The influence of underfill material properties on the fatigue life of Ball Grid Array (BGA) packages that are subjected to thermal cycling is investigated in this study. A finite element model is created using Ansys by assuming the existence of an infinite array of solder interconnects, cylindrical in shape, surrounded by underfill material. Axial stresses in the interconnects are determined as a temperature loading is applied. The results show that these normal stresses are on the same order of magnitude as the hydrostatic compressive stresses induced in the solder upon underfill curing. Therefore it is concluded that for the range of underfill properties tested, these Mode I cyclic stresses need to be considered in the development of a fracture-based fatigue life model. In addition, a guideline is provided to aide researchers in designing experiments that will replicate loads on fractured specimens that are consistent with those seen in aerospace applications.

Textilbeton ist ein Verbundwerkstoff aus einer Feinbetonmatrix und einer textilen Bewehrung, die aus sogenannten Rovings besteht. Nach Reißen der spröden Matrix sind diese Rovings in der Lage, die Risse in der Matrix zu überbrücken. In diesem Beitrag wird ein analytisches Modell vorgestellt, welches den Einfluss der Rovings auf das Rissverhalten erfassen kann. Die Wirkung der Fasern wird durch rissüberbrückende Spannungen approximiert. Dabei kommt unter Annahme linear elastischen Materialverhaltens das bruchmechanische Konzept der Methode der Gewichtsfunktionen zum Einsatz. Als ein spezielles Anwendungsgebiet des vorgestellten bruchmechanischen Konzeptes werden Risse im Bereich von Übergreifungen der textilen Bewehrung untersucht. Hier kann es, abhängig von der vorhandenen Übergreifungslänge, zum Auszug der Rovings kommen. Um diesen Versagensmechanismus zu verhindern, ist eine Mindestübergreifungslänge erforderlich.

An experimental technique for conducting low speed impact of adhesively bonded automotive composite joints is presented. Based on the use of a modified drop tower, mode I, II, and mixed mode values for critical energy release rate were determined for a composite/epoxy system and used to create a fracture failure envelope. Because load measurements become erratic and unreliable at higher test rates, displacement-based relationships were used to quantify these energy release rates. Displacement data was collected with an imaging system that utilized edge detection to determine displacement profiles, end displacements, and opening displacements where applicable. Because of the resolution of the image-based approach used, determining crack length experimentally was extremely difficult. As a result, numerical methods were developed to objectively determine the crack length based on the available experimental data in mode I, II, and mixed mode I/II configurations. This numerical method uses a nonlinear fit to determine mode I crack lengths and a theoretical model based on cubic equations for mode II and mixed-mode I/II, where the coefficients of the equations are determined by using both boundary and transition conditions that are a result of the test setup. A double cantilever beam (DCB) geometry was chosen to collect mode I data, an end-loaded split (ELS) geometry was used for mode II, and a single leg bend (SLB) geometry was used for mixed-mode I/II. These geometries were used to determine the fracture characteristics of adhesively bonded automotive composites to create fracture failure envelopes as well as provide mode I, II, and mixed-mode I/II data to be used in finite element models. The chosen adhesive exhibited unstable, stick-slip crack growth, which resulted in very few data points being collected from each static DCB specimen as well as drastic drops in energy release rate between initiation and arrest points. Unstable growth also created issues in dynamic testing, as data points surrounding these "stick-slip" events were lost due to the insufficient sampling rate of the available imaging system. Issues also arose with differences between thick and thin composite adherend specimens. These differences could result from additional curing in thick adherend composite specimens due to the adherends retaining heat. DSC testing was conducted on uncured adhesive using a 2, 5, and 10 minute hold at the cure temperature, and significant additional curing was observed between the two and five minute cures. Due to the difference in relative stiffness between the 12 and 36 ply composite, the local loading rate at the crack tip was lower in the 12 ply adherends, possibly allowing for a larger plastic zone and thus a higher energy release rate. As a result, tests were conducted on 36 ply composite specimens at rates of 1 mm/min and 0.1 mm/min to determine if there were loading rate effects. This testing showed that higher initiation energy relase rates were found at the lower test rate, thus reinforcing the local loading rate theory. Due to issues with plastic deformation in aluminum adherends, mode II and mixed-mode I/II data were collected using only composite adherends. Only one data point was collected per specimen as the crack propagated directly into the composite after initiating from the precrack, thus multiple tests were conducted to collect sufficient data for constructing a failure envelope. Once mode I, II and mixed-mode I/II fracture data was collected, a fracture failure envelope was created. This failure envelope, combined with a predetermined factor of safety, could provide some of the necessary tools for design with this adhesive/composite system. / Master of Science

Dans la conception et la fabrication des structures, l'assemblage des composants est une étape cruciale en termes de durabilité et de fiabilité. Les techniques l'assemblage dites mécaniques telles que le boulonnage, le rivetage et le soudage entre autres, ont longtemps été celles traditionnelles. Toutefois, les avancées dans l'étude et l'analyse de la fissuration au sein des matériaux ont permis de mettre en évidence certains de leurs inconvénients en tant que cause de rupture de ces structures à travers les concentrations de contraintes localisées et/ou l'altération mécanique ou thermique des propriétés locales des pièces assemblées. Ainsi, des techniques alternatives tel que le collage structural ont été développées permettant de s'affranchir ou plutôt de réduire ces effets indésirables lors de l'assemblage, pour le peu que le processus soit bien maîtrisé. Parmi les avantages les plus connus, le collage permet d'une part une meilleure transmission et répartition des efforts à l'interface réduisant ainsi l'endommagement en fatigue et augmentant la durée de vie de l'assemblage, et d'autre part, de conserver l'intégrité des pièces à assembler. D'autres avantages proviennent également de la conception des adhésifs structuraux qui, après l'application de traitements physico-chimiques permettent d'ajouter des propriétés thermiques, acoustiques et d'étanchéité.Malgré ces avantages, le collage souffre d'une réputation de non fiabilité due aux manques d'outils de prédiction du comportement des joints collés. En effet, les paramètres qui influent sur le comportement de l'interface sont nombreux et sont souvent sources de variabilité sur la résistance du joint de colle. L'étude de cette ténacité des joints d'adhésif s'effectue grâce à des essais de fissuration selon différents modes de rupture qui cherchent à mesurer l'énergie de fissuration de l'assemblage. La connaissance de cette énergie permet d'être prédictif dans la plupart des cas sur la propagation des fissures pour le peu que nous soyons en mesure de décrire et de prédire le comportement de l'interface.D'un point de vue numérique, de nombreuses techniques et formulations de loi de comportement ont été proposées dans un souci de reproduire le comportement de l'interface au sein des assemblages. Parmi ces dernières, celle des lois de zone cohésive semble être une voie des plus prometteuses en terme de modélisation et de simulation des interfaces par son caractère local et discret. Parmi les avantages qu'elles procurent demeurent la prise en compte intrinsèque de l'endommagement et des phénoménologies du comportement du joint collé. En outre, de nombreuses études ont été entreprises pour identifier ces lois de zone cohésive en comparant des observations issues d'essais de fissuration et des sorties de modèle où elles sont utilisées. Cette identification se fait au moyen d'algorithmes itératifs de minimisation d'une fonction coût qui mesure la métrique entre observations et sorties de modèles. Toutefois, peu d'importance est attachée d'une part, aux sensibilités des techniques de mesure employées par rapport aux paramètres de loi de zone cohésive, et d'autre part, sur les incertitudes associées aux paramètres de loi de zone cohésive identifiés. À notre connaissance, aucun travail sur ces deux derniers aspects n'a été mené et constitue ainsi le principal propos de ce mémoire de thèse. [...] / In the design and manufacture of structures, assembly of components is a crucial step in terms of durability and reliability. Mechanical assembly techniques such as bolting, riveting and welding, among others, have long been traditional. However, advances in the study and analysis of cracks within materials have made it possible to highlight some of their disadvantages as a cause of rupture of these structures through localized stress concentrations and / Mechanical or thermal alteration of the local properties of the assembled parts. Thus, alternative techniques such as structural bonding have been developed which make it possible to eliminate or rather reduce these undesirable effects during assembly, for the little that the process is well controlled. Among the best known advantages, bonding allows, on the one hand, a better transmission and distribution of forces at the interface, thus reducing fatigue damage and increasing the service life of the assembly and, on the other hand, maintain the integrity of the parts to be assembled. Other advantages also arise from the design of structural adhesives which, after the application of physicochemical treatments, make it possible to add thermal, acoustic and sealing properties.Despite these advantages, bonding suffers from a reputation for unreliability due to the lack of tools for predicting the behavior of bonded joints. Indeed, the parameters which influence the interface behavior are numerous and are often sources of variability on the strength of the bonded joint. The study of this toughness of the adhesive joints is carried out by means of crack tests according to different modes of fracture which seek to measure the assembly crack energy. The knowledge of this energy makes it possible to be predictive in most cases on cracks propagation for the little that we are able to describe and predict the interface behavior.From a numerical point of view, numerous techniques and formulations of interface law have been proposed in order to reproduce the interface behavior within the assemblies. Among the latter, that of the cohesive zone laws seems to be one of the most promising ways in terms of modeling and simulation of the interfaces by its local and discrete character. Among the advantages that they provide are the intrinsic consideration of damage and behavior phenomenologies of bonded joint. In addition, numerous studies have been undertaken to identify these cohesive zone laws by comparing observations from crack tests and model outputs where they are used. This identification is done by means of iterative minimization algorithms of a cost function which measures the metric between observations and models outputs. However, little importance is attached, on the one hand, to the sensitivities of the measurement techniques used in relation to the cohesive zone law parameters and, on the other hand, to the uncertainties associated with the identified cohesive zone law parameters. To our knowledge, no work on these two aspects has been conducted and is thus the main purpose of this thesis. [...]

L’objectif de ce travail de thèse est d’envisager les apports de l’Emission Acoustique (EA) en tant qu’outil de diagnostic et de surveillance des structures et ouvrages en bois. Nous avons appliqué cet outil et développé des méthodes de suivi de la fissuration. Si l’objectif affiché est l’utilisation de l’EA pour de la surveillance in-situ, un passage par des manipulations en laboratoire a été nécessaire pour valider les méthodes mises en œuvre. Des essais de chargement à déplacement imposé ont été réalisés sur des éprouvettes de Douglas (DCB à inertie constante) soumises à un chargement en mode I, pour deux teneurs en eaux distinctes. En parallèle du système d’acquisition acoustique, un système d’acquisition d’images a été utilisé pour suivre l’évolution de la fissuration sur les faces principales des éprouvettes.Dans un premier temps, nous avons constaté que la cinétique de fissuration était corrélée à l’énergie acoustique des signaux enregistrés. Une écoute globale, sans filtration des données, fournit une indication sur l’évolution de l’endommagement d’une structure.En effectuant un premier traitement des données, en considérant les évènements acoustiques et en utilisant des courbes de correction de localisation et d’amplitude des signaux, nous avons pu déterminer la position d’un (ou plusieurs) pic(s) d’activité acoustique. La courbe d’évolution de la position de ce(s) pic(s) d’activité donne un résultat similaire à celle de la pointe de fissure obtenue avec le système d’imagerie. Nous avons ainsi pu estimer un taux de restitution d’énergie moyen Gc. Dans le but de passer à des applications in situ, nous avons mis en œuvre cette méthode lors d’un essai de fluage sur une éprouvette à inertie variable. L’EA a su prendre le relais lorsque les relevés visuels étaient absents. L’EA a aussi pu fournir des informations complémentaires sur l’initiation et la propagation de la fissuration et ce, sur une durée surveillance longue.La méthode de détection des pics d’activités par EA montre que les évènements acoustiques de forte amplitude sont localisés de part et d’autre de la pointe de fissure obtenue par imagerie. Dans un deuxième temps, en effectuant un parallèle avec les méthodes développées dans les matériaux composites, le bois pouvant y être assimilé par certains aspects, nous avons pu, par une utilisation conjointe des outils statistiques, de l’imagerie électronique (MEB) et de l’analyse des formes d’ondes, identifier les mécanismes de ruine présents lors des essais.Après un travail de filtration des données obtenues sur des essais à mode de ruine choisi (traction, flexion et cisaillement), quatre familles d’évènements ont pu être mis en évidence. Par l’étude de leurs formes d’ondes respectives, ces familles ont pu être associées à de la rupture de fibre, de la fissuration de matrice, de la décohésion et du délaminage telles qu’on les retrouve dans les matériaux composites. L’étude au MEB a confirmé qu’une multitude de mécanismes étaient présents sur les plans de fissuration des éprouvettes et la vraisemblance des résultats obtenus.D’un point de vue quantitatif, deux mécanismes de ruine principaux ressortent : la rupture de fibres et la fissuration matricielle. Il s’agit là d’indicateurs dont l’évolution peut constituer un indicateur, précurseur à la ruine d’un ouvrage. Le travail effectué dans cette thèse constitue un pas dans l’emploi de l’EA dans la surveillance des structures et des ouvrages en bois et laisse entrevoir d’autres emplois notamment en mécanique de la rupture et dans l’étude des zones d’élaboration. / The aim of this thesis is to consider what Acoustic Emission (AE) can provide as a tool for diagnosis and assessment of wood structures and works. We applied this tool and developed methods for tracking crack propagation. If our intention is using AE for the in-situ monitoring, we have to do experiments in laboratory to validate the methods developped. Loading tests under imposed displacement were conducted on Douglas samples (DCB constant inertia) subjected to a loading in mode I, for two levels of moisture content. In tandem of the acoustic emission emission system, an image acquisition system was used to record crack propagation on the main faces of the samples.First, we showed that the cracking kinetics correlates with the acoustic energy of the recorded signals. A global analysis, with unfiltered data, provides a good indication of the evolution of the damage within a structure. Then by performing a first data processing, by taking into account the acoustic events and by using correction curves of localization and amplitude, we were able to determine the position of one (or more) peak(s) of acoustic activity. The evolution curve of the position of this (these) peak(s) of activity gives a result similar of the crack tip evolution obtained with the digital image acquisition system. By this way we were able to estimate an average restoration level of critical energy Gc. In the purpose of making in situ applications, we have implemented this method during a creep test on a specimen with variable inertia. A previously loaded sample was placed to a relative humidity variation - from a humid atmosphere to a dry atmosphere. Only spot measurements of the crack tip position has been made. AE was able to take over when visual statements were absent. AE was also able to provide additional information on the initiation and propagation of cracks over a long term monitoring. The method for detecting peaks of activities by AE shows that acoustic events with high amplitude are located on both side of the crack tip obtained by imaging.Secondly, by comparing with the methods developed in composite materials, wood could be considered as such, we were able, by joint use of statistical tools, electronic imaging (SEM) and analysis of waveforms, to identify failure mechanisms which were present during testing. After processing data obtained on failure specific mode test (tensile, bending and shear), four clusters of events have been highlighted. By studying their respective waveforms and signal caracteristics, these families have been associated with the rupture of fiber, matrix cracking, debonding and delamination such as those found in composites. The study of SEM images made from owr samples has confirmed the presence of a multitude of mechanisms on the cracking path of the wood samples. This confirms the reasonableness of results obtained. From a quantitative perspective, two major failure mechanisms stand out: the breaking of fibers and matrix cracking. The evolution of these indicators may be a precursor to the ruin of a structure.The work undertaken in this thesis is a step in the use of AE in monitoring structures and wooden structures. It suggests other purposes for the use of AE in wood. We could imaging using AE in order to study the process zones by using mTDCB samples.

Textilbeton ist ein Verbundwerkstoff aus einer Feinbetonmatrix und einer textilen Bewehrung, die aus sogenannten Rovings besteht. Nach Reißen der spröden Matrix sind diese Rovings in der Lage, die Risse in der Matrix zu überbrücken. In diesem Beitrag wird ein analytisches Modell vorgestellt, welches den Einfluss der Rovings auf das Rissverhalten erfassen kann. Die Wirkung der Fasern wird durch rissüberbrückende Spannungen approximiert. Dabei kommt unter Annahme linear elastischen Materialverhaltens das bruchmechanische Konzept der Methode der Gewichtsfunktionen zum Einsatz. Als ein spezielles Anwendungsgebiet des vorgestellten bruchmechanischen Konzeptes werden Risse im Bereich von Übergreifungen der textilen Bewehrung untersucht. Hier kann es, abhängig von der vorhandenen Übergreifungslänge, zum Auszug der Rovings kommen. Um diesen Versagensmechanismus zu verhindern, ist eine Mindestübergreifungslänge erforderlich.

In packaging industries, the demand for usage of Low Density Poly Ethylene foil is of profound interest. In the past, research was carried out on finite and infinite plates with varying crack lengths but having constant crack width. In this thesis, a detailed analysis on crack initiation is carried out on finite plates by varying width of the hole. The hole shapes for stress analysis include circle, ellipse and rectangular notch. Initially, maximum stress is found out using Linear Elastic Fracture Mechanics (LEFM) theory and compared with Finite element method (FEM) results. Secondly using Elastic Plastic Fracture Mechanics theory (EPFM), critical stress and geometric function are evaluated theoretically by Modified Strip Yield Model (MSYM) and numerically by ABAQUS. Finally, a tensile test is conducted to validate the theoretical and numerical results.  By varying the width of the hole, a study on the parameters like critical stress, geometric function is presented. A conclusion is drawn that the effect of hole width should be considered when calculating fracture parameters.

Multilayer composite materials have a high tendency to interlaminar delamination when they are subjected to out-of-plane loading, because of their low-stiffness in the through-thickness (T-T) direction. The main aim of this research was to improve the interlaminar fracture toughness (IFT) of textile composites by using stitching as a T-T reinforcement technique. The intention was to provide greater delamination resistance and also to enhance the interlaminar fracture toughness between adjacent layers. In this research, E-glass 2x2 twill weave structure fabric layers and an epoxy resin were chosen as the base materials. Three different types of stitching; including the commonly-used modified lock-stitch and orthogonal-stitch (OS) geometries, the single-yarn orthogonal-stitch (SOS) and a newly-developed double-yarn orthogonal-stitch (DOS), as well as five different stitch densities were used to reinforce the multilayer preform lay-ups. The resin infusion moulding method was used to manufacture the E-glass/Epoxy 3D textile composites. The effect of stitched reinforcement on the Mode I-IFT mechanism was examined by performing double cantilever beam (DCB) tests and the Mode II-IFT mechanism by performing four-point bend end-notched flexure (4ENF) tests, respectively. Optical microscopy and scanning electron microscopy (SEM) imaging techniques were used to study the fracture surfaces of the stitched composite specimens, to assess the improvement in IFT mechanisms imparted by the stitched reinforcement used. The effect of stitching was analysed by comparing the various stitching geometries, stitch densities and the mechanical properties highlighted by the Mode I-IFT and Mode II-IFT results. It was found that the use of the novel double-yarn orthogonal-stitch (DOS) reinforcement allied with the use of high stitch densities gave the greatest improvement on both Mode I-IFT and Mode II-IFT tests. Moreover, in every case, the use of DOS and high stitch densities gave a significant improvement of 74.5% in Mode I-IFT and 18.3% for Mode II-IFT tests when compared with unstitched samples. It has been shown that the novel DOS stitch geometry yields significant benefits over established stitching techniques in respect of stitched reinforcement for laminated composite preforms. Besides this, the double column 5x5 mm stitch pattern reveals the highest delamination resistance performance among all the stitching formations tested for Mode I-IFT and II-IFT.

La motivació de la tesis deriva en el interès de la indústria aeronàutica a explotar, per mitjà d'un disseny adaptat, la utilització del gir d'esquerda per protegir els reforços situats davant una esquerda que s'està propagant en la xapa d'una estructura integral. L'objectiu principal és l'avaluació i predicció del gir d'esquerda en situacions de càrrega pròximes a Mode I, proporcionant una eina de modelització i un criteri confident. L'entorn industrial sota el qual s'ha realitzat aquest treball requereix una predicció ràpida del comportament estructural proporcionant informació útil als constructors. Per aquest motiu la predicció del gir d'esquerda s'ha investigat utilitzant la teoria linear elàstica de la mecànica de la fractura (LEFM) i l'anàlisi amb elements finits (FEA).Durant aquest treball s'ha demostrat la importància i necessitat de caracteritzar el camp de tensions a la punta de l'esquerda amb el factor d'intensitat de tensió (SIF) conjuntament amb un segon paràmetre. La tensió uniforme, no singular, normal a la línea de l'esquerda i dependent en la geometria i càrrega de la proveta, es a dir la tensió T, ha estat seleccionada com a segon paràmetre per dur a terme les prediccions del gir d'esquerda.El criteri més desenvolupat per predir el gir d'esquerda en situacions pròximes a Mode I és el proposat per Buczek, Herakovich, Boone et al., anomenat WEFO en la tesis. Aquest combina el criteri de tensió principal màxima amb la tensió T i considera efectes d'anisotropia. LEFM s'ha utilitzat també en la predicció del gir d'esquerda sota càrregues quasi estàtiques controlant en tot moment la plastificació del lligament.En la investigació d'eines de modelització/simulació s'ha tingut en compte les capacitats d'aquestes en el camp de la mecànica de la fractura, de disseny, d'implementació, així com la complexitat d'ús. Tot i que hi ha un gran ventall de Softwares que compleixen els requeriments assenyalats, només aquells que es trobaven a l'abast de l'autor s'han analitzat. StressCheck ha estat escollit com a resultat de la investigació. L'avaluació de la propagació de l'esquerda en provetes compactes en tensió (CT) i en provetes amb dos elements reforçants (2SP) sota els règims de Paris i Forman ha estat satisfactòria.Un pas important ha estat la implementació de la capacitat d'extracció de la tensió T. La demostració de la fiabilitat en el seu càlcul s'ha demostrat mitjançant resultats en la literatura i càlculs analítics en provetes de doble biga en volada (DCB). Un aspecte a tenir en compte és la importància en realitzar anàlisis no linears geomètrics pel càlcul del SIF i la tensió T.Prediccions en la trajectòria de l'esquerda s'han realitzat en base amb els resultats obtinguts en l'estudi de modelització. La millor trajectòria s'ha predit per mitjà del criteri WEFO. No obstant, les diferents trajectòries obtingudes per una esquerda propagant-se en la direcció T-L o L-T no són comparables amb els resultats experimentals.Aquestes deficiències estan relacionades en la definició del punt d'inestabilitat de l'esquerda. Algunes referències posen de manifest que hi ha experiències on l'esquerda es comporta de forma estable tot i mostrar T > 0. Per un altre banda, els criteris WEF i WEFO defineixen la inestabilitat dependent d'una distancia específica del material, rc. Però la seva definició no és única i no existeix cap acord sobre el seu càlcul.L'autor proposa un criteri derivat dels criteris existents i basant-se en els assajos, simulacions i resultats obtinguts. Aquest deriva del treball de Pettit i la tensió T normalitzada, TR, proposada per Pook. La fiabilitat d'aquest criteri es demostra amb la proveta DCB. Les prediccions de la trajectòria de l'esquerda en la proveta cruciforme no són tant satisfactòries. Tot i així, s'ha d'accentuar que el criteri desenvolupat proporciona la predicció més acurada. / The motivation of this thesis started from the interest of aeronautical industry to exploit the utilization of crack turning to protect stiffeners in front of an approaching skin-crack in integral structures by a tailored design. The main objective was to assess and predict crack turning under nearly Mode I situations on structures that reproduce aeronautical conditions by providing a modelling tool and a reliable criterion. The industrial environmental in which this work has been carried out requires a fast prediction of the structural behaviour to provide useful inputs to aircraft designers. It is for this reason that the crack turning prediction was investigated by means of LEFM and FEA. During this work it has been shown the importance and necessity of a second parameter for the characterisation of the stress field at the crack tip besides the SIF. Among the different proposed second parameters, the uniform non-singular stress, normal to the crack line and dependent on the type of loading and specimen geometry, i.e. the T-stress, was selected for crack turning predictions due to both calculation simplicity and its independence of the crack tip distance. The most developed criterion for crack turning predictions near Mode I loading is the criterion proposed by Buczek, Herakovich and Boone et al., called the WEFO-criterion. This is the Maximal Principal Stress criterion implemented with the T-stress and taking into account anisotropic effects. A challenge of this thesis was to overcome the lack of prediction on crack turning provided by this last criterion.Although the validity of LEFM is restricted, it was applied for the prediction of crack turning for quasi-static loading while paying attention to possible plastification. A screening of existent commercial and non commercial tools was carried out in respect to their fracture mechanics capabilities, their design abilities, implementation as well as their complexity. Although, there are many software possibilities, only those within the reach of the author were evaluated. This resulted in the selection of the commercial tool StressCheck®. The assessment of crack propagation on compact tension and two stringer specimens governed by the Paris and Forman regimes was satisfactory compared with experimental results using the material data from simple standard specimens.An important step was the implementation of the T-stress extraction facility in the tool and the evidence of its reliability. The latter was proved by literature and analytical calculations on DCB specimens. An important finding was the importance to perform geometric non-linear analyses for computing SIF and T-stress to find values comparable with literature data and analytical calculations. Taking into account the results obtained on the modelling study, crack path predictions were performed. The best prediction by means of existing criteria was reached by the WEFO-criterion. Different crack paths were predicted for a crack propagating in T-L or L-T directions. However, these predictions were not satisfactorily reliable: the point in the crack path where crack turning should take place was not predicted adequately. Additionally, the crack paths were similar for T L and L-T directions. These deficiencies are related with the definition of the crack path instability. Some literature results have shown that in some experiences the crack behaved in a stable manner even if T > 0. Moreover, WEF and WEFO criteria define crack instability to be related with a material specific distance, rc, but, there is no agreement about its definition. Based on tests, simulation results and observations noted during this work, a compilation criterion was proposed. This is based on the work of Pettit and the normalised T-stress, TR, proposed by Pook. Its reliability was successfully proved on the DCB. The crack path predictions on the CFS were not as satisfactory. But even at its worst the developed criterion was the most accurate.

In systems subjected to long-term loading, subcritical crack growth is the principal mechanism causing the time-dependent deformation and failure of rocks. Subcritical crack growth is environmentally-assisted crack growth, which can allow cracks to grow over a long period of time at stresses far smaller than their failure strength and at tectonic strain rates. The characteristics of subcritical crack growth can be described by a relationship between the stress intensity factor and the crack velocity. This study presents the results of studies conducted to validate the constant stress-rate test for determining subcritical crack growth parameters in Coconino sandstone, compared with the conventional testing method, the double torsion test. The results of the constant stress-rate test are in good agreement with the results of double torsion test. More importantly, the stress-rate tests can determine the parameter A with a much smaller standard deviation than the double torsion test. Thus the constant stress-rate test seems to be both a valid and preferred test method for determining the subcritical crack growth parameters in rocks. We investigated statistical aspects of the constant stress-rate test. The effects of the number of tests conducted on the subcritical crack growth parameters were examined and minimum specimen numbers were determined. The mean and standard deviation of the subcritical crack growth parameters were obtained by randomly selecting subsets from the original strength data. In addition, the distribution form of the subcritical crack growth parameters and the relation between the parameter n and A were determined. We extended the constant stress-rate test technique to modes II and III subcritical crack growth in rocks. The experimental results of the modes I, II and III tests show that the values of the subcritical crack growth parameters are similar to each other. The subcritical crack growth parameter n value for Coconino sandstone has the range of 34 to 38 and the parameter A has the range of 1.02x10⁻² to 6.52x10⁻² m/s. The effect of confining stress, specimen size, and water saturation on subcritical crack growth under mode II loading has also been investigated. Finally strength parameters for Coconino sandstone were determined experimentally, including tensile strength, uniaxial compressive strength, cohesion, internal friction angle, in-plane / our-of-plane shear strength and the fracture toughness under mode I, II, and III loading.