Parametric dislocation dynamics: A thermodynamics-based approach to investigations of mesoscopic plastic deformation (original) (raw)
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Curved Parametric Segments for the Stress Field of 3-D Dislocation Loops
Journal of Engineering Materials and Technology, 1999
Under applied mechanical forces, strong mutual interaction or other thermodynamic forces, dislocation shapes become highly curved. We present here a new method for accurate computations of self and mutual interactions between dislocation loops. In this method, dislocation loops of arbitrary shapes are segmented with appropriate parametric equations representing the dislocation line vector. Field equations of infinitesimal linear elasticity are developed on the basis of isotropic elastic Green’s tensor functions. The accuracy and computational speed of the method are illustrated by computing the stress field around a typical (110)-[111] slip loop in a BCC crystal. The method is shown to be highly accurate for close-range dislocation interactions without any loss of computational speed when compared to analytic evaluations of the stress field for short linear segments. Moreover, computations of self-forces and energies of curved segments are guaranteed to be accurate, because of the c...
Le Journal de Physique IV, 2001
The elastic field of complex 3-D dislocation ensembles is described by differential geometric representations, which allow computer simulations of mesoscopic plastic deformation without additional ad hoc approximations for short-range dislocation reactions. The simple vector forms of differential geometry are independent of the coordinate system, and facilitate studies of dislocation generation, pileup formation, grainboundary interaction, finite-length dipole nucleation and break-up, junction nucleation and destruction, interaction with defect clusters, and self-consistent boundary conditions. It is shown that the elastic field can be described in terms of simple combinations of three basic vectors and their dyadics in real and reciprocal space. These vectors are the unit tangent, Burgers vector, and unit radial vector between a source point on the dislocation and a field point. With the only limitation being dislocation cores interpenetrating up to one Burgers vectors, a review of recent progress and examples of the aforementioned short-and long-range dislocation reactions are given, with particular emphasis on computational issues of space and time resolution.
Parametric dislocation dynamics of anisotropic crystals
Philosophical Magazine, 2003
Efficient computational methods for the elastic field, self force and interaction forces of three-dimensional (3D) dislocations in anisotropic elastic crystals are developed for 3D dislocation dynamics (DD). The elastic field of a general dislocation loop is determined by incorporating numerically evaluated derivatives of Green's functions in the fast sum method of Ghoniem and Sun. Self-forces of dislocation loops are calculated by numerical integrations performed on the dislocation line, and several approximation methods to the full integration are also explored. Strong effects of elastic anisotropy on many ingredients of DD are shown (e.g. the elastic field, self-forces, operation of Frank-Read sources, dipole formation and break-up and dislocation junction strength). Large-scale 3D DD simulations are carried out for copper single crystals. It is found that the dislocation microstructure and strain-hardening behaviour are also strong functions of elastic anisotropy.
Journal of The Mechanics and Physics of Solids, 2015
A thermodynamically consistent, large strain phase field approach to dislocation nucleation and evolution at the nanoscale is developed. Each dislocation is defined by an order parameter, which determines the magnitude of the Burgers vector for the given slip planes and directions. The kinematics is based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions. The relationship between the rates of the plastic deformation gradient and the order parameters is consistent with phenomenological crystal plasticity. Thermodynamic and stability conditions for homogeneous states are formulated and satisfied by the proper choice of the Helmholtz free energy and the order parameter dependence on the Burgers vector. They allow us to reproduce desired lattice instability conditions and a stress-order parameter curve, as well as to obtain a stress-independent equilibrium Burgers vector and to avoid artificial dissipation during elastic deformation. The Ginzburg-Landau equations are obtained as the linear kinetic relations between the rate of change of the order parameters and the conjugate thermodynamic driving forces. A crystalline energy coefficient for dislocations is defined as a periodic step-wise function of the coordinate along the normal to the slip plane, which provides an energy barrier normal to the slip plane and determines the desired, mesh-independent height of the dislocation bands for any slip system orientation. Gradient energy contains an additional term, which excludes the localization of a dislocation within a height smaller than the prescribed height, but it does not produce artificial interface energy. An additional energy term is introduced that penalizes the interaction of different dislocations at the same point. Non-periodic boundary conditions for dislocations are introduced which include the change of the surface energy due to the exit of dislocations from the crystal.
Accuracy and convergence of parametric dislocation dynamics
Modelling and Simulation in Materials Science and Engineering, 2002
In the parametric dislocation dynamics (PDD), closed dislocation loops are described as an assembly of segments, each represented by a parametric space curve. Their equations of motion are derived from an energy variational principle, thus allowing large-scale computer simulations of plastic deformation. We investigate here the limits of temporal and spatial resolution of strong dislocation interactions. The method is demonstrated to be highly accurate, with unconditional spatial convergence that is limited to distances of the order of interatomic dimensions. It is shown that stability of dislocation line shape evolution requires very short time steps for explicit integration schemes, or can be unconditionally stable for implicit time integration schemes. Limitations of the method in resolving strong dislocation interactions are established for the following mechanisms: dislocation generation, annihilation, dipole and junction formation, pileup evolution.
Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications
This paper reviews the methods and techniques developed to simulate dislocation dynamics on a mesoscopic scale. Attention is given to techniques of acceleration and to the implementation of special boundary conditions. Typical results concerning the deformation of a bulk crystal, the effect of image forces and the combination with a finite-element code to simulate the indentation test are presented. The limits and future development of each application are discussed. 755 756 M Verdier et al modelling the behaviour of bulk crystal, and for situations where a complex boundary is required, such as surfaces taking into account image forces or indentation of a crystal. In the last part, typical results concerning each case are presented and the limit of the various methods are discussed.
Dislocation motion controlled by interactions with crystal lattice: modelling and experiments
International Materials Reviews, 2005
In an attempt to establish a correct physical description of the mechanical behaviour of a crystal, the present paper presents first a critical review of two dislocation mobility processes: glide in covalent crystals, and pure climb at high temperatures. Models are presented together with experimental data to test them. The study then gathers available information about the way dislocations multiply, are held up in the substructure and the resultant work hardening of the crystal.
Modelling and Simulation in Materials Science and Engineering, 2008
In this paper, the main characteristics of Frank-Read (F-R) sources used in a mechanism-based discrete dislocation plasticity (M-DDP) analysis are estimated by employing a recently developed non-singular continuum elastic theory of dislocations. The critical nucleation stress, τ nuc , is determined more accurately because the dislocation core effects are considered precisely by atomistically-informing the dislocation dynamics simulations. The nucleation time is calculated and compared with the previous predictions. The dependence of the drag coefficient of dislocations on dislocation line orientation, which affects the nucleation time and also the shape of the emitted dislocation loop, is considered. In M-DDP simulations, τ nuc used for sources is calculated based on the assumption of an infinite domain. In reality, however, the critical nucleation stress is affected by other F-R sources. It is proposed in this paper that the critical nucleation stress should be modified by considering the effects of other dislocation sources. To this end, τ nuc should be determined for an F-R source in a finite cell with periodic boundary conditions. of the core region, indirectly accounting for the effects of the dislocation core, must be added. Useful discussions about the core cut-off parameters can be found in and .
2020
Efficient computational methods for the elastic field, self force and interaction forces of three-dimensional (3D) dislocations in anisotropic elastic crystals are developed for 3D dislocation dynamics (DD). The elastic field of a general dislocation loop is determined by incorporating numerically evaluated derivatives of Green's functions in the fast sum method of Ghoniem and Sun. Self-forces of dislocation loops are calculated by numerical integrations performed on the dislocation line, and several approximation methods to the full integration are also explored. Strong effects of elastic anisotropy on many ingredients of DD are shown (e.g. the elastic field, self-forces, operation of Frank-Read sources, dipole formation and break-up and dislocation junction strength). Large-scale 3D DD simulations are carried out for copper single crystals. It is found that the dislocation microstructure and strain-hardening behaviour are also strong functions of elastic anisotropy. } 1. Intr...
Journal of Engineering Materials and Technology, 2012
In latent interactions of dislocations, junction formation is one of the most important phenomena that contribute to the evolution of strength. In this work, the latent hardening coefficients for pure aluminum are estimated using 3D multiscale dislocation dynamics program (MDDP). Three well-known junction configurations, namely, the Hirth lock, the glissile junction, and the Lomer lock, are studied using 3D discrete dislocation dynamics simulations. The evolution of strength is discussed as a function of the resolved shear stress (RSS) and the number of junctions for the three junctions investigated. Hirth lock and Lomer lock are found to be the weakest and strongest junctions, respectively. Collinear reaction of dislocations does not form a junction but causes a higher strength than a Lomer lock. Quantitative and qualitative results are compared with those found in the literature.