Construction and justification of Paris-like fatigue laws from Dugdale-type cohesive models

Radhi Abdelmoula (1) , Jean-Jacques Marigo (2) , Thibaut Weller (3)

1 PMTM - Propriétés mécaniques et thermodynamiques des matériaux
2 LMS - Laboratoire de mécanique des solides
3 M3 - Modélisation Mathématique en Mécanique

We propose a construction of fatigue laws from cohesive forces models in the case of a crack submitted to a mode I cyclic loading. Taking the cumulated opening as the memory variable and the surface energy density associated with Dugdale's model, we explicitly construct the fatigue law which gives the crack growth rate by cycle d'/dN in terms of the stress intensity factor KI. In particular, we recover a Paris law with an exponent 4, i.e., d'/dN = CKI 4, when KI is small, the coefficient C being explicitly expressed in terms of the material parameters. Furthermore, the law can be applied in the full range of values of KI and can be extended to non simple cycles.

Mots clés: Fatigue; Fracture mechanics; Cohesive force; Cyclic loading; Variational approach; Complex analysis

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Radhi Abdelmoula, Jean-Jacques Marigo, Thibaut Weller. Construction and justification of Paris-like fatigue laws from Dugdale-type cohesive models. Annals of Solid and Structural Mechanics, 2010, 1, pp.139-158. ⟨10.1007/s12356-010-0011-3⟩. ⟨hal-00682995⟩