Nanostructurally small cracks (NSC): A review on atomistic modeling of fatigue

Abstract

Fatigue is one of the most damaging mechanisms in structural components. With the development of structural nanomaterials, it is imperative to investigate the fatigue damage phenomena at the atomic scale. To study fatigue behavior at the nanoscale, one must apply non-continuum modeling frameworks, such as molecular statics (MS), molecular dynamics (MD), and Monte Carlo (MC) methods. To date, only MD and MS simulations using embedded atom method (EAM) and modified embedded atom method (MEAM) potentials have been conducted, and this paper reviews these simulations of the nanoscale fatigue-crack growth in nickel and copper including single crystals, bicrystals, and polycrystals. A nanoscale size middle tension (MT) specimen with the lateral side applied periodic boundary conditions was used to investigate the fatigue behavior in nickel and copper single crystals. Simulation results revealed that the cyclic plastic deformation at the crack tip was the main influencing factor for fatigue-crack growth. Two main nanoscale mechanisms of crack propagation were observed: (1) the main cracks linked with the voids nucleated in front of crack tip due to high dislocation density generated by the cyclic loading; and (2) the main cracks broke the atomic bonds in the crack plane without much plasticity. For the bicrystals and polycrystals, the grain boundaries exerted resistance to the crack propagation. To study the interactions between cracks and grain boundaries, four cases of grain boundary interfaces for copper and two cases of grain boundaries for nickel were simulated. In copper bicrystals, the crack path deviated and moved from one grain to another for high misorientations, while there were voids nucleating at grain boundaries in front of the crack tip that linked back with the main crack. Similar to macroscale fatigue, dislocation substructures were observed to develop in the atomic lattice during cyclic loading. In nickel bicrystals, for large misorientations, the cracks were stopped by grain boundaries. For small misorientations, the crack propagated through the grain boundary, but the growth rate was reduced due to the resistance of the grain boundary. Fatigue-crack growth rates for nanocracks were computed and compared with growth rates published in the literature for microstructurally small cracks (micron range) and long cracks (millimeter range). A nanostructurally small crack (NSC) was introduced in terms of the CTOD. The quantified NSC growth rates in copper single crystals were very similar with those experimentally measured for small cracks (micron range) and with those at stress-intensity-factor ranges lower than the threshold for long cracks (millimeter range). The atomistic simulations indicated that reversible plastic slip along the active crystallographic directions at the crack tip was responsible for advancing the crack during applied cycling. In the case of single or double plastic slip localization at the crack tip, a typical Mode I fatigue crack arose along a slip band and then grew into a mixed Mode I + II crack growth mechanism. For crystal orientations characterized by multiple slip systems concomitantly active at the crack tip, the crack advance mechanism was characterized by nanovoid nucleation in the high density nucleation region ahead of the crack tip and by linkage with the main crack leading to crack extension. To facilitate observations of fatigue-crack growth, the simulation of a copper polycrystal was performed at low temperature 20 K as well. The crack propagated along persistent slip bands within the grain. The crack propagated along grain boundaries when the angle between the direction of crack propagation and the grain boundary was small, while it was impeded by the grain boundary when the angle was large. The results obtained for the crack advance as a function of stress intensity amplitude are consistent with experimental studies and a Paris law exponent of approximately two.