HotQC simulation of nanovoid growth under tension in copper

Abstract

We apply the HotQC method of Kulkarni et al. (J Mech Phys Solids 56:1417-1449 to the study of quasistatic void growth in copper single crystals at finite temperature under triaxial expansion. The void is strained to 30% deformation at initial temperatures and nominal strain rates ranging from 150 to 600 K and from 2.5×10 5 to 2.5×10 11 s −1 , respectively. The interatomic potential used in the calculations is Johnson's Embedded-Atom Method potential Johnson (Phys Rev B 37:3924-3931, 1988). The computed pressure versus volumetric strain is in close agreement with that obtained using molecular dynamics, which suggests that inertia effects are not dominant for the void size and conditions considered. Upon the attainment of a critical or cavitation strain of the order of 20%, dislocations are abruptly and profusely emitted from the void and the rate of growth of the void increases precipitously. Prior to cavitation, the crystal cools down due to the thermoelastic effect. Following cavitation dislocation emission causes rapid local heating in the vicinity of the void, which in turn sets up a temperature gradient and results in the conduction of heat away from the void. The cavitation pressure is found to be relatively temperature-insensitive at low temperatures and decreases markedly beyond a transition temperature of the order of 250 K.

Summation rules for a fully nonlocal energy-based quasicontinuum method

“…Void growth in infinite crystals subject to remote loading has been investigated by the QC method before, see e.g. Marian et al (2005Marian et al ( , 2008 and Ariza et al (2012), but not in a macroscopic boundary value problem such as the nanoindentation scenario studied here. Results of the microstructure evolution from the initial void to the final defect network are shown in Fig.…”

A $\Gamma$-Convergence Analysis of the Quasicontinuum Method

“…Examples of such applications include: dislocations and plasticity [44,50,61]; nanoindentation [58,31,32]; nanovoid growth [40,41]; fracture [43,45,44]; grain boundaries [56]; and others. Extensions to finite-temperature, be it at equilibrium [22,55,42,62], or with heat conduction accounted for [33,3,6], greatly extend the range of applicability of the method.The mathematical analysis of the quasicontinuum method is comparatively more …”

Finite-temperature non-equilibrium quasi-continuum analysis of nanovoid growth in copper at low and high strain rates

“…In particular, we aim to determine the critical strain rate _ e c below which the process is ostensibly quasistatic and microinertia can be safely neglected. Ariza et al (2012) have estimated the critical strain rate separating the quasistatic and dynamic regimes on the basis of analytical expressions for the dynamic expansion of a spherical void in a rigidplastic material (Ortiz and Molinari, 1992). Here, instead, we proceed to determine the critical strain rate directly by comparing the results of test quasistatic and dynamic calculations at different volumetric strain rates.…”

“…In this study, we overcome these difficulties by means of the finite-temperature quasicontinuum method (HotQC) of Kulkarni et al (Kulkarni et al, 2008;Ariza et al, 2012;Ponga et al, 2012;Venturini et al, 2014). The aim of HotQC is to account for thermal effects, including atomic-level heat conduction, without the need for tracking every thermal vibration of the atoms.…”