An Eulerian-Based Formulation for Studying the Evolution of the Microstructure under Plastic Deformations
S. Ahmadi; B.L. Adams and D.T. Fullwood

doi:10.3970/cmc.2009.014.141
Source CMC: Computers, Materials, & Continua, Vol. 14, No. 2, pp. 141-170, 2009
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Keywords Microstructure, Microstructure Function, Continuity Equation, Conservation Principles, CMC.
Abstract In this paper, a model is introduced to examine the evolution of the microstructure function under plastic deformations. This model is based upon a double continuity relationship that conserves both material particles in the mass space and orientations in the orientation space. An Eulerian description of the motion of material particles and orientations is considered, and continuity relations are derived for both spaces. To show how the proposed model works, two different case studies are provided. In the mass space, the continuity relation is used to examine the evolution of the microstructure function of a two-phase (isotropic) material; while, in the orientation space, this model is used to simulate the evolution of the microstructure of a randomly textured fcc material that has been cold rolled to a rolling reduction of 70%. In addition, in both case studies, our Eulerian continuity model is compared against the Lagrangian models that are widely used in the literature for texture predictions. Results show that by selecting an appropriate grid size for both workspaces the proposed Eulerian continuity model can accurately predict the evolution of the microstructure for large plastic deformations.
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