Dislocation Kink Chain Model Versus String Model

Abstract

The Peierls stress for dislocation motion causes characteristic nonlinearities of the micro‐stress‐strain law of dislocations. Contrary to the string model, the nonlinear stress‐strain law of kinked dislocations can be the source of amplitude‐dependent internal friction and modulus defect at amplitudes which are below or comparable to the breakaway stress from pinning points. Under the assumption that double‐kink generation can be neglected, in terms of a bias stress experiment, the following points have been found to be the essential difference between the dislocation string model and the kink model: (1) The anelastic strain as measured by low‐amplitude oscillations increases with bias stress for the string model, whereas it decreases for the kink model, due to the exhaustion of geometric kink motion. (2) The restoring force of kinked dislocations is one to three orders of magnitude more sensitive to bias stress than is the restoring force of dislocation strings. The conditions for measurable changes of the restoring force are, for the kink model, ε> (10⁻¹ b/L) (sin φ+5kT/Gb²a), and for the string model ε> 10⁻¹ πb/L (ε is the bias stress in units of shear modulus G, L is the line length, φ is the average angle against close‐packed direction, b is the Burgers vector, a is the lattice constant, and T is the temperature).