Improved stress and displacement fields around V-notches with end holes

Abstract

The complex potential method is used to derive the asymptotic stress field around the V-notches with end holes (VO-notches). Although the classical methods take into account only the singular stress terms, herein the stress distribution is presented in the asymptotic form considering both singular and non-singular terms. In order to calculate the coefficients of the singular and non-singular terms of the stress distribution, an over-deterministic method is employed. Based on the over-deterministic method, the nodal displacement values for a large number of points around the VO-notch are obtained from finite element analysis and fitted to the asymptotic displacement field. The method is then applied to two laboratory test specimens containing VO-notches with three different notch angles and four notch tip radii under mode I loading condition. Moreover, by comparing the results obtained from the truncated stress series with the output stress results of the finite element analysis, the accuracy of the calculated coefficients is evaluated. Finally, by using some numerical examples, it is shown that the proposed asymptotic stress distribution can appropriately describe the stress field around sharp V-, key-hole and U-notches. The results obtained for all mentioned notch types show that neglecting the higher order terms can result in significant errors while considering the first two non-singular stress terms presents very good results.