How to get a correct estimate of the plastic zone size for shear-mode fatigue cracks?

Abstract

It was found that standardly calculated sizes of plastic zones ahead of mode II and mode III cracks during fatigue experiments close to threshold loading were very large and the stresses in the specimen net cross section without stress concentration were close to the yield stress. This represents a theoretical contradiction, since at threshold loading the plastic zones should be very small. In order to clarify the situation, results from three approaches were compared: (i) linear-elastic fracture mechanics, (ii) nonlinear Hutchinson-Rice-Rosengren (HRR) stress field and (iii) elastic-plastic finite element analysis considering nonlinear material behaviour according to the cyclic stress-strain curve. It was explained that, unlike under mode I loading, the plastic zone size should not be calculated using the applied maximum stress intensity factor (SIF). Instead, the effective SIF range needs to be used for calculation of stress fields ahead of the crack tip and, consequently the plastic zone sizes. Using these values realistic plastic zone sizes were obtained (less than 50μm). It also implies that stress in the specimen net cross section should not be calculated directly. A large part of loading applied to the specimen in terms of force or torque is transferred by fracture surfaces.