Interaction of multiple parallel cracks in a pre-stressed orthotropic elastic plane

Pre-stressed structures have been widely applied in aerospace, deep mining, and civil engineering fields. This paper presents a theoretical analysis of the interaction of multiple parallel cracks in a pre-stressed orthotropic elastic material. The pseudo-traction method and complex potential method are applied to solve an associated mixed boundary-value problem. First, we derive two kinds of fundamental solutions for a pair of normal and tangential concentrated forces acting at any point on an isolated crack. Then, with these solutions, a system of Fredholm integral equations are derived by superposition. The interaction of multiple parallel cracks in a pre-stressed orthotropic elastic plane is analyzed. Numerical results show that the pre-stress has little influence on the stress intensity factors when two cracks are collinear or two cracks are far away from each other (D-h > 2a or D-v > 5a). For closer two parallel cracks, K-I decreases with increasing pre-stress sigma(0) under normal loading and K-II increases with increasing pre-stress sigma(0) under shear loading.

Automated summary

This paper presents a theoretical analysis of the interaction of multiple parallel cracks in a pre-stressed orthotropic elastic material. The pseudo-traction method and complex potential method are applied to solve the problem. The results show that the pre-stress has little influence on the stress intensity factors when two cracks are collinear or far away from each other, but it affects the stress intensity factors for closer cracks under different loading conditions.