Advancements in material science and manufacturing techniques are enabling the use of lightweight metal alloys and polymer composites in several combinations and shapes for producing more efficient and lightweight structures for automotive applications without compromising strength, stiffness and/or durability. When evaluating the strength of the structure, the joints are of importance. For multi-material structures adhesives are often the best type of joints. However, traditional finite element methods using stress criteria cannot accurately predict the failure of these adhesive joints under static loading. In this thesis work a strength and fatigue model, formulated using energy release rate theory, is implemented in a post processing tool. Given a finite element model of an adhesive joint and a list of boundary elements and nodes this tool calculates the energy release rates in mode I and mode II, and if the fracture toughness of the adhesive is known, a prescribed mixed-mode failure index is calculated. To evaluate its predictions joint strength results are correlated to experiments. Specimens with combined shear and normal load forms the underlying experimental setup with change in strain rate and adhesive thickness as varying parameters. Methods for implementing the model for a car body structure with multiple adhesive joints is investigated, the tool proves to be scalable, however, the required finite element setup at the adhesive boundaries may not be present in a car body model and thus further work needs to carried out to accommodate irregularities like non-matching mesh in the car body finite element model. This model may be used for assessing the strength and durability of a car body structure comprising different materials joined together using adhesives.

Das geometrische In-plane-Moireverfahren wird benutzt, um das Deformationsfeld um einen Riss in einem geschweißten Verbund zweier unterschiedlicher Metalle sowie in homogenen Proben dieser Materialien zu untersuchen. Konkret werden Vierpunktbiegeproben benutzt, wobei die Grenzflächen der Verbundproben durch Explosionsschweißen (Sprengplattieren) hergestellt werden. In Verbindung mit der digitalen Bildverarbeitung wird das Feld der Verschiebungen zum Zeitpunkt der Rissinitiierung als primäres Resultat aus den Isothetenfeldern ermittelt. Aus diesen Verschiebungsfeldern lassen sich mittels eines Approximationsverfahrens weitere Größen wie Verzerrungen und Spannungsgrößen an der Oberfläche ableiten. Zusätzlich werden dreidimensionale elastisch-plastische FEM-Berechnungen für die homogenen Proben und die Proben mit Grenzflächenriss durchgeführt. Das J-Integral wird aufgrund der experimentell und numerisch gewonnenen Daten für den Rissinitiierungszeitpunkt berechnet. Außerdem findet ein Vergleich mit J-Integralwerten statt, die mit Methoden der Materialprüfnormen bestimmt werden.

Bauteile mit Rissen können mit Hilfe der Bruchmechanik bewertet werden. Da die Ermittlung der Rissspitzenbeanspruchung nicht immer analytisch gelingt, ist die Nutzung numerischer Verfahren von Vorteil. Nach einer kurzen Einführung in die Bruchmechanik wird an zwei Beispielen die Vorgehensweise diskutiert.

[pt] Como proposto até agora na literatura técnica, a modelagem de trincas pelo método dos elementos de contorno é melhor executada recorrendo a uma solução fundamental hiper-singular – na chamada formulação dual –, uma vez que somente com a solução fundamental singular, as questões topológicas resultantes não são abordadas adequadamente. Uma abordagem mais natural pode contar com a representação direta da singularidade da ponta da trinca, como já proposto no âmbito do método híbrido dos elementos de contorno – com a implementação de funções de tensão generalizadas de Westergaard. Por outro lado, avaliações matemáticas recentes indicam que a formulação convencional dos elementos de contorno – com base na solução fundamental de Kelvin – é capaz de representar precisamente altos gradientes de tensão e lidar com topologias extremamente complicadas, desde que as integrações numéricas sejam resolvidas adequadamente. Propomos neste trabalho que, independentemente da configuração, uma estrutura trincada seja representada geometricamente como apareceria em experimentos de laboratório, com abertura de trinca na faixa de micrômetros (O alcance dos nanômetros é matematicamente viável na presente formulação, mas não é realista em termos de mecânica do contínuo). Devido ao esquema de integração numérica recém-desenvolvido, é possível obter uma avaliação da precisão de máquina de todas as grandezas e resultados de tensões consistentemente avaliados em pontos internos tão próximos da ponta da trinca quanto se queira. É importante ressaltar que não são introduzidas questões topológicas artificiais, o condicionamento da álgebra linear é mantido sob controle e é sempre possível obter uma convergência dos resultados tão alta quanto se queira. Os desenvolvimentos atuais se aplicam a problemas bidimensionais. Algumas ilustrações numéricas mostram que resultados altamente precisos são obtidos para trincas representadas com apenas alguns elementos de contorno quadráticos, geralmente curvos – e alguns pontos de integração de Gauss-Legendre por elemento – e que a avaliação numérica da integral J acaba sendo simples (embora não computacionalmente barato) e, na verdade, o meio mais confiável de obter fatores de intensidade de tensões. / [en] As hitherto proposed in the technical literature, the boundary element modelling of cracks is best carried out resorting to a hypersingular fundamental solution – in the frame of the so-called dual formulation –, since with the singular fundamental solution alone the ensuing topological issues would not be adequately tackled. A more natural approach might rely on the direct representation of the crack tip singularity, as already proposed in the frame of the hybrid boundary element method – with implementation of generalized Westergaard stress functions. On the other hand, recent mathematical assessments indicate that the conventional boundary element formulation – based on Kelvin’s fundamental solution – is in fact able to precisely represent high stress gradients and deal with extremely convoluted topologies provided only that the numerical integrations be properly resolved. We propose in this work that independently of configuration a cracked structure be geometrically represented as it would appear in laboratory experiments, with crack openings in the range of micrometers. (The nanometer range is actually mathematically feasible in the present formulation but not realistic in terms of continuum mechanics.) Owing to the newly developed numerical integration scheme, machine precision evaluation of all quantities may be achieved and stress results consistently evaluated at interior points arbitrarily close to crack tips. Importantly, no artificial topological issues are introduced, linear algebra conditioning is well kept under control and arbitrarily high convergence of results is always attainable. The present developments apply to two-dimensional problems. Some numerical illustrations show that highly accurate results are obtained for cracks represented with just a few quadratic, generally curved, boundary elements – and a few Gauss-Legendre integration points per element – and that the numerical evaluation of the J-integral turns out to be straightforward (although not computationally cheap) and actually the most reliable means of obtaining stress intensity factors.

[pt] O uso de todos os tipos de amianto na construção civil tem diminuído drasticamente devido a problemas sérios de saúde associados a sua manipulação. De fato é previsto banir totalmente o seu uso, dentro de um curto espaço de tempo, nos países desenvolvidos bem como nos em desenvolvimento. Na necessidade de se encontrar um substituto adequado para o amianto, tem-se pesquisado compósitos de argamassa reforçada com fibras vegetais e polpas celulósicas. Devido ao processo de polpação, que remove as impurezas não celulósicas, como a lignina e a hemicelulose, diminuindo o ataque às fibras, sem a necessidade de recorrer a modificações na matriz cimentícia, as polpas celulósicas podem ser o substituto ideal para o amianto. Assim sendo, o principal objetivo desta dissertação é determinar experimentalmente as características mecânicas e os parâmetros de fratura de compósitos de matriz cimentícia reforçada por polpa de bambu refinada e sem refino. As polpas celulósicas foram utilizadas nas porcentagens de 8 e 14 por cento em relação à massa do cimento, porcentagens estas que, conforme a literatura, são associadas à otimização da energia absorvida no ensaio de flexão. A avaliação do comportamento mecânico dos compósitos considerados neste trabalho foi realizada através de ensaios de compressão e impacto, bem como de flexão em três pontos em espécimes não entalhados e em outros contendo entalhes de raios de curvatura diferentes. Propriedades mecânicas, tais como módulo de elasticidade, resistência à compressão, ao impacto e à flexão, bem como integral J na carga máxima, são apresentadas e discutidas em termos de aspectos microestruturais e fractográficos dos corpos de prova ensaiados. / [en] As handling and manipulation of asbestos pose grave health hazards, its use in civil construction has been drastically dwindling and will in fact be completely prohibited, in a few years, in developed countries. With the need arising to find an adequate substitute, vegetable fibers and cellulosic pulps have been considered to be viable alternatives. Taking into account the fact that the process for pulp production entails the removal of impurities, such as lignin and hemicellulose, cellulosic pulps seem to be the ideal substitute to asbestos, as their use does not necessitate modifications in the cementitious matrix. Accordingly, the purpose of this work is to experimentally determine basic mechanical characteristics and pertinent fracture parameters of bamboo pulp reinforced cement. Refined and non-refined pulps were used in the proportions of 8 and 14 percent of the weight of dry cement. These percentages were adopted as they imply, according to literature, in optimizing the energy absorbed by the composite in bend loading. Evaluation of the mechanical behavior of the composites considered in this work was realized by means of compression and impact testing. Three point bend tests were also carried out using unnotched as well as notched specimens of different notch root radii. Mechanical properties such as modulus of elasticity, compressive, impact and bend strengths, and J integral at maximum load are presented and discussed in terms of pertinent microstructural and fractographic aspects of test specimens.

[pt] O estudo da resistência à fratura dos materiais é de grande importância para desenvolvimentos de projetos, seleção de materiais e avaliação do comportamento dos materiais perante a presença de um defeito no componente. Há inúmeras normas que envolvem geometrias padronizadas para determinação desta propriedade mecânica, no entanto nem todo componente em serviço possui as mesmas condições encontradas nas geometrias padronizadas, como é o caso de materiais dúcteis empregados em estruturas com espessuras de paredes finas e elevada pressão interna. Nesta dissertação foram estudados dois materiais com diferentes limites de escoamento confeccionados conforme geometria tipo SEN(T) de fixação por garras, a qual não é padronizada pela ASTM. Com isso, foi realizada uma pesquisa com o emprego desta geometria com variação de 0,2 a 0,8 da relação entre a dimensão idealizada inicialmente para a trinca e a largura do corpo de prova, e entalhes laterais com redução de 20 porcento foram confeccionados nos corpos de prova do material mais dúctil. Após, foi realizada a pré-trinca de fadiga e iniciado o ensaio de tenacidade à fratura. Este último foi desenvolvido adotando o método compliance, o qual permite que com apenas um corpo de prova seja realizado descarregamentos parciais permitindo assim a determinação de J e incremento de trinca em cada posição, possibilitando plotar a curva-R Os resultados obtidos determinaram que mesmo com a/W diferente daqueles indicados por norma para levantamento da curva-R, é possível obter uma curva-R para a/W=0,2. Existe uma limitação em aplicar a geometria SEN(T) que não possuem extensa ductilidade. / [en] The study of resistance to fracture of the materials is very important for developing new projects, making materials specifications and also for evaluating materials behaviour under presence of a crack in a component. There are uncountables standards which apply normalized specimens due to determine this mechanical property, however some components in service doesn t act under same conditions as the specimen chosen, for instance ductile materials applied in components with thin thickness and high intern pressure. In this dissertation was studied two diferente of materials with distinct yield limits fabricated according to SEN(T) geometry with clamped fixing, which one is not acceptable by ASTM. Thus, a research has been carried out using this geomerty with a variation of 0,2 to 0,8 of the relation between the idealized initially for the crack and the width of the proof body ratio and side-grooves with 20 percent reducted were made in the specimens with higher ductility. After that, the procedure for doing fatigue pre-crack was initialized, followed by fracture toughness test. This last one was developed adopting the unloading compliance technique, which one allows that more than one aplications of force and displacement can be realized in only one specimen then the value of J and crack extension can be calculated and the R-curve will be plotted. The results obtained showed even with a a/W ratio diferente of those indicated by standards, is possible to constructo a qualified R-curve for a/W=0,2. In additon to the results, there is a limitation in applying a SEN(T) geometry in materials that don t present extensive ductility.

Le pop-in est un phénomène d’instabilité de propagation de fissure observé lors d’essais de ténacité sur certains matériaux. Ce phénomène a été observé sur l’alliage d’aluminium 6061-T6 qui a été identifié pour constituer des éléments de structure essentiels du cœur du réacteur de recherche Jules Horowitz. Cette thèse a été initiée pour comprendre l’origine de ce phénomène sur l’aluminium 6061-T6 et en proposer une modélisation à bases physiques qui pourra être utilisée pour l’exploitation et l’interprétation des essais de ténacité, notamment à l’état irradié.Les différentes pistes identifiées dans la littérature ont été testées expérimentalement. Des revenus (4/8/12/16 h) ont été appliqués afin d’obtenir différents comportements mécaniques. Des essais de traction avec corrélation d’images ont montré que les pop-ins observés ne sont pas dus à un effet PLC. Ils ne correspondent pas non plus à une hétérogénéité microstructurale ; ils ne sont pas liés à des mécanismes d’endommagement, car la rupture est typiquement ductile, qu’un pop-in soit intervenu ou non. Ces mécanismes et les différentes microstructures ont été comparés par le biais de plusieurs techniques (MEB, EBSD, EDS, Sonde Atomique Tomographique, tomographie, laminographie et nanolaminographie par rayonnement synchrotron). Les pop-ins sont donc uniquement le résultat d’une accélération de la rupture ductile.En réalité, ils sont dus à une interaction entre deux paramètres : une résistance réduite du matériau à la propagation de fissure (i.e. un faible module de déchirement) et une complaisance importante du dispositif d’essai (i.e. une faible raideur). Afin d’investiguer ce deuxième paramètre, un dispositif innovant a été conçu, permettant de faire varier la raideur de la machine d’essai lors d’essais de ténacité. Deux critères analytiques, l’un basé sur la courbe force-ouverture, l’autre sur l’intégrale J, ont été établis, permettant de quantifier les conditions d’amorçage et d’arrêt de pop-in de façon fiable.Pour prendre en compte le rôle central du durcissement vis-à-vis de la propagation ductile, un nouveau critère de germination piloté par les contraintes a été introduit dans un unique modèle GTN. Cela permet de simuler et de reproduire par éléments finis les différentes courbes de ténacité J-Δa en modifiant uniquement la loi élastoplastique. En rajoutant des ressorts dans les modélisations et avec un pilotage adapté, les pop-ins sont simulés avec succès, et restent exploitables avec les critères analytiques.Des études sur éprouvettes irradiées réalisées dans des enceintes blindées ont montré que l’augmentation des pop-ins avec l’irradiation résultait de la diminution du module de déchirement, elle-même due au durcissement. De même qu’à l’état non irradié, les pop-ins apparaissent donc à cause de l’interaction du module de déchirement avec le dispositif d’essai, et non pas à cause d’une gamme d’élaboration industrielle non maitrisée. / Pop-in is a phenomenon of crack propagation instability observed during toughness tests on some materials. This phenomenon has been observed on the 6061-T6 aluminum alloy, which has been identified as an essential structural element of the core of the Jules Horowitz research reactor. This thesis was initiated to understand the origin of this phenomenon on 6061-T6 aluminum and to propose a physics-based modeling, usable for the exploitation and interpretation of toughness tests, especially in the irradiated state.The different origins identified in the literature have been experimentally tested. Different aging times (4/8/12/16h) were applied to obtain different mechanical behaviors. Tensile tests with image correlation have shown that the observed pop-ins are not due to a PLC effect. Nor do they correspond to microstructural heterogeneity; they are not linked to different fracture mechanisms, because the rupture is typically ductile, whether a pop-in is involved or not. These mechanisms and the different microstructures were compared using several techniques (SEM, EBSD, EDS, Atom Probe Tomography, tomography, synchrotron laminography and nanolaminography). Pop-ins are therefore only the result of an acceleration of the ductile fracture.In fact, they are due to an interaction between two parameters: the reduced material crack growth toughness (i.e. the low tearing modulus), and the significant compliance of the test device (i.e. the low stiffness). In order to investigate this second parameter, an innovative setup has been designed to vary the machine stiffness during toughness tests. Two analytical criteria, one based on the load-opening curve, the other on the J-integral, have been established, making it possible to reliably quantify the conditions for initiation and arrest of pop-in.To take into account the central role of hardening for ductile propagation, a new stress-controlled nucleation criterion has been introduced into a single GTN model. This makes it possible to simulate and capture by finite elements the various J-Δa toughness curves by modifying only the elastoplastic law. By adding springs in the models and with an adapted control, the pop-ins are successfully simulated, and remain exploitable with the analytical criteria.Studies on irradiated specimens carried out in hot cells have shown that the increase in pop-ins with irradiation results from the decrease in the tearing modulus, itself due to hardening. As in the non-irradiated state, pop-ins thus appear solely because of the interaction between the tearing modulus and the test device stiffness, and not because of a range of industrial development not mastered.

O Jateamento com granalha (shot peening, em inglês) é um processo de fabricação amplamente utilizado em indústrias mecânicas, automotivas, navais, aeronáuticas e outras indústrias metalúrgicas. O objetivo principal é induzir tensões residuais de compressão para melhorar a vida à fadiga das peças e estruturas. A modelagem e simulação do processo são muito difíceis, pois envolvem a consideração de muitos e complexos aspectos. Este trabalho propõe um método de modelagem tridimensional utilizando o método dos elementos finitos para a simulação numérica desse processo assim como a sua influência na propagação de trinca, considerando efeitos pouco estudados, como o amolecimento do material devido ao aumento da temperatura na peça durante os impactos, ao comportamento elasto-plástico das granalhas e a rugosidade da peça tratada nos parâmetros da trinca. A modelagem proposta para simular o processo de jateamento com granalhas inclui: (i) análise dinâmica explícita, (ii) modelagem tridimensional, (iii) cálculo da velocidade real das granalhas, (iv) modelo de contato com coeficientes de atrito estático e dinâmico entre as áreas em contato, (v) o modelo constitutivo de Johnson-Cook para o comportamento do material alvo, (vi) um comportamento elasto-plástico multilinear para as granalhas, (vii) a consideração da cobertura real de uma área dada da superfície jateada, (viii) a consideração do aumento da temperatura no material durante o processo e (ix) o relaxamento de tensões residuais devido a este aumento de temperatura. As simulações numérico-computacionais para investigar a influência do processo em fenômenos, tais como fadiga e propagação de trinca, necessitou uma nova abordagem para a incorporação das tensões residuais num modelo de elementos finitos. Além disso, foram realizados vários ensaios quase-estáticos e dinâmicos para a determinação dos parâmetros do modelo constitutivo de Johnson-Cook para o aço AISI 5160. Para a avaliação das metodologias propostas, as tensões residuais foram introduzidas e avaliadas em uma mola parabólica automotiva, sendo que as tensões residuais foram avaliadas através da técnica de difração de raios-X, a intensidade e a cobertura do processo de jateamento com granalha na mola foram avaliadas com Lupa e rugosímetro. Também, dados experimentais de ensaios de fadiga relatados na literatura, realizados em corpos de prova tipo CT foram utilizados. A modelagem numérica do processo de jateamento com granalha desenvolvida neste trabalho consegue prever com sucesso os perfis das tensões residuais, com valores bem próximos aos obtidos experimentalmente. A investigação numérica do efeito do processo na vida à fadiga e fratura das peças comprovou a sua influência nos parâmetros de propagação de trinca nas regiões afetadas pelo processo, ocasionando um amplo aumento da vida à fadiga, e confirmou o relaxamento das tensões residuais devido aos ciclos de carregamento conforme as observações experimentais na literatura. / Shot peening is a manufacturing process widely used in the mechanical, automotive, marine, aeronautical and other metallurgical industries. The main purpose is to induce residual compression stresses to improve fatigue life. The modeling and simulation of the process are very difficult as they involve the consideration of many and complex aspects. This work proposes a three-dimensional modelling method using the finite element method for the numerical simulation of this process as well as its influence on crack propagation, considering little studied effects such as softening of the material due to the increase in temperature in the part during impacts , the elastic-plastic behavior of the shot and the roughness of the treated part in the crack parameters. The proposed modelling approach to simulate the shot peening process includes: (i) explicit dynamic analysis, (ii) three-dimensional modeling, (iii) calculation of the real velocity of the shot, (iv) contact model with static and dynamic friction coefficients between the contact areas, (v) the Johnson-Cook constitutive model for target material behavior, (vi) a multilinear elasto-plastic behavior for the shot, (vii) consideration of real coverage in a given area of the peened surface, (viii) consideration of temperature increase in the material during the process and (ix) relaxation of residual stresses due to this rise in temperature. Numerical-computational simulations to investigate the influence of the shot peening process on phenomena, such as fatigue and crack propagation, required a new approach for the incorporation of residual stress in a finite element model. In addition, several quasi-static and dynamic tests were carried out to determine the parameters of the constitutive Johnson-Cook model for AISI 5160 steel. To assess the proposed methodologies, the residual stresses were introduced and evaluated in an automotive parabolic spring, with the residual stresses being evaluated by the X-ray diffraction technique, the intensity and coverage of the shot peening process for the spring were evaluated with magnifying glass and roughness gauge. Also, fatigue tests available in the literature, carried out on types of CT specimens, were used. The numerical modeling of the shot peening process developed in this work can successfully predict the residual stress profiles, with values close to those obtained experimentally. The numerical investigation of the effect of the process in the fatigue life and fracture of the pieces proved its influence in the parameters of crack propagation in the regions affected by the process, causing a wide increase of the fatigue life, and confirmed the relaxation of the residual stresses due to the cycles loading according to experimental observations in the literature.

Double cantilever beam (DCB) specimens with distinct intermetallic microstructures and different geometries were fractured under different mode ratios of loading, ψ, to obtain critical strain energy release rate, Jc. The strain energy release rate at crack initiation, Jci, increased with phase angle, ψ, but remained unaffected by the joint geometry. However, the steady-state energy release rate, Jcs, increased with the solder layer thickness. Also, both the Jci and Jcs decreased with the thickness of the intermetallic compound layer. Next, mode I and mixed-mode fracture tests were performed on discrete (l=2 mm and l=5 mm) solder joints arranged in a linear array between two copper bars to evaluate the J = Jci (ψ) failure criteria using finite element analysis. Failure loads of both the discrete joints and the joints in commercial electronic assemblies were predicted reasonably well using the Jci from the continuous DCBs. In addition, the mode-I fracture of the discrete joints was simulated with a cohesive zone model which predicted reasonably well not only the fracture loads but also the overall load-displacement behavior of the specimen. Additionally, the Jci calculated from FEA were verified estimated from measured crack opening displacements in both the continuous and discrete joints. Finally, the pad-crater fracture mode of solder joints was characterized in terms of the Jci measured at various mode ratios, ψ. Specimens were prepared from lead-free chip scale package-PCB assemblies and fractured at low and high loading rates in various bending configurations to generate a range of mode ratios. The specimens tested at low loading rates all failed by pad cratering, while the ones tested at higher loading rates fractured in the brittle intermetallic layer of the solder. The Jci of pad cratering increased with the phase angle, ψ, but was independent of surface finish and reflow profile. The generality of the J =Jci(ψ) failure criterion to predict pad cratering fracture was then demonstrated by predicting the fracture loads of single lap-shear specimens made from the same assemblies.

Double cantilever beam (DCB) specimens with distinct intermetallic microstructures and different geometries were fractured under different mode ratios of loading, ψ, to obtain critical strain energy release rate, Jc. The strain energy release rate at crack initiation, Jci, increased with phase angle, ψ, but remained unaffected by the joint geometry. However, the steady-state energy release rate, Jcs, increased with the solder layer thickness. Also, both the Jci and Jcs decreased with the thickness of the intermetallic compound layer. Next, mode I and mixed-mode fracture tests were performed on discrete (l=2 mm and l=5 mm) solder joints arranged in a linear array between two copper bars to evaluate the J = Jci (ψ) failure criteria using finite element analysis. Failure loads of both the discrete joints and the joints in commercial electronic assemblies were predicted reasonably well using the Jci from the continuous DCBs. In addition, the mode-I fracture of the discrete joints was simulated with a cohesive zone model which predicted reasonably well not only the fracture loads but also the overall load-displacement behavior of the specimen. Additionally, the Jci calculated from FEA were verified estimated from measured crack opening displacements in both the continuous and discrete joints. Finally, the pad-crater fracture mode of solder joints was characterized in terms of the Jci measured at various mode ratios, ψ. Specimens were prepared from lead-free chip scale package-PCB assemblies and fractured at low and high loading rates in various bending configurations to generate a range of mode ratios. The specimens tested at low loading rates all failed by pad cratering, while the ones tested at higher loading rates fractured in the brittle intermetallic layer of the solder. The Jci of pad cratering increased with the phase angle, ψ, but was independent of surface finish and reflow profile. The generality of the J =Jci(ψ) failure criterion to predict pad cratering fracture was then demonstrated by predicting the fracture loads of single lap-shear specimens made from the same assemblies.