Strain and the quantitative characterization of anisotropic microstructures
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INTRODUCTION
A quantitative description of microstructure is essential to the development of analytical expressions relating structure to processing and properties of materials. Relationships describing the anisotropy of material properties that depend on microstructure must include analytical descriptions of the anisotropic nature of microstructure. In a polycrystalline metal or alloy, the most significant morphological microstructural features are the networks of internal interfaces separating the phases and individual grains within phases. Global volume averages, such as the commonly employed ‘‘grain size,’’ do not contain sufficient information to account for the spatial heterogeneity and morphological anisotropy of microstructural features. Complete characterization of these interfaces requires information not only on the spatial orientation and distribution of the boundaries but also on the difference between the crystallographic orientations of grains or phases separated by the boundaries, perhaps including the sense of the vector normal to the interface.[1] Suitable stereological measurements on plane sections having various orientations relative to a reference coordinate system determine the former. The latter requires additional information on the orientation of grains in the section, typically obtained from a diffraction technique, such as orientation imaging microscopy. For the application illustrated in the present work, the misorientation across boundaries is not considered, and a simpler representation suffices. In such cases, an orientation distribution function (ODF)* of internal surface normals *In this paper, the ODF refers to the distribution density of a particular feature of the microstructure, in this case the orientation of normals to internal surfaces, and is not to be confused with the crystallite ODF employed to describe the spatial orientation of crystallographic directions in textured materials.
CRAIG S. HARTLEY, formerly Program Manager, Air Force Office of Scientific Research, Arlington, VA 22203, is Consultant, El Arroyo Enterprises, Sedona, AZ 86336. Manuscript submitted February 21, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS A
provides a simple and convenient method of describing the spatial anisotropy of the network of internal interfaces. The present work illustrates this approach, but does not specifically consider the spatial heterogeneity of the interface orientation distribution. In an attempt to relate a measure of the distortion of the grain boundary network to the bulk deformation of aluminum in uniaxial tension, Rachinger[2] defined the average strain in grains in terms of the ratio of the mean linear intercept with grain boundaries in the tensile direction before and after deformation. Later, Hensler and Gifkins[3] employed a similar approach to measure strain in the creep of commercial Mg alloys. Both approaches relied on observations on a single plane of observation and did not attempt to account for the three-dimensional character of the grain boundary network. Flinn
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