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Pergamon J Mech Phys Solids Vol 42 No 11 pp 1653 1677 1994 Copyright 1994 Elsevier Science Ltd Printed in Great Britain All rights reserved 0022 5096 94 7 00 0 00 0022 5096 94 00052 2 EMERGENCE OF CRACKS BY MASS TRANSPORT IN ELASTIC CRYSTALS STRESSED AT HIGH TEMPERATURES B SUN Z SUO and A G EVANS Mechanical and Environmental Engineering Department Materials Department University of California Santa Barbara CA 93106 U S A Received 10 June 1994 in revisedform 11 July 1994 ABSTRACT Single crystals are used under high temperatures and high stresses in hostile environments usually gases A void produced in the fabrication process can change shape and volume as atoms migrate under various thermodynamic forces A small void under low stress remains rounded in shape but a large void under high stress evolves to a crack The material fractures catastrophically when the crack becomes sufficiently large In this article three kinetic processes are analyzed diffusion along the void surface diffusion in a low melting point second phase inside the void and surface reaction with the gases An approximate evolution path is simulated with the void evolving as a sequence of spheroids from a sphere to a pennyshaped crack The free energy is calculated as a functional of void shape from which the instability conditions are determined The evolution rate is calculated by using variational principles derived from the balance of the reduction in the free energy and the dissipation in the kinetic processes Crystalline anisotropy and surface heterogeneity can be readily incorporated in this energetic framework Comparisons are made with experimental strength data for sapphire fibers measured at various strain rates 1 INTRODUCTION Inorganic solids stressed at elevated temperatures often fail by creep deformation and rupture These processes involve diffusion along grain boundaries and dislocation cell boundaries motivated by applied stresses They have been comprehensively studied Chan and Page 1993

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