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Instabilities of nucleation and growth of a phase change defect
Department of Mechanical and Aerospace Engineering
University of California San Diego
La Jolla, CA 92093-0411
Abstract
A defect of phase change in density and moduli modeled as a self-similarly expanding Eshelby ellipsoidal inclusion can nucleate and grow under a critical loading. The ellipsoid possesses the “lacuna” property with the particle velocity vanishing in the interior domain, which allows the constant stress Eshelby property and the inclusion to grow as a whole. The energetics for nucleation and growth are derived from the energy-momentum tensor and first principles. The solution obtains the flow of energies across a moving phase boundary at the balancing of which (which expresses the vanishing of the M integral) the interface presents no obstacle, and, at that critical loading, an arbitrarily small phase change defect nucleates and grows at constant potential energy. By breaking the symmetry it expands as a flattened Eshelby ellipsoidal inclusion, which minimizes the losses to move the phase boundary, and the critical pressure is obtained for nucleation and growth of an inhomogeneous inclusion under high pressure. The solution explains the generation of a shear seismic source with Double Couple radiation in deep earthquakes and the generation of failure waves with a zone of micro-fractures (in tension) under compressive loading in lima glass. The methodology has wider applications to a range of physical phenomena, such as amorphization defects and defects in alloys, planetary impacts, etc.