Orientation and strain dependence of stored energy of cold work in axisymmetric copper
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INTRODUCTION
CURRENT microplastic theories, which constrain polycrystalline deformation to a discrete set of slip systems in the crystal, predict variations in the level of slip (dislocation) activity depending upon grain orientation. In the Taylor ~and Bishop and Hill2 theories, this variation is given by the Taylor factor. It prescribes the ratio of slip activity to imposed strain as a function of crystallite orientation. It is reasonable to expect that evidence of this slip inhomogeneity would persist in the microstructure of deformed metal alloys since some 10 pct of the energy of deformation is stored in the metal. This remnant can be in the form of stacking faults, vacancies, tangled dislocations, cell walls, or macroscopic residual stresses. Kallend and Huang recently reported a correlation between X-ray line broadening and the Taylor factor in 50 pct cold rolled copper sheet. 3 In their investigation, stored energy (calculated from line broadening) was measured from composite specimens for approximately 30 different orientations in the pole figure and for three different pole figures. Based upon an analytical technique requiring the crystallite orientation distribution function (ODF), it was then possible to deconvolve the stored energy as a function of crystal orientation. The essential assumption necessary for their analysis is that the source of broadening is isotropic at the crystallite level. Their results indicated an increasing stored energy with increasing Taylor factor, although substantial scatter was present (particularly at high Taylor factors). There have been three major goals in this study: first, to investigate further the correlation reported by Kallend and Huang and extend their results to axisymmetric textures; second, to estimate the strength of the correlation as a function of strain level, and third, to evaluate the influence of strain path on the evolution of the Taylor factor and on the established correlation. This last goal is a concern since the texture present at a given strain level has evolved as a consequence of strain. Any correlation of stored energy with Taylor factor is most correctly expressed in terms of a "strain averaged Taylor factor". In axisymmetric textures it DAVID D. SAM, formerly Graduate Student of Mechanical Engineering at Brigham Young University, is Engineer, Applied Technology Organization, Eastman Kodak Company, Kodak Park, Rochester, NY 14650. BRENT L. ADAMS, Associate Professor, is with the Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602. Manuscript submitted July 1, 1985. METALLURGICALTRANSACTIONSA
is not necessary to perform the deconvolution of stored energy since the orientation distribution function is given in only two angles (e.g., the inverse pole figure). The obvious limitation to a study of axisymmetric textures is that only a few distinct orientations will be present in the inverse pole figure. The original assumption of isotropic broadening at the crystallite level has been retained in the present analysi
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