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

Abstract : 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.
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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, Springer Berlin Heidelberg, 2010, 1, pp.139-158. ⟨10.1007/s12356-010-0011-3⟩. ⟨hal-00682995⟩

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