Higher order stress terms in sharp notch problems under pure-out-of-plane loading

Current paper studies the effects of higher order terms (HOTs) on the stress and displacement fields around sharp V-notched components under pure antiplane shear (mode III) loading. For this aim, two V-notched test samples each containing four different notch angles are simulated in a finite element (FE) commercial software. Subsequently, the over-deterministic technique is used as an approach to calculate the coefficients of singular and nonsingular terms out of the nodal displacement values. To verify the accuracy of the values calculated as the coefficients, the stress field reconstructed from the truncated series expansions is compared with the direct nodal outputs of FE analysis. The results demonstrate that the use of nonsingular terms of the asymptotic series expansion is necessary only in the case that the distribution of stress at far distances from the notch tip is sought and the notch angle is small. To check the stability of the results, some of the parameters which affect accurate determination of unknown coefficients and convergence of the numerical results are studied.

Automated summary

This study investigates the effects of higher order terms on the stress and displacement fields around sharp V-notched components under pure antiplane shear loading. The use of nonsingular terms is necessary only when seeking stress distribution far from the notch tip and with small notch angles. Parameters affecting accurate determination of unknown coefficients and convergence of the numerical results were also studied to check the stability of the results.