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A Critical Plane Theory For Multiaxial Fatigue of Elastomers
E. Verron, A. Andriyana, M. Aït-Bachir

Last modified: 2015-02-05

Abstract


In this paper, a critical plane theory dedicated to fatigue crack initiationin elastomers is derived. The approach is based on experimental observations whichstate that the initiation of a macroscopic fatigue crack results from the growth of smallflaws initially present in a bulk material. Our derivation is based on the definition of anidealized Representary Volume Element that consists in the distribution of small cracksin the bulk material. In order to solve the problem without considering singularities,these cracks are assimilated to material surfaces defined in the undeformed referenceconfiguration. With the help of the Configurational Mechanics theory, the virtualenergy release rate associated with all possible changes of position of all possiblematerial planes is derived to mimic the growth of small cracks. The critical plane, i.e.the plane in which the macroscopic crack will develop, is then defined as the materialplane that maximizes this quantity. A careful solving of the corresponding optimizationproblem establishes that the critical plane orientation is the eigenvector of theconfigurational (Eshelby) stress tensor associated with its smallest eigenvalues. Theapproach is illustrated on the simple problem of simultaneous tension and torsion forwhich we explicitly calculate fatigue crack orientation.

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