A mathematical model for gravity-induced distortion during liquid-phase sintering
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I.
INTRODUCTION
LIQUID-PHASE sintering is used in the fabrication of high-performance materials ranging from dental amalgams to cemented carbides. The presence of a liquid phase enhances the sintering rate. 1~1Initially, the mixed powders are heated to a temperature at which a liquid forms. The liquid gives rapid densification as a consequence of the capillary force exerted by the wetting liquid on the solid particles.t21 The elimination of porosity occurs as the system minimizes its surface energy. During rearrangement, the compact responds as a viscous mass to the capillary action, with a continuously decreasing densification rate. The same attributes that allow rapid densification also contribute to weakness of the compact during sintering; thus, there are problems with compact slumping and distortion during liquidphase sintering. Large dimensional changes take place during densification, often as large as 20 pct linear shrinkage. The large shrinkage coupled with the low viscosity make it impractical to provide sintering support for complex shapes. Tungsten heavy alloys are susceptible to gravitational forces during liquid-phase sintering. They have a large density difference between the liquid and solid phases, which leads to solid settling, giving nonuniform sintered properties.13 71 Large dimensional changes have been associated with gravitational flow during the liquid-phase sintering of heavy alloys, resulting in microstructural variations with position within a compact. 18j Simultaneous with the microstructural changes during sintering, gravity acts to cause distortion. Figure 1 is a photograph of a tungsten heavy-alloy "top hat" sample. Note the nonuniform variation in compact diameter with height due to an apparent self-compression and viscous flow during sintering. This article focuses on the latter aspect of liquid-phase sintering. R. RAMAN, Staff Member, is with Process Modelling & Design, BDM Federal Corp., Arlington, VA 22203-1618. RANDALL M. GERMAN, Brush Chair Professor in Materials, is with the Pennsylvania State University, University Park, PA, 16802-6809. Manuscript submitted September 14, 1993.
METALLURGICAL AND MATERIALS TRANSACTIONS A
II.
SINTERING
Top hat samples having a composition of 88 wt pct W, 8.4 wt pct Ni, and 3.6 wt pct Fe were subjected to sintering at various times to measure the time-dependent distortion. An illustration of the sample geometry is given in Figure 2. The phase equilibrium temperature for liquid formation in this system is 1705 K. However, the liquid-formation temperature was observed to be 1738 K when the components were mixed as elemental powders, which are not initially in phase equilibrium. The observed liquid-formation temperature was used in selecting the sintering cycle. The heating rate was fixed at 10 K / m i n until 1673 K and 5 K / m i n to 1773 K. During heating, the samples were held at 1073 K for one hour to reduce any remaining oxide. The sintering temperature was maintained at 1773 --- 5 K. The samples were cooled at 3 K / m i n to 1700 K to m
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