A life prediction method is developed for spot-welds subject to fatigue loading. Stress intensity factors are used with the Walker equation to develop two crack growth approaches to the problem. The predictions fit data for lap joint configurations well, but not so for peel joint geometries. / Master of Science

Structural health monitoring (SHM) is the process of using measurements of a structure's response to known excitations and trying to determine if damage has occurred to the structure. This also fits the description of non-destructive evaluation (NDE). The main difference is that NDE takes place while the structure is out of service and SHM is intended to take place while the structure is in service. As such, SHM provides the opportunity to provide early warning against structural failure. This thesis intends to advance the state of the art in SHM by examining two approaches to SHM: vibration based and impedance based, and to associate these with the NDE method of stress intensity factors. By examining these methods the goal is to try and answer some of the important questions in SHM process. The first is to experimentally validate a crack model and to see how small of a crack can be detected by vibration methods. The second is to use the concept of stress intensity factor to perform an SHM type of measurement to determine the remaining life of a structure once the impedance method has determined that damage has occurred. The measurement system considered consists of using several different piezoceramic materials as self-sensing actuators and sensors. The structures are a simple beam and a more complex lug element used in aircraft applications. The approach suggested here is to use the impedance and vibration methods to detect crack initiation and then to use the proposed stress intensity method to measure the stress intensity factor of the structure under consideration. / Master of Science

Components of turbines, combustion chambers, multi-layered electronic packaging structures and nuclear reactors are subjected to transient thermal loads during their service life. In the presence of a discontinuity like crack or dislocation, the thermal load creates high temperature gradient, which in turn causes the stress intensification at the crack tips. If proper attention is not paid in the design and maintenance of components on this high stress in the vicinity of crack tips, it may lead to instability in the system and decrease in the service life. The concepts of thermal fracture mechanics and its major parameter called transient thermal stress intensity factors can greatly help in the assessment of stability and residual life prediction of such structures. The evaluation of thermal stress intensity factors becomes computationally difficult when the body constitutes of two different materials or is non-homogenous or made of composites. Fracture at bi-material interface is different from its homogenous counterpart because of mixed mode stress condition that prevails at the crack tip even when the geometry is symmetric and loading unidirectional. Because of this, the mode 1 and mode 2 stress intensity factors can not be decoupled to represent tension and shear stress fields as can be done in the case of homogeneous materials. Mathematically, the stress intensity factors at bi-material interfaces are complex due to oscillatory singularity that exists at the crack tip. Although plenty of literature is available for bi-material systems subjected to mechanical loads, very little information is available on problems related to thermal loads. Besides, problems related to transient thermal loads need special attention, since no thermal weight functions are available and the existing methods are computationally expensive. Therefore, the present investigation has been undertaken to develop computational and analytical approaches for obtaining the Mode 1 and Mode 2 stress intensity factors for bi-material interface crack problems using conservation of energy principle in conjunction with the weight function approach for various kinds of thermal loads. In the beginning of the studies, a method to extract the Mode 1 and Mode 2 stress intensity factors for bi-material interface crack subjected to mechanical load is proposed using the concept of Jk integrals. This is extended to thermal loads using J2 line integral and J2 domain integral. Furthermore, weight functions are analytically derived for thermal bi-material stress intensity factors and a computational scheme is developed. These methods are validated for several benchmark problems with known solutions.

Neste trabalho os problemas de determinação dos Fatores de Intensidade de Tensão KI e KII estáticos e dinâmicos são tratados numericamente utilizando uma formulação alternativa do Método dos Elementos de Contorno (MEC) com solução fundamental de Kelvin e matriz de massa para os problemas dinâmicos. A trinca é suposta retangular inicialmente, com suas faces não-coincidentes. Tanto as faces da trinca, quanto o contorno externo são discretizados em elementos de contorno reto com variação de forças de deslocamentos quadráticas, não havendo, portanto distinção entre elementos de trinca e de contorno externo. Integrais analíticas também são obtidas para o elemento linear isoparamétrico. As células de domínio apresentam formato triangular e suas integrais são solucionadas semi-analiticamente. Quanto às integrais de contorno, essas são obtidas analiticamente segundo eixos de referência locais, procedendo-se em seguida a rotação pra eixos globais. O algoritmo de Houbolt é empregado como integrador temporal. Exemplos numéricos da determinação desses Fatores de Intensidade de Tensão são mostrados e comparados com resultados analíticos e resultados numéricos disponíveis na literatura. / In this work the stress intensity factors KI and KII for static and dynamic two-dimensional problem are obtained numerically by an alternative mass matrix boundary element formulation. The crack is considered a rectangular hole inside the domain and its faces are not coincident. Both crack faces and boundary are discretized by straight boundary elements with quadratic approximation. Domain cells are triangular with linear approximation and their integrals are developed semi-analytically. Boundary integrals are analytically performed, for linear and quadratic approximations. They are performed at local co-ordinate axes and transformed to global co-ordinate axes. The Houbolt algorithm is used to integrate the matrix time differential equation along time. Numerical examples are shown in order to compare the results obtained by the proposed formulation and the ones presents in literature.

The main objective of this study is to evaluate mixed mode stress intensity factors for inclined embedded cracks in functionally graded materials. Fracture analysis of inclined cracks requires the calculation of both Mode I and Mode II stress intensity factors ( I K , II K ). In this study, k J -integral is used to calculate I K and II K . Equivalent domain integral approach is utilized to evaluate the k J - integral around the crack tip. The present study aims at developing a finite element model to study inclined crack problems in graded media under thermomechanical loading. A two dimensional finite element model is developed for inclined cracks located in a functionally graded medium. Structural and thermal problems are solved using two dimensional finite elements namely 8- noded triangles. Material properties are sampled directly at the integration points of the elements, as required by the numerical integral evaluation. The main results of the study are the stress intensity factors at the crack tip for functionally graded materials subjected to thermomechanical loading.

The main objective of this study is to examine the three-dimensional surface crack problems in orthotropic materials subjected to mechanical or thermal loading. The cracks are modeled and embedded in the orthotropic material by considering semielliptical crack front geometry. In the model special elements are embedded in the crack front region, in this way it is possible to include crack tip singular fields along the crack front. Three-dimensional finite element analyses are conducted to obtain mode I stress intensity factors. The stress intensity factor is calculated by using the displacement correlation technique. In the analysis, collapsed 20-node iso-parametric elements are utilized to simulate strain singularity around the semi-elliptical crack front. The surface crack problem is analyzed under both mechanical and thermal stresses. In the case of mechanical loading, uniform tension and fixed grip tension loading cases are applied on the model. In thermal analysis, thermal boundary conditions are defined. Comparisons of the results generated to those available in the literature verify the developed techniques.

An elastic FGM layer bonded to a semi-infinite linear elastic, isotropic, homogeneous half plane is considered. The half plane contains periodic cracks perpendicular to the interface. Mechanical loading is applied through crack surface pressure, resulting in a mode I crack problem. The plane elasticity problem described above is formulated by using Fourier transforms and Fourier series. A singular integral equation is obtained for the auxiliary variable, namely derivative of the crack surface displacement. Solution is obtained, and stress intensity factors are calculated for various values of crack period, crack length, crack location, layer thickness and material gradation.

Afin d'assurer le contrôle de son parc de production d'électricité, EDF doit maîtriser le vieillissement de ses installations pour en garantir le bon fonctionnement dans la durée. Dans ce but, il est nécessaire de disposer d’outils performants pour le modéliser et simuler la propagation des défauts dans les structures.Dans ces travaux de thèse, on s’intéresse à la propagation de fissures avec la méthode X-FEM et notamment à l’étape de localisation de la fissure par une technique de courbes de niveau. Nous avons proposé une approche fondée sur une méthode de propagation d’information de distance dite fast marching method pour rendre cette étape plus robuste. Elle est applicable à tous types de mailles,linéaires ou quadratiques.De plus, le calcul du taux de restitution d’énergie et des facteurs d’intensité de contrainte en pointe de fissure doit être suffisamment précis pour permettre de calculer la direction et l’avancée de la fissure. Dans ce but, nous avons proposé d’étudier une méthode d’intégrale de domaine pour laquelle on soulève plusieurs difficultés liées à la représentation de la fissure dans un espace tridimensionnel. Plusieurs améliorations sont proposées pour rendre les calculs plus précis et plus robustes.Dans le cas des fissures à front courbe, nous avons identifié les limites de l'utilisation des champs asymptotiques obtenus en pointe de fissure sous l'hypothèse des déformations planes comme champs auxiliaires d’une méthode d’intégrale d’interaction et nous avons proposé de nouveaux champs de déplacements auxiliaires qui prennent en compte la courbure du front de fissure. Toutes ces approches sont développées et validées dans le logiciel code_aster. / In order to ensure the control of its nuclear power plants, EDF must guarantee that they function effectively over the long term. For this purpose, it is necessary to have efficient tools tomodel and simulate crack propagation in structures. In this PhD work, we are interested in the propagation of cracks with the X-FEM method which allows using the same mesh as for a structure without default. We target especially the reconstruction of thelevel sets that characterize the position of the crack after propagation. We have proposed a fast marching method approach based on the propagation of distance information from the crack surface to the whole structure to make this step more robust in the X-FEM propagation process. It is applicable to all types of meshes, linear or quadratic. The calculation of information characteristic of thecrack status such as the energy release rate and the stress intensity factors must be accurate enough to obtain the direction and advance of the crack front ateach propagation step. For this purpose, we proposed to study a domain integral method, for which several difficulties related to the representation of the crackin a three-dimensional space are identified. Several improvements are proposed to make the calculations more accurate and more robust. In the case of curved cracks front, we have identified the limitations of using asymptotic fields obtained under the plane deformation hypothesis as auxiliary fields of an interaction integral method and we have proposed new auxiliary displacement fields that take into account the curvature of the crack front. All these methods are developed and validated with EDF software code_aster.

Original analytical theories are developed for partitioning mixed-mode fractures on rigid interfaces in laminated orthotropic double cantilever beams (DCBs) based on 2D elasticity by using some novel methods. Note that although the DCB represents a simplified case, it provides a deep understanding and predictive capability for real applications and does not restrict the analysis to a simple class of fracture problems. The developed theories are generally applicable to so-called 1D fracture consisting of opening (mode I) and shearing (mode II) action only with no tearing (mode III) action, for example, straight edge cracks, circular blisters in plates and shells, etc. A salient point of the methods is to first derive one loading condition that causes one pure fracture mode. It is conveniently called the first pure mode. Then, all other pure fracture modes can be determined by using this pure mode and the property of orthogonality between pure mode I modes and pure mode II modes. Finally, these 2D-elasticity-based pure modes are used to partition mixed-mode fractures into contributions from the mode I and mode II fracture modes by considering a mixed-mode fracture as the superposition of pure mode I and mode II fractures. The partition is made in terms of the energy release rate (ERR) or the stress intensity factor (SIF). An analytical partition theory is developed first for a DCB composed of two identical linear elastic layers. The first pure mode is obtained by introducing correction factors into the beam-theory-based mechanical conditions. The property of orthogonality is then used to determine all other pure modes in the absence of through-thickness-shear forces. To accommodate through-thickness shear forces, first two pure through-thickness-shear-force pure modes (one pure mode I and one pure mode II) are discovered by extending a Timoshenko beam partition theory. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness-ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II ERR correction factor. Both correction factors closely follow a normal distribution around a symmetric DCB geometry. The property of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a DCB with bending moments, axial forces and through-thickness shear forces. Fracture on bimaterial interfaces is an important consideration in the design and application of composite materials and structures. It has, however, proved an extremely challenging problem for many decades to obtain an analytical solution for the complex SIFs and the crack extension size-dependent ERRs, based on 2D elasticity. Such an analytical solution for a brittle interfacial crack between two dissimilar elastic layers is obtained in two stages. In the first stage the bimaterial DCB is under tip bending moments and axial forces and has a mismatch in Young s modulus; however, the Poisson s ratios of the top and bottom layers are the same. The solution is achieved by developing two types of pure fracture modes and two powerful mathematical techniques. The two types of pure fracture modes are a SIF-type and a load-type. The two mathematical techniques are a shifting technique and an orthogonal pure mode technique. In the second stage, the theory is extended to accommodate a Poisson s ratio mismatch. Equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be transformed into cases for which the analytical solution does exist. It is now possible to use a completely analytical 2D-elasticity-based theory to calculate the complex SIFs and crack extension size-dependent ERRs. The original partition theories presented have been validated by comparison with numerical simulations. Excellent agreement has been observed. Moreover, one partition theory is further extended to consider the blister test and the adhesion energy of mono- and multi-layered graphene membranes on a silicon oxide substrate. Use of the partition theory presented in this work allows the correct critical mode I and mode II adhesion energy to be obtained and all the experimentally observed behaviour is explained.

Neste trabalho os problemas de determinação dos Fatores de Intensidade de Tensão KI e KII estáticos e dinâmicos são tratados numericamente utilizando uma formulação alternativa do Método dos Elementos de Contorno (MEC) com solução fundamental de Kelvin e matriz de massa para os problemas dinâmicos. A trinca é suposta retangular inicialmente, com suas faces não-coincidentes. Tanto as faces da trinca, quanto o contorno externo são discretizados em elementos de contorno reto com variação de forças de deslocamentos quadráticas, não havendo, portanto distinção entre elementos de trinca e de contorno externo. Integrais analíticas também são obtidas para o elemento linear isoparamétrico. As células de domínio apresentam formato triangular e suas integrais são solucionadas semi-analiticamente. Quanto às integrais de contorno, essas são obtidas analiticamente segundo eixos de referência locais, procedendo-se em seguida a rotação pra eixos globais. O algoritmo de Houbolt é empregado como integrador temporal. Exemplos numéricos da determinação desses Fatores de Intensidade de Tensão são mostrados e comparados com resultados analíticos e resultados numéricos disponíveis na literatura. / In this work the stress intensity factors KI and KII for static and dynamic two-dimensional problem are obtained numerically by an alternative mass matrix boundary element formulation. The crack is considered a rectangular hole inside the domain and its faces are not coincident. Both crack faces and boundary are discretized by straight boundary elements with quadratic approximation. Domain cells are triangular with linear approximation and their integrals are developed semi-analytically. Boundary integrals are analytically performed, for linear and quadratic approximations. They are performed at local co-ordinate axes and transformed to global co-ordinate axes. The Houbolt algorithm is used to integrate the matrix time differential equation along time. Numerical examples are shown in order to compare the results obtained by the proposed formulation and the ones presents in literature.