Three-dimensional Dislocation Dynamics Research Articles

STI構造に対する三次元転位動力学シミュレーションの適用(技術OS3-1 半導体デバイス,技術OS3 電子・情報機器と材料力学)

STI構造に対する三次元転位動力学シミュレーションの適用(技術OS3-1 半導体デバイス,技術OS3 電子・情報機器と材料力学)

Statistical Dislocation Dynamics – Multiplication and Long Range Interactions

AbstractWe discuss dislocation multiplication and long range interactions in the framework of threedimensional (3-D) statistical dislocation dynamics. It is found that the long range interactions render the conservation equation for the ensemble-averaged dislocation density nonlinear and nonlocal. It is also shown that the conservation equation for the dislocation density must be supplemented by a gauge constraint in order to account for dislocation multiplication.

Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics

A three-dimensional discrete dislocation dynamics plasticity model is presented. The approach allows realistic boundary conditions on the specimen, as both stress and displacement fields of the dislocations are incorporated in the formulation. Emphasis is placed on various technical details in the formulation as well as on the implementation. The current implementation includes features necessary to model conservative motion of dislocations in presence of surfaces. These include details of the discretization of the evolving dislocation structure, the handling of junction formation and destruction, cross-slip and boundary conditions. Special attention is given to the treatment of dislocations that partly glide out of the material, including the treatment of image forces via the finite-element method.

A multiscale model of plasticity

A framework for investigating size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale is presented. The model is based on fundamental physical laws that govern dislocation motion and their interaction with various defects and interfaces. Particularly, the multi-scale framework merges two scales, the nano-microscale where plasticity is determined by explicit three-dimensional dislocation dynamics analysis providing the material length-scale, and the continuum scale where energy transport is based on basic continuum mechanics laws. The result is a hybrid elasto-viscoplastic simulation model coupling discrete dislocation dynamics with finite element analyses. With this hybrid approach, one can address complex size-dependent problems including, dislocation boundaries, dislocations in heterogeneous structures, dislocation interaction with interfaces and associated shape changes and lattice rotations, as well as deformation in nano-structured materials, localized deformation and shear bands.

Modelling of irradiation-induced hardening in metals using dislocation dynamics

A new simulation technique (three-dimensional dislocation dynamics) enabling the capture of a hardening effect in metals due to irradiation is reported. When bombarded with high-energy particles, metals accrue internal damage. In irradiated Pd, for example, damage takes the form of interstitial loops. Such loops are nano-sized and typically have a high number density. The stress field of a loop is given from dislocation theory. It is shown here the hardening is due to the elastic interaction of gliding dislocations with a high number of spatially dispersed interstitial loops. Results are found to correlate well with experiments.

Mechanical property degradation in irradiated materials: A multiscale modeling approach

High-energy particle irradiation of low stacking fault energy, face centered cubic (fcc) metals produces significant degradation of mechanical properties, as evidenced in tensile tests performed at or near room temperature. Post-irradiation microstructural examination reveals that approximately 90% of the radiation-induced defects in copper are stacking fault tetrahedra (SFT). Radiation damage is an inherently multiscale phenomenon involving processes spanning a wide range of length and time scales. Here we present a multiscale modeling methodology to study the formation and evolution of defect microstructure and the corresponding mechanical property changes under irradiation. At the atomic scale, molecular dynamics (MD) simulations have been used to study the evolution of high energy displacement cascades, SFT formation from vacancy rich regions of displacement cascades, and the interaction of SFTs with moving dislocations. Defect accumulation under irradiation is modeled over diffusional length and time scales by kinetic Monte Carlo (KMC), utilizing a database of displacement cascades generated by MD. The mechanical property changes of the irradiated material are modeled using three-dimensional dislocation dynamics (DD). Key input into the DD includes the spatial distribution of defects produced under irradiation, obtained from KMC, and the fate of dislocation interactions with SFTs, obtained from MD.

The treatment of traction-free boundary condition in three-dimensional dislocation dynamics using generalized image stress analysis

Recent attention has been given to the proper treatment of the planar traction-free surfaces which typically bound a computational box in three-dimensional dislocation dynamics. This paper presents an alternative to the use of the finite-element method for this purpose. Here, to annul the tractions produced by a sub-surface dislocation segment on a finite-area free surface S, a combination of an image dislocation segment, and a distribution of N prismatic rectangular Volterra dislocation loops meshing S is utilized. The image dislocation segment, with the proper sign selection of the Burgers vector components, annuls the shear stresses, and the normal stress component is annulled discretely at N collocation points representing the centers of the loops. The unknowns in this problem are the magnitudes of the N Burgers vectors for the loops. Once these are determined, one can back calculate the Peach–Koehler force acting on the sub-surface segment and representing the effect of the free surface. As expected, the accuracy of the method improves as the loops continuously decrease in size.

Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis

A numerical methodology to incorporate anisotropic elasticity into three-dimensional dislocation dynamics codes has been developed, employing theorems derived by Lothe [J. Lothe, Philos. Mag. 15 (1967) 353], Brown [L.M. Brown, Philos. Mag. 15 (1967) 363], Indenbom and Orlov [V.L. Indenbom, S.S. Orlov, Sov. Phys. Crystallogr. 12 (6) (1968) 849], and Asaro and Bamett [R.J. Asaro, D.M. Barnett, in: R.J. Arsenault, J.R. Beeler Jr., J.A. Simmons (Eds.), Computer Simulation for Materials Applications, Part 2. Nuclear Metallurgy, Vol. 20, p. 313]. The formalism is based on the stress field solution for a straight dislocation segment of arbitrary orientation in three-dimensional space. The general solution is given in a complicated closed integral form. To reduce the computation complexity, look-up tables are used to avoid heavy computations for the evaluation of the angular stress factor ( Σ ij ) and its first derivative term ( Σ ij ′). The computation methodology and error analysis are discussed in comparison with known closed form solutions for isotropic elasticity. For the case of Mo single crystals, we show that the difference between anisotropic and isotropic elastic stress fields can be, for some components of the stress tensor, as high as 15% close to the dislocation line, and decrease significantly away from it. This suggests that short-range interactions should be evaluated based on anisotropic elasticity, while long-range interactions can be approximated using long-range elasticity.

Discrete dislocation modeling in three-dimensional confined volumes

Plastic deformation of micron-sized specimens or smaller cannot be described by continuum plasticity, as the discrete nature of the dislocations can no longer be ignored. This paper presents a three-dimensional dislocation dynamics plasticity method developed for the study of plasticity of such small specimens. The approach includes two components: (i) plasticity is described by the dynamics of individual, discretized three-dimensional dislocation loops; (ii) a finite element model supplies ‘image fields’ that incorporate traction or displacement boundary conditions on the specimen. A circular dislocation loop is used to validate the chosen discretization of the dislocation. The critical stress for activating a Frank–Read source confirms the used line-tension description. A tensile test of a free-standing thin film illustrates the incorporation of the boundary conditions into the model. Particular attention is given to the treatment of dislocation loops that have glided partly out of the body, leaving a step at the surface.