Nonsingular Stress Distribution of Edge Dislocations near Zero-Traction Boundary

Abstract

Among many types of defects present in crystalline materials, dislocations are the most influential in determining the deformation process and various physical properties of the materials. However, the mathematical description of the elastic field generated around dislocations is challenging because of various theoretical difficulties, such as physically irrelevant singularities near the dislocation-core and nontrivial modulation in the spatial distribution near the material interface. As a theoretical solution to this problem, in the present study, we develop an explicit formulation for the nonsingular stress field generated by an edge dislocation near the zero-traction surface of an elastic medium. The obtained stress field is free from nonphysical divergence near the dislocation-core, as compared to classical solutions. Because of the nonsingular property, our results allow the accurate estimation of the effect of the zero-traction surface on the near-surface stress distribution, as well as its dependence on the orientation of the Burgers vector. Finally, the degree of surface-induced modulation in the stress field is evaluated using the concept of the L2-norm for function spaces and the comparison with the stress field in an infinitely large system without any surface.

Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

“…Nevertheless, qualitative agreement with experimental results alone is not sufficient for the model to be accepted as reliable; quantitative agreement between theory and experiment also needs to be scrutinized using realistic parameter values [53]. In addition, when considering a realistic metallic specimen of a finite size, it is necessary to consider the attractive force exerted by the outer surface of the specimen on the dislocations inside [54,55]. To accomplish these tasks, numerical simulations based on coupled differential equations will be discussed in future work.…”