The effect of residual stress field induced by cyclic loading on crack initiation in a cracked sheet

The residual stress and displacement fields near the tip of a Mode I crack in a sheet observed after a loading-unloading cycle are analyzed. It is shown that after the first unloading the maximum tensile residual stresses are localized at a distant from the crack tip point and their magnitudes can reach the one third of the yielding limit, whereas the crack tip is compressed by residual stressess equaled to the yielding limit. The second loading of the residually prestressed cracked sheet is revealed can result in the origin of a new distant plastic flow zone, localized near the maximum tensile prestressed element. A method of determining the plastic flow localization parameters that describe the position of the schematic segment-like plastic flow zones on the line extending the crack is proposed. The two-zone plastic flow localization is analyzed in the framework of the Dugdale model of the near crack tip yielded zone. The exact formula for the crack opening displacement in the sheet loaded after a loading-unloading cycle is obtained.