Simulation of cavitation processes in superplastic deformation
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NTRODUCTION
CONCURRENT cavitation is commonly observed during superplastic deformation in metallic and ceramic materials. Cavities nucleate usually at grain boundaries, due to a stress concentration. When the concentrated stress at grain boundaries cannot be relaxed sufficiently by diffusion or by dislocation motion, it is often relaxed by cavity formation. In superplastic deformation, cavity nuclei grow by diffusion for small sizes and by grain-boundary sliding, namely, plastic deformation in the matrix, for large sizes.[1,2] The final process of cavitation is the coalescence between them. The coalescence accelerates the growth rate noticeably and leads to premature failure. In particular, the coalescence in a direction normal to the stress axis limits tensile ductility significantly. Such cavitation processes—nucleation, growth, and coalescence—have been studied extensively by experimental and theoretical methods.[1–15] Most work, however, was concentrated on a particular mechanism in the total cavitation process. Although several models have been proposed for each cavitation process,[2–7] little work has considered the total process. The total process was first considered in a simulation by Nicolaou and Semiatin.[14] They regarded the three cavitation processes as a continuous one activated during the entire deformation process. In order to take the respective cavitation processes into account simultaneously, a simulation method would be the best. The simulation by Nicolaou and Semiatin,[14] however, seems to have some problems in the modeling. They neglected the increment of strain due to cavitation and the effect of cavitation on the Poisson’s ratio, which decreases with increasing cavity volume fraction. In the present study, we formulate the cavity growth rate by incorporating the BYUNG-NAM KIM, Senior Researcher, and KEIJIRO HIRAGA, Director, are with Fine-Grained Refractory Materials Group, National Institute for Materials Science, Ibaraki 305-0047, Japan. Contact e-mail: Kim. [email protected]. Manuscript submitted October 8, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
effect of the Poisson’s ratio and develop a model for simulating cavitation behavior, including nucleation, growth, and coalescence processes. II. MODELING CAVITATION The modeling for simulating cavitation behavior in three dimensions is described in this section. We assume that the virgin material is homogeneous and isotropic and has no pre-existent cavities. The external loading condition is uniaxial tension. A. Cavity Nucleation When the microscopic tensile stress ( ⬘) acts on a grain boundary, Raj and Ashby[3] calculated the cavity nucleation rate (˙ , the number of cavities generated per unit time and area) using a classical nucleation theory. According to their analysis, ˙ is very low at low ⬘ values, whereas it increases rapidly with increasing ⬘ values. The rapid increase in ˙ is dominated by an exponential factor, indicating that this factor is the most essential part of the model. In the present modeling, we focus
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