Mixed mode weight functions for an elliptical subsurface crack under shear loadings

• 2D mixed mode weight functions (MMWFs) for elliptical subsurface cracks are derived.
• Under shear loading, coupling effects are considered by matrix form of the WF.
• The proposed MMWFs can be used under any 2D shear stress distribution.
• Mixed mode SIFs of the crack front can be calculated easily using the MMWFs.
• MMWFs method is accurate and 60 times faster than FE method.

In this paper, mixed mode weight functions (MMWFs) for elliptical subsurface cracks under shear loadings are derived. Reference mixed mode stress intensity factors (MMSIFs), calculated by finite element analysis (FEA), under uniform shear loadings are used to derive MMWFs. The cracks have aspect ratios and crack depth to crack length ratios in the ranges of 0.2–1.0 and 0.05 to infinity, respectively. MMWFs are verified to calculate MMSIFs for any point of the crack front under linear and nonlinear two dimensional (2D) loadings. The derived MMWFs could be effectively used for evaluation of fatigue crack growth under complicated 2D stress distributions.