Spall strength

Spall strength ${\displaystyle (\sigma _{sp})}$ is defined as the maximum tensile stress a material can withstand under dynamic loading conditions before internal failure occurs due to spallation. Spallation is a high-rate fracture phenomenon in which a material experiences rapid void nucleation, growth, and coalescence due to the release of compressive shock waves and the subsequent formation of tensile waves. Unlike traditional tensile strength, spall strength is measured under conditions involving shock loading, making it highly strain rate dependent. The critical importance of spall strength spans across high-energy physics, aerospace engineering, and planetary science, where materials are frequently exposed to extreme dynamic stresses.

Mathematically, spall strength can be expressed using the relation:

${\displaystyle \sigma _{sp}={\frac {1}{2}}\rho _{0}c_{B}(\Delta u+\delta )}$

where ${\displaystyle \rho _{0}}$ is the material's initial density, ${\displaystyle c_{B}}$ is the bulk sound speed, ${\displaystyle \Delta u}$ is the pull-back velocity (the observed drop in free-surface velocity due to spallation), and ${\displaystyle \delta }$ is a correction factor accounting for material and wave attenuation effects.