Experimental determination of dynamic constitutive parameters for aluminum foams
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摘要: 基于泡沫材料的动态刚性-线性硬化塑性-刚性卸载(D-R-LHP-R)模型，结合连续性方程，动量守恒方程及刚体的运动方程，得到了激波在泡沫材料中的量纲一消失位置Xs/L0和动态屈服应力Yi、激波波速cp、冲击初始应变εi之间的如下关系式: $\frac{X_{\mathrm{s}}}{L_{0}}=\exp \left(-\frac{\rho_{0} c_{\mathrm{p}} v_{\mathrm{i}}}{Y}\right)=\exp \left(1-\frac{\sigma_{\mathrm{i}}}{Y}\right)=\exp \left(-\frac{\rho_{0} c_{\mathrm{p}}^{2} \varepsilon_{\mathrm{i}}}{Y}\right)$ 采用Taylor-Hopkinson装置进行实验，当直接测得泡沫铝试样密度ρ0、边界初始应力σi、初始打击速度vi、泡沫铝杆原长L0及激波在泡沫铝杆中消失长度Xs后，利用方程式(a)可反演求得D-R-LHP-R模型下的泡沫铝动态应力应变曲线。最后通过与泡沫铝准静态实验数据对比，表明该泡沫铝是应变率敏感性材料。
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关键词:
- 固体力学 /
- 动态力学特性 /
- 动态刚性-线性硬化塑性-刚性卸载(D-R-LHP-R)模型 /
- 泡沫铝 /
- 激波
Abstract: Based on the dynamic Rigid-Linear Hardening Plastic-Rigid Unloading (D-R-LHP-R) model of foam materials and starting from the displacement continuity equation, the momentum conservation equation and the motion equation of rigid part, the relation between the critical position for shock disappearanceXs' the yield stress Y, the shock velocity cp as well as the impact boundary strain εi can be determined as follows: $\frac{X_{\mathrm{s}}}{L_{0}}=\exp \left(-\frac{\rho_{0} c_{\mathrm{p}} v_{\mathrm{i}}}{Y}\right)=\exp \left(1-\frac{\sigma_{\mathrm{i}}}{Y}\right)=\exp \left(-\frac{\rho_{0} c_{\mathrm{p}}^{2} \varepsilon_{\mathrm{i}}}{Y}\right)$ Among the parameters in the above equation, the specimen density ρ0, the boundary stress σi, the impact velocity vi, the undeformed length of the specimen Xs, and the original length of the specimen L0, can be easily measured from the Taylor cylinder-Hopkinson bar impact experiments. Therefore, the constitutive parameters strees and strain of the R-LHP-R model can be finally reversely determined for the tested aluminum foam by using the above experimental parameters and Eq(a). The comparison of stress-strain between the quasi-static compressive curve and the R-LHP-R model indicates the strain rate sensitivity of the tested aluminum foams. -
图 4 Taylor-Hopkinson实验测得的边界应力
Figure 4. Boundary stress measured by the Taylor-Hopkinson experiment
图 5 Taylor-Hopkinson实验测得的ln(Xs/L0) -vi曲线
Figure 5. Relationship of ln(Xs/L0) and vi in the Taylor- Hopkinson experiment for the aluminum foams
图 6 泡沫铝动态屈服应力随密度的变化
Figure 6. Experimental dynamic yield stress vs. density of aluminum foams
图 7 泡沫铝Taylor-Hopkinson实验测得的ln(Xs/L0)-σi曲线
Figure 7. Relationship of ln(Xs/L0) and σi in the Taylor- Hopkinson experiment for the aluminum foams
图 8 泡沫铝Taylor-Hopkinson实验测得的激波波速cp随密度ρ0的变化
Figure 8. Relation of shock wave velocity cp and density ρ0 in the Taylor-Hopkinson experiment for the aluminum foams
图 9 泡沫铝Taylor-Hopkinson实验测得的εi -ln(Xs/L0)曲线
Figure 9. Relation of initial strain εi and ln(Xs/L0) in the Taylor-Hopkinson experiment for the aluminum foams
图 10 不同密度范围泡沫铝材料的D-R-PLH-L模型和准静态实验对比
Figure 10. Comparisons of stress between D-R-LHP-R model and quasi-static experiment for the aluminum foams with different density
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