Modeling of supersolidus liquid phase sintering: II. Densification
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I.
INTRODUCTION
THE rate of densiflcation during liquid phase sintering (LPS) is dependent on the dominant mass transport mechanism. [1,2] In developing analytical sintering models, one important treatment is to consider the theological behavior at the sintering temperature. As early as the 1940s, Frenkel [3j developed the first sintering theory, in which a slow deformation of particles was described as a viscous flow process under the influence of surface tension. Further viscosity-related sintering kinetics using inorganic glasses were studied by Kuczynski[4] and Exner and Petzow. [5] Recently, German[6] proposed a theory for supersolidus liquid phase sintering (SLPS), in which densification is through a viscous flow process involving the formation of liquid films along the interfaces in polycrystalline, prealloyed particles. With the increase in the amount of liquid, particles lose their rigidity and fragment into a viscous solid-liquid mixture. The capillary force coupled with the low strength of the viscous mixture leads to repacking and densification. The purpose of this work, along with a companion article, [7] is to analyze the rheological characteristics of a viscous mixture during SLPS. Dilatometric studies were used to monitor instantaneous densification. Analyses of the effect of rheology on shrinkage and shrinkage rate have been carried out based on model calculations of the capillary force and microstructural parameters. II.
BACKGROUND
The viscous flow of a solid-liquid mixture can be viewed as a grain-sliding process. Consider the individual grains in a two-particle model, as sketched in Figure 1. The relative sliding of the grains with respect to each other results in rearrangement of the particles, leading to densification. The shear rate ~, between two grains can be expressed as
YIXIONG LIU, Research Associate, RAJIV TANDON, Research Assistant, and RANDALL M. GERMAN, Brush Chair Professor in Materials, are with the Engineering Science and Mechanics Department, The Pennsylvania State University, University Park, PA, 16802-6809. Manuscript submitted October 10, 1994. METALLURGICALAND MATERIALSTRANSACTIONSA
Fig. 1--Schematic diagram of a two-particle polycrystalline prealloyed system showing partial coalescence. Also shown are grains surrounded by a liquid film. The presence of a shear stress facilitates relative grain motion leading to rearrangement via grain sliding.
V = 7 A
[11
where V is the relative grain sliding velocity and h is the mean liquid film thickness, i.e., the average value of liquid film thickness along the grain boundaries. The resistance of a fluid to shear is termed as the viscosity B and is defned by the ratio of the shear stress r to shear rate 5, as "r n
=
-
7
9
[2]
Combining Eqs. [1] and [2] gives the flow velocity T'A v =
m
[31
The capillary force between two particles can be converted to an equivalent external pressure, which provides a compressive stress normal to the neck section,t8,9]From simulation of the viscous sintering of two particles via the fini
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