[pt] O Método Estendido dos Elementos Finitos (XFEM) consiste em uma técnica para modelagem explícita de fraturas. Este método carrega toda a estrutura do método dos elementos finitos e baseia-se no Método da Partição da Unidade. O método tem como essência a adição de funções de enriquecimento ao campo dos deslocamentos contínuos, de modo a representar descontinuidades no modelo. O referido método permite a inserção da fratura no modelo de forma independente da malha e apresenta a grande vantagem de não requerer a atualização da mesma à medida que a fratura se propaga. Neste trabalho, foi desenvolvida uma implementação do XFEM para análises bidimensionais de propagação de fraturas com base na Mecânica da Fratura Linear Elástica (MFLE). Essa implementação foi feita para o programa ABAQUS através da sub-rotina UEL. A propagação da fratura ocorre de forma automática em um único processamento. O critério de propagação da fratura adotado baseia-se nos fatores de intensidade de tensão. Estes, por sua vez, tem seus cálculos efetuados com uso da integral de interação na forma de domínio equivalente. Utiliza-se o critério da máxima tensão tangencial para determinação da direção de propagação. O modelo foi aplicado à análise de propagação de fraturas em estruturas com material quase-frágil. Obtiveram-se excelentes resultados na predição da trajetória de propagação da fratura, comprovando a aplicação vantajosa do XFEM na modelagem de fraturas em Modo I e em modo misto de carregamento em estruturas. / [en] The Extended Finite Element Method (XFEM) is a powerful technique for the explicit modeling of fractures. This method has the background of the Finite Element Method and is based on the Partition Unity Method. The essential idea of the method is the addition of enrichment functions to the displacement field approximation for the representation of the discontinuities in the model. The crack geometry is modeled independently of the mesh and remeshing with crack growth is unnecessary. This thesis presents an ABAQUS implementation of XFEM through the UEL subroutine for two-dimensional analysis of fracture propagation following the Linear Elastic Fracture Mechanics theory. Fracture propagation occurs in an automatic procedure. The fracture criterion is based on the stress intensity factors. The domain form of the interaction integral was used for the computation of the stress intensity factors and the maximum circumferential stress criterion was used to determine the fracture propagation direction. The model was applied to the analysis of the propagation of fractures in structures of quasi-brittle material. The implementation shows good results in the prediction of the fracture propagation trajectories and proves the efficiency of the XFEM in Mode I and mixed mode fracture analyzes.

[pt] O processo de fraturamento hidráulico tem sido amplamente usado para aumentar o volume de petróleo e gás extraído na indústria petroleira. Durante a injeção de fluido, uma região determinada do reservatório é fraturada com a finalidade de aumentar a permeabilidade do meio poroso, de tal forma que o fluxo do fluido desde o reservatório para o poço seja favorecido notoriamente. Porém, este processo pode ocasionar danos ambientais tais como contaminação de aguas subterrâneas, vazamentos de gás, fraturas indesejadas nas camadas capeadoras pela injeção de agua e atividade sísmica fazendo primordial um estudo rigoroso do fraturamento hidráulico com a finalidade de reduzir os riscos potenciais associados a esta operação. Umas das metodologias usadas para projetar o fraturamento hidráulico é a simulação computacional. É possível determinar o volume injetado e a potência da bomba de injeção necessária para obter a geometria de fratura (comprimento, abertura e altura) desejada. A modelagem numérica através de elementos coesivos acoplados do processo de fraturamento hidráulico pode ser efetuada considerando o processo transiente ou permanente, tendo geometrias da fratura e curvas de injeção diferentes. Neste trabalho foi simulado numericamente o modelo KGD nos regimes de fluxo transiente e permanente para dois casos de estudo, (1) injeção numa única camada e (2) injeção em três camadas com contraste de tensões e poropressões entre elas. O estudo numérico foi desenvolvido usando o método dos elementos finitos com modelo de zona coesiva no software Abaqus o qual foi comparado com as soluções analíticas do KGD no regime dominado pela rigidez (Vértice-K) para uma camada e de Simonson e Fung para três camadas. / [en] The hydraulic fracturing process has been widely used to improve oil and gas recovery in the petroleum industry. During the fluid injection, the desired section of rock formation is fractured in order to increase the permeability of the medium that can facilitate the flow of oil to a producing well. However, this process can lead to potential environmental risks such as seismic activity, unwanted fractures in cap layers by water injection, water contamination and gas leakage making primordial to develop a rigorous study in order to reduce this environmental risks associated to hydraulic fracturing. One of the studies developed to design the hydraulic fracturing is computational simulation to determine the fluid volume and hydraulic horsepower required in order to produce the wanted fracture geometry (length, opening and height). The numerical modelling of fracturing process by using fully coupled cohesive element hydraulic can be carried out considering either a steady state or a transient analysis, which modify the fracture geometry and injection pressure. In this work, the KGD model is simulated in transient and steady analysis for two cases: (1) injection in a single layer formation and (2) injection in tri-layered formation with stress and porepressure contrast between them. The numerical simulation of a hydraulic fracturing is carried out using the finite element method with the zone cohesive model in Abaqus whose results are compared with analytical solutions of toughness-dominated propagation regime for the one layer formation model and Simonson and Fung analytical solutions for tri-layered formations model.

Both joint sets and fault-related fractures serve as important conduits for fluid flow. In the former case, they can strongly influence both permeability and permeability anisotropy, with implications for production of water, hydrocarbons and contaminant transport. The latter can affect issues of fluid flow, such as whether a given fault seals or leaks, and fault mechanics. These fractures are commonly interpreted as Natural Hydraulic Fractures (NHFs), i.e., mode 1 fractures produced when pore fluid pressure exceeds the tensile strength of the rock. Various mathematical models have been a rich source of hypotheses to explain the formation and propagation of NHFs, but have provided only limited information and nothing about processes of fracture initiation in originally intact rock. Recent laboratory experiments of French et al. (2012) have advanced our understanding of mechanical controls on fracture initiation and spacing. Here, detailed analysis of both through-going fracture surfaces, non-through-going fractures, in experimentally deformed samples provide a deeper understanding of NHF processes and resulting geometric features in porous siliciclastic sedimentary rocks. Observations indicate that both fracture planarity and microcrack damage (which has not previously been reported for opening mode fractures) vary significantly depending on the degree of mechanical heterogeneity and anisotropy of the host rock. Variations reflect mechanical controls on fracture initiation and propagation, suggesting that fracture spacing may in part reflect the distribution of mechanical heterogeneities. These data indicate that the more homogeneous the rock, the greater the microcrack damage surrounding a given NHF, increasing expected fracture-associated permeability for a given fracture aperture.

The demand for higher velocities and heavier axle loads for freight trains leads to higher forces on the railway wheels which in turn lead to an increase in stresses on and below the surface of the wheel-rail contact. By time, this induces wear on the wheels which consequently lead to higher maintenance costs and in some cases accidents. The ability to predict the evolution of wheel profiles due to uniform wear has been demonstrated with a rather accurate precision in most operational conditions. These wear models are based on wear coefficients and since they are not usually valid for real operational conditions, the models are generally calibrated against real-life scenarios in order to adjust the coefficients from test conditions to real-life lubrication conditions. This engineering approach can be useful in prediction of wear in systems where the materials and contact conditions do not vary. However, when addressing material development focused on reducing specific damage modes, the approach is of limited use because the obtained wear coefficients are not directly related to material properties. Therefore, attempts towards developing physical fracture propagation models that relates to the contact conditions and material properties have been made. The purpose has been to retrieve vital information about where a fracture initiates and how it propagates. In the long run, it is of great interest to be able to attain information about how a material particle is removed from the contact surface. Studies for this type of model was done in the 70’s and 80’s mainly with pin-disk experiments but has not been utilized in the specific field of wheel-rail contact. The thesis is part of the FR8RAIL project arranged by the European rail initiative Shift2Rail. Literature studies have been the basis for the thesis in order to gain vital insights into fracture mechanics and other related fields. The physical fracture propagation models have been constructed in the FE software Abaqus with the implementation of the XFEM. For the 2D model, the fracture initiates at the top of the implanted inclusion when the friction coefficient is  and propagates upwards a few elements. For , the fracture initiates at the right surface boundary where the pressure distribution and traction is applied. The fracture propagation angle increases relative to the surface as the friction coefficient value is increased. The fracture for the 3D model extends broader compared to the 2D model at the top of the inclusion in the case of . The fracture initiates at the same surface location as for the 2D model for . The fracture propagation is however non-existent due to convergence problems. The FE-models constructed are initial steps towards analysing the fracture propagation and closely related phenomena for a railway freight wheel in detail. At the end of the thesis, the simplified models give mainly information about the fracture initiation, propagation and its patterns. From this first phase, further adjustments and improvements can take place in order to eliminate the margins of error. In the long run, fully integrated models with further implementations such as detailed microstructure for the contact conditions, plastic behaviour for the material, and complete three-dimensional models can finally be employed. / Efterfrågan på högre hastigheter och tyngre axelbelastningar för godståg leder till högre krafter på järnvägshjulen som i sin tur leder till ökade spänningar på och under ytan vid hjul-räl-kontakten. Med tiden induceras slitage på hjulen som följaktligen leder till höga underhållskostnader och i vissa fall olyckor. Förmågan att förutse utvecklingen av hjulprofiler på grund av enhetligt slitage har visats kunna ske med en noggrann precision under de flesta driftsförhållanden. Dessa slitagemodeller bygger på slitagekoefficienter, och eftersom de vanligtvis inte är giltiga under realistiska driftsförhållanden är modellerna i allmänhet kalibrerade mot verkliga händelseförlopp för att justera koefficienterna från testförhållandena till realistiska smörjförhållanden. Detta tekniska tillvägagångssätt kan vara användbart vid prognos av slitage i system där material och kontaktförhållanden inte varierar. När man addresserar materialutveckling inriktad på att reducera specifika skadelägen är emellertid tillvägagångssättet av begränsad användning eftersom de erhållna slitagekoefficienterna inte är direkt relaterade till materialegenskaper. Därför har försök gjorts till att utveckla fysikaliska sprickbildningsmodeller som relateras till kontaktförhållanden och materialegenskaper. Syftet har varit att erhålla viktig information om var en spricka initieras och hur den fortskrider. I det långa loppet är det även av stor vikt att kunna erhålla information om hur en materialpartikel avlägsnas från kontaktytan. Studier för denna typ av modeller har gjorts på 70- och 80-talet i huvudsak med stift- och skivexperiment men har inte använts inom det specifika området för hjul-räl-kontakt. Avhandligen ingår i FR8RAIL-projektet som arrangeras av det europeiska järnvägsinitiativet Shift2Rail. Literaturstudier har varit grunden för avhandlingen för att få väsentlig insikt i frakturmekanik och andra relaterade områden. De fysiska sprickbildningsmodellerna har konstrueras i FE-mjukvaran Abaqus med XFEM som implementering. För 2D-modellen initieras sprickan överst vid den implanterade imperfektionen när friktionskoefficienten är  och propagerar uppåt några få element. För  initieras sprickan på högra ytgränsen där tryckfördelning och friktionskraft appliceras. Utbredningsvinkeln för sprickan ökar relativt till ytan då friktionskoefficienten ökar. Sprickan för 3D-modellen breder ut sig mer jämfört med 2D-modellen överst vid imperfektionen då . Sprickan initieras på samma ytplats som för 2D-modellen vid . Sprickbildningen är dock obefintlig på grund av konvergensproblem. De konstruerade FE-modellerna är initiala steg mot att analysera sprickutbredningen och närbesläktade fenomen för ett godstågs järnvägshjul i detalj. I slutet av avhandlingen ger de förenklade modellerna huvudsakligen information om sprickinitiering, utbredning och dess mönster. Ytterligare justeringar och förbättringar kan ske efter denna första fas i syfte att eliminera felmarginalerna. På lång sikt kan slutligen helt integrerande modeller med ytterligare implementeringar såsom detaljerad mikrostruktur för kontaktförhållandena, oelastiskt materialbeteende och kompletta tredimensionella modeller användas. / FR8RAIL