The interaction of C atoms with a screw and an edge dislocation is modelled at an atomic scale using an empirical Fe-C interatomic potential based on the Embedded Atom Method (EAM) and molecular statics simulations. Results of atomic simulations are compared with predictions of elasticity theory. It is shown that a quantitative agreement can be obtained between both modelling techniques as long as anisotropic elastic calculations are performed and both the dilatation and the tetragonal distortion induced by the C interstitial are considered. Using isotropic elasticity allows to predict the main trends of the interaction and considering only the interstitial dilatation will lead to a wrong interaction.
Non-singular dislocation continuum theories are studied. A comparison between Peierls-Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analyzed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realist…
The interaction between vacancies and edge dislocations in face centered cubic metals (Al, Au, Cu, Ni) is studied at different length scales. Using empirical potentials and static relaxation, atomic simulations give us a precise description of this interaction, mostly in the case when the separation distance between both defects is small. At larger distances, elasticity theory can be used to predict this interaction. From the comparison between both approaches we obtain the minimal separation distance where elasticity applies and we estimate the degree of refinement required in the calculation…
In classical elasticity theory the stress-field of a dislocation is characterized by a $1/r$-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces for the order parameter, resulting in non-physical (and discretization-dependent) predictions for the interaction between dislocations and phase-, twin- or grain-boundaries. We introduce a framework based on first strain gradient elasticity to regularize the dislocation core. It is shown that the use of strain energy density …
The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods employed in Discrete Dislocation Dynamics (DDD) simulations to eliminate these singularities: (1) considering a cutoff parameter, (2) spreading the Burgers vector (CAWB theory), and (3) using gradient elasticity. Each of these methods includes an extra length parameter to regularize the elastic fields. In this article, we show that these regularization paramete…
Dislocation interactions at the crack nucleation site were investigated in near-alpha titanium alloy Ti-6242Si subjected to low cycle fatigue. Cyclic plastic strain in the alloy resulted in dislocation pile-ups in the primary alpha grains, nucleated at the boundaries between the primary alpha and the two-phase regions. These two phase regions provided a barrier to slip transfer between primary alpha grains. We suggest that crack nucleation occurred near the basal plane of primary alpha grains by the subsurface double-ended pile-up mechanism first conceived by Tanaka and Mura. Superjogs on the …
The theory of anisotropic generalized plane strain of line forces and dislocation lines is embedded in three-dimensional elasticity of point forces and dislocation densities. Embedding in real space is achieved by slicing in reciprocal space using the projection-slice theorem.
A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains
Hydrogen atoms absorbed by metals in the hydrogen-containing environments can lead to the premature fracture of the metal components used in load-bearing conditions. Since metals used in practice are mostly polycrystalline, grain boundaries (GBs) can play an important role in hydrogen embrittlement of metals. Here we show that the reaction of GB with lattice dislocations is a key component in hydrogen embrittlement mechanism for polycrystalline metals. We use atomistic modeling methods to investigate the mechanical response of GBs in alpha-iron with various hydrogen concentrations. Analysis in…
The dislocation structures appearing in highly mis-oriented soft/hard grain pairs in near-alpha titanium alloy Ti6242Si were examined with and without the application of load holds (dwell) during fatigue. Dislocation pile-up in a soft grain resulted in internal stresses in an adjacent hard grain which could be relaxed by dislocation multiplication at localized Frank-Read sources, a process assisted by the provision of a relaxation time during a load hold. The rate of this process is suggested to be controlled by <c+a> pyramidal cross-slip and <a> basal junction formation. A high density of <a>…
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distortion and stress regularization at a dislocation core and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for the consistent separa…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale. Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions, which can be generally provided by atomistic modeling or experiments. The magnitude and phase of …
The action functional for a linear elastic medium with dislocations is given. The equations of motion following from this action reproduce the Peach-Köhler and Lorentzian forces experienced by dislocations. The explicit expressions for singular and finite parts of the self-force acting on a curved dislocation are derived in the framework of linear theory of elasticity of an isotropic medium. The velocity of dislocation is assumed to be arbitrary but less than the shear wave velocity. The slow speed and near-sonic motions of a dislocation are investigated. In the near-sonic limit, the explicit …
Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain `critical' velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied s…
In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalized continuum theory possesses a weak nonlocal character with two internal material lengths and provides a mechanics of defects without singularities. Gradient elasticity of bi-Helmholtz type gives a natural and physical regularization of the classical singularities of defects, based on higher order partial differential equations. Point defects embedded in an isotropic solid are considered as eigen…
This paper evaluates qualitatively as well as quantitatively the accuracy of a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for dislocations by a direct comparison with an equivalent molecular statics simulation. To this end, a two-dimensional microstructural specimen subjected to simple shear is considered, consisting of a central soft phase flanked by two hard-phase regions. A hexagonal atomic structure with equal lattice spacing is adopted, the interactions of which are described by the Lennard--Jones potential with phase specific depths of its energy well. During loading…
Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations
University of Luxembourg（卢森堡大学）；University of Exeter（埃克塞特大学）；Universitat Politècnica de Catalunya (UPC)（加泰罗尼亚理工大学）；Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech)（UPC-巴塞罗那科技数学研究所）；University of Galway（高威大学）
Nanoindentation, a common technique for probing the mechanical properties of crystalline materials, exhibits both surface and bulk-dominated responses that are linked to the parent crystal's elasticity and plasticity. For FCC crystals, the nanoindentation response is primarily controlled by the indented-grain's crystalline orientation and dislocation density. However, the indentation properties, such as hardness, have ambiguous significance at the nanoscale due to tip-specific size effects. Through extensive discrete dislocation dynamics simulations of flat-punch nanoindentation on FCC single …
The alpha/beta interface in Ti-6Al-2Sn-4Zr-6Mo (Ti-6246) is investigated via centre of symmetry analysis, both as-grown and after 10% cold work. Semi-coherent interface steps are observed at a spacing of 4.5 +/-1.13 atoms in the as-grown condition, in good agreement with theory prediction (4.37 atoms). Lattice accommodation is observed, with elongation along [-1 2 -1 0]alpha and contraction along [1 0 -1 0]alpha . Deformed alpha exhibited larger, less coherent steps with slip bands lying in {110}beta. This indicates dislocation pile-up at the grain boundary, a precursor to globularisation, off…
