A weight function for 2D subsurface cracks under general loading conditions

A procedure for evaluating the fracture mechanics parameters of a subsurface two-dimensional crack parallel to the boundary in an elastic half plane is presented. A Weight Function (WF) with a matrix structure is proposed, to account for the coupling effects between modes I and II, typical in non-symmetrical problems. In order to face any loading condition, the WF was formulated by symmetric and anti-symmetric components and the ‘multiple reference loading’ approach was used to derive their analytical expressions. To this purpose, a parametric Finite Element (FE) analysis was set up and the Stress Intensity Factors (SIFs) were determined for several independent loading conditions. The analysis was carried out for different ratios between crack length and in-depth position and, consequently, the dependence of the WF on this parameter was studied. The WF accuracy was assessed by considering different loading and the method applied for evaluating the SIFs produced by a point-like load travelling on the semi-plane surface. The results indicated that the correct fracture mechanics analysis requires crack closure (either complete or partial) to be taken into account. Consequently, the crack opening displacement (COD) components under general loading conditions have to be evaluated. On the basis of the WF, the related Green Function (GF) was also derived by which the COD components can be efficiently evaluated for any applied load including the contact due to crack closure.