Crack tip stress fields for thin, cracked plates in bending, shear and twisting: A comparison of plate theory and three-dimensional elasticity theorysolutions
A. Zucchini et al., Crack tip stress fields for thin, cracked plates in bending, shear and twisting: A comparison of plate theory and three-dimensional elasticity theorysolutions, INT J FRACT, 104(4), 2000, pp. 387-407
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 > 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 quad
ratically through the thickness as in plate theory, but are nearly constant
, except in the neighborhood of the free surface. Quadratic variation, as p
redicted by plate theory, is observed for r > h. Energy release rates based
on the Kirchhoff and Reissner theories agree well with those computed by m
eans of three dimensional finite element analyses.