Quantitative characterization of microstructures of liquid-phase-sintered two-phase materials
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27/4/04
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Quantitative Characterization of Microstructures of Liquid-Phase-Sintered Two-Phase Materials JIANXIN LIU and ZHIGANG ZAK FANG Many powder metallurgy materials have a common microstructure character—spherical or equiaxed particles embedded in a matrix. This article presents an analytical approach that establishes relationships between a broad range of three-dimensional (3-D) microstructure parameters and two-dimensional (2-D) measurements for these materials. Specifically, the grain coordination number, measured dihedral angle, connectivity, and contiguity are directly related to the solid volume fraction, interfacial energies (equilibrium dihedral angle), and grain size. The volume fraction, the equilibrium dihedral angle, and the grain sizes are treated as independent variables. Other microstructural parameters can be expressed as functions of these independent variables. Results show that when the mean grain size is smaller than a critical value, these microstructure parameters change rapidly as the grain grows during processing at high temperatures. When the mean grain size is larger than a critical value, these microstructure measurements approach corresponding stable values.
I.
INTRODUCTION
MANY powder metallurgy materials share a common microstructure character—spherical or equiaxed particles embedded in a matrix. These materials include liquid-phasesintered tungsten heavy alloys,[1] liquid-phase-sintered cemented tungsten carbide, copper alloy infiltrated stainless steels,[2] and other artificially designed and fabricated composites.[3] Figure 1 is a typical representation of their microstructures. Important parameters that describe the microstructure of these two-phase materials include volume fractions, particle or grain sizes, mean free path (MFP), dihedral angles, contiguity, connectivity, and grain coordination number. Accurate measurement and characterization of these parameters are important for understanding densification, microstructure evolution, and mechanical properties. Many of these microstructural parameters are threedimensional (3-D) features that can not be measured directly, for example, the dihedral angle. Conventionally, measurements made on two-dimensional (2-D) cross sections are used to approximate or represent 3-D features. This approach is often inadequate. Another approach is to establish analytical relationships between 2-D and 3-D parameters and to compute 3-D parameters from 2-D measurements. Although the latter approach is preferred over the former one, the validity of existing methods for converting 2-D measurements to 3-D features is often limited and has narrow restrictive assumptions. The objective of the present work is to establish broadly applicable theoretical relationships between microstructural parameters involving both 2-D and 3-D quantities. Specifically, the grain coordination number, dihedral angle, connectivity, and contiguity are directly related to measurable independent variables including the solid volume fraction, the equilibri
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