Continuum dislocation dynamics modeling of the deformation of FCC single crystals
A continuum dislocation dynamics model was developed for simulation of the deformation of Face Centred Cubic (FCC) single crystals. In this model, dislocations are described by a set of vector fields, one per slip system, whose evolution is governed by curl-type kinetic equations describing the transport of dislocation lines. These kinetic equations are closed by specifying the velocity field in terms of a mobility law in which the driving force is obtained by solving the Cauchy¡¯s equilibrium equation for stress. The coupled kinetic equations and crystal mechanics equations are numerically solved in a staggered fashion using a custom finite element approach featuring the use of Galerkin and Least Squares finite element methods for the mechanics and dislocation kinetics parts, respectively, on a mesh generated on an FCC superlattice. The spatial resolution of the mesh was determined based on the annihilation distance between opposite dislocations. Cross slip rates from discrete dislocation simulation have been incorporated into the continuum model by time coarse graining involving time series analysis. The overall model provides a full solution of the crystal deformation problem, including the space and time evolution of the dislocation density and all internal elastic and plastic fields. Under periodic boundary conditions, the model has been applied to predict the stress-strain behaviour of FCC crystal as well as the dislocation patterns for both monotonic and cyclic loading conditions. For monotonic loading, the cell structure is predicted and the wavelength is detected and shown to satisfy the empirical similitude law. The dislocation patterns are found to depend on the loading mode, monotonic versus cyclic, as well as the crystal orientation. For cyclic loading, the famous vein structure was also predicted by the model and the composition of dislocation veins are analysed. All results are compared with experiments and other discrete dislocation dynamics simulations, yielding a good agreement. An important finding of this investigation is that cross slip was found to be critical in triggering cell structure formation under monotonic loading and that the average cell size evolution was found to strongly depend on the cross slip rate.
Trice, Purdue University.
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