Theoretical equation for steady-state dislocation creep

Publisher Website
Google Scholar
Abstract
This is the second of two papers concerned with the effects of jog-drag upon the rate of creep. The earlier paper dealt with the case in which the dislocations formed a three-dimensional Frank network. The present work is concerned with the case in which most of the dislocations have formed themselves into cell-walls. The resultant creep equation is similar to the one previously derived except that it now contains a parameter K, the ratio of the cell-diameter to the mean dislocation spacing. The effect of this parameter is dramatic. Thus in the previous work, appropriate to the case where the dislocations are in a uniform three-dimensional network (K = 1), the exponent of stress, n = d (log)/d (log σ), was theoretically always near to the value 3. However, for a cellular structure (K ∼ 10), the value of n falls from higher values towards 3 as the stress is reduced. For example for gold at half its absolute temperature of melting, n falls from approximately 7 at σ= 10−3 μ to 3 at σ = 10−4 μ (σ = stress: μ= shear modulus). At large values of K the equations reduce to one found by Garofalo (1965) and give a good fit to data over a wide range of stresses and temperatures.