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Zyklische Kohäsivzonenmodelle beschreiben irreversibles Separationsverhalten und Schädigungsakkumulation unter zyklischer Belastung. In der vorliegenden Arbeit wird die Formulierung zyklischer Kohäsivzonenmodelle systematisiert und ihr Potenzial zur Simulation von Ermüdungsvorgängen analysiert. Die Kohäsivspannungs-Separations-Beziehungen werden auf Basis etablierter thermodynamischer Konzepte der Schädigungsmechanik aufgestellt. Zyklische Schädigungsakkumulation wird über die Entwicklungsgleichung der Schädigungsvariablen unter Berücksichtigung einer zustandsabhängigen Dauerfestigkeit beschrieben. Das Kohäsivzonenmodell wird erfolgreich für die Simulation von Werkstoffermüdung angewandt. Numerisch mithilfe der Methode der finiten Elemente erzeugte Rissfortschrittskurven bilden das experimentell beobachtete Ermüdungsrisswachstumsverhalten in allen Bereichen ab. Über Parameterstudien wird der Einfluss der einzelnen Modellparameter ermittelt. Darüber hinaus wird die Anwendung des zyklischen Kohäsivzonenmodells auf die Simulation von Wöhler-Versuchen vorgestellt und der Probengrößeneffekt auf das Ermüdungsverhalten untersucht. Der Zusammenhang zwischen den lokalen Beanspruchungszuständen in der Kohäsivzone und dem vorhergesagten globalen Versagensverhalten wird aufgeklärt. Die gewonnenen Erkenntnisse bilden die Grundlage für ein Konzept zur Identifikation der Kohäsivparameter, das auf der Auswertung von Wöhler- und Rissfortschrittskurven beruht. / Cyclic cohesive zone models describe irreversible separation behaviour and damage accumulation under cyclic loading. In the present thesis, the formulation of cyclic cohesive zone models is systemised and their potential to simulate fatigue processes is analysed. The relation between traction and separation is described based on established thermodynamical concepts of damage mechanics. Cyclic damage accumulation is controlled by a damage evolution equation taking into account a state-dependent endurance limit. The cohesive zone model is applied successfully to the simulation of material fatigue. Fatigue crack growth rate curves, which were obtained numerically by means of the finite element method, reproduce the experimentally observed behaviour in all stages. The influences of the particular parameters of the model are determined by parametric studies. In addition, simulations of uniaxial fatigue tests using the cyclic cohesive zone model are presented. Furthermore, the size effect on the fatigue behaviour is investigated. The relation between the local states within the cohesive zone and the predicted global failure modes is explained. These findings form the foundation for a concept of parameter identification which bases on the evaluation of Wöhler-curves and fatigue crack growth rate curves.

This thesis presents a novel hybrid prognostic methodology, integrating physics-based and data-driven prognostic models, to enhance the prognostic accuracy, robustness, and applicability. The presented prognostic methodology integrates the short-term predictions of a physics-based model with the longer term projection of a similarity-based data-driven model, to obtain remaining useful life estimations. The hybrid prognostic methodology has been applied on specific components of two different engineering systems, one which represents accelerated, and the other a nominal degradation process. Clogged filter and fatigue crack propagation failure cases are selected as case studies. An experimental rig has been developed to investigate the accelerated clogging phenomena whereas the publicly available Virkler fatigue crack propagation dataset is chosen after an extensive literature search and dataset analysis. The filter clogging experimental rig is designed to obtain reproducible filter clogging data under different operational profiles. This data is thought to be a good benchmark dataset for prognostic models. The performance of the presented methodology has been evaluated by comparing remaining useful life estimations obtained from both hybrid and individual prognostic models. This comparison has been based on the most recent prognostic evaluation metrics. The results show that the presented methodology improves accuracy, robustness and applicability. The work contained herein is therefore expected to contribute to scientific knowledge as well as industrial technology development.

The design of complex structures demands the prediction of possible fracture-dominant failure processes, due to the existence of unavoidable preexistent flaws and other defects, as well as sharps and cracks. On one hand, the complexity of the structure and the presence of many defects to be accounted for in the modeling can become the computational effort impracticable. On the other hand, it is important to seek the development of a computational framework based on some numerical method to study these problems. A way to overcome the difficulties mentioned, therefore making feasible the analysis of complex structures with many cracks, flaws and other defects, consists of combining a representative mechanical modeling with an efficient numerical method. This is precisely the fundamental aim of this work. Firstly, the Splitting Method is used aiming to build a representative modeling. Secondly, the Generalized Finite Element Method (GFEM) is chosen as an efficient numerical method, in which enrichment strategies of the approximated solution using stress functions in particular can be explored. The GFEM framework also allows avoiding the excessive refinement of the mesh, which increases the computational effort in conventional finite element analysis. In the Splitting Method, a kind of decomposition method, the original problem is subdivided in local and global problems which are then combined by imposing null traction at the crack surfaces. In this work, the Splitting Method was completely programmed in Python language and its use extended to analyze crack propagation including fatigue crack growth. The generated code presents in addition to several features related to Fracture Mechanics concepts, as the computation of the stress intensity factor (mode I and II) trough J Integral. Some examples are presented to depict the propagation of the cracks in multisite damage structures. It is shown that for this kind of problems the enrichment strategy provided by GFEM is essential. Moreover, the final example demonstrates that the computational tool allows for investigation of different possible crack scenarios with a low cost analysis. One concludes about the representativeness and efficiency of the methodology hereby proposed. / O projeto de estruturas complexas demanda a previsão de possíveis processos de ruptura governados por fraturamento, devido à existência de inevitáveis defeitos pré-existentes, como entalhes e fissuras. Por um lado, a complexidade da estrutura e a presença de muitos defeitos a serem considerados no modelo podem tornar a análise inviável devido ao esforço computacional necessário. Por outro lado, é importante procurar desenvolver uma estrutura computacional baseada em métodos numéricos para estudar estes problemas. Um modo de superar as dificuldades mencionadas, portanto tornando possível a análise de estruturas complexas com muitas fissuras e outros defeitos, consiste em combinar um modelo mecânico que seja representativo com um método numérico eficiente. Este é precisamente o objetivo fundamental deste trabalho. Primeiramente, o Método da Partição é utilizado para a construção de um modelo representativo. Em segundo lugar, o Método dos Elementos Finitos Generalizados (GFEM) é empregado por ser um método numérico eficiente, no qual as estratégias de enriquecimento da solução aproximada usando funções de tensão, em particular, podem ser exploradas. A estrutura do GFEM também permite evitar o excessivo refinamento da malha, que aumenta o esforço computacional em análises convencionais nas quais se utiliza o método dos elementos finitos. No Método da Partição, um tipo de método de decomposição, o problema original é subdividido em problemas locais e globais que são então combinados impondo-se a nulidade do vetor de tensões na superfície da fissura. Neste trabalho, o Método da Partição foi completamente programado em linguagem Python® e sua utilização estendida para analisar a propagação de fissuras, incluindo-se a associação do crescimento com a resposta em fadiga. Além disso, o código gerado apresenta diversas características relacionadas aos conceitos da Mecânica da Fratura, como o cálculo do fator de intensidade de tensão (modos I e II) mediante a Integral J. Alguns exemplos são apresentados para ilustrar a propagação de fissuras em estruturas multi-fraturadas. Mostra-se que para este tipo de problemas a estratégia de enriquecimento fornecida pelo GFEM é essencial. Além disso, o exemplo final comprova que a ferramenta computacional permite a investigação de diferentes possíveis cenários de fissuras com uma análise de baixo custo. Conclui-se sobre a representatividade e eficiência da metodologia proposta.

[pt] O presente trabalho teve como objetivos avaliar a influência de heterogeneidades metalúrgicas sobre o limiar de propagação de trincas de fadiga e apresentar alternativas de materiais para a fabricação de eixos virabrequins de motores Diesel / gás natural de unidades geradoras de plantas termoelétricas, uma vez que tais componentes mecânicos fabricados com aço DIN 34CrNiMo6 vêm apresentando falhas por fadiga com baixo número de ciclos de carregamento. Corpos de prova foram usinados de aços SAE 4140, SAE 4340 e DIN 42CrMo4. Inicialmente, conduziram-se ensaios de tração para a determinação das propriedades mecânicas dos materiais. Ensaios de propagação de trincas de fadiga foram realizados em espécimes do tipo C(T) entalhados, submetidos a um carregamento cíclico. Pré-trincas de fadiga, com comprimentos variando entre 1,3 mm e 1,6 mm, foram induzidas nos corpos de prova de acordo com a norma ASTM E647. Em sequência, foram levantadas as curvas da/dN versus delta K dos materiais, com ênfase para a determinação da variação do fator de intensidade de tensão do limiar de propagação (delta Kth) de cada aço. Neste contexto, o aço SAE 4140 apresentou um valor de (delta Kth) superior aos demais, o que significa que suporta maiores tamanhos de trinca antes do início da propagação. Análises por técnicas de microscopia evidenciaram a presença de inclusões na região de propagação das trincas, dando origem a um caminho preferencial para o crescimento das mesmas. Os resultados destas análises indicaram a presença de uma menor quantidade de inclusões no aço SAE 4140, permitindo uma associação desta característica microestrutural com o valor do delta Kth do material. Desta maneira, no que se refere à iniciação de trincas de fadiga, o aço SAE 4140 apresenta-se como alternativa viável para substituição do aço 34CrNiMo6 na fabricação de eixos virabrequins para motores de usinas termoelétricas. / [en] The present study had as objectives to evaluate the influence of metallurgical heterogeneities on the fatigue cracking propagation threshold and to present alternative materials for the manufacture of crankshafts of diesel / natural gas engines of thermoelectric plants generating units, since such components mechanics manufactured with DIN 34CrNiMo6 steel has been presenting faults due to fatigue with a low number of loading cycles. Test specimens were machined from SAE 4140, SAE 4340 and DIN 42CrMo4 steels. Initially, tensile tests were conducted to determine the mechanical properties of the materials. Fatigue crack propagation tests were performed on C(T) specimens subjected to cyclic loading. Fatigue pre-cracks, with lengths ranging from 1.3 mm to 1.6 mm, were induced in the test specimens according to ASTM E647. In sequence, da/dN versus delta K curves of the materials were raised, with emphasis on the determination of the tensile strength factor of the propagation threshold (delta Kth) of each steel. In this context, the steel SAE 4140 presented a value of (delta Kth) superior to the others, which means to support larger crack sizes before the beginning of the propagation. Analysis by microscopy techniques evidenced the presence of inclusions in the region of crack propagation, giving rise to a preferential path for their growth. The results of these analyzes indicated the presence of a smaller number of inclusions in the steel SAE 4140, allowing an association of this microstructural characteristic with the value of the delta Kth of the material. In this way, with regard to the initiation of fatigue cracks, the SAE 4140 steel is presented as a viable alternative for the replacement of 34CrNiMo6 steel in the manufacture of crankshafts for motors of thermoelectric power plants.

Este trabalho visa determinar a razão de carga cíclica R através da medida, na superficie de fratura, da relação entre a largura inter-estrias (s) e a altura da estria (H). É de conhecimento que o espaçamento (s) se correlaciona com a taxa de crescimento da trinca da/dN, enquanto que a curva da/dN x &#916K depende da razão de carga R. Para esta avaliação, corpos de prova do tipo compacto C(T) foram extraídos na orientação LT do centro de uma placa laminada da liga de alumínio SAE-AMS 7475 T7351 para realização dos ensaios de propagação de trinca por fadiga. Estes ensaios foram realizados de duas formas diferentes. A primeira, para obtenção de dados relativos à região II da curva da/dN x &#916K, sendo, neste caso, utilizadas quatro diferentes razões de carga (R=O,1; R=0,3; R=0,5; R=0,7). No outro caso, os ensaios de fadiga foram realizados sob &#916K constante e utilizados os mesmos quatro níveis de razão de carregamento R para determinação da curva da/dN x &#916K constante. Os níveis de &#916K aplicados foram tomados na região de Paris da curva da/dN x &#916K. A análise fratográfica por microscopia eletrônica foi conduzida nas superfícies dos corpos de prova do ensaio de fadiga com &#916K constante. Isto foi feito para determinar os espaçamentos inter-estria (s) e a altura H das estrias para cada nível de &#916K aplicado. Observou-se que a taxa de crescimento da trinca (da/dN) e o espaçamento inter-estrias (s) sofrem influência direta com a variação do fator de intensidade de tensão (&#916K), entretanto, observou-se, também, que a relação de proporcionalidade de 1:1 entre eles somente é válida para níveis de da/dN variando entre 0,1 a 1 &#956/ciclo. Os valores da morfologia da estrias (H/s) sofrem influência significativa com o aumento da razão de carga R, entretanto, ficou evidenciado que o fator de intensidade de tensão máxima Kmáx. não tem influência nesta relação. Evidenciou-se que a largura da estria corresponde à taxa de crescimento da trinca (da/dN), e que a relação entre a altura e o espaçamento da estria (H/s) possui uma correspondência direta com a razão de carga R, que tem influência significativa sobre a propagação de trinca por fadiga. / This work aims at to method to determine the load ratio R through of measure, on the fractured of surfaces the relation between the width striation spacing (s) and the height of the striation (H). It is of knowledge that the spacing (s), if correlates with the fatigue crack growth rates da/dN, whereas the curve da/dN x &#916K depends on the load ratio R. For this evaluation compact tension C(T) specimens had been extracted in the L- T orientation of a laminate plate of the aluminum alloy SAE-AMS 7475 T7351.These test had been carried out of two different forms. The first one, for attainment of relative data to region II of the curve da/dN x &#916K, being, in this in case that used four different load ratios (R=O,1; R=0,3; R=0,5; R=0,7). In the other in case that, the fatigue crack growth rates had been carried out under &#916K constant and used same the four levels of load ratios R for determination of the curve of constant da/dN x &#916K. The applied levels of &#916K had been taken in the region II of the curve da/dN x &#916K. The fractographic analysis for electronic microscopy was lead on the surfaces of the specimens tested in fatigue with constant &#916K. This was made to determine the striation spacing (s) and height (H) of the striations for each constant level of &#916K. It was observed that the fatigue crack growth rates (da/dN) and the striation spacing (s) suffers direct influence with the variation of &#916K. Also, was observed that the relation of proportionality of 1:1 between them is only valid for levels of da/dN in the range of 0,1 to 1,0 mm/cycle. The values of the relationship of the striation dimensions (H/s) suffer significant influence with the increasing of load ratios R. However, were evidenced that the value of Kmax. does not have influence in this relationship. It was found that the width of the striation corresponds to the value of (da/dN) and that the relation between the height and the striation of spacing (H/s) had a direct correspondence with the load ratios R that has signifficant effect on the fatigue crack growth rates.

Fretting fatigue is a damage process that may arise in engineering applications where small cyclic relative displacements develop inside contacts leading to detrimental effects on the material fatigue properties. Fretting is located in regions not easily accessible, which makes it a dangerous phenomenon. It is therefore important to be able to make reliable predictions of the fretting fatigue lives. The work presented in this thesis has its focus on different aspects related to fretting fatigue in the titanium alloy Ti-17. A fretting experiment was developed which allowed for separate control of the three main fretting loads. Initially, the evolution of the coefficient of friction inside the slip region was investigated experimentally and analytically. Subsequently, 28 fretting tests were performed in which large fatigue cracks developed. The fretting tests were firstly evaluated with respect to fatigue crack initiation through five multiaxial fatigue criteria. The criteria predicted a too high fretting fatigue limit. A possible clue to the discrepancy was found in the fretting induced surface roughness with the asperity-pit interactions. The fatigue growth of the large fretting cracks was numerically modelled through a parametric crack growth procedure. The predicted lives were compared to the experimental outcome. The numerical simulations showed that linear elastic fracture mechanics was an appropriate tool for the prediction of fretting fatigue propagation lives in the long crack regime. Fatigue cracks spend most of their propagation life in the small crack regime. The possibility of modelling the small crack behaviour is therefore very important from the engineering point of view. The fatigue growth of through thickness short cracks was studied experimentally and numerically in the four-point bend configuration. It was found that linear elastic fracture mechanics and closure-free material growth data furnished conservative estimates for cracks longer than 50 μm. One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental results on fretting life with or without shot peening were simulated. The fatigue life enhancement in shot peened specimens could be explained by slower crack growth in the surface material layer with residual compressive stresses. / QC 20100827

Design based on damage tolerance concepts has become mandatory in high technology structures. These concepts are also essential for evaluating life extension of aged structures which are in service beyond originally stipulated life. Fracture analysis of such structures in the presence of single or multiple three-dimensional flaws is essential for this approach. Surface cracks are the most commonly occurring flaws and development of accurate methods of analysis for such cracks is essential for structural integrity evaluation of newly designed or aged structures. The crack fronts of these surface flaws are usually approximated mathematically to be of either part-elliptical or part-circular in geometry. In this thesis, some of the issues related to fatigue crack growth of single and multiple surface cracks are studied in detail. Here emphasis is given to the development of simple and accurate post-processing techniques to estimate stress intensity factors for surface cracks, development and/or implementation of simple numerical methods to simulate three-dimensional single and multiple cracks in fatigue and their experimental verification. Modified virtual crack closure integral (MVCCI) technique for estimation of strain energy release rates has been improved (chapter II) to deal with curved crack front and unequal elements across the crack front. The accuracy of this method is evaluated and presented in this chapter for certain benchmark surface flaw problems. The improved MVCCI is used in the investigation of interaction between multiple surface cracks in three-dimensional solids. The interaction effects are studied for both interacting and coalescing phases as observed to occur in the growth of multiple surface cracks. Extensive numerical work is performed to study the effects of various parameters such as aspect ratio, thickness ratio, interspacing on the interaction factors. These solutions are used in formulating empirical equations to estimate interaction factors. This facilitated the development of a simple semi-analytical method to study fatigue crack growth of multiple cracks. The growth of surface cracks under fatigue loading in the finite width specimens of an aero-engine superalloy has been studied experimentally (presented in chapter III). Four configurations for single semi-elliptical cracks are considered. Fatigue crack growth is simulated by two models viz. two degrees of freedom and "multi degrees of freedom with ellipse fit'. These models are sometimes referred to as semi-analytical models as the crack growth is predicted by numerical integration combining Paris equation with an empirical form of stress intensity factor solution. In order to use two degrees of freedom model for fatigue crack growth prediction of semi-elliptical cracks, empirical solution for the Ml range of geometric parameters for stress intensity factor is required for the considered configurations. The available Newman-Raju solution is useful for this purpose within a limited range of surface crack length to width (c/W) of the specimen. Based on the present finite element results, the empirical equations are developed for extended values of c/W. It is well understood that the fatigue prediction for two-dimensional crack can be improved by inclusion of crack closure effects. Usually, in semi-analytical models for growth of surface cracks under fatigue loading, the crack closure is included as a ratio of crack closure factor at surface and depth locations of semi-elliptical crack. In the present work, this ratio for the considered material of specimens is obtained by an experimental study. The difference in characteristics of preferred propagation path between semi-elliptical crack in a finite width plate and a wide plate is clearly brought out. Current crack growth predictions for most of the structures are based on the presence of only a single crack. However, in structures several cracks may initiate simultaneously within a stress critical zone and may interact depending upon their geometry, spatial location, structure geometry and mode of loading. In this work various configurations of twin semi-elliptical cracks have been studied by experiments. The beachmarks created on the specimens during experiments are used in the investigation of crack shape progression during fatigue. A three degrees of freedom crack growth model for interacting and coalescing cracks has been proposed. The experimentally determined crack shape and lives have been compared with the corresponding values from numerical simulation. The correlation of experimental results with numerical predictions was carried out through improved MVCCI for eight-noded brick elements. This has worked well in the configurations analysed. However, it is known in literature that there are benefits of using 20-noded singular elements. There could be special situations where the regular elements could fail, and singular elements could be essential. For this purpose, further development of MVCCI were carried out using 20-noded quarter-point elements (presented in chapter IV). Also a novel technique of decomposed crack closure integral (DCCI) was developed (presented in chapter V) for both regular and singular elements to represent the variation of MVCCI more accurately along the crack front. It is well known that quarter-point elements at crack front produce the required singularity at the crack tip and give accurate stress distribution with fewer degrees of freedom than conventional elements. Thus to develop more efficient post-processing tools, the MVCCI expressions are formulated for 20-noded singular quarter-point element for various assumptions regarding stress and displacement distributions in the elements across the crack front. A comprehensive study is presented (chapter IV) on MVCCI for 20-noded singular brick element including various simplified expressions for three-dimensional part-through cracks in pure and mixed-mode state of deformation of fracture. The developed MVCCI expressions are also valid for 15-noded quarter-point Penta elements. The reduction in model size can further be obtained if 12-noded three-dimensional singular element is employed at the crack front and eight-noded elements are used away from the crack front. The MVCCI expressions are also developed for 12-noded singular element and their accuracy is evaluated by numerical solutions. Presently, MVCCI, estimates the average stress intensity factor at the center of each element along the crack front. In this thesis, a Decomposed Crack Closure Integral (DCCI) is formulated to represent an assumed variation of stress intensity factor along the crack front in each element. The DCCI is formulated for 8-noded brick, 20-noded conventional brick and 20-noded singular brick elements. The numerical examples presented here deal with three-dimensional problems of patch repair technology and part-through cracks. The technique showed a major advantage for the patch repair problems where SIF variations along the crack front are of significance and large mesh sizes are computationally expensive. This along with MVCCI for 12-noded and 20-noded singular elements formed a part of the work on development of accurate and effective post-processing tools. It is expected that the present work will be helpful in damage tolerance design and assessment of aerospace structures and the experimental work performed as a part of this thesis will enhance confidence in the damage tolerance analysis. The thesis is concluded in chapter VI presenting the contributions of this thesis and projecting future lines of work possible in this area.

The design of complex structures demands the prediction of possible fracture-dominant failure processes, due to the existence of unavoidable preexistent flaws and other defects, as well as sharps and cracks. On one hand, the complexity of the structure and the presence of many defects to be accounted for in the modeling can become the computational effort impracticable. On the other hand, it is important to seek the development of a computational framework based on some numerical method to study these problems. A way to overcome the difficulties mentioned, therefore making feasible the analysis of complex structures with many cracks, flaws and other defects, consists of combining a representative mechanical modeling with an efficient numerical method. This is precisely the fundamental aim of this work. Firstly, the Splitting Method is used aiming to build a representative modeling. Secondly, the Generalized Finite Element Method (GFEM) is chosen as an efficient numerical method, in which enrichment strategies of the approximated solution using stress functions in particular can be explored. The GFEM framework also allows avoiding the excessive refinement of the mesh, which increases the computational effort in conventional finite element analysis. In the Splitting Method, a kind of decomposition method, the original problem is subdivided in local and global problems which are then combined by imposing null traction at the crack surfaces. In this work, the Splitting Method was completely programmed in Python language and its use extended to analyze crack propagation including fatigue crack growth. The generated code presents in addition to several features related to Fracture Mechanics concepts, as the computation of the stress intensity factor (mode I and II) trough J Integral. Some examples are presented to depict the propagation of the cracks in multisite damage structures. It is shown that for this kind of problems the enrichment strategy provided by GFEM is essential. Moreover, the final example demonstrates that the computational tool allows for investigation of different possible crack scenarios with a low cost analysis. One concludes about the representativeness and efficiency of the methodology hereby proposed. / O projeto de estruturas complexas demanda a previsão de possíveis processos de ruptura governados por fraturamento, devido à existência de inevitáveis defeitos pré-existentes, como entalhes e fissuras. Por um lado, a complexidade da estrutura e a presença de muitos defeitos a serem considerados no modelo podem tornar a análise inviável devido ao esforço computacional necessário. Por outro lado, é importante procurar desenvolver uma estrutura computacional baseada em métodos numéricos para estudar estes problemas. Um modo de superar as dificuldades mencionadas, portanto tornando possível a análise de estruturas complexas com muitas fissuras e outros defeitos, consiste em combinar um modelo mecânico que seja representativo com um método numérico eficiente. Este é precisamente o objetivo fundamental deste trabalho. Primeiramente, o Método da Partição é utilizado para a construção de um modelo representativo. Em segundo lugar, o Método dos Elementos Finitos Generalizados (GFEM) é empregado por ser um método numérico eficiente, no qual as estratégias de enriquecimento da solução aproximada usando funções de tensão, em particular, podem ser exploradas. A estrutura do GFEM também permite evitar o excessivo refinamento da malha, que aumenta o esforço computacional em análises convencionais nas quais se utiliza o método dos elementos finitos. No Método da Partição, um tipo de método de decomposição, o problema original é subdividido em problemas locais e globais que são então combinados impondo-se a nulidade do vetor de tensões na superfície da fissura. Neste trabalho, o Método da Partição foi completamente programado em linguagem Python® e sua utilização estendida para analisar a propagação de fissuras, incluindo-se a associação do crescimento com a resposta em fadiga. Além disso, o código gerado apresenta diversas características relacionadas aos conceitos da Mecânica da Fratura, como o cálculo do fator de intensidade de tensão (modos I e II) mediante a Integral J. Alguns exemplos são apresentados para ilustrar a propagação de fissuras em estruturas multi-fraturadas. Mostra-se que para este tipo de problemas a estratégia de enriquecimento fornecida pelo GFEM é essencial. Além disso, o exemplo final comprova que a ferramenta computacional permite a investigação de diferentes possíveis cenários de fissuras com uma análise de baixo custo. Conclui-se sobre a representatividade e eficiência da metodologia proposta.