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

Abstract

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 (Dh>2a or Dv>5a). For closer two parallel cracks, KI decreases with increasing pre-stress σ0 under normal loading and KII increases with increasing pre-stress σ0 under shear loading.