On Stress Distribution Near a Mode I Crack Tip under Plane Stress Conditions

The paper considers a mathematical model of stress distribution in the yeilding zone near the tip of a normal tensile crack (mode I crack) in a perfectly plastic solid under plane stress conditions. The von Mises yield criterion is adopted. Based on the formal statics formularion of the problem (indepentently of kinematical equations), exact formulas are obtained for calculating stresses within the plastic zone localized near the tip of the crack. A comparison of the exact results obtained in the article with the results of a numerical analysis of stress distribution given by Hutchinson in 1968 is presented.