The dislocation network theory of creep

Abstract

The dislocation network theory of creep is considered in detail. The operative mechanisms dictating the creep response to an applied stress are the glide multiplication of dislocations in the network by an Orowan mechanism driven by the applied stress and a stress-independent dislocation annihilation mechanism controlled by climb and driven by the reduction of the elastic stored energy of the dislocations. Equating the rates of these processes for steady state gives rise to a pseudo-equilibrium network spacing. This spacing is a function of stress and the ratio (α) of glide and climb mobilities.

An expression is derived for the steady-state rate of creep given by

where ε is the creep rate, kT the thermal energy, D the self-diffusion coefficient, G the shear modulus, b the Burgers vector and [sgrave] the applied stress. The equation has the limit for infinite glide velocity of the Dorn equation (Bird, Mukherjee and Dorn 1969). The right-hand side of the equation reduces to ([sgrave]/G)³. This is a theoretical upper limit to the rate of creep by a network mechansim. Creep rates are often less than those predicted by the equation and this may be because glide is not always easy.

The influence of dislocation pipe diffusion contribution to creep is calculated for different α values. Predictions are made for behaviour following a stress change during creep. These involve anelastic contributions to creep by the network, incubation periods after a stress reduction, and considerations of the time taken for the network to become re-established after a stress increment. The relative importance and magnitude of these effects are calculated.