The Finite Element Method (FEM) has been and is one of the most
used numerical methods for the estimation of characterizing
parameters in Fracture Mechanics. In the case of Linear-Elastic
Fracture Mechanics (LEFM), a number of procedures exist which
allow the evaluation of the stress intensity factor K (or
equivalently, the energy release rate G) from a finite element
analysis (FE). This analysis has enabled to study crack
propagation and life estimation issues.

In recent years the application of Extend Finite Element Method
(X-FEM) has proved a very effective tool for numerical modelling
of cracks in MFEL, which provides significant benefits in the
numerical modelling of crack propagation. The main advantages are
that the finite element mesh need not comply with crack boundaries
to account for the lack of geometric continuity, and also, mesh
regeneration is not necessary in the crack growth simulations.
Therefore, a single mesh, which is often generated easily, can be
used for any crack length and orientation.

The contributions made in this Thesis are related to three
aspects: modelling of crack face contact with X-FEM, modelling of
the propagation direction in fretting fatigue with complete
contact and life estimation, also in complete contact. In the last
two cases, the numerical estimations have been correlated with
experimental results.

Some fatigue problems may exhibit situations of contact between
crack faces along the cycles, and therefore, cracks experience
contact closure processes between their faces. This Thesis will
utilize a mortar-based formulation to set the contact between the
crack faces. A segmentation of the crack is performed based on the
intersection with the underlying mesh. Also, the method X-FEM has
been implemented in the program ABAQUS, which has allowed to
implement the crack face contact routines in X-FEM through point
constraints and by the mortar method.

Moreover, crack initiation in fretting fatigue in complete contact
conditions (using multiaxial fatigue criteria) has been studied.
We have simulated the crack propagation path in its two phases
I/II using X-FEM, through the application of traditional
orientation criteria and other criteria proposed in this Thesis.

Finally, the effect of the values of KI obtained by X-FEM has
been studied. It has been compared with the values obtained
analytically for the life estimation in fretting fatigue in
conditions of complete contact, also studying the effect of
multiaxial fatigue criteria and the effect of propagation laws in
the life estimation.