A numerical study of cavity growth controlled by surface diffusion
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The growth of grain boundary cavities is examined using a finite difference numerical scheme. The mechanism studied is that proposed by Chuang and Rice in which atoms are driven by gradients in curvature along the surface of the cavity to the grain boundary. Atomic transport in the grain boundary is assumed to be fast compared to that along the cavity surface. In the present paper the shape evolution of an initially lenticular cavity is followed in detail and in this respect the treatment differs from the Chuang-Rice approach in which a steady-state crack-like configuration is assumed. This allows us to examine the effects of capillarity and transients on the growth process. For an isolated cavity on an infinite boundary, it is found that the Chuang-Rice treatment accurately describes cavity growth once the steady state is achieved. The effect of capillarity is manifested by an incubation period during which a 'nose' protrudes from the tip of the cavity. It is the nose of the cavity that behaves like the Chuang-Rice steady-state crack. An array of cavities is also studied to determine the effects of cavity interaction on the growth process. The results of this investigation compare favorably with rupture data for silver containing implanted grain boundary water vapor bubbles. 1979.
