Analysis and optimization of trajectories for Ballistic Missiles Interception

Intercontinental Ballistic Missiles are capable of placing a nuclear warhead at more than 5,000 km away from its launching base. With the lethal power of a nuclear warhead a whole city could be wiped out by a single weapon causing millions of deaths. This means that the threat posed to any country from a single ICBM captured by a terrorist group or launched by a 'rogue' state is huge. This threat is increasing as more countries are achieving nuclear and advanced launcher capabilities. In order to suppress or at least reduce this threat the United States created the National Missile Defense System which involved, among other systems, the development of long-range interceptors whose aim is to destroy incoming ballistic missiles in their midcourse phase. The Ballistic Missile Defense is a high-profile topic that has been the focus of political controversy lately when the U.S. decided to expand the Ballistic Missile system to Europe, with the opposition of Russia. However the technical characteristics of this system are mostly unknown by the general public. The Interception of an ICBM using a long range Interceptor Missile as intended within the Ground-Based Missile Defense System by the American National Missile Defense (NMD) implies a series of problems of incredible complexity: - The incoming missile has to be detected almost immediately after launch. - The incoming missile has to be tracked along its trajectory with a great accuracy. - The Interceptor Missile has to implement a fast and accurate guidance algorithm in order to reach the incoming missile as soon as possible. - The Kinetic Kill Vehicle deployed by the interceptor boost vehicle has to be able to detect the reentry vehicle once it has been deployed by ICBM, when it offers a very low infrared signature, in order to perform a final rendezvous manoeuvre. - The Kinetic Kill Vehicle has to be able to discriminate the reentry vehicle from the surrounding debris and decoys. - The Kinetic Kill Vehicle has to be able to implement an accurate guidance algorithm in order to perform a kinetic interception (direct collision) of the reentry vehicle, at relative speeds of more than 10 km/s. All these problems are being dealt simultaneously by the Ground-Based Missile Defense System that is developing very complex and expensive sensors, communications and control centers and long-range interceptors (Ground-Based Interceptor Missile) including a Kinetic Kill Vehicle. Among all the technical challenges involved in this interception scenario, this thesis focuses on the algorithms required for the guidance of the Interceptor Missile and the Kinetic Kill Vehicle in order to perform the direct collision with the ICBM. The involved guidance algorithms are deeply analysed in this thesis in part III where conventional guidance strategies are reviewed and optimal guidance algorithms are developed for this interception problem. The generation of a realistic simulation of the interception scenario between an ICBM and a Ground Based Interceptor designed to destroy it was considered as necessary in order to be able to compare different guidance strategies with meaningful results. As a consequence, a highly representative simulator for an ICBM and a Kill Vehicle has been implemented, as detailed in part II, and the generation of these simulators has also become one of the purposes of this thesis. In summary, the main purposes of this thesis are: - To develop a highly representative simulator of an interception scenario between an ICBM and a Kill Vehicle launched from a Ground Based Interceptor. -To analyse the main existing guidance algorithms both for the ascent phase and the terminal phase of the missiles. Novel conclusions of these analyses are obtained. - To develop original optimal guidance algorithms for the interception problem. - To compare the results obtained using the different guidance strategies, assess the behaviour of the optimal guidance algorithms, and analyse the feasibility of the Ballistic Missile Defense system in terms of guidance (part IV). As a secondary objective, a general overview of the state of the art in terms of ballistic missiles and anti-ballistic missile defence is provided (part I).

Modelo simplificado de pocos grados de libertad, para simular el impacto de una roca sobre una viga de hormigón armado

Durante mucho tiempo se han estudiado los efectos producidos por el impacto de objetos sobre estructuras, inicialmente la gran mayoría de los estudios se centraban en el impacto de proyectiles de tipo balístico dado el interés que se tenía en el diseño de estructuras capaces de soportar el impacto de dichos proyectiles. Dada la falta de capacidad de cálculo para resolver el problema que tuviera en cuenta el comportamiento global de la estructura junto con el comportamiento local, los estudios se centraban básicamente en la zona de impacto. El momento en el cual se pueden realizar cálculos que requieren de múltiples iteraciones para llegar a una solución satisfactoria al complejo problema planteado no se produce hasta la llegada de los modernos ordenadores. En el presente estudio se establece un sistema de múltiples grados de libertad (SMDF, System of Multiple Degrees of Freedom), que permite el estudio del impacto de una roca sobre una viga de hormigón armado teniendo en cuenta factores que afectan al ámbito local y global de la estructura analizada. El sistema se resuelve a través de un método de resolución implícita como es el método de Newmark, el cual nos permite, sin tener que acceder a un programa de elementos finitos, obtener una solución suficientemente aproximada al problema planteado con un coste computacional relativamente bajo. En el documento se comprueba el modelo propuesto con los resultados existentes de unos ensayos a escala real, y se plantean diversas hipótesis analizando las diferentes respuestas del sistema a la variación de las condiciones de partida. The effects produced by the impact of objects on structures have been studied for a long time. Initially, the vast majority of studies focused on the impact of ballistic missiles, due to the particular interest in the design of these structures being capable to withstand the impact such projectiles. Due to the lack of calculation capacity to solve the problem of taking into account the global behavior of the structure together with the local behavior, the studies focused mainly on the impact zone. The moment in which calculations that required multiple iterations could be performed with satisfactory solutions for the complex problem presented did not arrive until the introduction of modern computers. The present study establishes a System of Multiple Degrees of Freedom, which allows the study of the impact of a rock on a reinforced concrete beam, taking into account factors that affect the local and global behavior of the structure analyzed. The system is solved using an implicit solution method as is the Newmark method, which allows us, without using a finite element program, to obtain a sufficiently approximate solution to the problem with a relatively low computational cost. This paper tests the proposed model with existing results obtained in large-scale tests, and analyses the response of the system to various changing scenarios to the starting conditions.

An Experimental and Numerical Study of Ballistic Impacts on a Turbine Casing Material at Varying Temperatures

An experimental and numerical study of ballistic impacts on steel plates at various temperatures (700ºC, 400ºC and room temperature) has been carried out. The motivation for this work is the blade‐off event that may occur inside a jet engine turbine. However, as a first attempt to understand this complex loading process, a somewhat simpler approach is carried out in the present work. The material used in this study is the FV535 martensitic stainless steel, which is one of the most commonly used materials for turbine casings. Based on material test data, a Modified Johnson‐Cook (MJC) model was calibrated for numerical simulations using the LS‐DYNA explicit finite element code (see Figure 1). To check the mesh size sensitivity, 2D axisymmetric finite element models with three different mesh sizes and configurations were used for the various temperatures. Two fixed meshes with 64 and 128 elements over the 2mm thick plate and one mesh with 32 elements over the thickness with adaptive remeshing were used in the simulations. The formation of adiabatic shear bands in the perforation process has been found critical in order to achieve good results. Adiabatic shear bands are formed by the temperature rise due to the accumulation of plastic strain during impact (see Figure 2). The influence of the thermal softening in the plastic model has hence been analyzed for the room temperature impact tests, where the temperature gradient is highest

Ballistic performance of nanocrystalline and nanotwinned ultrafine crystal steel

Because of their remarkable mechanical properties, nanocrystalline metals have been the focus of much research in recent years. Refining their grain size to the nanometer range (<100 nm) effectively reduces their dislocation mobility, thus achieving very high yield strength and surface hardness—as predicted by the Hall–Petch relation—as well as higher strain-rate sensitivity. Recent works have additionally suggested that nanocrystalline metals exhibit an even higher compressive strength under shock loading. However, the increase in strength of these materials is generally accompanied by an important reduction in ductility. As an alternative, efforts have been focused on ultrafine crystals, i.e. polycrystals with a grain size in the range of 500 nm to 1 μm, in which “growth twins” (twins introduced inside the grain before deformation) act as barriers against dislocation movement, thus increasing the strength in a similar way as nanocrystals but without significant loss of ductility. Due to their outstanding mechanical properties, both nanocrystalline and nanotwinned ultrafine crystalline steels appear to be relevant candidates for ballistic protection. The aim of the present work is to compare their ballistic performance against coarse-grained steel, as well as to identify the effect of the hybridization with a carbon fiber–epoxy composite layer. Hybridization is proposed as a way to improve the nanocrystalline brittle properties in a similar way as is done with ceramics in other protection systems. The experimental campaign is finally complemented by numerical simulations to help identify some of the intrinsic deformation mechanisms not observable experimentally. As a conclusion, nanocrystalline and nanotwinned ultrafine crystals show a lower energy absorption than coarse-grained steel under ballistic loading, but under equal impact conditions with no penetration, deformation in the impact direction is smaller by nearly 40%. This a priori surprising difference in the energy absorption is rationalized by the more important local contribution of the deviatoric stress vs. volumetric stress under impact than under uniaxial deformation. Ultimately, the deformation advantage could be exploited in the future for personal protection systems where a small deformation under impact is of key importance.

Grain size gradient length scale in ballistic properties optimization of functionally graded nanocrystalline steel plates

The last few years have highlighted the existence of two relevant length scales in the quest to ultrahigh-strength polycrystalline metals. Whereas the microstructural length scale – e.g. grain or twin size – has mainly be linked to the well-established Hall–Petch relationship, the sample length scale – e.g. nanopillar size – has also proven to be at least as relevant, especially in microscale structures. In this letter, a series of ballistic tests on functionally graded nanocrystalline plates are used as a basis for the justification of a “grain size gradient length scale” as an additional ballistic properties optimization parameter.

Influence of the Fiber Alignment in the Ballistic Performance of Dyneema Non-Woven Fabrics

The aim of this study was the determination of the deforming micromechanisms of needlepunched felts subjected to impact loads. A large experimental campaign has been carried out to analyze the influence of the fiber alignment in the ballistic performance. Ballistic limit curves of predeformed samples were compared. The fiber realignment was experimentally measure by means of 2D X-Ray diffraction. Higher specific absorption was observed for samples with a more isotropic mechanical response. A constitutive physicallybased model was developed within the context of the finite element method, which provided the constitutive response for a mesodomain including micromechanical aspects as fiber alignment, fiber sliding and pull-out. The macroscopic response has been validated with the experimental results, showing a very good agreement. The absorbed energy by the material during the impact was predicted and the fiber realignment evolution was also obtained.

Analysis of the Fracture of Reinforced Concrete Flat Elements Subjected to Explosions. Experimental Procedure and Numerical Validation

Many of the material models most frequently used for the numerical simulation of the behavior of concrete when subjected to high strain rates have been originally developed for the simulation of ballistic impact. Therefore, they are plasticity-based models in which the compressive behavior is modeled in a complex way, while their tensile failure criterion is of a rather simpler nature. As concrete elements usually fail in tensión when subjected to blast loading, available concrete material models for high strain rates may not represent accurately their real behavior. In this research work an experimental program of reinforced concrete fíat elements subjected to blast load is presented. Altogether four detonation tests are conducted, in which 12 slabs of two different concrete types are subjected to the same blast load. The results of the experimental program are then used for the development and adjustment of numerical tools needed in the modeling of concrete elements subjected to blast.

Estudio de la capacidad de arranque de una dinamita gelatinosa frente a una dinamita de seguridad

The objective of this project is to show that the permissible explosive called 20 SR is able to pull out the coal in the normal conditions of blasting in a satisfactory way and to set up the equivalence between the 20 SR and gelatin dynamite (Goma 2 ECO). To achieve this goal some blasting were done, changing the conditions of the blasting and the powder factor for the 20 SR. To analyze the fragmentation base on the analysis of the images of the rock blasted, a commercial software was used. The results from this analysis were compared with the results from the theoretical model for fragmentation created by Kuz – Ram. After all, it was showed that the 20 SR explosive is able to pull out the coal for different coal rock compositions. As the result of this project we can conclude that the 20 SR seems to be able to pull out the coal in normal blasting conditions, using the powder factor as a proportion of the “ballistic mortar” between the two explosives.

Flow and fracture behaviour of high performance alloys

Based on our needs, that is to say, through precise simulation of the impact phenomena that may occur inside a jet engine turbine with an explicit non-linear finite element code, four new material models are postulated. Each one of is calibrated for four high-performance alloys that can be encountered in a modern jet engine. A new uncoupled material model for high strain and ballistic is proposed. Based on a Johnson-Cook type model, the proposed formulation introduces the effect of the third deviatoric invariant by means of three different Lode angle dependent functions. The Lode dependent functions are added to both plasticity and failure models. The postulated model is calibrated for a 6061-T651 aluminium alloy with data taken from the literature. The fracture pattern predictability of the JCX material model is shown performing numerical simulations of various quasi-static and dynamic tests. As an extension of the above-mentioned model, a modification in the thermal softening behaviour due to phase transformation temperatures is developed (JCXt). Additionally, a Lode angle dependent flow stress is defined. Analysing the phase diagram and high temperature tests performed, phase transformation temperatures of the FV535 stainless steel are determined. The postulated material model constants for the FV535 stainless steel are calibrated. A coupled elastoplastic-damage material model for high strain and ballistic applications is presented (JCXd). A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson-Cook failure criterion. The weakening in the elastic law and in the Johnson-Cook type constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. A transversely isotropic material model for directionally solidified alloys is presented. The proposed yield function is based a single linear transformation of the stress tensor. The linear operator weighs the degree of anisotropy of the yield function. The elastic behaviour, as well as the hardening, are considered isotropic. To model the hardening, a Johnson-Cook type relation is adopted. A material vector is included in the model implementation. The failure is modelled with the Cockroft-Latham failure criterion. The material vector allows orienting the reference orientation in any other that the user may need. The model is calibrated for the MAR-M 247 directionally solidified nickel-base superalloy.

Estudio de la capacidad de arranque de una dinamita gelatinosa frente a una dinamita de seguridad

El presente proyecto pretende demostrar que el explosivo de seguridad 20 SR es capaz de arrancar el carbón de forma satisfactoria en las condiciones de disparo habituales y establecer la equivalencia práctica de dicho explosivo con una dinamita gelatinosa (Goma 2ECO). Para conseguir este objetivo se realizaron una serie de voladuras, variando las condiciones de disparo y los consumos específicos de la dinamita de seguridad. Se utilizó un software de análisis fotográfico para el estudio de la fragmentación en la pila y también se compararon los resultados obtenidos con el modelo teórico de fragmentación de Kuz – Ram. Los resultados demostraron la capacidad de arranque de la dinamita de seguridad, para diferentes composiciones de carbón. Del estudio parece deducirse que la dinamita de seguridad 20 SR es capaz de arrancar el carbón en condiciones de disparo habituales utilizando un consumo específico proporcional a la relación de la potencia del péndulo balístico de ambos explosivos. ABSTRACT The objective of this project is to show that the permissible explosive called 20 SR is able to pull out the coal in the normal conditions of blasting in a satisfactory way and to set up the equivalence between the 20 SR and gelatin dynamite (Goma 2 ECO). To achieve this goal some blasting were done, changing the conditions of the blasting and the powder factor for the 20 SR. To analyze the fragmentation base on the analysis of the images of the rock blasted, a commercial software was used. The results from this analysis were compared with the results from the theoretical model for fragmentation created by Kuz – Ram. After all, it was showed that the 20 SR explosive is able to pull out the coal for different coal rock compositions. As the result of this project we can conclude that the 20 SR seems to be able to pull out the coal in normal blasting conditions, using the powder factor as a proportion of the “ballistic mortar” between the two explosives.

Flow and fracture behaviour of FV535 steel at different triaxialities, strain rates and temperatures

The new generation jet engines operate at highly demanding working conditions. Such conditions need very precise design which implies an exhaustive study of the engine materials and behaviour in their extreme working conditions. With this purpose, this work intends to describe a numerically-based calibration of the widely-used Johnson–Cook fracture model, as well as its validation through high temperature ballistic impact tests. To do so, a widely-used turbine casing material is studied. This material is the Firth Vickers 535 martensitic stainless steel. Quasi-static tensile tests at various temperatures in a universal testing machine, as well as dynamic tests in a Split Hopkinson Pressure Bar, are carried out at different triaxialities. Using ABAQUS/Standard and LS-DYNA numerical codes, experimental data are matched. This method allows the researcher to obtain critical data of equivalent plastic strain and triaxility, which allows for more precise calibration of the Johnson–Cook fracture model. Such enhancement allows study of the fracture behaviour of the material across its usage temperature range.

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

Estudio del comportamiento del hormigón de alta resistencia reforzado con fibras de acero frente al impacto de proyectiles

En la presente investigación se buscó estudiar el efecto de la adición de fibras metálicas como refuerzo en hormigones de alta resistencia, y en especial su comportamiento frente al impacto de proyectiles. Se efectuó el estudio sobre un hormigón de alta resistencia (HAR), analizando los aspectos mecánicos, durabilidad y trabajabilidad para su colocación en obra. Las pruebas de laboratorio se llevaron a cabo en el Laboratorio de Materiales de Construcción de la Escuela Técnica Superior de Caminos Canales y Puertos de la UPM y los ensayos balísticos en la galería de tiro cubierta del Polígono de Experiencia de Carabanchel, adscrito a la Dirección General de Infraestructura del Ministerio de la Defensa. La caracterización del HAR empleado en el estudio se centró en los aspectos de resistencias mecánicas a compresión, tracción, flexotracción, tenacidad a flexotracción, punzonamiento, retracción, fluencia, temperatura interna y resistencia al impacto de proyectiles, siempre buscando de manera primordial analizar el efecto de la adición de fibras en el hormigón de alta resistencia. El programa de ensayos balísticos comprendió la fabricación de 47 placas de hormigón de diferentes espesores, desde 5 a 40 cm., 26 de dichas placas eran de HAR con una adición de fibras metálicas de 80 kg/m3, 11 de ellas eran de HAR sin fibras y 10 de un hormigón de resistencia convencional con y sin fibras; sobre dichas placas se efectuaron diversos impactos con proyectiles de los cuatro calibres siguientes: 7.62 AP, 12.70 M8, 20 mm APDS y 25 mm APDS. Las pruebas mostraron que el HAR presenta una mayor resistencia a los impactos de proyectiles, aunque sin la adición de fibras su fragilidad es un serio inconveniente para su utilización como barrera protectora, la adición de fibras reduce considerablemente la fragmentación en la cara posterior “scabbing” y en menor medida en la cara anterior “spalling”. También se incrementa la capacidad del hormigón a la resistencia de múltiples impactos. Se efectuó un estudio de las diferentes formulas y modelos, en especial el modelo desarrollado por Moreno [60], que se vienen utilizando para el diseño de barreras protectoras de hormigón contra impacto de proyectiles, analizando su viabilidad en el caso del hormigón de alta resistencia, hormigón para el cual no fueron desarrolladas y para el que no existen bases de cálculo específicas. In this research we have tried to study the effect of adding metallic fibres as a means of reinforcing high strength concrete, and especially its behaviour when impacted upon by projectiles. The study was carried out using high strength concrete (HSC), analysing its mechanical facets, durability and malleability when used in construction. The laboratory tests took place in the Laboratorio de Materiales de Construcción of the Escuela Técnica Superior de Caminos Canales y Puertos of the Universidad Politécnica de Madrid, and the ballistic tests were carried out in the covered shooting gallery of the Polígono de Experiencias in Carabanchel (Madrid), belongs to the Departamento de Infraestructura of the Ministerio de Defensa. The aspects of the HSC studied are its mechanical strength to compression, traction, flexotraction, resilience to flexo-traction, shear strength, creep, shrinkage, internal temperature and strength to the impact of projectiles, always looking to analyse the effect of adding fibres to HSC. The ballistic testing process required the construction of 47 concrete plates of different thicknesses, from 5 to 40 cm, 26 made which HSC containing of 80 kg/m3 metallic fibres of, 11 made of HSC without fibres, and 10 made with concrete of normal strength with and without fibres. These plates were subjected to a variety of impacts by four projectile, 7.62 AP, 12.70 M8, 20 mm APDS and 25 mm APDS. The results showed that HSC has a greater resistance to the impact of projectiles, although without the addition of fibres, its fragility makes it much less suitable for use as a protective barrier. The addition of fibres reduces considerably frontal fragmentation, known as “scabbing”, and to a lesser extent causes fragmentation of the reverse side, known as “spalling”. In addition, the concrete’s capacity to resist multiple impacts is improved by its letter ductility. A study was carried out on the various formulae and models used to design protective concrete barriers impacted on by projectiles, analysing their viability in the case of HSC for which they were not developed and for which no specific calculations exist.

Analysis of punching of a reinforced concrete slab within IRIS_2012

As part of the IRIS_2012 international benchmark, simulations were conducted to analyse impacts on reinforced concrete slabs by both rigid and deformable missiles. The analytical results were compared with physical tests conducted by the Technical Research Center VTT of Finland. In the impact discussed here, a rigid missile perforates the concrete slab. The missile is a thick steel tube filled with concrete with a total mass of 47.4 kg and strikes the target at 136 m/s. The target is a 250 mm thick, reinforced concrete slab that spans 2 m by 2 m and is held in a rigid supporting frame. Characterisation tests were provided for calibration of the parameters of the concrete models selected by the participants. Having reproduced those tests, the authors developed models for the slab and the missile. A damaged plasticity model was used for the concrete and the rebars were explicitly represented. The results obtained were very satisfactory in respect of the damage patterns caused in the concrete and the reinforcement; also, the calculated and measured values of the energy spent by the missile in perforating the slab differed by only 4%.

Concrete constitutive model, calibration and applications

A methodology has been developed for characterising the mechanical behaviour of concrete, based on the damaged plasticity model, enriched with a user subroutine (V)USDFLD in order to capture better the ductility of the material under moderate confining pressures. The model has been applied in the context of the international benchmark IRIS_2012, organised by the OECD/NEA/CSNI Nuclear Energy Agency, dealing with impacts of rigid and deformable missiles against reinforced concrete targets. A slightly modified version of the concrete damaged plasticity model was used to represent the concrete. The simulation results matched very well the observations made during the actual tests. Particularly successful predictions involved the energy spent by the rigid missile in perforating the target, the crushed length of the deformable missile, the crushed and cracked areas of the concrete target, and the values of the strains recorded at a number of locations in the concrete slab.