The ʺstress intensity factorsʺ concept is known from Irwin (1948, 1957) who linked these to the energy release rate (crack extension force per unit length of the crack front) in the case of a crack in a two-dimensional crack analysis. In practice (to be used in three dimensions), the crack is viewed planar (Ox1x3) with a straight front running indefinitely in the x3-direction, perpendicular to the crack propagation x1-direction. In this situation, the utility of the stress intensity factor is apparent. For an arbitrary crack front in three dimensions, please see what follows.
What is the concept of the stress intensity factor as defined by Irwin and its utility?
The ʺstress intensity factorsʺ concept is known from Irwin (1948, 1957) who linked these to the energy release rate (crack extension force per unit length of the crack front) in the case of a crack in a two-dimensional crack analysis. In practice (to be used in three dimensions), the crack is viewed planar (Ox1x3) with a straight front running indefinitely in the x3-direction, perpendicular to the crack propagation x1-direction. In this situation, the utility of the stress intensity factor is apparent.
In the general case in three dimensions for a crack with arbitrary crack front, the goal is to reach the crack extension force G per unit length of the crack front. We just need to ask two questions:
(1) What is the definition of G?
(2) How to obtain the crack-tip stresses necessarily involved in the expression of G?
For (1) the definition of G, we may refer to Bilby and Eshelby (1968) or to our works (for the elliptical crack (see 2021) and the rough conoidal crack (2022), recently).
For (2), it is required to be able to calculate the matrix (6 components) of the stresses. We are using the idea that the crack-front is a dislocation (see our works on non-planar cracks). Hence, we need a clear modelling to proceed in practice. We know no other procedure.
Then you will discover the limitation of the concept of the stress intensity factors as defined by Irwin as being able to provide all the six stress components at the tip of the crack and their connexion with G.
The GIc method is already outdated by non linear plastic principles such as GF.
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