Coarse-grained atomistic simulation of dislocations

This paper presents a new methodology for coarse-grained atomistic simulation of dislocation dynamics. The methodology combines an atomistic formulation of balance equations and a modified finite element method employing rhombohedral-shaped 3D solid elements suitable for fcc crystals. With significantly less degrees of freedom than that of a fully atomistic model and without additional constitutive rules to govern dislocation activities, this new coarse-graining (CG) method is shown to be able to reproduce key phenomena of dislocation dynamics for fcc crystals, including dislocation nucleation and migration, formation of stacking faults and Lomer-Cottrell locks, and splitting of stacking faults, all comparable with fully resolved molecular dynamics simulations. Using a uniform coarse mesh, the CG method is then applied to simulate an initially dislocation-free submicron-sized thin Cu sheet. The results show that the CG simulation has captured the nucleation and migration of large number of dislocations, formation of multiple stacking fault ribbons, and the occurrence of complex dislocation phenomena such as dislocation annihilation, cutting, and passing through the stacking faults. The distinctions of this method from existing coarse-graining or multiscale methods and its potential applications and limitations are also discussed.     

A constitutive model for creep-plasticity interaction based on dislocation dynamics

A glide-plus-climb micromechanism of dislocation evolution with the formation of subgrains is proposed for modelling of the creep-plasticity interaction (CPI). The long-range internal stress can be divided into the resistance for dislocation climb in subgrain boundaries and that for dislocation glide within grains or subgrains. Their evolution equations are then derived based on dislocation dynamics. Furthermore, a unified constitutuve model for CPI is developed from Orowan's formula. Theoretical calculations on the basis of this model show a very good agreement between the model prediction and experimental results of benchmark tests for 2 1/4 Cr-1 Mo steel at 600°C.     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.     

A computational method for dislocation-precipitate interaction

A new computational method for the elastic interaction between dislocations and precipitates is developed and applied to the solution of problems involving dislocation cutting and looping around precipitates. Based on the superposition principle, the solution to the dislocation-precipitate interaction problem is obtained as the sum of two solutions: (1) a dislocation problem with image stresses from interfaces between the dislocation and the precipitate, and (2) a correction solution for the elastic problem of a precipitate with an initial strain distribution. The current development is based on a combination of the parametric dislocation dynamics (PDD) and the boundary element method (BEM) with volume integrals.The method allows us to calculate the stress field both inside and outside precipitates of elastic moduli different from the matrix, and that may have initial coherency strain fields. The numerical results of the present method show good convergence and high accuracy when compared to a known analytical solution, and they are also in good agreement with molecular dynamics (MD) simulations. Sheared copper precipitates (2.5 nm in diameter) are shown to lose some of their resistance to dislocation motion after they are cut by leading dislocations in a pileup. Successive cutting of precipitates by the passage of a dislocation pileup reduces the resistance to about half its original value, when the number of dislocations in the pileup exceeds about 10. The transition from the shearable precipitate regime to the Orowan looping regime occurs for precipitate-to-matrix elastic modulus ratios above approximately 3-4, with some dependence on the precipitate size. The effects of precipitate size, spacing, and elastic modulus mismatch with the host matrix on the critical shear stress (CSS) to dislocation motion are presented.     

Continuum dynamics of the formation,migration and dissociation of self-locked dislocation structures on parallel slip planes

In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum dynamics of straight dislocations distributed on two parallel slip planes is modelled through upscaling the underlying discrete dislocation dynamics. Two continuum velocity field quantities are introduced to facilitate the discrete-to-continuum transition. The first one is the local migration velocity of dislocation ensembles which is found fully independent of the short-range dislocation correlations. The second one is the decoupling velocity of dislocation pairs controlled by a threshold stress value, which is proposed to be the effective flow stress for single slip systems. Compared to the almost ubiquitously adopted Taylor relationship, the derived flow stress formula exhibits two features that are more consistent with the underlying discrete dislocation dynamics: (i) the flow stress increases with the in-plane component of the dislocation density only up to a certain value, hence the derived formula admits a minimum inter-dislocation distance within slip planes; (ii) the flow stress smoothly transits to zero when all dislocations become geometrically necessary dislocations. A regime under which inhomogeneities in dislocation density grow is identified, and is further validated through comparison with discrete dislocation dynamical simulation results. Based on the findings in this article and in our previous works, a general strategy for incorporating short-range dislocation correlations into continuum models of dislocations is proposed.     

A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes

We present a self-consistent formulation of 3-D parametric dislocation dynamics (PDD) with the boundary element method (BEM) to describe dislocation motion, and hence microscopic plastic flow in finite volumes. We develop quantitative measures of the accuracy and convergence of the method by considering a comparison with known analytical solutions. It is shown that the method displays absolute convergence with increasing the number of quadrature points on the dislocation loop and the surface mesh density. The error in the image force on a screw dislocation approaching a free surface is shown to increase as the dislocation approaches the surface, but is nevertheless controllable. For example, at a distance of one lattice parameter from the surface, the relative error is less than 5% for a surface mesh with an element size of 1000×2000 (in units of lattice parameter), and 64 quadrature points. The Eshelby twist angle in a finite-length cylinder containing a coaxial screw dislocation is also used to benchmark the method. Finally, large scale 3-D simulation results of single slip behavior in cylindrical microcrystals are presented. Plastic flow characteristics and the stress-strain behavior of cylindrical microcrystals under compression are shown to be in agreement with experimental observations. It is shown that the mean length of dislocations trapped at the surface is the dominant factor in determining the size effects on hardening of single crystals. The influence of surface image fields on the flow stress is finally explored. It is shown that the flow stress is reduced by as much as 20% for small single crystals of size less than .     

Modeling of thermally activated dislocation glide and plastic flow through local obstacles

A unified phenomenological model is developed to study the dislocation glide through weak obstacles during the first stage of plastic deformation in metals. This model takes into account both the dynamical responses of dislocations during the flight process and thermal activations while dislocations are bound by obstacle arrays. The average thermal activation rate is estimated using an analytical model based on the generalized Friedel relations. Then, the average flight velocity after an activation event is obtained numerically by discrete dislocation dynamics (DD). To simulate the dynamical dislocation behavior, the inertia term is implemented into the equation of dislocation motion within the DD code. The results from the DD simulations, coupled with the analytical model, determine the total dislocation velocity as a function of the stress and temperatures. By choosing parameters typical of the face centered cubic metals, the model reproduces both obstacle control and drag control motion in low and high velocity regimes, respectively. As expected by other string models, dislocation overshoots of obstacles caused by the dislocation inertia at the collisions are enhanced as temperature goes down.     

Investigations of pipe-diffusion-based dislocation climb by discrete dislocation dynamics

A new numerical dislocation climb model based on incorporating the pipe diffusion theory (PDT) of vacancies with 3D discrete dislocation dynamics (DDD) is developed. In this model we hold that the climb rate of dislocations is determined by the gradient of the vacancy concentration on the segment, but not by the mechanical climb force as traditionally believed. The nodal forces on discrete dislocation segments in DDD simulation are transferred to PDT to calculate the vacancy concentration gradient. This transfer establishes a bridge connecting the DDD and PDT. The model is highly efficient and accurate. As verifications, two typical climb-involved examples are predicted, e.g. the activation of a Bardeen-Herring source as well as the shrinkage and annihilation of prismatic loops. Finally, the model is applied to study the breakup process of an infinite edge dislocation dipole into prismatic loops. This coupling methodology provides us a useful tool to intensively study the evolution of dislocation microstructures at high temperatures.     

关联参照模型和位错发射过程的分子动力学模拟

提出关联参照模型和随位错位置变化的柔性位移边界条件．提供了一个在固定位移边界条件下位错穿越边界的方法．应用三维分子动力学方法研究了体心立方（ＢＣＣ）金属晶体钼裂尖发射位错的力学行为．