Effects of applied stress level on plastic zone size and opening stress ratio of a fatigue crack

Based on a complex function method developed by Budiansky and Hutchinson [J Appl Mech, 1978;45:267], a theoretical analysis of the effects of the applied stress level on fatigue crack closure under large-scale yielding conditions is conducted. Firstly, we obtain the explicit expression for the crack opening displacement in plastic zone under large-scale yielding conditions from the Dugdale model. The expression, along with that of the plastic zone size under large-scale yielding conditions, is then introduced into the Budiansky and Hutchinson model to account for the effects of the applied stress level over a large stress range on the reversed-to-forward ratio and the opening stress ratio of fatigue cracks. We show that both the ratios decrease with the increasing applied stress level. The present results are compared with the experimental data, the finite element calculations and the prediction of the Newman equation.