Asymptotic characterisation of nearly-sharp notch root stress fields

A solution procedure is developed for characterising the stress state at the root of a notionally sharp notch, but possessing a small root radius, using two nested asymptotic solutions: an outer asymptote representing a sharp semi-infinite V-notch and an inner solution representing a semi-infinite rounded notch. The two asymptotes are matched to each other remote from the notch root, and to an example finite notch using a generalised stress intensity factor. It follows that the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very near the root. On the other hand, the notch in a finite body diverges from the sharp semi-infinite notch in the far field. Providing that the notch root radius is sufficiently small, it follows that there is an intermediate field where the singular field does characterise the behaviour of the finite radiused notch, and this is quantified.