A Constitutive Relation of Aluminum Foam Coupled with Temperature and Strain Rate
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摘要: 根据分离式Hopkinson压杆实验以及准静态实验得到的泡沫铝材料在不同温度以及不同应变率下的应力-应变曲线，分析了泡沫铝本构方程中温度效应与应变率效应之间的耦合关系，即温度越高，泡沫铝的应变率效应越显著。基于Sherwood和Frost提出的泡沫材料本构关系框架，对常温下的应变率敏感系数进行了温度项修正，修正后的本构方程在高温高应变率下与实验结果具有较好的一致性。最终得到泡沫铝在一定密度范围内包含温度项、应变率项较为完备的本构方程。Abstract: The results of split Hopkinson pressure bar (SHPB) and quasi-static compression tests for aluminum foam at different strain rates and temperatures are used to explore its constitutive relation.It is revealed that there is a coupling of the temperature effect and the strain rate effect, namely the higher the temperature is, the more significant the strain rate effect of the aluminum foam is.In the framework of Sherwood and Frost constitutive relation, with appropriate correction of the strain rate sensitivity coefficient considering the coupling effects between temperature and strain rate, a constitutive equation of aluminum foam is proposed.The results show that the revised constitutive equation can fit the experimental results well in the density, temperature and strain rate ranges considered.
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Key words:
- temperature effect /
- strain rate effect /
- aluminum foam /
- constitutive relation
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图 1 常温下泡沫铝的应力-应变拟合结果与实验结果的比较
Figure 1. Comparison between calculated and experimental stress-strain curves for aluminum foam at room temperature
图 2 高应变率下泡沫铝的应力-应变拟合结果与实验结果的比较
Figure 2. Comparison between calculated and experimental stress-strain curves for aluminum foam at high strain rate
图 3 高温下未修正模型得到的泡沫铝应力-应变拟合曲线与实验曲线的比较
Figure 3. Comparison between calculated and experimental stress-strain curves for aluminum foam using the unmodified model at high temperature
图 4 高温下由修正后的本构方程得到的泡沫铝应力-应变拟合曲线与实验曲线的比较
Figure 4. Comparison between calculated and experimental stress-strain curves for aluminum foam using the modified constitutive equation at high temperature
图 5 泡沫铝的坍塌应力随温度的变化
Figure 5. Variation of collapse stress with temperature for aluminum foam
图 6 应变率敏感系数随温度的变化
Figure 6. Variation of strain rate sensitivity coefficient with temperature
图 7 不同密度的泡沫铝应力-应变实验曲线与拟合曲线
Figure 7. Comparison between calculated and experimental stress-strain curves for aluminum foam with different density
表 1 形状函数的拟合参数值
Table 1. Fitting parameters of shape function
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 261 -6 490 7.3×104 -4.55×105 1.73×106 -4.2×106 6.54×106 -6.31×106 3.45×106 -8.16×105 
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表 2 本构方程参数
Table 2. Parameters of constitutive equation
m A B C0 k 1.084 2.546 0.269 5.13×10-3 3.948
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