Texture clustering and long-range disorientation representation methods: application to 6022 aluminum sheet
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I. INTRODUCTION
THE materials science of polycrystalline materials begins with the premise that quantitative representations of microstructure determine material properties and performance. There exists a rich complexity of microstructures in these materials, and progress in relating a microstructure to properties depends upon understanding those aspects of microstructure that are pertinent to the properties of interest. In the case of linear properties, such as elastic stiffness, thermal and electrical conductivity, thermal expansion, etc., rigorous bounds on properties are known to have first-order dependence upon phase and phase-orientation distributions by volume fraction. Refined bounds on linear properties are known to depend upon higher-order details of microstructure, such as the spatial placement of phase and orientation, in addition to volume fractions.[1] Two-point phase and orientation correlation functions (OCFs) are known to carry firstorder information about spatial placement. From two-point correlation functions, substantially narrowed bounds on linear properties have been recovered.[1,2] Volume-fraction distributions and the two-point correlation functions are readily recovered from experimental characterization of crystallographic orientation (texture) by the new method known as orientation imaging microscopy (OIM)[3,4] or by automated electron backscattered diffraction (EBSD). In an OIM system, the sample is tilted by 70 deg with respect to the incident electron beam. For each pixel in an OIM map, the electron beam in spot mode generates an electron backscattered Kikuchi pattern. By automatically analyzing the Kikuchi pattern obtained from all the pixels in the inspection window, a map with detailed local orientation information is generated. Only single-phase polycrystals are of interest in this
P.S. LEE, Senior Applications Development Engineer, is with KLATencor, San Jose, CA 95134. H.R. PIEHLER and A.D. ROLLETT, Professors, are with the Materials Science and Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213. Contact e-mail: rollett@andrew. cmu.edu B.L. ADAMS, Professor, is with the Mechanical Engineering Department, Brigham Young University, Provo, UT 84602. Manuscript submitted January 2, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS A
article, and, thus, we refer to the two-point orientation correlation functions simply as OCFs. In a broad context, OCFs have been studied since 1987.[5,6,7] The motivation for this article is a study of the development of surface roughness during plastic deformation of aluminum sheet, specifically, age-hardenable alloys based on the Al-Mg-Si system that fall under the 6xxx series of commercial alloys.[8] In this study, an attempt was made to relate the spatial characteristics of the surface roughening to the microstructure (including texture) of the material. Spectral analysis of the surface-height data consistently shows maxima at wavelengths that are several multiples of the grain size. This suggested that the spatial organization
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