Simulation numérique de l'initiation de la rupture à l'échelle atomique

Abstract : In mechanical engineering, failure is a risk that must be anticipated and is still a threat for structures. The failure of pre-cracked systems occurs when the energy released by the propagation of the pre-existing crack exceeds a critical threshold (Griffith's energy release rate) which represents a property of the material. On the contrary, the failure of systems without pre-existing defects occurs when the applied stress reaches the strength, also property of the material. The existence of two criteria for failure suggests different driving mechanisms, which raises the question of intermediate cases with moderate stress concentrations. Different existing approaches are consistent with the two limit cases but there is no clear consensus in the scientific community.In this work, we study the mechanisms of brittle failure on the atomic scale in order to understand the underlying physical mechanisms. Macroscopic failure comes from the breaking of bonds at the atomic scale. We therefore use molecular simulation techniques to study the elementary physics of brittle failure initiation. Two types of atomic structure are studied. The first one is a triangular lattice toy model whose simplicity allows precise analytical interpretation of the molecular simulation results. The study is extended to a more realistic system: graphene. This material, which has a high strength and a rather low toughness in comparison, has one of the smallest process zones compared to other brittle materials, which makes it possible to apply the concepts of brittle failure up to the nanometric scale of molecular simulation. We first investigate the failure of materials at 0K. At this temperature, an atomic system is in static equilibrium. The breaking of bonds can be treated as instability. The analysis of the energy profile of the atomic system provides a means of identifying the mechanisms of failure. We show that we can identify failure initiation by looking for negative or zero eigenvalues of the Hessian matrix. The corresponding eigenvectors indicate the modes of failure and show the appearance of transition bands between motions of groups of atoms for intact systems, whose width recalls the size of the process zone, generally introduced in macroscopic theories of failure initiation. We also study the effect of defects on the instability modes and their degeneracy. This study provides a general technique to capture fracture initiation mechanisms irrespective of the stress concentration in the structure. We focus afterwards on finite temperatures. We study the combined effects of temperature, system size and loading rate. Starting from the kinetic theory, we identify general scaling laws providing a size-loading rate-temperature equivalence and relating the strength and toughness to the limit at 0K. The difference between the scaling law of strength and that of toughness lies in the fact that failure is not sensitive to the size of the pre-cracked system but to the number of crack tips. This indicates an essential statistical difference between strength and fracture failures which makes it possible to better understand the transition from one to the other.In order to better understand the transition between the two types of failure, we treat the case of elliptic holes with different aspect ratios and we focus at the same time on the effect of this transition on instability modes. We study in the last part the case of non-periodic structures with free surfaces. We determine the various parameters characterizing this situation and the effect of the presence of surface phenomena on instability modes
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Sabri Souguir. Simulation numérique de l'initiation de la rupture à l'échelle atomique. Matériaux. Université Paris-Est, 2018. Français. ⟨NNT : 2018PESC1082⟩. ⟨tel-02137493⟩

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