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## ENSURING FATIGUE PERFORMANCE VIA LOCATION-SPECIFIC LIFING IN AEROSPACE COMPONENTS MADE OF TITANIUM ALLOYS AND NICKEL-BASE SUPERALLOYS

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).

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.

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.

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.

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.

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.

### Categories

### Keywords

Crystal plasticity finite element (CPFE)Statistically equivalent microstructuresGenetic AlgorithmUncertainty QuantificationFirst order second moment (FOSM)fatigue life estimationMicrostructure-Sensitive ModelingPlastic strain energy densityMarkov chain Monte CarloMetropolis-Hastings AlgorithmBayesian inferenceNickel-base superalloysInclusionsRR1000718PlusAdditive manufacturingPowder metallurgy (PM)Critical inclusion sizeResidual strainLinear Friction Weld (LFW)Energy dispersive X-ray diffraction (EDD)Ti-6Al-4VTi-5Al-5V-5Mo-3CrBackscatter electron imagingHigh Cycle Fatigue (HCF)Anomalous mean stress sensitivityHigh R ratioStrain heterogeneityDigital Image Correlation (DIC)Micro-textured regions (MTRs)Macrozones

### Funding

#### Rolls-Royce Corporation

#### DARPA (Grant/contract numbers N66001-14-1-4041 and HR0011-12-C-0037)

#### LIFT (Grant Number LIFT TMP-3a)

#### NSF (Grant Number CMMI 16-51956)

#### Purdue University (Lynn Fellowship from OIGP and Teaching Scholarship from the School of Aeronautics and Astronautics)

### History

#### Degree Type

Doctor of Philosophy#### Department

Aeronautics and Astronautics#### Campus location

West Lafayette#### Advisor/Supervisor/Committee Chair

Dr. Michael D. Sangid#### Additional Committee Member 2

Dr. Weinong Chen#### Additional Committee Member 3

Dr. Fionn P. E. Dunne#### Additional Committee Member 4

Dr. Ganesh Subbarayan#### Additional Committee Member 5

Dr. Tyler N. Tallman### Licence

### Exports

### Categories

### Keywords

Crystal plasticity finite element (CPFE)Statistically equivalent microstructuresGenetic AlgorithmUncertainty QuantificationFirst order second moment (FOSM)fatigue life estimationMicrostructure-Sensitive ModelingPlastic strain energy densityMarkov chain Monte CarloMetropolis-Hastings AlgorithmBayesian inferenceNickel-base superalloysInclusionsRR1000718PlusAdditive manufacturingPowder metallurgy (PM)Critical inclusion sizeResidual strainLinear Friction Weld (LFW)Energy dispersive X-ray diffraction (EDD)Ti-6Al-4VTi-5Al-5V-5Mo-3CrBackscatter electron imagingHigh Cycle Fatigue (HCF)Anomalous mean stress sensitivityHigh R ratioStrain heterogeneityDigital Image Correlation (DIC)Micro-textured regions (MTRs)Macrozones