Abstract : The AM1 superalloy blades of aeronautical High Pressure turbines are cooled by a complex system of micro-channels, located at the leading edge and near the trailing edge. These micro-channels constitute preferential sites for damage and crack initiation, phenomena which have to be taken into account in the design of turbine blades. The aim of this work was, first, to carry out an experimental study on perforated specimens with different hole diameters. The effect of the stress gradient on the crack initiation (300 µm criterion for the crack length) has been demonstrated qualitatively as well as quantitatively. However, the use of a maximum stress (or maximum strain) criterion is not sufficient as a failure criterion since it overestimates the risk of failure and does not take into account the length scale or geometrical effects. A volume average method has been proposed in order to take into account the stress gradient effect in the lifetime calculation. It has significantly improved the lifetime predictions. At the same time, an anisotropic fatigue damage model has been developed. In this model, plasticity is coupled with damage in order to describe the micro-initiation stage. The model identification and validation have been realised with respect to existing experimental data on unperforated samples and on the results of the experimental campaign carried out in this work, on perforated specimens. Finally, in order to take into account the stress gradients in the high stress concentration regions, the volume average method has been applied to the results obtained with the previously described model and has provided encouraging results.