Atomistic simulations of tension–compression asymmetry in dislocation nucleation for copper grain boundaries

Abstract

Atomistic simulations are used to investigate how grain boundary structure influences dislocation nucleation under uniaxial tension and compression for a specific class of symmetric tilt grain boundaries that contain the E structural unit. After obtaining the minimum energy grain boundary structure, molecular dynamics was employed based on an embedded-atom method potential for copper at 10 K. Results show several differences in dislocation nucleation with respect to uniaxial tension and compression. First, the average nucleation stress for all 〈1 1 0〉 symmetric tilt grain boundaries is over three times greater in compression than in tension for both the high strain rate and quasistatic simulations. Second, partial dislocations nucleate from the boundary on the {1 1 1} slip plane under uniaxial tension. However, partial and full dislocations nucleate from the boundary on the {1 0 0} and {1 1 1} slip planes under uniaxial compression. The full dislocation nucleation on the {1 0 0} plane for boundaries with misorientations near the coherent twin boundary is explained through the higher resolved shear stress on the {1 0 0} plane compared to the {1 1 1} plane. Last, individual dislocation nucleation mechanisms under uniaxial tension and compression are analyzed. For the vicinal twin boundary under tension, the grain boundary partial dislocation is emitted into the lattice on the same {1 1 1} plane that it dissociated onto. For compression of the vicinal twin, the 1/3〈1 1 1 〉 disconnection is removed through full dislocation emission on the {1 0 0} plane and partial dislocation emission parallel to the coherent twin boundary plane, restoring the boundary to the coherent twin. For the $\mathrm{\Sigma }19$ boundary, the nearly simultaneous emission of numerous partial dislocations from the boundary result in the formation of the hexagonal close-packed (HCP) phase.

Introduction

Much of the recent scientific interest in nanocrystalline materials has regarded the improved functional and mechanical properties as well as the atomic-level mechanisms of plastic deformation in the grain boundaries [1], [2], [3], [4], [5], [6], [7], [8], [9]. In particular, small grain sizes (on the order of 10 nm) result in the heterogeneous nucleation and emission of dislocations from the grain boundaries (GBs). These deformation mechanisms are confirmed with in situ transmission electron microscopy (HRTEM) experiments, which have shown grain boundaries emitting partial dislocations that form stacking faults and deformation twins in nanocrystalline (nc) Al and Cu [10], [11]. While some insight into the deformation mechanisms of nc materials has been obtained from in situ HRTEM experiments [10], [11], [12], these experiments are often very difficult to perform. In many cases, atomic simulations of plasticity phenomena actually preceded the experimental observation of the same phenomena. For example, Yamakov and coworkers predicted deformation twinning in aluminum with molecular dynamics simulations [13], [14] prior to the experimental TEM evidence of deformation twinning in nanocrystalline aluminum by Chen and colleagues [2]. The good agreement between calculated and experimentally observed deformation mechanisms motivates using atomistic simulations to examine deformation mechanisms at the nanoscale, as experiments at this scale are often difficult to perform.

Recently, experiments have used nanoindentation techniques (i.e., compression) to test mechanical behavior in materials with small volumes. Uniaxial compression experiments have primarily been used at smaller scales since they do not require gripping the specimen, as with uniaxial tension tests. For example, recent experiments [15], [16], [17], [18], [19] have used focused ion beam (FIB) milling to machine a cylindrical column that remains attached to the bulk substrate at one end. After fabricating the columns, a nanoindentor with a flat tip is used to test the plastic response of the column under uniaxial compression. These results have suggested that dislocation nucleation is the rate limiting process at small volumes, not dislocation motion. However, there still remain questions about the differences in response between tension and compression. For example, are there differences in the nucleation stresses for dislocation nucleation between tension and compression? Are there differences in the dislocation nucleation mechanisms? Do dislocations nucleate on the {1 1 1} slip plane of maximum resolved shear stress? These research questions provide the motivation for the current work.

As previously mentioned, atomistic simulations can be used to probe the differences in mechanical behavior and mechanisms between tension and compression. Prior literature has focused very little on the effect of uniaxial loading (tension vs. compression) in materials with small volumes. In one recent example, Tschopp and McDowell [20] used atomistic simulations to show an asymmetry in the stress required for homogeneous dislocation nucleation under an applied uniaxial tensile and compressive load. These simulations are applicable to nucleation of dislocations in perfect single crystals with no initial dislocation content. For some loading axis orientations, a higher nucleation stress is required in uniaxial compression than tension, and vice versa for other loading axis orientations. This work suggests that the resolved stress normal to the maximum Schmid factor slip plane (on which the dislocation nucleates) may be important for dislocation nucleation. But it is still not known how interfaces affect the nucleation stress asymmetry or the dislocation nucleation mechanisms from grain boundaries. Simulations examining this area may provide insight into the plasticity of nanocrystalline metals and materials at small volumes, such as in the aforementioned FIB machined nano-columns.

To address these questions, nine 〈1 1 0〉 symmetric tilt grain boundaries (STGBs) with the E structural unit were deformed under uniaxial tension and uniaxial compression applied perpendicular to the boundary until the dislocation nucleation event. To the author’s knowledge, this is the first work to investigate the differences in dislocation nucleation from specific grain boundaries under tension and compression. Additionally, this work will compare dislocation nucleation via an applied strain rate with a quasistatic incremental approach. Last, the mechanisms of dislocation nucleation are compared between tension and compression for a few select boundaries. In low stacking fault energy copper, partial dislocations emit from the grain boundary during tension and full dislocations emit during compression. The slip plane that dislocations nucleate on may be different in tension and compression as well. This highlights the important nature of the resolved stress normal to the dislocation nucleation slip plane. Also, the grain boundary structure (more specifically, the dislocation content and organization within the grain boundary) plays an important role in the dislocation nucleation and emission process.