Development of orientation coherence in plane-strain deformation
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INTRODUCTION
TRADITIONALLY, the measures of microstructure in polycrystalline solids, at the scale of average grain size, are separated into two distinct categories--morphological and orientational. For example, grain size and grain shape belong to the first category, while the crystallite orientation distribution function (ODF) [~,2'3] falls into the second category. Each category has been found to he important in the prediction of polycrystalline properties. For example, Hall t4/ and Petch [5~ showed that the yield strength of polycrystalline a-iron is inversely proportional to the square root of the average grain diameter. On the other hand, the incorporation of the ODF in models predicting elastic tr] and plastic ETI anisotropy of polycrystals was also fairly successful. There now exists considerable evidence, as was pointed out by Adams et al. ,[8] that these two measures must ultimately be combined in order to improve the modeling of polycrystalline behavior. As a recent example, Molinari e t a / . [91 showed that improvements in the prediction of texture development over the 1938 Taylor model are realized when approximate grain shape and neighboringgrain viscoplastic interactions are taken into consideration. It is clear from the definition of the ODF (and the way it is measured) that it contains no information concerning the spatial correlation between grains with different orientations. The stationary two-point orientation coherence function (OCF), which gives the probability density for the simultaneous occurrence of crystallites of specified orientations separated by a vector, was proposed tS) to serve this need. A series-expansion representation of the two-point OCF was proposed by Morris TONG-TSUNG WANG was a Doctoral Student, Department of Mechanical Engineering, Brigham Young University, at the time of this research. BRENT L. ADAMS, Associate Professor, is with the Department of Mechanical Engineering, Yale University, New Haven, CT 06520-2157. PETER R. MORRIS, formerly Visiting Scholar, Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, is retired. Manuscript submitted April 10, 1989. METALLURGICAL TRANSACTIONS A
et a/.; tl~ all boundary conditions (see Eqs. [2] and [3] in Section II) with which the two-point OCF is associated are satisfied explicitly by this rigorous representation. In a companion paper, [11] we describe, in extensive detail, the microstructure of 1100 aluminum ingot. This material was shown to exhibit random texture and random nearest-neighbor orientation coherence structure, a state which provides an ideal reference for the study of structure evolution during subsequent deformation. In the present study, the effect of plane-strain deformation on the crystallite orientation coherence relationship is investigated using the conditional two-point OCF. The explicit r-dependence of the OCF (see Section II) is important in this study. A sample from the ingot is deformed in a channel die to a strain corresponding to 20 pct height reduction. Sections with d
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