Crack tip stress fields for thin, cracked plates in bending, shear and twisting: A comparison of plate theory and three-dimensional elasticity theory solutions

Abstract

A three-dimensional finite element study of crack tip fields in thin plates under bending, shearing, and twisting loads is carried out to study the relation of the plate theory crack tip fields to the actual, three dimensional crack tip fields. In the region r>0.5h the Kirchhoff theory is a good approximation of the three dimensional stress fields for symmetric plate bending. The Reissner theory gives a good approximation in the region r<0.1h. Similar results are found for the shear and twisting problems, although for pure shear loading, the Kirchhoff theory is a good approximation somewhat farther r>h from the crack tip than in the bending problem. In the case of shear loading the near tip out-of-plane shear stresses do not vary quadratically through the thickness as in plate theory, but are nearly constant, except in the neighborhood of the free surface. Quadratic variation, as predicted by plate theory, is observed for r>h. Energy release rates based on the Kirchhoff and Reissner theories agree well with those computed by means of three dimensional finite element analyses.