Publications

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When metals plastically deform, the density of line defects called dislocations increases and the microstructure is continuously refined, leading to the strain hardening behavior. Using discrete dislocation dynamics simulations, we demonstrate the fundamental role of junction formation in connecting dislocation microstructure evolution and strain hardening in face-centered cubic (fcc) Cu. The dislocation network formed consists of line segments whose lengths closely follow an exponential distribution. This exponential distribution is a consequence of junction formation, which can be modeled as a one-dimensional Poisson process. According to the exponential distribution, two non-dimensional parameters control microstructure evolution, with the hardening rate dictated by the rate of stable junction formation. Among the types of junctions in fcc crystals, we find that glissile junctions make the dominant contribution to strain hardening.

Three-dimensional discrete dislocation dynamics methods (3D-DDD) have been developed to explicitly track the motion of individual dislocations under applied stress. At present, these methods are limited to plastic strains of about one percent or less due to high computational cost associated with the interactions between large numbers of dislocations. This limitation motivates the construction of minimalistic approaches to efficiently simulate the motion of dislocations for higher strains and longer time scales. In the present study, we propose geometrically projected discrete dislocation dynamics (GP-DDD), a method in which dislocation loops are modeled as geometrical objects that maintain their shape with a constant number of degrees of freedom as they expand. We present an example where rectangles composed of two screw and two edge dislocation segments are used for modeling gliding dislocation loops. We use this model to simulate single slip loading of copper and compare the results with detailed 3D-DDD simulations. We discuss the regimes in which GP-DDD is able to adequately capture the variation of the flow stress with strain rate in the single slip loading condition. A simulation using GP-DDD requires ∼40 times fewer degrees of freedom for a copper single slip loading case, thus reducing computational time and complexity.

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The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel–hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation’s line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank–Read source using discrete dislocation dynamics.

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A robust molecular-dynamics simulation method for calculating dislocation core energies has been developed. This method has unique advantages: It does not require artificial boundary conditions, is applicable for mixed dislocations, and can yield converged results regardless of the atomistic system size. Utilizing a high-fidelity bond order potential, we have applied this method in aluminium to calculate the dislocation core energy as a function of the angle β between the dislocation line and the Burgers vector. These calculations show that, for the face-centered-cubic aluminium explored, the dislocation core energy follows the same functional dependence on β as the dislocation elastic energy: Ec=Asin2β+Bcos2β, and this dependence is independent of temperature between 100 and 300 K. By further analyzing the energetics of an extended dislocation core, we elucidate the relationship between the core energy and the core radius of a perfect versus an extended dislocation. With our methodology, the dislocation core energy can accurately be accounted for in models of dislocation-mediated plasticity.

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Efficient time integration is a necessity for dislocation dynamics simulations of work hardening to achieve experimentally relevant strains. In this work, an efficient time integration scheme using a high order explicit method with time step subcycling and a newly-developed collision detection algorithm are evaluated. First, time integrator performance is examined for an annihilating Frank-Read source, showing the effects of dislocation line collision. The integrator with subcycling is found to significantly out-perform other integration schemes. The performance of the time integration and collision detection algorithms is then tested in a work hardening simulation. The new algorithms show a 100-fold speed-up relative to traditional schemes. Subcycling is shown to improve efficiency significantly while maintaining an accurate solution, and the new collision algorithm allows an arbitrarily large time step size without missing collisions.