Chapter 5: Dislocation Theory

Dislocation Theory begins by categorizing observation techniques, ranging from historical etch-pit and decoration methods to advanced transmission electron microscopy (TEM), which utilizes diffraction contrast to visualize the strain fields of lattice defects. The text rigorously defines the Burgers vector through the Burgers circuit, distinguishing between pure edge, pure screw, and mixed dislocation loops based on the geometric relationship between the dislocation line and its slip vector. Significant attention is given to the energetics of dislocations, describing how the strain energy per unit length is proportional to the shear modulus and the square of the Burgers vector, and how line tension acts to minimize this energy. The narrative progresses to dislocation behavior in specific crystal structures, particularly Face-Centered Cubic (fcc) lattices, where unit dislocations dissociate into partials (such as Shockley partials) separated by stacking faults, or form immobile sessile dislocations like Frank partials and Lomer-Cottrell barriers. Complex interactions are explored, including the forces between parallel dislocations, the nonconservative process of dislocation climb facilitated by vacancy diffusion, and the geometric consequences of intersection, which produces kinks and jogs. The chapter further elucidates mechanisms of dislocation multiplication, primarily the Frank-Read source and cross-slip, which allow a single source to generate extensive slip bands. Finally, it examines the elastic interaction between point defects and dislocations, leading to phenomena like impurity atmospheres, and analyzes the stress concentrations arising from dislocation pile-ups against barriers, which are critical for understanding strain hardening and fracture initiation