Chapter 4: Plastic Deformation of Single Crystals

Plastic Deformation of Single Crystals begins by establishing the fundamentals of crystal geometry, utilizing Miller indices to map crystallographic planes and directions within common metallic structures like face-centered cubic, body-centered cubic, and hexagonal close-packed lattices. A significant portion of the text focuses on lattice imperfections, distinguishing between point defects such as vacancies and interstitial atoms, and critical line defects known as dislocations, which are categorized as edge or screw types based on their relationship to the Burgers vector. The mechanism of slip is detailed as the primary mode of plastic deformation, where blocks of the crystal slide over one another along specific high-density planes and directions, constituting a slip system. The text explains the theoretical discrepancy between the high shear stress required to deform a perfect lattice and the much lower observed strength of real metals, attributing this facility of movement to the propagation of dislocations and overcoming forces like the Peierls-Nabarro force. Essential calculations are introduced through the concept of Critical Resolved Shear Stress and Schmid's Law, which determine when yielding occurs based on the orientation of the slip plane relative to the applied tensile axis. The discussion extends to the macroscopic behavior of single crystals under tension, analyzing glide strain and the geometrical rotation of slip planes toward the tensile axis during elongation. Complex deformation behaviors in face-centered cubic crystals are mapped using stereographic projections to predict primary and conjugate slip systems, eventually leading to duplex slip. Alternative deformation mechanisms are explored, specifically mechanical and annealing twinning, which create mirror-image lattice reorientations and differ distinctly from slip in terms of atomic movement and speed. The chapter also covers the influence of stacking-fault energy on dislocation substructures and the formation of inhomogeneous features like deformation bands and kink bands. Finally, the text provides an in-depth look at strain hardening, or work hardening, breaking down the flow curve into stages of easy glide, linear hardening, and dynamic recovery, while explaining the underlying dislocation interactions such as pile-ups, back stress, cross-slip, and the formation of sessile locks like Lomer-Cottrell barriers.