Insight on physical meaning of finite-width-correction factors in stress intensity factor (K) solutions of fracture mechanics

Abstract

The physical meaning of the finite-width-correction factors (FWCF), which commonly appear in stress intensity factor solutions of fracture mechanics, is mysterious. The present work is an attempt to resolve this mystery. Specifically, it is shown that for the middle-crack-tension (M(T)) specimen and for the embedded-circular-crack in a specimen of round cross-section, the FWCF factor is related to the average net-section stress for a given crack size. An increase in K at the crack tip means an increase in the average net-section stress ahead of the crack, in addition to the increase in the level of normal stress in the near-tip (or singularity-dominated) zone of fracture mechanics. It is also shown that this increase in net-section stress can be determined, in a straightforward manner, using a simple approach based on strength of materials (SOM). The agreement between the net-section stress determined from the strength of materials approach and that from fracture mechanics is surprisingly good. This connection between the finite-width-correction factor and the net-section stress has not been demonstrated before, and, hence it provides a new point of view to analyze fracture mechanics problems. More importantly, the connection validates the correlation of fatigue crack growth on the basis of the change in the net-section cyclic strain energy, which has recently been demonstrated by the author elsewhere.