Capturing the Role of Microstructure through Non-Local Crystal Plasticity
William Counts1,2, Michael Braginsky1, Corbett Battaile1
1Sandia National Laboratories, Albuquerque, NM 87185 2 Georgia Institute of Technology, Atlanta, GA
Over the years, a number of researchers have shown that conventional solid mechanics approaches that do not incorporate different length scales cannot capture much of the experimentally observed phenomena linked to microstructure e.g. grain boundaries. For example, local approaches cannot predict grain-boundary-mediated strengthening of polycrystals (i.e. the Hall-Petch effect) or the formation of dislocation-based subgrain microstructures. To overcome this deficiency, a non-local crystal plasticity model is proposed. The model is based on an integral approximation of the curl of the inverse elastic deformation gradient that is used to calculate geometrically necessary dislocation (GND) density. In addition, in order to model the Hall-Petch effect, the kinematics is expanded from the standard FeFp decomposition to include prior deformation history. The deformation history rigorously determines the initial density of dislocations geometrically necessary to form the compatible polycrystal used as the undeformed state, and, thus, the initial yield stress. We will present the computational approach in detail, and demonstrate its utility in providing scale sensitivity to polycrystal plasticity simulations of deformation in FCC metals.
Sandia is a multiprogram laboratory operated by Sandia Corp., a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
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