Multiscale modeling of the plastic behaviour in single crystal tungsten: from atomistic to crystal plasticity simulations

En una planta de fusión, los materiales en contacto con el plasma así como los materiales de primera pared experimentan condiciones particularmente hostiles al estar expuestos a altos flujos de partículas, neutrones y grandes cargas térmicas. Como consecuencia de estas diferentes y complejas condiciones de trabajo, el estudio, desarrollo y diseño de estos materiales es uno de los más importantes retos que ha surgido en los últimos años para la comunidad científica en el campo de los materiales y la energía. Debido a su baja tasa de erosión, alta resistencia al sputtering, alta conductividad térmica, muy alto punto de fusión y baja retención de tritio, el tungsteno (wolframio) es un importante candidato como material de primera pared y como posible material estructural avanzado en fusión por confinamiento magnético e inercial. Sin embargo, el tiempo de vida del tungsteno viene controlado por diversos factores como son su respuesta termo-mecánica en la superficie, la posibilidad de fusión y el fallo por acumulación de helio. Es por ello que el tiempo de vida limitado por la respuesta mecánica del tungsteno (W), y en particular su fragilidad, sean dos importantes aspectos que tienes que ser investigados. El comportamiento plástico en materiales refractarios con estructura cristalina cúbica centrada en las caras (bcc) como el tungsteno está gobernado por las dislocaciones de tipo tornillo a escala atómica y por conjuntos e interacciones de dislocaciones a escalas más grandes. El modelado de este complejo comportamiento requiere la aplicación de métodos capaces de resolver de forma rigurosa cada una de las escalas. El trabajo que se presenta en esta tesis propone un modelado multiescala que es capaz de dar respuestas ingenieriles a las solicitudes técnicas del tungsteno, y que a su vez está apoyado por la rigurosa física subyacente a extensas simulaciones atomísticas. En primer lugar, las propiedades estáticas y dinámicas de las dislocaciones de tipo tornillo en cinco potenciales interatómicos de tungsteno son comparadas, determinando cuáles de ellos garantizan una mayor fidelidad física y eficiencia computacional. Las grandes tasas de deformación asociadas a las técnicas de dinámica molecular hacen que las funciones de movilidad de las dislocaciones obtenidas no puedan ser utilizadas en los siguientes pasos del modelado multiescala. En este trabajo, proponemos dos métodos alternativos para obtener las funciones de movilidad de las dislocaciones: un modelo Monte Cario cinético y expresiones analíticas. El conjunto de parámetros necesarios para formular el modelo de Monte Cario cinético y la ley de movilidad analítica son calculados atomísticamente. Estos parámetros incluyen, pero no se limitan a: la determinación de las entalpias y energías de formación de las parejas de escalones que forman las dislocaciones, la parametrización de los efectos de no Schmid característicos en materiales bcc,etc. Conociendo la ley de movilidad de las dislocaciones en función del esfuerzo aplicado y la temperatura, se introduce esta relación como ecuación de flujo dentro de un modelo de plasticidad cristalina. La predicción del modelo sobre la dependencia del límite de fluencia con la temperatura es validada experimentalmente con ensayos uniaxiales en tungsteno monocristalino. A continuación, se calcula el límite de fluencia al aplicar ensayos uniaxiales de tensión para un conjunto de orientaciones cristalográticas dentro del triángulo estándar variando la tasa de deformación y la temperatura de los ensayos. Finalmente, y con el objetivo de ser capaces de predecir una respuesta más dúctil del tungsteno para una variedad de estados de carga, se realizan ensayos biaxiales de tensión sobre algunas de las orientaciones cristalográficas ya estudiadas en función de la temperatura.-------------------------------------------------------------------------ABSTRACT ----------------------------------------------------------Tungsten and tungsten alloys are being considered as leading candidates for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for the design of magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield and low longterm disposal radioactive footprint. However, tungsten also presents a very low fracture toughness, mostly associated with inter-granular failure and bulk plasticity, that limits its applications. As a result of these various and complex conditions of work, the study, development and design of these materials is one of the most important challenges that have emerged in recent years to the scientific community in the field of materials for energy applications. The plastic behavior of body-centered cubic (bcc) refractory metals like tungsten is governed by the kink-pair mediated thermally activated motion of h¿ (\1 11)i screw dislocations on the atomistic scale and by ensembles and interactions of dislocations at larger scales. Modeling this complex behavior requires the application of methods capable of resolving rigorously each relevant scale. The work presented in this thesis proposes a multiscale model approach that gives engineering-level responses to the technical specifications required for the use of tungsten in fusion energy reactors, and it is also supported by the rigorous underlying physics of extensive atomistic simulations. First, the static and dynamic properties of screw dislocations in five interatomic potentials for tungsten are compared, determining which of these ensure greater physical fidelity and computational efficiency. The large strain rates associated with molecular dynamics techniques make the dislocation mobility functions obtained not suitable to be used in the next steps of the multiscale model. Therefore, it is necessary to employ mobility laws obtained from a different method. In this work, we suggest two alternative methods to get the dislocation mobility functions: a kinetic Monte Carlo model and analytical expressions. The set of parameters needed to formulate the kinetic Monte Carlo model and the analytical mobility law are calculated atomistically. These parameters include, but are not limited to: enthalpy and energy barriers of kink-pairs as a function of the stress, width of the kink-pairs, non-Schmid effects ( both twinning-antitwinning asymmetry and non-glide stresses), etc. The function relating dislocation velocity with applied stress and temperature is used as the main source of constitutive information into a dislocation-based crystal plasticity framework. We validate the dependence of the yield strength with the temperature predicted by the model against existing experimental data of tensile tests in singlecrystal tungsten, with excellent agreement between the simulations and the measured data. We then extend the model to a number of crystallographic orientations uniformly distributed in the standard triangle and study the effects of temperature and strain rate. Finally, we perform biaxial tensile tests and provide the yield surface as a function of the temperature for some of the crystallographic orientations explored in the uniaxial tensile tests.

Elasto-plastic structural stability of arches

The elastic-plastic structural stability behaviour of arches is analysed in the present work.The application of the developed mathematical model, allows to determine the elastic-plastic equilibrium paths, looking for critical points, bifurcation or limit, along those paths, associated to the critical load, in case it comes to happen.The equilibrium paths in the elastic-plastic behaviour when compared with the paths in the linear elastic behaviour, may show that, due to influence of the material plasticity, modifications paths appear and consequently alterations in the values of its critical loads.

Small strain elastic behaviour of unsaturated soil investigated by bender/extender element testing

The aim of this project was to investigate very small strain elastic behaviour of soils under unsaturated conditions, using bender/extender element (BEE) testing. The behaviour of soils at very small strains has been widely studied under saturated conditions, whereas much less work has been performed on very small strain behaviour under unsaturated conditions. A suction-controlled double wall triaxial apparatus for unsaturated soil testing was modified to incorporate three pairs of BEEs transmitting both shear and compression waves with vertical and horizontal directions of wave transmission and wave polarisation. Various different techniques for measuring wave travel time were investigated in both the time domain and the frequency domain and it was concluded that, at least for the current experimental testing programme, peak-to-first-peak in the time domain was the most reliable technique for determining wave travel time. An experimental test programme was performed on samples of compacted speswhite kaolin clay. Two different forms of compaction were employed (i.e. isotropic and anisotropic). Compacted kaolin soil samples were subjected to constant suction loading and unloading stages at three different values of suction, covering both unsaturated conditions (s= 50kPa and s= 300kPa) and saturated conditions (s=0). Loading and unloading stages were performed at three different values of stress ratio (η=0, η=1 and η=-1 ). In some tests a wetting-drying cycle was performed before or within the loading stage, with the wetting-drying cycles including both wetting-induced swelling and wetting-induced collapse compression. BEE tests were performed at regular intervals throughout all test stages, to measure shear wave velocity Vs and compression wave velocity Vp and hence to determine values of shear modulus G and constrained modulus M. The experimental test programme was designed to investigate how very small strain shear modulus G and constrained modulus M varied with unsaturated state variables, including how anisotropy of these parameters developed either with stress state (stress-induced anisotropy) or with previous straining (strain-induced anisotropy). A new expression has been proposed for the very small strain shear modulus G of an isotropic soil under saturated and unsaturated conditions. This expression relates the variation of G to only mean Bishop’s stress p* and specific volume v, and it converges to a well-established expression for saturated soils as degree of saturation approaches 1. The proposed expression for G is able to predict the variation of G under saturated and unsaturated conditions at least as well as existing expressions from the literature and it is considerably simpler (employing fewer state variables and fewer soil constants). In addition, unlike existing expressions from the literature, the values of soil constants in the proposed new expression can be determined from a saturated test. It appeared that, in the current project at least, any strain-induced anisotropy of very small strain elastic behaviour was relatively modest, with the possible exception of loading in triaxial extension. It was therefore difficult to draw any firm conclusion about evolution of strain-induced anisotropy and whether it depended upon the same aspects of soil fabric as evolution of anisotropy of large strain plastic behaviour. Stress-induced anisotropy of very small strain elastic behaviour was apparent in the experimental test programme. An attempt was made to extend the proposed expression for G to include the effect of stress-induced anisotropy. Interpretation of the experimental results indicated that the value of shear modulus was affected by the values of all three principal Bishop’s stresses (in the direction of wave transmission, the direction of wave polarisation and the third mutually perpendicular direction). However, prediction of stress-induced anisotropy was only partially successful, and it was concluded that the effect of Lode angle was also significant.

Characterisation and investigation of local variations in mechanical behaviour in cast aluminium using gradient solidification, Digital Image Correlation and finite element simulation

Due to design and process-related factors, there are local variations in the microstructure and mechanical behaviour of cast components. This work establishes a Digital Image Correlation (DIC) based method for characterisation and investigation of the effects of such local variations on the behaviour of a high pressure, die cast (HPDC) aluminium alloy. Plastic behaviour is studied using gradient solidified samples and characterisation models for the parameters of the Hollomon equation are developed, based on microstructural refinement. Samples with controlled microstructural variations are produced and the observed DIC strain field is compared with Finite Element Method (FEM) simulation results. The results show that the DIC based method can be applied to characterise local mechanical behaviour with high accuracy. The microstructural variations are observed to cause a redistribution of strain during tensile loading. This redistribution of strain can be predicted in the FEM simulation by incorporating local mechanical behaviour using the developed characterization model. A homogeneous FEM simulation is unable to predict the observed behaviour. The results motivate the application of a previously proposed simulation strategy, which is able to predict and incorporate local variations in mechanical behaviour into FEM simulations already in the design process for cast components.

The crack tip strain field of AISI 4340 - Part III - Hydrogen influence

This paper studied the influence of hydrogen and water vapour environments on the plastic behaviour in the vicinity of the crack tip for AISI 4340. Hydrogen and water vapour (at a pressure of 15 Torr) significantly increased the crack tip opening displacement. The crack tip strain distribution in 15 Torr hydrogen was significantly different to that measured in vacuum. In the presence of sufficient hydrogen, the plastic zone was larger, was elongated in the direction of crack propagation and moreover there was significant creep. These observations support the hydrogen enhanced localised plasticity model for hydrogen embrittlement in this steel. The strain distribution in the presence of water vapour also suggests that SCC in AISI 4340 occurs via the hydrogen enhanced localised plasticity mechanism. (C) 1999 Kluwer Academic Publishers.

Bearded capuchin monkeys` and a human`s efficiency at cracking palm nuts with stone tools: field experiments

Wild bearded capuchins, Cebus libidinosus, in Fazenda Boa Vista, Brazil crack tough palm nuts using hammer stones. We analysed the contribution of intrinsic factors (body weight, behaviour), size of the nuts and the anvil surface (flat or pit) to the efficiency of cracking. We provided capuchins with local palm nuts and a single hammer stone at an anvil. From video we scored the capuchins` position and actions with the nut prior to each strike, and outcomes of each strike. The most efficient capuchin opened 15 nuts per 100 strikes (6.6 strikes per nut). The least efficient capuchin that succeeded in opening a nut opened 1.32 nuts per 100 strikes (more than 75 strikes per nut). Body weight and diameter of the nut best predicted whether a capuchin would crack a nut on a given strike. All the capuchins consistently placed nuts into pits. To provide an independent analysis of the effect of placing the nut into a pit, we filmed an adult human cracking nuts on the same anvil using the same stone. The human displaced the nut on proportionally fewer strikes when he placed it into a pit rather than on a flat surface. Thus the capuchins placed the nut in a more effective location on the anvil to crack it. Nut cracking as practised by bearded capuchins is a striking example of a plastic behaviour where costs and benefits vary enormously across individuals, and where efficiency requires years to attain. (C) 2009 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Evaluation of energy level to be absorbed by tractor ROPS: Actual Tests, Simulation and Computation

A highly dangerous situations for tractor driver is the lateral rollover in operating conditions. Several accidents, involving tractor rollover, have indeed been encountered, requiring the design of a robust Roll-Over Protective Structure (ROPS). The aim of the thesis was to evaluate tractor behaviour in the rollover phase so as to calculate the energy absorbed by the ROPS to ensure driver safety. A Mathematical Model representing the behaviour of a generic tractor during a lateral rollover, with the possibility of modifying the geometry, the inertia of the tractor and the environmental boundary conditions, is proposed. The purpose is to define a method allowing the prediction of the elasto-plastic behaviour of the subsequent impacts occurring in the rollover phase. A tyre impact model capable of analysing the influence of the wheels on the energy to be absorbed by the ROPS has been also developed. Different tractor design parameters affecting the rollover behaviour, such as mass and dimensions, have been considered. This permitted the evaluation of their influence on the amount of energy to be absorbed by the ROPS. The mathematical model was designed and calibrated with respect to the results of actual lateral upset tests carried out on a narrow-track tractor. The dynamic behaviour of the tractor and the energy absorbed by the ROPS, obtained from the actual tests, showed to match the results of the model developed. The proposed approach represents a valuable tool in understanding the dynamics (kinetic energy) and kinematics (position, velocity, angular velocity, etc.) of the tractor in the phases of lateral rollover and the factors mainly affecting the event. The prediction of the amount of energy to be absorbed in some cases of accident is possible with good accuracy. It can then help in designing protective structures or active security devices.

In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Ageing societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the hierarchical organization of bone. Here, we investigate the mechanical response under monotonic and cyclic compression of both single osteonal lamellae and macroscopic samples containing numerous osteons. Micropillar compression tests in a scanning electron microscope, microindentation and macroscopic compression tests were performed on dry ovine bone to identify the elastic modulus, yield stress, plastic deformation, damage accumulation and failure mechanisms. We found that isolated lamellae exhibit a plastic behaviour, with higher yield stress and ductility but no damage. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behaviour of bone at the microscale to a quasi-brittle response driven by the growth of cracks along interfaces or in the vicinity of pores at the macroscale.

Nuevo concepto de elementos estructurales horizontales de vidrio : placa autoportante y pretensada en forma de pi

En los últimos años, podemos darnos cuenta de la importancia que tienen las nuevas aplicaciones de vidrio especialmente en edificios turísticos donde el vértigo juega un papel importante en la visita. Sin embargo los sistemas constructivos no tienen un especial interés porque el vidrio laminado está siempre soportado por otro elemento de acero o incluso vidrio en forma de retícula. En la presente tesis voy a desarrollar una nueva solución de elemento autoportante de vidrio de gran tamaño haciendo seguro el uso del elemento para andar en el aire. El sueño de muchos arquitectos ha sido diseñar un edificio completamente transparente y a mí me gustaría contribuir a este sueño empezando a estudiar un forjado de vidrio como elemento estructural horizontal y para ello debemos cumplir requerimientos de seguridad. Uno de los objetivos es lograr un elemento lo más transparente y esbelto posible para el uso de pasarelas en vestíbulos de edificios. Las referencias construidas son bien conocidas, pero por otro lado Universidades europeas estudian continua estudiando el comportamiento del vidrio con diferentes láminas, adhesivos, apilados, insertos, sistemas de laminado, pretensado, pandeo lateral, seguridad post-rotura y muchos más aspectos necesarios. La metodología llevada a cabo en esta tesis ha sido primeramente diseñar un elemento industrial prefabricado horizontal de vidrio teniendo en cuenta todos los conceptos aprendidos en el estado del arte y la investigación para poder predimensionar el elemento. El siguiente paso será verificar el modelo por medio de cálculo analítico, simulación de elementos finitos y ensayos físicos. Para realizar los ensayos hay un paso intermedio teniendo que cambiar la hipótesis de carga uniforme a carga puntal para realizar el ensayo de flexión a 4 puntos normalizado y además cambiar a escala 1:2 para adaptarse al espacio de ensayo y ser viable económicamente. Finalmente compararé los resultados de tensión y deformación obtenidos por los tres métodos para extraer conclusiones. Sin embargo el problema de la seguridad no ha concluido, tendré que demostrar que el sistema es seguro después de que se produzca la rotura y para ello sólo dispongo de los ensayos como medio de demostración. El diseño es el resultado de la evolución de una viga tipo “I”; cuando es pretensada para obtener más resistencia, aparece el problema de pandeo lateral y éste es solucionado con una viga con sección en “T” cuya unión es resuelta con un cajeado longitudinal en la parte inferior del elemento horizontal. Las alas de éste crecen para recoger las cargas superficiales creando a su vez un punto débil en la unión que a su vez se soluciona duplicando la sección “TT” y haciendo trabajar dicho tablero de forma tan óptima como una viga continua. Dicha sección en vidrio como un único elemento pretensado es algo inédito. Además he diseñado unas escuadras metálicas en los extremos de los nervios como apoyo y placa de pretensión, así como una hendidura curva en el centro de los nervios para alojar los tirantes de acero de modo que al pretensar el tirante la placa corrija al menos la deformación por peso propio. Realizados los cambios geométricos de escala y las simplificaciones en el laminado y el adhesivo se programan la extracción de resultados desde 3 estadios diferentes: Sin pretensión y con pretensión de 750 Kg y de 1000Kg en cada nervio. Por cada estadio y por cada uno de los métodos, cálculo, simulación y ensayos, se extraen los datos de deformación y tensión en el punto medio de un nervio con el objetivo de hacer una comparación de resultados para obtener unas conclusiones, siempre en el campo de la elasticidad. Posteriormente incrementaré la carga hasta el momento de la rotura de la placa y después hasta el colapso teniendo en cuenta el tiempo y demostrando una rotura segura. El vidrio no tendrá un comportamiento plástico pero habrá sido controlado su comportamiento frágil manteniendo una carga y una deformación aceptable. ABSTRACT Over the past few years we have realized the importance of the new technologies regarding the application of glass in new buildings, especially those touristic places were the views and the heights are the reason of the visit. However, the construction systems of these glass platforms are not usually as interesting, because the laminated glass is always held by another steel substructure or even a grid-formed glass element. Throughout this thesis I am going to develop a new solution of a self-bearing element with big dimensions made out of glass, ensuring a safe solution to use as an element to walk on the air. The dream of many architects has been to create a building completely transparent, and I would like to contribute to this idea by making a glass slab as a horizontal structural element, for which we have to meet the security requirements. One of the goals is to achieve an element as transparent and slim as possible for the use in walkways of building lobbies. The glass buildings references are well known, but on the other hand the European Universities study the behaviour of the glass with different interlayers, adhesives, laminating systems, stacking, prestressed, buckling, safety, breakage and post-breakage capacity; and many other necessary aspects. The methodology followed in this thesis has been to first create a horizontal industrial prefabricated horizontal element of glass, taking into account all the concepts learned in the state of art and the investigation to be able to predimension this element. The next step will be to verify this model with an analytic calculus, a finite element modelling simulation and physical tests. To fulfil these tests there is an intermediate step, having to change the load hypothesis from a punctual one to make the test with a four points normalized deflexion, and also the scale of the sample was changed to 1:2 to adapt to the space of the test and make it economically possible. Finally, the results of tension and deformation obtained from the three methods have been compared to make the conclusions. However, the problem with safety has not concluded yet, for I will have to demonstrate that this system is safe even after its breakage, for which I can only use physical tests as a way of demonstration. The design is the result of the evolution of a typical “I” beam, which when it is prestressed to achieve more resistance, the effect of buckling overcomes, and this is solved with a “T” shaped beam, where the union is solved with a longitudinal groove on the inferior part of the horizontal element. The boards of this beam grow to cover the superficial loads, creating at the same time a weak point, which is solved by duplicating the section “TT” and therefore making this board work as optimal as a continuous beam. This glass section as a single prestressed element is unique. After the final design of the “π” glass plate was obtained and the composition of the laminated glass and interlayers has been predimensioned, the last connection elements must be contemplated. I have also designed a square steel shoe at the end of the beams, which will be the base and the prestressed board, as well as a curved slot in the centre of the nerves to accommodate the steel braces so that when this brace prestresses the board, at least the deformation due to its self-weight will be amended. Once I made the geometric changes of the scale and the simplifications on the laminating and the adhesive, the extraction on results overcomes from three different stages: without any pretension, with a pretension of 750 kg and with a pretension of 1000 kg on each rib. For each stage and for each one of the methods, calculus, simulation and tests, the deformation datum were extracted to obtain the conclusions, always in the field of the elasticity. Afterwards, I will increase the load until the moment of breakage of this board, and then until the collapse of the element, taking into account the time spent and demonstrating a safe breakage. The glass will not have a plastic behaviour, but its brittle behaviour has been controlled, keeping an acceptable load and deflection.

Ultrasonic and X-ray computed tomography characterization of progressive fracture damage in low-porous carbonate rocks

This paper studies the fracturing process in low-porous rocks during uniaxial compressive tests considering the original defects and the new mechanical cracks in the material. For this purpose, five different kinds of rocks have been chosen with carbonate mineralogy and low porosity (lower than 2%). The characterization of the fracture damage is carried out using three different techniques: ultrasounds, mercury porosimetry and X-ray computed tomography. The proposed methodology allows quantifying the evolution of the porous system as well as studying the location of new cracks in the rock samples. Intercrystalline porosity (the smallest pores with pore radius < 1 μm) shows a limited development during loading, disappearing rapidly from the porosimetry curves and it is directly related to the initial plastic behaviour in the stress–strain patterns. However, the biggest pores (corresponding to the cracks) suffer a continuous enlargement until the unstable propagation of fractures. The measured crack initiation stress varies between 0.25 σp and 0.50 σp for marbles and between 0.50 σp and 0.85 σp for micrite limestone. The unstable propagation of cracks is assumed to occur very close to the peak strength. Crack propagation through the sample is completely independent of pre-existing defects (porous bands, stylolites, fractures and veins). The ultrasonic response in the time-domain is less sensitive to the fracture damage than the frequency-domain. P-wave velocity increases during loading test until the beginning of the unstable crack propagation. This increase is higher for marbles (between 15% and 30% from initial vp values) and lower for micrite limestones (between 5% and 10%). When the mechanical cracks propagate unstably, the velocity stops to increase and decreases only when rock damage is very high. Frequency analysis of the ultrasonic signals shows clear changes during the loading process. The spectrum of treated waveforms shows two main frequency peaks centred at low (~ 20 kHz) and high (~ 35 kHz) values. When new fractures appear and grow the amplitude of the high-frequency peak decreases, while that of the low-frequency peak increases. Besides, a slight frequency shift is observed towards higher frequencies.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Expressão geofísica-estrutural do lineamento transbrasiliano na porção central da Bacia do Parnaíba (Maranhão-Piauí)

The objective of this study was to characterize the structural-geophysical expression of the Transbrasiliano Lineament (TBL) in the east-central portion of the Parnaíba Basin. The TBL corresponds to a major Neoproterozoic NE-trending shear zone related to the Brasiliano orogenic cycle, with dextral strike-slip kinematics, underlying (but also laterally exposed in the NE and SW basin edges) the sedimentary section of the Parnaíba Basin. In this study, the interpretation of gravity and magnetic anomaly maps is consistent with the TBL kinematics, the signature of the geophysical anomalies corresponding to the high (plastic behaviour) and subsequent declining temperature (ductile to brittle behaviour) stages during Brasiliano and late Brasiliano times. The pattern of residual gravity anomalies is compatible with an S-C dextral pair shaping the geological bodies of an heterogeneous basement, such as slices of gneisses and granulites (positive anomalies), granitic and low-medium grade metasedimentary rocks (negative anomalies). Such anomalies curvilinear trends, ranging from NNE (interpreted as S surfaces) to NE (C surfaces), correspond to flattening surfaces (S), while the NE rectilinear trend must represent a C band. The narrower magnetic anomalies also display NNE to NE (S surfaces) trends and should correspond to similar (although narrower and more discontinuous) sources in the equivalent anomaly patterns. Pre-Silurian pull-apart style grabens may contribute to the NE negative gravimetric anomalies, although this interpretation demands control by seismic data analysis. On the other hand, the curvilinear anomalies associated to contractional trends are incompatible with their interpretation as pre-Silurian graben, in both maps. In the (reduced to the pole) magnetic anomalies map, most of these are again associated to low-temperature shear zones (C planes) and faults, juxtaposing distinct blocks in terms of magnetic properties, or eventually filled with basic bodies. It is also possible that some isolated magnetic anomalies correspond to igneous bodies of late-Brasiliano or Mesozoic age. The basement late discontinuities pattern can be interpreted in analogy to the Riedel fractures model, with steep dipping surfaces and a sub-horizontal movement section. This study also explored 2D gravity modeling controlled by the interpretation of a dip seismic line as regards to the Transbrasiliano Lineament. The rock section equivalent to the Jaibaras Group occupying a graben structure (as identified in the seismic line) corresponds to a discrete negative anomaly superimposed to a gravimetric high, once again indicating a stronger influence of older crystalline basement rocks as gravimetric sources, mainly reflecting the heterogeneities and anisotropies generated at high temperature conditions and their subsequent cooling along the TBL, during the Brasiliano cycle.

Expressão geofísica-estrutural do lineamento transbrasiliano na porção central da Bacia do Parnaíba (Maranhão-Piauí)

The objective of this study was to characterize the structural-geophysical expression of the Transbrasiliano Lineament (TBL) in the east-central portion of the Parnaíba Basin. The TBL corresponds to a major Neoproterozoic NE-trending shear zone related to the Brasiliano orogenic cycle, with dextral strike-slip kinematics, underlying (but also laterally exposed in the NE and SW basin edges) the sedimentary section of the Parnaíba Basin. In this study, the interpretation of gravity and magnetic anomaly maps is consistent with the TBL kinematics, the signature of the geophysical anomalies corresponding to the high (plastic behaviour) and subsequent declining temperature (ductile to brittle behaviour) stages during Brasiliano and late Brasiliano times. The pattern of residual gravity anomalies is compatible with an S-C dextral pair shaping the geological bodies of an heterogeneous basement, such as slices of gneisses and granulites (positive anomalies), granitic and low-medium grade metasedimentary rocks (negative anomalies). Such anomalies curvilinear trends, ranging from NNE (interpreted as S surfaces) to NE (C surfaces), correspond to flattening surfaces (S), while the NE rectilinear trend must represent a C band. The narrower magnetic anomalies also display NNE to NE (S surfaces) trends and should correspond to similar (although narrower and more discontinuous) sources in the equivalent anomaly patterns. Pre-Silurian pull-apart style grabens may contribute to the NE negative gravimetric anomalies, although this interpretation demands control by seismic data analysis. On the other hand, the curvilinear anomalies associated to contractional trends are incompatible with their interpretation as pre-Silurian graben, in both maps. In the (reduced to the pole) magnetic anomalies map, most of these are again associated to low-temperature shear zones (C planes) and faults, juxtaposing distinct blocks in terms of magnetic properties, or eventually filled with basic bodies. It is also possible that some isolated magnetic anomalies correspond to igneous bodies of late-Brasiliano or Mesozoic age. The basement late discontinuities pattern can be interpreted in analogy to the Riedel fractures model, with steep dipping surfaces and a sub-horizontal movement section. This study also explored 2D gravity modeling controlled by the interpretation of a dip seismic line as regards to the Transbrasiliano Lineament. The rock section equivalent to the Jaibaras Group occupying a graben structure (as identified in the seismic line) corresponds to a discrete negative anomaly superimposed to a gravimetric high, once again indicating a stronger influence of older crystalline basement rocks as gravimetric sources, mainly reflecting the heterogeneities and anisotropies generated at high temperature conditions and their subsequent cooling along the TBL, during the Brasiliano cycle.

Advances in single-shot, dry drilling of composite/metal stacks

Carbon fibre reinforced polymers (CFRP) are increasingly being used in the aerospace, automotive and defence industry due to their high specific stiffness and good corrosion resistance. In a modern aircraft, 50-60% of its structure is made up of CFRP material while the remainder is mostly a combination of metallic alloys (typically aluminium or titanium alloys). Mechanical fastening (bolting or riveting) of CFRP and metallic components has thus created a pressing requirement of drilling several thousand holes per aircraft. Drilling of stacks in a single-shot not only saves time, but also ensures proper alignment when fasteners are inserted, achieving tighter geometric tolerances. However, this requirement poses formidable manufacturing challenges due to the fundamental differences in the material properties of CFRP and metals e.g. a drill bit entering into the stack encounters brittle and abrasive CFRP material as well as the plastic behaviour of the metallic alloy, making the drilling process highly non-linear.

Over the past few years substantial efforts have been made in this direction and majority of the research has tried to establish links between how the process parameters (feed, depth of cut, cutting speed), tooling (geometry, material and coating) and the wear of the cutting tool affect the hole quality. Similarly, multitudes of investigations have been conducted to determine the effects of non-traditional drilling methods (orbital, helical and vibration assisted drilling), cutting zone temperatures and efficiency of chip extraction on the hole quality and rate of tool wear during single shot drilling of CFRP/alloy stacks.

In a timely effort, this paper aims at reviewing the manufacturing challenges and barriers faced when drilling CFRP/alloy stacks and to summarise various factors influencing the drilling process while detailing the advances made in this fertile research area of single-shot drilling of stack materials. A survey of the key challenges associated with avoiding workpiece damage and the effect these challenges have on tool design and process optimisation is presented. An in depth critique of suitable hole making methods and their aptness for commercialisation follows. The paper concludes by summarising the future work required to achieve repeatable, high quality single shot drilled holes in CFRP/alloy stacks.