A non-singular continuum theory of dislocations

Three general expressions are presented: the first is the interaction energy between two non‐parallel straight dislocation segments, the second is the interaction energy between two parallel straight segments, and the third is the self‐energy of a straight segment. These can be used to determine the total energy of any dislocation configuration made up of piecewise straight segments. They differ from previous expressions in the literature primarily in that they are given completely in vector notation and in that the self‐energy includes a core traction term. The expressions are limited to the case of a linear, isotropic, infinite continuum. As an example, the formulas are applied to the case of a stacking‐fault tetrahedron.

Explicit expressions for the energy of dislocation configuration made up of piecewise straight segments

Theory of dislocation loops in multilayered anisotropic solids with magneto-electro-elastic couplings

The classical expression for the elastic self-stress and the elastic self-energy of dislocation loops in a linear elastic continuum by line integrals show singularities and require a cut-off distance p along the dislocation line. Somewhat different singularities exist in the core region of straight dislocation lines and require a cut-off radius r o perpendicular to the dislocation line. These singularities can be avoided when the singular Volterra dislocation line is replaced by a distribution of infinitesimal dislocations. The width of this distribution and the core energy E A cannot be derived from continuum theory but depends on the atomic arrangement in the crystal lattice. It is shown that by using the Peierls model and the concept of Peierls dislocations the values of r o and E A can be calculated for the different materials and physically realistic values for the cut-off parameters can be obtained.

Cálculo eficiente de las energías de formación de escalones dobles en materiales BCC

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.

Multiscale Modelling of Irradiation Induced Effects on the Plasticity of Fe and Fe-Cr

Three dimensional stress field expressions for straight dislocation segments

A comparison is made of the models of Bullough and Foreman [1], and of Kröner [2] and Jøssang et al. [3] for determining the self‐energy of a straight dislocation. The differences and their physical implications are pointed out. It is concluded that, from a physical point of view, the methods of Kröner and Jøssang et al. are the more correct ones. A discrepancy between the formula of Jøssang et al. [3] and that of de Wit [4] for the interaction energy between two straight dislocation segments is shown to disappear when an error in de Wit's formula is corrected.

A continuum theory is formulated to simultaneously address thermoelasticity, plasticity, and twinning in anisotropic single crystals subjected to arbitrarily large deformations. Dislocation glide and deformation twinning are dissipative mechanisms, while energy storage mechanisms associated with dislocation lines and twin boundaries are described via scalar internal state variables. In the inelastic regime, for highly symmetric orientations and rate independent shear strength, the Rankine–Hugoniot conditions and constitutive relations can be reduced to a set of algebraic equations to be solved for the material response. In a case study, the model describes the thermomechanical behavior of single crystals of alumina, i.e., sapphire. Resolved shear stresses necessary for glide or twin nucleation are estimated from nonlinear elastic calculations, theoretical considerations of Peierls barriers and stacking fault energies, and observations from both quasi-static and shock compression experiments. Residual elastic volume changes, predicted from nonlinear elastic considerations and approximated dislocation line energies, are positive and proportional to the dislocation line density and twin boundary area density. Analytical solutions to the planar shock problem are presented for c-axis compression of sapphire wherein rhombohedral twinning modes are activated.

Growing process of a dislocation emitted from a Frank-Read source in silicon is simulated using the 3-D Discrete Dislocation (DD) method. In the proposed method, any dislocation line is divided into a set of segments and each segment is moved both by the elastic interaction and under the crystallographic local rule in the Cellular Automata method(CA). In the present study, geometric change of the dislocation line, the self and interaction energy and stress distribution of the field are obtained.

A 3D model is presented that addresses an evolution of flexible dislocation lines at high temperatures. The model is based on the linear theory of elasticity. A smooth dislocation line is approximated by a piecewise curve composed of short straight dislocation segments. Each dislocation segment is acted upon by a Peach-Koehler force due to a local stress field. All segment-segment interactions as well as an externally applied stress are considered. A segment mobility is proportional to the Peach-Koehler force, temperature-dependent factors control climb and glide motion of the segments. The potential of the model is demonstrated in simulations of simple high temperature processes including interactions of dislocations with secondary particles.

Ionic liquids (ILs) hold great promise in many fields including energy storage and generation, mechanical, pharmaceutical, synthetic and separation applications to name just a few. For any given application, the desired physical properties of the ideal IL may differ substantially from others and no widely applicable patterns or trends to facilitate intuitive design. The origins of physical properties lie in the characteristics of the intermolecular energetics, which consist of a complex interplay between electrostatic and dispersion forces. This thesis investigates and develops computational methodologies for calculating a reliable description of the intermolecular interactions for this challenging class of solvents and electrolytes of the future. The electrostatic approximation used in classical molecular dynamics (MD) where atomic partial charges are assigned was investigated in terms of methods based on density matrix partitioning, and the restrained electrostatic potentials (RESP) approaches. It was found that the “geodesic” atomic partial charge scheme, part of the RESP family, produced the most accurate charges. This was measured in terms of (a) charge convergence with increasing basis set size; (b) charge invariance with changes to the coordinate system; (c) insensitivity to minor structural changes on the resulting charges; (d) adequate capture of charge transfer effects; and (e) the preservation of symmetric of charges in symmetric molecules. Although charges can vary dramatically depending on the scheme used, the careful use of atomic partial charge schemes may still produce reliable forcefields, or at least serve as a rapid diagnostic tool to quantify electrostatic interactions and charge transfer. In moving towards unbiased a priori descriptions of IL intermolecular interactions, second-order Moller-Plesset perturbation theory (MP2) was used with the linear-scaling fragment molecular orbital (FMO) framework to assess the extent to which dispersion forces play a role in the intermolecular energetics. ILs of increasing size were examined such that the many-body effects may be captured. The dispersion energy contribution formed up to 20% of the total interaction energy. Furthermore, the interaction energy as produced by FMO was within 1 kJ mol−1 of the full-wavefunction MP2 interaction energy when three-body effects were included. As the dispersion interaction is purely a quantum mechanical phenomenon, correlated quantum mechanical methods, such as MP2 or coupled-cluster approaches, are required to provide an unbiased account of these effects. Ab initio methods such as MP2 and CCSD(T) scale formally as N⁵ an N⁷, respectively, with chemical system size. While the FMO approach provides a marked improvement in efficiency, the counterpoise (CP) approach to correcting the basis set superposition error (BSSE) is not amenable to fragmented approaches and requires each ion in the cluster to be calculated in the basis set of the entire system. In order to remove this bottleneck, the spin-component scaled second-order Moller Plesset perturbation theory (SCS-MP2) methodology was refined by fitting 174 non-CP corrected interaction energies at the MP2/cc-pVTZ level of theory to CP corrected CCSD(T)/CBS benchmark energies. This has resulted in an implicit BSSE correction that may be used within the highly efficient FMO framework, and is shown to yield results on par with or exceeding the accuracy of MP2/cc-pVQZ for clusters of two and four ion pairs (IPs). This new approach as been termed SCS-IL-MP2. An alternative dispersion corrected density functional theory (DFT) approach, DFT- D3, was assessed and refined in view of producing accurate interaction energies at the same CCSD(T)/CBS quality. The same test set of 174 ILs was used to fit the SCS-IL-MP2 approach was used to refit the DFT-D3 approach for both the Hartree-Fock (HF) wavefunction and the PBE and BLYP density functionals (DFs). In most cases, the selection of the DF and associated DFT-D version 3 (DFT-D3) parameters differed negligibly with all reaching within 1 to 2 kJ mol−1 per IP. HF-D3 parameters, on the other hand, showed a substantial improvement, particularly when used with the Becke-Johnson (BJ) damping function. Refitted HF-D3 and the BJ damping function was able to consistently provide interaction energy errors below 5 kJ mol−1 per IP. It would be worthwhile further investigating the application of the refined HF-D3 in its ability to produce reliable energies and geometries over a more diverse set of ILs. Both the SCS-IL-MP2 and new DFT-D3 approaches may be applied to the highly scal- able FMO framework. These form the core elements of the quantum chemistry toolbox for the study and understanding of the physicochemical properties of ILs that have so far been only superficially characterised by electronic structure theory. From this starting point, a rigorous and unbiased a priori understanding of the intermolecular interactions and resulting physicochemical properties may be predicted by means of efficient ab initio molecular dynamics (AIMD) techniques.

Structure and energy of (1 1 1) low-angle twist boundaries in Al, Cu and Ni

The detrimental effects of the H on the mechanical properties of the metals are known for more than a century. One of the most important degradation mechanisms is H embrittlement (HE). In this thesis, we examined a few famous proposed mechanisms in the field by performing careful atomistic simulations. Moreover, novel mechanisms which can be responsible for HE process in metals are demonstrated in this work. First, we used atomistic simulations to investigate the effects of segregated H on the behavior of cracks along various symmetric tilt grain boundaries in fcc Nickel. Mode I fracture behavior is then studied, examining the influence of H in altering the competition between dislocation emission (“ductile” behavior) and cleavage fracture (“brittle” behavior) for intergranular cracks. Simulations revealed that the embrittling effects of H atoms are limited. We examined the effect of H atoms on the nucleation of intergranular cracks in Ni. The theoretical strengths are $\sim$ 25 GPa and the yield strengths are $\sim$ 10 GPa, so that (i) the theoretical strength is always well above the yield strength, with or without H, and (ii) both strengths are far above the bulk plastic flow stress, $\sigma_y^B$ of Ni and Ni alloys. So H does not significantly facilitate nucleation of intergranular cracks. We performed simulations of the interactions between dislocations, H atoms, and vacancies to assess the viability of a recently-proposed mechanism for the formation of nanoscale voids in Fe-based steels in the presence of H. The effectiveness of annihilation/reduction processes is not reduced by the presence of H in the vacancy clusters because typical V-H cluster binding energies are much lower than the vacancy formation energy, except at very high H content in the cluster. Experimental observations of nanovoids on the fracture surfaces of steels must be due to as-yet undetermined processes. The possible strengthening effects of H atoms in metals at low temperature is examined via the solute strengthening (SS) theory. The results of the SS theory can explain recent experimental observations of strengthening of H-charged polycrystalline nickel at low temperature. Moreover, the possible softening/hardening effects of H atoms due to their interaction with the pre-existing with solutes are demonstrated and for the first time, a softening process in nickel alloys is shown. The effect of the H atoms in increasing the precipitate hardening in $\alpha$-Iron is also shown in this thesis. The direct molecular dynamics simulations of the bow out of an edge dislocation in H-free and H-charged samples reveals that the presence of H atoms decreases the magnitude of the bow out of the dislocation. The hardening effect of H on the interaction of dislocations and grain boundaries in nickel is also investigated in this thesis. To this end, we simulated the interaction of mixed and screw dislocations with the grain boundaries that have access to the slip planes in nickel. The presence of H atoms along the grain boundaries induces stress in the neighborhood of the grain boundary. These stress fields can repel/attract mixed dislocations while the screw dislocations are not interacting with them. The simulation of the interaction of the mixed dislocations with the H-free and H-charged GBs shows hardening due to the presence of H atoms. The simulations of the screw dislocations do not show significant hardening due to the presence of this stress fi