Modeling dislocations in a polycrystal using the generalized finite element method.

Abstract

Modeling the interaction of dislocations with internal boundaries and free surfaces is essential to understanding the effect of material microstructure on dislocation motion. However, discrete dislocation dynamics methods rely on infinite domain solutions of dislocation fields which makes modeling of heterogeneous materials difficult. A finite domain dislocation dynamics capability is under development that resolves both the dislocation array and polycrystalline structure in a compatible manner so that free surfaces and material interfaces are easily treated. In this approach the polycrystalline structure is accommodated using the GFEM, and the displacement due to the dislocation array is added to the displacement approximation. Shown in figure 1 are representative results from simulations of randomly placed and oriented dislocation sources in a cubic nickel polycrystal. Each grain has a randomly assigned (unique) material basis, and available glide planes are chosen accordingly. The change in basis between neighboring grains has an important effect on the motion of dislocations since the resolved shear on available glide planes can change dramatically. Dislocation transmission through high angle grain boundaries is assumed to occur by absorption into the boundary and subsequent nucleation in the neighboring grain. Such behavior is illustrated in figure 1d. Nucleation from the vertically oriented source in the bottom right grain is due to local stresses from dislocation pile-up in the neighboring grain. In this talk, the method and implementation is presented as well as some representative results from large scale (i.e., massively parallel) simulations of dislocation motion in cubic nano-domain nickel alloy. Particular attention will be paid to the effect of grain size on polycrystalline strength.