Strain rate dependence of spall strength for solid and molten lead and tin

Abstract

Dynamic tensile (spall) fracture of pure Pb and Sn in solid and molten states is investigated by MD simulations. The influence of unwettable inclusions on the spall strength is revealed. Mechanical model of fracture is fitted to MD data at the strain rate $10^{\mathrm {9}}$$\hbox {s}^{\mathrm {-1}}$ and used for calculation of the rate dependencies of spall strength in the range from $10^{\mathrm {4}}$$\hbox {s}^{\mathrm {-1}}$ to $10^{\mathrm {9}}$$\hbox {s}^{\mathrm {-1}}$ in comparison with the experimental data. The model takes into account homogeneous nucleation of pores, activation of pores on unwettable inclusions or other heterogeneities and change in pore size, which is viscous for melt and elastic-plastic for solid. In the case of pure uniform material, the homogeneous nucleation gives a slow decrease in spall strength with decreasing strain rate; the calculated values significantly exceed experimental results for moderate strain rates of $10^{\mathrm {4}}$–$10^{\mathrm {5}}$$\hbox {s}^{\mathrm {-1}}$. Accounting of unwettable inclusions removes this contradiction and provides correspondence to experimental data. A power-law size distribution of inclusions gives in the case of melt the power-law dependence of spall strength on strain rate that coincides with the experimental data for molten Sn. In the case of solid metal, the spall strength at moderate strain rates is determined by the yield strength. Therefore, the initial power law decrease in the spall strength is replaced by almost constant level at moderate strain rates. This behavior corresponds to the existing experimental data for solid Pb. Transfer to the homogeneous nucleation mode takes place for solid and molten metals at ultra-high strain rates, when the concentration of pores activated on the existing heterogeneities is not enough for the stress relaxation.