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

Abstract

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

The dislocation configurational energy density in discrete dislocation plasticity

“…Stroh [13] proposed a crack nucleation mechanism based on a stress criterion in which the stress concentration induced by a group of piled-up dislocations within an infinite medium was calculated analytically. The stress fields established were recently validated using DDP modelling by Zheng et al [14]. Tanaka and Mura [15], suggested that slip bands on the material surface are a potential site for fatigue crack nucleation and modelled the forward and reverse plastic flow using dislocation dipoles that move irreversibly on parallel layers.…”

Fatigue Performance of the Novel Titanium Alloy Timetal 407

“…The empirically derived Evans-Bache model was later supported by crystal plasticity modelling reported by Zheng et al [18]. Their results suggested that compared to standard cyclic loading, facet formation and crack initiation was encouraged under dwell conditions due to a large increase in the dislocation density within the grains favourably orientated for time-dependent slip.…”

The role of dwell hold on the dislocation mechanisms of fatigue in a near alpha titanium alloy

“…In contrast, cross-slip was observed in the LCF case but there was no activation of a dislocation source. Therefore it is inferred that the source was activated under dwell because the critical stress for source activation could be achieved as a result of time-dependent load shedding from the soft grain during the load holds [30].…”

“…TEM studies on the same alloy showed that a prism pile-up in the soft grain nucleated non-connected a dislocations in the hard grain under LCF [29]. DDP studies showed the nucleation of basal slip in the hard grain due to the higher stresses generated by the strong pile-ups in the soft grain under dwell [30]. However, such experimental work on dislocations has not been reported under dwell fatigue and the DDP calculations are 2D and are therefore unable to capture events such as dislocation cross-slip and dissociation.…”