Elastic-plastic behavior analysis of an arbitrarily oriented crack near an elliptical inhomogeneity with generalized Irwin correction

A theoretical model is developed to investigate the fracture behavior for an elliptical inhomogeneity embedded in an elastic-plastic matrix. It contains an arbitrarily oriented crack under a uniform stress field at infinity. In the model, the generalized Irwin approach is applied for plastic zone correction for crack-tip yielding. The distributed dislocation technique is utilized to formulate the present problem. The effective stress intensity factors, the plastic zone size and the crack tip opening displacement are evaluated by solving the formulated singular integral equations. The solution takes into account the plastic zone size at the crack tips and thus could provide accurate stress intensity factors and crack tip opening displacements for the assessment of crack growth. In the numerical examples, the case under a y-direction uniaxial tension is considered. The effects of the ellipse's aspect ratio, the shear moduli ratio and the normalized crack-inhomogeneity distance are investigated. The results show that the shapes of the inhomogeneity and the material combinations have significant influences. Crack propagation may be hindered if the inhomogeneity is close to circular or a hole and the crack inclination angle is close to 90°.