Experimental determination of dynamic constitutive parameters for aluminum foams

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.