The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular dislocations is developed for linearly elastic, infinitely extended, homogeneous, and isotropic media. Dislocation loops and straight dislocations are investigated. Using the theory of gradient elasticity, the non-singular fields which are produced by arbitrary dislocation loops are given. `Modified' Mura, Peach-Koehler, and Burgers formulae are presented in the framework of gradient elasticity theory. These formulae are given in terms of an elementary function, which regularizes the classical expressions, obtained from the Green tensor of the Helmholtz-Navier equation and bi-Helmholtz-Navier equation. Using the mathematical method of Green's functions and the Fourier transform, exact, analytical, and non-singular solutions were found. The obtained dislocation fields are non-singular due to the regularization of the classical singular fields.
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…
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.
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 …
On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Liénard-Wiechert tensor potentials
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…
A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains
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…
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）
Hydrogen segregation around a straight screw dislocation in bcc iron
Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE) - UMR CNRS 7356（环境工程科学实验室）；Laboratoire des Sciences des Procédés et des Matériaux (LSPM) - UPR 3407（工艺与材料科学实验室）
Mn enrichment at dislocations in Fe-Mn alloys due to segregation and spinodal decomposition along the dislocation line is studied via modeling and experimental characterization. To model these phenomena, both finite-deformation microscopic phase-field chemomechanics (MPFCM) and Monte Carlo molecular dynamics (MCMD) are employed. MPFCM calibration is carried out with the same Fe-Mn MEAM-based potential used in MCMD, as well as CALPHAD data. Simulation results for Mn segregation to, and spinodal decomposition along, straight screw and edge dislocations as well as dislocation loops, are compared …
Variational approach to determine the properties of dislocations at finite deformation
Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳研究物理中心固体物理与光学研究所）；Department of Materials Physics, Eötvös Loránd University（厄特沃什·罗兰大学材料物理系）
We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach-Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence f…
To allow for `relativistic'-like core contraction effects, an anisotropic regularization of steadily-moving straight dislocations of arbitrary orientation is introduced, with two scale parameters $a_\parallel$ and $a_\perp$ along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When $a_\perp/a_\parallel\to 0$, the model reduces to the Peierls-Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite $a_\parallel$ and $a_\perp$, fields are everywhere differentiable. Applying the author's so-called `causal' …
In this work, we present a 3D Phase Field Dislocation Dynamics (PFDD) model for body-centered cubic (BCC) metals. The model formulation is extended to account for the dependence of the Peierls barrier on the line-character of the dislocation. Simulations of the expansion of a dislocation loop belonging to the $\left\{110\right\} \left<111\right>$ slip system are presented with direct comparison to Molecular Statics (MS) simulations. The extended PFDD model is able to capture the salient features of dislocation loop expansion predicted by MS simulations. The model is also applied to simulate th…
