Densification and shape distortion in liquid-phase sintering
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I. INTRODUCTION
FROM a technological viewpoint, dimensional control is one of the most important practical problems in liquidphase sintering. Shrinkage gradients in a sintered powder compact are traditionally attributed to gradients in green density introduced during pressing.[1] Reduced shrinkage during sintering at the bottom of the compacts is attributed to the friction between the compacts and the substrate material.[2,3] Although relatively weak and often ignored, gravity provides another fundamental stress that acts during sintering. Gravity is not isotropic, so it induces anisotropic shrinkage during sintering, especially in liquid-phase sintering.[4,5,6] A geometry described as an “elephant foot” shape was observed for gravity-induced distorted W-Ni-Fe powder compacts. This is due to viscous flow enhanced by gravity, producing a progressive stress at the bottom that exceeds the system strength. Densification and shape distortion during liquid-phase sintering depend on the driving forces and the resistance to viscous deformation.[3] However, how densification and shape distortion occur and the exact conditions that lead to viscous flow are not well understood. In this article, the driving forces and the resistance to viscous flow accompanying densification and shape distortion during liquid-phase sintering are discussed, particularly for wetting systems with a high solid solubility in the liquid. The driving force for densification is the capillary force. The driving force for shape distortion could be surface tension and gravitational force. Resistance to viscous flow is provided by the solid bonds, which can induce rigidity if there is sufficient grain connectivity. Because the capillary force decreases with densification and the driving force for shape distortion is extremely small, densification and shape distortion depend on loss of compact rigidity. A principle for predicting densification and shape distortion is outlined.
JIANXIN LIU, Research Associate, and RANDALL M. GERMAN, Brush Chair Professor in Materials, are with the P/M Lab, Department of Engineering, Science and Mechanics, The Pennsylvania State University, University Park, PA 16802-6809. Manuscript submitted April 13, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
II. BACKGROUND A. Solid-Bonding Structure The main contribution to the rigidity of a solid-liquid mixture is solid bonding between particles and grains, depending on if the solid contacts form a percolation structure. The initial mechanism of sintering densification and distortion in liquid-phase sintering is rearrangement via viscous flow. During liquid-phase sintering, if a high level of solid-grain bonding exists, then the system is rigid and no viscous flow occurs. Alternatively, if no bonding occurs, the loss of rigidity results in compact-shape loss along with easy densification. The percolation thresholds of three-dimensional networks have been calculated using Monte Carlo simulations or other techniques.[7,8] According to percolation theory, 1.5 average contacts per g
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