A great number of industrial thermo-mechanical systems are facing today transitory regimes with different speeds according to the functioning frequencies. Enhancing their performance imposes the use of new materials of different types; multimaterials is a good example. In fact, these new materials may be constituted of different layers where the layers are associated together in a way to enhance the mechanical and thermal behavior of the system. They may be also constituted of a substrate dressed by a succession of slim layers obtained by thermal projection.In a given system, the constituting materials are generally subject to cyclic thermal or mechanical solicitations. It is very important to know at best their thermomechanical behavior in elastic and plastic regimes. Therefore, the study done during this thesis work, limited here uniquely to periodical solicitations resulting from thermal sources, deals with the evolution of the damage of these materials under multiple forms of thermal fatigue in plastic and elastic functioning regimes.The imposed solicitations are obtained from a periodical thermal source (rectangular, triangular and sinusoidal form). The thermal loss resulting from the convection is also considered. On the mechanical side, the material is considered fixed on one of its extremities and free on the other one (subject to strain). The mechanical stress and strain in the material come essentially from the differences between the coefficients of thermal dilation and the gradient of temperature in the material. The transitory and variable thermal behavior of the material permits to track the evolution and the distribution of the stress and strain in the material.The study of the damage is performed according the given case, either using models directly established from the thermomechanical elastic behavior, or using models that need a thermo-elastoplastic study. In the two cases, and because the majority of damage models (Lemaître and Chaboche) seen in the literature are valid and can be applied only to uniform and homogeneous materials, a research of an equivalent material to the studied multi-material was necessary. The equivalency between the real material and the equivalent one is based mainly on thermal equivalent criteria. The study provides in the two cases the damage evolution in the multimaterial function of the geometric parameters, depending on the form of the imposed thermal solicitations such as the heat transfer coefficient, the amplitude, the period and the shape of the imposed thermal flow.An application of these models to an internal combustion engine is proposed at the end of this thesis. It gives a prediction of the number of cycles (lifetime) of the cylinder of the engine depending on the used functioning conditions.
