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Nanomécanique des champs de défauts cristallins

Abstract : The research activities presented in this manuscript essentially concern the deve- lopment of theoretical models and numerical methods for the investigation of plastic deformation mediated by dislocations and by interfaces, such as grain boundaries, at the nanometric scale. The proposed continuum mechanics models constitute ex- tensions of a field dislocation mechanics theory that will be recalled in the first chapter, along with applications to dislocation core structures and to piezoelectric media. In the second chapter, we present an elastoplastic model of disclination and dislocation fields. The introduction of disclinations in a higher order model that considers elastic curvatures and couple stresses, allows rendering rotation disconti- nuities, which makes the theory appealing for studying grain boundary type defects. In this manuscript, we essentially present research conducted on the core structures and elastic fields of tilt grain boundaries, as well as interface mediated plasticity mechanisms, in particular shear coupled boundary migration. Although this model is used at an interatomic spatial resolution, it remains continuous and allows cap- turing the spatial evolution of elastic curvatures at the core of crystal defects. We also show how the transport equations that govern the evolution of defect densities allow predicting the evolution of grain boundaries and the associated plasticity. In the third chapter, we present spectral methods developed to numerically solve the equations of the field dislocation mechanics model. The proposed methods are an alternative to finite element techniques and consist in solving the equations in the Fourier space. Because the calculation of Fourier transforms uses fast algorithms and the convolution integrals involved in the balance of stresses become simple products in the Fourier space, these spectral approaches are numerically very attractive. It is however important to take care of numerical stability and accuracy issues. In this manuscript, we present methods developed for stable and accurate solutions of the static equations of the field dislocation mechanics model. We then present a spectral method devoted to the solution of the dislocation density transport equation. In the fourth and last chapter, we present a summary and perspectives related to these research activities.
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Submitted on : Wednesday, October 30, 2019 - 3:07:18 PM
Last modification on : Wednesday, November 3, 2021 - 8:56:31 AM


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Taupin Vincent. Nanomécanique des champs de défauts cristallins. Mécanique des matériaux [physics.class-ph]. Université de Lorraine; Ecole Doctorale C2MP, 2019. ⟨tel-02339226⟩



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