An analysis of the effect of cavity nucleation rate and cavity coalescence on the tensile behavior of superplastic mater
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RODUCTION
SUPERPLASTIC metals are an important class of material for metal-forming processes, because of their high ductilities.[1,2] However, many superplastic alloys exhibit cavitation during deformation, resulting in either premature failure and/or degradation of the mechanical properties of the final product.[3,4] Thus, a significant amount of experimental and theoretical research has been conducted to develop an understanding of cavitation and its influence on deformation processes. The objective of the present effort was to develop a framework for describing the coupled phenomena which occur on both a microscopic scale (i.e., cavity nucleation, growth, and coalescence) as well as on a macroscopic scale (i.e., macroscopic instability and flow localization/necking). By this means, a model was formulated that enables the prediction of quantities which describe microscopic and macroscopic tensile behavior, such as cavity-size distribution and tensile ductility. II. BACKGROUND The formulation of the present model relies heavily on previous work by a number of researchers. Because of its
P.D. NICOLAOU, formerly Research Scientist, UES Inc., Dayton, OH 45432-1894, is R & D Scientist, Silver and Baryte Ores Mining Co. S.A., 10672, Athens, Greece. S.L. SEMIATIN, Senior Scientist, is with Materials Processing/Processing Science, Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/MLLM, Wright-Patterson Air Force Base, OH 45433-7817. A.K. GHOSH, Professor, is with the Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109. Manuscript submitted February 22, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
importance, these previous concepts and approaches are summarized here as a prelude to the description of the integrating framework developed and applied in the present work. This background information is broken into three sections, which describe cavitation mechanisms and phenomenology, microscopic models of tensile ductility, and macroscopic models of tensile ductility. A. Cavitation Mechanisms/Phenomenology Cavitation occurs via three often overlapping stages during tensile deformation: cavity nucleation, growth of individual cavities, and cavity coalescence. 1. Cavity nucleation Several possible cavity nucleation mechanisms have been established, including (1) intragranular slip intersections with nondeformable second-phase particles and grain boundaries, (2) sliding of grains along grain boundaries, which is not fully accommodated by diffusional transport into those regions, and (3) vacancy condensation on grain boundaries.[5] The cavity nucleation rate (N ) is defined as the number of cavities nucleated per unit area and unit strain. Experimental observations have shown that N may either be constant or decrease or increase with strain; however, such strain dependencies are usually not strong. Thus, for the purpose of this study, N was assumed to have a constant value. Measurements have shown than N can be bracketed between 104 and 106 cavities/mm3/un
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