Critical behavior in spallation failure of metals

Abstract

Using molecular dynamics with an accurate many-body potential, we studied the rapid expansion of Ta metal following the high compression (50 to 100 GPa) induced by high velocity $(2\mathrm{}$ to $4$ km/s) impact. We find that catastrophic failure in this system coincides with a critical behavior characterized by a void distribution of the form $N\left(v\right)\mathrm{}\propto V^{-\tau },$ with $\tau \sim \mathrm{2.2.}$ This corresponds to a threshold in which percolation of the voids results in tensile failure. We define an order parameter $(\phi ,$ the ratio of the volume of the largest void to the total void volume) which changes rapidly from ∼0 to ∼1 when the metal fails and scales with as $\phi \propto (\rho -{\rho }_c{)}^{\beta }$ with exponent $\beta \sim 0.4,$ where $\rho$ is the total void fraction. We found similar behavior for FCC Ni suggesting that this critical behavior is a universal characteristic for failure of solids in rapid expansion.