  In a recent very interesting and illuminating proposal, Yao et al. (2014)
have discussed the use of the strain energy release rate (SERR) as a parameter
to characterize fatigue delamination growth in composite materials. They
consider fatigue delamination data strongly affected by R-curve behaviour due
to fibres bridging and argue that a better approach is to correlate the crack
advance with the total work per cycle measured in the testing machine. This
seems to work better than estimating the compliance as a linear fit of
experimental curves from Modified Compliance Calibration ASTM standards
equations for the SERR in the classical Linear Elastic Fracture Mechanics
framework. We show however that if we assume indeed linear behaviour (i.e.
LEFM), the approach they introduce is perfectly equivalent to the SERR one,
i.e. Paris type of laws. As well known form Barenblatt and Botvina, fatigue
crack growth is a weak form of scaling, and it gives Paris classical dependence
only when the crack is much longer than any other characteristic sizes. Paris'
law is not a fundamental law of physics, is not an energy balance equation like
Griffith, and strong size effects due to cohesive zones have been found already
in concrete by Bazant. The proposal is very simple, and interesting as it would
seem to suggest that a proper scaling with a cohesive model at crack tip could
be predicted, although this doesn't seem to have been attempted in the
Literature. The main drawback of the present proposal is that it is not
predictive, but purely observational, as it requires the actual measurement of
work input during the fatigue process.
