Jaber Rezaei Mianroodi

Strongly non-local modelling of dislocation transport and pile-up

The purpose of this work is the continuum modelling of transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading. To this end, the underlying model for dislocation wall interaction is based on the non-singular Peierls–Nabarro (PN) model for the dislocation stress field. For simplicity, attention is restricted to walls consisting of single-sign dislocations and to continuous wall distributions on a single glide plane. In this context, the influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly non-local (WNL; short-range) are studied in the context of interaction- and external-load-driven wall pile-up at a boundary. The pile-up boundary is modelled via a spatially dependent dislocation mobility which decreases to zero at the boundary. The pile-up behaviour predicted by the current SNL-based continuous wall distribution modelling is consistent with that predicted by discrete wall distribution modelling. Both deviate substantially from the pile-up behaviour predicted by WNL-based continuous wall distribution modelling. As such, it is clearly essential to account in continuum models for the intrinsic SNL character of the interaction between same-sign dislocations ‘close’ to the boundary. Gradient-based WNL ‘approximation’ of this interaction is not justified.

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 Müller et al. (2007). The SFFE of Fe at 0 K is calculated to be −20 mJ/m, 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/m is obtained at 298 K, increasing to between 70 and 80 mJ/m 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).