Response: Discussion of ?Prediction of threshold stress intensity for fatigue crack growth using a dislocation model,? by A. T. Yokobori, Jr.

Abstract

USAWe express our appreciation to Dr. Yokobori for his interest in our paper [l] and for bringing to our attention their earlier paper [2] on dislocation dynamics theory for fatigue crack growth. The discussion of our paper centers on two points, namely that the dislocation models in [I] and [2] are essentially the same, except [2] was published earlier, and a more important issue that there should be two requirements to be satisfied before a dislocation can be nucleated at the crack tip. These requirements are the stress and energy which are claimed to providerespectively -the necessary and sufficient conditions for the dislocation generation.From the historical perspective, we note that the nucleation of a dislocation from a crack tip was first treated by Armstrong [3]. The sl~sequent models including those of Rice and Thompson [4] as well as [I] and [2] are only modifications thereof.Refs. [1,2], however, are concerned with dislocation generation at a subcritical size crack and therefore could be related to the fatigue crack growth process.Contrary to that claimed in [2], dislocation modeling of fatigue crack growth is also not new and was treated earlier by Weertman [5]. Also, concerning Yokobori's comments on the priority of their dislocation model for the prediction of threshold stress intensity, we fail to see any discussion in [2] pertaining to the threshold stress intensity.Nevertheless, presuming that it is implicit in their equations, we shall now address the more fundamental question concerning the necessity for the two requirements.If their analysis [2] is correct, both force and energy considerations should give the same equilibrium configuration except in cases where there are non-conservative forces present, such as friction.In such cases equilibrium becomes path history dependent, and energy then provides a more fundamental parameter for the determination of the equilibrium configurations [6,7,8]. For the particular problem involving a dislocation generation from the crack tip, the path history is fixed and therefore force or energy should both give the same result.Yokobori et al. [2] arrived at two requirements only because they analyzed two different problems which were not interconnected by them.For the stress requirement they use a force equilibrium on a preexisting dislocation at the crack tip. Their expressions are incomplete in terms of the nucleation aspect since an important component, namely self energy of the dislocation, is ignored.In order for a dislocation to come out from a crack tip work has to be done to overcome the self energy of the dislocation, in addition to the image and ledge forces considered in [2]. These are precisely the terms considered in our paper [I]. In