On the theory and numerical modeling of spall fracture in pure liquids

TL;DR

This paper introduces a phase-flip model for simulating spall fracture in pure liquids, capturing rapid failure mechanisms and aligning well with molecular dynamics results, with practical formulas for spall strength estimation.

Contribution

It presents a thermodynamically consistent phase-flip model for liquid spallation, including new formulas for strain rate, fractured mass, and spall strength evaluation.

Findings

Model agrees with molecular dynamics simulations

Derived nonlinear formulas for spall strength and attenuation

Universal correction factor for spall pulse attenuation

Abstract

A novel phase-flip model is proposed for thermodynamically consistent and computationally efficient description of spallation and cavitation in pure liquids within the framework of ideal hydrodynamics. Aiming at ultra-fast dynamic loads, the spall failure of a liquid under tension is approximated as an instantaneous decomposition of metastable states upon reaching the spinodal stability limit of an appropriate two-phase liquid-gas equation of state. The spall energy dissipation occurs as entropy jumps in two types of discontinuous solutions, namely, in hypersonic spall fronts and in pull-back compression shocks. Practical application of the proposed model is illustrated with numerical simulations and a detailed analysis of a particular problem of symmetric plate impact. The numerical results are found to be in good agreement with the previously published molecular-dynamics simulations. Also, new approximate nonlinear formulae are derived for evaluation of the strain rate, fractured mass, and spall strength in terms of the observed variation of the free-surface velocity. The new formula for the spall strength clarifies complex interplay of the three first-order nonlinear correction terms and establishes a universal value of the correction factor for attenuation of the spall pulse, which in the limit of weak initial loads is independent of the equation of state.