泡沫铝材料动态本构参数的实验确定

丁圆圆; 杨黎明; 王礼立

doi:10.11883/1001-1455(2015)01-0001-08

泡沫铝材料动态本构参数的实验确定

doi: 10.11883/1001-1455(2015)01-0001-08

宁波大学力学与材料科学研究中心，浙江宁波 315211

基金项目: 国家自然科学基金项目(11032001);宁波大学王宽诚幸福基金项目

详细信息

作者简介:
丁圆圆(1987—), 男, 硕士研究生

通讯作者:
杨黎明, yangliming@nbu.edu.cn

中图分类号: O347
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- 被引次数: 1
出版历程
- 收稿日期: 2013-06-13
- 修回日期: 2013-08-20
- 刊出日期: 2015-01-25

Experimental determination of dynamic constitutive parameters for aluminum foams

Mechanics and Materials Science Research Center, Ningbo UniversityNingbo 315211, Zhejiang, China

摘要

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X_s/L₀和动态屈服应力Y_i、激波波速c_p、冲击初始应变ε_i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σ_i、初始打击速度v_i、泡沫铝杆原长L₀及激波在泡沫铝杆中消失长度X_s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。
- 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 disappearanceX_s' the yield stress Y, the shock velocity c_p as well as the impact boundary strain ε_i 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 σ_i, the impact velocity v_i, the undeformed length of the specimen X_s, 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.
- solid mechanics /
- dynamic mechanical characteristics /
- dynamic rigid-linear hardening plastic-rigid unloading(D-R-LHP-R) model /
- aluminum foam /
- shock wave

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图 1(a) D-R-LHP-R模型

Figure 1(a). D-R-LHP-R model

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图 1(b) Taylor实验模型

Figure 1(b). Taylor experimental device

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图 2 Taylor-Hopkinson实验装置

Figure 2. Taylor-Hopkinson experimental device

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图 3 泡沫铝中激波停止的位置

Figure 3. Stopped location of shock wave in the aluminum foams

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图 4 Taylor-Hopkinson实验测得的边界应力

Figure 4. Boundary stress measured by the Taylor-Hopkinson experiment

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图 5 Taylor-Hopkinson实验测得的ln(X_s/L₀) -v_i曲线

Figure 5. Relationship of ln(X_s/L₀) and v_i in the Taylor- Hopkinson experiment for the aluminum foams

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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

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图 7 泡沫铝Taylor-Hopkinson实验测得的ln(X_s/L₀)-σ_i曲线

Figure 7. Relationship of ln(X_s/L₀) and σ_i in the Taylor- Hopkinson experiment for the aluminum foams

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图 8 泡沫铝Taylor-Hopkinson实验测得的激波波速c_p随密度ρ₀的变化

Figure 8. Relation of shock wave velocity c_p and density ρ₀ in the Taylor-Hopkinson experiment for the aluminum foams

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图 9 泡沫铝Taylor-Hopkinson实验测得的ε_i -ln(X_s/L₀)曲线

Figure 9. Relation of initial strain ε_i and ln(X_s/L₀) in the Taylor-Hopkinson experiment for the aluminum foams

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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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图 11 通过D-R-LHP-R模型和Taylor-Hopkinson实验求得的边界应力对比

Figure 11. Comparisons of the boundary stress-time curves determined by D-R-LHP-R model and measured by the Taylor-Hopkinson experiment

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