A semi-analytical stress correction method for bi-material Mode-III V-notches

This article proposes a method to correct the numerical near singularity stress field in vicinity of reentrant corners by a semi-analytical solution. The approach pertains to perfectly bonded bi-material interface V-notches with arbitrary opening angles under Mode-III loading. The method addresses dissimilar joints with sharp corners in large-scale numerical engineering models where high-resolution discretization becomes computationally expensive.

The method is therefore particularly useful for fatigue lifetime analysis of shear-bending dominated large utility multi material structures such as compound castings, aircraft wings and wind turbine rotor blades to name a few. The solution for the governing Laplace equation is obtained by separation of variables in conjunction with the eigenvalue expansion method yielding the bi-material notch singularity exponent.

The notch stress intensity factor is then used to fit the analytical singular near field to the numerical far field utilizing the fact that the latter is more accurately predicted. The analytical anti-plane shear stress correction method is valid for any geometry subject to arbitrary remote loading conditions.

The accuracy of the approach is investigated by numerical stress analysis of a slender beam subject to axial torsion for different notch opening angles.