An implicit gradient application to fatigue of sharp notches and weldments

This paper addresses the problem of stress singularities at the tip of sharp V-notches by means of a non-local implicit gradient approach. A non-local equivalent stress is defined as a weighted average of a local stress scalar quantity computed on the assumption of linear elastic material behaviour. In the case of a crack, we propose an analytical solution for the non-local equivalent stress at the crack tip when the local equivalent stress assumes the analytical form proposed by Irwin. For open notches, several numerical procedures are possible. For welded joints, we assume that the material obeys a linear elastic constitutive law. In this case, the non-local equivalent stress obtained from the implicit gradient approach is assumed as the effective stress for assessments of joint fatigue. Using the principal stress as local equivalent stress and a notch tip or weld toe radius equal to zero, we analyse many series of are welded joints made of steel and subjected to either tensile or bending loading, and we propose a unifying fatigue scatter band. If the welded joints are subjected only to mode I loading, an analytical relationship between the relevant Notch Stress Intensity Factors (NSIF) of mode I and the effective stress is established; otherwise, the effective stress is evaluated by means of a simplified numerical analysis. For complex welded structures, however, a completely numerical solution is proposed; when different crack initiation sites are present (i.e. either weld toes or roots), the proposed approach correctly estimates the actual critical point.