A finite element approach for the analysis of variable core dislocations

A finite element description of variable core edge dislocations in the context of linear elasticity is presented in this work. The approach followed is based on a thermal analogue and the integral representation of dislocations through stresses. The objective of a variable core defect concept is to eliminate the stress singularity experienced at the dislocation core. This is accomplished assuming that the displacement discontinuity is achieved gradually over some distance. To implement this concept in a finite element scheme, we first model purely rotational crystal defects considering an appropriate pseudo-temperature distribution, which produces a dislocation array of increasing width. Accordingly, we simulate a discrete edge dislocation of linearly increasing width. This description of dislocation core is closer to experimental observations and has a physically anticipated behaviour reproducing the Volterra dislocation away from the core. Further, interactions of variable core dislocations with free boundaries and coupled dislocation partials are investigated. In all cases, we recover the analytical solutions for the stress distributions and the total strain energy