Diffraction strain/stress analysis has been widely used in the determination of residual and applied stresses in the surface layers and bulk volumes of materials for a long time. The technique has been used for almost 100 years. However, there are still issues that have not been yet addressed.In this dissertation, we address these issues. The basic theory of diffraction strain/stress analysis is extensively reviewed and the weaknesses of the analysis are explained carefully. The current definitions that have been used for describing residual stresses are unified under this expanded analysis. In addition, the homogeneous continuum analysis is extended to the polycrystalline materials under various loading types. To search for answers to the questions asked in this dissertation, finite element modeling. was used. This approach provides both local and global stress and strain information at all locations of a virtual specimen. The results show that St. Venant regions such as edges, voids, or geometric constraints cause local inhomogeneous strain/stress distribution which can cause deviations from linear deformation theory. Even if the far-field load region is sampled by X-rays, the representative volume element should be determined by preliminary experiments because almost all single-phase polycrystalline materials (with the exception of tungsten) are composite materials within which variations of elastic moduli are observed along with sample directions. In the multiphase polycrystalline materials, this problem becomes more serious due to the differential deformation of each phase with respect to each other. Therefore, an experimenter needs to be careful during the experiment, in acquiring representative data; this requires significant preparation and material characterization. With the findings of the dissertation, a set of rules are written for users and experimenters to apply during or before the experiments to collect accurate and representative data.

As crucial infrastructure systems remain in service up to and beyond their originally intended service lives, there has been a significant increase in efforts to quantify their current strength and remaining life span. Suspension bridges are of particular concern due to their impact on commerce, low repairability, and high replacement cost. As such, quantification of the performance of suspension bridge main cables at elevated temperatures is necessary for a holistic safety assessment. These cables are the primary load-carrying members, and are susceptible to vehicular fires near the midspan and anchorage where the cable sweeps low to the deck. Due to the dearth of empirical data regarding the thermomechanical properties of main cables, previous studies were forced to rely on thermomechanical properties derived for different materials, geometries, and scales. It is the chief goal of this dissertation to fill this void in high-temperature empirical data. First, the high temperature stress-strain behavior of the constituent ASTM A586 wires is examined. The coldworked wires are highly susceptible to recovery at elevated temperatures, which has the power to undo the primary strengthening mechanism. Large decreases in elastic modulus, yield stress, and ultimate stress are observed at elevated temperature. The high temperature stress-strain curves are fully parameterized, and a procedure for generating stress-strain curves at temperatures between 22°C and 724°C is provided. Next, the post-fire performance of the wire is quantified. Wires are heated to various temperatures up to 842°C and then allowed to cool before being tensile tested. The results of this testing show that a significant portion of the high-temperature strength-loss observed in the in-situ tests persists after cool-down. Exposure to elevated temperatures reduces strength and fundamentally alters the shape of the stress-strain curves of the heated and cooled wires. These post-fire stress-strain curves are fully parameterized, and a procedure for recreating them between 22°C and 842°C is provided. Next, the metallurgical underpinnings for the observed changes in mechanical behavior at and after high-temperature exposure are explored using neutron diffraction techniques. Two engineering beamline experiments generate peak-narrowing data that sheds light on the evolving dislocation density and crystallite size in this wire during and after heating. Results confirm that the decreases in wire strength that persist after cool-down are the product of recovery; temperatures in excess of 700°C decrease wire dislocation density to values similar to those of undeformed structural materials. Finally, the thermal conductivity of the main cable is addressed. The air voids and point contacts between the wires create a complex (and anisotropic) heat transfer situation within main cables. A one-to-one, 8200 kg mock-up of a panel of a suspension bridge main cable is constructed, instrumented, and heated. The data provided by the internal temperature sensors is used to tune the thermal conductivity of a representative finite element via a gradient descent algorithm. The resulting temperature-dependent thermal conductivity function allows the complex internal heat transfer of the main cable to be accurately approximated by a monolithic section with conductivity tuned to the measured behavior of a physical main cable. Cumulatively, the results of these studies shows that the thermomechanical properties of main cables are not well represented by previous approximations that are based on other materials and applications. The properties derived herein will facilitate more accurate performance estimates of suspension bridges subjected to fires than previously possible.

Vibrations of nuclei in crystals govern various properties such as thermal expansion, phase transitions, and elasticity, and the quasiharmonic approximation (QHA) is the simplest nontrivial approximation which includes the effects of vibrational anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate the quasiharmonic approximation by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO₂) using density functional theory with three exchange-correlation functionals. The convergence of the two complementary strain parametrizations is evaluated for the computed thermal expansion. The temperature dependent lattice parameter and thermal expansion computed within the QHA is compared with experimental measurements. The QHA results are compared to measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. We then demonstrate the generalized quasiharmonic approximation in a non-cubic material, ferroelectric lead titanate, computing the temperature and stress dependence of the full elastic constant tensor. The irreducible derivative approach is employed for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We use density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimentally measured lattice parameters close to 0 K. The quasiharmonic approximation overestimates the measured temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed. The next material we study is zirconium nitride, employing the quasiharmonic approximation with the irreducible derivative approach to compute the phonons and thermal expansion. Density functional theory is used with two exchange-correlation functionals. We investigate the difference between the measured and computed optical phonon branches, showing that volume effects, two-phonon scattering, and nitrogen vacancies do not explain the discrepancy between the measurement and computation. The temperature dependent lattice parameter is computed within the QHA, where the thermal expansion is overestimated as compared with existing experimental measurements.