Investigation des effets de taille dans le cadre de plasticité crystalline à gradient

At mesoscopic scales, typically between hundreds of nanometers and a few tens of micrometers, numerous studies have revealed size effects on the inelastic behavior of metallic materials. In fact, the smaller the specimen size, the higher the macroscopic stress response. This results in the general expression, emph{smaller is stronger}. Given the exponential trend towards miniaturization, the correct modeling of these effects has become a necessity in many fields of engineering. Classical plasticity theories, which consider only the displacements as degrees of freedom (DOF) and do not include internal length scale(s), are unable to reproduce these effects. To overcome this limitation, approaches within the mechanics of generalized continuum media, which incorporate the addition of extra DOF have been proposed in the literature. Such approaches include strain gradient (crystal) plasticity (SGCP) theories, in which one (or more) plastic variable is also utilized as a DOF. These approaches are able to take into account the gradient of plastic deformations, which has been experimentally shown to be related to size effects. Thanks to their interesting features, these theories have attracted a great deal of scientific interest in recent years, leading to the development of numerous SGP models. Nevertheless, most of these models exhibit peculiar size effects under specific , under specific non-proportional loading conditions. These include the emergence of "elastic gaps", which refer to a delay in plastic flow following an infinitesimal change in boundary conditions. The existence of these "elastic gaps" has not been substantiated by experimental evidence, and their physical nature remains a subject of debate.In this thesis, we propose to investigate the physical nature of certain size effects, in particular "elastic gaps", and to provide an improved description of plasticity at small-scales. To this end, original small-scale experiments, involving for the first time non-proportional loading, as well as advanced simulations based on discrete dislocation dynamics (DDD), have been carried out. First, we demonstrate that the DDD model predicts the experimentally observed size effects for proportional loading, thereby validating our methodology with DDD. The increase in yield stress and the presence of Asaro's type III kinematic hardening were discussed. This numerical DDD approach was then used to demonstrate, for the first time in the context of non-proportional loading types of the tension-bending (tension is maintained during bending), tension-passivation or bending-passivation, that "elastic gaps" might not be physical. These numerical results were then employed to develop gradient-enhanced crystal plasticity models. In a second step, based on the DDD results, an improvement of an existing SGCP model, which uses plastic slips as an additional DOFs and avoids "elastic gaps", is proposed. Analytical solutions for shear problems have been presented. High-order kinematic hardening modeling is discussed. We have shown that the model faithfully replicates the various features of the DDD results. One shortcoming of the model is the order of magnitude of the evolution of the yield stress as a function of the size of the studied domain. This aspect is addressed by a micromorphic approach proposed later. In this context, high-order dissipative terms have also been introduced for the first time. Finally, small-scale experimental tests have been reported. Using proportional (simple) tension and bending tests, size effects have been observed. Concerning non-proportional tension-bending loading, further analysis and improvements are required in order to conclude from an experimental point of view on the "elastic gaps".