Fatigue crack-tip plasticity revisited - The issue of shape addressed

The problems pertaining to the fatigue loading of engineering structures under single overloads and variable amplitude loading involve the estimation of plasticity affected zones ahead of the crack-tip. The most widely used model for fatigue crack-tip plasticity estimation is based on Dugdale's model, which is valid for plane stress conditions and assumes, contrary to the findings of various experimental and numerical investigations, that the plasticity zone is of vanishingly small height. Plasticity and its influence on the rate at which fatigue cracks grow came to be widely acknowledged particularly after the phenomenon of crack closure was discovered by Elber, Since crack closure involves the plasticity in the wake of the advancing crack, Newman modified Dugdale's model by attaching appendages of plastically deformed material to the flanks of the crack. Several modifications to the Dugdale's model appeared subsequently in the literature, In this work after a survey of crack-tip plasticity, a novel way of estimating plasticity affected zones is presented. Three important parameters: Poisson's ratio nu, load ratio epsilon and shape ratio beta that affect the size and shape of the zone are identified. Two yield criteria, the von Mises and Tresca, are compared. It was found that an increase in the value of nu has, in general, a shrinkage effect on the zone size, while, an increase in epsilon is found to have a swelling effect. The value of beta was found to increase dramatically for high values of nu.