On the analysis of singular stress fields Part 1: finite element formulation and application to notches

The state of stress at the apex of a notch is characterized by a unique singular spatial distribution. The use of a special finite element to enable this stress state to be represented in a genreal model is discussed and details of the implementation are provided. Separately, an analytical description of the stress state is found from Williams' asymptotics and the generalized stress intensity factor for the configuration is found. This enables the region of domination of the singular term to be found and hence the domain within which any notch root singular process zone is controlled by the singular field to be quantified.