Master Sintering Curve for Densification Derived from a Constitutive Equation with Consideration of Grain Growth: Applic
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THE concept of a master sintering curve (MSC) was initially developed by Su and Johnson[1] as a practical way to describe the densification of a compact along any given complex sintering cycle. The original derivation was carried out using the combined-stage sintering model,[2] which simulates solid state sintering by grain boundary or bulk diffusion from the initial to the final stage. The terms related to the microstructure were separated from the temperature-dependent terms on opposite sides of the sintering-rate equation. In such a way, both sides can be integrated independently along any heating schedule if the following conditions are fulfilled: (a) the microstructural evolution (both grain size and geometry) only depends on density for any given powder and green body; and (b) one diffusion mechanism dominates in the sintering process; i.e., the activation energy (Q) for sintering does not change during the thermal cycle. The obtained MSC can only be
S.J. PARK, Associate Research Professor, is with the Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39759. Contact e-mail: [email protected] S.H. CHUNG, Senior Researcher, is with Hyundai Steel Co., Songak-Myeon, Dangjin-Gun, Chungnam, 343-711, South Korea. J.M. MARTI´N, Staff Researcher, is with the Centro de Estudios e Investigaciones TTcnicas de Guipn˜zcoa (CEIT) and TECNUN, 20018 San SebastiOˆn, Spain. JOHN L. JOHNSON, Research Director, is with ATI Alldyne, Huntsville, AL 35806. RANDALL M. GERMAN, Associate Dean of Engineering, Professor of Mechanical Engineering, is with College of Engineering, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-1326. Manuscript submitted February 4, 2008. Article published online October 9, 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
applied to powder compacts made from the same powder and by the same green-body process. Condition (a) is usually satisfied, as the same basic atomic transport mechanics are often responsible for both densification and microstructural evolution; two exceptions are when significant surface diffusion or exaggerated grain growth occurs.[1] Recently, the MSC concept has been expanded to track other common situations found during sintering. First, several mechanisms often operate simultaneously over a given temperature interval; if the proportional contribution of each basic sintering mechanism does not vary with temperature, then the MSC can still be applied.[3] The resultant constant activation energy will be just a weighted average of the values corresponding to the multiple mechanisms. This is usually called the apparent activation energy for sintering. Second, when the apparent activation energy is not constant, i.e., the basic mechanisms change with temperature, the sintering cycle can be split into consecutive stages that are integrated separately, each one with its own constant apparent activation energy. An example is solid state sintering followed by liquid phase sintering when the temperature is increased.[3] Finally, the MSC ha
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