QUANTIFICATION OF SIZE AND STRAIN RATE EFFECTS IN
W.Liang and M.Zhou
Georgia Institute of Technology, US
Nanoscale plasticity has drawn significant attention in recent years. Extensive Experimental and numerical studies have been conducted in this field. In previous molecular dynamics (MD) simulations, the Nose-Hoover isothermal procedure was often used to maintain a constant temperature. This is purely a numerical scheme aimed at limiting temperature increases. However, it is important to note that this treatment is artificial and is inconsistent with the dynamic nature of the deformation. At strain rates on the order of or higher, there is not sufficient time for the specimens to exchange heat with the environment. The deformation of nanowires is more close to an adiabatic process rather than an isothermal process. Consequently, more realistic treatments of the issue should entail proper account of temperature increases and should avoid artificial or arbitrary numerical schemes.
In this paper, the effects of size and strain rate on the tensile deformation of Cu nanowires are analyzed. The analysis uses MD simulations with an embedded atom method (EAM) potential (Daw and Baskes (1984)). The cross-sectional dimensions of the nanowires vary from 5 to 20 lattice spacings (or 1.8-7.2 nm). The length of the specimens is 60 lattice spacings (or 21.6 nm). Deformations under spacing strain rates between and are analyzed. The variation of yield stress with specimen size and deformation rate is studied. It is found that the yield stress (stress at which plastic deformation initiates) decreases with specimen size, while increases with loading rate. On the other hand, ductility (strain at which total separation occurs) increases with specimen size and strain rate (see Figs. 1-2). The influences of specimen size are a result of enhanced opportunities for dislocation motion at larger sizes. The influence of rate is due to the dynamic wave effect or phonon drag that impedes the motion of dislocations.
The deformation of nanowires is an intrinsically dynamic process. Proper distinction between internal stress and externally applied stress (traction) must be made. In the current analysis, both the internal stress and externally applied traction are tracked. This allows the fully dynamic nature of the deformation process to be quantified. Historically, one of the most commonly used methods to calculate stress in an MD system is the virial stress. The virial stress includes a kinetic energy part and an interatomic force part. Zhou (2002) has shown that the kinetic energy term in the virial stress causes it to violate balance of momentum if it is interpreted as a form of mechanical stress. The conclusion is that the interatomic force part of the virial stress alone fully constitutes the Cauchy stress. This new understanding is reflected and used in this paper. In particular, the analysis focuses on the level of errors that may be caused in stress calculation when the kinetic energy term is included. It is found that the relative error varies as the deformation progresses. At the onset of yielding, the level of error is on the order of 2-4%. However, at large plastic strains, the error is typically of the order of 30% and can exceed 100% toward late stages of deformation when fracture initiates.
NSTI Nanotech 2003 Conference Technical Program Abstract