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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.

Le but de ce travail est la caractérisation du comportement au délaminage des composites stratifiés en mode mixte I+II+III, en se focalisant en particulier sur le verrou scientifique que représente le mode III pur. Cette thèse repose sur un travail à la fois expérimental et numérique, validant numériquement les tests existants et ceux développés. La mise en perspective des résultats obtenus a permis, d'un coté, de mieux appréhender l'importance de la distribution des taux de restitution d'énergie, GI, GII et GIII, le long du front de fissure sur le la détermination de la ténacité du composite et d'un autre coté, de proposer et d'améliorer les méthodes de caractérisation. Avant d'évoquer le délaminage en mode mixte, nos efforts se sont d'abord concentrés sur la caractérisation du délaminage en mode III pur. Deux essais de type " Edge Crack Torsion " (ECT) disponibles dans la littérature ont été réalisés. La distribution de GIII le long du front de fissure a été déterminée par la méthode des éléments finis (MEF) en utilisant la technique de fermeture virtuelle de fissure (VCCT). La capacité de ces tests est compromise par : 1. La participation du mode II non nul ; 2. La forte variation de GIII près des bords de l'éprouvette. Ces problèmes rendent la détermination de la ténacité en mode III pur, GIIIC, difficile et imprécise. Par la suite, un nouveau test a été proposé, nommé "Edge Ring Crack Torsion" test (ERCT ou ERT-III). Il s'appuie sur une éprouvette possédant une fissure de front circulaire, l'absence d'extrémités sur le front de fissure permet de supprimer les effets de bords. Après l'optimisation et la modification de la géométrie du dispositif dans le test ERCT original, GIII le long du front de fissure reste presque constant avec très peu de modes parasites. La formule proposée par Tada est appliquée pour déterminer GIIIC. Il est démontré qu'en général, si la variation de GIII est faible le long du front de fissure, la ténacité déterminée par une solution " closed-form " concorde bien avec celle obtenue numériquement. En fait, la répartition de GIII peut être influencée par divers facteurs, tels que la nature des stratifiés, la géométrie du dispositif expérimental et la géométrie des éprouvettes. L'interaction de ces facteurs a été aussi abordée dans cette étude. En outre, une étude numérique de sensibilité aux défauts a permis de vérifier la robustesse de l'essai proposé vis-à-vis de différents défauts qui sont inhérent à tout travail expérimental. Enfin, une géométrie d'éprouvette optimisée est donnée avec une méthodologie permettant de réduire les fluctuations de GIII. L'utilisation de l'éprouvette ERC a été généralisée à la caractérisation du délaminage pour deux autres modes purs : l'essai de traction permet de solliciter ERC en mode I pur et celui de flexion sollicite ERC en mode II pur, nommé ERCTE ou ERC-I et ERCF ou ERC-II, respectivement. Les avantages du test ERCT sont bien conservés. La réalisation des essais ERC-I, ERC-II et ERC-III permet de mesurer la ténacité de chacun des trois modes purs sur des éprouvettes ayant la même géométrie. Finalement, nous avons étudié numériquement la faisabilité de réaliser les essais de délaminage en mode mixte I + II, I + III et I + II + III sur les éprouvettes ERC. Il s'avère que le rapport modal en mode mixte peut être obtenu dans une large gamme en faisant varier la géométrie de l'éprouvette et en combinant les modes de chargement. Aucun mode indésirable n'est présent lors des essais en mode mixte I+II ou en mode mixte I+III. Cependant la distribution de GI, GII et GIII ne sont pas complètement uniforme, mais sa variation reste assez petite. En conclusion, les tests ERC proposés dans cette étude sont prometteurs pour la caractérisation du comportement au délaminage en mode mixte des composites. Il serait possible, dans un avenir proche, de proposer un critère de délaminage en mode mixte I+II+III basé sur une étude utilisant des essais sur éprouvettes ERC. / The aim of this research work is to characterize the delamination behavior of laminate composite materials under the three pure modes and mixed modes, focusing especially on the complex issue of mode III. Both experimental and numerical works were performed, validating the existing and new testing methods. Correlation between the results obtained aims, on the one hand to better understand the distribution of strain energy release rates (GI, GII, GIII) along the crack front; on the other hand, to propose and improve testing methods, and to propose and validate simple approaches for determination of delamination toughness. Pure mode III testing methods are studied. Firstly, two kinds of Edge Crack Torsion tests were carried out, the distribution of GIII along the crack front were determined by finite element analysis (FEA) using virtual crack closure technique (VCCT). The performances of these tests are compromised by the drawbacks: (1) A participation of mode II component cannot be completely eliminated; (2) The distribution of GIII along the crack front is not uniform especially near the sides. After a study of existing tests, a novel mode III testing method was proposed, named Edge Ring Crack Torsion test (ERCT or ERC-III later). In the ERC specimen, the total absence of sides in the circular crack front leads to no edge effects. As a result, pure mode III delamination is achieved and the distribution of GIII along the crack front is quite uniform. In fact, the values of GIII along the crack front are nearly constant after optimizing and modifying the geometry of device in the original ERCT test. A closed-form solution proposed by Tada is applied to determine mode III delamination toughness. In ERCT test, the results calculated by Tada formula agree well with the ones calculated by VCCT when the distribution of GIII is relatively uniform. Actually, a numerical study shows that the distribution of GIII can be affected by different factors related to the nature of laminates tested, the geometry of test device and the geometry of the specimens. The interactive effect of above factors was also discussed in this study. In order to understand the influence of potential defaults on the performance of ERCT test, sensitivity study has been performed on the relative position of the crack front, the circularity of the crack front and the specimen shape. Optimum specimen's relative pre-crack geometry is given and a method for reducing the variation is provided. Then the application of ERC specimen was generalized to other pure delamination modes characterization. Pure mode I can be realized if ERC specimens are loaded in tension, named ERCTE or ERC-I, so can pure mode II if ERC specimens are loaded in flexion, named ERCF or ERC-II. The distribution of the strain energy release rates was also evaluated by FEA using VCCT. These tests keep most advantages of ERC-III test. Pure mode I and pure mode II delamination are achieved respectively and the distribution of GI or GII along the crack front is quite uniform. The realization of ERC-I, ERC-II and ERC-III allows to measure the toughness of each of three pure modes without any interference from geometry of specimens. Finally, we have studied numerically the feasibility to realize the delamination tests in mixed mode I+II, I+III and I+II+III by using ERC specimen. Firstly, the mixed mode ratio can be obtained in a large range by varying the geometry of the specimen and by combining loading modes. Secondly, no unwanted mode is presented for mixed mode I+II and mixed mode I+III; Thirdly, the distribution of strain energy release rates are not completely uniform but its variation is small enough to be accepted. In conclusion, ERC tests are promising testing methods for characterization of mixed mode delamination behavior. It will be possible to propose a mixed mode I+II+III delamination criterion based on the investigation by ERC tests in a close future.

An experimental evaluation of the mixed-mode fracture behavior of bonded composite joints is presented. Commonly used experimental techniques for characterizing the mode I, mixed-mode I/II, mode II, and mode III fracture behavior have been employed for the purpose of developing a fracture envelope to be utilized in the automotive design process. These techniques make use of such test geometries as the double cantilever beam (DCB), asymmetric double cantilever beam (ADCB), single-leg bend (SLB), end-loaded split (ELS), and split cantilever beam (SCB) specimens. Symmetric versions of the DCB, SLB, and ELS specimens produced mode mixities of 0°, 41°, and 90° respectively, while the testing of ADCB specimens allowed for mode mixities of 18°, 31°. Pronounced stick-slip behavior was observed for all specimen test geometries under both quasi-static and dynamic loading conditions. Due to the nature of the adhesive studied, a limited number of data points were obtained under mode I loading conditions. A significant increase in the number of measurable crack initiation events was observed for mixed-mode I/II loading conditions, where stick slip behavior was less pronounced. Additionally, a comparison of the measured fracture energies obtained under mixed-mode I/II loading conditions reveals that the addition of a small mode II component results in a decrease in the mode I fracture energy by roughly 50%, as the crack was driven to the interface between the adhesive layer and composite adherends. Furthermore, the propensity of debonds to propagate into the woven composite laminate adherends under mode II loading conditions limited the number of crack initiation points that could be obtained to one or two usable data points per specimen. A limited number of experimental tests using the SCB specimen for mode III fracture characterization, combined with a numerical analysis via finite element analysis, revealed a significant mode II contribution toward the specimen edges. Similarly, FE analyses on full bond width and half bond width SCB specimens was conducted, and results indicate that by inducing a bond width reduction of 50%, the mode II contribution is greatly decreased across the entire width of the specified crack front. To provide a means for comparison to results obtained using the standard DCB specimen, an alternative driven wedge test specimen geometry was analyzed, as this geometry provided a significant increase in the number of measurable data points under mode I loading conditions. A three-dimensional finite element analysis was conducted to establish ratios of simple beam theory results to those obtained via FEA, GSBT/GFEA, were of particular interest, as these ratios were used to establish correction factors corresponding to specific crack lengths to be used in correcting results obtained from an experimental study utilizing a driven wedge technique. Corrected results show good agreement with results obtained from traditional mode I double cantilever beam tests. Finally, bulk adhesive experiments were conducted on compact tension specimens to establish a correlation between adhesively bonded composite joint and bulk adhesive fracture behavior under mode I loading conditions. Measured fracture energy values were shown to gradually drop across a range of applied loading rates, similar to the rate-dependent behavior observed with both the DCB and driven wedge specimens. Application of the time-temperature superposition principle was explored to determine whether or not such techniques were suitable for predicting the fracture behavior of the adhesive studied herein. Good correlation was established between the fracture energy values measured and the value of tan d obtained from dynamic mechanical analysis tests conducted at corresponding reduced test rates. / Master of Science