In-plane and out-of-plane stress field solutions for V-notches with end holes

Closed form expressions of stress distributions for V-notches with end holes and varying opening angles are presented. The solution for the elastic plane problem is obtained by means of the Kolosov-Muskhelishvili approach by using a reduced number of complex terms. The exponents of the potential functions are simple combinations of Williams' eigenvalues for pointed V-notches in mode I and mode II. The degree of accuracy of the new solution, which is approximate, is found to be very satisfactory for engineering applications. When the V-notch opening angle is equal to zero, the solution matches the keyhole notch solutions already reported in the literature by Neuber (for mode I) and by Kullmer and Radaj (mode I and mode II) and based on the Airy stress function. In parallel, the out-of-plane problem is solved by means of an holomorphic function H(z) where the exponent is still linked to the leading order eigenvalue of the pointed V-notch in mode III. For this loading mode the solution is exact. When the notch opening angle is equal to zero and also the notch root radius tends to zero the solution matches Kullmer's keyhole notch solution.