Two scale damage model and related numerical issues for thermo-mechanical High Cycle Fatigue R. Desmorat 1 , A. Kane 1 , M. Seyedi 1 ∗ , J.P. Sermage 2 1 LMT-Cachan 61. avenue du Pr´ esident Wilson 94235 Cachan - FRANCE 2 EDF/R&D – LaMSID 1 avenue du G´ en´ eral de Gaulle F-92141 Clamart Cedex, France 15 janvier 2007 R´ esum´ e On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Ele- ment (RVE), a three-dimensional two scale damage model has been propo- sed for High Cycle Fatigue applications. It is extented here to anisothermal cases and then to thermo-mechanical fatigue. The modeling consists in the micromechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at microscale, altogether with Eshelby-Kr¨ oner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or anisothermal, mecha- nical, thermal or thermo-mechanical. A robust numerical scheme is propo- sed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE 2005) has been developped. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo- mechanical fatigue are detailed. 1 Introduction Various components of structures are subjected to thermo-mechanical loading during service. In nuclear power plants the operational feedback from PWRs has * now at BRGM, Orl´ eans, France 1 * Manuscript