Análisis experimental y por el método de los elementos finitos del estado de tensiones en uniones carpinteras de empalme de llave

In this research, the halved and tabled traditional timber scarf joint is analyzed. This joint consists in two end joint pieces usually subjected to tension. Initially, the study is discussed from an experimental point of view. In this way, 3 critical cross-sections are established (section of the notch, section of the horizontal plane and reduced section) and mechanical tests are performed to achieve the failure on each of critical sections by changing the geometry of the joint. The study is completed by developing a finite element model which allows verify experimental results and extend the analysis to other geometries. This model has to simulate the real behavior of the material which is being studied, so mechanical tests are performed to obtain the elastic constants and the coefficients of friction of the material. In the reduced section, an abrupt decrease of the effective cross-section takes place, and this effect is also experimentally analyzed. These tests indicate that a crack is initiated before the bending-tension failure occurs in the reduced section. The test material consists of wood of Pinus sylvestris L. coming from the “Valsaín´s Sawmill” (Segovia) with “premium quality” according to the nonstructural wood visual classification of sawmill. It is observed that initiation of a crack, in the mortise (bottom of reduced section), and shear stress concentration, at the initial part of the heel (beginning of horizontal plane), completely determine the mechanical behaviour of the joint, resulting in 3 failure modes: local compression failure in the section of the notch, shear failure in the horizontal plane, and failure of stresses concentration, mainly perpendicular to the grain tension, at the bottom of reduced section. The geometric optimization is obtained for halved and tabled traditional scarf joint, when the joint has made with similar properties of wood than tested specimens, for any height and width of the cross-section. It is considered the failure due to the initiation of a crack in reduced section, by applying a correction coefficient into the usual equation used to design the members subjected to both tension and bending. Therefore, it is possible to obtain, analytically, the design conditions to be met of the 3 critical cross-sections. According to the theoretical optimization, the tension strength of complete cross-section is reduced until 14%, when using this type of joint. The experimental optimization indicates even a greater reduction, until 6%. En el presente trabajo de investigación se analiza el comportamiento mecánico de las uniones tradicionales de empalme de llave, que consisten en dos piezas unidas por sus testas transmitiéndose entre ellas principalmente un esfuerzo de tracción. Inicialmente, el estudio se aborda desde un punto de vista experimental. De este modo, se establecen las 3 secciones críticas o de estudio (sección del encaje, sección rasante del cogote y sección reducida) y se realizan ensayos mecánicos, variando la geometría de la unión, para alcanzar la rotura en cada una de ellas. Se completa el estudio mediante la elaboración de un modelo por elementos finitos que permite verificar los resultados experimentales y ampliar el análisis a otras geometrías. Este modelo debe simular el comportamiento real del material objeto de estudio, por lo que se realizan ensayos para obtener las constantes elásticas y los coeficientes de rozamiento del mismo. También se analiza, experimentalmente, el efecto entalladura que reduce bruscamente la sección completa del tirante, estableciendo que el fallo por flexotracción en la sección reducida de la pieza, no llega a producirse por el inicio previo de una grieta. El material de ensayo consiste en madera de Pinus sylvestris L. (pino silvestre) procedente del Aserradero de Valsaín (Segovia) y de calidad “Extra” o “Primera” según la clasificación visual no estructural del aserradero. Se observa que el inicio de una grieta en la mortaja del rediente y la concentración de tensiones tangenciales en la parte inicial del cogote, determinan completamente el comportamiento mecánico de la unión, dando lugar a 3 modos distintos de rotura: fallo por compresión en la sección del encaje, fallo por cortante en la sección rasante y fallo por concentración de tensiones, principalmente tracciones perpendiculares, en el rebaje de la sección reducida. Se consigue optimizar geométricamente cualquier empalme de llave confeccionado con madera de características similares a la ensayada, para cualquier valor de la altura y de la anchura de la sección. Se considera el agotamiento en la sección reducida causado por el inicio de grieta, mediante la aplicación de un coeficiente corrector en la expresión habitual de agotamiento por flexotracción, en consecuencia, finalmente es posible obtener, de modo analítico, un valor del índice de agotamiento en cada una de las 3 secciones de estudio. La optimización teórica del empalme de llave indica que la capacidad resistente del tirante bruto se reduce al 14%, cuando se coloca este tipo de unión tradicional. Experimentalmente se obtiene, que, para la sección ensayada, la capacidad resistente del tirante bruto se reduce todavía más, llegando al 6%.

Comportamiento a fatiga por cortante de elementos lineales de hormigón armado sin cercos

Las estructuras de hormigón son susceptibles de sufrir los efectos asociados a las acciones de fatiga cuando estas se ven sometidas a un elevado número de cargas repetidas. Muchas de estas estructuras no requieren armadura transversal para cumplir los condicionantes de dimensionamiento estático como por ejemplo las losas superiores de tableros de puentes, los muros de contención, las losas de transición de puentes, las torres eólicas o las estructuras marítimas. La mayor parte de los códigos de diseño vigentes no incluyen una comprobación específica del nivel de seguridad a cortante de estas estructuras para acciones de fatiga, y aquellas que lo hacen prefieren utilizar expresiones de tipo empírico basadas en curvas S-N que relacionan el número de ciclos resistentes con el valor de la carga aplicada. A pesar de que el empleo de curvas S-N es de gran utilidad desde un punto de vista práctico, estas curvas no permiten comprender el proceso de rotura por cortante para cargas repetidas. El objetivo principal de esta Tesis es el de estudiar el comportamiento a cortante de elementos de hormigón armado sin cercos sometidos a fatiga. Además, el análisis es ampliado al estudio del comportamiento transversal de los voladizos de las losas superiores de tableros de puentes de hormigón que de forma habitual son diseñados sin armadura de cortante. De forma habitual estos elementos se diseñan atendiendo a criterios de dimensionamiento estáticos sin tener en cuenta la resistencia a cortante cuando se ven sometidos a cargas cíclicas. A pesar de que las cargas de fatiga son inferiores a aquellas que producen el fallo estático, es importante tener en cuenta el comportamiento de estos elementos ante cargas repetidas. Los trabajos experimentales existentes en vigas de hormigón armado sin cercos evidenciaron diferencias significativas entre los modos de fallo ante cargas estáticas y cíclicas. Estos trabajos llegaron a la conclusión de que estos elementos diseñados para tener un fallo dúctil por flexión pueden llegar a desarrollar un tipo de fallo frágil por cortante cuando se ven sometidos a cargas repetidas. El proceso de rotura por cortante en elementos de hormigón armado sin cercos sometidos a fatiga es un proceso complejo que debe ser estudiado en profundidad debido al carácter frágil de este tipo de fallo. Los trabajos experimentales permitieron comprobar que el origen de este fallo tiene lugar tras la formación de una fisura de cortante a partir de una fisura de flexión formada durante los primeros ciclos en el vano de cortante. Tras la formación de esta fisura, esta se va propagando hacia la cabeza de compresión hasta que finalmente se produce el fallo como consecuencia de la destrucción de la cabeza de compresión cuando la altura alcanzada por esta es insuficiente para resistir la fuerza de compresión aplicada en esta zona. Por otra parte, la propagación de esta fisura diagonal puede desarrollarse por completo en el instante en el que esta se forma derivando en un tipo de fallo por cortante más frágil que el anterior. El proceso de fatiga es estudiado en esta Tesis mediante un modelo mecánico. Por una parte, se propone un modelo predictivo para determinar el número de ciclos acumulados hasta que se forma la fisura diagonal en función del estado tensional que se tiene en la punta de una fisura crítica de flexión formada en los primeros ciclos. Por otra parte, la resistencia a fatiga tras la formación de la fisura diagonal se analiza teniendo en cuenta el daño por fatiga acumulado en la cabeza de compresión y las variables que afectan a la propagación de esta fisura de cortante. Para la evaluación de la resistencia a fatiga tras la formación de la fisura crítica de cortante en este tipo de elementos, se plantea un modelo teórico basado en conceptos de Mecánica de la Fractura adaptados al hormigón. Este modelo puede ser aplicado a vigas de hormigón armado sin cercos de canto constante o variable siguiendo diferentes procedimientos. Una campaña experimental ha sido llevada a cabo con el objetivo de estudiar el comportamiento a cortante de vigas de hormigón armado sin cercos de canto variable sometidas a cargas estáticas y de fatiga. Se han desarrollado un total de diez ensayos estáticos y de fatiga para diferentes niveles de carga y esbelteces de cortante, teniendo lugar diferentes modos de fallo. Estos elementos fueron diseñados para reproducir, a escala real y de forma simplificada, los voladizos laterales de las losas superiores de tableros de puentes de carretera de hormigón. Los resultados experimentales demostraron que el tipo de fallo desarrollado depende de varios parámetros como por ejemplo el nivel de carga máxima, el nivel de oscilación de tensiones en la armadura longitudinal, la esbeltez de cortante o la calidad del hormigón utilizado entre otros. Para valores similares de esbeltez de cortante, los ensayos de fatiga realizados permitieron comprobar que la rotura por cortante de estos elementos está asociada a niveles de carga máxima elevados, mientras que el fallo por fatiga de la armadura longitudinal tiene mayor probabilidad de ocurrir en elementos sometidos a elevados niveles de oscilación de tensiones en esta armadura. Además, estos ensayos han sido analizados a través del modelo propuesto para tratar de comprender el comportamiento resistente de estos elementos sometidos a cargas de fatiga. Concrete structures are able to suffer fatigue when they are subjected to high number of cyclic loads. Many of these need not shear reinforcement to satisfy static design requirements, such as bridge deck slabs, retaining walls, bridge approach slabs, wind towers or maritime structures among others. Many codes of practice do not include a verification of the shear fatigue safety. Moreover, those which include it still prefer empirical S-N-based approaches that provide the number of cycles as a function of applied forces. S-N models are practical but they do not provide information to understand the shear fatigue process. The main objective of this Thesis is to study shear behaviour of reinforced concrete elements without stirrups subjected to fatigue loads. In addition, the analysis is extended in order to study the transverse behaviour of cantilever slabs of concrete bridges that traditionally are designed without shear reinforcement. These elements usually are designed on the basis of static strength and it is unusual that codes consider fatigue strength of concrete in shear. Accordingly, it is important to take into account the fatigue behaviour of structural members subjected to cyclic loads although these loads are lower than those which produce the static failure. Existing experimental works show important differences between the static and cyclic failure modes of reinforced concrete beams without stirrups. These works concluded that beams without transverse reinforcement, designed to have a ductile failure mode in flexure, can submit a brittle shear failure mode when they are subjected to repeated loads. Shear fatigue failure of reinforced concrete beams without stirrups is a rather complex process from the mechanical viewpoint. Since it leads to a brittle failure mode it should be better understood. Experimental evidence indicates that a diagonal crack first develops from the inclination of flexural cracks in the shear span. Thereafter, the diagonal crack propagates into the compression zone. Failure normally takes place by the destruction of the compression zone when its depth is too small to resist the applied force. The propagation of the diagonal crack can also be instantaneous, leading to sudden diagonal cracking fatigue failure rather than shear-compression failure. Fatigue process is studied in this Thesis on a mechanical basis. On the one hand, a predictive model is derived to obtain the number of cycles up to diagonal cracking, as a function of the stress state at the tip of a critical flexural crack. On the other hand, the residual fatigue strength after diagonal cracking is analyzed taking into account the fatigue damage accumulated by the compression zone and the variables affecting the propagation of the diagonal crack. In order to assess the residual fatigue strength after diagonal cracking of such elements, a theoretical model is proposed based on concepts from fracture mechanics adapted to concrete. This model can be successfully applied for straight or haunched reinforced concrete beams without stirrups following different procedures. In order to achieve a more advanced knowledge in this subject, an experimental campaign has been carried out with the aim of study the shear behaviour of reinforced concrete haunched beams without stirrups subjected to static and fatigue loads. A total of ten static and fatigue tests have been performed with distinct load levels and shear span-to-depth ratios, presenting different failures modes. These elements were designed to reproduce in a simplified form the cantilever slab of concrete bridges at real scale. Experimental results showed that the type of failure depends on several parameters as for example the maximum load level, the stress oscillation level on the longitudinal reinforcement, the shear span-to-depth ratio or the quality of the concrete used among others. For a similar value of the shear span-to-depth ratio, tests evidenced that shear fatigue failure is related to high maximum load levels, while steel fatigue failure is easier to occur in elements subjected to high stress oscillation level on the reinforcement bars. Besides, these tests have been analyzed through the proposed model in order to clarify the structural behaviour of such elements subjected to fatigue loads.

Estimación de la resistencia de estructuras de hormigón armado reforzadas a cortante mediante FRP

El empleo de refuerzos de FRP en vigas de hormigón armado es cada vez más frecuente por sus numerosas ventajas frente a otros métodos más tradicionales. Durante los últimos años, la técnica FRP-NSM, consistente en introducir barras de FRP sobre el recubrimiento de una viga de hormigón, se ha posicionado como uno de los mejores métodos de refuerzo y rehabilitación de estructuras de hormigón armado, tanto por su facilidad de montaje y mantenimiento, como por su rendimiento para aumentar la capacidad resistente de dichas estructuras. Si bien el refuerzo a flexión ha sido ampliamente desarrollado y estudiado hasta la fecha, no sucede lo mismo con el refuerzo a cortante, debido principalmente a su gran complejidad. Sin embargo, se debería dedicar más estudio a este tipo de refuerzo si se pretenden conservar los criterios de diseño en estructuras de hormigón armado, los cuales están basados en evitar el fallo a cortante por sus consecuencias catastróficas Esta ausencia de información y de normativa es la que justifica esta tesis doctoral. En este pro-yecto se van a desarrollar dos metodologías alternativas, que permiten estimar la capacidad resistente de vigas de hormigón armado, reforzadas a cortante mediante la técnica FRP-NSM. El primer método aplicado consiste en la implementación de una red neuronal artificial capaz de predecir adecuadamente la resistencia a cortante de vigas reforzadas con este método a partir de experimentos anteriores. Asimismo, a partir de la red se han llevado a cabo algunos estudios a fin de comprender mejor la influencia real de algunos parámetros de la viga y del refuerzo sobre la resistencia a cortante con el propósito de lograr diseños más seguros de este tipo de refuerzo. Una configuración óptima de la red requiere discriminar adecuadamente de entre los numerosos parámetros (geométricos y de material) que pueden influir en el compor-tamiento resistente de la viga, para lo cual se han llevado a cabo diversos estudios y pruebas. Mediante el segundo método, se desarrolla una ecuación de proyecto que permite, de forma sencilla, estimar la capacidad de vigas reforzadas a cortante con FRP-NSM, la cual podría ser propuesta para las principales guías de diseño. Para alcanzar este objetivo, se plantea un pro-blema de optimización multiobjetivo a partir de resultados de ensayos experimentales llevados a cabo sobre vigas de hormigón armado con y sin refuerzo de FRP. El problema multiobjetivo se resuelve mediante algoritmos genéticos, en concreto el algoritmo NSGA-II, por ser más apropiado para problemas con varias funciones objetivo que los métodos de optimización clásicos. Mediante una comparativa de las predicciones realizadas con ambos métodos y de los resulta-dos de ensayos experimentales se podrán establecer las ventajas e inconvenientes derivadas de la aplicación de cada una de las dos metodologías. Asimismo, se llevará a cabo un análisis paramétrico con ambos enfoques a fin de intentar determinar la sensibilidad de aquellos pa-rámetros más sensibles a este tipo de refuerzo. Finalmente, se realizará un análisis estadístico de la fiabilidad de las ecuaciones de diseño deri-vadas de la optimización multiobjetivo. Con dicho análisis se puede estimar la capacidad resis-tente de una viga reforzada a cortante con FRP-NSM dentro de un margen de seguridad espe-cificado a priori. ABSTRACT The use of externally bonded (EB) fibre-reinforced polymer (FRP) composites has gained acceptance during the last two decades in the construction engineering community, particularly in the rehabilitation of reinforced concrete (RC) structures. Currently, to increase the shear resistance of RC beams, FRP sheets are externally bonded (EB-FRP) and applied on the external side surface of the beams to be strengthened with different configurations. Of more recent application, the near-surface mounted FRP bar (NSM-FRP) method is another technique successfully used to increase the shear resistance of RC beams. In the NSM method, FRP rods are embedded into grooves intentionally prepared in the concrete cover of the side faces of RC beams. While flexural strengthening has been widely developed and studied so far, the same doesn´t occur to shearing strength mainly due to its great complexity. Nevertheless, if design criteria are to be preserved more research should be done to this sort of strength, which are based on avoiding shear failure and its catastrophic consequences. However, in spite of this, accurately calculating the shear capacity of FRP shear strengthened RC beams remains a complex challenge that has not yet been fully resolved due to the numerous variables involved in the procedure. The objective of this Thesis is to develop methodologies to evaluate the capacity of FRP shear strengthened RC beams by dealing with the problem from a different point of view to the numerical modeling approach by using artificial intelligence techniques. With this purpose two different approaches have been developed: one concerned with the use of artificial neural networks and the other based on the implementation of an optimization approach developed jointly with the use of artificial neural networks (ANNs) and solved with genetic algorithms (GAs). With these approaches some of the difficulties concerned regarding the numerical modeling can be overcome. As an alternative tool to conventional numerical techniques, neural networks do not provide closed form solutions for modeling problems but do, however, offer a complex and accurate solution based on a representative set of historical examples of the relationship. Furthermore, they can adapt solutions over time to include new data. On the other hand, as a second proposal, an optimization approach has also been developed to implement simple yet accurate shear design equations for this kind of strengthening. This approach is developed in a multi-objective framework by considering experimental results of RC beams with and without NSM-FRP. Furthermore, the results obtained with the previous scheme based on ANNs are also used as a filter to choose the parameters to include in the design equations. Genetic algorithms are used to solve the optimization problem since they are especially suitable for solving multi-objective problems when compared to standard optimization methods. The key features of the two proposed procedures are outlined and their performance in predicting the capacity of NSM-FRP shear strengthened RC beams is evaluated by comparison with results from experimental tests and with predictions obtained using a simplified numerical model. A sensitivity study of the predictions of both models for the input parameters is also carried out.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Crack mechanical failure in ceramic materials under ion irradiation: case of lithium niobate crystal

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion- generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

High fidelity simulations of failure in fiber-reinforced composites

Los ensayos virtuales de materiales compuestos han aparecido como un nuevo concepto dentro de la industria aeroespacial, y disponen de un vasto potencial para reducir los enormes costes de certificación y desarrollo asociados con las tediosas campañas experimentales, que incluyen un gran número de paneles, subcomponentes y componentes. El objetivo de los ensayos virtuales es sustituir algunos ensayos por simulaciones computacionales con alta fidelidad. Esta tesis es una contribución a la aproximación multiescala desarrollada en el Instituto IMDEA Materiales para predecir el comportamiento mecánico de un laminado de material compuesto dadas las propiedades de la lámina y la intercara. La mecánica de daño continuo (CDM) formula el daño intralaminar a nivel constitutivo de material. El modelo de daño intralaminar se combina con elementos cohesivos para representar daño interlaminar. Se desarrolló e implementó un modelo de daño continuo, y se aplicó a configuraciones simples de ensayos en laminados: impactos de baja y alta velocidad, ensayos de tracción, tests a cortadura. El análisis del método y la correlación con experimentos sugiere que los métodos son razonablemente adecuados para los test de impacto, pero insuficientes para el resto de ensayos. Para superar estas limitaciones de CDM, se ha mejorado la aproximación discreta de elementos finitos enriqueciendo la cinemática para incluir discontinuidades embebidas: el método extendido de los elementos finitos (X-FEM). Se adaptó X-FEM para un esquema explícito de integración temporal. El método es capaz de representar cualitativamente los mecanismos de fallo detallados en laminados. Sin embargo, los resultados muestran inconsistencias en la formulación que producen resultados cuantitativos erróneos. Por último, se ha revisado el método tradicional de X-FEM, y se ha desarrollado un nuevo método para superar sus limitaciones: el método cohesivo X-FEM estable. Las propiedades del nuevo método se estudiaron en detalle, y se concluyó que el método es robusto para implementación en códigos explícitos dinámicos escalables, resultando una nueva herramienta útil para la simulación de daño en composites. Virtual testing of composite materials has emerged as a new concept within the aerospace industry. It presents a very large potential to reduce the large certification costs and the long development times associated with the experimental campaigns, involving the testing of a large number of panels, sub-components and components. The aim of virtual testing is to replace some experimental tests by high-fidelity numerical simulations. This work is a contribution to the multiscale approach developed in Institute IMDEA Materials to predict the mechanical behavior of a composite laminate from the properties of the ply and the interply. Continuum Damage Mechanics (CDM) formulates intraply damage at the the material constitutive level. Intraply CDM is combined with cohesive elements to model interply damage. A CDM model was developed, implemented, and applied to simple mechanical tests of laminates: low and high velocity impact, tension of coupons, and shear deformation. The analysis of the results and the comparison with experiments indicated that the performance was reasonably good for the impact tests, but insuficient in the other cases. To overcome the limitations of CDM, the kinematics of the discrete finite element approximation was enhanced to include mesh embedded discontinuities, the eXtended Finite Element Method (X-FEM). The X-FEM was adapted to an explicit time integration scheme and was able to reproduce qualitatively the physical failure mechanisms in a composite laminate. However, the results revealed an inconsistency in the formulation that leads to erroneous quantitative results. Finally, the traditional X-FEM was reviewed, and a new method was developed to overcome its limitations, the stable cohesive X-FEM. The properties of the new method were studied in detail, and it was demonstrated that the new method was robust and can be implemented in a explicit finite element formulation, providing a new tool for damage simulation in composite materials.

An experimental and numerical study of ductile failure under quasi-static and impact loadings of Inconel 718 nickel-base superalloy

A numerical and experimental study of ballistic impacts at various temperatures on precipitation hardened Inconel 718 nickel-base superalloy plates has been performed. A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion has been implemented in LS-DYNA non-linear finite element code to model the mechanical behaviour of such an alloy. The ballistic impact tests have been carried out at three temperatures: room temperature (25 °C), 400 °C and 700 °C. The numerical study showed that the mesh size is crucial to predict correctly the shear bands detected in the tested plates. Moreover, the mesh size convergence has been achieved for element sizes on the same order that the shear bands. The residual velocity as well as the ballistic limit prediction has been considered excellent for high temperature ballistic tests. Nevertheless, the model has been less accurate for the numerical simulations performed at room temperature, being though in reasonable agreement with the experimental data. Additionally, the influence that the Lode angle had on quasi-static failure patterns such as cup-cone and slanted failure has been studied numerically. The study has revealed that the combined action of weakened constitutive equations and Lode angle dependent failure criterion has been necessary to predict the previously-mentioned failure patterns

Micromechanical basis for shear strength of rock discontinuities

The theoretical basis for evaluating shear strength in rock joints is presented and used to derive an equation that governs the relationship between tangential and normal stress on the joint during situations of slippage between the joint faces. The dependent variables include geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness. The effect roughness is studied, and the aforementioned formula is used to analyse joints under different conditions. A mathematical expression is deduced that explains Barton's value for the joint roughness coefficient (JRC) according to the roughness geometry. In particular, when the Hoek and Brown failure criterion is used for a rock in the contact with the surface roughness plane, it is possible to determine the shear strength of the joint as a function of the relationship between the uniaxial compressive strength of the wall with the normal stress acting on the wall. Finally, theoretical results obtained for the geometry of a three-dimensional joint are compared with those of the Barton's formulation