If the creeping metal contains a dislocation network, then a recoverable strain (ξ) can be produced by dislocation bow; its equilibrium magnitude for a uniaxially stressed specimen containing a network of simple geometry can be calculated from equations developed by Mott and, also, by Friedel.
In the present work, the more general relationship between the strain tensor, ξij and the external stress tensor, σij, is developed for equilibrium and also for the approach to equilibrium following an arbitrary change in σij.
The approach is based on the behavior of the surface representing the orientation dependence of the recoverable strain which an isotropic metal is potentially capable of exhibiting when stressed. It is posited that this surface is always a sphere whose equilibrium position in deviatoric external stress space is symmetrical about the vector (σ1′, σ2′, σ3′).The sphere's center is displaced from the origin of coordinates and its radius is altered by the application of stress state, σij for time, t.
This treatment is shown to lead to equilibrium strains which obey the Levy-Mises and volume-conservation criteria. The flow rules for the approach to equilibrium following any arbitrary stress change are formulated and solved for the particular case of Newtonian irradiation creep where a measure of agreement with experimental data is found to exist.
The equations for the equilibrium recoverable strain are rewritten in a form algebraically identical to Hookes law, and data are analyzed which reveal that the analog for recoverable strain, of Poisson's ratio (ν′) can be less than 0.5 (so that volumetric strains occur); while at stresses and temperatures that favor climb, the analog of Young's modulus, E′, approaches the theoretical value (equal to twice E, Young's modulus) for a Mott-Friedel dislocation network.