13 resultados para Mechanical components

em Universidad Politécnica de Madrid


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Liquid crystal devices are being used in many non-display applications in order to construct small devices controlled by low voltage electronics without mechanical components. In this work, we present a novel liquid crystal device for laser beam steering. In this device the orientation of the liquid crystal molecules can be controlled. A change in the liquid crystal orientation results in a change of the refractive index. When a laser beam passes through the device, the beam will be deviated (Fig.1) and the device works a prism. The main difference between this device and a prism is that in the device the orientation profile of the liquid crystal molecules can be modified so that the laser beam can be deviated a required angle: the device is tuneable.

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In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

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Profiting by the increasing availability of laser sources delivering intensities above 109 W/cm2 with pulse energies in the range of several Joules and pulse widths in the range of nanoseconds, laser shock processing (LSP) is being consolidating as an effective technology for the improvement of surface mechanical and corrosion resistance properties of metals and is being developed as a practical process amenable to production engineering. The main acknowledged advantage of the laser shock processing technique consists on its capability of inducing a relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly, the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Following a short description of the theoretical/computational and experimental methods developed by the authors for the predictive assessment and experimental implementation of LSP treatments, experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (specifically Al and Ti alloys) under different LSP irradiation conditions are presented. In particular, the analysis of the residual stress profiles obtained under different irradiation parameters and the evaluation of the corresponding induced surface properties as roughness and wear resistance are presented.

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Outline: • Introduction • Process Experimental Setup • Experimental Procedure • Experimental Results for Al2024-T351 and Ti6Al4V - Residual stresses - Tensile Strength - Fatigue Life • Discussion and Outlook - Prospects for technological applications of LSP

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Laser shock processing (LSP) is being increasingly applied as an effective technology for the improvement of metallic materials surface properties in different types of components as a means of enhancement of their corrosion and fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, follow-on experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (especially Al and Ti alloys) under different LSP irradiation conditions are presented along with a practical correlated analysis on the protective character of the residual stress profiles obtained under different irradiation strategies and the evaluation of the corresponding induced properties as material specific volume reduction at the surface, microhardness and wear resistance. Additional remarks on the improved character of the LSP technique over the traditional “shot peening” technique in what concerns depth of induced compressive residual stresses fields are also made through the paper.

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Damages -reduced in fruit packing lines is a major cause of grace reduction and quality loos in fresh marks: fruit. Fruit must be treated gently during in sir handling to improve their qualityin order to get a good price in a competitive market. The correct post-hardvest handling in fruit packing lines is a prerequisite to cut down the heavy post-harvest losses. Fruit packing lines must be evaluated, studying their design, the impacts applied to the fruits, the characteristics of the materials, etc. This study establishes the possibility of carrying out modifications and tests in a packing line during a long period of time. For this purpose, an experimental fruit packing line has been designed and located in the Agricultural Engineering Department of the Polythecnic University of Madrid with the aim of improving mechanical devices and fruit handling conditions to minimize damage to fruit. The experimental line consists of several transporting belts, one rollers transporter, one sizer, one elevator, one singularizer, and three trays to receive the calibrated fruit. The line has a length of 6.15 m and a width cf 1.9 m. Movement of the different components is regulated by electric motors with variable velocity electronically controlled. The height of the transfer points is variable and can be easily modified. The experimental line has been calibrated using two instrumented spheres IS 100 (8.8 cm Ø and6.2cm Ø). Average acceleration values obtained in all the transfers of the experimental line lay under 80 g's, although there is big variation for some of them being some values above 100 g's.

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Laser shock processing (LSP) is increasingly applied as an effective technology for the improvement of metallic materials mechanical properties in different types of components as a means of enhancement of their fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses fields into metallic components allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, experimental results on the residual stress profiles and associated mechanical properties modification successfully reached in typical materials under different LSP irradiation conditions are presented. In this case, the specific behavior of a widely used material in high reliability components (especially in nuclear and biomedical applications) as AISI 316L is analyzed, the effect of possible “in-service” thermal conditions on the relaxation of the LSP effects being specifically characterized. I.

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Laser shock processing (LSP) is being increasingly applied as an effective technology for the improvement of metallic materials mechanical and surface properties in different types of components as a means of enhancement of their corrosion and fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, follow-on experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (especially Al and Ti alloys characteristic of high reliability components in the aerospace, nuclear and biomedical sectors) under different LSP irradiation conditions are presented along with a practical correlated analysis on the protective character of the residual stress profiles obtained under different irradiation strategies. Additional remarks on the improved character of the LSP technique over the traditional “shot peening” technique in what concerns depth of induced compressive residual stresses fields are also made through the paper

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The target is to evaluate the mechanical behavior of Ti and La2O3 dispersed W alloy, processed by HIP and compare it with a reference pure-W. Tests were performed in both oxidant (air) and inert (vacuum) atmosphere in a temperature range from -196 to 1200 °C.

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It has been demonstrated that mechanical alloying and subsequent consolidation by hot isostatic pressing (HIP) is a successful route to produce dispersion strengthened W alloys with properties satisfying the design requirements of particular plasma facing components in the fusion reactor. However, the presence of the alloying element as a phase filling large interstices between W particles appears to reduce the mechanical properties of these alloys. In order to limit this phase separation induced by the HIP treatment and the detrimental effects on the mechanical properties, the enhancement of the mechanical alloying process, and the effect of a postconsolidation heat treatment in an reducing atmosphere, have been investigated.

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Laser shock processing (LSP) is increasingly applied as an effective technology for the improvement of metallic materials mechanical properties in different types of components as a means of enhancement of their fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses fields into metallic components allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view)are presented in this paper. Concretely, experimental results on the residual stress profiles and associated mechanical properties modification successfully reached in typical materials under different LSP irradiation conditions are presented. In this case, the specific behavior of a widely used material in high reliability components (especially in nuclear and biomedical applications) as AISI 316L is analyzed, the effect of possible “in-service” thermal conditions on the relaxation of the LSP effects being specifically characterized.

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Los fieltros son una familia de materiales textiles constituidos por una red desordenada de fibras conectadas por medio de enlaces térmicos, químicos o mecánicos. Presentan menor rigidez y resistencia (al igual que un menor coste de procesado) que sus homólogos tejidos, pero mayor deformabilidad y capacidad de absorción de energía. Los fieltros se emplean en diversas aplicaciones en ingeniería tales como aislamiento térmico, geotextiles, láminas ignífugas, filtración y absorción de agua, impacto balístico, etc. En particular, los fieltros punzonados fabricados con fibras de alta resistencia presentan una excelente resistencia frente a impacto balístico, ofreciendo las mismas prestaciones que los materiales tejidos con un tercio de la densidad areal. Sin embargo, se sabe muy poco acerca de los mecanismos de deformación y fallo a nivel microscópico, ni sobre como influyen en las propiedades mecánicas del material. Esta carencia de conocimiento dificulta la optimización del comportamiento mecánico de estos materiales y también limita el desarrollo de modelos constitutivos basados en mecanismos físicos, que puedan ser útiles en el diseño de componentes estructurales. En esta tesis doctoral se ha llevado a cabo un estudio minucioso con el fin de determinar los mecanismos de deformación y las propiedades mecánicas de fieltros punzonados fabricados con fibras de polietileno de ultra alto peso molecular. Los procesos de deformación y disipación de energía se han caracterizado en detalle por medio de una combinación de técnicas experimentales (ensayos mecánicos macroscópicos a velocidades de deformación cuasi-estáticas y dinámicas, impacto balístico, ensayos de extracción de una o múltiples fibras, microscopía óptica, tomografía computarizada de rayos X y difracción de rayos X de gran ángulo) que proporcionan información de los mecanismos dominantes a distintas escalas. Los ensayos mecánicos macroscópicos muestran que el fieltro presenta una resistencia y ductilidad excepcionales. El estado inicial de las fibras es curvado, y la carga se transmite por el fieltro a través de una red aleatoria e isótropa de nudos creada por el proceso de punzonamiento, resultando en la formación de una red activa de fibra. La rotación y el estirado de las fibras activas es seguido por el deslizamiento y extracción de la fibra de los puntos de anclaje mecánico. La mayor parte de la resistencia y la energía disipada es proporcionada por la extracción de las fibras activas de los nudos, y la fractura final tiene lugar como consecuencia del desenredo total de la red en una sección dada donde la deformación macroscópica se localiza. No obstante, aunque la distribución inicial de la orientación de las fibras es isótropa, las propiedades mecánicas resultantes (en términos de rigidez, resistencia y energía absorbida) son muy anisótropas. Los ensayos de extracción de múltiples fibras en diferentes orientaciones muestran que la estructura de los nudos conecta más fibras en la dirección transversal en comparación con la dirección de la máquina. La mejor interconectividad de las fibras a lo largo de la dirección transversal da lugar a una esqueleto activo de fibras más denso, mejorando las propiedades mecánicas. En términos de afinidad, los fieltros deformados a lo largo de la dirección transversal exhiben deformación afín (la deformación macroscópica transfiere directamente a las fibras por el material circundante), mientras que el fieltro deformado a lo largo de la dirección de la máquina presenta deformación no afín, y la mayor parte de la deformación macroscópica no es transmitida a las fibras. A partir de estas observaciones experimentales, se ha desarrollado un modelo constitutivo para fieltros punzonados confinados por enlaces mecánicos. El modelo considera los efectos de la deformación no afín, la conectividad anisótropa inducida durante el punzonamiento, la curvatura y re-orientación de la fibra, así como el desenredo y extracción de la fibra de los nudos. El modelo proporciona la respuesta de un mesodominio del material correspondiente al volumen asociado a un elemento finito, y se divide en dos bloques. El primer bloque representa el comportamiento de la red y establece la relación entre el gradiente de deformación macroscópico y la respuesta microscópica, obtenido a partir de la integración de la respuesta de las fibras en el mesodominio. El segundo bloque describe el comportamiento de la fibra, teniendo en cuenta las características de la deformación de cada familia de fibras en el mesodominio, incluyendo deformación no afín, estiramiento, deslizamiento y extracción. En la medida de lo posible, se ha asignado un significado físico claro a los parámetros del modelo, por lo que se pueden identificar por medio de ensayos independientes. Las simulaciones numéricas basadas en el modelo se adecúan a los resultados experimentales de ensayos cuasi-estáticos y balísticos desde el punto de vista de la respuesta mecánica macroscópica y de los micromecanismos de deformación. Además, suministran información adicional sobre la influencia de las características microstructurales (orientación de la fibra, conectividad de la fibra anisótropa, afinidad, etc) en el comportamiento mecánico de los fieltros punzonados. Nonwoven fabrics are a class of textile material made up of a disordered fiber network linked by either thermal, chemical or mechanical bonds. They present lower stiffness and strength (as well as processing cost) than the woven counterparts but much higher deformability and energy absorption capability and are used in many different engineering applications (including thermal insulation, geotextiles, fireproof layers, filtration and water absorption, ballistic impact, etc). In particular, needle-punched nonwoven fabrics manufactured with high strength fibers present an excellent performance for ballistic protection, providing the same ballistic protection with one third of the areal weight as compared to dry woven fabrics. Nevertheless, very little is known about their deformation and fracture micromechanisms at the microscopic level and how they contribute to the macroscopic mechanical properties. This lack of knowledge hinders the optimization of their mechanical performance and also limits the development of physically-based models of the mechanical behavior that can be used in the design of structural components with these materials. In this thesis, a thorough study was carried out to ascertain the micromechanisms of deformation and the mechanical properties of a needle-punched nonwoven fabric made up by ultra high molecular weight polyethylene fibers. The deformation and energy dissipation processes were characterized in detail by a combination of experimental techniques (macroscopic mechanical tests at quasi-static and high strain rates, ballistic impact, single fiber and multi fiber pull-out tests, optical microscopy, X-ray computed tomography and wide angle X-ray diffraction) that provided information of the dominant mechanisms at different length scales. The macroscopic mechanical tests showed that the nonwoven fabric presented an outstanding strength and energy absorption capacity. It was found that fibers were initially curved and the load was transferred within the fabric through the random and isotropic network of knots created by needlepunching, leading to the formation of an active fiber network. Uncurling and stretching of the active fibers was followed by fiber sliding and pull-out from the entanglement points. Most of the strength and energy dissipation was provided by the extraction of the active fibers from the knots and final fracture occurred by the total disentanglement of the fiber network in a given section at which the macroscopic deformation was localized. However, although the initial fiber orientation distribution was isotropic, the mechanical properties (in terms of stiffness, strength and energy absorption) were highly anisotropic. Pull-out tests of multiple fibers at different orientations showed that structure of the knots connected more fibers in the transverse direction as compared with the machine direction. The better fiber interconnection along the transverse direction led to a denser active fiber skeleton, enhancing the mechanical response. In terms of affinity, fabrics deformed along the transverse direction essentially displayed affine deformation {i.e. the macroscopic strain was directly transferred to the fibers by the surrounding fabric, while fabrics deformed along the machine direction underwent non-affine deformation, and most of the macroscopic strain was not transferred to the fibers. Based on these experimental observations, a constitutive model for the mechanical behavior of the mechanically-entangled nonwoven fiber network was developed. The model accounted for the effects of non-affine deformation, anisotropic connectivity induced by the entanglement points, fiber uncurling and re-orientation as well as fiber disentanglement and pull-out from the knots. The model provided the constitutive response for a mesodomain of the fabric corresponding to the volume associated to a finite element and is divided in two blocks. The first one was the network model which established the relationship between the macroscopic deformation gradient and the microscopic response obtained by integrating the response of the fibers in the mesodomain. The second one was the fiber model, which took into account the deformation features of each set of fibers in the mesodomain, including non-affinity, uncurling, pull-out and disentanglement. As far as possible, a clear physical meaning is given to the model parameters, so they can be identified by means of independent tests. The numerical simulations based on the model were in very good agreement with the experimental results of in-plane and ballistic mechanical response of the fabrics in terms of the macroscopic mechanical response and of the micromechanisms of deformation. In addition, it provided additional information about the influence of the microstructural features (fiber orientation, anisotropic fiber connectivity, affinity) on the mechanical performance of mechanically-entangled nonwoven fabrics.

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Tungsten (W) and its alloys are very promising materials for producing plasma-facing components (PFCs) in the fusion power reactors of the near future, even as a structural part in them. However, whereas the properties of pure tungsten are suitable for a PFC, its structural applications are still limited due to its low toughness, ductile to brittle transition temperature and recrystallization behaviour. Therefore, many efforts have been made to improve its performance by alloying tungsten with other elements. Hence, in this investigation, the thermo-mechanical performance of two new tungsten-tantalum materials has been evaluated. Materials with We5wt.%Ta and We15wt.%Ta were processed by mechanical alloying (MA) and later consolidation by hot isostatic pressing (HIP), with distinct settings for each composition. Thus, it was possible to determine the relationship between the microstructure and the addition of Ta with the macroscopic mechanical properties. These were measured by means of hardness, flexural strength and fracture toughness, in the temperature range of 300e1473 K. The microstructure and the fracture surfaces features of the tested materials were analysed by Field Emission Scanning Electron Microscopy (FESEM).