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A novel approach, based on the tensor character of the stress intensity at the crack
front, is presented with the aim of correlating the influence of typical in- and outof-
plane constraint cases to the apparent fracture toughness of materials under
mode-I loading in the scope of the LEFM. The analysis demonstrates the
invariability of the stress intensity tensor ij k at the crack front, irrespective of the
specimen thickness, and the necessity of considering, additionally, the constraint
tensor ij t , corresponding to the second constant term in Williams expansion to
explain the different fracture toughnesses resulting from the loss of constraint.
Both components of tij , the xx t , or conventional T-stress, and the out-of-plane
component zz t are evaluated under different constraint conditions showing, in
general, higher values for zz t than for xx t , notably for min B < B . The approach
proposed represents an extension of the current biparametric approach, based on
the T-stress that proves to be only capable to cope with in-plane constraint cases.