Influence of Grain Boundary Structure on Dislocation Nucleation in FCC Metals

Mark A. Tschopp    School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245, USA
Air Force Research Laboratory (UTC), Wright-Patterson Air Force Base, Dayton, OH 45433, USA

Douglas E. Spearot    Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701, USA

David L. McDowell    Woodruff School of Mechanical Engineering, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA

1 Introduction

According to materials scientist and philosopher Cyril Stanley Smith, the structure of materials is best described as a multilevel architecture, with “interplay of perfection and imperfection” among all length scales [1,2]. This point of view asserts that a clear understanding of material behavior at each length scale is imperative to elucidate the technological or economic value of a material [1]. However, many theories of macroscopic material behavior are not based on direct evaluation of micro- or nanoscale mechanisms. Two examples are the kinematic hardening model in continuum plasticity, which was posed to describe experimental observation of the Bauschinger effect [3], and the Hall–Petch relationship [4,5], which describes the increase in yield strength associated with the decrease in the grain size for metallic polycrystalline materials. Both Hall [4] and Petch [5] envisioned grain boundaries as obstacles to dislocation motion (resulting in dislocation pile-ups) and assumed that yield occurred once the stress exerted on the neighboring grain by the dislocation pile-up reached a critical value. Experimental observations of this type are of tremendous scientific importance; however, it is highly desirable to directly study the underlying material micro- and nanostructure with the aim of developing constitutive models that capture the activity and interaction of atomic-scale structure and associated mechanisms. For example, both experiments (cf. [6–8]) and simulations (cf. [9–12]) have reported that material softening occurs once the grain size is reduced below a critical grain diameter, which cannot be predicted by the classical Hall–Petch relationship. Moreover, it is understood that scale effects in plasticity occur over a range of mechanisms and scales.

This work focuses on modeling the atomic level mechanisms associated with the structure and inelastic behavior of homophase grain boundaries (GBs) on the nanoscale and developing structure–property relationships that incorporate these nanoscale observations. Several experimental studies on polycrystalline metallic samples have reported that interface structure has an effect on material properties, such as grain boundary energy, mobility, corrosion, crack nucleation and ductility (cf. [13,14]). Most of the published experimental investigations indicate that there is some correlation between the occurrence of “special” coincident site lattice boundaries and material properties; however, results published in the literature do not point to a universal relationship. In nanocrystalline materials, the grain boundaries play a more profound role in material behavior due to the increased interfacial area associated with the decrease in the grain size. In addition, nanoscale confinement severely limits the operation of traditional dislocation sources, such as Frank–Read sources [15], mandating that the grain boundaries participate directly in the accommodation of the applied strain. Thus, grain boundary dislocation emission and absorption [16–39], which may be coupled with atomic shuffling [38–40], stress assisted grain boundary sliding [38–45] and grain rotation [46], have all been observed in computational studies as potential grain boundary deformation mechanisms. Conceivably, the activation of each grain boundary mechanism depends on several factors, including the electronic details of the material (intrinsic and unstable stacking fault energies), the grain size, the structure of the grain boundaries and the deformation conditions (strain state and strain rate).

The objective of this work is to use atomistic simulations to examine the structure and dislocation nucleation/emission behavior of symmetric and asymmetric tilt grain boundaries in FCC copper and aluminum. Discrete atomic scale mechanisms associated with dislocation nucleation are incorporated into a first-order constitutive model for the tensile strength of tilt grain boundaries. This atomistically motivated constitutive model explicitly incorporates the orientation dependence of the opposing lattice regions and the influence of porosity within the interface region through an average measure based on coordination. Furthermore, this work provides a detailed understanding of the influence of grain boundary structure on dislocation nucleation which is critical for the advancement of grain boundary engineering concepts. Recall that the objective of grain boundary engineering [47] is to increase the percentage of “special” grain boundaries and to reduce the connectivity of “random” grain boundaries through material processing. Reducing the connectivity of random boundaries is found to be particularly important, as polycrystalline samples with a properly oriented continuous path of weak boundaries would be susceptible to failure regardless of the percentage of special interfaces [48]. Schuh et al. [14] reported that the fraction of special grain boundaries can be increased through sequential cycles of straining and annealing. As a result, enhancements in corrosion resistance, creep resistance and crack nucleation and growth resistance under various loading conditions have been observed experimentally. Of particular effectiveness is the introduction of annealing twins [49], which are essentially highly coherent GBs. Molecular dynamics simulations in this work provide a more refined definition of “special” with regard to how grain boundary structure affects dislocation nucleation.

This chapter is organized as follows. The remainder of this section focuses on concepts related to grain boundary geometry and structure in metallic crystalline materials. Section 2 provides a brief overview of atomistic simulation techniques (equations of motion, interatomic potentials, etc.) and the specific simulation geometries used in this work to model grain boundary structure and dislocation nucleation. Section 3 discusses the dependence of grain boundary structure and energy on the misorientation angle/axis in the case of symmetric tilt grain boundaries and the inclination angle for asymmetric tilt grain boundaries. Section 4 investigates the relationship between interface structure and dislocation nucleation in symmetric and asymmetric tilt GBs. Section 5 presents a first-order, atomistically-inspired model designed to correlate the strength required for dislocation nucleation with interface structure via the interface free volume and the resolved stresses on the primary slip plane for uniaxial loading. To capture the influence of the lattice orientation, atomistic simulations of homogeneous dislocation nucleation in single crystals are also discussed. Section 6 discusses how atomic-level information of dislocation nucleation from grain boundaries can impact research in plasticity, micromechanics and grain boundary engineering techniques. A summary of major contributions in this work is provided in Section 7.

1.1 Overview of grain boundary geometry

In general, solid–solid interfaces between crystalline regions may be classified into two categories: homophase and heterophase [50]. The set of homophase interfaces includes grain boundaries, twins and stacking faults in pure metals, whereas heterophase interfaces exist in binary and other material systems in which the composition and/or the Bravais lattice change across the interface plane. For homophase boundaries (such as those in this work), the degree of coherency is a function of the misorientation angle of the interface, the boundary plane orientation, and the nanoscale translations that exist to minimize the interface energy in the local neighborhood of the boundary. From a macroscopic perspective, planar interfaces between two crystal regions have five degrees of freedom [13,50,51], i.e., an interface is fully characterized by a misorientation angle, θ, a misorientation axis vector, M, and the normal vector to the interface plane, N. Fig. 1 shows a schematic of the misorientation scheme. Boundaries for which the normal to the interface plane is perpendicular to the misorientation axis (⊥N) are defined as “tilt” interfaces, as shown in Fig. 1(a). Similarly, boundaries for which the normal to the interface plane is parallel to the misorientation axis are defined as “twist” interfaces. Grain boundaries in actual polycrystalline materials may have both tilt and twist character, as shown in Fig. 1(b). From a microscopic perspective, interfaces between crystal lattices have three addition degrees of freedom associated with the mutual nanoscale...