Analytical and numerical evaluation of the interaction energy between screw dislocation and inhomogeneous inclusion

Abstract

Interaction energy between dislocations and inhomogeneities is an important topic in the study of the trapping mechanism and the motion of dislocations. However, analytical solutions for the interaction energy are difficult to derive because of the complex integral over the inclusion domain and material mismatch, while numerical computations involve singularities from dislocations. The present work proposes an effective iterative computational scheme, via the numerical equivalent inclusion method (NEIM) in conjunction with the two-dimensional fast Fourier transform (2D-FFT) algorithm, for handling the elastic field due to a screw dislocation interacting with an arbitrarily shaped inhomogeneous inclusion. The resultant elastic energy and interaction energy may be conveniently obtained by summing the contributions from the elementary solutions. By employing the EIM, the work also presents a closed-form evaluation for the circular inhomogeneity case, in which the effectiveness of the EIM for the non-uniform equivalent eigenstrains is examined. Benchmark examples are provided to validate the present work, and parametric studies are further conducted to demonstrate the effectiveness of the current scheme.