简论金属材料JC本构模型的精确性

周琳; 王子豪; 文鹤鸣

doi:10.11858/gywlxb.20190721

On the Accuracy of the Johnson-Cook Constitutive Model for Metals

doi: 10.11858/gywlxb.20190721

CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, China

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Author Bio:
ZHOU Lin (1988－), female, doctoral student, major in impact dynamics. E-mail: zlxzh@mail.ustc.edu.cn

Corresponding author: WEN Heming (1965－), male, Ph.D, professor, major in impact dynamics. E-mail: hmwen@ustc.edu.cn

摘要

摘要: 通过比较JC模型预测结果与6种金属（2024-T351铝合金、6061-T6铝合金、OFHC无氧铜、4340高强钢、Ti-6Al-4V钛合金和Q235软钢）在不同应变率及温度下的实验数据，对JC本构模型的精确性进行了关键评估。为了进一步评估其精确性，采用JC本构模型和失效准则对平头弹正撞2024-T351铝合金靶板进行数值模拟，并与实验结果比较。结果表明：JC本构模型只适用于中、低应变率和温度下的Mises材料，对非Mises材料该模型预测的剪切应力-应变曲线和失效与实验结果吻合较差；同时，JC本构模型的精度随应变率和温度的提高而降低，特别是在高应变率条件下利用实验得到的动态增强因子进行相应数值模拟时，所得计算结果与弹道穿透实验结果不一致，说明其表达式（即准静态应力-应变关系×动态增强因子）是不恰当的。
- JC本构模型 /
- 金属 /
- 应力-应变曲线 /
- 应变率效应 /
- 温度效应 /
- 失效准则
Abstract: A critical assessment is made herein on the accuracy of the Johnson-Cook (JC) constitutive model by comparing the model predictions with the test data for 2024-T351 aluminum alloy, 6061-T6 aluminum alloy, OFHC copper, 4340 steel, Ti-6Al-4V alloys and Q235 mild steel. These materials are selected because their test data are more complete in terms of true stress-true strain relationships, strain rate effects, temperature effects and failure. To further assess its accuracy numerical results for the ballistic perforation of plates made of 2024-T351 aluminum alloy using the JC constitutive model are also presented and compared with corresponding test data. It transpires that the JC constitutive model is applicable to Mises materials at quasi-static to intermediate strain rates and low to moderate temperature. It also transpires that for non-Mises materials the agreement between the model predictions and the test results are poor in terms of shear stress-shear strain curve and fracture strain. Furthermore, the accuracy of the JC model decreases with increasing strain rate, temperature and, above all, it fails to produce consistent results at high strain rates when the experimentally obtained dynamic increase factors (DIF) are employed in the calculations implying the form of the model’s equation (namely, quasi-static stress-strain curve multiplied by DIF) may be inadequate at least for the scenarios where high strain rates are involved.
- Johnson-Cook constitutive model /
- metal /
- stress-strain curve /
- strain rate effect /
- temperature effect /
- fracture criterion

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Figure 1. Comparison of the JC model with the true stress-true strain curves obtained from tension and torsion tests

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Figure 2. Comparison of the JC model with the test data for 2024-T351 aluminum alloy

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Figure 7. Comparison of the JC model with the test data for Q235 mild steel

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Figure 3. Comparison of the JC model with the test data for 6061-T6 aluminum alloy

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Figure 4. Comparison of the JC model with the test data for OFHC copper

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Figure 5. Comparison of the JC model with the test data for 4340 steel

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Figure 6. Comparison of the JC model with the test data for Ti-6Al-4V alloys

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Figure 8. Comparison of DIF vs. strain rate at different plastic strains at room temperature

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Figure 9. Comparison of the JC model predictions with the tensile test data for 2024-T351 aluminum alloy

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Figure 14. Comparison of the JC model predictions with the compression test data for Q235 mild steel

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Figure 10. Comparison of the JC model predictions with the tensile test data for 6061-T6 aluminum alloy

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Figure 11. Comparison of the JC model predictions with the compression test data for OFHC copper

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Figure 12. Comparison of the JC model predictions with the tensile test data for 4340 steel

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Figure 13. Comparison of the JC model predictions with the compression test data for Ti-6Al-4V

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Figure 15. Dependence of the equivalent strain to fracture on the stress triaxiality on some metal

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Figure 16. Finite element model used in the numerical simulations

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Figure 17. Comparison of the JC constitutive model with the test data for 2024-T351 aluminum alloy

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Figure 18. Comparison of the numerically predicted residual velocities with the test results for the perforation of the 4 mm-thick 2024-T351 aluminum alloy plates struck normally by the 5.5 mm-diameter flat-ended projectile^[21]

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Table 1. Values of constants in the Johnson-Cook constitutive model and Johnson-Cook fracture criterion

Materials	A/MPa	B/MPa	n	C	m	${\dot \varepsilon _0}/{\rm s}^{-1}$	T_m/K	D₁	D₂	D₃
2024-T351 Al^[3–4]	340	510	0.510	0.002	1.890	9.0×10^–5	775	–0.070	1.020	–1.620
6061-T6 Al^[5–8]	265	170	0.314	0.007	1.316	1.0×10^–3	855	–0.070	0.810	–1.240
OFHC copper^{[1, 9–13]}	50	340	0.425	0.011	0.883	1.0×10^–5	1356	0.540	4.890	–3.030
4340 steel^[1–2]	792	846	0.582	0.009	1.030	2.0×10^–3	1793	0.050	3.440	–2.120
Ti-6Al-4V alloy^[14–17]	938	947	0.636	0.013	0.779	1.0×10^–5	1933	0.200	3.590	–3.800
Q235 mild steel^[18–20]	293	543	0.489	0.045	0.942	2.1×10^–3	1795	0.070	6.116	–3.445

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Table 2. Values of various parameters for 2024-T351 aluminum alloy

$\rho $/(kg·m^–3)	E/GPa	v	$\chi $	C_p/(J·kg^–1·K^–1)	C₀/ (m·s^–1)	s₁	${\varGamma _0}$
2700	72	0.3	0.9	875	5328	1.338	2

JC Model	A/MPa	B/MPa	n	C	m	${\dot \varepsilon _0}$/s^–1	T_m/K
This paper	340	510	0.510	0.002	1.890	9.0×10^–5	775
Ref.[25]	352	440	0.42	0.0083	1.7	3.3×10^–4	775

JC Model	D₁	D₂	D₃	D₄	D₅
This paper	–0.070	1.020	–1.620	0.011	0
Ref.[25]	0.13	0.13	–1.5	0.011	0

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