Seminar of Prof. Anthony Gravouil, INSA Lyon, Dec. 16th, 2012

Three-dimensional crack growth simulations require both an accurate geometrical modeling of the crack and front shapes and a precise quantification of interface displacement and traction fields. Tribological fatigue like rolling fatigue, fretting fatigue involve three-dimensional crack problems in which the interfacial crack behavior is mainly governed by complex sequences of contact/friction states. In this context, enriched finite element methods (coupled for instance with a level set modeling of the possible non-planar crack shape) are very well suited to model discontinuous physical behaviors independently of a given initial mesh. These enrichments avoid the mesh compatibility of the crack with the bulk, the remeshing and the field interpolation when dealing with crack propagation modeling. However, many cases require to impose constraints on the enriched interfaces: Dirichlet boundary conditions, contact or frictional interfaces, etc... Unfortunately, imposing these constraints involves two drawbacks: On the one hand, it imposes to discretize the crack interface to address displacement and traction fields using interface elements based on bulk finite elements cut by the crack. Hence it involves a mesh dependency between the interface and the bulk. This work presents the key procedures to undertake the crack face contact problem when using X-FEM under a global-local approach. The use of the locally two-scale approach in a three field weak formulation ensures that sufficiently refined crack faces can be incorporated into the numerical models, avoiding an unaffordable refinement of the bulk mesh at the component level and thus keeping the spirit of the X-FEM. The need of the stabilization for the solution in the contact tractions is evidenced, especially for contact problems where sliding is important. For that purpose, a dedicated non-linear solver is introduced. A thorough numerical verification of the pro- posed methodology is presented. The combination of the three-scale X-FEM model and the non-linear solver enables the accurate resolution of the crack face frictional contact with a low computational cost and good stability properties. The application of the procedure to a 3D fretting fatigue test is then presented. The correlation with experimental testing is performed, taking into consideration the actual crack resulting from the tests by means of automated 3D crack geometry reconstruction. The contact state evolution is presented and gives an idea of the potential of the methodology developed, which is capable of analyzing several cracks simultaneously with high accuracy while keeping a reasonable computational cost thanks to the multi-scale approach. Such an approach can also be applied to a wide range of engineering applications implying complex frictional effects on 3D crack propagation