Dislocation modeling in face-centered cubic metals : from atomistics to continuum

Dislocations in fcc crystals are studied here in several length and time scale regimes starting from atomistic calculations up to continuum models. Temperature-dependence of the stacking fault free energy (SFFE) for Fe is calculated utilizing the thermodynamic integration and a reference free energy model for solids based on the quasi-harmonic approximation. The underlying molecular dynamics (MD) simulation is based on the bond order potential for Fe of Mueller et al. (2007). The SFFE of Fe at 0 K is calculated to be −20 mJ/m2, negative due to the fact that the fcc phase is unstable at this temperature. The SFFE increases with temperature and becomes positive at around 200 K. Depending on system size, an SFFE for Fe between 5.5 and 9.1 mJ/m2 is obtained at 298 K, increasing to between 70 and 80 mJ/m2 at 1000 K. Next, the interaction between dislocations and stacking faults at low temperatures is studied with the help of MD. Observed interaction types in Cu include annihilation, penetration, and growth. Of particular importance is the mixed screw-edge character of the partial dislocations involved and the fact that the screw part cross slips more easily than its edge counterpart. The interaction of curved dislocations with twinned crystal is also studied with MD. In two of the in-plane shear loading directions, jerky stress flow is observed. Upon closer investigation, the jerky behavior is related to the fast motion of twin boundary. Next, the Peierls-Nabarro (PN) and Volterra (V) dislocation models are employed for dislocation-mediated bulk twin nucleation and growth. The dynamic model is applied to the modeling of variable dislocation separation in the twin. In this context, dislocations are closest together at the twin tip and increase in separation away from the tip. The phase field model for dislocation is based on periodic microelasticity (Wang et al. 2001, Bulatov & Cai 2006, Wang & Li 2010) to model the strongly non-local elastic interaction of dislocation lines via their (residual) strain fields. The energy storage is modeled here with the help of the ”interface” energy concept and model of Cahn & Hilliard (1958) (see also Allen & Cahn 1979, Wang & Li 2010). The current approach is applied to determine the phase field free energy for Al and Cu. The identified models are then applied to simulate dislocation dissociation, stacking fault formation, glide and dislocation reactions in these materials. Transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading is also studied. The underlying model for dislocation wall interaction is based on the non-singular PN model. The influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly non-local (WNL; short-range), are studied. The pile-up behavior predicted by the current SNL-based continuous wall distribution modeling is consistent with that predicted by discrete wall distribution modeling (e.g., Roy et al. 2008, de Geus et al. 2013). Both deviate substantially from the pile-up behavior predicted by WNL-based continuous wall distribution modeling (e.g., Dogge 2014, Chapter 2)

Modeling Dislocation-Stacking Fault Interaction Using Molecular Dynamics

In a number of fcc materials such as copper or aluminum, as well as more complex materials such as twinning induced plasticity (TWIP) steels, the interaction between dislocations and other defects such as stacking faults or twins plays an important role in the hardening behavior of such materials. Interactions of dislocation and twin or stacking fault layers have been studied in this work using molecular dynamics. Depending on the material and the loading conditions, possible interaction modes include (i) penetration of the dislocation into the faulted layer, (ii) reduction of the faulted layer after interaction, (iii) growth of the faulted layer after interaction. Such studies up to this point have been performed without temperature control near zero K (0 to 2 K). In this work, we extend the previous studies to higher temperature with the help of two methods, both based on molecular dynamics (MD) modeling. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Effect of Twin Boundary Motion and Dislocation-Twin Interaction on Mechanical Behavior in Fcc Metals

The interplay of interface and bulk dislocation nucleation and glide in determining the motion of twin boundaries, slip-twin interaction, and the mechanical (i.e., stress-strain) behavior of fcc metals is investigated in the current work with the help of molecular dynamics simulations. To this end, simulation cells containing twin boundaries are subject to loading in different directions relative to the twin boundary orientation. In particular, shear loading of the twin boundary results in significantly different behavior than in the other loading cases, and in particular to jerky stress flow. For example, twin boundary shear loading along ⟨ 112 ⟩ results in translational normal twin boundary motion, twinning or detwinning, and net hardening. On the other hand, such loading along ⟨ 110 ⟩ results in oscillatory normal twin boundary motion and no hardening. As shown here, this difference results from the different effect each type of loading has on lattice stacking order perpendicular to the twin boundary, and so on interface partial dislocation nucleation. In both cases, however, the observed stress fluctuation and “jerky flow” is due to fast partial dislocation nucleation and glide on the twin boundary. This is supported by the determination of the velocity and energy barriers to glide for twin boundary partials. In particular, twin boundary partial edge dislocations are significantly faster than corresponding screws as well as their bulk counterparts. In the last part of the work, the effect of variable twin boundary orientation in relation to the loading direction is investigated. In particular, a change away from pure normal loading to the twin plane toward mixed shear-normal loading results in a transition of dominant deformation mechanism from bulk dislocation nucleation/slip, to twin boundary motion