Fatigue crack growth in engineered structures reduces the structures load carrying capacity and will eventually lead to failure. Cycles required to grow a crack from an initial length to the critical length is called the fatigue fracture life. In this thesis, five different methods for analyzing the fatigue fracture life of a center cracked plate were compared to experimental data previously collected by C.M. Hudson in a 1969 NASA report studying the R-ratio effects on crack growth in 7075-T6 aluminum alloy. The Paris, Walker, and Forman fatigue crack growth models were fit the experimental data. The Walker equation best fit the data since it incorporated R-ratio effects and had a similar Root Mean Square Error (RMSE) compared to the other models. There was insufficient data in the unstable region of crack growth to adequately fit the Forman equation. Analytical models were used as a baseline for all fatigue fracture life comparisons. Life estimates from AFGROW and finite elements with mid-side nodes moved to their quarter point location compared very with the analytical model with errors less than 3%. The Virtual Crack Closure Technique (VCCT) was selected as a method for crack propagation along a predefined path. Stress intensity factors (SIFs) for shorter crack lengths were found to be low, resulting in an overestimated life of about 8%. The eXtended Finite Element Method with Phantom Nodes (XFEM-PN) was used, allowing crack propagation along a solution dependent path, independent of the mesh. Low SIFs throughout growth resulted in life estimates 20% too large. All finite element analyses were performed in Abaqus 6-13.3. An integrated polynomial method was developed for calculating life based on Abaqus' results, leading to coarser meshes with answers closer to the analytical estimate. None of the five methods for estimating life compared well with the experimental data, with analytical errors on life ranging from 10-20%. These errors were attributed to the limited number of crack growth experiments run at each R-ratio, and the large variability typically seen in growth rates. Monte Carlo simulations were run to estimate the distribution on life. It was shown that material constants in the Walker model must be selected based on their interrelation with a multivariate normal probability density function. Both analytical and XFEM-PN simulations had similar coefficients of variation on life of approximately 3% with similar normal distributions. It was concluded that Abaqus' XFEM-PN is a reasonable means of estimating fatigue fracture life and its variation, and this method could be extended to other geometries and three-dimensional analyses. / Master of Science

Lors de l'opération d’usinage à grande vitesse, la résistance à l'usure des outils de coupe est améliorée par l’utilisation des revêtements mono ou multicouches sur les faces actives de l’outil. Cependant, le chargement thermomécanique généré à l'interface outil-pièce affecte considérablement les zones de contact. Par cet effet, plusieurs modes d'usure tels que la fissuration, l’abrasion, l’adhésion et le délaminage du revêtement peuvent se manifester. L'étude du comportement des revêtements et de leurs différents modes de dégradation permet de mieux comprendre leur impact sur la durée de vie de l'outil et ainsi optimiser le procédé d'usinage. Dans ce travail de thèse, une approche numérique multi-étapes a été proposée pour prédire l'usure des outils de coupe revêtus. Cette approche est composée par trois principales étapes. La première consiste à effectuer une simulation éléments finis de l’usinage pour une courte durée (jusqu’à la stabilisation du chargement à l’interface outil/pièce). La deuxième étape consiste à récupérer ce chargement et de l’utiliser comme une entrée du modèle XFEM/Level-set. Ce dernier permet d’analyser le comportement des couches de revêtement sans recours à un maillage conforme aux interfaces. Par conséquence, la distorsion du maillage est évitée lorsque le profil d'outil usé est mis à jour, ainsi que le temps de calcul CPU est drastiquement réduit. La dernière étape de cette approche consiste à calculer le taux d’usure et ainsi prédire le déplacement des nœuds de l’outil de coupe affectés par l’usure. Les essais expérimentaux ont permis d’une part d’identifier les paramètres de contact outil/pièce, et d’autre part de valider l’approche proposée / In high speed machining, wear resistance of the cutting tools is improved by depositing single or multilayered coatings on their surface. However, the thermomechanical loading generated at the tool-workpiece interface greatly affects the contact zones. For this purpose, several wear modes such as cracking, abrasion, adhesion and delamination of the coating can be occurred. The study of the coatings behavior and their different degradation modes lead to better understanding of their impact on the tool life and machining process under optimal conditions. In this PhD thesis work, a multi-step numerical approach has been proposed to predict wear of the coated cutting tools. This approach involves three main steps. The first is to perform a finite element simulation of the orthogonal cutting for a short time (until the loading stabilization at the tool/workpiece interface). The second step is to recover this loading and use it as an input for the XFEM/Level-set model. The latter allow to take into account the coating layers presence without any need of mesh conforming to the interfaces. As a result, the mesh distortion is avoided when the worn tool profile is updated, as well as the CPU calculation time is drastically reduced. The final step of this approach is to convert the wear rate equation into a nodal displacement, thus representing the cutting tool wear. Based on the experimental tests, a procedure for identifying tool/workpiece contact parameters, and for calibrating the wear equation for each coating layer has been proposed. Experimental trials have been also used to validate the proposed approach

abstract: A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

Ces travaux se sont attachés au développement, à l’implémentation et à la validation d’une stratégie numérique pour la simulation de l’évolution d’un endommagement localisé susceptible de conduire à l’apparition, puis à la propagation de fissures dans une structure complexe, incompressible. Nous avons abordé cet objectif général en procédant par étapes.Dans un premier temps, nous avons développé une méthodologie numérique innovante pour la propagation de fissures dans le cadre de la mécanique de la rupture fragile. Cette méthodologie a deux caractéristiques importantes : incluant l’enrichissement Heaviside de la méthode XFEM dans le cadre de modélisation Arlequin, cette méthodologie permet de ne pas remailler la structure initiale, au cours de la propagation de la fissure. Attachant un patch Arlequin local en fond de la fissure qui se propage, elle permet d’approcher, avec la précision nécessaire, le comportement local des champs mécaniques. Cette méthodologie a été implémentée et testée numériquement. Dans un deuxième temps, nous avons étendu cette méthodologie pour la prise en compte de l’endommagement par fatigue. Dans l’approche développée, l’initiation et la propagation de fissures sont pilotées par l’évolution du champ d’endommagement. Un modèle heuristique représentatif, fournissant les incréments de propagation d’une fissure à partir des champs d’endommagement et de contraintes au voisinage de sa pointe, est proposé. En utilisant des modèles physiques représentatifs des difficultés liées à la problématique d’initiation et de propagation de fissures, sous l’effet d’un endommagement par fatigue, nous avons montré, à travers des essais numériques, une faisabilité globale de notre approche. Dans un troisième temps, nous nous sommes intéressés à la prise en compte de la contrainte d’incompressibilité dans une modélisation Arlequin. L’intégration de cette contrainte pose pour la formulation Arlequin continue et/ou discrète des questions spécifiques : comment gérer la double contrainte dans la zone de couplage en continu et en discret ?, comment traiter les éléments partiellement incompressibles ? Des réponses sont données et étayées théoriquement et/ou numériquement. Enfin, nous avons proposé un ensemble de procédures pratiques, permettant d’évaluer, de manière générale et performante, une intersection de maillages tridimensionnels. Ces développements, nécessaires à la mise en œuvre opérationnelle du cadre Arlequin dans des codes industriels, sont validés par des résultats de calculs Arlequin 3D. / Résumé en anglais non disponible.

An investigation into the thermo-mechanical closure effect when a fluid leaks through a crack is presented here. The extended finite element method is the modelling scheme adopted for this, and the application of heat flux and pressure jump conditions along the crack is one of the novel contributions of this work. By modelling the fluid as one dimensional steady state and obtaining a heat transfer coefficient, it has been shown here that coupling the fluid with the structure is possible all within a single element. Convergence studies done with analytical models as a benchmark demonstrate the accuracy of the new method. Simulations are performed with the new element for conditions seen in both gas cooled and water cooled reactors. Significant crack closure is observed when the bulk fluid temperature is 20oC hotter than the structure. It was also found that the amount of closure due to crack wall heating varies depending on the external boundary conditions, this is quantified in the thesis.

The Method of Difference Potentials (DPM) has proven an efficient tool for the solution of boundary value problems (BVPs) in various fields of research including acoustics and fluid mechanics. The method converts the solution of problems of complex geometry to the multiple solutions of a simple, well defined auxiliary problem, on which efficient solvers can be used, and which also avoids the numerical computation of stiffness matrices. So far, most problems solved by the method have been considered for regular domains. Here the method is considered for the solution of Linear Elastic Fracture Mechanics (LEFM) problems. These problems contain a crack which introduces irregularities into the solution space in the form of a discontinuity across the crack boundary and a strain singularity at the crack tip. The relative ease with which the DPM can solve problems of complex geometry makes it particularly attractive for LEFM problems due to the often complex geometries of cracks and the possibility of multiple cracks. The DPM is developed here for the solution of crack problems with the aim of demonstrating the method's potential within this field. As part of this development, for the first time the DPM is combined with the Finite Element Method (FEM). In particular the Extended Finite Element Method (XFEM) is used in order to deal with the irregularities at the crack. Using a geometrical enrichment scheme for the XFEM, near-optimal convergence rates are achieved. The computation time is then significantly reduced by introducing a system of basis functions along the physical boundary of the problem. Applying the DPM with the XFEM, the discontinuity and singularity are dealt with entirely within the XFEM space, therefore avoiding the need to approximate the singularity along the physical crack boundary. With the intention of further reducing the computation time, a Fast Fourier Transform (FFT) algorithm is provided for the solution of the enriched auxiliary problem. The algorithm utilises the regular grid of the auxiliary problem to provide a potentially fast solution method. The above research was applied using Matlab. A Matlab script was written formulating the DPM and XFEM along with various interpolation functions required for the utilisation of the system of boundary basis functions. These included local spline functions and Lagrange polynomials. The FFT algorithm was also applied within Matlab. A Python script was also written for the application of a simple DPM algorithm within Code_Aster, EDF's open source finite element code for thermo-mechanical analyses. These developments are documented in two academic journal papers submitted during the course of the PhD and included in the appendix of this thesis. The Python script for the application of the method within Code_Aster is also included in the appendix.

El Método de los Elementos Finitos (MEF) se ha afianzado durante las últimas décadas como una de las técnicas numéricas más utilizadas para resolver una gran variedad de problemas en diferentes áreas de la ingeniería, como por ejemplo, el análisis estructural, análisis térmicos, de fluidos, procesos de fabricación, etc. Una de las aplicaciones donde el método resulta de mayor interés es en el análisis de problemas propios de la Mecánica de la Fractura, facilitando el estudio y evaluación de la integridad estructural de componentes mecánicos, la fiabilidad, y la detección y control de grietas. Recientemente, el desarrollo de nuevas técnicas como el Método Extendido de los Elementos Finitos (XFEM) ha permitido aumentar aún más el potencial del MEF. Dichas técnicas mejoran la descripción de problemas con singularidades, con discontinuidades, etc., mediante la adición de funciones especiales que enriquecen el espacio de la aproximación convencional de elementos finitos. Sin embargo, siempre que se aproxima un problema mediante técnicas numéricas, la solución obtenida presenta discrepancias con respecto al sistema que representa. En las técnicas basadas en la representación discreta del dominio mediante elementos finitos (MEF, XFEM, ...) interesa controlar el denominado error de discretización. En la literatura se pueden encontrar numerosas referencias a técnicas que permiten cuantificar el error en formulaciones convencionales de elementos finitos. No obstante, por ser el XFEM un método relativamente reciente, aún no se han desarrollado suficientemente las técnicas de estimación del error para aproximaciones enriquecidas de elementos finitos. El objetivo de esta Tesis es cuantificar el error de discretización cuando se utilizan aproximaciones enriquecidas del tipo XFEM para representar problemas propios de la Mecánica de la Fractura Elástico Lineal (MFEL), como es el caso del modelado de una grieta. / González Estrada, OA. (2010). Estimación y acotación del error de discretización en el modelado de grietas mediante el método extendido de los elementos finitos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/7203 / Palancia

The eXtended Finite Element Method is a partition of unity based method, particularly suitable for modelling crack propagation phenomena, without knowing a priori the crack path. Its numerical implementation is mostly achieved with stand-alone codes. The implementation of the eXtended Finite Element Method in commercial FEA softwares is still limited, and the most famous one including such capabilities is Abaqus TM. However, due to its relatively recent intro-duction, XFEM technique in Abaqus has been proved to provide trustable results only in few simple benchmark problems involving linear elastic material models.In this work, we present an assessment of the applicability of the eXtendend Finite Element Method in Abaqus, to deal with fracture mechanics problems of rubber-like materials. Results are provided for both Neo-Hookean and Arruda-Boyce material models, under plane strain conditions. In the rst part of this work, a static analysis for the pure Mode-I and for a 45o mixed-Mode load condition, whose objective has been to evaluate the ability of the XFEM technique in Abaqus, to correctly model the stress and displacement elds around a crack tip, has been performed. Outcomes from XFEM analysis with coarse meshes have been compared with the analogous ones obtained with highly re ned standard FEM discretizations. Noteworthy, despite the remarkable level of accuracy in analyzing the displacement eld at the crack tip, concerning the stress eld, the adoption of the XFEM provides no bene ts, if compared to the standard FEM formulation. The only remarkable advantage is the possibility to discretize the model without the mesh con-forming the crack geometry. Furthermore, the dynamic process of crack propagation has been analyzed by means of the XFEM. A 45o mixed-Mode and a 30o mixed-Mode load condition are analyzed. In particular, three fundamental aspects of the crack propagation phenomenon have been investigated, i.e. the instant at which a pre-existing crack starts to propagate within the body under the applied boundary conditions, the crack propagation direction and the predicted crack propagation speeds. According to the obtained results, the most inuent parameters are thought to be the elements size at the crack tip hand the applied displacement ratev. Severe diculties have been faced to attain convergence. Some reasonable motivations of the unsatisfactory convergence behaviour are proposed.

Using experimental data obtained from standard fracture test configurations, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in the fracture mechanics literature as the Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture-mechanics-based crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and a lower surface that are connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or a mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of the crack is determined by the critical energy release rate. The adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The interfacial surface material is implemented through an interface element, which is incorporated in ABAQUS using the user defined element (UEL) option. A procedure is established to formulate a rate dependent model based on experiments carried out on compact tension test specimens. The rate dependent model is incorporated into the interface element approach to capture the unstable crack growth observed in experiments under quasi-static loading conditions. The compact tension test gives the variation of the fracture toughness with the rate of loading, this information is processed and a relationship between the fracture toughness and the rate of the opening displacement is established. The cohesive-decohesive zone model is implemented through a material model to be used in an explicit code (LS-DYNA). Dynamic simulations of the standard test configurations for Mode I (Double Cantilever Beam) and Mode II (End Load Split) are carried out using the explicit code. Verification of these coupon tests leads to the crash analysis of realistic structures like the square composite tube. Analyses of bonded and unbonded square tubes are presented. These tubes shows a very uncharacteristic failure mode: the composite material disintegrates on impact, and this has been captured in the analysis. Disadvantages of the interface element approach are well documented in the literature. An alternative method, known as the Extended Finite Element Method (XFEM), is implemented here through an eight-noded quadrilateral plane strain element. The method, based on the partition-of-unity, is used to study simple test configuration like the three-point bend problem and a double cantilever beam. Functionally graded materials are also simulated and the results are compared to the experimental results available in the literature. / Ph. D.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15580号 / 工博第3292号 / 新制||工||1497(附属図書館) / 28101 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 杉浦 邦征, 教授 田村 武, 准教授 宇都宮 智昭 / 学位規則第4条第1項該当