Grain boundary contribution to the bauschinger effect in beta-brass bicrystals
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INTRODUCTION
BICRYSTAL studies have been carried out to simplify the experimental conditions for attempts to predict polycrystalline stress-strain behavior ( e . g . , References 1 through 7). Chalmers and his co-workers 2'4observed that the region of complex slip in the vicinity of a bicrystal boundary can cause increased strengthening in a macroscopically incompatible bicrystal. Thus, bicrystals can be treated as a composite material consisting of a grain boundary region and a region away from the grain boundary3'7-9 in which the strain is constant in both constituents. Chuang and Margolin7 obtained the average stress in the grain boundary region in shear incompatible/3-brass bicrystals, which was about twice the average stress in the region away from the grain boundary. In a subsequent tricrystal study, Lee and Margolin I~ found that the grain boundary region extends farther from the boundary in tricrystals than in bicrystals. Hook and Hirth5'6 have demonstrated that elastic anisotropy in Si-Fe bicrystals influenced plastic flow at the grain boundary of bicrystals. They have shown, Figure 1, how secondary stresses, r'z and r'~. arise in a shear incompatible bicrystal. The secondary stresses have a significant role in determining activation of secondary slip near the grain boundary and on strengthening the bicrystal. 7']~ Moreover, these secondary stresses originating at the bicrystal boundary increase the effective Young's modulus in shear incompatible bicrystals by increasing the stress required to produce a given compressive elastic strain. H It has been proposed ]2 that as a result of the apparently higher modulus, the grain boundary region will recover more rapidly on unloading after prior strain. Thus, at zero load the bicrystal grain boundary region will be under reverse stress, while the region away from the grain boundary will still be under forward stress. Thereby, on reverse loading, reverse slip will take place at the grain boundary first. Evidence of slip reversal from the grain boundary in/3-Ti upon stress reversal was reported. 12 HIROSHI YAGUCHI is Staff Research Engineer, Inland Steel Research Laboratories, East Chicago, IN 46312. HAROLD MARGOLIN is Professor, Department of Metallurgy and Materials Science, Polytechnic University, Brooklyn, NY 11201. Manuscript submitted September 3, 1985. METALLURGICALTRANSACTIONS A
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Fig. 1 - Schematic illustration showing how stresses ---~'~zand -+"r,.z arise from incompatibility of the elastic strain %: after Hook and Hirthl 5
The early work of Woolley 13 on the Bauschinger effect indicated that for a wide range of single phase materials, the magnitude of the Bauschinger effect was independent of grain size. However, 13 years later Gokyu et al. 14 found a grain size dependence of the Bauschinger effect in copper, a-brass, and mild steel. The Bauschinger strain, /33/4, in smaller grain sizes was larger than that in larger grain sizes. Also, Saleh and Margolin 15observ
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