Steady state vacancy concentration around a plastic crack
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INTRODUCTION
THE importance
of understanding the high temperature crack growth behavior has been well recognized in recent research efforts. ~-s Undoubtedly, several complex crack tip processes that can take place simultaneously at high temperature contribute to the difficulty in determining the precise changes in a crack or a void. 6 In particular, the grain boundaries in a polycrystalline material or interfaces in twophase materials alter the crack behavior at high temperature to a large extent] On the other hand, in a ductile material the plastic deformation associated with the crack, blunting the tip is also responsible for the complexity of the high temperature crack growth behavior/Several transport processes including surface and bulk diffusion, condensation and evaporation, and grain boundary diffusion play a significant role in determining the high temperature crack phenomena. 6 In order to delineate the effect of the individual factors, it is necessary to consider several idealized situations in which the influence of each parameter can be determined. It has been first of all recognized that a spatially varying elastic field gives rise to stress assisted diffusion of any species such as vacancies, interstitials, or solute atoms. 9 The solution to the diffusion equation provides the concentration of each species, thereby enabling the flux to be determined. In particular, the steady state concentration of vacancies around an edge dislocation 1~has been solved and its climb rate obtained. Similarly, the solution to the diffusion equation has been used to determine the steady state vacancy concentration around an elastic crack tip. In turn, the diffusional flux of vacancies to the crack leading to either growth or closure has also been evaluated/ However, it should be emphasized that in the diffusional climb movement of an edge dislocation and the growth of an elastic crack, the presence of other structural features has not been taken into account. On the other hand, experimentally it has been found that high temperature fracture results from intergranular crack growth behavior wherein grain boundary diffusion of vacancies to the crack tip is responsible for higher crack growth rates. In an attempt to explain these experimental observations, a simplified high temperature crack K. JAGANNADHAM, formerly Assistant Professor, Department of Engineering Science and Mechanics, Tennessee Technological University, Cookeville, TN 38501, is now Associate Metallurgist, Metallurgy and Ceramics Division, Ames Laboratory, Ames, IA 50010. Manuscript submitted September 10, 1982. METALLURGICALTRANSACTIONS A
growth model has been developed s wherein the effect of plastic zone at the crack tip has also been incorporated in a semi-quantitative manner. Now, the steady state vacancy concentration around a plastic crack tip will be analyzed taking into account only the bulk diffusion of vacancies to the crack tip. The presence of all other structural features will also be neglected so that a quantitative evaluation of the ef
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