The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340 K. The total adiabatic potential of a system of sodium atoms is represented by a pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the results to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. The fluctuation averages make a large contribution to the elastic constants, and the uncertainties in these averages are the dominant uncertainties in the elastic constants. The strictly volume-dependent terms are very large. The ensemble correction is small but significant at higher temperatures. Surprisingly, the volume derivatives of the two-body potential make large contributions to the stresses and the elastic constants. The effects of finite potential range and finite system size are discussed, as well as the effects of quantum corrections and electronic excitations. The agreement of theory and experiment is very good for the magnitudes of C₁₁ and C₁₂. The magnitude of C₄₄ is consistently small by ∼9 kbar for finite temperatures. This discrepancy is most likely due to the neglect of three-body contributions to the potential. The agreement of theory and experiment is excellent for the temperature dependences of all three elastic constants. This result illustrates a definite advantage of MD compared to lattice dynamics for conditions where classical statistics are valid. MD methods involve direct calculations of anharmonic effects; no perturbation treatment is necessary.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Dr. Richard W. Neu; Committee Member: Dr. David L. McDowell; Committee Member: Dr. W. Steven Johnson.

Dynamic loading of polycrystalline metallic materials can result in brittle or ductile fracture depending on the loading rates, geometry, and material type. At high strain rates, mechanical energy due to plastic deformation may lead to significant temperature rise and shear localization due to thermal softening. These shear bands reduce the stress-bearing capacity of the material and act as a precursor to ductile fracture (e.g. cracks that develop rapidly on top of a shear band). Reliable models are needed to predict the response of metals subject to dynamic loads. Understanding the heat transfer physics in thermo-mechanical problems when cracks are developed is of great importance. In particular, capturing the interplay between heat conduction and crack propagation is still an open research field. To accurately capture the heat transfer physics across crack surfaces, damage models degrading thermal-conductivity are necessary. In this thesis, a novel set of isotropic thermal-conductivity degradation functions is derived based on a micro-mechanics void extension model of Laplace's equation. The key idea is to employ an analytical homogenization process to find the effective thermal-conductivity of an equivalent sphere with an expanding spherical void. The closed-form solution is obtained by minimization of the flux differences at the outer surfaces of the two problems, which can be achieved using the analytical solution of Laplace's equations, so-called spherical-harmonics. Additionally, a new anisotropic approach is proposed in which thermal-conductivity, which depends on the phase-field gradient, is degraded solely across the crack. We show that this approach improves the near-field approximation of temperature and heat flux compared with isotropic degradation when taking the discontinuous crack solutions as reference. To demonstrate the viability of the proposed (isotropic and anisotropic) approaches, a unified model, which accounts for the simultaneous formation of shear bands and cracks, is used as a numerical tool. In this model, the phase-field method is used to model crack initiation and propagation and is coupled to a temperature-dependent visco-plastic model that captures shear bands. Benchmark problems are presented to show the necessity of the anisotropic thermal-conductivity approach using physics-based degradation functions in dynamic fracture problems. On the other hand, the computational burden in dynamic fracture problems with localized solution features is highly demanding. Iterative methods used for their analysis often require special treatment to be more efficient. Specifically, the nonlinear thermomechanical problems we study in this thesis lead to strain localizations, such as shear bands and/or cracks, and iterative solvers may have difficult time converging. To address this issue, we develop a novel updating domain decomposition preconditioner for parallel solution of dynamic fracture problems. The domain decomposition method is based on the Additive Schwarz Method (ASM). The key idea is to decompose the computational domain into two subdomains, a localized subdomain that includes all localized features of the solution and a healthy subdomain for the remaining part of the domain. In this way, one can apply different solvers in each subdomain, i.e. focus more effort in the localized subdomain. In this work, an LU solver is applied in both subdomains, however, while the localized subdomain is solved exactly at every nonlinear iteration, the healthy subdomain LU operator is reused and only selectively updated. Hence, significant CPU time savings associated with the setup of the preconditioner can be achieved. In particular, we propose a strategy for updating the preconditioner in the healthy subdomain. The strategy is based on an idealized performance-based optimization procedure that takes into account machine on-the-fly execution time. Three dynamic fracture problems corresponding to different failure modes are investigated. Excellent performance of the proposed updating preconditioner is reported in serial and parallel simulations.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Sitaraman, Suresh; Committee Member: Peak, Russell; Committee Member: Ume, Charles

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.

Directionally solidified (DS) nickel-base superalloys are used in high temperature gas turbine engines because of their high yield strength at extreme temperatures and strong low cycle fatigue (LCF) and creep resistance. Costly inspecting, servicing, and replacing of damaged components has precipitated much interest in developing models to better predict service life. Turbine blade life modeling is complicated by the presence of notches, dwells, high temperatures and temperature gradients, and highly anisotropic material behavior. This work seeks to develop approaches for predicting the life of hot sections of gas turbines blade material CM247LC DS subjected to LCF, dwells, and stress concentrations while taking into consideration orientation and notch effects. Experiments were conducted on an axial servo-hydraulic MTS® testing machine. High temperature LCF tests were performed on smooth and notched round-bar specimens in both longitudinal and transverse orientations with and without dwells. Experimental results were used to develop and validate an analytical life prediction model. An analytical model based on a multiaxial Neuber approach predicts the local stress-strain response at a notch and other geometric stress concentrations. This approach captures anisotropy through a multiaxial generalization of the Ramberg-Osgood relation using a Hill's type criterion. The elastic notch response is determined using an anisotropic elastic finite element analysis (FEA) of the notch. The limitations of the simpler analytical life-modeling method are discussed in light of FEA using an anisotropic elastic-crystal viscoplastic material model. This life-modeling method provides a quick alternative to time demanding elastic-plastic FEA allowing engineers more design iterations to improve reliability and service life.

ZnO nanowires and nanorods are a new class of one-dimensional nanomaterials with a wide range of applications in NEMS. The motivation for this work stems from the lack of understanding and characterization of their thermomechanical behaviors essential for their incorporation in nanosystems. The overall goal of this work is to develop a fundamental understanding of the mechanisms controlling the responses of these nanostructures with focus on: (1) development of a molecular dynamics based framework for analyzing thermomechanical behaviors, (2) characterization of the thermal and mechanical behaviors in ZnO nanowires and (3) development of models for pseudoelasticity and thermal conductivity. The thermal response analyses show that the values of thermal conductivity are one order of magnitude lower than that for bulk ZnO due to surface scattering of phonons. A modified equation for phonon radiative transport incorporating the effects of surface scattering is used to model the thermal conductivity as a function of wire size and temperature. Quasistatic tensile loading of wires show that the elastic moduli values are 68.2-27.8% higher than that for bulk ZnO. Previously unknown phase transformations from the initial wurtzite (WZ) structure to graphitic (HX) and body-centered-tetragonal (BCT-4) phases are discovered in nanowires which lead to a more complete understanding of the extent of polymorphism in ZnO and its dependence on load triaxiality. The reversibility of the WZ-to-HX transform gives rise to a novel pseudoelastic behavior with recoverable strains up to 16%. A micromechanical continuum model is developed to capture the major characteristics of the pseudoelastic behavior accounting for size and temperature effects. The effect of the phase transformations on the thermal properties is characterized. Results obtained show that the WZ→HX phase transformation causes a novel transition in thermal response with the conductivity of HX wires being 20.5-28.5% higher than that of the initial WZ-structured wires. The results obtained here can provide guidance and criteria for the design and fabrication of a range of new building blocks for nanometer-scale devices that rely on thermomechanical responses.

Porous ceramic-metal composites, or cermets, such as nickel zirconia (Ni-YSZ), are widely used as the anode material in solid oxide fuel cells (SOFC). These materials need to enable electrochemical reactions and provide the mechanical support for the layered cell structure. Thus, for the anode supported planar cells, the thermomechanical behavior of the porous cermet directly affects the reliability of the cell. Porous cermets can be viewed as three-phase composites with a random heterogeneous microstructure. While random in nature, the effective properties and overall behavior of such composites can still be linked to specific stochastic functions that describe the microstructure. The main objective of this research was to develop the relationship between the thermomechanical behavior of porous cermets and their random microstructure. The research consists of three components. First, a stochastic reconstruction scheme was developed for the three-phase composite. From this multiple realizations with identical statistical descriptors were constructed for analysis. Secondly, a finite element model was implemented to obtain the effective properties of interest including thermal expansion coefficient, thermal conductivity, and elastic modulus. Lastly, nonlinear material behaviors were investigated, such as damage, plasticity, and creep behavior. It was shown that the computational model linked the statistical features of the microstructure to its overall properties and behavior. Such a predictive computational tool will enable the design of SOFCs with higher reliability and lower costs.

The current trend in electronics manufacturing is to decrease the size of electronic components while attempting to increase processing power and performance. This is leading to increased interest in thinner printed wiring boards and finer line widths and wire pitches. However, mismatches in the thermomechanical properties of materials used can lead to warpage, hindering these goals. Warpage can be problematic as it leads to misalignments during package assembly, reduced tolerances, and a variety of operational failures. Current warpage prediction techniques utilize isotropic volume averaging to estimate effective material properties in layers of copper mixed with interlayer dielectric material. However, these estimates do not provide material properties with sufficient accuracy to predict warpage, as they contain no information about the orientation of the copper traces. This thesis describes the development of a new technique to predict the warpage of a particular substrate. The technique accounts for both the trace pattern planar density and planar orientation in determining effective orthotropic material properties for each layer of a multi-layer substrate. Starting with the trace pattern image, this technique first divides the trace pattern into several smaller areas for a given layer of the substrate and then uses image processing techniques to determine the copper percentage and average trace orientation in each small area. The copper percentage and average trace direction orientation are used in conjunction with the material properties of copper and the dielectric material to calculate the effective orthotropic material properties of each smaller area of the substrate. A finite-element model is then created where each layer is represented as a concatenation of several small areas with independent directional properties, and such a model is then subjected to sequential thermal excursion as seen in the actual fabrication process. The results from the models have been compared against experimental data with a great degree of accuracy. The modeling technique and the results obtained clearly demonstrate the need for the proposed subdivisional orthotropic material property calculations, as opposed to homogeneous isotropic properties typically used for each layer in computational simulations, as these more accurate directional properties are capable of predicting warpage with higher accuracy.

Hot sections of gas engine turbines require specialized materials to withstand extreme conditions present during engine operation. Nickel-base superalloys are typically used as blades and disks in the high pressure turbine section because they possess excellent fatigue strength, creep strength and corrosion resistance at elevated temperatures. Components undergo thermomechanical fatigue conditions as a result of transient engine operation. Sharp geometric features, such as cooling holes in blades or fir-tree connections in disks, act as local stress raisers. The material surrounding these features are potential sites of localized inelastic deformation and crack formation. To reduce customer costs associated with unnecessary overhauls or engine down-time, gas turbine manufacturers require accurate prediction methods to determine component endurances. The influence of stress concentration severity on thermomechanical fatigue crack formation is of particular importance as cracks often initiate in these hot spots. Circumferentially notched specimens were utilized to perform thermomechanical fatigue experiments on blade material CM247LC DS and disk material PM IN100. A parametric study on CM247LC DS was performed utilizing four notched specimens. Experimental results were coupled with finite element simulations utilizing continuum based constitutive models. The effects of applied boundary conditions on crack initiation life was studied in both alloys by performing experiments under remotely applied force and displacement boundary conditions. Finite element results were utilized to develop a life prediction method for notched components under thermomechanical fatigue conditions.