Dislocation dynamics theory for fatigue crack growth

Abstract

A B S T R A C T Dislocation group dynamics theory is used to deduce a power type expression for fatigue crack growth. In general, the results reflect only a single rate process, and thus one activation energy which is small compared to those in usual rate processes. The frequency dependence for this power function type fatigue crack growth rate was also obtained, and yield reasonable agreement with experimental results from the literaturel

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

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USA

We 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. 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]. 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].

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“…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. 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. The sl~sequent models including those of Rice and Thompson [4] as well as [I] and [2] are only modifications thereof.…”

Creep and creep–fatigue crack growth

“…A new crack growth model for creep-fatigue environment effects was developed by Evans and Saxena (2009) incorporating a thermally activated dislocation model of Yokobori et al (1975) and an environmentally assisted time-dependent crack growth model to predict the creep-fatigue-environment interactions in creepbrittle materials. This new model addresses the issues more comprehensively by including effects of temperature.…”

The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion

“…Equation (37) has shown, in particular, that K is unbounded when arrest is at the crack edge itself. More generally, intersection (and thus arrest) occurs at some t o > d when (3) are satisfied. Since dt*/ds >1 O, 0 < t* < s for s > d, t* = t o at some subsequent time s o = t o + R(to).…”

“…As pointed out in [2], however, the glide dislocation may also be fundamental to the physical process of fracture. For example, Yokobori et al [3] and Rice and Thomson [4] relate crack propagation to dislocation nucleation near an existing crack, while Tirosh and McClintock [5] represent stress and strain effects in cracked bars under torsion by assembling screw dislocations near the crack.…”