Static and fatigue failure of quasi-brittle materials at a V-notch using a Dugdale model

The prediction of crack nucleation at stress concentration points in brittle and quasi-brittle materials may generally rely on either an Irwin-like criterion, involving a critical value of the generalized stress intensity factor of the singularity associated to the stress concentration, or on cohesive zone models. Leguillonʹs criterion enters the first category and combines an energy condition and a stress one. Thanks to matched asymptotics procedures, the associated numerical values at crack initiation under quasi-static monotonic loadings are shown to be comparable to those obtained using the Dugdale cohesive zone model. Both approaches are therefore adapted to the description of brittle and quasi-brittle fracture. A macroscopic Paris-like propagation law is derived from the Dugdale model through a relevant cumulating law at the microscopic scale of the process zone. Comparisons with experimental results are performed and display good agreement. The important matter of nucleation and growth of a fatigue crack at the root of a V-notch is finally addressed. A general Paris law featuring the elastic singularity exponent and then dependent on the V-notch angle can be expressed for small cyclic loadings in the early growth stage.