Solution for the stress and displacement fields in the vicinity of a V-notch of negative wedge angle in plane problems of elasticity

The method is presented of modeling displacement, strain and stress fields in the two-dimensional problems of elasticity considering the presence of V-shaped notches with any positive or negative angle. The analytical expressions for stress and strain states at the tip of a V-notch were obtained for two cases of deformation: opening (mode I) and sliding (mode II). This was achieved assuming the appropriate Airy function in polar coordinates with an origin at the notch tip. A new definition of the stress intensity factors was proposed. The analytical predictions were compared with the numerical results obtained using the finite element method. Finite elements with linear-stress distribution and finite elements with asymptotic-stress distribution were used in the mesh idealization.