Construction of a relaxation model

Any misfit dislocations already present do not contribute to strain rate. 

The average threading dislocation speed utd can be expressed in terms of the average driving force G h,p) acting on it, which was defined in (7.21), as 

It is recognized here that 7, as well as density n, thickness h and temperature T, may vary with time t. Since the thickness and temperature are normally controlled parameters in a relaxation process, the histories h t) and T(t) can be assumed to be known for many circumstances. However, n t) is an internal variable that cannot be controlled. The density evolves during a relaxation process in a way that has not yet been captured in a concise and generally applicable representation. This evolution includes contributions resulting from nucleation, multiplication, annihilation and blocking. For most purposes, it is probably adequate to postulate that n(t) evolves according to a rate equation of the form 

Suppose that n(t) is scaled by some reference threading dislocation density rh-. Furthermore, attention is limited for the time being to cases of relaxation at constant temperature. Then (7.28) can be rewritten as 

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