Low cycle fatigue is an important valving parameter of materiale which are exposed random alternate strain during their operation. The alternate strain in that material is caused by temperature fluctuations during operation and outages such as aircraft engines. Tests of low cycle fatigue were performed on samples of superalloy Inconel 738LC at stable room temperature at 23°C. The actual experiment took place at certain intervals, consisting of cycling itself, and observing changes in surface relief by light and electron microscopy. There was observed significant surface relief at an early stage of low cycle fatigue. We compared results of measurement with other different observation methods.

Um die Leistung und Lebensdauer von energietechnischen Komponenten weiter zu steigern, sind höhere Leistungen, Leistungsdichten sowie Prozesswirkungsgrade zentrale Bestandteile künftiger Entwicklungen. Mit steigernden Leistungsdichten erhöhen sich auch stetig die Belastungen der einzelnen Komponenten. Zusammen mit neuen Werkstoffen und technologischem Fortschritt, wie beispielsweise verbesserten Kühltechnologien oder strömungstechnischen Optimierungen ermöglicht auch eine verbesserte Kenntnis der Belastungsbedingungen und des Schädigungsverhaltens höhere Leistungen und Leistungsdichten. Aktuelle Gasturbinen und oft auch Kraftwerkskomponenten unterliegen zusätzlich zu den mechanischen und zeitlich variablen thermischen Beanspruchungen auch großen örtlichen thermischen Gradienten, die die Lebensdauer der Komponenten stark beeinflussen. Diese thermischen Gradienten induzieren zum einen zusätzliche Beanspruchungen und die örtlich variablen Temperaturfelder führen zum anderen zu stark variierenden Werkstofffestigkeiten. In dieser Arbeit wird ein Prüfstand zur realistischen Prüfung eines typischen Gasturbinenschaufelmaterials Mar-M247 entwickelt und mit diesem eine systematische experimentelle Untersuchung des Einflusses thermischer Gradienten auf die niederzyklische Ermüdungsfestigkeit unter erhöhten Temperaturen durchgeführt. Im weiteren Teil der Arbeit wird ein visko-elasto-plastisches Materialmodell weiterentwickelt, um die lokal unsymmetrische Beanspruchung der Proben unter zyklischer Last realistisch abbilden zu können. Mit Hilfe von Experimenten aus der Literatur werden dabei zunächst die Grenzen und Möglichkeiten des Modells diskutiert, um es dann auf den konkreten Werkstoff anzupassen. Der wesentliche Vorteil des entwickelten Modells liegt in der verbesserten Beschreibung des zyklischen Kriechens und zyklischen Relaxierens (Ratcheting) insbesondere unter einachsiger Beanspruchung und in der nachträglichen Anpassungsmöglichkeit des spezifischen Ratchetingterms nach der Anpassung aller anderen Materialparameter. Die Analyse der experimentell ermittelten Lebensdauern erfolgt sowohl mit ingenieurmäßigen Methoden basierend auf der spannungsabhängigen Lebensdauerbeschreibung nach Basquinund Wöhler als auch mittels eines lokalen bruchmechanischen Ansatzes, der es ermöglicht,sowohl die Rissinitiierung als auch den Rissfortschritt unter variabler Temperatur und kombinierter Kriech- und Ermüdungsbeanspruchung zu beschreiben. Das Material- und Lebensdauermodell werden zusammen im letzten Teil der Arbeit eingesetzt, um das Verformungs- und Lebensdauerverhalten der untersuchten Proben zu berechnenund es kann gezeigt werden, dass sich die Versuche mit sehr guter Qualität wiedergeben lassen.:Versicherung i Abstract iii Kurzfassung v List of abbreviations and symbols xi 1 Introduction 1 2 Objective 5 3 State of the art 7 3.1 Thermal and mechanical loading of gas turbine components . . . . . . . . . . 7 3.2 Material characterisation of nickel-based superalloys . . . . . . . . . . . . . . 9 3.3 Deformation modelling based on constitutive material laws . . . . . . . . . . 13 3.3.1 Ramberg-Osgood material law . . . . . . . . . . . . . . . . . . . . . . 13 3.3.2 Strain and stress tensor . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.3 Thermodynamic principles . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Elasto-visco-plastic material models . . . . . . . . . . . . . . . . . . . . . . . 15 3.4.1 Isotropic hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4.2 Kinematic hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4.3 Kinematic hardening for improved simulation of ratcheting . . . . . . 18 3.4.4 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Failure at elevated temperatures . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.5.1 Fundamental fatigue life models . . . . . . . . . . . . . . . . . . . . . 24 3.5.2 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5.3 Crack growth models for fatigue loading . . . . . . . . . . . . . . . . . 28 3.5.4 Creep crack growth based on C(t) and C ∗ . . . . . . . . . . . . . . . . 33 3.5.5 Temperature dependency and normalization methods . . . . . . . . . 35 3.5.6 Lifetime under temperature variation . . . . . . . . . . . . . . . . . . . 37 3.5.7 Influence of mean stresses on lifetime . . . . . . . . . . . . . . . . . . . 38 3.5.8 Influence of oxidation on failure at elevated temperatures . . . . . . . 42 3.5.9 Constitutive damage and crack growth models . . . . . . . . . . . . . 45 3.6 Experimental methods for the generation of large homogeneously distributed heat flux densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6.1 Resistance heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6.2 Inductive heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.6.3 Convective heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.6.4 Laser based heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.6.5 Radiation heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Conclusion on the state of the art . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Development of a test system for cyclic fatigue tests under homogeneous surface temperature conditions 59 4.1 Boundary conditions for the development . . . . . . . . . . . . . . . . . . . . 59 4.2 Concept for a test system with a new highly focusing heating . . . . . . . . . 60 4.2.1 Simulation of heat fluxes of different furnace geometries by ray-tracing 60 4.3 Definition of reflection and transmission coefficient . . . . . . . . . . . . . . . 64 4.3.1 Simulation of the radiation behaviour for the furnace concepts . . . . 66 4.4 Analytical calculation of heat transfer inside the hollow specimen . . . . . . . 71 4.5 Finite element calculation of temperature distribution in the specimen wall . 73 4.6 Design and evaluation of the specimen internal cooling system . . . . . . . . . 75 4.6.1 Installation of heating and development of the load train . . . . . . . 81 5 Experimental investigation 85 5.1 Measurement of surface temperatures and thermal gradients . . . . . . . . . . 87 5.1.1 Measurement of surface temperature . . . . . . . . . . . . . . . . . . . 87 5.1.2 Axial surface temperature distribution . . . . . . . . . . . . . . . . . . 90 5.1.3 Measurement of thermal gradients across specimen wall . . . . . . . . 92 5.2 Results of isothermal ratcheting tests . . . . . . . . . . . . . . . . . . . . . . . 96 5.3 Deformation behaviour of cyclic tests with superimposed thermal gradients . 98 5.3.1 Variation of mean strain and mean stress . . . . . . . . . . . . . . . . 98 5.4 Termination criteria for the tests . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.4.1 Measurement of modulus of elasticity . . . . . . . . . . . . . . . . . . 101 5.5 Low cycle fatigue life of Mar-M247 with and without superimposed thermal gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.6 Results of hollow cylindrical specimen testing with thermal gradients . . . . . 108 6 Microstructural investigation 113 7 Deformation modeling with improved ratcheting simulation based on small scale strain theory 123 7.1 Modeling of ratcheting behaviour of Mar-M247 . . . . . . . . . . . . . . . . 123 7.1.1 Improvement of uniaxial ratcheting description for the Armstrong- Frederick-model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.1.2 Evaluation of the proposed model for multiaxiality . . . . . . . . . . . 129 7.2 Application of the deformation model on Mar-M247 . . . . . . . . . . . . . 132 8 Lifetime calculation of the nickel-base-superalloy Mar-M247 based on engineering and crack growth methods 139 8.1 Modification of the Krämer crack growth model . . . . . . . . . . . . . . . . 139 8.2 Choice of basic variable for the fatigue crack growth and crack initiation . . . 140 8.3 Oxidation based crack growth model . . . . . . . . . . . . . . . . . . . . . . . 142 8.4 Creep crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 8.5 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.6 Fatigue life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.6.1 Extension of the Paris crack growth model based on intrinsic defect size152 8.6.2 Crack length independent formulation of J-integral . . . . . . . . . . . 154 8.7 Combined model for comprehensive description of the crack-initiation and -growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.7.1 Comparison to crack growth experiments . . . . . . . . . . . . . . . . 161 8.7.2 Comparison to fatigue experiments . . . . . . . . . . . . . . . . . . . . 164 9 Application of material and crack growth model to the experiments with superimposed thermal gradient 167 9.1 Geometry function for the hollow specimen investigated . . . . . . . . . . . . 167 9.2 Application of the crack growth model on non-isothermal tests . . . . . . . . 170 9.2.1 Calculation of the stress strain field of hollow cylindrical specimen subjected to thermally induced stress gradients with the elasto-visco- plastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.2.2 Calculated crack growth behaviour under locally non-isothermal con- ditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 10 Conclusion and outlook 181 Bibliography 185

<p dir="ltr">In structural metallic components, a material’s lifecycle begins with the processing route, to produce a desired structure, which dictates the in-service performance. The variability of microstructural features as a consequence of the processing route has a direct influence on the properties and performance of a material. In order to correlate the influence processing conditions have on material performance, large test matrices are required which tend to be time consuming and expensive. An alternative route to avoid such large test matrices is to incorporate physics-based process modeling and lifing paradigms to better understand the performance of structural materials. By linking microstructural information to the material’s lifecycle, the processing path can be modified without the need to repeat large-scale testing requirements. Additionally, when a materials system is accurately modeled throughout its lifecycle, the performance predictions can be leveraged to improve the design of materials and components.</p><p dir="ltr">Ni-based superalloys are a material class widely used in many critical aerospace components exposed to coupling thermal and mechanical loads due to their increased resistance to creep, corrosion, oxidation, and strength characteristics at elevated temperatures. Many Ni-based superalloys undergo high-temperature forging to produce a desired microstructure, targeting specific strength and fatigue properties in order to perform under thermo-mechanical loads. When in-service, these alloys tend to fail as a consequence of thermo-mechanical fatigue (TMF) from either inclusion- or matrix- driven failure. In order to produce safer, cheaper and more efficient critical aerospace components, the micromechanical deformation and damage mechanisms throughout a Ni-based superalloy’s lifecycle must be understood. This research utilizes process modeling as a tool to understand the damage and deformation of inclusions in a Ni-200 matrix throughout radial forging as a means to optimize the processing conditions for improved fatigue performance. In addition, microstructural sensitive performance modeling for a Ni-based superalloy is leveraged to understand the influence TMF has on damage mechanisms.</p><p dir="ltr">The radial forging processing route requires both high temperatures and large plastic deformation. During this process, non-metallic inclusions (NMIs) can debond from the metallic matrix and break apart, resulting in a linear array of smaller inclusions, known as stringers. The evolution of NMIs into stringers can result in matrix load shedding, localized plasticity, and stress concentrations near the matrix-NMI interface. Due to these factors, stringers can be detrimental to the fatigue life of the final forged component. By performing a finite element model of the forging process with cohesive zones to simulate material debonding, this research contributes to the understanding of processing induced deformation and damage sequences on the onset of stringer formation for Alumina NMIs in a Ni-200 matrix. Through a parametric study, the interactions of forging temperature, strain rate, strain per pass, and interfacial decohesion on the NMI damage evolution metrics are studied, specifically NMI particle separation, rotation, and cavity formation. The parametric study provides a linkage between the various processing conditions parameters influence on detrimental NMI morphology related to material performance.</p><p dir="ltr">The microstructural characteristics of Ni-based superalloys, as a consequence of a particular processing route, creates a variability in TMF performance. The micromechanical failure mechanisms associated with TMF are dependent on various loading parameters, such as temperature, strain range, and strain-temperature phasing. Insights on the complexities of micromechanical TMF damage are studied via a temperature-dependent, dislocation density-based crystal plasticity finite element (CPFE) model with uncertainty quantification. The capabilities of the model’s temperature dependency are examined via direct instantiation and comparison to a high-energy X-ray diffraction microscopy (HEDM) experiment under coupled thermal and mechanical loads. Unique loading states throughout the experiment are investigated with both CPFE predictions and HEDM results to study early indicators of TMF damage mechanisms at the grain scale. The mesoscale validation of the CPFE model to HEDM experimental data provides capabilities for a well-informed TMF performance paradigm under various strain-temperature phase profiles. </p><p dir="ltr">A material’s TMF performance is highly dependent on the temperature-load phase profile as a consequence of path-dependent thermo-mechanical plasticity. To investigate the relationship between microstructural damage and TMF phasing effects, the aforementioned CPFE model investigates in-phase (IP) TMF, out-of-phase (OP) TMF, and iso-thermal (ISO) loading profiles. A microstructural sensitive performance modeling framework with capabilities to isolate phasing (IP, OP, and ISO) effects is presented to locate fatigue damage in a set of statistically equivalent microstructures (SEMs). Location specific plasticity, and grain interactions are studied under the various phasing profiles providing a connection between microstructural material damage and TMF performance.</p>

<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>

The challenges faced in today’s industry require materials capable of working in chemically aggressive environments at elevated temperature, which has fueled the development of oxidation resistant materials. All-Oxide Ceramic Matrix Composites (OCMC) are a promising material family due to their inherent chemical stability, moderate mechanical properties, and low weight. However, limited information exists regarding their behavior when in contact with other high-temperature materials such as superalloys. In this work three sets of tribological tests were performed: two at room temperature and one at elevated temperature (650 °C). The tests were performed in a pin-on-disk configuration testing Inconel 718 (IN-718) pins against disks made with an aluminosilicate geopolymeric matrix composite reinforced with alumina fibers (N610/GP). Two different loads were tested (85 and 425 kPa) to characterize the damage on both materials. Results showed that the pins experienced ~ 100 % wear increase when high temperature was involved, while their microstructure was not noticeably affected near the contact surface. After high temperature testing the OCMC exhibited mass losses two orders of magnitude higher than the pins and a sintering effect under its wear track, that led to brittle behavior. The debris generated consists of alumina and suggests a possible crystallization of the originally amorphous matrix which may destabilize the system. The data suggests that while the composite’s matrix is stable, wear will not develop uncontrollably. However, as soon as a critical load/temperature combination is attained the matrix is the first component to fail exposing the reinforcement to damage which drastically deteriorates the integrity of the component.