One-dimensional models of thermal activation under shear stress

The analysis of thermal activation under shear stress in three- and even two-dimensional models presents unresolved problems. The analysis of one-dimensional models presented here may illuminate the study of more realistic models. For the model in which as many dislocations are poised for backward jumps as for forward jumps, the experimental activation volume V ^?e(σ_a) under applied stresses close to σ_a is different from the true activation volume V(σ) evaluated at σ = σ_a. The relations between the two are developed. A model is then discussed in which fewer dislocations are available for backward than for forward jumps. Finally, the appropriateness of the hyperbolic sine approximation for moderately low stresses is defined and shown to be very limited.