Ces travaux de thèse sont consacrés au développement d'un algorithme de résolution de problèmes non-linéaires pour lesquels il existe une variabilité sur certains paramètres du modèle ou du chargement définis par leur intervalle de définition. Le cadre d'étude est le projet SINAPS@, qui a pour but d'évaluer les incertitudes dans les structures de génie civil, et de quantifier leur influence sur la réponse mécanique globale d’une structure sujette à un aléa sismique. Contrairement aux approches statistiques ou probabilistes classiques, une résolution déterministique est privilégiée dans notre étude. Cependant, afin de réduire le coût de calcul de cette famille de problèmes, une approche de type réduction de modèle PGD est mise en place, pour laquelle les paramètres incertains sont considérés comme des variables supplémentaires du problème. Cette méthode est mise en place au sein de l'algorithme LATIN, qui utilise une approche itérative pour résoudre le caractère non-linéaire des équations rencontrées lors de la résolution du problème mécanique. Ces travaux présentent donc l'extension de l'algorithme classique temps-espace LATIN-PGD à des problèmes paramétriques, pour lesquels les paramètres sont considérés comme des variables additionnelles dans la définition des quantités d’intérêt, ainsi que l'application de cette méthode à un modèle endommageant avec refermeture de fissure, présentant une variabilité à la fois sur des paramètres matériaux et sur l'amplitude du chargement. La faisabilité de ce couplage est illustrée par des exemples numériques sur des structures en béton armé pour divers types de chargement cycliques (traction—compression, flexion). / This thesis is dedicated to the development of an algorithm for the resolution of nonlinear problems for which there is a variability on some of the model parameters or on the loading conditions, which are only described by their intervals of variation. This study is part of the SINAPS@ project, which aims at evaluating the uncertainties in civil engineering structures and to quantify their influence on the global mechanical response of a structure to a seismic hazard. Unlike statistical or probabilistic approaches, we rely here on a deterministic approach. However, in order to reduce the computation cost of such problems, a PGD-based reduced-order modeling approach is implemented, for which the uncertain parameters are considered as additional variables of the problem. This method was implemented into the LATIN algorithm, which uses an iterative approach to solve the nonlinear aspect of the equations of the mechanical problem. This work present the extension of the classical time-space LATIN—PGD algorithm to parametric problems for which the parameters are considered as additional variables in the definition of the quantities of interest, as well as the application of such method to a damage model with unilateral effect, highlighting a variability on both material parameters and the loading amplitude. The feasibility of such coupling is illustrated on numerical examples for reinforced concrete structures subjected to different types of cyclic loading conditions (tension—compression, bending).

<p>Rolling contact fatigue (RCF) is a common cause of failure in tribological machine components such as rolling-element bearings (REBs). Steels selected for RCF applications are subject to various material processes in order to produce martensitic microstructures. An effect of such material processing is the retention of the austenitic phase within the steel microstructure. Retained austenite (RA) transformation in martensitic steels subjected to RCF is a well-established phenomenon. In this investigation, a novel approach is developed to predict martensitic transformations of RA in steels subjected to RCF. A criteria for phase transformations is developed by comparing the required thermodynamic driving force for transformations to the energy dissipation in the microstructure. The method combines principles from phase transformations in solids with a damage mechanics framework to calculate energy availability for transformations. The modeling is then extended to incorporate material alterations as a result of RA transforming within the material. A continuum damage mechanics (CDM) FEM simulation is used to capture material deterioration, phase transformations, and the formation of internal stresses as a result of RCF. Crystal lattice orientation is included to modify energy requirements for RA transformation. Damage laws are modified to consider residual stresses and different components of the stress state as the drivers of energy dissipation. The resulting model is capable of capturing microstructural evolution during RCF.</p> <p>The development and stability of internal stresses caused by RA transformation in bearing steel material was experimentally investigated. Specimens of 8620 case carburized steel were subjected to torsional fatigue at specific stress levels for a prescribed number of cycles. X-ray diffraction techniques were used to measure residual stress and RA volume fraction as a function of depth in the material. A model is set forth to predict compressive residual stress in the material as a function of RA transformation and material relaxation. Modeling results are corroborated with experimental data. In addition, varying levels of retained austenite (RA) were achieved through varying undercooling severity in uniformly treated case carburized 8620 steel. Specimens were characterized via XRD and EBSD techniques to determine RA volume fraction and material characteristics prior to rolling contact fatigue (RCF). Higher RA volume fractions did not lead to improvement in RCF lives. XRD measurements after RCF testing indicated that little RA decomposition had occurred during RCF. The previously established RCF simulations were modified to investigate the effects of RA stability on RCF. The results obtained from the CDM FEM captured similar behavior observed in the experimental results. Utilizing the developed model, a parametric study was undertaken to examine the effects of RA quantity, RA stability, and applied pressure on RCF performance. The study demonstrates that the energy requirements to transform the RA phase is critical to RCF performance.</p>

<p dir="ltr">Rolling contact fatigue (RCF) is one of the leading causes of failure in critical tribological components such as rolling element bearings (REBs), gears, cam and followers, etc. This is especially paramount for advanced aerospace applications where REB components need to operate for billions of RCF cycles before routine maintenance or inspection is performed. The rolling motion between the rolling elements and raceway produces RCF, wherein a complex, non-proportional, alternating contract stress is applied over a small material volume. Moreover, the highly localized stress occurs on the same length scale as microstructural features such as carbides, inclusions, grain size, hardness gradients from carburization, surface roughness, thereby amplifying their effect on fatigue performance. Therefore, the objective of this dissertation is to investigate critical microstructural modifications and their effects on RCF performance via experiments and computational modeling.</p><p dir="ltr">Initially, an investigation was undertaken to investigate surface roughness effects on RCF. The surface roughness of various REBs was measured through optical surface profilometry and used to construct rough surface pressure distributions, which were then used in a continuum damage mechanics (CDM) finite element (FE) framework. The results demonstrated that life is reduced as lambda ratio decreases. It was also observed that a 2-parameter Weibull cumulative distribution function can describe the relationship between the near surface orthogonal shear stress concentration and ratio of surface failures.</p><p dir="ltr">Next, the enhancement to RCF life from grain size refinement of through hardened bearing steels was studied. To capture the effects of grain refinement, torsion stress-life data of various grain size were used in the RCF model. A predictive life equation for different grain sizes was constructed based on the exponential trend observed between grain size and life from the simulation data. The life equation was then used to calculate the quotient of RCF at two different grain sizes. This quotient was defined as the life improvement ratio and it was observed that this investigation’s ratios compared well with existing life improvement ratios from RCF experiments.</p><p dir="ltr">Hardness gradient is a common microstructural modification to improve RCF life of tribo-components. Variation of hardness gradients is prevalent in case hardened (i.e. case carburized) bearing materials. Therefore, the CDM-FE RCF model was modified to investigate the effects of various hardness gradient types and depths on fatigue life improvement. The simulation results enabled the identification of potentially optimal gradients aimed to mitigate manufacturing challenges and provided the foundation for the construction of a general fatigue life equation.</p><p dir="ltr">A fundamental study to understand the impact various common RCF failure criteria have on RCF life estimation was then conducted using computational modeling. To capture the variation of a material’s resistance to fatigue, the critical CDM damage parameters were assumed to follow a probabilistic distribution instead of a singular value. The CDM-FE model was modified to consider the shear reversal, the octahedral shear stress, the maximum shear stress, the Fatemi-Socie criteria, and the Dang Van multi-axial fatigue parameter as failure criteria. Simulation life results revealed that the CDM-FE model with shear reversal and Fatemi-Socie criteria best match empirical predictions from well-established RCF life theory. Notably, the Fatemi-Socie exhibited the best agreement over all operating conditions.</p><p dir="ltr">The next investigation focused on the cleanliness of aerospace-quality bearing steels. Torsion fatigue experiments established the stress-life (S-N) relation for three common aerospace quality bearing steels. The S-N data was later used to calibrate the RCF model’s damage equation, which considered the Fatemi-Socie criteria following conclusions from a previous investigation. Simulation results were observed to corroborate well with RCF experiments that were conducted for all three materials, while noting the simulations offered a significant time saving. As a result, a subsequent investigation focused on establishing the stress-life relationship for one of the aerospace quality bearing steels through a combined experimental and analytical approach. Good corroboration was observed between simulations and experiments at three contact pressures. This finding is particularly significant as it strengthens the reliability of computational RCF model as an efficient means to assess the RCF performance of bearing materials.</p><p dir="ltr">Furthermore, the detailed investigation on RCF performance of each critical microstructural modifications and their respective effect greatly improves the state-of-the-art. The findings emanating from the various investigations offer informed fatigue design recommendations that aid in the selection of rolling element bearings for critical tribological and aerospace applications.</p>

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<p>Carbon-fiber reinforced polymers (CFRPs) are often used in the aerospace and automotive  industries for their high strength-to-weight ratios and corrosion resistance. A new class of  composites – known as Prepreg Platelet Molded Composites (PPMCs) – offers further  advantageous such as high forming capabilities with modest compromises in strength and stiffness.  One such property of PPMCs that have garnered interest over the years is their apparent  insensitivity to notches. Previous studies have researched the effect of specimen size and platelet  length on its effect on the open-hole performance of PPMCs. Research however has focused on  thinner samples with smaller hole sizes and neglected thicker samples with larger holes.  Additionally, while platelet sizes have been investigated for unnotched samples, platelet width on  notched samples is less clear from the literature. The present thesis offers some investigations to  aid in filling this knowledge gap. </p> <p><br></p> <p>The objective of this work is to study two parameters that could influence the performance of PPMCs under open-hole tension. First, thick (7.6 mm) specimens are subjected to large hole  sizes (up to 19.08 mm) to investigate their behavior in comparison to the smaller sample sizes  previously investigated in the literature. Through-thickness DIC measurements are taken to  investigate strain gradients in these thicker specimens. Second, various platelet widths are tested  to research their influence on notch insensitivity of open-hole tensile PPMC specimens. Lastly, a  finite element based continuum damage mechanics model is implemented to predict macro-level  structural properties using only material properties of the parent prepreg. It is found that large holes  in thick samples increase notch sensitivity compared to other samples of similar diameter-to-width  ratios. Narrower platelets were found to produce higher unnotched strengths, while wider platelets  offered more notch insensitivity. Lastly, the finite element model developed was found to  qualitatively replicate features and failure modes that are exhibited by PPMCs, though strength  predictions became inaccurate at larger specimen sizes. Recommendations are made for future  work on the basis of these findings.   </p>

This thesis deals with the design process of a tensile test specimen geometry with the intention that the specimen will show failure in a shear band during a tensile test. The triggered shear band is linked to a characteristic length lc, which is required for a nonlocal approach to continuum damage mechanics that predicts the life expectancy of a combustion chamber independent of the FEM mesh size. To predict if a specimen will fail in the preferred manner, numerical simulations have been performed and were analysed with the newly defined failure-in-shear-band indicator. Ductile failure modes and the fracture process depend strongly on the stress state. Therefore the indicator is formulated as a function of the Lode parameter and the stress triaxiality. Several double-notched bar specimens have been designed with different notch radii and notch depths. The failure-in-shear-band indicator implies promising values for a small notch radius and larger notch depth. Tensile tests were performed on four specimens which successfully failed in a shear band. Furthermore, a first statement on the magnitude of the characteristic length of CuAgZr is given. / Detta arbete behandlar designprocessen för en dragprovstavskonfiguration framtagen för att uppvisa brott i ett skjuvband under draghållfasthetsprovning. Initiering av skjuvbandet är kopplat till en karakteristisk längd lc, som krävs för att kunna använda en icke lokal metod för att analysera kontinuerlig skademekanik oberoende av maskstorleken i den numeriska modellen. Metoden är utvecklad för att kunna uppskatta den förväntade livslängden för en förbränningskammare. För att förutsäga om ett provobjekt kommer att gå sönder på det sätt som önskashar datorsimuleringar utförts och analyserats med den nyligen definierade indikatorn för skjuvbrott. Plastisk deformation, och så småningom brott, är starkt beroende avspänningstillståndet. Indikatorn är därför formulerad som en funktion av en s.k. Lode parametern och det treaxliga spänningstillståndet. Flera provstavsgeometrier har utformats med dubbla brottanvisningar vars radie och storlek varierats. Indikatorn för skjuvbrott ger lovande värden för små radier och ett större anvisningsdjup. Draghållfasthetsprovning utfördes på fyra provkroppar som uppvisade önskat skjuvbrott. Dessutom erhölls en första indikation om storleken på den karakteristiska längden för CuAgZr.

Styrene-Butadiene Rubber (SBR) is a form of rubber compound that is widely used in the tire industry. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. In this study, a material aging model that can predict the hyperplastic response of styrene-butadiene rubber (SBR) was mathematically developed using an integrated testing and continuum damage model framework. Coupling between the mechanical changes of SBR to the change in the chemical properties, specifically crosslink density (CLD) was also investigated. SBR dogbone shaped samples were accelerated aged in an aging oven at various temperatures and aging periods. Subsequently, hyperelastic tests were conducted to obtain the high strain response taking the 'Mullin's effect' into consideration. These responses were calibrated to different hyperelastic material models and the Arruda-Boyce model was chosen, due to its stable behavior and optimal fit. An aging evolution function was developed based on the variation in the model coefficients. This damage model is able to predict the hyperelastic response of SBR as it ages. A user material subroutine (UMAT) was also implemented in Abaqus based on the obtained aging evolution function to predict the stress response of SBR for varied applications. Additionally, to couple the chemical variations with the hyperelastic response, the rubber structure and composition was probed using Fourier-transform infrared spectroscopy (FTIR). The degradation of additives and SBR polymer chains were analyzed microscopically to explain the impact on the macroscopic properties. This study helps to correlate the change in crosslink density to ameliorate mechanical properties, such as strain at break, modulus, and stiffness. The effects of aging on the viscoelastic properties of SBR were also studied. Dynamic Mechanical Analysis (DMA) was used to characterize the viscoelastic response. Master curves of storage and loss modulus were generated using the time-temperature superposition principle (TTSP). The friction coefficient was estimated from the storage and loss modulus using a simplified form of the Persson equation [1]. CLD was also estimated from DMA data. Wear experiments were conducted on the Dynamic Friction Tester (DFT) for various aging conditions. The estimated friction coefficient was compared to the one from the experiments. Archard's law was used to correlate the frictional energy to the volume loss during wear experiments. Correlation between the wear and the viscoelastic properties of SBR is also studied. Finally, the lifetime of SBR for various aging temperatures is predicted using various models. [1] M. Ciavarella, "A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses," J. Tribol., vol. 140, no. 1, 2018, doi: 10.1115/1.4036917. / Master of Science / Elastomers or rubbers are they are generally referred to are an indispensable part of human life. They are made up of long-chain polymer units linked to one other through crosslinks. This peculiar morphology of rubbers is what gives them their unique characteristics. There are as many as 40,000 known products that use some form of rubber as the primary raw material. Apart, from this, they are also widely used in aviation and aerospace, automobiles, dampers and absorbers, civil engineering, electronics, medical, toys, clothing, sports, footwear, and so on. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. Over the last couple of years, it has also played a pivotal role in personal protective equipment (PPE) and masks worn by billions of people and frontline workers all over the globe. The fact that rubber is included in the EU's list of critical raw materials highlights its global importance. However, over the past several years, the rubber supply has dwindled. COVID-19 also caused disruptions in the supply chain of rubber. As the effects of COVID-19 are fading, there has been a spike in the demand for rubber; the primary reason being automotive tires! Even though substantial research is being conducted to try and replace rubber as a raw material with synthetic alternatives such as polyurethane, the excellent blend of damping, friction and wear characteristics, heat dissipation provided by natural rubber cannot be replicated by any of these laboratory compounds. Hence, at this time, there is an increased need to conserve and improve the longevity of rubber compounds. Styrene-Butadiene Rubber (SBR) is a form of a rubber compound that is widely used in the tire industry. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. The present study aims to model changes in the hyperelastic (large stretching) behavior of SBR using a Continuum Damage Mechanics (CDM) approach. This mathematical model is translated into ABAQUS, a finite element analysis software to study the mechanical response of components with various geometries and loading conditions. Secondly, the effects of aging on the viscoelastic behavior of SBR is studied. This helps us to estimate the cross-link density (CLD) as well as the friction coefficient of SBR as it is aged. The impact of aging on the wear and friction properties of SBR is studied experimentally. Finally, using various mechanical and chemical models the lifetime of SBR is estimated for various aging temperatures. Thus, the end goal of the study is to drive the development of new rubber compounds that will help improve the service life of rubbers and also have a positive impact on the environment.

Using experimental data obtained from standard fracture test configurations, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in the fracture mechanics literature as the Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture-mechanics-based crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and a lower surface that are connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or a mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of the crack is determined by the critical energy release rate. The adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The interfacial surface material is implemented through an interface element, which is incorporated in ABAQUS using the user defined element (UEL) option. A procedure is established to formulate a rate dependent model based on experiments carried out on compact tension test specimens. The rate dependent model is incorporated into the interface element approach to capture the unstable crack growth observed in experiments under quasi-static loading conditions. The compact tension test gives the variation of the fracture toughness with the rate of loading, this information is processed and a relationship between the fracture toughness and the rate of the opening displacement is established. The cohesive-decohesive zone model is implemented through a material model to be used in an explicit code (LS-DYNA). Dynamic simulations of the standard test configurations for Mode I (Double Cantilever Beam) and Mode II (End Load Split) are carried out using the explicit code. Verification of these coupon tests leads to the crash analysis of realistic structures like the square composite tube. Analyses of bonded and unbonded square tubes are presented. These tubes shows a very uncharacteristic failure mode: the composite material disintegrates on impact, and this has been captured in the analysis. Disadvantages of the interface element approach are well documented in the literature. An alternative method, known as the Extended Finite Element Method (XFEM), is implemented here through an eight-noded quadrilateral plane strain element. The method, based on the partition-of-unity, is used to study simple test configuration like the three-point bend problem and a double cantilever beam. Functionally graded materials are also simulated and the results are compared to the experimental results available in the literature. / Ph. D.