4) in addition, the processing method of truncating the curve from the convention yield point will lose the data point information between the theoretical yield point and the convention yield point, and introduce error. SUMMARY

[0004] To solve the above problems, the present application provides a method for calculating elastic-plastic constitutive parameters, which iteratively optimizes and calculates the constitutive parameters by using the true stress-true strain curve, and the specific technical solutions are as follows:

[0005] S1: using uniaxial tensile test to obtain the true stress-true strain curve of the experiment, and performing intercept processing to obtain the curve after intercept processing;

[0006] S2: based on the curve after intercept processing, data points are extracted according to the arc length, and data compression is performed;

[0007] S3: selecting an elastic model and a plastic model, and setting a constitutive parameter vector for the selected elastic and plastic models, obtaining the true strain data of the experiment according to the extracted data points, and performing nonlinear analysis on the abscissa, i.e. the true strain, of each data point extracted on the true stress-true strain curve of the experiment based on the true strain data of the experiment and the constitutive parameter vector, to obtain the proportion of elasticity and plasticity in the strain increment at each data point, and calculating the true stress-true strain curve of the model.

[0008] S4: According to the calculated model of true stress-true strain curve, the constitutive parameter vector is optimized, and the true stress-true strain curve of the model is recalculated based on the updated constitutive parameter vector, until the optimized condition parameter converges, and the constitutive parameter after iterative optimization is obtained.

[0009] Further, step S1, the acquisition of true stress-true strain curve, is as follows:

[0010] The engineering strain and true strain of the gauge section are obtained, the true stress at each time is calculated based on the cross-sectional area of the original sample gauge section, and the true stress-true strain curve of the experiment is obtained.

[0011] Further, the intercept processing is to remove the part with negative slope in the true stress-true strain curve of the experiment.

[0012] Further, step S2, the data compression, is as follows:

[0013] S201: Calculate the arc length of the curve after intercept processing;

[0014] S202: Determine the number of target data points after data compression;

[0015] S203: Based on the number of target data points, calculate the theoretical average point interval arc length;

[0016] S204: Extract data points and obtain the total number of extracted data points, calculate the residual based on the total number and the number of target data points;

[0017] S205: Based on the residual, determine whether it converges, if not, update the average point interval arc length, return to step S204 to execute again, until convergence is obtained, and the extracted data points at convergence are obtained.

[0018] Further, the residual is the difference between the total number of extracted data points and the number of target data points.

[0019] Further, in step S1, the slope of the point near 0.002 true strain on the true stress-true strain curve of the experiment and the origin is taken as the initial value of the elastic modulus of the linear elastic model, and the true stress value of the point is taken as the initial value of the theoretical yield strength.

[0020] Further, in step S3, the nonlinear analysis is as follows:

[0021] S301: The total strain (i.e. horizontal coordinate) increment of any adjacent data points is decomposed into elastic strain increment and plastic strain increment according to the addition principle, and the corresponding total strain rate is decomposed into elastic strain rate and plastic strain rate through the corresponding time increment;

[0022] S302: express the stress at the corresponding time point with the elastic strain increment and the selected elastic constitutive relation and the plastic strain increment and the selected plastic (viscous) constitutive relation respectively, and construct a nonlinear equation;

[0023] S303: calculate the elastic strain increment, the plastic strain increment and the true stress corresponding to each time point of the data point.

[0024] Further, the optimization updates the constitutive parameter vector, specifically as follows:

[0025] S401: construct a reduced objective function;

[0026] S402: reduce the argument to [0, 1], and reduce the argument to [0, 1];

[0027] S403: based on the reduced argument, the true stress of the experiment and the true stress calculated in the current step S3, calculate the optimization objective function;

[0028] S404: update the constitutive parameter vector by the optimization algorithm until the optimization objective function converges.

[0029] Further, the optimization objective function is specifically as follows:

[0030]

[0031] Wherein, i is the serial number of the data point, n is the total number of data points, σ i is the experimental true stress, is the model calculated true stress, ω i is the reduced argument, and is expressed as follows:

[0032]

[0033] Wherein, Δε i is the experimental true strain increment.

[0034] The beneficial effects of the present application are as follows:

[0035] 1. Since the number of general uniaxial tensile sampling points is very large, up to thousands of points, the data redundancy is too large, and the argument (true strain) often appears local non-monotonic oscillation, in order to remove redundancy and improve the optimization efficiency in the later period, the data needs to be compressed and verified, and according to the requirements, thousands of points are compressed to tens to hundreds of points, the present application calculates according to the arc length, accurately extracts the data points, ensures the representativeness of the curve, and avoids serious changes in the overall appearance of the curve.

[0036] 2. The method comprises the following steps of: performing nonlinear analysis on the extracted data points, decomposing the elastic part and the plastic part, calculating the true stress-true strain curve, constructing an optimization objective function through a reduced independent variable, and updating a constitutive parameter vector by using an optimization algorithm to realize global optimization of all parameters in the elastic-plastic constitutive relation at one time, better meet the mechanical theory, improve the calculation accuracy, and make the obtained constitutive model parameters more friendly to finite element application. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a schematic diagram of the overall process of the method;

[0038] Figure 2 is a schematic diagram of the data point extraction process;

[0039] Figure 3 is a schematic diagram of the nonlinear strain decomposition process;

[0040] Figure 4 is a schematic diagram of the iterative optimization process of the constitutive parameters. DETAILED DESCRIPTION

[0041] In the following description, the technical solutions in the embodiments of the present application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0042] In the description of the embodiments of the present application, it should be noted that the terms "first", "second" are only used for differentiation and description, and cannot be understood as indicating or implying relative importance.

[0043] Embodiment 1

[0044] Embodiment 1 of the present application discloses a method for calculating elastic-plastic constitutive parameters, as shown in the figure, the specific steps are as follows: Figure 1

[0045] S1: Perform uniaxial tensile test to obtain the true stress-true strain curve of the test, and perform intercept processing, and based on the intercepted curve.

[0046] In this embodiment, the true stress-true strain curve of the test is obtained as follows:

[0047] The engineering strain and true strain of the gauge section are obtained, the true stress at each time is calculated based on the cross-sectional area of the original sample gauge section, and the true stress-true strain curve of the test is obtained.

[0048] The intercept processing is to remove the part with negative slope in the obtained true stress-true strain curve of the test. ​

[0049] And in the true stress-true strain curve slope is negative part removed, and then from the last 10% cut, get the curve after removal.

[0050] S2: based on the curve after intercept processing, according to the arc length extraction data points, data compression;

[0051] Combined Figure 2 As shown in the specific process is as follows:

[0052] S201: calculate the arc length of all data points of the curve after intercept processing:

[0053]

[0054] Where, i represents the label of the data point in the curve after intercept processing, Δx i The horizontal coordinate increment at the i-th data point, that is, the strain increment, Δy i The vertical coordinate increment at the i-th data point, that is, the stress increment;

[0055] S202: determine the target number of data points n_obj after data compression;

[0056] S203: based on the target number of data points, calculate the theoretical average point interval arc length:

[0057]

[0058] Where, k is a coefficient, generally selected to be 1-3 to optimize the initial point and improve the operation speed.

[0059] S204: extract data points and obtain the total number of extracted data points, based on the total number and the target number of data points, calculate the residual;

[0060] Specifically, starting from the i-th data point, calculate the arc length, when its length first exceeds l test0 The point number j at this time is set, and the horizontal and vertical coordinates of the j-th point are taken out. The horizontal and vertical coordinates here refer to the two-dimensional coordinate system established when calculating the arc length. The arc length is zero, and j is assigned to i. Until i reaches the last point of all data, the arc length calculation is completed;

[0061] Get the total number of extracted data points n_test, and calculate the residual: resid1=n_test-n_obj

[0062] S205: based on the residual, judge whether it converges or not, if not, update the theoretical average point interval arc length by using nonlinear equation solution method (secant method, dichotomy), return to step S204 to execute again, until convergence, that is, the residual resid1≤convergence precision, the convergence precision is generally 2-10;

[0063] The data points in the calculation process are obtained when convergence is obtained.

[0064] As shown in Table 1 below, based on a linear elastic constitutive equation (σ=Eε el ) and a Voce-Hockett-Sherby plasticity constitutive equation From the 3400 data points of the original data, the optimization results when the number of different sampling points are selected by the above data point extraction method;

[0065] Table 1: Optimization results under different numbers of sampling points based on the Voce-Hockett-Sherby plasticity constitutive equation;

[0066] E σ0 Δσ b n Error Time to compute 200 points 180643 309 911 6.623 0.439 0.1598％ 100s 150 points 180052 324 892 6.847 0.449 0.1583％ 80s 100 points 180769 322 894 6.852 0.448 0.1587％ 49s 50 points 179784 325 894 6.731 0.446 0.1586％ 32s 30 points 180134 333 889 6.658 0.447 0.1600％ 19s

[0067] S3: Select a linear elastic model (σ=Eε el ) and a “Hollomon-Ludwik hardening model + additive viscous over-stress model” (σ=σ0+Hεn+kmεm) In the case of uniaxial tension, it can be proved that ), specify a certain set of constitutive parameter vectors p=(E, σ0, H, n, k, m) T , calculate the model true stress-true strain curve based on the sequence points of the true strain on the experimental true strain-true stress curve;

[0068] In this embodiment, the slope of the point near the true strain amount 0.002 on the true stress-true strain curve and the origin is taken as the initial value E ini of the elastic modulus of the linear elastic model, and the true stress value of the point is taken as the initial value σ0

[0069] According to the extracted data points, the true strain data is obtained, and based on the true strain data and the constitutive parameter vector, the nonlinear analysis is performed on each data point extracted on the experimental true stress-true strain curve, the proportion of elasticity and plasticity in the strain increment at each data point is obtained, and the true stress-true strain curve of the model is calculated;

[0070] As shown in FIG. 1, the specific process is as follows: Figure 3

[0071] S301: Decompose the total strain increment dε i+1 of any adjacent sequence number i and i+1 data points into elastic increment and plastic increment The specific representation is as follows:

[0072]

[0073] Wherein, ε i+1 and ε​i respectively represent the true strain of i+1 and i data points, i.e. the horizontal coordinate value of the corresponding point on the true stress-true strain curve of the experiment, where the horizontal coordinate refers to the coordinate system of the true stress-true strain curve of the experiment;

[0074] By corresponding time increment dt i+1 = t i+1 -t i , the corresponding total strain rate is decomposed into elastic strain rate and plastic strain rate The specific expression is as follows:

[0075]

[0076] S302: Express the stress at the corresponding time by the elastic strain increment and the selected elastic constitutive relation and the plastic strain increment and the selected plastic constitutive relation respectively, and construct a nonlinear equation;

[0077] The expression based on the elastic strain increment is as follows:

[0078]

[0079] where E represents the linear elastic modulus, represents the true stress calculated at the i th data point, represents the stress expressed by the elastic strain increment of the i+1 data point at the i+1 time.

[0080] The expression based on the plastic strain increment is as follows:

[0081]

[0082] where, represents the stress expressed by the plastic strain increment of the i+1 data point at the i+1 time, H represents the strain intensity coefficient, and n represents the strain hardening index, represents the plastic strain of the i data point, σ0 represents the theoretical yield strength of the material, m represents the strain rate sensitivity factor of the material, and k represents the strain rate intensity coefficient, represents the yield strength of the material at the current strain, represents the over-stress caused by the strain rate effect.

[0083] The expression of the nonlinear equation is as follows:

[0084]

[0085] S303: Calculate the elastic strain, plastic strain and true stress of the data points at each time;

[0086] The elastic strain is calculated as follows:

[0087]

[0088] wherein, and respectively represent the elastic strain at i and i+1 time;

[0089] The plastic strain is calculated as follows:

[0090]

[0091] wherein, and respectively represent the plastic strain at i and i+1 time;

[0092] The true stress calculation process of the model is as follows:

[0093] First, the true stress is calculated according to the following formula:

[0094]

[0095] determine whether is less than is calculated as follows:

[0096]

[0097] wherein, n represents the strain hardening index.

[0098] If it is less than, then is output as the true stress calculation result of the model;

[0099] Otherwise, according to the above nonlinear equation, solve and according to the following formula, re-update the calculation of true stress;

[0100]

[0101] S4: optimize the update of the constitutive parameter vector, and re-execute step S3 until the optimized condition parameter converges, to obtain the converged constitutive parameters.

[0102] The optimization of the update of the constitutive parameter vector is as follows:

[0103] S401: construct a reduced target equation:

[0104] S402: reduce the independent variable, reduce the range of the independent variable to [0, 1], and the reduced independent variable is represented as follows:

[0105]

[0106] S403: Based on the reduced independent variable, the true stress of the experiment and the true stress calculated in the current step S3, an optimization objective function is constructed, as follows:

[0107]

[0108] where ω i is the reduced independent variable, and is expressed as follows:

[0109]

[0110] The optimization objective function is a monotonically non-decreasing function that uses the cumulative deviation of the small polygon area on the true stress-true strain curve of each experiment in the numerical integration process from the small polygon area calculated at the corresponding position, considers the topographic information of the curve, and eliminates the influence of the data range of the horizontal and vertical coordinates of the test results of different samples on the calculation results in a reduced form, thereby achieving comprehensive fitting of different experiments under multiple strain rates and / or comprehensive fitting of repeated experiments under a single strain rate.

[0111] Table 2 below shows a comparison table of fitting results when the curve is cut off at different horizontal coordinates:

[0112] E σ0 Δσ b n Error Cut-off to 10% 179784 325 894 6.731 0.446 0.1586％ Cut-off to 9% 180134 333 889 6.658 0.447 0.1600％ Cut-off to 8% 179761 359 838 7.885 0.482 0.1550％ Cut-off to 7% 179527 376 808 8.766 0.505 0.1500％ Cut-off to 6% 178446 399 769 10.024 0.535 0.1534％ Cut-off to 5% 178553 403 755 10.682 0.546 0.1571％

[0113] When different horizontal coordinate ranges are selected, the error value after fitting does not change substantially, eliminating the error introduced by the difference in curves, and enabling the common optimization of multiple curves.

[0114] S404: Update the constitutive parameter vector through an optimization algorithm until the optimization objective function converges.

[0115] Taking the true stress-true strain curve of a certain material as an example;

[0116] Using the curve data, the constitutive parameters calculated based on existing methods (based on Voce-Hockett-Sherby plastic constitutive) are as follows:

[0117] E = 183100

[0118] The constitutive parameters calculated based on the present method (based on linear elastic constitutive and Voce-Hockett-Sherby plastic constitutive collaborative optimization) are as follows:

[0119] E = 215891

[0120] A finite element model is established, the boundary conditions consistent with the experiment are input, and the length change-simulation force information of the gauge section is output. The curve is plotted together with the experimental force for comparison. The accuracy of the present method is significantly higher than that of existing methods; and when At this time, the calculated The 1085 MPa obtained by the present method is very close to that obtained by the existing method, and it can be known that the present method is a reasonable improvement of the existing method.

[0121] The present application is not limited to the foregoing specific embodiments. The present application extends to any novel one, or any novel combination, of the features disclosed in this specification, and to any novel method or process steps disclosed, or any novel combination thereof.

Claims

1. A method for calculating elastoplastic constitutive parameters, characterized in that, include: S1: Conduct a uniaxial tensile test, obtain the true stress-true strain curve of the experiment, and perform truncation processing to obtain the truncation-processed curve. S2: Based on the truncated curve, data points are extracted according to the arc length, and data compression is performed. The specific process is as follows: S201: Calculate the arc length of the truncated curve; S202: Determine the number of target data points required after data compression; S203: Calculate the theoretical average arc length of the sampling interval based on the number of target data points; S204: Extract data points and obtain the total number of extracted data points. Calculate the residuals based on the total number of extracted data points and the target number of data points. S205: Determine whether convergence has occurred based on the residuals. If convergence has not occurred, update the average sampling interval arc length and return to step S204 to re-execute until convergence is achieved, and obtain the data points extracted at the time of convergence. S3: By selecting a good elastic and plastic model, setting the constitutive parameter vector, obtaining the true strain data of the experiment based on the extracted data points, and performing nonlinear analysis on each data point extracted from the true stress-true strain curve of the experiment based on the true strain data and constitutive parameter vector, obtaining the proportion of elasticity and plasticity in the strain increment at each data point, and calculating the true stress-true strain curve of the model. Nonlinear analysis, the specific process is as follows: S301: Decompose the total strain increment of any adjacent data points into elastic strain increment and plastic strain increment, and decompose the corresponding total strain rate into elastic strain rate and plastic strain rate through the corresponding time increment. S302: The stress at the corresponding time moment is expressed by elastic strain increment and selected elastic constitutive model and plastic strain increment and selected plastic constitutive model, respectively, and a nonlinear equation is constructed; S303: Calculate the elastic strain, plastic strain, and true stress corresponding to each data point at each time point; S4: Based on the calculated true stress-true strain curve of the model, optimize and update the constitutive parameter vector. Based on the updated constitutive parameter vector, return to step S3 to recalculate the true stress-true strain curve of the model until the optimized condition parameters converge, and obtain the iteratively optimized constitutive parameters.

2. The method for calculating elastoplastic constitutive parameters according to claim 1, characterized in that, Step S1, obtaining the true stress-true strain curve, is as follows: The engineering strain and true strain of the gauge length segment are obtained, and the true stress at each moment is calculated based on the cross-sectional area of ​​the gauge length segment of the original specimen to obtain the true stress-true strain curve.

3. The method for calculating elastoplastic constitutive parameters according to claim 1, characterized in that, The truncation process involves removing the portion of the true stress-true strain curve with a negative slope.

4. The method for calculating elastoplastic constitutive parameters according to claim 1, characterized in that, The residual is the difference between the total number of extracted data points and the target number of data points.

5. The method for calculating elastoplastic constitutive parameters according to claim 1, characterized in that, In step S1, the slope of the point on the true stress-true strain curve near the origin with true strain of 0.002 is taken as the initial value of the elastic modulus of the linear elastic model, and the true stress value at that point is taken as the initial value of the theoretical yield strength.

6. The method for calculating elastoplastic constitutive parameters according to claim 1, characterized in that, The optimization and update of the constitutive parameter vector is as follows: S401: Construct the reduced objective function; S402: Reduce the independent variable to [0, 1]; S403: Based on the reduced independent variables, the true stress of the experiment, and the true stress calculated in the current step S3, construct the optimization objective function; S404: Update the constitutive parameter vector through the optimization algorithm until the optimization objective function converges.

7. The method for calculating elastoplastic constitutive parameters according to claim 6, characterized in that, The optimization objective function is as follows: in, For data point sequence numbers, The total number of data points. To test true stress, Calculate the true stress for the model. To reduce the independent variable, it is represented as follows: in, This represents the true strain increment in the experiment.

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