CN108169019B - Identification method of quasi-static plastic compressive stress strain parameter - Google Patents

Identification method of quasi-static plastic compressive stress strain parameter Download PDF

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CN108169019B
CN108169019B CN201711434396.0A CN201711434396A CN108169019B CN 108169019 B CN108169019 B CN 108169019B CN 201711434396 A CN201711434396 A CN 201711434396A CN 108169019 B CN108169019 B CN 108169019B
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黄树海
陈强
赵祖德
胡传凯
夏祥生
舒大禹
柴舒心
黄志伟
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Southwest Institute of Technology and Engineering of China South Industries Group
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Abstract

The invention discloses a method for identifying a quasi-static plastic compressive stress strain parameter, which comprises the following steps: (1) and carrying out a compression test on the blank under the conditions of quasi-static plastic compression deformation with different deformation temperatures and strain speeds to obtain data of testing stress and testing strain and a structure of a deformation state. (2) Respectively establishing a logarithmic function of stress-strain under the condition of isothermal constant strain rate
Figure 657650DEST_PATH_IMAGE002
The method is used for fitting the relation between the test stress and the test strain and obtaining peak strain, peak stress, steady-state strain and steady-state stress according to the curve of the strain hardening rate and the stress. (3) And on the basis of the logarithmic function of the stress-strain obtained by optimization, solving the minimum value of the optimized objective function to obtain the dynamic recrystallization critical strain and the dynamic recrystallization critical stress. The method can be applied to the quasi-static thermal simulation compression behavior research of various metal materials such as pure copper, magnesium, titanium, aluminum, steel and the like.

Description

Identification method of quasi-static plastic compressive stress strain parameter
Technical Field
The invention relates to a method for identifying a quasi-static plastic compressive stress strain parameter.
Background
A lot of researches are carried out at home and abroad on the quasi-static thermal simulation compression deformation of the metal material, and the data of the actual stress-strain curve of the metal material at different temperatures and different strain rates and the rules of work hardening, dynamic recovery and dynamic recrystallization of the metal material are analyzed, wherein the critical stress sigma of the dynamic recrystallization iscDynamic recrystallization critical strain epsiloncPeak stress σpPeak strain epsilonpSteady state stress σssSteady state strain epsilonssSaturation stress σsatSaturation strain εsatKey parameters of equal stress strain parametric material analysis. The research on the thermal simulation compression test at home and abroad can be basically divided into three aspects: firstly, analyzing the critical stress sigma of dynamic recrystallization according to the actual stress-strain curve datacDynamic recrystallization critical strain epsiloncPeak stress σpPeak strain epsilonpSteady state stress σssSteady state strain epsilonssSaturation stress σsatSaturation strain εsatThe parameters (such as figure 1) of equal stress strain are further analyzed for laws such as dynamic recrystallization rate proportion, dynamic recovery rate proportion and the like, but because the data fluctuation of an actual stress-strain curve is large, the error is large when the parameters such as critical strain and the like are calculated; secondly, according to the actual stress-strain curve data, the influence of strain, temperature and strain rate on the stress is simply considered, and a fitting function of the stress-strain curve is established, but the dynamic recrystallization critical stress sigma cannot be effectively calculated by adopting the functioncDynamic recrystallization critical strain epsiloncPeak stress σpPeak strain epsilonpSteady state stress σssSteady state strain epsilonssSaturation stress σsatSaturation strain εsatAn iso-stress strain parameter; thirdly, the two methods have good application effect in the thermal simulation test analysis of some materials, but the same method is adopted to replace a material for research, the result is not satisfactory, and meanwhile, the error shadow of the material test is causedAnd the stress strain parameters are difficult to effectively identify due to noise.
Disclosure of Invention
The invention provides a method for identifying a quasi-static plastic compressive stress strain parameter.
In order to realize the purpose, the following technical scheme is adopted:
a method for identifying a quasi-static plastic compressive stress strain parameter is characterized by comprising the following steps:
(1) and (3) carrying out a compression test on the blank under the condition of quasi-static plastic compression deformation with different deformation temperatures and strain speeds to obtain data of the test stress sigma (MPa) and the test strain epsilon and a deformation state tissue.
(2) Under the condition of isothermal constant strain rate, respectively establishing logarithmic functions of stress sigma (MPa) -strain epsilon, namely
Figure BDA0001525553020000021
Is used to fit the test stress sigma (MPa) to the test strain epsilon. Wherein ln σ -is a logarithmic value of σ (MPa), a10A fixed constant, a11-a fixed constant, g (epsilon) -a non-linear function related to the accuracy of the curve. The first partial derivative of the stress sigma (MPa) to the strain epsilon obtains the function of the strain hardening rate theta (MPa) and the strain epsilon, namely
Figure BDA0001525553020000022
Where f' (ε) is the first order partial derivative of f (ε) versus strain ε. Drawing a curve of the strain hardening rate theta (MPa) and the stress sigma (MPa) by taking theta (MPa) as a y axis and sigma (MPa) as an x axis, wherein when the theta (MPa) value is equal to 0 for the first time, the corresponding stress value is the peak stress sigma (MPa)p(MPa); when the value of theta (MPa) is equal to 0 for the second time, the corresponding stress value is the steady state stress sigmass(MPa). Will peak stress sigmap(MPa), Steady State stress σss(MPa) are respectively substituted into
Figure BDA0001525553020000023
By a function, i.e. the corresponding peak strain ε can be determinedpSteady state strain epsilonss。
(3) Under the condition of isothermal constant strain rate, the strain rate is optimized
Figure BDA0001525553020000031
On the basis of functions, solving
Figure BDA0001525553020000032
Optimizing the minimum value of the objective function to obtain the critical strain epsilon of dynamic recrystallizationcThen e is addedcSubstituting into f (epsilon) function to obtain dynamic recrystallization critical stress sigmac(MPa). Where f ' (ε) is the first order partial derivative of f (ε) for strain ε, f ' (ε) is the second order partial derivative of f (ε) for strain ε, and f ' (ε) is the third order partial derivative of f (ε) for strain ε.
(4) Under the condition of isothermal constant strain rate to
Figure BDA0001525553020000033
The function is based on
Figure BDA0001525553020000034
For optimizing the solution target, the obtained dynamic recrystallization critical strain epsiloncSubstituted to solve the saturation stress sigmasat(MPa). Based on the H (epsilon) function, the saturation stress sigmasat(MPa) substitution, using ε0≤ε≤εcAnd fitting and solving corresponding stress and strain data to obtain a dynamic parameter r value. Wherein epsilon0Is the initial yield strain; sigma0(MPa) is the initial yield stress; h (epsilon)c) Is H (. epsilon.) at a critical strain (. epsilon.)cLogarithmic stress (MPa); h' (ε)c) Is a first order partial derivative function of H (epsilon) to strain epsilon and at critical strain epsiloncLogarithmic stress (MPa); h' (εc) Is a second order partial derivative function of H (epsilon) to strain epsilon and at critical strain epsiloncLogarithmic stress (MPa).
(5) By the same method, different temperatures T (K) and different strains are respectively calculated
Rate of speed
Figure BDA0001525553020000035
(s-1) Critical stress σ of dynamic recrystallization under the conditionsc(MPa), dynamic recrystallization critical strain εcPeak stress σp(MPa), peak strain εpSteady state stress σss(MPa), steady state strain εssSaturation stress σsat(MPa), saturation strain εsatAnd (4) equal stress strain parameters.
To ensure the accuracy of the fit of the f (epsilon) function,
g(ε)＝a0+a1·ε+a2·lnε+a3·ε·lnε+a4·ε2·lnε+a5·ε·(lnε)2+a6·ε2+a7·(lnε)2+a8·ε3+a9·(lnε)3wherein a is0～a9Constants are fixed for the parameters.
The invention considers the curve change relation of stress-strain and the internal relation of the related parameters of dynamic recovery and dynamic recrystallization, and theoretically establishes the identification method of the two relation unified parameters. The method can be applied to the quasi-static thermal simulation compression behavior research of various metal materials such as pure copper, magnesium, titanium, aluminum, steel and the like.
Drawings
FIG. 1 illustrates a conventional stress parameter identification method;
FIG. 2 comparison of fitted stress to measured stress;
FIG. 3 is a graph of θ versus σ;
FIG. 4 comparison of dynamic recovery stress with actual test stress;
fig. 5 accounts for the calculated stress of strain hardening and softening versus the actual test stress.
Detailed Description
The present invention is further illustrated by the following examples.
Example 1
Pure copper at 973K and strain rate of 0.001s-1、0.01s-1、0.1s-1、1s-1By plastic compression deformation under the conditions ofAnalyzing the actual stress-strain curve as a function
Figure BDA0001525553020000041
Wherein g (epsilon) ═ a0+a1·ε+a2·lnε+a3·ε·lnε+a4·ε2·lnε+a5·ε·(lnε)2+a6·ε2+a7·(lnε)2+a8·ε3+a9·(lnε)3Fitting the data of the test stress sigma (MPa) and the test strain epsilon to obtain relevant parameters shown in the table 1, wherein the fitting data is superposed with the actual data and is in good agreement (shown in figure 2).
TABLE 1 functional parameters obtained by fitting
Parameter(s) Rate 0.001s-1 Rate 0.01s-1 Rate 0.1s-1 Rate 1s-1
a0 -21.5339 2.168704 4.894689 -8.365287525
a1 -2.15795 -8.661 4.877212 -33.09897556
a2 -1.60582 -3.96626 -1.04577 11.95766033
a3 -13.5023 -25.0041 -0.22359 -23.39395923
a4 -41.8773 44.19009 8.930568 -82.15664264
a5 24.99818 -7.62626 -1.11898 27.35370292
a6 20.08262 45.16822 0.012868 14.73895482
a7 0.90138 -1.0589 -0.36437 5.831534023
a8 6.979891 -31.4562 -3.93913 33.34818856
a9 0.079134 -0.05345 -0.03666 0.642977417
a10 321.0155 861.3232 -5956.44 -4122.842017
a11 348.2782 862.4106 -5921.65 -4098.927887
By using
Figure BDA0001525553020000051
Wherein
Figure BDA0001525553020000052
The data of the strain epsilon is substituted into the above formula and calculatedUntil the strain hardening rate theta is reached, and theta (MPa) is taken as a y axis, and sigma (MPa) is taken as an x axis, a graph of the strain hardening rate theta (MPa) and stress sigma (MPa) is drawn as shown in figure 3, when the value of theta (MPa) is equal to 0 for the first time, the corresponding stress value is the peak stress sigma (MPa)p(MPa); when the value of theta (MPa) is equal to 0 for the second time, the corresponding stress value is the steady state stress sigmass(MPa). From FIG. 3, it can be found that 0.001s is a strain rate-1、0.01s-1、0.1s-1The curve of (sigma) (MPa) -theta (MPa) can easily determine the peak stress sigmap(MPa) and Steady State stress σss(MPa) according to
Figure BDA0001525553020000053
Function, i.e. the peak strain ε can be determinedpSteady state strain epsilonss(ii) a Strain rate 1s-1The σ (MPa) - θ (MPa) curve of (A) has no point of intersection with the zero line because at the strain rate of 1s-1Under the conditions of (1), there is no significant dynamic recrystallization, and therefore its peak stress σp(MPa) and Steady State stress σssThe stress corresponding to the minimum value of the curve is taken in (MPa). The solved relevant parameters are shown in table 2.
Table 2 solved peak stress-strain and steady state stress-strain parameters
Peak strain epsilonp 0.15 0.2 0.45 0.5
Peak stress sigmap/MPa 34.92 47 64.859 85.294
Steady state strain epsilonss 0.6 0.7 0.5 0.55
Stress σ in steady statess/MPa 26.94 40.191 63.748 84.745
Obtained by optimization
Figure BDA0001525553020000061
On the basis of a function of
Figure BDA0001525553020000062
The minimum value of the function is the optimization target and is input at epsilon0≤ε≤εpData corresponding to epsilon, ln sigma in range, where epsilon0Is the initial yield strain,. epsilonpSolving by adopting a nonlinear optimization method for peak value strain to obtain the dynamic recrystallization critical strain epsiloncThen, the σ ═ exp (f (ε) is reusedc) ) function to determine the dynamic recrystallization critical stress sigmac(MPa). The solved relevant parameters are shown in table 3.
Table 3 solved dynamic recrystallization critical stress strain parameters
Critical strain epsilonc 0.05 0.1043 0.131627 0.246389857
Critical stress sigmac/MPa 27.22351 41.12364 58.4571 79.89196924
To be provided with
Figure BDA0001525553020000063
The function is based on
Figure BDA0001525553020000064
For optimizing the solution target, the obtained dynamic recrystallization critical strain epsiloncSubstituted to solve the saturation stress sigmasat(MPa). Based on the H (epsilon) function, the saturation stress sigmasat(MPa) substitution, using ε0≤ε≤εcAnd fitting and solving corresponding stress and strain data to obtain a dynamic parameter r value. Wherein epsilon0At initial yield strain, σ0(MPa) is the initial yield stress. The relevant parameters are shown in table 4.
Table 4 saturation stress and r values obtained by solving
Initial strain epsilon0 0.035 0.035 0.035 0.035
Initial stress sigma0/MPa 25.8 32.2 42.4 46
Saturation stress sigmasat/MPa 39.86402 49.80309 65.65132 85.294
r 7.96734 8.469085 10.48994 7.467198018
On the basis of this, use
Figure BDA0001525553020000071
Calculating to obtain dynamic recovery stress sigmarec(MPa) and establishes σrecA plot of (MPa) - ε (as in FIG. 4); then use
Figure BDA0001525553020000072
Calculation of dynamic recrystallization stress σdrx(MPa), wherein the values of k and n are shown in Table 5, and the comprehensive dynamic recovery stress sigmarec(MPa), dynamic recrystallization stress σdrx(MPa), the secondary strain hardening stress of the original actual test and the like, and the comparison between the calculated stress of strain hardening and softening and the actual test stress (as shown in figure 5), it can be found that the stress-strain parameter calculated by the method of the invention has very high precision.
The k and n values obtained by solving in Table 5
Parameter(s) Rate 0.001s-1 Rate 0.01s-1 Rate 0.1s-1
Value of n 2.499405 3.135853 2.949087
k value 0.196604 0.235749 2.274279

Claims (2)

1. A method for identifying a quasi-static plastic compressive stress strain parameter is characterized by comprising the following steps:
(1) performing a compression test on the blank under the condition of quasi-static plastic compression deformation with different deformation temperatures and strain speeds to obtain data of test stress sigma and test strain epsilon and a deformation state organization;
(2) under the condition of isothermal constant strain rate, respectively establishing a logarithmic function of stress sigma-strain epsilon, namely
Figure FDA0001525553010000011
Fitting the relation between the test stress and the test strain epsilon; where ln σ is the logarithmic value of σ, a10A fixed constant, a11-a fixed constant, g (epsilon) -a non-linear function related to the accuracy of the curve;
the first partial derivative of the stress sigma to the strain epsilon obtains the function of the strain hardening rate theta and the strain epsilon, namely
Figure FDA0001525553010000012
Drawing a curve of the strain hardening rate theta and the stress sigma by taking theta as a y axis and sigma as an x axis, wherein when the theta value is equal to 0 for the first time, the corresponding stress value is the peak stress sigmap(ii) a When the value of theta is equal to 0 for the second time, the corresponding stress value is the steady state stress sigmass；
Will peak stress sigmapSteady state stress σssRespectively substitute for
Figure FDA0001525553010000013
By a function, i.e. the corresponding peak strain ε can be determinedpSteady state strain epsilonss；
(3) Under the condition of isothermal constant strain rate, the strain rate is optimized
Figure FDA0001525553010000014
On the basis of functions, solving
Figure FDA0001525553010000015
Optimizing the minimum value of the objective function to obtain the critical strain epsilon of dynamic recrystallizationcThen e is addedcSubstituting into f (epsilon) function to obtain dynamic recrystallization critical stress sigmac；
(4) Under the condition of isothermal constant strain rate to
Figure FDA0001525553010000021
The function is based on
Figure FDA0001525553010000022
For optimizing the solution target, the obtained dynamic recrystallization critical strain epsiloncSubstituted to solve the saturation stress sigmasat(ii) a Based on the H (epsilon) function, the saturation stress sigmasatSubstitution, application of epsilon0≤ε≤εcFitting and solving corresponding stress and strain data to obtain a dynamic parameter r value; wherein epsilon0Is the initial yield strain; sigma0Is the initial yield stress; h (epsilon)c) Is H (. epsilon.) at a critical strain (. epsilon.)cThe logarithmic stress of (d); h' (ε)c) Is a first order partial derivative function of H (epsilon) to strain epsilon and at critical strain epsiloncThe logarithmic stress of (d); h' (εc) Is a second order partial derivative function of H (epsilon) to strain epsilon and at critical strain epsiloncThe logarithmic stress of (d);
(5) by the same method, different temperatures T (K) and different strain rates are obtained by calculation
Figure FDA0001525553010000023
Critical stress σ of dynamic recrystallization under the conditionscDynamic recrystallization critical strain epsiloncPeak stress σpPeak strain epsilonpSteady state stress σssSteady state strain epsilonssSaturation stress σsatSaturation strain εsatA parameter.
2. The method for identifying a quasi-static plastic compressive stress-strain parameter of claim 1, wherein: to ensure the accuracy of the fit of the f (epsilon) function,
g(ε)＝a0+a1·ε+a2·lnε+a3·ε·lnε+a4·ε2·lnε+a5·ε·(lnε)2+a6·ε2+a7·(lnε)2+a8·ε3+a9·(lnε)3，
wherein a is0～a9Constants are fixed for the parameters.
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