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A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method. (English) Zbl 1173.74385
Summary: A fatigue crack model addressing frictional contact along crack faces and multi-axial non-proportional sollicitations is proposed. In this respect, an X-FEM numerical model coupled with unilateral contact with friction is presented within the linear elastic fracture mechanics framework (LEFM). Hysteresis effects are addressed through an incremental formulation. Furthermore, a modified LATIN iterative solver and a local convergence indicator adapted for the frictional contact problem are proposed. It ensures the local convergence of the normal and tangential problems independently. A generalized expression for the \(J\)-integral under frictional contact conditions is derived. In the same way, a path-independent domain interaction integral is implemented in order to extract the mode I and mode II stress intensity factors. The crack propagation direction is predicted according to Hourlier’s criterion adapted to multi-axial non-proportional sollicitations. Crack growth predictions are presented for three fatigue crack lengths under rolling contact loading. Stress intensity factors (SIF) are computed and the crack growth direction is determined. These numerical results agree quantitatively with previous results obtained according to a reference model.

MSC:
74R10 Brittle fracture
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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