Impact loading induces damage as shock waves reflect off free surfaces, creating tension and initiating the nucleation, growth, and coalescence of a pore network. Typically, this is simulated by examining the behavior of a spherical shell under an isochoric approximation. This shell stems from a model of porous materials, simplifying the analysis by excluding potential pore interactions mediated by waves. While various inertial and visco-inertial models in this domain exist (Mercier Molinari 2001; Wilkerson 2014), uncertainties persist regarding the loading range and initial pore configuration leading to the dominance of inertial over viscous terms.
Behavioral patterns within the solution of the spherical shell growth equation are investigated using both analytical and numerical approach, employing a simplified viscoplastic model for the pore matrix. The adjustable parameters critical to damage evaluation encompass the initial porosity, loading deviation from the cavitation threshold, initial external radius of the hollow sphere (indicative of spatial pore density), and the loading rate. These parameters can be gauged against material properties that collectively define a viscous time scale, a typical velocity, and an ‘inertial’ length scale, contingent upon the viscoplastic parameters and material density.
The key factor determining the transition from a viscosity- to an inertia-dominated regime is the initial external radius of the hollow sphere relative to the inertial length scale, observed across a wide range of loading rates. Surprisingly, this transition exhibits minimal susceptibility to loading rate in typical dynamic conditions. Nevertheless, the experimental sensitivity to the loading rate strongly suggests the influence of another factor, potentially linked to the nucleation step process.