Dislocation Accumulation Due to Plastic Slip

First, the accumulationAccumulation of dislocations and annihilationAnnihilation of dislocationsDislocation annihilation of statistically stored dislocationsStatistically stored dislocations due to emission of dislocation loopsDislocation loops is described and formulated. The important concepts of dislocation mean free pathDislocation mean free path and annihilation distanceAnnihilation distanceDislocation annihilation are introduced and strain hardening associated with slip deformation are shown for some cases with simplified parameter sets. Next, the spatial gradient of plastic shear strain and geometrically necessary dislocations are explained in detail and extended to three-dimensional space. The direction vectors and characteristic angles of the geometrically necessary dislocations in 3-D space are derived and used to visualize the emission of prismatic dislocation loops from a micrometer-sized void.