Impact-Induced Phase Transformations in Elastic Solids: A Continuum Study Including Numerical Simulations for GeO₂

Author: Winfree, Nancy A.

Year: 1999

Degree: Dissertation (Ph.D.)

Advisors: Knowles, James K.; Ahrens, Thomas J.

Committee Members: Knowles, James K.; Ahrens, Thomas J.

Option: Applied Mechanics

DOI: 10.7907/4dhf-fj83

Abstract

This thesis applies recently developed continuum theories of diffusionless phase transformations in solids to the study of impact problems involving materials which can experience such phase changes. Our objective is to compare the theoretical predictions against certain experimental results.

In the experiments of interest, a face-to-face impact occurs between a disk of amorphous germanium dioxide and another material, either tungsten or an aluminum alloy. The GeO₂ is believed to transform to another phase if sufficient compressive stress is achieved.

We model these experiments using one-dimensional finite elasticity. Phase-changing materials are represented by non-convex potential energy functions. This can produce phase boundaries that propagate subsonically or supersonically with respect to the slower longitudinal wave speed of the two phases. When a subsonic phase boundary is possible, it is not uniquely determined by the fundamental field equations and jump conditions. Uniqueness is obtained by invoking a nucleation criterion to control the initiation of the new phase, and a kinetic relation to govern its evolution.

The experiments considered here are sufficiently long in duration (≈ 3 µs) that several reflections and wave interactions occur, and the analysis becomes analytically intractable. Accordingly, a finite-difference method of Godunov type is employed to analyze these experiments numerically. Methods of Godunov type treat adjoining discretized spatial elements as the two sides of a Riemann problem, which is typically solved approximately by linearizing around the initial conditions on each side. Fortuitously, all constitutive models employed in this thesis are such that the required Riemann problems can be solved exactly without too much effort.

Simulations utilizing the numerical method demonstrate that the impact response of a material is sensitive to the kinetic relation that enters the model. It appears the theory may offer a plausible description of the experiments, though the restrictions placed on the constitutive models herein seem too severe to provide a good quantitative match to the experimental results.

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