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Assessment of the contribution of plastic strain gradient effects to the fatigue threshold of ductile materials

Abstract:

The decreasing size of the plastic zone of a large crack growing by fatigue as the applied stress intensity factor range∆ K decreases implies a concomitant increase of the plastic strain gradient there. In a ductile, crystalline material, a plastic gradient must be resolved by storing a density of Geometrically Necessary Dislocations (GND) proportional to it. Such density represents an extra amount of dislocations superposed to the dislocation density that would locally accumulate without the presence of gradients for the same local plastic deformation in any volume element of the plastic zone (the size-independent Statistically Stored Dislocations (SSD) density). The net effect of the gradients is to progressively hinder the plasticity at the crack tip as∆ K decreases. For materials where the crack advance per cycle∆ a can be assumed proportional to the crack tip opening displacement∆ a∝ CTOD, the sole effect of the plastic gradients leads to predict a fatigue threshold effect. In this paper such contribution to the fatigue threshold has been quantified for ferritic steels by performing FEM calculations (ABAQUS® code) using a gradient-dependent continuum plasticity model based on the storage of GND and an appropriate constitutive equation of the Voce type. Further refinements of the model can easily be proposed.