The purpose of this work was to develop a practical method for constitutive modelling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene (PE) is increasingly used as a structural material, for example in pipes installed by trenchless methods where relatively low stiffness of PE reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows to use it for sewer, gas and water lines. Polyethylene exhibits time-dependent constitutive behaviour, which is also dependent on the applied stress level resulting in nonlinear stress-strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modelling approaches have been derived from it. In order to be able to realistically utilize the nonlinear modelling approaches in design, a simple method is needed for finding the constitutive formulation for a specific polyethylene type. In this study, time-dependent constitutive relationships for polymers are investigated for polyethylene materials. Creep tests on seven polyethylene materials were conducted and the experimental results indicate strong nonlinear viscoelasticity in the material responses. Creep tests on seven materials were conducted for 24 hours for modelling purposes. However, creep tests up to fourteen days were performed on one material to study long-term creep behaviour. Multiple-stepped creep tests were also investigated. Constant rate (load and strain rate) tensile tests were conducted on two of the seven polyethylene materials. A practical approach to nonlinear viscoelastic modelling utilizing both multi-Kelvin element theory and power law functions to model creep compliance is presented. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is achieved by comparisons with the results of different tensile creep tests, with one dimensional step loading test results and with test results from load and displacement rate loading.

Random Glass Mat Thermoplastic (GMT) composites are increasingly being used by the automotive industry for manufacturing semi-structural components. The polypropylene based materials are characterized by superior strength, impact resistance and toughness. Since polymers and their composites are inherently viscoelastic, i.e. their mechanical properties are dependent on time and temperature. They creep under constant mechanical loading and the creep rate is accelerated at elevated temperatures. In typical automotive operating conditions, the temperature of the polymer composite part can reach as high as 80°C. Currently, the only known report in the open literature on the creep response of commercially available GMT materials offers data for up to 24 MPa at room temperature. In order to design and use these materials confidently, it is necessary to quantify the creep behaviour of GMT for the range of stresses and temperatures expected in service. The primary objective of this proposed research is to characterize and model the creep behaviour of the GMT composites under thermo-mechanical loads. In addition, tensile testing has been performed to study the variability in mechanical properties. The thermo-physical properties of the polypropylene matrix including crystallinity level, transitions and the variation of the stiffness with temperature have also been determined. In this work, the creep of a long fibre GMT composite has been investigated for a relatively wide range of stresses from 5 to 80 MPa and temperatures from 25 to 90°C. The higher limit for stress is approximately 90% of the nominal tensile strength of the material. A Design of Experiments (ANOVA) statistical method was applied to determine the effects of stress and temperature in the random mat material which is known for wild experimental scatter. Two sets of creep tests were conducted. First, preliminary short-term creep tests consisting of 30 minutes creep followed by recovery were carried out over a wide range of stresses and temperatures. These tests were carried out to determine the linear viscoelastic region of the material. From these tests, the material was found to be linear viscoelastic up-to 20 MPa at room temperature and considerable non-linearities were observed with both stress and temperature. Using Time-Temperature superposition (TTS) a long term master curve for creep compliance for up-to 185 years at room temperature has been obtained. Further, viscoplastic strains were developed in these tests indicating the need for a non-linear viscoelastic viscoplastic constitutive model. The second set of creep tests was performed to develop a general non-linear viscoelastic viscoplastic constitutive model. Long term creep-recovery tests consisting of 1 day creep followed by recovery has been conducted over the stress range between 20 and 70 MPa at four temperatures: 25°C, 40°C, 60°C and 80°C. Findley’s model, which is the reduced form of the Schapery non-linear viscoelastic model, was found to be sufficient to model the viscoelastic behaviour. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the non-linear model has been developed. The non-linear parameters in the Findley’s non-linear viscoelastic model have been found to be dependent on both stress and temperature and have been modeled as a product of functions of stress and temperature. The viscoplastic behaviour for temperatures up to 40°C was similar indicating similar damage mechanisms. Moreover, the development of viscoplastic strains at 20 and 30 MPa were similar over all the entire temperature range considered implying similar damage mechanisms. It is further recommended that the material should not be used at temperature greater than 60°C at stresses over 50 MPa. To further study the viscoplastic behaviour of continuous fibre glass mat thermoplastic composite at room temperature, multiple creep-recovery experiments of increasing durations between 1 and 24 hours have been conducted on a single specimen. The purpose of these tests was to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles and also to co-relate the development of viscoplastic strains with progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in-situ. A viscoplastic model developed from partial data analysis, as proposed by Nordin, had excellent agreement with experimental results for all stresses and times considered. Furthermore, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. These tests further validate the technique proposed for numerical separation of viscoplastic strains employed in obtaining the non-linear viscoelastic viscoplastic model parameters. These tests also indicate that the viscoelastic strains during creep are affected by the previous viscoplastic strain history. Finally, the developed comprehensive model has been verified with three test cases. In all cases, the model predictions agreed very well with experimental results.

The purpose of this work was to develop a practical method for constitutive modelling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene (PE) is increasingly used as a structural material, for example in pipes installed by trenchless methods where relatively low stiffness of PE reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows to use it for sewer, gas and water lines. Polyethylene exhibits time-dependent constitutive behaviour, which is also dependent on the applied stress level resulting in nonlinear stress-strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modelling approaches have been derived from it. In order to be able to realistically utilize the nonlinear modelling approaches in design, a simple method is needed for finding the constitutive formulation for a specific polyethylene type. In this study, time-dependent constitutive relationships for polymers are investigated for polyethylene materials. Creep tests on seven polyethylene materials were conducted and the experimental results indicate strong nonlinear viscoelasticity in the material responses. Creep tests on seven materials were conducted for 24 hours for modelling purposes. However, creep tests up to fourteen days were performed on one material to study long-term creep behaviour. Multiple-stepped creep tests were also investigated. Constant rate (load and strain rate) tensile tests were conducted on two of the seven polyethylene materials. A practical approach to nonlinear viscoelastic modelling utilizing both multi-Kelvin element theory and power law functions to model creep compliance is presented. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is achieved by comparisons with the results of different tensile creep tests, with one dimensional step loading test results and with test results from load and displacement rate loading.

Random Glass Mat Thermoplastic (GMT) composites are increasingly being used by the automotive industry for manufacturing semi-structural components. The polypropylene based materials are characterized by superior strength, impact resistance and toughness. Since polymers and their composites are inherently viscoelastic, i.e. their mechanical properties are dependent on time and temperature. They creep under constant mechanical loading and the creep rate is accelerated at elevated temperatures. In typical automotive operating conditions, the temperature of the polymer composite part can reach as high as 80°C. Currently, the only known report in the open literature on the creep response of commercially available GMT materials offers data for up to 24 MPa at room temperature. In order to design and use these materials confidently, it is necessary to quantify the creep behaviour of GMT for the range of stresses and temperatures expected in service. The primary objective of this proposed research is to characterize and model the creep behaviour of the GMT composites under thermo-mechanical loads. In addition, tensile testing has been performed to study the variability in mechanical properties. The thermo-physical properties of the polypropylene matrix including crystallinity level, transitions and the variation of the stiffness with temperature have also been determined. In this work, the creep of a long fibre GMT composite has been investigated for a relatively wide range of stresses from 5 to 80 MPa and temperatures from 25 to 90°C. The higher limit for stress is approximately 90% of the nominal tensile strength of the material. A Design of Experiments (ANOVA) statistical method was applied to determine the effects of stress and temperature in the random mat material which is known for wild experimental scatter. Two sets of creep tests were conducted. First, preliminary short-term creep tests consisting of 30 minutes creep followed by recovery were carried out over a wide range of stresses and temperatures. These tests were carried out to determine the linear viscoelastic region of the material. From these tests, the material was found to be linear viscoelastic up-to 20 MPa at room temperature and considerable non-linearities were observed with both stress and temperature. Using Time-Temperature superposition (TTS) a long term master curve for creep compliance for up-to 185 years at room temperature has been obtained. Further, viscoplastic strains were developed in these tests indicating the need for a non-linear viscoelastic viscoplastic constitutive model. The second set of creep tests was performed to develop a general non-linear viscoelastic viscoplastic constitutive model. Long term creep-recovery tests consisting of 1 day creep followed by recovery has been conducted over the stress range between 20 and 70 MPa at four temperatures: 25°C, 40°C, 60°C and 80°C. Findley’s model, which is the reduced form of the Schapery non-linear viscoelastic model, was found to be sufficient to model the viscoelastic behaviour. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the non-linear model has been developed. The non-linear parameters in the Findley’s non-linear viscoelastic model have been found to be dependent on both stress and temperature and have been modeled as a product of functions of stress and temperature. The viscoplastic behaviour for temperatures up to 40°C was similar indicating similar damage mechanisms. Moreover, the development of viscoplastic strains at 20 and 30 MPa were similar over all the entire temperature range considered implying similar damage mechanisms. It is further recommended that the material should not be used at temperature greater than 60°C at stresses over 50 MPa. To further study the viscoplastic behaviour of continuous fibre glass mat thermoplastic composite at room temperature, multiple creep-recovery experiments of increasing durations between 1 and 24 hours have been conducted on a single specimen. The purpose of these tests was to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles and also to co-relate the development of viscoplastic strains with progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in-situ. A viscoplastic model developed from partial data analysis, as proposed by Nordin, had excellent agreement with experimental results for all stresses and times considered. Furthermore, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. These tests further validate the technique proposed for numerical separation of viscoplastic strains employed in obtaining the non-linear viscoelastic viscoplastic model parameters. These tests also indicate that the viscoelastic strains during creep are affected by the previous viscoplastic strain history. Finally, the developed comprehensive model has been verified with three test cases. In all cases, the model predictions agreed very well with experimental results.

A verified elasto-viscoplastic finite element model is used to develop a better understanding of the performance of embankments with geosynthetic reinforcement constructed over rate-sensitive soil. The interaction between reinforcement and prefabricated vertical drains (PVDs) and their effects on time-dependent behaviour of embankments are examined. For rate-sensitive soils, the generation of creep-induced pore pressures following the end of construction is evident along the potential slip surface. As a result, the minimum factor of safety with respect to embankment stability occurs after the end of construction. The combined use of reinforcement and PVDs are shown to provide an effective means of minimizing creep-induced excess pore pressure, increasing overall stability, and decreasing deformation of the embankments. The combined effects of the viscoelastic properties of geosynthetic reinforcement (polyester, polypropylene and polyethylene) and the rate-sensitive nature of foundation soils on the performance of embankments are examined. The effect of various factors, including reinforcement type (i.e., stiffness and viscosity), soil viscosity, construction rate and allowable long-term reinforcement strain, on the time-dependent behaviour of embankments are considered. The long-term performance of reinforced embankments is investigated for different maximum allowable long-term reinforcement strains. From a series of finite element analyses, the ideal allowable reinforcement strains to minimize embankment deformation while providing optimum long-term service height of the embankment, considering the effect of soil and reinforcement viscosity, are proposed for soils similar to those examined in this study. The currently proposed design methods for embankments with creep-susceptible reinforcement over rate-sensitive soils appear to be overly conservative. This study proposes a refined approach for establishing the allowable long-term reinforcement strains that are expected to provide adequate performance while reducing the level of conservativeness of reinforced embankment design. Finally, a previously developed elasto-viscoplastic constitutive model is modified to incorporate the effect of soil structure using a state-dependent fluidity parameter and damage law. The model was evaluated against data from a well-documented case study of a reinforced test embankment constructed on a sensitive Champlain clay deposit in Saint Alban, Quebec. The benefit of basal reinforcement and the effect of reinforcement viscosity are then discussed for these types of soil deposits. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2011-01-21 22:26:40.133

[pt] Este trabalho apresenta uma técnica numérica. baseada no Método de Decomposição do Operador (Operator Splitting Method) e algorítimos sequenciais associados (product formula algorithm) para simular o fenômeno de propagação de ondas em barras elasto-viscoplásticas. Este método tem boas propriedades de estabilidade e preciaão mesmo quando um esquema explícito de baixa ordem é utilizado na integração temporal. Esta técnica numérica é usada para simular carregamentos cíclicos de alta frequência em barras de aço austenítico a altas temperaturas. / [en] The present work presents a numerical technique ( based on the Operator Split Method associated with product formula algorithm ) for simulating the wave propagation phenomenon in bars with any kind of elastic-viecoplastic oonstitutive equations. This method has very good properties of stability and precision even if explicit time evolution schemes are used. This numerical technique is used to simulate high frequency cyclic loadings in austenitic steel bars at high temperatures.

Today, there is a great focus on downsizing the engines, this means that the engines are made smaller in size but retain the same power. This in combination with the drive to increase the power of the engines has led to the engine components being exposed to high thermal loads. Today’s engines also use very high cylinder pressure. The high thermal loads in combination with the high cylinder pressure have led to that the engine components are often very close to their material limits, so close that damage is common. This places high requirements on the materials, which makes the material selection a critical part of the engineering process.The main focus in this thesis work has been to develop and investigate a FEM model that can be used to quickly evaluate materials in an exhaust manifold that is exposed to thermo-mechanical fatigue (TMF). The model was then used to verify a material selection made for an existing exhaust manifold. One of AVL’s own software programs has also been evaluated, to see if it is a viable alternative to ABAQUS when preforming TMF simulations.The material selection made in this master thesis had the restriction that the exhaust manifold should not fail due to low cycle fatigue (LCF) when exposed to TMF. The goal has been to minimize the mass of the exhaust manifold by selecting a strong material with low density. The reason for this is because today there is a big focus on energy efficient cars with low emission levels. The simplest way to achieve this is to minimize the mass of the vehicle.The simulations conducted in this work has been performed in two different software’s, ABAQUS and AVL Fire M. In AVL Fire M flow simulations and steady-state heat transfer simulations have been performed. In ABAQUS, steady-state and transient heat transfer simulations and stress-strain simulations have been performed.The material selection process showed that Inconel 601 is the most suitable material for an exhaust manifold exposed to TMF. The simulations using Inconel 601 showed that this material will not fail due to LCF.The FEM model that was developed in this thesis was a lot faster compared to the existing TMF model used at AVL.CPU time for the existing model: 14 days 13 hours 14 minutes and 30 seconds (Core time).CPU time for the model developed in this thesis: 1 day 6 hours 37 minutes and 49 seconds (Core time).Two alternative models have been proposed for TMF simulations, one that uses the model developed in this thesis and one that is a combination of the existing model and the model developed in this work.

Le but principal de ce travail est la présentation de la formulation mathématique et l’analyse des propriétés viscoplastiques du fluide magnétorhéologique dans des conditions d’exploitation d’amortisseur ainsi que la détermination des dimensions optimum de l’orifice d’écoulement du fluide MR dans le dispositif de ce type. Une analyse particulière de la littérature a été effectuée. Nous nous sommes limités à deux types d’amortisseurs: l’amortisseur LORD RD 1005-3 et le prototype d’amortisseur T-MR SiMR 132 DG. Les résultats expérimentaux ont permis de déterminer la limite élastique et la contrainte maximale de cisaillement du fluide MR sous tension en fonction de différentes vitesses de cisaillement, différentes intensités du courant, températures et hauteurs d’orifice d’écoulement. Les modèles viscoplastiques identifiés ont permis de simuler le comportement du fluide MR et de comparer les résultats numériques avec ceux obtenus par des mesures. On a constaté une bonne concordance des courbes tracées dans ces deux cas, ce qui permet de conclure qu’il est possible d’utiliser les modèles viscoplastiques des métaux pour décrire le comportement du fluide magnétorhéologique. / The main goal of this dissertation is a mathematical description and an analysis of viscoplasticproperties of magnetorheological fluid, in operational conditions of the damper’s work, as well as the determining the optimum, in view of indicated values of parameters, size of the gap for the MR fluid to flow, in these devices. A detailed analysis of literature was made. The scope of research work has been limited to two types of magnetorheological devices: the shock absorber LORD RD 1005-3 and the MR damper prototype T-MR SiMR -132 DG. On the basis of performed experiments, it has been estimated i.e.: conventional yield point and the maximum shear stress of analyzed MR fluid, including variable shear rate, intensity of current flowing in a solenoid, liquid’s temperature and the gap height. Identified viscoplastic models were used to develop a simulation that verifies the proposed mathematical model which describes the behaviour of MR fluid in operating gap of machine’s head, with data derived from performed experiments.

[pt] É considerado neste trabalho um modelo mecânico para simulação do comportamento anisotérmico de materiais inelásticos submetidos a carregamentos dinâmicos. O trabalho tem como motivação o estudo, através de simulações numéricas, dos efeitos da propagação da onda de tensão no meio, e de fenômenos como o aquecimento e a degradação local induzida pelas deformações inelásticas. A equação da energia com seus termos de acoplamentos entre os efeitos térmico e mecânico é incluída na modelagem. A teoria constitutiva utilizada baseia-se na mecânica do dano contínuo no contexto de variáveis internas sendo particularizada para materiais elastoviscoplásticos e aplicado ao caso de uma barra solicitada axialmente. O sistema não linear de equações diferenciais parciais resultante do modelo é resolvido através do uso uma técnica de decomposição do operador que permite a aplicação de procedimentos numéricos clássicos de solução. Dentre estes procedimentos, foi usado no trabalho, o método de Glimm. Exemplos numéricos retratando a evolução do dano e da temperatura induzida pela deformação plástica devido a carregamentos de impacto e de alta frequência, são apresentados e analisados. Comparações entre simulações com os modelos isotérmico e anisotérmico permitem caracterizar as influências da equação da energia e do dano. / [en] This work presents a mechanical model for simulating the anisothermal behavior of damageable inelastic solids under dynamical loadings. The main motivation of this study is to investigate, by means of numerical simulations, the thermomechanical coupling in a simple one-dimensional problem involving the wave propagation phenomenon in a damageable non-isothermal solid. To achieve this goal, the equation of energy is taken into account in the modeling with the coupling terms between the thermal and mechanical effects. The damageable inelastic mechanical behavior is describe by means of an internal variable constitutive theory and the analysis is restricted to elastoviscoplastic solids. The resulting system of non linear partial differential equations is solved by using an operator splitting technique, along with classical numerical procedures such as the Glimm s method. Numerical examples which illustrate the damage and temperature evolution induced by the plastic deformation process due to impact and cyclic loadings are presented and analyzed. A suitable comparative analysis between simulations with and without the thermomechanical couplings shows the situations under which these terms are relevant.

[pt] Um estudo experimental é realizado para investigar o fenômeno de fratura num fluido não Newtoniano viscoplástico através de expansão abrupta com simetria axial. Uma visualização foi, então, efetuada usando uma técnica simples, com adição de pequenas partículas esféricas ao fluido de teste. Neste trabalho três soluções de Carbopol 676, que representou o fluido viscoplástico, foram preparadas e submetidas ao escoamento laminar e lento, com número de Reynolds no tubo a jusante abaixo de 0,1. Três razões de aspecto, a saber, de 2,0 6,0 e 12,5, foram estudadas nesta estreita faixa de regime laminar. Perdas de carga na expansão foram determinadas a partir de medidas experimentais de pressões diferenciais num determinado trecho (antes e após a expansão) para três vazões volumétricas diferentes. Um modelo de um fluido Newtoniano Generalizado foi emprego para descrever o comportamento mecânico do material, com a função da viscosidade de Herschel-Bulkley, que envolve três parâmetros reológicos: tensão limite de escoamento (T0), índice de consistência (K) e índice de comportamento (n). / [en] An experimental study is accomplished to investigate the fracture phenomenon in a non Newtonian viscoplastic material trhougth and abrupt expansion with axial symmetry. A visualization was then performed using a simple technique, with addition of small spherical particles to the test fluid. Aqueous solutions of carbopol 676 at three different concentrations were prepared and submited to creeping flow, with Reynolds number at the larger tube below than 0,1. Three expansion ratios, namely, 2,0 6,0 and 12,5, were studied in this narrow range of laminar flow. Pressure losses ar the expansion plane were determined from experimental measurement of everall pressure differentials along the tubing, for three different flow rates. The generalized Newtonian fluid model was used to describe the mechanical behavior of the material, with the viscosity of the Herschel-Bulkley type, which involves three rheological parameters the yield stress (T0), consistency index (K) and the behaviour index (n).