Atomistic Modeling of Grain Boundaries and Dislocation Processes in Metallic Douglas E. Spearot Department of Mechanical Engineering, University of Arkansas, Polycrystalline Materials Fayetteville, AR 72701 e-mail: [email protected] The objective of this review article is to provide a concise discussion of atomistic mod- eling efforts aimed at understanding the nanoscale behavior and the role of grain bound- David L. McDowell aries in plasticity of metallic polycrystalline materials. Atomistic simulations of grain G. W. Woodruff School of Mechanical boundary behavior during plastic deformation have focused mainly on three distinct Engineering, configurations: (i) bicrystal models, (ii) columnar nanocrystalline models, and (iii) 3D Georgia Institute of Technology, nanocrystalline models. Bicrystal models facilitate the isolation of specific mechanisms Atlanta, GA 30332-0405; that occur at the grain boundary during plastic deformation, whereas columnar and 3D School of Materials Science and Engineering, nanocrystalline models allow for an evaluation of triple junctions and complex stress Georgia Institute of Technology, states characteristic of polycrystalline microstructures. Ultimately, both sets of calcula- Atlanta, GA 30332-0405 tions have merits and are necessary to determine the role of grain boundary structure on material properties. Future directions in grain boundary modeling are discussed, includ- ing studies focused on the role of grain boundary impurities and issues related to linking grain boundary mechanisms observed via atomistic simulation with continuum models of grain boundary plasticity. ͓DOI: 10.1115/1.3183776͔ Keywords: grain boundaries, atomistic simulation, dislocations, plasticity 1 Introduction These twins are reckoned to lead directly to an increase in the fraction of desirable boundaries and to a reduction in the connec- Experiments on polycrystalline metallic samples have indicated that grain boundary structure can affect many material properties tivity of the undesirable boundaries within the network. In addi- related to fracture and plasticity, such as grain boundary energy, tion, crack growth may be arrested at triple junctions that contain ⌺ grain boundary mobility, crack nucleation, and ductility ͓1,2͔. Al- at least two 3 boundaries. though several authors have proposed correlations between mate- Although experiments are of critical importance, quantitative rial properties and grain boundary misorientation ͓2–5͔͑quantified information aimed at identifying the nanoscale mechanisms that via the ⌺ value of a boundary in the coincident site lattice ͑CSL͒ promote grain boundary influences on dislocation slip transfer is notation ͓6͔͒, agreement between published experimental results currently inaccessible to experiments, aside from very limited in in the literature does not yet point to a universal relationship. situ high-resolution transmission electron microscopy ͑TEM͒ Instead, based on experimental evidence, grain boundaries are studies ͓12,13͔. Inherently, grain boundaries are interfaces with typically classified as having either “desirable” or “undesirable” nanoscale thickness comprised of ordered defect structures and performance or properties with respect to each behavior of inter- some degree of disordered atomic arrangement, depending on the est. extent of prior nonequilibrium processing and/or deformation. This qualitative approach has been used in conjunction with the Their influence on material properties extends across multiple concept of grain boundary ͑GB͒ engineering ͓7͔, the goal of higher length scales. Atomistic simulations have provided an av- which is to increase the percentage of desirable grain boundaries enue to study the underlying mechanisms associated with plastic- or interfaces within the GB character distribution and to reduce ity, such as dislocation nucleation, dislocation migration, disloca- the number and connectivity of undesirable boundaries through tion slip transfer, grain boundary migration and sliding, grain material processing techniques. Reducing the connectivity of un- rotation, and atom shuffling. desirable boundaries is particularly important, as polycrystalline The objective of this article is to provide a concise review of samples with a properly oriented continuous path of undesirable atomistic modeling efforts aimed at understanding the nanoscale boundaries would be susceptible to failure in terms of desired GB behavior and the role of grain boundaries in plasticity of metallic network properties regardless of the percentage of desirable inter- polycrystalline materials. The common goal of the atomistic mod- faces ͓8͔. For example, several authors have shown that the frac- eling efforts discussed in this article is to enhance predictive mod- tion of low-order CSL boundaries can be increased through se- quential straining and annealing cycles ͓2͔. As a result, els for failure in metallic materials, such as those presented by ͓ ͔ ͓ ͔ enhancements in corrosion resistance ͓4͔, creep resistance ͓9͔, and Ashmawi and Zikry 14,15 , Bieler and co-workers 16–18 , and ͓ ͔ ͓ ͔ crack nucleation and growth resistance under various loading con- Yamakov and co-workers 19,20 . For example, Bieler et al. 18 ditions ͓10͔ have been observed experimentally. Of particular ef- proposed a fracture initiation parameter in limited ductility metal- fectiveness is the introduction of ⌺3 ͑111͒ annealing twins ͓11͔. lic materials. This parameter is constructed as a criterion for dam- age nucleation, accounting for slip interaction and incompatibili- ties at a grain boundary. The accuracy of such a model could be Contributed by the Materials Division of ASME for publication in the JOURNAL OF enhanced significantly with additional knowledge of grain bound- ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received February 2, 2009; final manuscript received April 3, 2009; published online August 27, 2009. Assoc. ary structure and its potential influence on dislocation mechanisms Editor: Hanchen Huang. in the local neighborhood of the grain boundary. Journal of Engineering Materials and Technology OCTOBER 2009, Vol. 131 / 041204-1 Copyright © 2009 by ASME Downloaded 23 Oct 2011 to 164.107.78.222. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm Fig. 1 „a… Schematic diagram of the five macroscopic degrees of freedom associated with a grain boundary „adapted from ⌺ Ref. †1‡…. „b… Atomic structure of a symmetric tilt 5 „210… Ã Š001‹ interface. Translations parallel and perpendicular to the interface plane result in a periodic repeating structure at the interface. Fig. 2 Schematic illustration of „a… a bicrystal grain boundary model, „b… a 3D periodic nanocrystalline model, and „c… a co- lumnar nanocrystalline model. Periodic boundary conditions 2 Grain Boundaries in Metallic Materials are typically applied in all directions for each model to avoid Grain boundaries are planar defects with nanoscale thickness, the influence of free surfaces on the mechanisms associated which accommodate misorientation of adjoining regions of uni- with dislocation activity. For the bicrystal model, this results in a repeating planar defect in the Y-direction. form ͑or nearly uniform͒ crystallographic orientation. In ductile coarse-grain metals, the migration of dislocations ͑which are ͒ nucleated at Frank–Read sources within the grain interiors is ar- while the inverse density of coincident lattice points is defined as rested by grain boundaries due to slip incompatibility between ⌺. The CSL notation is considered as a tool to characterize grain neighboring grains. Both Hall ͓21͔ and Petch ͓22͔ envisioned dis- boundary geometry because the pattern of coincident atomic sites location “pile-up” at the grain boundaries based on experimental leads directly to a definable periodic geometry at the interface. evidence and proposed that yield occurred in ductile polycrystal- Atomistic simulations by Sutton and co-workers ͓26–29͔ showed line materials once the stress exerted on the neighboring grain by that the structure of symmetric tilt interfaces in face-centered cu- the dislocation pile-up reaches a critical value, resulting in the bic ͑FCC͒ metals may be viewed as a linear combination of Hall–Petch equation ͓23͔. In metallic materials with poor ductility, “structural units.” With this tool, several authors attempted to cor- grain boundaries may serve as nucleation sites for microvoids and relate character and/or distribution of the interface structural units the path for crack propagation during fracture. For example, Wa- to material properties or specific dislocation mechanisms. Unfor- tanabe ͓7͔ envisioned a connected network of undesirable grain tunately, several limitations of the structural unit model ͑SUM͒ boundaries within a brittle material as the path of least resistance limit the success of such correlations. First, it is difficult to iden- for crack propagation. In most work on GB engineering, as dis- tify structural units with three-dimensional character, as is com- cussed previously, undesirable boundaries are viewed as weaker monly the case with twist boundaries. Second, the SUM has lim- than others using arguments based on geometry ͑neighboring ited applicability for interfaces with mixed tilt and twist grain orientations and CSL designation͒ or composition ͑presence characteristics or if high index misorientation axes are examined of impurities͒. ͓30͔. Third, it is difficult to quantify the degree of elastic distor- From a geometric perspective, interfaces between