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

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 re lation of the plate theory crack tip fields to the actual, three dimensiona l crack tip fields. In the region r > 0.5h the Kirchhoff theory is a good a pproximation of the three dimensional stress fields for symmetric plate ben ding. The Reissner theory gives a good approximation in the region r < 0.1h . Similar results are found for the shear and twisting problems, although f or pure shear loading, the Kirchhoff theory is a good approximation somewha t farther r > It from the crack tip than in the bending problem. In the cas e of sheer loading the near tip out-of-plane shear stresses do not vary qua dratically through the thickness as in plate theory, but are nearly constan t, except in the neighborhood of the free surface. Quadratic variation, as predicted by plate theory, is observed for r > h. Energy release rates base d on the Kirchhoff and Reissner theories agree well with those computed by means of three dimensional finite element analyses.