On the asymptotic character of the stresses near notches in plane problems

Analytical expressions are derived by the conformal mapping techniques of Muskhelishvili for the asymptotic character of the stress fields at the root of notches, re-entrant corners, etc. in plane bodies. It is shown that the stress field can be expressed as the product of a rapidly varying term, which depends only on the known geometry, and a slowly varying term which is associated with the nominal stresses. Using the derived expressions, together with a few stress, strain, or photoe/astic measurements at arbitrary points within the notch region, the entire stress field around the notch can be predicted. This includes the location and magnitude of maximum stress. The suggested technique is applied to a notch with parabolic shape and is shown to yield highly accurate results.