Sharp notch roots subject to in-plane and anti-plane loading: An alternative normalisation of the eigenfields & their application to example problems

The state of stress at a sharp notch is characterised by the classical Williams eigenfunction expansion for in-plane loading, and a corresponding anti-plane solution. Excluding the case when the internal notch angle is 2π (a crack), the solutions have differing orders of singularity, and hence, between any pair of modes of loading, there is an internal implied length scale. Here we bring out those length scales, and show how the three generalised stress intensity factors may be replaced by equivalent parameters having a much more direct physical interpretation. The revised form of the semi-infinite notch solutions are then applied to example geometries, showing how the characteristics of the notch-root process zone may be inferred without further calculation.