NSF GB Project

Novel Atomistic-Continuum Simulation of Sequential Grain Boundary-Dislocation Slip Transfer Reactions


NSF Award#: 1232878 (Georgia Institute of Technology)

                       1233113  (University of Florida)


Project Abstract


     The research objective of this award is to advance the concurrent atomistic-continuum (CAC) simulation method to explore slip transfer at grain boundaries. Lack of such a method is a current obstacle to progress towards developing constitutive relations that reflect the structure and behavior of grain boundaries, for example in polycrystal plasticity. The problem is complicated by the need to account for long range interactions of dislocation fields while also considering the atomic-level structural detail of the interface. This research will explore processes of sequential dislocation reactions with bicrystal interfaces by maintaining full atomistic resolution of the interface reactions and successively coarse graining the field description away from the interfaces at distances that are normally inaccessible to fully resolved molecular dynamics. Such a capability will enable parametric studies of dislocation-grain boundary slip transfer reactions over the full range of grain boundary degrees of freedom, including tilt and twist boundaries, as well as asymmetric boundaries that often have faceted structure and can give rise to profuse dislocation nucleation. Nanotwinned structures with a wide range of twin spacing will also be considered. This work will use state-of-the-art embedded atom method potentials which have proven quite accurate for fcc metals such as Cu in modeling various aspects of dislocation nucleation, formation of stacking faults, and dislocation interactions.


The CAC Methodology


     Fundamental to the CAC method is a unified formulation of atomistic and continuum representation of balance laws.  The new formulation generalizes Kirkwood’s statistical mechanical theory of transport processes to have a two-level structural description of materials. It describes the structure of a crystalline material in terms of a continuously-distributed lattice cells, but with a group of discrete atoms situated in each lattice cell at sub-structural level, in exactly the same way with the solid state physics approach in describing the structure of all crystals; correspondingly, the atomic deformation is expressed as the sum of the lattice deformation and the subscale internal deformation relative to the lattice, which is consistent with lattice dynamics description of the dynamics of atoms in crystals.


      This concurrent two-level material description then leads to (1) a new formalism by which fluxes (stress and heat flux) consist of components representing the distortions of lattice cells and the rearrangement of atoms within the cells, and (2) a new mathematical representation of balance laws that can be used to solve for both the motion of the continuously-distributed lattice cells and the internal motion of atoms within each lattice cell. Under elastic distortion, the new balance equations can fully reproduce the phonon dispersion relations. The information of the arrangements of atoms as well as the interaction of atoms in the crystal is thus all built in the formulation. As a result, this new formulation enables us to model a general crystalline material as a continuous collection of material points or lattice cells, but embedded within each material point is a group of discrete atoms. The concurrently coupled continuum-atomistic features make this formulation distinct from all existing coarse-grained atomistic or multiscale formulations.  More details about the formulation can be found in the following articles:


· Chen Y. (2009), “Reformulation of microscopic balance equations for multiscale materials modeling”, Journal of Chemical Physics, 130, 134706.

· Xiong L., Tucker G., McDowell D. L., and Chen Y. (2011), “Coarse-Grained Atomistic Simulation of Dislocations”, Journal of Mechanics and Physics of Solids, 59, 160-177.

· Chen Y., Zimmerman J., Krivtsov A., and McDowell D. L. (2011), “Assessment of atomistic coarse-graining methods”, International Journal of Engineering Science.


CAC Code and Algorithm Development


The current CAC code has two versions:

    The FORTRAN version, which was developed and continues to be developed by Liming Xiong, Qian Deng, Shengfeng Yang, Xiang Chen, and  Shuozhi Xu, employs  the spatial domain decomposition parallelization algorithm with various interatomic potentials being implemented.

     The C++ version, which  is currently developing by Adrian Diaz,  employs the Mesh Partitioning algorithms.


Journal Publications


S Xu, L Xiong, Y Chen, DL McDowell (2016), “Sequential slip transfer of mixed character dislocations across Σ3 coherent twin boundary in FCC metals: A concurrent atomistic-continuum study ”, npj Computational Materials, 2, 15016 (PDF).

L Xiong, J Rigelesaiyin, X Chen, S Xu, DL McDowell, Y Chen (2016), “Coarse-grained elastodynamics of fast moving dislocations”, Acta Materialia 104, 143-155 (PDF).

PA Pluchino, X Chen, M Garcia, L Xiong, DL McDowell, Y Chen (2016),”Dislocation migration across coherent phase interfaces in SiGe superlattices”, Computational Materials Science 111, 1-6 (PDF).

S Xu, R Che, L Xiong, Y Chen, DL McDowell (2015), “A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals”, International Journal of Plasticity 72, 91–126 (PDF)

L Xiong, S Xu, DL McDowell, Y Chen  (2015), “Concurrent atomistic-continuum simulations of dislocation-void interactions in fcc crystals International Journal of Plasticity (PDF).

Zexi Zheng Xiang Chen, Bowen Deng, Aleksandr Chernatynskiy, Shengfeng Yang, Liming Xiong and Youping Chen, (2014), “Phonon thermal transport through tilt grain boundaries in strontium titanate “, J. Appl. Phys. 116, 073706 (PDF).

Liming Xiong , David L. McDowell, Youping Chen (2014), “Sub-THz Phonon drag on dislocations by coarse-grained atomistic simulations”, International Journal of Plasticity, 55,  268-278  (PDF).

Xiong, Liming; Chen, Xiang; Zhang, Ning; McDowell, David L.; Chen, Youping (2014), “Prediction of phonon properties of 1D polyatomic systems using concurrent atomistic-continuum simulation” Archive of Applied Mechanics (PDF).




Coarse-Grained Elastodynamics of Fast Moving Dislocations

      We have made a first attempt to characterize the complexity of nonuniformly moving dislocations in anisotropic crystals from atomistic to microscale, including the energy intensities as well as the wavelengths of acoustic phonons emitted from sonic dislocations, and the velocity-dependent stress fluctuations around the core of nonuniformly moving dislocations. Instantaneous dislocation velocities and phonon drag effects on the dislocation motions are quantified and analyzed. Mach cones in a V-shaped pattern of the phonon wave-fronts are observed in the wake of the sonic dislocations. Analysis of simulation results based on a wavelet transform show that the faster a dislocation is moving, the longer the emitted phonon wavelength. The dislocation velocity drops dramatically with the occurrence of the interactions between dislocations and phonon waves reflected from the boundaries of specimens. The concurrent atomistic-continuum modeling framework is demonstrated to be the first multiscale method that explicitly treats the strong coupling between the long-range elastic fields away from the dislocation core, the highly nonlinear time-dependent stress field within the core, and the evolutions of the atomic-scale dislocation core structures. As such, it is shown that this method is capable in predicting elastodynamics of dislocations in the presence of inertia effects associated with sonic dislocations in micron-sized anisotropic crystalline materials from the atomic level, which is not directly accessible to the recent elastodynamic discrete dislocation model (read more).




Figure 1 (upper) Snapshots of dislocation motion by MD and CAC simulations; Due to the symmetry of the specimen configuration about the y axis, only the left part of the specimen in MD and the right part of the specimen in CAC are displayed and compared; The color, red or blue, respectively, indicates the tensile or compressive stress along the y direction.  It is seen that phonon waves are emitted from  accelerating dislocations in both CAC and MD simulations. (lower) Phonon energy intensity distributions associated with the acoustic waves emitted from the fast moving dislocations with velocity v =2900 m/s at t =5 ps by MD and CAC simulations. 



CAC Simulation of Dislocation Multiplication from Frank-Read Source (download the movie)

Research details: Cu and Al  bicrystals containing a Σ3 coherent twin boundary (CTB), with a pair of cylindrical holes introduced in the incoming grain, are modeled (1) with full atomistic resolution within 7 nm in the vicinity of CTB, around the holes, and at the otherwise zigzag boundaries, and (2) with discontinuous finite elements, each of which contains 2197 atoms, away from the CTB, holes, and boundaries. We choose a uniform element size employing continuous first order shape functions and solved by 1st order Gaussian quadrature because it strikes a balance between high accuracy and high efficiency.  Four dislocation/GB interaction modes are identified in Al, which are affected by (a) applied shear stress, (b) dislocation line length, and (c) dislocation line curvature. Our results elucidate the discrepancies between atomistic simulations and experimental observations of dislocation-GB reactions and highlight the importance of directly modeling sequential dislocation slip transfer reactions using fully 3-D models.



Figure 2. Snapshots of dislocation loop multiplication in Cu subject to the applied shear stress  between a pair of cylindrical holes, which serve as an FR source. Atoms are colored by adaptive common neighbor analysis: red are of HCP local structure, blue are not coordinated as either FCC or HCP, and all FCC atoms are deleted. In (b), the dislocation reaches the critical semicircular configuration; then it continues growing in (c) until a dislocation loop is formed in (d). In (e), the segments of dislocation loop with edge component are swept out at the stress free boundaries, leaving a curved dislocation moving along the positive y direction towards the CTB. While all distances labelled here are for Cu, similar phenomena are observed for Al.