Incorporating dislocation substructure into crystal plasticity theory

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Butler, George C.
McDowell, David L.
Stock, Stuart R.
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Polycrystal models, beginning with the work of Sachs (1928) and Taylor (1938), have been used to predict very complex material behavior. The basis of these models is single crystal plasticity theory, which is then extended to model an actual (polycrystalline) material composed of a large number of single crystals or grains. Crystal plasticity models are formulated at the scale of the individual grain, which is viewed as a fundamental material element. To first order this is a reasonable approximation, and results in qualitatively good predictions. However, it is also well known that the grain is not a uniform entity, and that a great deal of non-uniform activity, including the development of well-defined dislocation structures, occurs within individual grains. The goals of this research are to complete an experimental data set for validation of material modeling, and to then improve the physical basis of predictive polycrystal plasticity models. Preferred orientations (textures) of oxygen free high conductivity (OFHC) copper were measured using reflection x-ray diffraction techniques. Monotonic strain paths included a variety of strain levels for both compression and torsion. One of the significant contributions of this research was the measurement of textures resulting from non-monotonic deformation histories, specifically compressive prestrain (to two different levels) followed by torsion to an effective plastic strain of 1.00. We also concluded synchrotron radiation experiments to map Laue images to examine subgrain microtexture formation at various stages of finite deformation. The second major contribution is to polycrystal plasticity modeling. Improvements to the plasticity model were achieved by including the effects of gradually developing, sub-grain scale microstructures, without explicitly modeling the structures, in terms of both crystallographic texture formation and work hardening. The effects of these microstructures were incorporated through the use of new internal state variables. They result in a broadening of the peaks of the macroscopic texture and a reduction of the rate of texture formation. Predictions of crystallographic orientation distributions were verified by plotting stereographs, which were shown to match measured crystallographic textures. The microstructural hardening law was introduced through a new form of latent hardening, which was shown to match experimental stress-strain behavior more closely than the basic model of Pierce, Asaro, and Needleman (1982). This latent hardening form augmented a Taylor-type term, which reflected statistically stored dislocations in the slip system hardness. Significantly, this improvement was also noted in the case of non-monotonic loading, which the standard model could not predict even to first order. Also, in the course of this research a planar double slip model was used as a precursor to the full three-dimensional modeling. The objective was to use the planar model to test various formulations, at least qualitatively, since it is a simpler model. As a result of comparisons between the three-dimensional simulations and the planar ones, the planar model was shown to be an insufficient tool for developing new texture and hardening evolution schemes as compared to the three-dimensional models. The planar model was unsuitable for modeling any but the most basic crystal plasticity relations and most simple deformation paths in a qualitative manner.
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