Three-dimensional evaluation of the T-stress in centre cracked plates

Thick three-dimensional (3-D) finite element models of centre cracked plates are used to study the variation in the biaxiality factor with the crack aspect ratio a/w. The use of two widely accepted methods to evaluate the T-stress in two-dimensions, namely the boundary layer method and the displacement field method, to calculate the T-stress in three-dimensions is studied. It is shown that the boundary layer method gives results that compare rather well with the two-dimensional plane strain values (maximum difference of 6 percent), while the displacement field method results are about 15 percent lower. Two parameters are shown to affect the three-dimensional evaluation of the biaxiality factor, namely the material's Poisson's ratio and the specimen's thickness t. The biaxiality factor is directly proportional to and inversely proportional to t. Three-dimensional analysis is required to assess correctly the effect of and t on .