<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>

Friction Spot Welding (FSpW) é um processo de solda ponto por fricção, que opera na fase sólida do material e permite unir duas ou mais chapas de metal sobrepostas. Além de ser bastante usado para soldar materiais leves, ele também é aplicável a qualquer material que apresente boa plasticidade. Neste trabalho são analisados dois materiais: AA Alclad 2024-T351 e AA 2024-T351, diferindo entre si no uso, ou não, da camada de proteção contra a corrosão (Alclad). As uniões são feitas sob os mesmos parâmetros do processo, previamente estudados para o material com Alclad. Dois parâmetros são utilizados: um dito ótimo, capaz de produzir soldas com bom desempenho mecânico e reprodutibilidade e um segundo, dito insuficiente, por produzir soldas de baixo desempenho mecânico e baixa reprodutibilidade. Pretende-se, com este trabalho, avaliar os efeitos que a camada Alclad pode acarretar nas juntas soldadas, em seu desempenho mecânico, no modo de fratura, na microestrutura e na geometria da junta. Os resultados apresentam uma grande influência do Alclad, tendo em vista que durante o processo o recobrimento migra das superfícies das chapas para o centro da solda. Assim, uma interface deste material, que possui baixa resistência mecânica, é criada, influenciando negativamente o desempenho da junta e alterando o modo de fratura. O principal escopo desta dissertação é realizar uma análise da fratura do ensaio de cisalhamento, com o uso do método de elementos finitos. Portanto, fazse necessário estudar e desenvolver um modelo numérico capaz de representar a nucleação, coalescimento, formação de uma ou mais trincas e a consequente propagação até a fratura do corpo. Para a realização da análise utilizou-se o modelo numérico de fratura Johnson-Cook (JC), o qual expressa a tensão equivalente como uma função da deformação plástica, da taxa de deformação e da temperatura. Realizou-se, ainda, um estudo acerca das teorias do Continuum Damage Mechanics (CDM), bem como se fez necessário obter novos parâmetros para o modelo, que descrevessem o fenômeno e o material. Nesse sentido, serão realizadas duas análises, sendo que a primeira considera o efeito da camada de Alclad e, a segunda, considera uma solda livre de defeitos. Espera-se identificar os locais em que trinca é nucleada e analisar a resposta da junta, passo a passo, durante a propagação da trinca, até a fratura completa do corpo. E, por fim, avaliar a interferência no modelo numérico da presença da camada contra a corrosão Alclad. / Friction Spot Welding (FSpW) is a friction spot weld process, it operates in the solid-state of the material and allows joining two or more sheets in overlap configuration. It is used to join light weight materials, also is suitable to any material that shows good ductility. In this work two different materials are analyzed AA Alclad 2024-T351 e AA 2024-T351, between them the use, or not, of the corrosion protection layer Alclad. The welds are made under the same process parameters previously studied to the material with Alclad. Two parameters are utilized: the first one is the optimum parameter capable to produce welds with good mechanical performance and reproducibility, and another one inadequate because it produces joins with poor mechanical response and reproducibility. It is intended with this work, to evaluate the effects that the Alclad layer can cause in the welds, in its mechanical performance, fracture mode, microstructure and geometry of the join. The results showed a considerable influence of the Alclad, considering that during the process, it migrates from the sheet surface to the center of the weld. Thus, an interface of this material, that has a very low hardness, is created, influencing negatively the performance of the weld and changing the fracture mode. The aim of this dissertation is to perform an analysis of the fracture from the lap shear test, using the finite element method. Therefore, becomes necessary study and develop a numerical model capable to represent the nucleation, coalescence, formation of one or more cracks and, the consequent propagation until the fracture of the body. To perform the analysis it was used the numerical model of fracture called Johnson-Cook (JC), which expresses the equivalent stress as a function of the plastic deformation, the strain rate and the temperature. It was also made a study about the Continuum Damage Mechanics (CDM) theories, and it was necessary to obtain new parameters for the model, that describe the phenomenon and the material. In this sense, it will be performed two analyses, and the first considers the Alclad layer and, the second, considers a weld without defects. It is expected to identify the places where the crack nucleated, and analyze the behavior of the weld, step by step, during the crack propagation, until the complete fracture of the component. And, finally, evaluate the interference in the numerical model of the presence of the protection corrosion layer Alclad.

Friction Spot Welding (FSpW) é um processo de solda ponto por fricção, que opera na fase sólida do material e permite unir duas ou mais chapas de metal sobrepostas. Além de ser bastante usado para soldar materiais leves, ele também é aplicável a qualquer material que apresente boa plasticidade. Neste trabalho são analisados dois materiais: AA Alclad 2024-T351 e AA 2024-T351, diferindo entre si no uso, ou não, da camada de proteção contra a corrosão (Alclad). As uniões são feitas sob os mesmos parâmetros do processo, previamente estudados para o material com Alclad. Dois parâmetros são utilizados: um dito ótimo, capaz de produzir soldas com bom desempenho mecânico e reprodutibilidade e um segundo, dito insuficiente, por produzir soldas de baixo desempenho mecânico e baixa reprodutibilidade. Pretende-se, com este trabalho, avaliar os efeitos que a camada Alclad pode acarretar nas juntas soldadas, em seu desempenho mecânico, no modo de fratura, na microestrutura e na geometria da junta. Os resultados apresentam uma grande influência do Alclad, tendo em vista que durante o processo o recobrimento migra das superfícies das chapas para o centro da solda. Assim, uma interface deste material, que possui baixa resistência mecânica, é criada, influenciando negativamente o desempenho da junta e alterando o modo de fratura. O principal escopo desta dissertação é realizar uma análise da fratura do ensaio de cisalhamento, com o uso do método de elementos finitos. Portanto, fazse necessário estudar e desenvolver um modelo numérico capaz de representar a nucleação, coalescimento, formação de uma ou mais trincas e a consequente propagação até a fratura do corpo. Para a realização da análise utilizou-se o modelo numérico de fratura Johnson-Cook (JC), o qual expressa a tensão equivalente como uma função da deformação plástica, da taxa de deformação e da temperatura. Realizou-se, ainda, um estudo acerca das teorias do Continuum Damage Mechanics (CDM), bem como se fez necessário obter novos parâmetros para o modelo, que descrevessem o fenômeno e o material. Nesse sentido, serão realizadas duas análises, sendo que a primeira considera o efeito da camada de Alclad e, a segunda, considera uma solda livre de defeitos. Espera-se identificar os locais em que trinca é nucleada e analisar a resposta da junta, passo a passo, durante a propagação da trinca, até a fratura completa do corpo. E, por fim, avaliar a interferência no modelo numérico da presença da camada contra a corrosão Alclad. / Friction Spot Welding (FSpW) is a friction spot weld process, it operates in the solid-state of the material and allows joining two or more sheets in overlap configuration. It is used to join light weight materials, also is suitable to any material that shows good ductility. In this work two different materials are analyzed AA Alclad 2024-T351 e AA 2024-T351, between them the use, or not, of the corrosion protection layer Alclad. The welds are made under the same process parameters previously studied to the material with Alclad. Two parameters are utilized: the first one is the optimum parameter capable to produce welds with good mechanical performance and reproducibility, and another one inadequate because it produces joins with poor mechanical response and reproducibility. It is intended with this work, to evaluate the effects that the Alclad layer can cause in the welds, in its mechanical performance, fracture mode, microstructure and geometry of the join. The results showed a considerable influence of the Alclad, considering that during the process, it migrates from the sheet surface to the center of the weld. Thus, an interface of this material, that has a very low hardness, is created, influencing negatively the performance of the weld and changing the fracture mode. The aim of this dissertation is to perform an analysis of the fracture from the lap shear test, using the finite element method. Therefore, becomes necessary study and develop a numerical model capable to represent the nucleation, coalescence, formation of one or more cracks and, the consequent propagation until the fracture of the body. To perform the analysis it was used the numerical model of fracture called Johnson-Cook (JC), which expresses the equivalent stress as a function of the plastic deformation, the strain rate and the temperature. It was also made a study about the Continuum Damage Mechanics (CDM) theories, and it was necessary to obtain new parameters for the model, that describe the phenomenon and the material. In this sense, it will be performed two analyses, and the first considers the Alclad layer and, the second, considers a weld without defects. It is expected to identify the places where the crack nucleated, and analyze the behavior of the weld, step by step, during the crack propagation, until the complete fracture of the component. And, finally, evaluate the interference in the numerical model of the presence of the protection corrosion layer Alclad.

Friction Spot Welding (FSpW) é um processo de solda ponto por fricção, que opera na fase sólida do material e permite unir duas ou mais chapas de metal sobrepostas. Além de ser bastante usado para soldar materiais leves, ele também é aplicável a qualquer material que apresente boa plasticidade. Neste trabalho são analisados dois materiais: AA Alclad 2024-T351 e AA 2024-T351, diferindo entre si no uso, ou não, da camada de proteção contra a corrosão (Alclad). As uniões são feitas sob os mesmos parâmetros do processo, previamente estudados para o material com Alclad. Dois parâmetros são utilizados: um dito ótimo, capaz de produzir soldas com bom desempenho mecânico e reprodutibilidade e um segundo, dito insuficiente, por produzir soldas de baixo desempenho mecânico e baixa reprodutibilidade. Pretende-se, com este trabalho, avaliar os efeitos que a camada Alclad pode acarretar nas juntas soldadas, em seu desempenho mecânico, no modo de fratura, na microestrutura e na geometria da junta. Os resultados apresentam uma grande influência do Alclad, tendo em vista que durante o processo o recobrimento migra das superfícies das chapas para o centro da solda. Assim, uma interface deste material, que possui baixa resistência mecânica, é criada, influenciando negativamente o desempenho da junta e alterando o modo de fratura. O principal escopo desta dissertação é realizar uma análise da fratura do ensaio de cisalhamento, com o uso do método de elementos finitos. Portanto, fazse necessário estudar e desenvolver um modelo numérico capaz de representar a nucleação, coalescimento, formação de uma ou mais trincas e a consequente propagação até a fratura do corpo. Para a realização da análise utilizou-se o modelo numérico de fratura Johnson-Cook (JC), o qual expressa a tensão equivalente como uma função da deformação plástica, da taxa de deformação e da temperatura. Realizou-se, ainda, um estudo acerca das teorias do Continuum Damage Mechanics (CDM), bem como se fez necessário obter novos parâmetros para o modelo, que descrevessem o fenômeno e o material. Nesse sentido, serão realizadas duas análises, sendo que a primeira considera o efeito da camada de Alclad e, a segunda, considera uma solda livre de defeitos. Espera-se identificar os locais em que trinca é nucleada e analisar a resposta da junta, passo a passo, durante a propagação da trinca, até a fratura completa do corpo. E, por fim, avaliar a interferência no modelo numérico da presença da camada contra a corrosão Alclad. / Friction Spot Welding (FSpW) is a friction spot weld process, it operates in the solid-state of the material and allows joining two or more sheets in overlap configuration. It is used to join light weight materials, also is suitable to any material that shows good ductility. In this work two different materials are analyzed AA Alclad 2024-T351 e AA 2024-T351, between them the use, or not, of the corrosion protection layer Alclad. The welds are made under the same process parameters previously studied to the material with Alclad. Two parameters are utilized: the first one is the optimum parameter capable to produce welds with good mechanical performance and reproducibility, and another one inadequate because it produces joins with poor mechanical response and reproducibility. It is intended with this work, to evaluate the effects that the Alclad layer can cause in the welds, in its mechanical performance, fracture mode, microstructure and geometry of the join. The results showed a considerable influence of the Alclad, considering that during the process, it migrates from the sheet surface to the center of the weld. Thus, an interface of this material, that has a very low hardness, is created, influencing negatively the performance of the weld and changing the fracture mode. The aim of this dissertation is to perform an analysis of the fracture from the lap shear test, using the finite element method. Therefore, becomes necessary study and develop a numerical model capable to represent the nucleation, coalescence, formation of one or more cracks and, the consequent propagation until the fracture of the body. To perform the analysis it was used the numerical model of fracture called Johnson-Cook (JC), which expresses the equivalent stress as a function of the plastic deformation, the strain rate and the temperature. It was also made a study about the Continuum Damage Mechanics (CDM) theories, and it was necessary to obtain new parameters for the model, that describe the phenomenon and the material. In this sense, it will be performed two analyses, and the first considers the Alclad layer and, the second, considers a weld without defects. It is expected to identify the places where the crack nucleated, and analyze the behavior of the weld, step by step, during the crack propagation, until the complete fracture of the component. And, finally, evaluate the interference in the numerical model of the presence of the protection corrosion layer Alclad.

Indiana University-Purdue University Indianapolis (IUPUI) / Additively manufactured (AM) metals have been increasingly fabricated for structural applications. However, a major hurdle preventing their extensive application is lack of understanding of their mechanical properties. To address this issue, the objective of this research is to develop a computational model to simulate the creep behavior of nickel alloy 718 manufactured using the laser powder bed fusion (L-PBF) additive manufacturing process. A finite element (FE) model with a subroutine is created for simulating the creep mechanism for 3D printed nickel alloy 718 components. A continuum damage mechanics (CDM) approach is employed by implementing a user defined subroutine formulated to accurately capture the creep mechanisms. Using a calibration code, the material constants are determined. The secondary creep and damage constants are derived using the parameter fitting on the experimental data found in literature. The developed FE model is capable to predict the creep deformation, damage evolution, and creep-rupture life. Creep damage and rupture is simulated as defined by the CDM theory. The predicted results from the CDM model compare well with experimental data, which are collected from literature for L-PBF manufactured nickel alloy 718 of creep deformation and creep rupture, at different levels of temperature and stress. Using the multi-regime Liu-Murakami (L-M) and Kachanov-Rabotnov (K-R) isotropic creep damage formulation, creep deformation and rupture tests of both the secondary and tertiary creep behaviors are modeled. A single element FE model is used to validate the model constants. The model shows good agreement with the traditionally wrought manufactured 316 stainless steel and nickel alloy 718 experimental data collected from the literature. Moreover, a full-scale axisymmetric FE model is used to simulate the creep test and the capacity of the model to predict necking, creep damage, and creep-rupture life for L-PBF manufactured nickel alloy 718. The model predictions are then compared to the experimental creep data, with satisfactory agreement. In summary, the model developed in this work can reliably predict the creep behavior for 3D printed metals under uniaxial tensile and high temperature conditions.

<div>Additively manufactured (AM) metals have been increasingly fabricated for structural applications. However, a major hurdle preventing their extensive application is lack of understanding of their mechanical properties. To address this issue, the objective of this research is to develop a computational model to simulate the creep behavior of nickel alloy 718 manufactured using the laser powder bed fusion (L-PBF) additive manufacturing process. A finite element (FE) model with a subroutine is created for simulating the creep mechanism for 3D printed nickel alloy 718 components.</div><div><br></div><div>A continuum damage mechanics (CDM) approach is employed by implementing a user defined subroutine formulated to accurately capture the creep mechanisms. Using a calibration code, the material constants are determined. The secondary creep and damage constants are derived using the parameter fitting on the experimental data found in literature. The developed FE model is capable to predict the creep deformation, damage evolution, and creep-rupture life. Creep damage and rupture is simulated as defined by the CDM theory.</div><div>The predicted results from the CDM model compare well with experimental data, which are collected from literature for L-PBF manufactured nickel alloy 718 of creep deformation and creep rupture, at different levels of temperature and stress. </div><div><br></div><div>Using the multi-regime Liu-Murakami (L-M) and Kachanov-Rabotnov (K-R) isotropic creep damage formulation, creep deformation and rupture tests of both the secondary and tertiary creep behaviors are modeled.</div><div>A single element FE model is used to validate the model constants. The model shows good agreement with the traditionally wrought manufactured 316 stainless steel and nickel alloy 718 experimental data collected from the literature. Moreover, a full-scale axisymmetric FE model is used to simulate the creep test and the capacity of the model to predict necking, creep damage, and creep-rupture life for L-PBF manufactured nickel alloy 718. The model predictions are then compared to the experimental creep data, with satisfactory agreement.</div><div><br></div><div>In summary, the model developed in this work can reliably predict the creep behavior for 3D printed metals under uniaxial tensile and high temperature conditions.</div>

Every moment of every day, at least hundreds of thousands of tires roll across a surface throughout the world. Tires are indisputably important in our daily life. The tire's primary component is rubber, which consumes energy when it rotates on a substrate due to the viscoelastic material's internal friction: a phenomenon referred to as rolling resistance. The interaction between the tire and the road surface is one of the most intricate and crucial phenomena in an automobile, because it is responsible for creating forces, moments, and deformation in the tire. Additionally, the road's roughness interacts with the tire and contributes significantly to its performance. This dissertation aims to develop a comprehensive physics-based model for predicting the rolling resistance of a viscoelastic material due to dynamic deformations caused by tire rotation using an analytical approach. The model was developed by proposing a Gaussian wave function propagating across a tire circumference's viscoelastic medium. The wave function was selected to describe the displacement field produced by tire-road interaction. Additionally, by adopting a multi-scale modeling technique, the model was upgraded to estimate rolling resistance while taking into account surface roughness at all length scales, from macroscopic to microscopic. Additionally, another mathematical model was developed using the Fourier series approach to evaluate the steady-state stress response and energy dissipation for any harmonic and non-harmonic periodic strain signals. Additionally, the dissertation strove to build a continuum damage mathematical model using a combined testing/modeling methodology to predict the aging of Styrene-Butadiene Rubber (SBR) after continuous exposure to the atmosphere. The obtained model was developed through the implementation of optimization techniques while formulating a mathematical model, which was then combined with a physics-based model to predict rolling resistance while taking into account rubber aging. Calibration of hyperelastic and viscoelastic material models with testing data was performed using an optimization technique that yielded sufficient results. The results of all mathematical models obtained in this dissertation are reported subsequently. The stress response of a viscoelastic material under harmonic and non-harmonic strain input yielded good agreement with the FEA model obtained using ABAQUS. The rolling resistance behavior under various operating conditions, including texture and aging effects, was reported, and the results aligned with the experimental results found in the literature. / Doctor of Philosophy / Every moment of every day, hundreds of thousands of automobile tires roll across a surface somewhere in the world. A tire is an undeniably important part of everyday life. Rubber is the tire's main component, and when it rotates on a surface, it loses energy, resulting in a force that resists motion, known as rolling resistance force. The contact between the tire and the road is one of the most complicated and important phenomena that happens in an automobile because it is responsible for the vehicle's dynamic performance in areas such as acceleration, stopping distance, and stability. Another factor that affects tire and car performance and should be taken into account is the road's roughness. This dissertation used an analytical method to come up with an accurate physics-based model for predicting the rolling resistance force of a viscoelastic material caused by tire rotation. The model was developed by assuming a Gaussian wave function would move across the tire circumference. Additionally, using a multi-scale modeling technique, the model was improved so that it could calculate the value of rolling resistance force considering surface roughness in all lengths of scale. This project also developed an additional mathematical model using the Fourier series method to determine how the stress response and energy dissipation would behave for any harmonic and nonharmonic periodic strain signals. Additionally, the dissertation presents the developing of a continuum damage mathematical model that could predict the material property of styrene-butadiene rubber (SBR) after being exposed to the air for a long time (i.e., aged). The model was developed based on experimental data and optimization techniques. This model was then combined with a physics-based model to predict rolling resistance force while taking aging into account. The material models were defined using an optimization method that yielded good results. The stress response of a viscoelastic material when it was subjected to harmonic and non-harmonic strain was in good agreement with the Finite Element Analysis (FEA) model made with ABAQUS. Rolling resistance behavior was observed, and the results were consistent with those found in the literature.

The Thesis deals with Strain-Space Plasticity and its implementation in Nonlinear Finite Element frame-work coupled with damage. Conventional Stress-Space Plasticity, though very popular amongst commercial nonlinear FEM software package, has severe limitations especially in dealing with perfect-plasticity situations and also for softening behaviour. Strain-Space Plasticity, when fully evolved, has the potential to replace the Stress-space Plasticity. The thesis is a welcome addition in furthering the understanding of Strain-Space Plasticity and its illustration to analyze practical engineering problems. Continuum Damage Mechanics (CDM) is an evolving area of Solid Mechanics with great potential for application in failure and integrity analyses. Research activities have been initiated by several research groups world-wide, thus demonstrating its acceptance as an area of mechanics in its own right .This thesis further demonstrates coupling of Continuum Damage Mechanics with Strain-Space Plasticity. The thesis has been organized into 11 chapters with a good review of Plasticity (Stress-Space as well as Strain-Space), CDM, Stainless-steel Plasticity as well as Adhesive Plasticity. Main research contributions include: Formulation, FEM implementation and benchmarking of Strain Space Plasticity for Plane-Stress, Plane Strain, Axi-symmetric as well as 3-D case. Both isotropic and kinematic hardening models have been implemented. Further, these implementations have been extended by coupling with Damage. Special illustrations have been made to practical situations involving constitutive modeling of Stainless-steel and structural-adhesive.