Modeling grain growth dependence on the liquid content in liquid-phase-sintered materials
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I.
INTRODUCTION
LIQUID-phase sintering (LPS) is a process for the densification of particulate materials such as tungsten carbide, silicon nitride, bronze, low alloy steels, stainless steels, tool steels, and various cermets.[1] The liquid provides a capillary force and high transport rate that give rapid densification. However, the high diffusivity leads to progressive microstructural coarsening. Several authors have considered the problem of solid-liquid coarsening.[2] Most of the models applied to liquid-phase-sintered structures are extrapolations of classic Ostwald ripening concepts developed for dilute solid contents. A dispersed grain structure allows use of a mean field concept for calculation of the coarsening rate. This has some substantiation in that the grain size typically increases with the cube root of isothermal hold time. However, the growth or contraction of a specific grain depends on the local environment, as established by various observations.[3,4,5] A recent model by DeHoff[6] has incorporated this effect, but for noncontacting grains. Semisolid systems, ranging from LPS materials to metalceramic composites, evidence coarsening behavior very different from the assumptions in Ostwald ripening models. These materials have intertwined liquid and solid phases that coarsen at elevated temperatures.[7,8,9] Consequently, there are many deficiencies with extending Ostwald ripening theories to semisolid alloys, as summarized in Table I. Liquid phase sintering is limited by Earth’s gravity, because there are few systems where the solid and liquid densities are equal. Mechanical stability dictates multiple grain contacts to avoid collapse of the solid grain structure under the action of gravity.[10,11] At these contacts, the grains form bonds. Once a steady state is achieved, the bond size depends RANDALL M. GERMAN, Brush Chair Professor of Materials, is with the Department of Engineering Science and Mechanics, P/M Lab, The Pennsylvania State University, University Park, PA 16802-6809. EUGENE A. OLEVSKY, Assistant Professor, is with the Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182-1323. Manuscript submitted March 19, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
only on the grain size and the dihedral angle, while the number of bonds per grain depends largely on the liquid content. Net shaping via LPS is most successful with less than 40 vol pct liquid and an intermediate dihedral angle (15 to 60 deg), giving sufficient rigidity to resist distortion. At high temperatures, the skeletal structure is not so strong that it inhibits densification. Consequently, the final microstructure consists of intertwined and connected solid and liquid networks. Grain agglomeration is a natural consequence of neck growth between contacting grains.[12,13] Thus, dilute solid systems exhibit solid grain agglomeration when processed in microgravity or neutral buoyancy conditions.[14–20] Further, LPS systems have varying dihedral angles (depending on the grain misorientations), a
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