Parallel TREE code for two-component ultracold plasma analysis

The TREE method has been widely used for long-range interaction {\it N}-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The program efficiently handles millions of particles evolved over long relaxation times requiring millions of time steps. Appropriate domain decomposition and dynamic data management were employed, and large-scale parallel processing was achieved using an intermediate level of granularity of domain decomposition and ghost TREE communication. Even though the computational load is not fully distributed in fine grains, high parallel efficiency was achieved for ultracold plasma systems of charged particles. As an application, we performed simulations of an ultracold neutral plasma with a half million particles and a half million time steps. For the long temporal trajectories of relaxation between heavy ions and light electrons, large configurations of ultracold plasmas can now be investigated, which was not possible in past studies

Statistical Thermodynamics of Dislocations in Solids

This review is a simplified summary of the thermodynamic dislocation theory, with special emphasis on the role of an effective temperature. Materials scientists, for decades, have asserted that statistical thermodynamics is not applicable to dislocations. By use of simple, first-principles analyses and comparisons with experimental data, I argue that these scientists have been wrong, and that this venerable field urgently needs to be revitalized because of its wide-ranging fundamental and technological importance. In addition to describing recent progress in understanding strain hardening, yielding, shear banding, and the like, I argue that the thermodynamic dislocation theory can lead to a much needed, first-principles understanding of brittle and ductile fracture in crystalline solids.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0028

Discrete dislocation dynamics modelling of mechanical deformation of nickel-based single crystal superalloys

Discrete dislocation dynamics (DDD) has been used to model the deformation of nickelbased single crystal superalloys with a high volume fraction of precipitates at high temperature. A representative volume cell (RVC), comprising of both the precipitate and the matrix phase, was employed in the simulation where a periodic boundary condition was applied. The dislocation Frank–Read sources were randomly assigned with an initial density on the 12 octahedral slip systems in the matrix channel. Precipitate shearing by superdislocations was modelled using a back force model, and the coherency stress was considered by applying an initial internal stress field. Strain-controlled loading was applied to the RVC in the [0 0 1] direction. In addition to dislocation structure and density evolution, global stress–strain responses were also modelled considering the influence of precipitate shearing, precipitate morphology, internal microstructure scale (channel width and precipitate size) and coherency stress. A three-stage stress–strain response observed in the experiments was modelled when precipitate shearing by superdislocations was considered. The polarised dislocation structure deposited on the precipitate/matrix interface was found to be the dominant strain hardening mechanism. Internal microstructure size, precipitate shape and arrangement can significantly affect the deformation of the single crystal superalloy by changing the constraint effect and dislocation mobility. The coherency stress field has a negligible influence on the stress–strain response, at least for cuboidal precipitates considered in the simulation. Preliminary work was also carried out to simulate the cyclic deformation in a single crystal Ni-based superalloy using the DDD model, although no cyclic hardening or softening was captured due to the lack of precipitate shearing and dislocation cross slip for the applied strain considered

Dislocation dynamics simulations of plasticity at small scales

As metallic structures and devices are being created on a dimension comparable to the length scales of the underlying dislocation microstructures, the mechanical properties of them change drastically. Since such small structures are increasingly common in modern technologies, there is an emergent need to understand the critical roles of elasticity, plasticity, and fracture in small structures. Dislocation dynamics (DD) simulations, in which the dislocations are the simulated entities, offer a way to extend length scales beyond those of atomistic simulations and the results from DD simulations can be directly compared with the micromechanical tests. The primary objective of this research is to use 3-D DD simulations to study the plastic deformation of nano- and micro-scale materials and understand the correlation between dislocation motion, interactions and the mechanical response. Specifically, to identify what critical events (i.e., dislocation multiplication, cross-slip, storage, nucleation, junction and dipole formation, pinning etc.) determine the deformation response and how these change from bulk behavior as the system decreases in size and correlate and improve our current knowledge of bulk plasticity with the knowledge gained from the direct observations of small-scale plasticity. Our simulation results on single crystal micropillars and polycrystalline thin films can march the experiment results well and capture the essential features in small-scale plasticity. Furthermore, several simple and accurate models have been developed following our simulation results and can reasonably predict the plastic behavior of small scale materials

Line-integral representations of the displacement and stress fields due to an arbitrary Volterra dislocation loop in a transversely isotropic elastic full space

AbstractTransversely isotropic materials or hexagonal crystals are commonly utilized in various engineering fields; however, dislocation solutions for such special materials have not been fully developed. In this paper, we present a comprehensive study on this important topic, where only Volterra dislocations of the translational type are considered. Based on the potential theory of linear elasticity, we extend the well-known Burgers displacement equation for an arbitrarily shaped dislocation loop in an isotropic elastic full space to the transversely isotropic case. Both the induced displacements and stresses are expressed uniformly in terms of simple and explicit line integrals along the dislocation loop. We introduce three quasi solid angles to describe the displacement discontinuities over the dislocation surface and extract a simple step function out of these angles to characterize the dependence of the displacements on the configuration of the dislocation surface. We also give a new explicit formula for calculating accurately and efficiently the traditional solid angle of an arbitrary polygonal dislocation loop. From the present line-integral representations, exact closed-form solutions in terms of elementary functions are further obtained in a unified way for the displacement and stress fields due to a straight dislocation segment of arbitrary orientation. The non-uniqueness of the elastic field solution due to an open dislocation segment is rigorously discussed and demonstrated. For a circular dislocation loop parallel to the plane of isotropy, a new explicit expression of the induced elastic field is presented in terms of complete elliptic integrals. Several numerical examples are also provided as illustration and verification of the derived dislocation solutions, which further show the importance of material anisotropy on the dislocation-induced elastic field, and reveal the non-uniqueness feature of the elastic field due to a straight dislocation segment

Line-integral representations for the elastic displacements, stresses and interaction energy of arbitrary dislocation loops in transversely isotropic bimaterials

AbstractThe elastic displacements, stresses and interaction energy of arbitrarily shaped dislocation loops with general Burgers vectors in transversely isotropic bimaterials (i.e. joined half-spaces) are expressed in terms of simple line integrals for the first time. These expressions are very similar to their isotropic full-space counterparts in the literature and can be easily incorporated into three-dimensional (3D) dislocation dynamics (DD) simulations for hexagonal crystals with interfaces/surfaces. All possible degenerate cases, e.g. isotropic bimaterials and isotropic half-space, are considered in detail. The singularities intrinsic to the classical continuum theory of dislocations are removed by spreading the Burgers vector anisotropically around every point on the dislocation line according to three particular spreading functions. This non-singular treatment guarantees the equivalence among different versions of the energy formulae and their consistency with the stress formula presented in this paper. Several numerical examples are provided as verification of the derived dislocation solutions, which further show significant influence of material anisotropy and bimaterial interface on the elastic fields and interaction energy of dislocation loops