R. E. Bolmaro, "Grain Axes Coincidence Model: Relaxed Constraints and Finite Strains Revisited", Texture, Stress, and Microstructure, vol. 22, Article ID 479398, 12 pages, 1994. https://doi.org/10.1155/TSM.22.187
Grain Axes Coincidence Model: Relaxed Constraints and Finite Strains Revisited
The problem of the kinematics of grain reorientation in polycrystalline plasticity has been addressed many times in the past. A particular grain and the matrix in which that grain is embedded must deform guaranteeing compatibility if no debonding or failure are allowed. This requirement is satisfied by the condition of keeping the main axes of the grain and the hole lodging that grain collinear and of the same size during the whole deformation process. It is not clear yet which one of the many definitions of spin should be considered and how the Taylor model is reproduced for nearly round crystals. The problem is directly connected with spin definitions in continuum mechanics and finite strains. The present paper will be concerned with a rigorous treatment of the many spins and rotations that affect a grain in a polycrystal. It will also be shown that this new treatment suggests a new kind of constraint relaxation that, unfortunately, can not be calculated “a priori” with complete ignorance of the kinetics. However some textures can be simulated. The Los Alamos Polycrystal Plasticity code was modified in order to allow relaxation of some strain components while keeping the reorientations less than a prescribed limit. The resultant textures show the same pattern but different strength than the ones obtained under Taylor assumptions. This Grain Axes Coincidence Model (GACM) has both the Taylor and the Relaxed Constraints and Self Consistent models as natural limits for round and very flat grains respectively. It is shown that the constraint relaxation concept that comes out from the GACM is qualitatively different from the usual in RC and SC models. Strain path changes under the new assumptions are also discussed.
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