Understanding the effects of aged microstructures on the thermomechanical fatigue (TMF) properties of nickel-base (Ni-base) superalloys remains unclear. Few experimental results are currently available in this area, and of the limited results available, some promote aged microstructures as beneficial, while others as detri- mental. The importance of these aged structures arises from the fact that when components used in the hot sections of gas turbine engines remain in service for ex- tended periods of time, the local temperature and stress provides the catalyst for the evolution of the microstructure. An experimental assessment of a negative misfit directionally solidified (DS) Ni- base superalloy was undertaken to characterize the aging kinetics and understand the influence of the TMF cycle temperature extremum, temperature-load phasing, mean strain, creep-fatigue, orientation effects, and microstructure on TMF fatigue crack initiation. To determine the effects of aging on the TMF response, the as-heat- treated alloy was artificially aged to three unique microstructures identified in the aging kinetics study. The experiments revealed that not all aged microstructures are detrimental to the fatigue life behavior. Specifically, when the γ′ precipitates age in a manner to align themselves parallel to the axis of the applied stress, an increase in the fatigue life over that of the as-heat-treated microstructure is observed for out-of-phase TMF with dwells. To extend the experimental understanding of the aged microstructures into ser- vice component design and life analysis, a temperature-dependent crystal viscoplas- ticity (CVP) constitutive model is developed to capture the sensitivity of the aged microstructure through embedding additional variables associated with the current state of the γ′ particles. As a result of the adaptations, the CVP model has the ability to describe the long-term aging effects of directional coarsening relevant to the analysis industrial gas turbine hot section components.

In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives.

Texture evolution is a vital component of many computational tools that link structure, properties and processes of polycrystalline materials. By definition, this evolution process involves the manipulation, via rotation, of points in orientation space. The computational requirements of the current methods being used to rotate crystalline orientations are a significant limiting factor in the drive to merge the texture information of materials into the engineering design process. The goal of this research is to find and implement a practical rotation algorithm that can significantly decrease the computation time required to rotate macroscopic and microscopic crystallographic textures. Three possible algorithms are considered in an effort to improve the computational efficiency and speed of the rotation process. The first method, which will be referred to as the Gel'fand method, is based on a paper, [1], that suggests a practical application of some of Gel'fand's theories for rotations [2]. The second method, which will be known as the streamline method, is a variation on the Gel'fand method. The third method will be known as the principal orientation method. In this method, orientations in Fourier space are written as linear combinations of points on the convex surface of the microstructure hull to reduce the number of points that must be rotated during each step in the texture evolution process. This thesis will discuss each of these methods, their strengths and weaknesses, and the accuracy of the computational results obtained from their implementation.

Reverse engineering - defined as extracting information about a product from the product itself - is a design tactic commonly used in industry from competitive benchmarking to product imitation. While reverse engineering is a legitimate practice - as long as the product was legally obtained - innovative products are often reverse engineered at the expense of the pioneering company. However, by designing products with built-in barriers to reverse engineering, competitors are no longer able to effectively extract critical information from the product of interest. Enabling the quantification of barriers to reverse engineering, this dissertation presents a set of metrics and parameters that can be used to calculate the barrier to reverse engineer any product as well as the time required to do so. To the original designer, these numerical representations of the barrier and time can be used to strategically identify and improve product characteristics so as to increase the difficulty and time to reverse engineer them. On the other hand, these quantitative measures enable competitors who reverse engineer original designs to focus their efforts on products that will result in the greatest return on investment. In addition to metrics that estimate the reverse engineering barrier and time, this dissertation also presents a methodology to strategically plan for, select, design, and implement reverse engineering barriers. The methodology presented herein considers barrier development cost, barrier effectiveness in various product components, impact on performance, and return on investment. This process includes sensitivity analysis, modeling of the return on investment, and exploration of multiobjective design spaces. The effectiveness of the presented methodology is demonstrated by making a solar-powered unmanned aerial vehicle difficult to reverse engineer. In the example, the propeller is selected to be the critical component where a series of voids are introduced to decrease the propeller weight and increase the flutter speed (a desirable attribute in propellers). Our tenet is that the use of such a framework contributes greatly to the sustainability of technological, economical, and security advantages enjoyed by those who developed the technology. Designers benefit because (i) products do not readily disclose trade secrets, (ii) competitive advantages can be maintained by impeding competitors from reverse engineering and imitating innovative products, and (iii) the return on investment can be increased.

Establishing process-structure-property relationships is an important objective in the paradigm of materials design in order to reduce the time and cost needed to develop new materials. A method to link phase field (process-structure relations) and microstructure-sensitive finite element (structure-property relations) modeling is demonstrated for subsolvus polycrystalline IN100. A three-dimensional (3D) experimental dataset obtained by orientation imaging microscopy performed on serial sections is utilized to calibrate a phase field model and to calculate inputs for a finite element analysis. Simulated annealing of the dataset realized through phase field modeling results in a range of coarsened microstructures with varying grain size distributions that are each input into the finite element model. A rate dependent crystal plasticity constitutive model that captures the first order effects of grain size, precipitate size, and precipitate volume fraction on the mechanical response of IN100 at 650°C is used to simulate stress-strain behavior of the coarsened polycrystals. Model limitations and ideas for future work are discussed.

In this research, the homogenization relations for elastic properties in isotropic and anisotropic materials are studied by applying two-point statistical functions to composite and polycrystalline materials. The validity of the results is investigated by direct comparison with experimental results. In todays technology, where advanced processing methods can provide materials with a variety of morphologies and features in different scales, a methodology to link property to microstructure is necessary to develop a framework for material design. Statistical distribution functions are commonly used for the representation of microstructures and also for homogenization of materials properties. The use of two-point statistics allows the materials designer to consider morphology and distribution in addition to properties of individual phases and components in the design space. This work is focused on studying the effect of anisotropy on the homogenization technique based on two-point statistics. The contribution of one-point and two-point statistics in the calculation of elastic properties of isotropic and anisotropic composites and textured polycrystalline materials will be investigated. For this purpose, an isotropic and anisotropic composite is simulated and an empirical form of the two-point probability functions are used which allows the construction of a composite Hull. The homogenization technique is also applied to two samples of Al-SiC composite that were fabricated through extrusion with two different particle size ratios (PSR). To validate the applied methodology, the elastic properties of the composites are measured by Ultrasonic methods. This methodology is then extended to completely random and textured polycrystalline materials with hexagonal crystal symmetry and the effect of cold rolling on the annealing texture of near- Titanium alloy are presented.

The methods of MSD are applied to the design of functionally graded materials. Analysis models are presented to allow the design of compliant derailleur for a case study and constraints are placed on the design. Several methods are presented for relating elements of the microstructure to the properties of the material, including Taylor yield theory, Hill elastic bounds, and precipitation hardening. Applying n-point statistics to the MSD framework is also discussed. Some results are presented for the information content of the 2-point correlation statistics that follow from the methods used to integrate functionally graded materials into MSD. For the compliant beam case study, the best design (98%Al-2%Li) was a 97% improvement over the worst (100%Al). The improvements were primarily due to the precipitation hardening, although anisotropy also significantly impacted the design. Under the constraints for the design, allowing the beam to be functionally graded had little effect on the overall design, unless there was significant stiffening occurring along with particulate formation.

Thermomechanical fatigue life prediction is important in the design of Ni-base superalloy components in gas turbine engines and requires a stress-strain analysis for accurate results. Crystal viscoplasticity models are an ideal tool for this stress-strain analysis of Ni-base superalloys as they can capture not only the anomalous yielding behavior, but also the non-Schmid effect, the strain rate dependence, and the temperature dependence of typically large grained directionally-solidified and single crystal alloys. However, the model is difficult to calibrate even for isothermal conditions because of the interdependencies between parameters meant to capture different but similar phenomena at different length scales, many tied to a particular slip system. The need for the capacity to predict the material response over a large temperature range, which is critical for the simulation of hot section gas turbine components, causes the determination of parameters to be even more difficult since some parameters are highly temperature dependent. Rapid parameter determination techniques are therefore needed for temperature-dependent parameterizations so that the effort needed to calibrate the model is reduced to a reasonable level. Specific parameter determination protocols are established for a crystal viscoplasticity model implemented in ABAQUS through a user material subroutine. Parameters are grouped to reduce interdependencies and a hierarchical path through the groups and the parameters within each group is established. This dual level hierarchy creates a logical path for parameter determination which further reduces the interdependencies between parameters, allowing for rapid parameter determination. Next, experiments and protocols are established to rapidly provide data for calibration of the temperature-dependencies of the viscoplasticity. The amount of data needed to calibrate the crystal viscoplasticity model over a wide temperature range is excessively large due to the number of parameters that it contains which causes the amount of time spent in the experimentation phase of parameter determination to be excessively large. To avoid this lengthy experimentation phase each experiment is designed to contain as much relevant data as possible. This is accomplished through the inclusion of multiple strain rates in each experiment with strain ranges sufficiently large to clearly capture the inelastic response. The experimental and parameter determination protocols were exercised by calibrating the model to the directionally-solidified Ni-bas superalloy DS-CM247LC. The resulting calibration describes the material's behavior in multiple loading orientations and over a wide temperature range of 20 °C to 1050 °C. Several parametric studies illustrate the utility of the calibrated model.

Additive manufacturing (AM) introduces high variability in the microstructure and defect distributions, compared with conventional processing techniques, which introduces greater uncertainty in the resulting fatigue performance of manufactured parts. As a result, qualification of AM parts poses as a problem in continued adoption of these materials in safety-critical components for the aerospace industry. Hence, there is a need to develop precise and accurate, physics-based predictive models to quantify the fatigue performance, as a means to accelerate the qualification of AM parts. The fatigue performance is a critical requirement in the safe-life design philosophy used in the aerospace industry. Fatigue failure is governed by the loading conditions and the attributes of the material microstructure, namely, grain size distribution, texture, and defects. In this work, the crystal plasticity finite element (CPFE) method is employed to model the microstructure-based material response of an additively manufactured Ni-based superalloy, Inconel 718 (IN718). Using CPFE and associated experiments, methodologies were developed to assess multiple aspects of the fatigue behavior of IN718 using four studies. In the first study, a CPFE framework is developed to estimate the critical characteristics of porosity, namely the pore size and proximity that would cause a significant debit in the fatigue life. The second study is performed to evaluate multiple metrics based on plastic strain and local stress in their ability to predict both the modes of failure as seen in fractography experiments and estimate the scatter in fatigue life due to microstructural variability as obtained from fatigue testing. In the third study, a systematic analysis was performed to investigate the role of the simulation volume and the microstructural constraints on the fatigue life predictions to provide informed guidelines for simulation volume selection that is both computationally tractable and results in consistent scatter predictions. In the fourth study, validation of the CPFE results with the experiments were performed to build confidence in the model predictions. To this end, 3D realistic microstructures representative of the test specimen were created based on the multi-modal experimental data obtained from high-energy diffraction experiments and electron backscatter diffraction microscopy. Following this, the location of failure is predicted using the model, which resulted in an unambiguous one to one correlation with the experiment. In summary, the development of microstructure-sensitive predictive methods for fatigue assessment presents a tangible step towards the adoption of model-based approaches that can be used to compliment and reduce the overall number of physical tests necessary to qualify a material for use in application.

<div>In this thesis, the role of location-specific microstructural features in the fatigue performance of the safety-critical aerospace components made of Nickel (Ni)-base superalloys and linear friction welded (LFW) Titanium (Ti) alloys has been studied using crystal plasticity finite element (CPFE) simulations, energy dispersive X-ray diffraction (EDD), backscatter electron (BSE) images and digital image correlation (DIC).</div><div><br></div><div>In order to develop a microstructure-sensitive fatigue life prediction framework, first, it is essential to build trust in the quantitative prediction from CPFE analysis by quantifying uncertainties in the mechanical response from CPFE simulations. Second, it is necessary to construct a unified fatigue life prediction metric, applicable to multiple material systems; and a calibration strategy of the unified fatigue life model parameter accounting for uncertainties originating from CPFE simulations and inherent in the experimental calibration dataset. To achieve the first task, a genetic algorithm framework is used to obtain the statistical distributions of the crystal plasticity (CP) parameters. Subsequently, these distributions are used in a first-order, second-moment method to compute the mean and the standard deviation for the stress along the loading direction (σ_load), plastic strain accumulation (PSA), and stored plastic strain energy density (SPSED). The results suggest that an ~10% variability in σ_load and 20%-25% variability in the PSA and SPSED values may exist due to the uncertainty in the CP parameter estimation. Further, the contribution of a specific CP parameter to the overall uncertainty is path-dependent and varies based on the load step under consideration. To accomplish the second goal, in this thesis, it is postulated that a critical value of the SPSED is associated with fatigue failure in metals and independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress-strain hysteresis loops, CPFE simulations are used to compute the (local) SPSED at each material point within polycrystalline aggregates of 718Plus, an additively manufactured Ni-base superalloy. A Bayesian inference method is utilized to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and -1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a log-normal distribution; for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude and are indicative of the scatter observed in the fatigue experiments. Further, the log-normal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.</div><div><br></div><div>Inclusions are unavoidable in Ni-base superalloys, which lead to two competing failure modes, namely inclusion- and matrix-driven failures. Each factor related to the inclusion, which may contribute to crack initiation, is isolated and systematically investigated within RR1000, a powder metallurgy produced Ni-base superalloy, using CPFE simulations. Specifically, the role of the inclusion stiffness, loading regime, loading direction, a debonded region in the inclusion-matrix interface, microstructural variability around the inclusion, inclusion size, dissimilar coefficient of thermal expansion (CTE), temperature, residual stress, and distance of the inclusion from the free surface are studied in the emergence of two failure modes. The CPFE analysis indicates that the emergence of a failure mode is an outcome of the complex interaction between the aforementioned factors. However, the possibility of a higher probability of failure due to inclusions is observed with increasing temperature, if the CTE of the inclusion is higher than the matrix, and vice versa. Any overall correlation between the inclusion size and its propensity for damage is not found, based on inclusion that is of the order of the mean grain size. Further, the CPFE simulations indicate that the surface inclusions are more damaging than the interior inclusions for similar surrounding microstructures. These observations are utilized to instantiate twenty realistic statistically equivalent microstructures of RR1000 – ten containing inclusions and remaining ten without inclusions. Using CPFE simulations with these microstructures at four different temperatures and three strain ranges for each temperature, the critical SPSED is calibrated as a function of temperature for RR1000. The results suggest that critical SPSED decreases almost linearly with increasing temperature and is appropriate to predict the realistic emergence of the competing failure modes as a function of applied strain range and temperature.</div><div><br></div><div>LFW process leads to the development of significant residual stress in the components, and the role of residual stress in the fatigue performance of materials cannot be overstated. Hence, to ensure fatigue performance of the LFW Ti alloys, residual strains in LFW of similar (Ti-6Al-4V welded to Ti-6Al-4V or Ti64-Ti64) and dissimilar (Ti-6Al-4V welded to Ti-5Al-5V-5Mo-3Cr or Ti64-Ti5553) Ti alloys have been characterized using EDD. For each type of LFW, one sample is chosen in the as-welded (AW) condition and another sample is selected after a post-weld heat treatment (HT). Residual strains have been separately studied in the alpha and beta phases of the material, and five components (three axial and two shear) have been reported in each case. In-plane axial components of the residual strains show a smooth and symmetric behavior about the weld center for the Ti64-Ti64 LFW samples in the AW condition, whereas these components in the Ti64-Ti5553 LFW sample show a symmetric trend with jump discontinuities. Such jump discontinuities, observed in both the AW and HT conditions of the Ti64-Ti5553 samples, suggest different strain-free lattice parameters in the weld region and the parent material. In contrast, the results from the Ti64-Ti64 LFW samples in both AW and HT conditions suggest nearly uniform strain-free lattice parameters throughout the weld region. The observed trends in the in-plane axial residual strain components have been rationalized by the corresponding microstructural changes and variations across the weld region via BSE images. </div><div><br></div><div>In the literature, fatigue crack initiation in the LFW Ti-6Al-4V specimens does not usually take place in the seemingly weakest location, i.e., the weld region. From the BSE images, Ti-6Al-4V microstructure, at a distance from the weld-center, which is typically associated with crack initiation in the literature, are identified in both AW and HT samples and found to be identical, specifically, equiaxed alpha grains with beta phases present at the alpha grain boundaries and triple points. Hence, subsequent fatigue performance in LFW Ti-6Al-4V is analyzed considering the equiaxed alpha microstructure.</div><div><br></div><div>The LFW components made of Ti-6Al-4V are often designed for high cycle fatigue performance under high mean stress or high R ratios. In engineering practice, mean stress corrections are employed to assess the fatigue performance of a material or structure; albeit this is problematic for Ti-6Al-4V, which experiences anomalous behavior at high R ratios. To address this problem, high cycle fatigue analyses are performed on two Ti-6Al-4V specimens with equiaxed alpha microstructures at a high R ratio. In one specimen, two micro-textured regions (MTRs) having their c-axes near-parallel and perpendicular to the loading direction are identified. High-resolution DIC is performed in the MTRs to study grain-level strain localization. In the other specimen, DIC is performed on a larger area, and crack initiation is observed in a random-textured region. To accompany the experiments, CPFE simulations are performed to investigate the mechanistic aspects of crack initiation, and the relative activity of different families of slip systems as a function of R ratio. A critical soft-hard-soft grain combination is associated with crack initiation indicating possible dwell effect at high R ratios, which could be attributed to the high-applied mean stress and high creep sensitivity of Ti-6Al-4V at room temperature. Further, simulations indicated more heterogeneous deformation, specifically the activation of multiple families of slip systems with fewer grains being plasticized, at higher R ratios. Such behavior is exacerbated within MTRs, especially the MTR composed of grains with their c-axes near parallel to the loading direction. These features of micro-plasticity make the high R ratio regime more vulnerable to fatigue damage accumulation and justify the anomalous mean stress behavior experienced by Ti-6Al-4V at high R ratios.</div><div><br></div>