Fatigue

Engineering etiquette dictates that a Paris’ type phenomenology replace Griffith’s model whenever “long” time crack propagation is contemplated; see (Paris et al., 1961). The substitution remains unmotivated in the literature, with the exception of a few numerical experiments in the cohesive framework, as in (Nguyen et al, 2001) or in (Roe and Siegmund, 2002). The Paris’ type models are difficult to calibrate and the apportionment of the relevant quantities among such contributing factors as material properties, geometry and loads is at best a perilous exercise.

In contrast, we propose to derive Paris’ type fatigue laws as a time asymptotics of the variational model. The three necessary ingredients are by now familiar to all surviving readers: a minimality principle, a cohesive type surface energy and irreversibility. The argument is most easily illustrated on a one-dimensional peeling test; the proofs of all statements in this section can be found in great details in (Jaubert, 2006), (Jaubert and Marigo, 2006). More general settings could be envisioned at the expense of mathematical rigor.