An analytical treatment of the fatigue performance of a cam-roller followler system as influenced by residual stresses induced by grinding, is developed. An approach based on an extended Hertzian analysis is used to determine the 3-D contact stress fields, which are then combined by elastic superposition with the residual stress fields. These residual stresses were measured previously by the x-ray diffraction technique and represent a range of grinding protocols from mild to abusive. The maximum cyclic component, generally occurring subsurface, is then identified in terms of an effective stress amplitude and mean which are used with a fatigue damage model to predict fatigue crack initiation. Results, pending experimental confirmation, appear reasonable and provide a useful basis for optimizing cam performance in terms of manufacturing and design parameters. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / Additive manufacturing (AM) or 3D printing has gained significant advancement in recent years. However the potential of 3D printed metals still has not been fully explored. A main reason is the lack of accurate knowledge of the load capacity of 3D printed metals, such as fatigue behavior under cyclic load conditions, which is still poorly understood as compared with the conventional wrought counterpart. The goal of the thesis is to advance the knowledge of fatigue behavior of 15-5 PH stainless steel manufactured through laser powder bed fusion process. To achieve the goal, a combined numerical and experimental study is carried out. First, using a rotary fatigue testing experiment, the fatigue life of the 15-5 PH stainless steel is measured. The strain life curve shows that the numbers of the reversals to failure increase from 13,403 to 46,760 as the applied strain magnitudes decrease from 0.214\% from 0.132\%, respectively. The micro-structure analysis shows that predominantly brittle fracture is presented on the fractured surface. Second, a finite element model based on cyclic plasticity including the damage model is developed to predict the fatigue life. The model is calibrated with two cases: one is the fatigue life of 3D printed 17-4 stainless steel under constant amplitude strain load using the direct cyclic method, and the other one is the cyclic behavior of Alloy 617 under multi-amplitude strain loads using the static analysis method. Both validation models show a good correlation with the literature experimental data. Finally, after the validation, the finite element model is applied to the 15-5 PH stainless steel. Using the direct cyclic method, the model predicts the fatigue life of 15-5 PH stainless steel under constant amplitude strain. The extension of the prediction curve matches well with the previously measured experimental results, following the combined Coffin-Manson Basquin Law. Under multi-amplitude strain, the kinematic hardening evolution parameter is incorporated into the model. The model is capable to capture the stresses at varied strain amplitudes. Higher stresses are predicted when strain amplitudes are increased. The model presented in the work can be used to design reliable 3D printed metals under cyclic loading conditions.

Cast aluminum alloys are common in automotive and aerospace applications due to their high strength-to-density ratio. Fracture data for cast aluminum alloys, such as fatigue life, tensile strength and elongation, are heavily affected by the structural defects, such as pores and bifilms. There have been numerous studies in which either fatigue performance or tensile deformation were characterized and linked to casting defects. However, a comprehensive study that correlates tensile and fatigue properties has not been reported. The present study is motivated to fill this gap. The main objective of the investigation is to analyze the link between tensile and fatigue performance of commonly used cast aluminum alloys, and determine whether fatigue performance of cast aluminum alloys can be predicted. To accomplish this task, four research questions were developed: (i) how well do equations developed to account for mean stress effects perform in cast aluminum alloys, especially in datasets with various levels of structural quality, (ii) is the strong correlation between fatigue life and structural quality index obtained from tensile data reported for A206 alloy castings applicable to other aerospace and automotive casting alloys, (iii) how do methods to estimate high cycle fatigue from tensile data perform with aluminum castings, and (iv) can the axial fatigue performance of an A356-T6 casting be predicted from rotating beam fatigue data. Among the three mean stress correction models analyzed by using seven datasets from the literature, the one developed by Walker with an adjustable exponent has provided the best fit. It has been hypothesized that the adjustable Walker parameter is related to the structural quality index, QT, estimated from tensile data. Results have shown that there is indeed a strong correlation between QT and the Walker parameter. Moreover the parameters of the xvi Weibull distribution estimated from corrected data have been found to be strongly influenced by the mean stress correction method used. Tensile and fatigue life data for 319, D357 and B201 aluminum alloy castings reported in the literature have been reanalyzed by using a maximum likelihood method to estimate Basquin parameters in datasets with run-outs, Weibull statistics for censored data and mean stress correction. After converting tensile data to QT, a distinct relationship has been observed between the expected fatigue life and mean quality index for all alloys. Moreover, probability of survival in fatigue life has been found to be directly linked to the proportions of the quality index distributions in two different regions, providing further evidence about the strong relationship between elongation, i.e., structural quality, and fatigue performance [1]. Specimen geometry has been found to make the largest difference whereas the two aerospace alloys, B201 and D357, with distinctly different microstructures, have followed the same relationship, reinforcing the findings in the literature that fatigue life in aluminum castings is mainly determined by the size distribution and number density of structural defects. Six methods to predict fatigue life from tensile data have been compared by using data from the literature as well as the experimental A356 data developed in this study. Results have shown that none of the six methods provide reliable results. The consistently poor performance of the methods developed for steels and wrought alloys can be attributed to the major structural defects, namely bifilms, in aluminum castings. A new method to estimate the S-N curve from tensile data have been developed by using data for seventy-one S-N curves have been collected and Basquin parameters have been determined. Analysis showed that there is a strong relationship between QT and the Basquin exponent. xvii The Basquin parameters estimated by using the empirical relationships developed in the present study have provided better fits to the same datasets tested for the six methods. Hence the model developed in this study is proposed as the most reliable method to estimate high cycle fatigue properties. Finally, three methods to convert rotating bending fatigue test results to uniaxial fatigue data have been investigated by using the data developed in this study. Results have indicated that the method developed by Esin, in which both the fatigue life and alternating stress are corrected, provide the best estimate. Analyses of fracture surfaces of broken specimens via scanning electron microscopy have shown that tensile, axial fatigue and rotating beam fatigue properties are all strongly influenced by the same structural defects, confirming the validity of the approach taken in this study.

This work employs statistical and Bayesian techniques to analyze mathematical forward models with several sources of uncertainty. The forward models usually arise from phenomenological and physical phenomena and are expressed through regression-based models or partial differential equations (PDEs) associated with uncertain parameters and input data. One of the critical challenges in real-world applications is to quantify uncertainties of the unknown parameters using observations. To this purpose, methods based on the likelihood function, and Bayesian techniques constitute the two main statistical inferential approaches considered here. Two problems are studied in this thesis. The first problem is the prediction of fatigue life of metallic specimens. The second part is related to inverse problems in linear PDEs. Both problems require the inference of unknown parameters given certain measurements. We first estimate the parameters by means of the maximum likelihood approach. Next, we seek a more comprehensive Bayesian inference using analytical asymptotic approximations or computational techniques. In the fatigue life prediction, there are several plausible probabilistic stress-lifetime (S-N) models. These models are calibrated given uniaxial fatigue experiments. To generate accurate fatigue life predictions, competing S-N models are ranked according to several classical information-based measures. A different set of predictive information criteria is then used to compare the candidate Bayesian models. Moreover, we propose a spatial stochastic model to generalize S-N models to fatigue crack initiation in general geometries. The model is based on a spatial Poisson process with an intensity function that combines the S-N curves with an averaged effective stress that is computed from the solution of the linear elasticity equations.

Sheet metal forming has an important place among metal forming processes. As the usage of sheet metal increases, the fatigue simulation and optimization of these parts become more important. This thesis study examines the change of the fatigue life of a sheet metal part after forming. A sphere-like shape is deep drawn and change in thickness and residual stresses are analyzed. To understand the effect of residual stresses, deep drawn parts with and without residual stress tested against the fatigue failure. In parallel, the forming process is simulated with an implicit finite element method (FEM). The success of forming simulation is discussed in the study. Thickness changes and residual stresses calculated with FEM are included in computer aided fatigue analysis. The effect of thickness changes is examined with the results of FEM analysis. The effectiveness of the whole simulation process is discussed by comparing the outputs of experiments and computational analysis.

abstract: The fatigue resistance of asphalt concrete (AC) plays an important role in the service life of a pavement. For predicting the fatigue life of AC, there are several existing empirical and mechanistic models. However, the assessment and quantification of the ‘reliability’ of the predictions from these models is a substantial knowledge gap. The importance of reliability in AC material performance predictions becomes all the more important in light of limited monetary and material resources. The goal of this dissertation research is to address these shortcomings by developing a framework for incorporating reliability into the prediction of mechanical models for AC and to improve the reliability of AC material performance prediction by using Fine Aggregate Matrix (FAM) phase data. The goal of the study is divided into four objectives; 1) development of a reliability framework for fatigue life prediction of AC materials using the simplified viscoelastic continuum damage (S-VECD) model, 2) development of test protocols for FAM in similar loading conditions as AC, 3) evaluation of the mechanical linkages between the AC and FAM mix through upscaling analysis, and 4) investigation of the hypothesis that the reliability of fatigue life prediction of AC can be improved with FAM data modeling. In this research effort, a reliability framework is developed using Monte Carlo simulation for predicting the fatigue life of AC material using the S-VECD model. The reliability analysis reveals that the fatigue life prediction is very sensitive to the uncertainty in the input variables. FAM testing in similar loading conditions as AC, and upscaling of AC modulus and damage response using FAM properties from a relatively simple homogenized continuum approach shows promising results. The FAM phase fatigue life prediction and upscaling of FAM results to AC show more reliable fatigue life prediction than the fatigue life prediction of AC material using its experimental data. To assess the sensitivity of fatigue life prediction model to uncertainty in the input variables, a parametric sensitivity study is conducted on the S-VECD model. Overall, the findings from this research show promising results both in terms of upscaling FAM to AC properties and the reliability of fatigue prediction in AC using experimental data on FAM. / Dissertation/Thesis / Doctoral Dissertation Civil and Environmental Engineering 2016

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Ausgangspunkt für die angestellten Untersuchungen bildet das Wissen um die unbefriedigende Treffsicherheit in der Lebensdauerabschätzung bei Belastungen mit ausgeprägten Mittelwertänderungen. Die Grundlage zur Weiterentwicklung theoretischer Lebensdauervorhersagemodelle auf Basis von Nenn- und örtlichen Beanspruchungen wurde mit experimentellen Untersuchungen an Werkstoff- und gekerbten Proben geschaffen, sowohl für einfache als auch gezielt abgeleitete, realitätsnahe komplexe Belastungs-Zeit-Abläufe. Es stehen zwei, ihrem zeitlich abhängigen Materialverhalten nach unterschiedliche Werkstoffe im Mittelpunkt der Betrachtungen. Ziel war es, die grundsätzliche zeitabhängige Reaktion der Werkstoffe auf die Belastung zu erkennen und diese Erkenntnisse mittels integra-len Parametern für die Verbesserung der Treffsicherheit der Lebensdauerabschätzung zu nutzen. Die Abschätzung der experimentell ermittelten Lebensdauern mit dem Nennspannungskonzept, die statistische Auswertung der Schädigungssummen und die Untersuchung der Korrelation von Schädigungssumme und zunächst frei wählbaren Parametern mittels multipler Regressionsanalyse führt zur Festlegung auf drei die Geometrie, den Werkstoff und die Belastung beschreibende Parameter. Bei beiden Werkstoffen wird durch Verwendung einer sogenannten korrigierten mit der Regressionsgleichung bestimmten Schädigungssumme eine Erhöhung der Treffsicherheit der Lebensdauervorhersage nachgewiesen. Den gesammelten Erfahrungen und Erkenntnissen entsprechend werden Empfehlungen zur Anwendung der behandelten Lebensdauerabschätzungsverfahren auf der Grundlage örtlicher Beanspruchungen gegeben. Mit den Versuchen innerhalb der Arbeit wurde eine experimentelle Basis geschaffen, die eine Weiterentwicklung von Ansätzen zur Berücksichtigung des transienten Materialverhaltens in Konzepten auf der Basis örtlicher Beanspruchungen ermöglicht.

Ausgangspunkt für die angestellten Untersuchungen bildet das Wissen um die unbefriedigende Treffsicherheit in der Lebensdauerabschätzung bei Belastungen mit ausgeprägten Mittelwertänderungen. Die Grundlage zur Weiterentwicklung theoretischer Lebensdauervorhersagemodelle auf Basis von Nenn- und örtlichen Beanspruchungen wurde mit experimentellen Untersuchungen an Werkstoff- und gekerbten Proben geschaffen, sowohl für einfache als auch gezielt abgeleitete, realitätsnahe komplexe Belastungs-Zeit-Abläufe. Es stehen zwei, ihrem zeitlich abhängigen Materialverhalten nach unterschiedliche Werkstoffe im Mittelpunkt der Betrachtungen. Ziel war es, die grundsätzliche zeitabhängige Reaktion der Werkstoffe auf die Belastung zu erkennen und diese Erkenntnisse mittels integra-len Parametern für die Verbesserung der Treffsicherheit der Lebensdauerabschätzung zu nutzen. Die Abschätzung der experimentell ermittelten Lebensdauern mit dem Nennspannungskonzept, die statistische Auswertung der Schädigungssummen und die Untersuchung der Korrelation von Schädigungssumme und zunächst frei wählbaren Parametern mittels multipler Regressionsanalyse führt zur Festlegung auf drei die Geometrie, den Werkstoff und die Belastung beschreibende Parameter. Bei beiden Werkstoffen wird durch Verwendung einer sogenannten korrigierten mit der Regressionsgleichung bestimmten Schädigungssumme eine Erhöhung der Treffsicherheit der Lebensdauervorhersage nachgewiesen. Den gesammelten Erfahrungen und Erkenntnissen entsprechend werden Empfehlungen zur Anwendung der behandelten Lebensdauerabschätzungsverfahren auf der Grundlage örtlicher Beanspruchungen gegeben. Mit den Versuchen innerhalb der Arbeit wurde eine experimentelle Basis geschaffen, die eine Weiterentwicklung von Ansätzen zur Berücksichtigung des transienten Materialverhaltens in Konzepten auf der Basis örtlicher Beanspruchungen ermöglicht.