O trabalho apresenta uma análise do desempenho de vários métodos de extração de fatores de intensidade de tensão a partir de soluções numéricas obtidas com o método dos elementos finitos generalizados (MEFG). A convergência dos fatores de intensidade de tensão é comparada com a da energia de deformação a fim de investigar a superconvergência dos métodos. Para extração dos fatores de intensidade de tensão e o cálculo da taxa de energia disponibilizada para propagação da fissura, implementam-se os métodos da integral de contorno (MIC), da função cutoff (MFC) e da integral-J no contexto do MEFG. Desenvolve-se a formulação dos métodos de extração de forma a obter uma implementação independente da malha utilizada na modelagem do problema. Aplica-se a extração dos fatores de intensidade de tensão, para modos puros e mistos, em problemas clássicos da mecânica da fratura. Verifica-se a convergência dos fatores de intensidade de tensão e da taxa de energia disponibilizada para a propagação da fissura, obtidos com cada método de extração, com o enriquecimento da ordem polinomial da solução do MEFG. Investiga-se a robustez dos métodos com relação ao tamanho dos domínios de extração / The performance of several techniques to extract stress intensity factors (SIF) from numerical solutions computed with the generalized finite element method (GFEM) is investigated. The convergence of the stress intensity factors is compared with the convergence of strain energy with the aim of investigate the superconvergence of the methods. The contour integral (CIM), the cutoff function (CFM) and the J-integral methods are considered to compute stress intensity factors and energy release rate. The proposed implementation of the extraction techniques is completely independent of the discretization used. Several numerical examples demonstrating the convergence of the computed stress intensity factors and the energy release rate, with the increasing of p order of the GFEM solution, are presented

Among all existing fuel cell technologies, the planar solid oxide fuel cell (SOFC) is the most promising one for high power density applications. A planar SOFC consists of two porous ceramic layers (the anode and cathode) through which flows the fuel and oxidant. These ceramic layers are bonded to a solid electrolyte layer to form a tri-layer structure called PEN (positive-electrolyte-negative) across which the electrochemical reactions take place to generate electricity. Because SOFCs operate at high temperatures, the cell components (e.g., PEN and seals) are subjected to harsh environments and severe thermomechanical residual stresses. It has been reported repeatedly that, under combined thermomechanical, electrical and chemical driving forces, catastrophic failure often occurs suddenly due to material fracture or loss of adhesion at the material interfaces. Unfortunately, there have been very few thermomechanical modeling techniques that can be used for assessing the reliability and durability of SOFCs. Therefore, modeling techniques and simulation tools applicable to SOFC will need to be developed. Such techniques and tools enable us to analyze new cell designs, evaluate the performance of new materials, virtually simulate new stack configurations, as well as to assess the reliability and durability of stacks in operation. This research focuses on developing computational techniques for modeling fracture failure in SOFCs. The objectives are to investigate the failure modes and failure mechanisms due to fracture, and to develop a finite element based computational method to analyze and simulate fracture and crack growth in SOFCs. By using the commercial finite element software, ANSYS, as the basic computational tool, a MatLab based program has been developed. This MatLab program takes the displacement solutions from ANSYS as input to compute fracture parameters. The individual stress intensity factors are obtained by using the volume integrals in conjunction with the interaction integral technique. The software code developed here is the first of its kind capable of calculating stress intensity factors for three-dimensional cracks of curved front experiencing both mechanical and non-uniform temperature loading conditions. These results provide new scientific and engineering knowledge on SOFC failure, and enable us to analyze the performance, operations, and life characteristics of SOFCs.

The aim of this study is to model three dimensional surface crack problems in fillet welds. It is assumed that weld material has the same material properties with the sheet metals. The surface crack is considered to occur at two regions / one at the weld root and the other at the weld toe. The surface crack is assumed to have a semi &ndash / elliptical crack front profile. The surface crack problem is analyzed under mechanical loading and the models are built up by three dimensional finite elements. Around the crack front, strain singularity is taken into account by using degenerated 20 &ndash / node quarter &ndash / point solid elements. The main results of this work are the stress intensity factors around the crack front for the test specimen model subjected to axial and bending loads.

The main objective of this study is to model and analyze a three dimensional inclined semi-elliptic surface crack in a Functionally Graded Material (FGM) coating bonded to a homogeneous substrate with a bond coat. The parametric analyses on FGMs are based upon zirconia-yttria (ZrO2-8wt%-Y2O3) FGM coating bonded to a substrate made of a nickel-based superalloy. It is assumed that there is a nickel-chromium&amp / #8211 / aluminum&amp / #8211 / zirconium (NiCrAlY) bond coat between the FGM coating and substrate. Metal-rich, linear variation, ceramic-rich and homogeneous ceramic FGM coating types are considered in the analyses. The inclined semi-elliptic surface crack problem in the FGM coating-bond coat-substrate system is analyzed under transient thermal loading. This problem is modeled and analyzed by utilizing three dimensional finite elements. Strain singularity around the crack front is simulated using collapsed 20 &amp / #8211 / node quarter &amp / #8211 / point brick elements. Three &amp / #8211 / dimensional displacement correlation technique is utilized to extract the mixed mode stress intensity factors around the crack front for different inclination angles of the semi-elliptic surface crack. The energy release rates around the crack front are also calculated by using the evaluated mixed mode stress intensity factors. The results obtained in this study are the peak values of mixed mode stress intensity factors and energy release rates around the crack front for various inclination angles of the semi-elliptic surface crack embedded in the FGM coating of the composite structure subjected to transient thermal loading.

The main aim of this study is to utilize a Jk-integral based computational method in order to calculate crack tip parameters for orthotropic functionally graded materials (FGMs). The crack is subjected to mixed mode thermal loading. Mixed mode thermal fracture analysis requires the calculation of mode-I and mode-II stress intensity factors (KI ,KII ). In addition to stress intensity factors, energy release rate and T-stress are calculated by means of Jk-integral. Jk-integral is defined as a line integral over a vanishingly small curve. Since it is difficult to deal with a line integral on a vanishing curve , Jk-integral is converted to a domain independent form containing area and line integrals by the help of plane thermoelasticity constitutive relations. Steady-state temperature distribution profiles in FGMs and the components of the Jk-integral are computed by means of the finite element method. In both thermal and structural analyses, finite element models that possess graded isoparametric elements are created in the general purpose finite element analysis software ANSYS. In the formulation of Jk-integral, all required engineering material properties are assumed to possess continuous spatial variations through the functionally graded medium. The numerical results are compared to the results obtained from Displacement Correlation Technique (DCT). The domain independence of Jk-integral is also demonstrated. The results obtained in this study show the effects of crack location and material property gradation profiles on stress intensity factors, energy release rate and T-stress.

The main objective of this study is to model the three dimensional surface cracking problem in Functionally Graded Material (FGM) coatings bonded to homogeneous substrates. The FGM coating is assumed to be a (ZrO2) &ndash / (Ti-6Al-4V) layer. Homogeneous ceramic, metal &ndash / rich, ceramic &ndash / rich and linear variation material compositions are considered in the analyses. The surface crack is assumed to have a semi &ndash / circular crack front profile. The surface crack problem in the FGM coating &ndash / substrate system is examined under mechanical and transient thermal loading. Structural and thermal problems are modeled using three dimensional finite elements. Strain singularity around the crack front is simulated using collapsed 20 &ndash / node quarter &ndash / point brick elements. Three - dimensional displacement correlation technique is utilized to extract the stress intensity factors. The main results of the study are the stress intensity factors around the crack front for FGM coating - substrate structures subjected to uniform tension, bending, fixed &ndash / grip tension, three point bending and transient thermal loading.

O trabalho apresenta uma análise do desempenho de vários métodos de extração de fatores de intensidade de tensão a partir de soluções numéricas obtidas com o método dos elementos finitos generalizados (MEFG). A convergência dos fatores de intensidade de tensão é comparada com a da energia de deformação a fim de investigar a superconvergência dos métodos. Para extração dos fatores de intensidade de tensão e o cálculo da taxa de energia disponibilizada para propagação da fissura, implementam-se os métodos da integral de contorno (MIC), da função cutoff (MFC) e da integral-J no contexto do MEFG. Desenvolve-se a formulação dos métodos de extração de forma a obter uma implementação independente da malha utilizada na modelagem do problema. Aplica-se a extração dos fatores de intensidade de tensão, para modos puros e mistos, em problemas clássicos da mecânica da fratura. Verifica-se a convergência dos fatores de intensidade de tensão e da taxa de energia disponibilizada para a propagação da fissura, obtidos com cada método de extração, com o enriquecimento da ordem polinomial da solução do MEFG. Investiga-se a robustez dos métodos com relação ao tamanho dos domínios de extração / The performance of several techniques to extract stress intensity factors (SIF) from numerical solutions computed with the generalized finite element method (GFEM) is investigated. The convergence of the stress intensity factors is compared with the convergence of strain energy with the aim of investigate the superconvergence of the methods. The contour integral (CIM), the cutoff function (CFM) and the J-integral methods are considered to compute stress intensity factors and energy release rate. The proposed implementation of the extraction techniques is completely independent of the discretization used. Several numerical examples demonstrating the convergence of the computed stress intensity factors and the energy release rate, with the increasing of p order of the GFEM solution, are presented

Stålbroars approximativa livslängd bestäms av stålets utmattningshållfasthet, då utmattning är en av de främsta anledningarna till att livslängden begränsas. I Sverige existerar ett antal broar som närmar sig slutet av sin livslängd, samtidigt som behovet för kapacitet och kraven på broarna ökar. Flertalet av dessa broar är i behov av upprustning. Däremot är det inte möjligt ur vare sig ett ekonomiskt- eller miljöperspektiv att byta ut alla broar, och därför behöver de broar som är mest kritiska prioriteras. Vid utmattningsdimensionering av stålbroar beaktas hela spänningsvidden, oavsett om spänningarna är i drag eller tryck. En spricka propagerar endast vid dragspänningar, vilket innebär att tryck- spänningar egentligen inte bör vägas in i samband med dimensionering. Detta innebär att en del stålbroar skulle kunna ha en längre livslängd än vad den traditionella dimensioneringen ger. Spänningsintensitetsfaktorn 𝐾 används inom brottmekaniken för att förutspå spänningsintensiteten i närheten av sprickspetsen, och appliceras till linjärelastiska material. Det finita elementprogrammet Abaqus användes när brodetaljen modellerades och analyserades. Brodetaljen representerar en balk med en påsvetsad anslutningsplåt, som utsätts för trafiklasten på en bro och en temperaturlast för att simulera egenspänningar. Detaljen representerar problematiken med utmattning i stålkonstruktionsdelar. Motivet för denna studie är att inga sprickor har hittats under inspektioner av liknande detaljer, det till trots att en del stålbroar teoretiskt sett förbrukat sin livslängd. Studien genomfördes med en mer avancerad modell än vad som vanligtvis skapas för bedömning av utmattning, med syftet att modellera verkligheten mer korrekt. Resultaten visar hur egenspänningarna bidrar till dragspänningar, vilket leder till sprickpropagering i modellen. Vid spricklängden 9,5 mm övergår spänningarna från drag till tryck, och då upphör spricktillväxten. Resultaten visar även att utmattningssprickor kan växa i stålkonstruktionsdelar som i huvudsak utsätts för nominella tryckspänningar, ifall höga egenspänningar uppstår vid anslutningsplåten. / Steel bridges estimated service life is determined by the fatigue strength of the steel, since fatigue is one of the main reasons for limiting the service life. In Sweden there is a number of bridges that approach the end of their service life, while the need of increasing the capacity and demands on bridges grows. The majority of these bridges is in need of reparation. On the other hand, it is not possible either from a financial- or environmental perspective to replace all bridges, and therefore the bridges that are most critical needs priority. In the case of fatigue design calculation of steel bridges, the entire stress range is taken into account, regardless of whether the stresses are in tension or pressure. A crack propagates only at tensile stresses, which means that pressure should not really be considered in the design calculations. This means that some steel bridges could have a longer life span than the traditional design calculation gives. The stress intensity factor K is used within the fracture mechanism to predict the stress intensity near crack tip, and is applied to linear elastic materials. The finite element program Abaqus was used when the bridge detail was modeled and analyzed. The bridge detail represents a beam with a welded connection plate, which is exposed to traffic load at the bridge and a temperature load to simulate residual stresses. The detail represents the problem of fatigue in steel structural parts. The motive for this study is that no cracks have been found during inspections of similar details, despite the fact that some steel bridges theoretically have consumed their longevity. The study is conducted with a more advanced model than usually created for assessment of fatigue, with the purpose of modeling the reality more correctly. The results show how the residual stresses cause tensile stresses, which leads to crack propagation in the model. At a crack length of 9,5 mm, the stresses change from tension to compression, and then the crack growth ceases. The results also indicate that fatigue cracking can grow in steel structural parts that are mainly exposed to compressive nominal stresses, if tensile residual stresses appear at the connection plate.

[pt] Inúmeros sistemas de Engenharia estão submetidos a cargas cíclicas durante longos tempos quando em serviço. Sendo assim, a determinação do desempenho de materiais no regime de super longa vida em fadiga (107–1012ciclos) tornou-se de grande relevância na estimativa da vida útil de componentes mecânicos e estruturas. Neste contexto, o uso de equipamentos de ensaios que operem em frequências ultrassônicas, normalmente em 20 kHz, viabilizou estudos sobre a resistência à fadiga de materiais em regime de altíssimo ciclo. Até o momento, a principal contribuição destes estudos foi mostrar que não existe um limite de fadiga para materiais após 107ciclos, o que permite questionar várias metodologias de projeto desenvolvidas ao longo dos anos com base em uma vida infinita do material sob condições cíclicas de carregamento. O presente trabalho teve como objetivo investigar a resistência à fadiga de altíssimo ciclo de dois aços estruturais, DIN 34CrNiMo6 e DIN 42CrMo4, adotados na fabricação de eixos virabrequins de centrais termoelétricas que falharam por fadiga em serviço, de maneira prematura. Os corpos de prova selecionados para os testes foram dos tipos ampulheta, ampulheta entalhado e cilíndrico entalhado, com dois diferentes raios de arredondamento. Os ensaios foram realizados em equipamento ultrassônico, com amplitude de tensões que variaram entre 0,3 – 0,5 do limite de resistência mecânica dos materiais e conduzidos até um número alvo de ciclos para falha de 109 ciclos. Considerando os ensaios de corpos de prova ampulheta, os resultados revelaram a maior resistência à fadiga do aço DIN 34CrNiMo6, apesar dos dois materiais apresentarem propriedades mecânicas semelhantes. Como poderia ser esperado, a presença de concentradores de tensão reduziu a vida em fadiga de ambos os materiais. Entretanto, o aço DIN 42CrMo4 apresentou a maior sensibilidade ao entalhe, com uma pequena diminuição do número de ciclo para a falha. / [en] The DIN 42CrMo4 e DIN 34CrNiMo6 steel behavior analysis in fatigue regime in very high cycle. The uncountable engineering systems are submitted loading cyclic during long time in services. So, the determination of material performance in regime in super long life in fatigue (107–1012cycles) belong the high relevance to estimate the live cycle of mechanical of components and structures. Based on it, the use of testing equipment to operate in ultrasonic frequency, normally in 20 kHz. That permits the studies about material fatigue resistance in very high cycle. In this moment, the main contribution of these studies was to demonstrate that no exist fatigue limit to material after 107 cycles, that it allows to question many projects methodologic that was developed long of years based on infinite material life under of loading cyclicals conditions. This present work had the objective to investigate the fatigue resistance in very high cycle of two structure steels (DIN 42CrMo4 and DIN 34CrNiMo6). These steels are used to manufacturing of crankshaft of thermoelectric central that failure due to fatigue in services in premature way. The selected specimens had the three types of format; Hourglass, notched Hourglass and notched Cylindrical with two different rounding of radius. These tests were performed in ultrasonic equipment, with variation of stress between 0,3 – 0,5 of material mechanical resistance and they are performed until maximum number of cycles per failure of 109 cycles. Considering the test of hourglass specimens, the results presented higher fatigue resistance of DIN 34CrNiMo6 steel, although DIN 42CrMo4 as same mechanical properties of DIN 34CrNiMo6 steel. And as it is waited the existence of stress concentrators accelerated the fatigue life in both materials. However, the DIN 42CrMo4 presented higher sensibility to notch, with small decrease of number of cycles to failure.

[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.