Thermocompression bonding of gold is a promising technique for the fabrication and packaging microelectronic and MEMS devices. The use of a gold interlayer and moderate temperatures and pressures results in a hermetic, electrically conductive bond. This paper documents work conducted to model the effect of patterning in causing pressure non-uniformities across the wafer and its effect on the subsequent fracture response. A finite element model was created that revealed pattern-dependent local pressure variations of more than a factor of three. This variation is consistent with experimental observations of bond quality across individual wafers A cohesive zone model was used to investigate the resulting effect of non-uniform bond quality on the fracture behavior. A good, qualitative agreement was obtained with experimental observations of the load-displacement response of bonds in fracture tests. / Singapore-MIT Alliance (SMA)

A multiple scale theory is developed for the prediction of damage evolution in heterogeneous viscoelastic media. Asymptotic expansions of the field variables are used to derive a global scale viscoelastic constitutive equation that includes the effects of local scale damage. Damage, in the form discrete cracks, is allowed to grow according to a micromechanically-based viscoelastic traction-displacement law. Finite element formulations have been developed for both the global and local scale problems. These formulations have been implemented into a two-scale computational model Numerical results are given for several example problems in order to demonstrate the effectiveness of the technique.

A multiple scale theory is developed for the prediction of damage evolution in heterogeneous viscoelastic media. Asymptotic expansions of the field variables are used to derive a global scale viscoelastic constitutive equation that includes the effects of local scale damage. Damage, in the form discrete cracks, is allowed to grow according to a micromechanically-based viscoelastic traction-displacement law. Finite element formulations have been developed for both the global and local scale problems. These formulations have been implemented into a two-scale computational model Numerical results are given for several example problems in order to demonstrate the effectiveness of the technique.

L’objectif principal de ce travail est la compréhension des mécanismes qui gouvernent la fissuration assistée par l’hydrogène dans les métaux, en s’appuyant sur l’analyse expérimentale de la propagation des fissures en atmosphère hydrogénant et de l’interaction entre hydrogène et défauts cristallins, et sur le développement d’un modèle de zone cohésive influencé par l’hydrogène.Des essais de propagation de fissure de fatigue ont été réalisés sous haute pression d'hydrogène gazeux sur le fer de pureté commerciale Armco. Les résultats montrent une forte influence de la pression, de la fréquence et de la valeur de ΔK sur la modification des modes de rupture, et, par conséquent, sur les vitesses de propagation. Afin d’identifier les paramètres physiques pertinents qui gouvernent les modes de rupture, une étude sur l’interaction entre hydrogène et défauts cristallins développés lors d’une sollicitation cyclique a été réalisée. Nous avons observé une augmentation de l’absorption totale d’hydrogène avec la déformation plastique cumulée, qui peut être attribuée à l’augmentation du piégeage de l'hydrogène par les dislocations générées au cours de la déformation. Ces données seront ensuite introduites dans un modèle pour reproduire la modification de la diffusion de l’hydrogène en pointe de fissure, et son effet sur la plasticité.Par ailleurs, des mesures de la déformation plastique hors plan en pointe de fissure en présence d’hydrogène ont permis de proposer une amélioration d’un modèle de zone cohésive en introduisant un effet de l’hydrogène sur le comportement plastique des éléments de volume. De plus, l'étude des composantes de la loi de diffusion de Krom a montré l'importance du gradient de contrainte hydrostatique sur la diffusion et l'accumulation de l'hydrogène en pointe de fissure. Le modèle prédit une forte dépendance de la propagation de fissures vis-à-vis de la diffusion de l’hydrogène en pointe de fissure, et est capable de simuler la propagation de fissure sous chargement statique, validant ainsi la superposition d’une composante de fissuration cyclique et d’une contribution statique (due à la présence d’hydrogène), et expliquant la transition des vitesses de propagation observée expérimentalement. / The main purpose of this work is to understand the mechanisms that govern hydrogen assisted cracking in metals, based on the experimental analysis of crack propagation data under gaseous hydrogen and the interaction between hydrogen and lattice defects on the one hand, and on the development of a cohesive zone model influenced by hydrogen on the other hand.Fatigue crack propagation tests were performed under high pressure of gaseous hydrogen on the Armco iron. The results show a strong influence of the pressure, the frequency and the ΔK value, on the modification of the failure modes and on the fatigue crack growth rates. In order to identify the physical parameters that govern the changing of the failure modes, a study on the interaction between hydrogen and the crystallographic defects developed during a cyclic loading was performed. We observe an increase in the total absorption of hydrogen with the cumulated plastic deformation, which can be attributed to the increase in the hydrogen trapping by the dislocations generated during the cyclic deformation. These data have to be introduced into a numerical model to reproduce the modification of the hydrogen diffusion at the crack tip, and its effect on plasticity.Moreover, measurements of the out-of-plane plastic deformation at the crack tip in presence of hydrogen have conducted to an improvement of the cohesive zone model by introducing an effect of hydrogen on the plastic behavior of the volume elements. In addition, the study of Krom diffusion law components has shown the importance of the hydrostatic stress gradient on the diffusion and accumulation of hydrogen at the crack tip. The model predicts a strong dependence of the crack propagation with respect to the hydrogen diffusion at the crack tip, and it is able to simulate the propagation under static load, thus validating the cyclic cracking and static cracking superposition, and explaining the transient regime in fatigue crack growth rates experimentally observed.

An alternative point of view with regard to understanding the mechanism of energy transfer involved to create new surface is considered in this study. A combination of transport equation and cohesive element is presented. A practical demonstration in 1-D is presented to simulate the mechanism of energy transfer in a damage zone model for both elastic and elastic-plastic materials. The combination of transport and cohesion element shows the extent elastic energy plays to supply the energy required for crack growth. Meanwhile, plastic energy dissipation for an elastic-plastic material is shown to be well described by the transport approach. The cohesive zone model is one of many alternative approaches used to simulate fatigue crack growth. The model incorporates a relationship between cohesive traction and separation in the zone ahead of a crack tip. The model introduces irreversibility into the constitutive relationships by means of damage accumulation with cyclic loading. The traction-separation relationship underpinning the cohesive zone model is not required to follow a predetermined path, but is dependent on irreversibility introduced by decreasing a critical cohesive traction parameter. The approach can simulate fatigue crack growth without the need for re-meshing and caters for constant amplitude loading and single overloading. This study shows the retardation phenomenon occurring in elastic plastic-materials due to single overloading. Plastic materials can generate a significant plastic zone at the crack which is shown to be well captured by the cohesive zone model approach. In a cohesive zone model, fatigue crack growth involves the dissipation of separation energy released per cycle. The crack advance is defined by the total energy separation dissipated term equal to the critical energy release rate or toughness. The effect of varying toughness with the assumption that the critical traction remains fixed is investigated here. This study reveals that varying toughness does not significantly affect the stress distribution along the crack path. However, plastic energy dissipation can significantly increase with toughness. A new methodology called the fast-track method is introduced to accelerate the simulation of fatigue crack growth. The method adopts an artificial material toughness. The basic idea of the proposed method is to decrease the number of cycle for computation by reducing the toughness. By establishing a functional relationship between the number of cycles and variable artificial toughness, the real number of cycles can be predicted. The proposed method is shown to be an excellent agreement with the numerical results for both constant amplitude loading and single overloading. A new approach to predict fatigue crack growth curves is presented. The approach combines the fast-track method and an extrapolation methodology. The basic concept is to establish a function relationship using the curve fitting technique applied to data obtained from preliminary calculation of fast-track methodology. It is shown in this thesis that the new methodology provides excellent agreement with an empirical model. The methodology is limited to constant amplitude loading and small scale yielding conditions. It is shown in the thesis that fatigue crack growth curves for variable amplitude loading can be predicted by using the data set for fatigue crack growth rate for constant amplitude loading. A retardation parameter can be deduced from the number of cycles delayed using the cohesive zone model. The retardation parameter is established by performing calculation for different toughness. This methodology is shown to give good agreement with results from empirical models for different variable amplitude loading conditions.

No description available.

Laminated carbon fibre-reinforced polymer (CFRP) composites are already well established in structural applications where high specific strength and stiffness are required. Damage in these laminates is usually localised and may involve numerous mechanisms, such as matrix cracking, laminate delamination, fibre debonding or fibre breakage. Microstructures in CFRPs are non-uniform and irregular, resulting in an element of randomness in the localised damage. This may in turn affect the global properties and failure parameters of components made of CFRPs. This raises the question of whether the inherent stochasticity of localised damage is of significance for application of such materials. This PhD project is aimed at developing numerical models to analyze the effect of material randomness on delamination damage in CFRP materials by the implementation of the cohesive-zone model (CZM) within the framework of the finite-element (FE) method. Both the unidirectional and cross-ply laminates subjected to quasi-static loading conditions were studied. The initiation and propagation in delamination of unidirectional CFRP laminates were analyzed. The CZM was used to simulate the progress of that failure mechanism in a pre-cracked double-cantilever beam (DCB) specimen loaded under mode-I employing initially, a two-dimensional FE model. Model validation was then carried out comparing the numerical results with experimental data. The inherent microstructural stochasticity of CFRP laminates was accounted for in the simulations, and various statistical realizations for a half-scatter of 50% of fracture energy were performed, based on the approximation of that parameter with the Weibull s two-parameter probability density function. More detailed analyses were undertaken employing three-dimensional DCB models, and a number of statistical realizations based on variation of fracture energy were presented. In contrast to the results of two-dimensional analyses, simulations with 3D models demonstrated a lower load-bearing capacity for most of the random models as compared to the deterministic model with uniform material properties. The damaged area and the crack lengths in laminates were analyzed, and the results showed higher values of those parameters for random realizations compared to the uniform case for the same levels of applied displacement. The effect of material randomness on delamination in CFRP cross-ply laminates was also investigated. Initially, two-dimensional finite-element analyses were carried out to study the effect of microstructural randomness in a cross-ply laminate under bending with the direct introduction of matrix cracks with varying spacings and delamination zones. A considerable variation in the stiffness for cases with different crack spacings suggested that the assumption of averaged distributions of defects can lead to unreliable predictions of structural response. Three-dimensional uniform, deterministic cross-ply laminate models subjected to a tensile load were analyzed to study the delamination initiation and propagation from the tips of a pre-existing matrix crack. The material s stochasticity was then introduced, and a number of random statistical realizations were analyzed. It was observed that by neglecting the inherent material randomness of CFRP laminates, the initiation conditions for delamination as well as the character of its propagation cannot be properly detected and studied. For instance, the delamination crack length value for all the simulated random statistical realizations predicted its higher magnitudes compared to the uniform (deterministic) case for the same value of applied strain. Furthermore, the location of delamination initiation was shown to be different for different random statistical realizations. Another aspect, emphasizing the importance of microstructural randomness, was the scatter in the magnitudes of global strain at the instance of initiation and subsequent propagation of delamination. In summary, the material randomness in CFRPs can induce randomness in localised damage and it can affect the global properties of laminates and critical failure parameters. These effects can be investigated computationally through the use of stochastic cohesive-zone elements.

<p>Within the European space programme, a new upper stage engine (Vinci) for the Ariane 5 launcher is being developed, and the Volvo Aero Corporation (VAC) is contributing with tur-bines for the fuel turbopumps. This MSc thesis investigates the possibility of designing the Turbine Exhaust Duct (TED) of the Vinci-engine in a carbon fibre composite material with adhesively attached titanium flanges. The focus of the project has been on stress analyses of the adhesive joints using Finite Element Methods (FEM), more specifically by using a cohe-sive zone material (CZM) to model the adhesive layer. Analysing adhesive joints is complex and an important part of the work has been to develop and concretise analysis methods for future use within VAC.</p><p>To obtain the specialised material parameters needed for a CZM analysis, FE-models of ten-sile test specimens were analysed and the results compared to those of equivalent experimen-tal tensile tests. These parameters were then used when analysing the TED geometry with load cases specified to simulate the actual operation conditions of the Vinci engine. Both two-dimensional axisymmetric and fully three-dimensional models were analysed and, addition-ally, a study was performed to evaluate the effect of cryogenic temperatures on the strength of the joint.</p><p>The results show that the applied thermal and structural loading causes local stress concentra-tions on the adhesive surface, but the stresses are not high enough to cause damage to the joint if a suitable joint design is used. Cryogenic temperatures (-150 °C) caused a significant strength reduction in the tensile specimens, partially through altered adhesive properties, but no such severe effects were seen in the temperature-dependent FE-analyses of the TED. It should be pointed out however, that some uncertainties about the material parameters exist, since these were obtained in a rather unconventional way. There are also several other impor-tant questions, beside the strength of the adhesive joint, that need to be answered before a metal-composite TED can be realised.</p> / <p>Volvo Aero deltar i utvecklingen av Vinci, en ny motor till det övre steget i den europeiska Ariane 5-raketen. Detta examensarbete behandlar möjligheten att tillverka ett turbinutlopp (TED) till vätgasturbinen i Vinci-motorn i kompositmaterial med flänsar i titan för att på så sätt uppnå en viktbesparing gentemot den tidigare konstruktionen i gjuten Inconel 718. Fokus har legat på att analysera hållfastheten i de limfogar som är tänkta att sammanfoga huvudröret med flänsarna, genom analyser med finita elementmetoden (FEM). Ett viktigt syfte har även varit att, för Volvo Aeros räkning, samla praktiska erfarenheter angående numerisk analys av limfogar, särskilt med användning av kohesiva zon-element för att modellera limfogen.</p><p>FEM-analyser har gjorts av provstavsmodeller, där resultaten sedan jämförts med experimen-tella dragprovsresultat för att ta fram lämpliga material- och modelleringsparametrar för ana-lys med kohesiva zonelement. Därefter tillämpades dessa parametrar i analyser av den verkli-ga TED-geometrin med relevanta lastfall framtagna för att simulera driftsförhållandena i Vin-ci-motorn. Lastfallsanalyser med både tvådimensionellt axisymmetriska och tredimensionella geometrimodeller genomfördes, liksom uppskattningar av limfogens styrka vid kryogena driftstemperaturer.</p><p>Resultaten pekar entydigt mot att en limfog med en ändamålsenlig tvärsnittsgeometri skulle hålla för de angivna lasterna utan att ta skada. De spänningskoncentrationer som uppstår ger lokalt höga spänningar i limmet, men inte på nivåer som skulle kunna orsaka brott. Det finns dock en viss osäkerhet angående riktigheten i materialparametrarna då en något okonventio-nell metod användes för att ta fram dessa. Flera stora frågor finns fortfarande kvar att besvara innan en metall-komposit konstruktion kan realiseras, inte minst hur flödeskammarens kom-plicerade geometri skall kunna tillverkas i kompositmaterial.</p>

Within the European space programme, a new upper stage engine (Vinci) for the Ariane 5 launcher is being developed, and the Volvo Aero Corporation (VAC) is contributing with tur-bines for the fuel turbopumps. This MSc thesis investigates the possibility of designing the Turbine Exhaust Duct (TED) of the Vinci-engine in a carbon fibre composite material with adhesively attached titanium flanges. The focus of the project has been on stress analyses of the adhesive joints using Finite Element Methods (FEM), more specifically by using a cohe-sive zone material (CZM) to model the adhesive layer. Analysing adhesive joints is complex and an important part of the work has been to develop and concretise analysis methods for future use within VAC. To obtain the specialised material parameters needed for a CZM analysis, FE-models of ten-sile test specimens were analysed and the results compared to those of equivalent experimen-tal tensile tests. These parameters were then used when analysing the TED geometry with load cases specified to simulate the actual operation conditions of the Vinci engine. Both two-dimensional axisymmetric and fully three-dimensional models were analysed and, addition-ally, a study was performed to evaluate the effect of cryogenic temperatures on the strength of the joint. The results show that the applied thermal and structural loading causes local stress concentra-tions on the adhesive surface, but the stresses are not high enough to cause damage to the joint if a suitable joint design is used. Cryogenic temperatures (-150 °C) caused a significant strength reduction in the tensile specimens, partially through altered adhesive properties, but no such severe effects were seen in the temperature-dependent FE-analyses of the TED. It should be pointed out however, that some uncertainties about the material parameters exist, since these were obtained in a rather unconventional way. There are also several other impor-tant questions, beside the strength of the adhesive joint, that need to be answered before a metal-composite TED can be realised. / Volvo Aero deltar i utvecklingen av Vinci, en ny motor till det övre steget i den europeiska Ariane 5-raketen. Detta examensarbete behandlar möjligheten att tillverka ett turbinutlopp (TED) till vätgasturbinen i Vinci-motorn i kompositmaterial med flänsar i titan för att på så sätt uppnå en viktbesparing gentemot den tidigare konstruktionen i gjuten Inconel 718. Fokus har legat på att analysera hållfastheten i de limfogar som är tänkta att sammanfoga huvudröret med flänsarna, genom analyser med finita elementmetoden (FEM). Ett viktigt syfte har även varit att, för Volvo Aeros räkning, samla praktiska erfarenheter angående numerisk analys av limfogar, särskilt med användning av kohesiva zon-element för att modellera limfogen. FEM-analyser har gjorts av provstavsmodeller, där resultaten sedan jämförts med experimen-tella dragprovsresultat för att ta fram lämpliga material- och modelleringsparametrar för ana-lys med kohesiva zonelement. Därefter tillämpades dessa parametrar i analyser av den verkli-ga TED-geometrin med relevanta lastfall framtagna för att simulera driftsförhållandena i Vin-ci-motorn. Lastfallsanalyser med både tvådimensionellt axisymmetriska och tredimensionella geometrimodeller genomfördes, liksom uppskattningar av limfogens styrka vid kryogena driftstemperaturer. Resultaten pekar entydigt mot att en limfog med en ändamålsenlig tvärsnittsgeometri skulle hålla för de angivna lasterna utan att ta skada. De spänningskoncentrationer som uppstår ger lokalt höga spänningar i limmet, men inte på nivåer som skulle kunna orsaka brott. Det finns dock en viss osäkerhet angående riktigheten i materialparametrarna då en något okonventio-nell metod användes för att ta fram dessa. Flera stora frågor finns fortfarande kvar att besvara innan en metall-komposit konstruktion kan realiseras, inte minst hur flödeskammarens kom-plicerade geometri skall kunna tillverkas i kompositmaterial.

<p>An advanced bulk constitutive model is used with a new cohesive zone model that is stress state and rate-dependent in order to simulate the ductile to brittle failure transition in polycarbonate. The cohesive zone model is motivated by experimental evidence that two different critical energies per unit area of crack growth exist in glassy polymers. A higher energy state is associated with ductile failure (slow crack growth), while a lower energy state is associated with brittle failure (fast crack growth). The model is formulated so that as rate or stress state changes within a simulation, the fracture energy and thus fracture mode may also change appropriately. The ductile to brittle transition occurs when the cohesive opening rate is over a threshold opening rate and when the stress state is close to plane strain in a fracture specimen. These effects are coupled. The principal contribution of this work is that this is the first time a single set of material input parameters can predict the transition from slow to fast crack growth as test loading rate and sample thickness are varied. This result enlisted the use of an advanced constitutive model and the new cohesive zone model with rate and stress-state dependencies in three-dimensional finite element analysis.</p> / Dissertation