The manufacturing of ductile materials generally inserts impurities into their microscopic composition. These impurities may detach from the surrounding matrix and even crack along progressive deformation. Due to the consequent incapacity of these undesirable particles of supporting any stress, these ductile materials are equivalently assumed to be porous. Porosity has been effectively shown to play a fundamental role in the mechanisms of ductile fracture. Many micromechanical models have been proposed since the 1970s with the aim of mathematically describing these mechanisms. Among them, the acclaimed Gurson model combines the averaging homogenization technique with the kinematic theorem of Limit Analysis to estimate the macroscopic yield criterion and porosity evolution law of porous ductile materials. However, the Gurson model and most of its extensions only account for isotropic ductile fracture. Thus, the purpose of the present work is to contribute to the conception of yield criteria for anisotropic porous ductile rupture. Three main contributions are hereby proposed by profiting from similar hypothesis to those of the Gurson model. The first contribution is the assessment of the influence of void morphology on overall yield criteria for those classes of materials. The second is the inclusion of an anisotropic yield criterion in the material matrix so that the macroscopic behavior presents matrix-induced anisotropy even for spherical cavities. The third and last advancement consists of generalizing the material matrix yield criterion of the Gurson model in order to include a linear transformation-based class of yield functions that has been widely used to represent specific high strength aluminum alloys. The results hereby presented highlight the consistency and robustness of the three formulations. Moreover, the role of the porosity on the modeling of yield behavior of aluminum alloys encourages further work regarding experimental parameter characterization. / A fabricação de materiais dúcteis insere impurezas em suas composições microscópicas. Essas impurezas podem se soltar da matriz circundante e até trincar durante um processo de deformação progressiva. Devido à consequente incapacidade destas partículas indesejáveis para suportar qualquer esforço, estes materiais dúcteis são equivalentemente assumidos como sendo porosos. Investigações experimentais têm extensamente mostrado que a porosidade desempenha um papel fundamental nos mecanismos de ruptura de materais dúcteis. Desde a década de 1970, vários modelos micromecânicos têm sido propostos para descrever esses mecanismos matematicamente. Entre eles, o célebre modelo de Gurson combina a técnica de homogeneização com o teorema cinemático da Análise Limite para estimar o critério de plastificação macroscópica e a lei de evolução da porosidade dos materiais dúcteis porosos. No entanto, o modelo de Gurson e a maioria de suas extensões consideram apenas situações de ruptura dúctil em meios isotrópos. O objetivo do presente trabalho é, portanto, contribuir para o desenvolvimento de critérios de plastificação para a ruptura dúctil de meios porosos anisotrópos. Três principais contribuições são propostas neste trabalho, as quais se valem de hipóteses semelhantes às do modelo de Gurson. A primeira contribuição é a avaliação da influência da morfologia do vazio nos critérios de plastificação macroscópica desta classe de materiais. A segunda é a inclusão de um critério de plastificação anisotrópico na representação da matriz do material, de modo que o comportamento macroscópico exiba anisotropia induzida por ela, mesmo para cavidades esféricas. O terceiro e último avanço é a generalização do critério de plasticidade da matriz de modo a incluir uma classe de funções de plastificação baseadas em transformações lineares. Esta classe de funcões tem sido amplamente utilizada com sucesso para modelar ligas de alumínio de alta resistência. Os resultados apresentados neste trabalho atestam a coerência e robustez das três formulações. Além disso, o papel da porosidade na modelagem da plasticidade das ligas de alumínio encoraja trabalhos futuros sobre a caracterização experimental de parâmetros de anisotropia.

La fabrication de matériaux ductiles insère généralement des impuretés dans leurs compositions microscopiques. Ces impuretés peuvent se détacher de la matrice environnante et même se fissurer lors d’une déformation progressive. En raison de la résultante incapacité de ces particules indésirables à supporter toute contrainte, ces matériaux ductiles sont, de manière équivalente, supposés être poreux. Il a été largement démontré que la porosité joue un rôle fondamental dans les mécanismes de la rupture ductile. Depuis les années 1970, de nombreux modèles micromécaniques ont été proposés dans le but de décriremathématiquement ces mécanismes. Parmi eux, le célèbre modèle de Gurson combine la technique d’homogénéisation avec le théorème cinématique de l’analyse limite pour estimer le critère de plastification macroscopique et la loi d’évolution de la porosité des matériaux ductiles poreux. Cependant, le modèle de Gurson, ainsi que la plupart de ses extensions, ne tient compte que de la rupture ductile isotrope. Le but du présent travail est donc de contribuer à la conception de critères de plastification pour la rupture ductile des milieuxporeux anisotropes. Trois contributions principales tirant parti d’hypothèses similaires à celles du modèle de Gurson sont ici proposées. La première contribution est l’évaluation de l’influence de la morphologie des vides sur les critères de plastification macroscopique de ces classes de matériaux. La deuxième est l’inclusion d’un critère de plastification anisotrope dans la matrice du matériau, de sorte que le comportement macroscopique présente une anisotropie induite par cette matrice, y compris pour les cavités sphériques. Le troisième et dernier progrès consiste à généraliser le critère de plastification de la matrice afin d’inclure une classe de fonctions de plastification basée sur des transformations linéaires. Cette classe de fonction a été largement employée avec succès pour représenter des alliages d’aluminium à haute résistance. Les résultats ici présentés soulignent la cohérence et la robustesse des trois formulations. En outre, le rôle de la porosité sur la modélisation de la plasticité des alliages d’aluminium incite à poursuivre les travaux sur la caractérisation expérimentale des paramètres d’anisotropie. / The manufacturing of ductile materials generally inserts impurities into their microscopic composition. These impurities may detach from the surrounding matrix and even crack along progressive deformation. Due to the consequent incapacity of these undesirable particles of supporting any stress, these ductile materials are equivalently assumed to be porous. Porosity has been effectively shown to play a fundamental role in the mechanisms of ductile fracture. Many micromechanical models have been proposed since the 1970s with the aim of mathematically describing these mechanisms. Among them, the acclaimed Gursonmodel combines the averaging homogenization technique with the kinematic theorem of Limit Analysis to estimate the macroscopic yield criterion and porosity evolution law of porous ductile materials. However, the Gurson model and most of its extensions only account for isotropic ductile fracture. Thus, the purpose of the present work is to contribute to the conception of yield criteria for anisotropic porous ductile rupture. Three main contributions are hereby proposed by profiting from similar hypothesis to those of the Gurson model. The first contribution is the assessment of the influence of void morphology on overall yield criteria for those classes of materials. The second is the inclusion of ananisotropic yield criterion in the material matrix so that the macroscopic behavior present matrix-induced anisotropy even for spherical cavities. The third and last advancement consists of generalizing the material matrix yield criterion of the Gurson model in order to comprehend a linear transformation-based class of yield functions that has been widely used to represent specific high strength aluminum alloys. The results hereby presented highlight the consistency and robustness of the three formulations. Moreover, the role of the porosity on the modeling of yield behavior of aluminum alloys encourages further work regarding experimental parameter characterization.

This numerical investigation of an advanced Gurson-Tvergaard-Needleman (GTN) model is an extension of the original work of Ben Bettaieb et al. (2011). The model has been implemented as a user-defined material model subroutine (VUMAT) in the Abaqus/explicit FE code. The current damage model extends the previous version by integrating the three damage mechanisms: nucleation, growth and coalescence of voids. Physically based void nucleation and growth laws are considered, including an effect of the kinematic hardening. These new contributions are based and validated on experimental results provided by high-resolution X-ray absorption tomography measurements. Also, the numerical implementation of the kinematic hardening in this damage extension has obliged to readapt the classical triaxiality definition. Besides, a secondary fracture initiation criterion based on the ultimate average inter-cavities distance has been integrated to localize and quantify with good accuracy the strain distribution just before the material fails apart. The current damage model is applied in industrial conditions to predict the damage evolution, the stress state and the fracture initiation in various tensile thin flat sheet geometries and the cross-die drawing tests.

Este trabalho investiga o comportamento dúctil de aços microligados classe API utilizado em tubulações na indústria do petróleo, e apresenta um estudo exploratório da aplicação da abordagem local e do modelo micromecânico de células computacionais para modelar a extensão estável de trinca em Modo I de abertura em aço ARBL. Ensaios laboratoriais na temperatura ambiente do aço API 5L X70 (utilizando corpos-de-prova normalizados) fornecem a curva de resistência à fratura (curva-R) do material. Esta curva foi utilizada para calibrar os parâmetros micromecânicos de células computacionais empregados no modelo. Este modelo foi utilizado para prever a pressão de colapso de dutos de paredes finas utilizados no transporte de gás, que apresentam defeitos longitudinais de diferentes razões entre profundidade de trinca e espessura de parede (a/t). As análises numéricas realizadas demonstram a capacidade da metodologia de células computacionais 2D em simular o rasgamento dúctil e o crescimento estável de trincas em corpos-de-prova de mecânica da fratura, assim como prever a pressão de colapso de estruturas tubulares contendo defeitos (trincas). / This study presents the experimental investigation of the ductile behaviour of microalloyed pipeline steel. Additionally, it extends the computational cell methodology to model Mode I crack extension in a high strength low alloy HSLA steel. Laboratory testing of an API 5L X70 steel at room temperature using standard, deep crack C(T) specimens provides the crack growth resistance curve to calibrate the micromechanics cell parameters for the material. The cell model incorporating the calibrated material-specific parameters is then applied to predict the burst pressure of a thin-walled gas pipeline containing longitudinal cracks with varying crack depth to thickness ratios (a/t). The numerical analyses demonstrate the capability of the computational cell approach to simulate ductile crack growth in fracture specimens and to predict the burst pressure of thin-walled tubular structures containing crack-like defects.

Este trabalho investiga o comportamento dúctil de aços microligados classe API utilizado em tubulações na indústria do petróleo, e apresenta um estudo exploratório da aplicação da abordagem local e do modelo micromecânico de células computacionais para modelar a extensão estável de trinca em Modo I de abertura em aço ARBL. Ensaios laboratoriais na temperatura ambiente do aço API 5L X70 (utilizando corpos-de-prova normalizados) fornecem a curva de resistência à fratura (curva-R) do material. Esta curva foi utilizada para calibrar os parâmetros micromecânicos de células computacionais empregados no modelo. Este modelo foi utilizado para prever a pressão de colapso de dutos de paredes finas utilizados no transporte de gás, que apresentam defeitos longitudinais de diferentes razões entre profundidade de trinca e espessura de parede (a/t). As análises numéricas realizadas demonstram a capacidade da metodologia de células computacionais 2D em simular o rasgamento dúctil e o crescimento estável de trincas em corpos-de-prova de mecânica da fratura, assim como prever a pressão de colapso de estruturas tubulares contendo defeitos (trincas). / This study presents the experimental investigation of the ductile behaviour of microalloyed pipeline steel. Additionally, it extends the computational cell methodology to model Mode I crack extension in a high strength low alloy HSLA steel. Laboratory testing of an API 5L X70 steel at room temperature using standard, deep crack C(T) specimens provides the crack growth resistance curve to calibrate the micromechanics cell parameters for the material. The cell model incorporating the calibrated material-specific parameters is then applied to predict the burst pressure of a thin-walled gas pipeline containing longitudinal cracks with varying crack depth to thickness ratios (a/t). The numerical analyses demonstrate the capability of the computational cell approach to simulate ductile crack growth in fracture specimens and to predict the burst pressure of thin-walled tubular structures containing crack-like defects.

L'actuel investigation numérique du Gurson-Tvergaard-Needleman (GTN) modèle avancé est une extension du travail de Ben Bettaieb et al. (2011). Le modèle a été implémenté à l'aide d'une sous routine (VUMAT) contenu dans le code commerciale d'éléments finis Abaqus/explicit. Le modèle d'endommagement améliore l'original en intégrant les trois mécanismes d'endommagement, la nucléation, la croissance, et la coalescence des cavités. Le modèle d'endommagement intègre les lois de nucléation et de croissance basés sur les phénomènes purement physiques. Ces nouvelles contributions incluant l'influence de l'écrouissage cinématique, ont été validées par les résultats de mesures expérimentales de tomographie à rayon X à haute résolution. Aussi, l'implémentation numérique de l'écrouissage cinématique dans le modèle modifié a contraint de proposer et de réarranger la définition de la triaxialité que l'on trouve habituellement dans la littérature. A coté de cela, un second critère d'initiation à la rupture basé sur l'ultime distance inter-cavités a été inclue afin de localiser et de quantifier avec plus de précision la distribution des déformations peu avant que le matériau ne casse complètement. L'actuel modèle d'endommagement a été appliqué dans des conditions industrielles pour prédire l'évolution de l'endommagement, l'état de contraintes, et l'initiation à la rupture pour différentes géométries de tôles et sur des essais d'emboutissage de tôles minces. / This numerical investigation of an advanced Gurson–Tvergaard–Needleman (GTN) model is an extension of the original work of Ben Bettaieb et al. (2011). The model has been implemented as a user-defined material model subroutine (VUMAT) in the Abaqus/explicit FE code. The current damage model extends the previous version by integrating the three damage mechanisms: nucleation, growth and coalescence of voids. Physically based void nucleation and growth laws are considered, including an effect of the kinematic hardening. These new contributions are based and validated on experimental results provided by high-resolution X-ray absorption tomography measurements. Also, the numerical implementation of the kinematic hardening in this damage extension has obliged to readapt the classical triaxiality definition. Besides, a secondary fracture initiation criterion based on the ultimate average inter-cavities distance has been integrated to localize and quantify with good accuracy the strain distribution just before the material fails apart. The current damage model is applied in industrial conditions to predict the damage evolution, the stress state and the fracture initiation in various tensile thin flat sheet geometries and the cross-die drawing tests.