A field dislocation mechanics approach to modelling the influence of microstructure on fatigue behaviour of nickel-based superalloys

Rangel, Joseph (2021). A field dislocation mechanics approach to modelling the influence of microstructure on fatigue behaviour of nickel-based superalloys. University of Birmingham. Ph.D.

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Abstract

The aim of the study was to use a continuum theory of dislocation transport to predict the influence of precipitate variations on the fatigue behaviour of a Nickel-based superalloy. The proposed computational framework explicitly models the development of dislocation slip bands and their interactions with \(\gamma^{\prime}\) precipitates and how these are connected to the macroscale stress-strain response. In the present field dislocation mechanics (FDM) treatment, the evolution of the dislocation field is described by a continuity equation for the dislocation density tensor, \(\alpha\). The numerical methods to solve the FDM equation set were developed and coupled to a commercial finite element scheme. The minimum length scale for the application of the FDM theory was determined using a discrete dislocation dynamics (DDD) model. Initial development simulations of FDM framework accurately simulated continuum dislocation pile-up distributions. From DDD simulations a probability distribution function for stress fluctuations associated with elastic interactions between individual dislocations was derived and incorporated into FDM framework. It was found that such fluctuations had no significant effect on slip band development or the stress-strain response of the distribution. Simulations of the FDM model with a \(\gamma^{\prime}\) microstructure show that yield occurs when slip bands span the full length of the simulated grain, shearing all of the particles in its path. The grain boundaries were treated as impenetrable barriers in the computational domains creating linear hardening effects post yield. Subsequently the FDM model was adapted to simulate cyclic loading under simple shear conditions. Predictions were presented for temperature dependant \(\gamma^{\prime}\) distributions representative of those found within a polycrystal Nickel-based superalloy. Bauschinger effects were predicted and shown to arise due to the reversal of accumulated plasticity on the slip systems, as new sources activated due to the change of the load direction and the existing dislocations from previous load shear back across the domain. Differences in fatigue behaviour at each temperature was caused by the influence of slip band\(\gamma^{\prime}\) interactions. These were induced by changes in volume fraction, cutting stress and dislocation line tension which govern the number slip events. Scatter in fatigue behaviour was observed at each temperature due to differences in the amount of accumulated plasticity on different slip bands; linked to dislocations interactions with \(\gamma^{\prime}\) particles. Analysis of the stress-strain response predicted softening under fatigue with a convergence of plastic strain range, \(\nabla\epsilon_{p}\), and stress range, \(\nabla\sigma\), to a steady-state fatigue loop.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):