A Line-Free Method of Monopoles for 3D Dislocation Dynamics

Citation

Deffo Nde, Arnold Durel (2019) A Line-Free Method of Monopoles for 3D Dislocation Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/23YV-3312. https://resolver.caltech.edu/CaltechTHESIS:08042018-083338014

Abstract

Despite the emergence of architected materials for various applications, metals still play a key role in engineering in general and aeronautics in particular. Turbine blades in jets engines for instance are made from single-crystal Nickel superalloys. As a result, studying the failure mechanism of these crystalline materials would help understand the limits of their applications. At the core of this mechanism are line defects called dislocations. Indeed, the plastic deformation of metals is governed by the motion of dislocation ensembles inside the crystal. In this thesis, we propose a novel approach to dislocation dynamics through the method of monopoles. In this approach, we discretize the dislocation line as a collection of points (or monopoles), each of which carries a Burgers "charge" and an element of line. The fundamental difference between our method and current methods for dislocation dynamics lies in the fact that the latter discretize the dislocation as a collection of line segments from which spans a need to keep track of the connectivity of the nodes. In our approach, we propose a "line-free" discretization where a linear connectivity or sequence between monopoles need not be defined. This attribute of the formulation offers significant computational advantages in terms of simplicity and efficiency. Through verification examples, we show that our method is consistent with existing results for simple configurations. We then build on this success to investigate increasingly complex examples, this with the ultimate goal of simulating the plastic deformation of a BCC grain in an elastic matrix.

Thesis Files