Implicit gradient and integral average effective stresses: Relationships and numerical approximations

This paper investigates two possible definitions of a non-local effective stress: the weighted average value and the implicit gradient solution. These definitions are usually applied for strength assessment, particularly in the high cycle fatigue regime, in the presence of notches, defects, cracks or welded joint toes or roots. The present research analyses their general relationship in plane notches. Then, the paper presents a numerical method for their assessment by means of a general FE tool. Different solutions are calculated and compared by evaluating the results obtained from different finite element method commercial software