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            <funder>The authors are grateful for financial support from Agence Nationale de la Recherche France ANR-09-BLAN-0025-01 and to company Griset for supplying copper. The authors thank also very much Professor Haël Mughrabi for the scientific discussions.</funder>
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                <term xml:lang="en">finite element</term>
                <term xml:lang="en">anisotropic elastic crystallinne</term>
                <term xml:lang="en">slip band</term>
                <term xml:lang="en">Very high cycle fatigue</term>
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              <p>The DISFAT project is a French project financially supported by the French National Agency for Research (ANR). It aims at a deeper understanding of mechanisms leading to crack initiation in metals and alloys under Very High Cycle Fatigue loading (VHCF). The VHCF regime is associated with stress magnitudes lower than the conventional fatigue limit and as a result, numbers of cycles higher than 109. Tests were carried out using an ultrasonic technique at loading frequency of 20 kHz. In the case of pure copper polycrystals, we previously showed that slip band (SB) activity and intrinsic dissipation were closely related.Dissipation and slip band amount increased with the number of cycles. At very small stress amplitudes, no slip band appeared at the specimen surface up to 108 cycles but the material was found to dissipate energy. These results revealed that the material never reached a steady state and so could break at higher number of cycles. In this paper, the morphology and the location of slip bands were characterized. Different types of slip bands depending on the stress amplitudes appeared at the specimen surface. The stress amplitude required to show the first slip bands decreases with the number of cycles. It is twice lower than the stress amplitude required to break the specimen for the same number of cycles. At the smallest stress amplitudes, slip bands were mostly found at twin boundaries. Quasi 3D finite element simulations taking into account the polycrystalline nature of the material emphasized the key role of the elastic anisotropy in slip band initiation. A criterion for slip band appearance was finally proposed.</p>
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