On a model of Dugdale crack in orthotropic bodies (Q2754666)

The well-known Dugdale crack model was formulated for isotropic thin plates (plane stress) under Treska plasticity condition. In this paper the model is generalized for orthotropic materials in view of the fact that plasticity conditions for an orthotropic material are essentially different from those for isotropic material. It is found that normal stresses within the plastic section of the crack tip are related through the main stress state and elastic constants of orthotropic solid. Equations for stresses in the plastic zone are derived for the plain stress and the plain strain. After determination of these stresses, the main stress state of the half-plane can be found in the form of Cauchy principal value integrals. Two particular examples (two-axial tension at infinity and constant pressure applied to the crack faces) are considered. Plastic stresses for these cases are determined.