Limiting conditions for a crack to initiate are, in practice, calibrated by means of a characteristic value of mode I stress intensity factor, which is experimentally determined through generally accepted procedures [1]. This critical value shows considerable variation when measured in plane stress or plane strain specimen geometries. Namely, plane stress critical stress intensity factor Ko has, roughly speaking, a value three times higher than that of plane strain critical stress intensity factor K~, as it is indicated in the typical curve of Fig. 1. This difference cannot be attributed to a kind of scaling effects since, at least in the case of plane strain conditions, experiments with specimens of considerably different dimensions give the same value of K~o.It would be worthless if we could avoid the use of critical stress intensity factors for the development and calibration of fracture criteria, where K~o and Ko play the role of a "failure parameter" characterizing the respective material. The presence of such a failure parameter is absolutely necessary in the mathematical formulation of any criterion. Otherwise failure of materials could be considered as a phenomenon quantitatively unique and independent from the nature of materials.Critical stress intensity factors cannot play the role of such a failure parameter exactly because their value shows a dependence on geometric factors like specimen thickness in case of plane stress and plane strain conditions. If critical stress intensity factors could serve as failure parameters (i.e., one of the mechanical properties of materials) then specimen thickness could also be considered as a material property! The question arising now is whether or not a failure parameter is hidden behind the variable behavior of critical stress intensity factors. In other words, does a mechanical quantity exposing the same value at the moment of crack initiation, regardless of the assumed plane stress or plane strain conditions, exist? If yes, then this quantity is the required failure parameter and critical SIFs vary from plane stress to plane strain in order for the material to achieve the same (critical) level of this quantity.
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