Comparative Analysis of 3 Constitutive Models for 93 Tungsten Alloy
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摘要: 在温度范围296~1 273 K、应变率范围0.000 5~6 000 s-1内, 对93钨合金材料(93%W-4.9%Ni-2.1%Fe)的力学行为进行了系统研究。实验结果表明：钨合金的塑性流动应力对温度和应变率非常敏感，它随温度的降低和应变率的增加而提高；真实塑性应变达到0.6时未出现剪切破坏。针对实验得到的应力-应变关系，分别进行了两种唯象本构模型(JC本构模型和KHL本构模型)和一种基于物理概念的本构模型(PB本构模型)的流动应力拟合。通过误差分析和应变率阶跃实验，对这3种本构模型的预测效果的精度进行了分析和评价。Abstract: In this research, we carried out a systematic study of the mechanical behaviors of the 93 tungsten alloy (93%W-4.9%Ni-2.1%Fe) with a temperature range of 296-1 273 K and a strain rate range of 0.000 5-6 000 s-1.The results demonstrate that the flow stress is highly dependent on the temperature and the strain rate:the flow stress increases with the decrease of temperature and the increase of strain rate, and the shear failure does not occur when the true plastic strain is up to 0.6.Then we introduced and established 3 constitutive models, including two phenomenological constitutive models, JC model and KHL model and one physically-based constitutive model, to fit the stress-strain relationship through a procedure of regression analysis and constrained optimization.Finally, we evaluated the fitted results of the 3 constitutive models through a fitting error analysis and a specific strain-rate jump experiment.
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Key words:
- tungsten alloy /
- plastic flow stress /
- constitutive model
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图 1 钨合金在不同应变率不同温度下的流动应力-塑性应变曲线
Figure 1. Flow stress-plastic strain curves of tungsten at different temperatures and strain rates
图 2 实验数据与JC模型拟合数据的对比(实心点代表实验数据，实线代表JC模型拟合数据)
Figure 2. Experimental data vs. fitted JC model description (The symbols represent the former while the solid lines represent the latter, with the same color for each temperature.)
图 3 实验数据与KHL模型拟合数据的对比(实心点代表实验数据，实线代表KHL模型拟合数据)
Figure 3. Experimental data vs. fitted KHL model description (The symbols represent the former while the solid lines represent the latter, with the same color for each temperature.)
图 4 实验数据与PB模型拟合数据的对比(实心点代表实验数据，实线代表PB模型拟合数据)
Figure 4. Experimental data vs. fitted PB model description (The symbols represent the former while the solid lines represent the latter, with the same color for each temperature.)
图 5 不同本构模型对实验数据的预测效果比较
Figure 5. Comparison of different constructive models in description of experimental data
图 6 不同本构模型对应变率跳跃试验的预测结果
Figure 6. Predictive results of different constructive models for the strain-rate jump test
图 7 不同本构模型对应变率跳跃试验的预测效果对比
Figure 7. Comparison of different constructive models in description of the strain-rate jump test
表 1 JC模型参数
Table 1. Determined values of JC model parameters
A/(MPa) B/(MPa) n C m 600.8 1 200 0.494 4 0.059 0 0.820 3 
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表 2 KHL模型参数
Table 2. Determined values of KHL model parameters
A/(MPa) B/(MPa) n1 n0 C m 264.5 523.4 2.296 0.299 6 0.113 4 1.063
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表 3 PB模型参数值
Table 3. Determined values of PB model parameters
a/(MPa) n σ0/(MPa) (k/G0)/(K-1) ${{{\dot \varepsilon }_0}}$/(s-1) p q 1 054.4 0.263 5 3 061.4 3.89×10-5 2×1010 0.5 1.5
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