Thermal Activation and Ductile vs. Brittle Behavior of Microcracks in 3D BCC Iron Crystals under Biaxial Loading by Atomistic Simulations

Abstract

We present the results of free 3D molecular dynamics (MD) simulations, focused on the influence of temperature on the ductile-brittle behavior of a pre-existing central Griffith through microcrack (1¯10)[110] (crack plane/crack front) under biaxial loading σA and σB in tension mode I. At temperatures of 300 K and 600 K, the MD results provide new information on the threshold values of the stress intensity factor K and the energy release rate G, needed for the emission of <111>{112} blunting dislocations that support crack stability. A simple procedure for the evaluation of thermal activation from MD results is proposed in the paper. 3D atomistic results are compared with continuum predictions on thermal activation of the crack induced dislocation generation. At elevated temperature T and biaxiality ratios σB/σA ≤ 0.8 dislocation emission in MD is observed, supported by thermal activation energy of about ~30 kBT. With increasing temperature, the ductile-brittle transition moves to a higher biaxiality ratios in comparison with the situation at temperature of ~0 K. Near the transition, dislocation emission occurs at lower loadings than expected by continuum predictions. For the ratios σB/σA ≥ 1, the elevated temperature facilitates (surprisingly) the microcrack growth below Griffith level.

Ductile-brittle transition at edge cracks (001)[110] in BCC iron under different loading rates in mode I: a 3D atomistic study

“…As for bcc iron, our recent MD simulations were focused mostly on the ductile crack orientation 110 110 ( ¯)[ ] that is not too sensitive to loading rate [4]. Dislocation emission presented in MD simulations [6,7] and its thermal activation in [8] are in agreement with the corresponding continuum predictions [9][10][11] and comply with the experimental observations presented in [4], which is encouraging. The black points come from [3], where longer crystals of the length L∼100 mm were used.…”

“…/ is the interplanar distance in the [110] direction along the crack front. The condition above is obeyed and the used thickness B is sufficient for a reliable description of the thermal activation, which is presented in [8] for temperature of 300 K and 600 K.…”

“…Newtonian equations of motion for the individual atoms are solved in all 3 directions x 1 , x 2 x 3 , using a stable time integration step h=1×10 -14 s, tested in [8].…”

“…Newtonian equations are solved with zero external forces. During the time integration of Newtonian equations, the total kinetic energy Ekin=Ekin(t) and the potential energy Epot=Epot (t, 0)=Epot(t) -Epot(0) in the system fluctuate [8]. With increasing time, Ekin gradually decreases and Epot increases since the atoms deviate from their equilibrium positions and the atomic lattice is subject to thermal expansion.…”

“…where á ñ Ekin t ( ) is the time averaged value of the total kinetic energy in the system in the steady state (see e.g. Figure 1(b) in [8]) with á ñ Ekin t ( ) =1.237×10 -14 J and T=295.1 K at time t=2000 h. In statistical mechanics (thermodynamics), the heated atomistic sample in the steady state corresponds to canonical ensemble (N,V,T) with a constant number of particles N, constant temperature T and constant volume…”