A numerical analysis of intergranular penny-shaped microcrack shrinkage controlled by coupled surface and interface diff
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3/12/04
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A Numerical Analysis of Intergranular Penny-Shaped Microcrack Shrinkage Controlled by Coupled Surface and Interface Diffusion PEIZHEN HUANG and JUN SUN An axisymmetric finite-element method is developed and applied to simulate healing evolution of intergranular penny-shaped microcracks. In the finite-element method, grain-boundary diffusion and surface diffusion are coupled by the boundary conditions at the triple circle of the penny-shaped microcrack surface and the grain-boundary plane. Matter is transported to the triple circle by grainboundary diffusion and is taken away from the microcrack tips and deposited onto the microcrack surfaces by surface diffusion, resulting in shrinkage of the intergranular microcracks. The numerical simulations show that the evolution processes of intergranular microcracks are controlled by equilibrium dihedral angle (defined by surface and grain-boundary tensions), microcrack spacing, ratio of grain-boundary diffusion to surface diffusion, and the applied pressure.
I. INTRODUCTION
AT elevated temperatures, microcracks or creep cavities may shrink by diffusional processes to reduce the deleterious effects of cracks on strength, leading to partial or complete recovery of the strength of the damage materials.[1–6] Similar transport mechanisms also may control or affect the processes of sintering and diffusion bonding.[7–11] Thus, investigations into intergranular microcrack shrinkage may also contribute to an improved fundamental understanding of sintering and diffusion bonding. Under many practical circumstances,[12,13,14] two types of diffusion, surface diffusion and grain-boundary diffusion, are widely recognized as the microcrack or void shrinkage mechanism. Matter is transported to the junctions between grain boundaries and microcracks by grain-boundary diffusion, and is taken away from the microcrack tips and deposited onto microcrack surfaces by surface diffusion, resulting in shrinkage of the microcracks. In the last two decades, following the classic work of Herring,[15] many efforts have been made to solve the diffusion equation for the void surface and to determine the evolution of the void shape during shrinkage[10,16,17] or growth[18,19,20] by finite-difference numerical techniques. Recently, a two-dimensional finite-element formulation for large change of shape due to surface diffusion was carried out by Sun and Suo.[21] We applied the method to develop a corresponding finite-element method for predicting the two-dimensional evolution behaviors of void and microcrack on the grain boundary by coupling surface diffusion and grain-boundary diffusion at the triple point of the microcrack surface and the grain boundary.[22,23] PEIZHEN HUANG, Associate Professor, formerly Post-doctoral fellow in the State Key Laboratory for Mechanical Behavior of Materials of XJTU, is now with the Department of Structure Engineering & Mechanics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, People’s Republ
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