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Plastic deformation of crystalline metals is facilitated by crystallographic defects called dislocations. In certain alloys at certain temperatures and loading rates, the motion of these dislocations can become chaotic and unstable. This is a phenomenon related to dynamic strain ageing called the Portevin���Le Ch��telier effect. The effect occurs when impurities, such as carbon and nitrogen, segregate to dislocations and obstruct their motion, leading to reduced ductility, hardening, and in the worst case, mechanical failure. In this thesis, I model plasticity with planar discrete dislocation plasticity. I extend planar discrete dislocation plasticity using anisotropic elasticity and introduce discrete diffusing solutes. This is used to understand the deformation of iron; and the onset and progression of the Portevin��� Le Ch��telier effect. Results from the model show that the nature of the diffusing solute field significantly affects the manifestation of the Portevin���Le Ch��telier effect. As the solute concentration increases, the iron specimen���s proof stress, flow stress and solute strengthening increases; and the serrations recorded in a stress-strain curve (symptomatic of the Portevin���Le Ch��telier effect) become smaller and occur at a slower frequency. Conversely, as the solute diffusivity increases, the serrations become larger and occur at a faster frequency. Furthermore, I show that anisotropic elasticity alters the mechanisms of plastic deformation of ��-iron at elevated temperatures; specifically, that a type edge dislocations, which are energetically unfavourable at moderate temperatures, are nucleated in increasing numbers. This agrees with experimental observations found in the literature but cannot be predicted by isotropic elastic models. The increase in a edge dislocations is symptomatic of the precipitous decrease in the yield strength of iron. My work has important consequences for the application of steels in elevated temperature environments such as generation IV very high temperature nuclear fission reactors.

A physically-based methodology for modelling microstructurally-sensitive fatigue crack growth has been developed and shown to capture many of the experimentally observed effects associated with microstructurally-sensitive fatigue crack growth, which currently contribute to the high levels of uncertainty in lifing models. Behaviours predicted by the model cover changes in rate and path due to interactions with local microstructural features including rate changes due to local crystal orientations, deflections and retardation at grain boundaries and crack path tortuosity within grains. The ability of the model to accurately capture these key behaviours has enabled their rationalisation within a physically-based, mechanistic framework. Open Access

This PhD project is concerned with fatigue crack nucleation in a range of superalloys, including single, oligo, and polycrystalline. An integrated experimental, characterisation and computational crystal plasticity study of cyclic plastic beam loading has been carried out on these alloys in order to assess quantitatively the mechanistic drivers for fatigue crack nucleation. The experimentally validated modelling provides knowledge of key microstructural quantities (accumulated slip, stress and GND density) at experimentally observed fatigue crack nucleation sites and it is shown that while each of these quantities is potentially important in crack nucleation, none of them in its own right is sufficient to be predictive. However, the local (elastic) stored energy density, measured over a length scale determined by the density of SSDs and GNDs, has been shown to predict crack nucleation sites in the mechanical tests. In addition, the stored energy is also able to correctly identify where secondary fatigue cracks are observed to nucleate in experiments. Further, experimental and crystal plasticity modelling studies have also been carried out to investigate non-proportionality and stress state effects in fatigue in a 316 stainless steel and Ni-based alloy RR1000 which have been shown to have substantial effects on fatigue life. Stored energy density has provided a consistent and unifying explanation for the experimental observations of fatigue life in differing loading regimes (both proportional and non-proportional). A single fatigue property (the critical stored energy density, equating to new surface energy) determined from axial fatigue data alone has been shown to provide good qualitative and reasonable quantitative prediction of the experimental observations of the complex loading, providing a mechanistic explanation for the fatigue behaviour. Open Access

Titanium alloys are widely used in gas turbine engines due to their high specific fatigue strength and ability to retain that strength up to temperatures in the range of 600°C. The alloy Ti-6Al-2Sn-4Zr-6Mo is used in the intermediate pressure compressor of the gas turbine engine, with a yield strength of around 1.1GPa. It has a microstructure of primary α laths within a β matrix. Between the primary α are much finer secondary α laths, creating a basketweave microstructure. These laths are multioriented, which gives the alloy its supreme strength and fatigue properties, which make it a prime candidate for an gas turbine engine component material. Within this thesis, microstructural control in Ti-6246 is examined in detail. The effect of chemistry, temperature and processing is investigated using a wide range of advanced microscopy techniques, including high resolution scanning transmission electron microscopy (HR-TEM), focussed ion beam (FIB) and nano beam electron diffraction (NBED). In addition to these techniques, mathematical approaches to the scientific questions are applied and compared. The kinetics of primary α are first examined using electro thermal mechanical testing (ETMT) to calculate the velocity of primary α growth at a variety of temperatures. This is then compared to an isothermal model, based upon the concentration of molybdenum in the matrix, and is found to be in good agreement with experimental results, with a peak in growth 40K below the β transus. Furthermore, the analytical model is used to compare the growth velocity of other titanium alloy systems, such as Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo, to examine the effects of oxygen and vanadium on the kinetics of lamellar α growth. The concentration of molybdenum at the primary α interface is also studied, and an increased concentration of molybdenum is found at the interface using scanning transmission electron microscopy-electron dispersive x-ray (STEM-EDX) and atom probe tomography (APT). This is also described mathematically with a model based on Fick's second law and matches the experimental results well. The α/β interface is characterised via high resolution scanning transmission electron microscopy (HR-STEM), both in a clean primary α interface (no secondary α) and a sample that has been cold rolled to 10% of its original height. Semi-coherent interface steps, or disconnections, can be seen around 4.5 atoms in length. This step feature has been mathematically predicted by both the PTMC and topological models, which are in good agreement. Additionally, a centre of symmetry analysis has been completed, highlighting a 1nm thick region approaching the interface with contraction along the [10-10]α and elongation along the [-12-10]β as the α lattice gradually approaches the β lattice. In the deformed sample, larger, incoherent interface stepsare seen, connected by {110}β slip bands. Finally, the introduction of dislocations via both hot and cold rolling is achieved, stimulating nucleation from defects within the β matrix. This results in the formation of multi-variant fine scale secondary α phase precipitation. This has been observed in situ by HR-TEM and nano beam electron diffraction (NBED), used to map the evolution of strain over time. Growth of fine scale secondary α occurred along {110} slip bands, with compression along the growth axis and elongation perpendicular to this. The fine scale α has been indexed using transmission Kikuchi diffraction (TKD). A processing route has been developed using lab based methods, through this proved problematic due to increased oxygen content and cooling rate fluctuation. Samples of as received (AR), straight through lab processing (STR) and straight through route with the addition of a warm roll (STR + Edit) to encourage nucleation from dislocations have been processed. High cycle fatigue (HCF), low cycle fatigue (LCF), fatigue crack growth (FCG) rate and threshold have been measured and compared. The STR has the highest HCF strength, whereas STR + Edit exhibits lower than expected HCF and LCF, though the fatigue crack growth rate is improved. Open Access

Ni superalloys are engineered material systems, where each microstructural feature conveys specific strengthening mechanisms. This project establishes experimental techniques which focus on understanding deformation in Ni superalloys; building upwards from single crystal CMSX-4, to polycrystalline FGH96, to carburised CMSX-4 & 10. The project combines micromechanical testing and material characterisation with the aim of extracting engineering properties, to help further advance the micromechanics field and aid in the development of new alloys. Micropillar compression experiments were used in this study and enable the analysis of deformation at characteristic strain(s) on the same length scale as the deformation processes. The critical resolved shear stress of pillars fabricated in {001} {011} {111} on single crystal CMSX-4 varied by 380 ± 10 MPa, 420 ± 15 MPa, 460 ± 16 MPa respectively, the resolved shear stress of pillars fabricated on individual grains on a polycrystal0 line sample, with nearly identical areas in the same orientation varies by less than 5% and these results were found to be consistent with literature. The critical resolved shear stress of pillars fabricated on single crystal CMSX-4, with carbide type phases captured on the top surface of the pillars varied by 400 ± 3.4 MPa, 420 ± 6 MPa 450 ± 23 MPa respectively, despite being the same crystal orientation and in similar locations ± 20 µm. The area fraction of the pillars mentioned above were; 5% 17% and 27% respectively. The variation in τcrss was found to be a consequence of the leeching of alloying elements, via the formation of carbide type phases which disrupted the ϒ/ϒ’ microstructure and disrupted the propagation of dislocations. The carbide size, area fraction, number density and shape abnormality were theorised to be proportional to the extent of ϒ/ϒ’ disruption. Transmission electron microscope (TEM), based analysis shows that the carbide type phases orientate themselves at junctions and dislocations tend to agglomerate around the phases at these points. Open Access

Microstructure formation and evolution in Pb-free solder alloys and solder joints on Cu substrates depend on the nucleation and growth of primary Cu6Sn5 and beta-Sn during solidification and thermal cycling in service. This thesis explores the mechanisms responsible for microstructure evolution at different stages during the lifetime of a solder joint. Cu6Sn5, a common intermetallic in Pb-free soldering, is usually first to nucleate and past work showed that aluminium additions can cause significant refinement of primary Cu6Sn5. In this work, it is showed that the mechanism of refinement is heterogeneous nucleation of Cu6Sn5 on either deltaCu33Al17 or gamma1Cu9Al4 coupled with significant constitutional supercooling ahead of growing Cu6Sn5 crystals. Cu-Al particles are shown to be effective catalytic nucleant particles in both hyper-eutectic Sn-4Cu-0.02Al and hypo-eutectic Sn-0.7Cu-0.05Al/Cu joints and share reproducible orientation relationships with Cu6Sn5. The growth of primary Cu6Sn5 also plays a role in determining the final microstructure. A deeper understanding of crystal growth mechanisms and transitions between different Cu6Sn5 morphologies is developed. It is shown that, for different composition and cooling rate combinations, Cu6Sn5 crystals undergo a faceted to non-faceted growth transition as a result of a kinetic interface roughening transition and a gradual change in mechanism from lateral growth governed by anisotropic attachment kinetics to continuous growth governed by diffusion and curvature. As the majority phase in most solder joints, betaSn nucleates at a later stage of solidification after Cu6Sn5 has nucleated. The nucleation of betaSn on the Cu6Sn5 layer in solder joints is studied in detail. It is shown that primary Cu6Sn5 is not a potent nucleant for Sn, but the Cu6Sn5 layer plays a key role in betaSn nucleation and microstructure formation in solder joints. Thermal contraction of Cu6Sn5, betaSn and other common phases in soldering is another important phenomenon that affects the performance of solder joints in service. Directional data on the anisotropic coefficient of thermal expansion (CTE) of Cu6Sn5 and other non-cubic intermetallics are measured and correlated with the directional Young’s modulus. Open Access