Elastic modeling of dislocations and solid solution strengthening in random alloys

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This manuscript gather my research activities focusing on dislocations and solid solution strengthening. These works have been conducted in Mateis laboratory (INSA-Lyon / CNRS) from 2018 to 2024, and benefited from a long and fruitful collaboration with David Rodney (ILM, Univ. Lyon 1 / CNRS). These research activities benefited from the following support:- A grant Impulsion from the University of Lyon IDEX (2019-2021) - 73 keuros over 2 years.- A JCJC ANR project INSPIRA (ANR-20-CE08-0019) (2021-2025) - 210 keuros over 5 years.Solid solution strengthened alloys of face-centered cubic structure (austenitic steels, 1xxx, 3xxx and 5xxx aluminum alloys) are widely used in many industrial applications due to their high yield strength, good fracture toughness and weldability. In these alloys, the random arrangement of solutes creates obstacles to the movement of dislocations, thereby increasing their flow stress. The recent development of high entropy alloys (HEA) - containing several elements in comparable quantities - takes full advantage of this solid solution strengthening mechanism to achieve exceptional mechanical properties. To model this solid solution hardening, we can distinguish two distinct approaches:(i) “Mean-field” models consider the elementary interactions between dislocations and solutes, and estimate a characteristic energy barrier. The flow stress is then defined as the stress to apply to overcome this barrier.(ii) Alternatively, we can consider that the dislocation interacts with a random force field originating from the solid solution. This point of view is fairly generic, and brings a number of situations under the same paradigm (crack front in a heterogeneous material, magnetic domain wall, fluid in a porous material, etc.). In particular, the study of the depinning transition in these systems has benefited from the development of methods derived from statistical physics.Viewpoint (i) allows the incorporation of dislocation/solute interactions parameterized from atomic calculations, but neglects the development of dislocation roughness with increasing applied stress. On the other hand, works related to viewpoint (ii) goes beyond some of these limitations; but their application to solid solution strengthening requires precise parametrization of the elastic behavior of the dislocation and the random force field emerging from the solid solution. The work described in this manuscript develops a multiscale approach of dislocations and their interactions with random solid solutions, thus bridging the gap between viewpoints (i) and (ii). The manuscript is organized as follows. First, a detailed description of these two points of view is first given in chapter 1. In chapter 2, the study of thermal fluctuations of dislocations and the comparison between atomistic calculations and analytical models allow parameterizing quantitatively a continuous description of dislocations. In particular, we propose a way of incorporating in a compact way the long-range elastic interactions characteristic of dislocations. Next, an elastic model of random solid solutions is proposed in chapter 3, based on the description of each solute atom as an elastic inclusion embedded in a continuous elastic medium. Statistical reasoning is then used to deduce the properties (variance and correlations) of the random force field acting on the dislocation. In particular, this force field is shown to display anisotropic correlations. In chapter 4, the evolution of dislocations in such an anisotropic stress field is studied by combining the results of chapters 2 and 3. This description enables better characterizing the development of the dislocation's roughness as a function of the applied stress, thus making it possible to exploit the methods and results of viewpoint (ii) and to discuss the assumptions underlying viewpoint (i). Finally, chapter 5 presents several outlooks for this work.

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