A Dugdale–Barenblatt Model for a Plane Stress Semi-Infinite Crack under Mixed Mode Concentrated Forces

Abstract

In this paper, a mixed mode Dugdale–Barenblatt model has been established for a semi-infinite crack in an ideally elastic-plastic thin plate loaded by a pair of self-equilibrating concentrated forces at the crack lips. Cohesive forces are introduced into a plastic strip in the elastic body. By superposing the two linear elastic fields, one evaluated with the external loads and the other with the cohesive forces, the problem is treated in Dugdale–Barenblatt's manner. The physical domain is mapped with a complementary domain of the unit circle by using the Schwartz–Cristoffel transformation. The Muskhelishvili complex potentials are used to find out the stress-intensity factors due to the two separated fields. The analytical approach leads to establish a few transcendence equations from which the quantities of interest, such as the direction and the length of the plastic strip, the crack opening distance etc., can easily be deduced by standard numerical methods.