Full incremental elastic field induced by a mode-I crack in a prestressed orthotropic material

Abstract

Prestressed structures are frequently encountered in civil engineering. This paper gives a theoretical analysis of a cracked orthotropic elastic plane with initial stress. The problem of an orthotropic composite with a crack parallel to a material principal axis under initial stress along the crack line reduces to a mixed boundary value problem. It is solved using the Fourier transform. Application of boundary and continuity conditions leads to dual integral equations. An analytical solution can be obtained. Full incremental elastic field in an infinite prestressed cracked orthotropic composite is derived explicitly for linearly distributed loading on the crack faces. The fracture parameters such as incremental stress intensity factor (SIF), crack opening displacement (COD), and the energy release rate (ERR) are all obtained. The results for a prestressed isotropic elastic medium with a crack can be reduced from the present. When prestress is removed, the explicit expressions of the elastic field induced by a crack embedded in an orthotropic composite are recovered. Finally, the influence of initial stress on the elastic stress field, incremental SIF, COD and ERR for a cracked orthotropic elastic plane are presented graphically.