On the crack opening displacement in a cracked sheet after a loading-unloading cycle

The residual stress and displacement fields near the tip of a crack in a sheet after a loading-unloading cycle are obtained. The effect of residual stress field on the yielding of the sheet in the course of a following loading is investigated. The problem is formulated within the context of the Dugdale model of the plastic flow zone near the crack tip. It is shown that the intensive plastic flow is localized, if only a right half-plane is considered, in the two zones (the first one is near the crack tip, the second one - distant from the crack tip), separated by the elastic field. The localization of yielding is analysed numerically as well as the effect of the residual stresses and the distant plastic zone on the crack opening displacement. A comprehensive asymptotic analysis to estimate the crack opening displacement (as the linear dimension of the distant plastic zone compared with the crack length is small) is given.