Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys

The focus of this paper is the mechanistic basis of the load shedding phenomenon that occurs under the dwell fatigue loading scenario. A systematic study was carried out using a discrete dislocation plasticity (DDP) model to investigate the effect of crystallographic orientations, localised dislocation behaviour and grain combinations on the phenomenon. Rate sensitivity in the model arises from a thermal activation process at low strain rates, which is accounted for by associating a stress- and temperature-dependent release time with obstacles; the activation energy was determined by calibrating an equivalent crystal plasticity model to experimental data. First, the application of Stroh's dislocation pile-up model of crack nucleation to facet fracture was quantitatively assessed using the DDP model. Then a polycrystalline model with grains generated using a controlled Poisson Voronoi tessellation was used to investigate the soft-hard-soft rogue grain combination commonly associated with load shedding. Dislocation density and peak stress at the soft/hard grain boundary increased significantly during the stress dwell period, effects that were enhanced by dislocations escaping from pile-ups at obstacles. The residual stress after dwell fatigue loading was also found to be much higher compared to standard fatigue loading. Taylor (uniform strain) and Sachs (uniform stress) type assumptions in a soft-hard grain combination have been assessed with a simple bicrystal DDP model. Basal slip nucleation in the hard grain was found to be initiated by high stresses generated by strong pile ups in the soft grain, and both basal and pyramidal slip nucleation was observed in the hard grain when the grain boundary orientation aligned with that of an active slip system in the soft grain. The findings of this study give new insight into the mechanisms of load shedding and faceting associated with cold dwell fatigue in Ti alloys used in aircraft engines

Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue

This paper addresses the role of grain boundary slip transfer and thermally-activated discrete dislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue in titanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies for titanium with respect to the misorientation angles. The grain boundary energies are utilised within a thermally-activated discrete dislocation plasticity model incorporating slip transfer controlled by energetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flow strength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown that significant stress redistribution from soft to hard grains occurs during the stress dwell, which is observed both for grain boundaries for which slip transfer is permitted and inhibited. However, the grain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses near the grain boundary after dwell, thus exacerbating the load shedding stress compared to an impenetrable grain boundary. The key property controlling the dwell fatigue response is argued to remain the time constant associated with the thermal activation process for dislocation escape, but the slip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozone does not significantly change the conclusions but does potentially lead to the possibility of a larger initial facet

Projector operators for the no-core shell model

Projection operators for the use within ab initio no-core shell model, are suggested.Comment: 3 page

Agterberg, Zheng, and Mukherjee Reply

Reply to Ikeda (arXiv:0712.3341).Comment: To appear in Phys. Rev. Let

Quantum dynamics of a qubit coupled with structured bath

The dynamics of an unbiased spin-boson model with Lorentzian spectral density is investigated theoretically in terms of the perturbation theory based on a unitary transformation. The non-equilibrium correlation function $P(t)$ and susceptibility $\chi^{\prime\prime}(\omega)$ are calculated for both the off-resonance case $\Delta\lesssim 0.5\Omega$ and the on-resonance case $\Delta\sim \Omega$. The approach is checked by the Shiba's relation and the sum rule. Besides, the coherent-incoherent transition point $\alpha_c$ can be determined, which has not been demonstrated for the structured bath by previous authors up to our knowledge.Comment: 25 pages, 11 figure