<p> A unified approach, employing effective phonon frequency distributions, is used to investigate effects of phonon anisotropy in the hcp metals.</p> <p> Phonon information is included by means of empirical force constant models, and pseudopotentials are used to describe the electron-ion interaction.</p> <p> Zinc and thallium superconducting gaps are determined as a function of position on the Fermi surface. The gap anisotropy is used to calculate thermodynamic properties.</p> <p> The normal state electron-phonon mass enhancement and the imaginary part of the electron self-energy are calculated as a function of temperature and Fermi surface position. Anisotropic transport scattering times are defined, calculated and used to obtain the polycrystalline and single crystal resistivities. Comparison is made with resistivities obtained by the variational approach.</p> / Thesis / Doctor of Philosophy (PhD)

Zirconium and its alloys have been extensively used in both heavy and light water nuclear reactors. Like other Hexagonal Close-Packed (HCP) materials, e.g. magnesium, zirconium alloys develop different textures during manufacturing process which result in highly anisotropic materials with different responses under different loading conditions. Slip and twinning are two major deformation mechanisms during plastic deformation of zirconium. This dissertation uses various experimental techniques and a crystal plasticity scheme in the finite element framework to study deformation mechanisms in HCP materials with an emphasis on twinning in Zircaloy-2. The current study is presented as a manuscript format dissertation comprised of four manuscript chapters. After a literature review in Chapter 2, Chapter 3 reports steps in developing a crystal plasticity finite element user material subroutine for modeling deformation in Zircaloy-2 at room temperature. It is shown in Chapter 3 that the developed rate dependent equations are capable of capturing evolution of key features, e.g., texture, lattice strains, and twin volume fractions, during deformation by twinning and slip. Chapter 4 reports various assumptions and approaches in modeling twinning where results are compared against neutron diffraction measurements from the literature. It is shown in Chapter 4 that the predominant twin reorientation scheme can explain texture development more precisely than the other schemes discussed. Chapter 5 and 6 are two connected chapters where in the first one the formation of twins is studied statistically and in the second one, local inception and propagation of twins is studied. Numerical results of these two chapters are compared with 2D electron backscattered diffraction measurements, both carried out by the author and from the literature. Results from these two connected chapters emphasize the important role of grain boundary geometry and stress concentration sites on twin nucleation and growth. The four manuscript chapters are followed by summarizing conclusions and suggestions for future work in Chapter 7. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2012-04-23 11:50:33.751

The deformation behaviour and twinning mechanisms of commercially pure titanium alloys were investigated using complementary diffraction techniques and crystal plasticity modelling. The main motivation for conducting this investigation was to improve understanding of the deformation of titanium to help achieve the long term aim of reducing manufacturing and design costs. The deformation behaviour was characterised with tension, compression and channel die compression tests for three important variables: orientation; temperature from 25 C to 600 C; and composition for two contrasting alloys, CP-G1 and CP-G4. The experimental data used to characterise the behaviour and determine the mechanisms causing it were: textures determined by X-ray diffraction; twin area fractions for individual modes determined using electron back-scatter diffraction; and lattice strains measured by neutron diffraction. A strong effect of the orientation–stress state conditions on the flow curves (flow stress anisotropy) was found. The propensity for prism hai slip was the dominant cause of the behaviour – samples that were more favourably oriented for prism hai slip had lower flow stresses. Twinning was the most significant secondary deformation mode in the CP-G1 alloy but only had a minor effect on flow stress anisotropy in most cases. In the CP-G4 alloy twinning generally did not play a significant role indicating that hc + ai slip modes were significant in this alloy. Differences in the flow stress anisotropy between the two alloys were found to occur largely in the elasto-plastic transition and initial period of hardening. Modelling results indicated that larger relative resolved shear stress values for secondary deformation modes in the higher purity alloy increased the initial anisotropy. Decreasing flow stresses with increasing temperature were largely caused by a decrease in the critical resolved shear stress (CRSS) values for slip, but also by a decrease in the Hall-Petch parameter for slip. The propagation of twinning was found to be orientation dependent through a Schmid law in a similar way to slip – it was activated at a CRSS and hardened so that an increasing resolved shear stress was required for it to continue operating. The CRSS values determined for the individual twin modes were – 65MPa, 180MPa, 83MPa for {1012}, {1122} and {1011} twinning, respectively. Further, twinning was found to be temperature insensitive except when the ability to nucleate twins posed a significant barrier (for {1011} twinning). Also, the CRSS for {1012} twinning was clearly shown to increase with decreasing alloy purity. A thorough method for determining crystal plasticity modelling parameters based on experimental data was formulated. Additionally, twinning was modelled in a physically realistic manner influenced by the present findings using the visco-plastic self-consistent (VPSC) model. In particular: the activity of twinning decreased in a natural way due to greater difficulty in its operation rather than through an enforced saturation; and hardening or softening due to changes in orientation and dynamic Hall-Petch hardening were important. The rigorous modelling procedure gave great confidence in the key experimental findings.