A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Design and development of new pressure sensors for aerodynamic applications

This artwork reports on two different projects that were carried out during the three years of Doctor of the Philosophy course. In the first years a project regarding Capacitive Pressure Sensors Array for Aerodynamic Applications was developed in the Applied Aerodynamic research team of the Second Faculty of Engineering, University of Bologna, Forlì, Italy, and in collaboration with the ARCES laboratories of the same university. Capacitive pressure sensors were designed and fabricated, investigating theoretically and experimentally the sensor’s mechanical and electrical behaviours by means of finite elements method simulations and by means of wind tunnel tests. During the design phase, the sensor figures of merit are considered and evaluated for specific aerodynamic applications. The aim of this work is the production of low cost MEMS-alternative devices suitable for a sensor network to be implemented in air data system. The last two year was dedicated to a project regarding Wireless Pressure Sensor Network for Nautical Applications. Aim of the developed sensor network is to sense the weak pressure field acting on the sail plan of a full batten sail by means of instrumented battens, providing a real time differential pressure map over the entire sail surface. The wireless sensor network and the sensing unit were designed, fabricated and tested in the faculty laboratories. A static non-linear coupled mechanical-electrostatic simulation, has been developed to predict the pressure versus capacitance static characteristic suitable for the transduction process and to tune the geometry of the transducer to reach the required resolution, sensitivity and time response in the appropriate full scale pressure input A time dependent viscoelastic error model has been inferred and developed by means of experimental data in order to model, predict and reduce the inaccuracy bound due to the viscolelastic phenomena affecting the Mylar® polyester film used for the sensor diaphragm. The development of the two above mentioned subjects are strictly related but presently separately in this artwork.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Estimating crustal deformation from geodetic data

By the end of the 19th century, geodesy has contributed greatly to the knowledge of regional tectonics and fault movement through its ability to measure, at sub-centimetre precision, the relative positions of points on the Earth’s surface. Nowadays the systematic analysis of geodetic measurements in active deformation regions represents therefore one of the most important tool in the study of crustal deformation over different temporal scales [e.g., Dixon, 1991]. This dissertation focuses on motion that can be observed geodetically with classical terrestrial position measurements, particularly triangulation and leveling observations. The work is divided into two sections: an overview of the principal methods for estimating longterm accumulation of elastic strain from terrestrial observations, and an overview of the principal methods for rigorously inverting surface coseismic deformation fields for source geometry with tests on synthetic deformation data sets and applications in two different tectonically active regions of the Italian peninsula. For the long-term accumulation of elastic strain analysis, triangulation data were available from a geodetic network across the Messina Straits area (southern Italy) for the period 1971 – 2004. From resulting angle changes, the shear strain rates as well as the orientation of the principal axes of the strain rate tensor were estimated. The computed average annual shear strain rates for the time period between 1971 and 2004 are γ˙1 = 113.89 ± 54.96 nanostrain/yr and γ˙2 = -23.38 ± 48.71 nanostrain/yr, with the orientation of the most extensional strain (θ) at N140.80° ± 19.55°E. These results suggests that the first-order strain field of the area is dominated by extension in the direction perpendicular to the trend of the Straits, sustaining the hypothesis that the Messina Straits could represents an area of active concentrated deformation. The orientation of θ agree well with GPS deformation estimates, calculated over shorter time interval, and is consistent with previous preliminary GPS estimates [D’Agostino and Selvaggi, 2004; Serpelloni et al., 2005] and is also similar to the direction of the 1908 (MW 7.1) earthquake slip vector [e.g., Boschi et al., 1989; Valensise and Pantosti, 1992; Pino et al., 2000; Amoruso et al., 2002]. Thus, the measured strain rate can be attributed to an active extension across the Messina Straits, corresponding to a relative extension rate ranges between < 1mm/yr and up to ~ 2 mm/yr, within the portion of the Straits covered by the triangulation network. These results are consistent with the hypothesis that the Messina Straits is an important active geological boundary between the Sicilian and the Calabrian domains and support previous preliminary GPS-based estimates of strain rates across the Straits, which show that the active deformation is distributed along a greater area. Finally, the preliminary dislocation modelling has shown that, although the current geodetic measurements do not resolve the geometry of the dislocation models, they solve well the rate of interseismic strain accumulation across the Messina Straits and give useful information about the locking the depth of the shear zone. Geodetic data, triangulation and leveling measurements of the 1976 Friuli (NE Italy) earthquake, were available for the inversion of coseismic source parameters. From observed angle and elevation changes, the source parameters of the seismic sequence were estimated in a join inversion using an algorithm called “simulated annealing”. The computed optimal uniform–slip elastic dislocation model consists of a 30° north-dipping shallow (depth 1.30 ± 0.75 km) fault plane with azimuth of 273° and accommodating reverse dextral slip of about 1.8 m. The hypocentral location and inferred fault plane of the main event are then consistent with the activation of Periadriatic overthrusts or other related thrust faults as the Gemona- Kobarid thrust. Then, the geodetic data set exclude the source solution of Aoudia et al. [2000], Peruzza et al. [2002] and Poli et al. [2002] that considers the Susans-Tricesimo thrust as the May 6 event. The best-fit source model is then more consistent with the solution of Pondrelli et al. [2001], which proposed the activation of other thrusts located more to the North of the Susans-Tricesimo thrust, probably on Periadriatic related thrust faults. The main characteristics of the leveling and triangulation data are then fit by the optimal single fault model, that is, these results are consistent with a first-order rupture process characterized by a progressive rupture of a single fault system. A single uniform-slip fault model seems to not reproduce some minor complexities of the observations, and some residual signals that are not modelled by the optimal single-fault plane solution, were observed. In fact, the single fault plane model does not reproduce some minor features of the leveling deformation field along the route 36 south of the main uplift peak, that is, a second fault seems to be necessary to reproduce these residual signals. By assuming movements along some mapped thrust located southward of the inferred optimal single-plane solution, the residual signal has been successfully modelled. In summary, the inversion results presented in this Thesis, are consistent with the activation of some Periadriatic related thrust for the main events of the sequence, and with a minor importance of the southward thrust systems of the middle Tagliamento plain.

Active fibre-reinforced composites with embedded shape memory alloys

This dissertation concerns active fibre-reinforced composites with embedded shape memory alloy wires. The structural application of active materials allows to develop adaptive structures which actively respond to changes in the environment, such as morphing structures, self-healing structures and power harvesting devices. In particular, shape memory alloy actuators integrated within a composite actively control the structural shape or stiffness, thus influencing the composite static and dynamic properties. Envisaged applications include, among others, the prevention of thermal buckling of the outer skin of air vehicles, shape changes in panels for improved aerodynamic characteristics and the deployment of large space structures. The study and design of active composites is a complex and multidisciplinary topic, requiring in-depth understanding of both the coupled behaviour of active materials and the interaction between the different composite constituents. Both fibre-reinforced composites and shape memory alloys are extremely active research topics, whose modelling and experimental characterisation still present a number of open problems. Thus, while this dissertation focuses on active composites, some of the research results presented here can be usefully applied to traditional fibre-reinforced composites or other shape memory alloy applications. The dissertation is composed of four chapters. In the first chapter, active fibre-reinforced composites are introduced by giving an overview of the most common choices available for the reinforcement, matrix and production process, together with a brief introduction and classification of active materials. The second chapter presents a number of original contributions regarding the modelling of fibre-reinforced composites. Different two-dimensional laminate theories are derived from a parent three-dimensional theory, introducing a procedure for the a posteriori reconstruction of transverse stresses along the laminate thickness. Accurate through the thickness stresses are crucial for the composite modelling as they are responsible for some common failure mechanisms. A new finite element based on the First-order Shear Deformation Theory and a hybrid stress approach is proposed for the numerical solution of the two-dimensional laminate problem. The element is simple and computationally efficient. The transverse stresses through the laminate thickness are reconstructed starting from a general finite element solution. A two stages procedure is devised, based on Recovery by Compatibility in Patches and three-dimensional equilibrium. Finally, the determination of the elastic parameters of laminated structures via numerical-experimental Bayesian techniques is investigated. Two different estimators are analysed and compared, leading to the definition of an alternative procedure to improve convergence of the estimation process. The third chapter focuses on shape memory alloys, describing their properties and applications. A number of constitutive models proposed in the literature, both one-dimensional and three-dimensional, are critically discussed and compared, underlining their potential and limitations, which are mainly related to the definition of the phase diagram and the choice of internal variables. Some new experimental results on shape memory alloy material characterisation are also presented. These experimental observations display some features of the shape memory alloy behaviour which are generally not included in the current models, thus some ideas are proposed for the development of a new constitutive model. The fourth chapter, finally, focuses on active composite plates with embedded shape memory alloy wires. A number of di®erent approaches can be used to predict the behaviour of such structures, each model presenting different advantages and drawbacks related to complexity and versatility. A simple model able to describe both shape and stiffness control configurations within the same context is proposed and implemented. The model is then validated considering the shape control configuration, which is the most sensitive to model parameters. The experimental work is divided in two parts. In the first part, an active composite is built by gluing prestrained shape memory alloy wires on a carbon fibre laminate strip. This structure is relatively simple to build, however it is useful in order to experimentally demonstrate the feasibility of the concept proposed in the first part of the chapter. In the second part, the making of a fibre-reinforced composite with embedded shape memory alloy wires is investigated, considering different possible choices of materials and manufacturing processes. Although a number of technological issues still need to be faced, the experimental results allow to demonstrate the mechanism of shape control via embedded shape memory alloy wires, while showing a good agreement with the proposed model predictions.

Sviluppo e validazione di un modello di film fluido per simulazioni CFD di motori a combustione interna

A wall film model has been implemented in a customized version of KIVA code developed at University of Bologna. Under the hypothesis of `thin laminar ow' the model simulates the dynamics of a liquid wall film generated by impinging sprays. Particular care has been taken in numerical implementation of the model. The major phenomena taken into account in the present model are: wall film formation by impinging spray; body forces, such as gravity or acceleration of the wall; shear stress at the interface with the gas and no slip condition on the wall; momentum contribution and dynamic pressure generated by the tangential and normal component of the impinging drops; film evaporation by heat exchange with wall and surrounding gas. The model doesn't consider the effect of the wavy film motion and suppose that all the impinging droplets adhere to the film. The governing equations have been integrated in space by using a finite volume approach with a first order upwind differencing scheme and they have been integrated in time with a fully explicit method. The model is validated using two different test cases reproducing PFI gasoline and DI Diesel engine wall film conditions.

Study of silicon-on-insulator multiple-gate MOS structures including band-gap engineering and self heating effects

The progresses of electron devices integration have proceeded for more than 40 years following the well–known Moore’s law, which states that the transistors density on chip doubles every 24 months. This trend has been possible due to the downsizing of the MOSFET dimensions (scaling); however, new issues and new challenges are arising, and the conventional ”bulk” architecture is becoming inadequate in order to face them. In order to overcome the limitations related to conventional structures, the researchers community is preparing different solutions, that need to be assessed. Possible solutions currently under scrutiny are represented by: • devices incorporating materials with properties different from those of silicon, for the channel and the source/drain regions; • new architectures as Silicon–On–Insulator (SOI) transistors: the body thickness of Ultra-Thin-Body SOI devices is a new design parameter, and it permits to keep under control Short–Channel–Effects without adopting high doping level in the channel. Among the solutions proposed in order to overcome the difficulties related to scaling, we can highlight heterojunctions at the channel edge, obtained by adopting for the source/drain regions materials with band–gap different from that of the channel material. This solution allows to increase the injection velocity of the particles travelling from the source into the channel, and therefore increase the performance of the transistor in terms of provided drain current. The first part of this thesis work addresses the use of heterojunctions in SOI transistors: chapter 3 outlines the basics of the heterojunctions theory and the adoption of such approach in older technologies as the heterojunction–bipolar–transistors; moreover the modifications introduced in the Monte Carlo code in order to simulate conduction band discontinuities are described, and the simulations performed on unidimensional simplified structures in order to validate them as well. Chapter 4 presents the results obtained from the Monte Carlo simulations performed on double–gate SOI transistors featuring conduction band offsets between the source and drain regions and the channel. In particular, attention has been focused on the drain current and to internal quantities as inversion charge, potential energy and carrier velocities. Both graded and abrupt discontinuities have been considered. The scaling of devices dimensions and the adoption of innovative architectures have consequences on the power dissipation as well. In SOI technologies the channel is thermally insulated from the underlying substrate by a SiO2 buried–oxide layer; this SiO2 layer features a thermal conductivity that is two orders of magnitude lower than the silicon one, and it impedes the dissipation of the heat generated in the active region. Moreover, the thermal conductivity of thin semiconductor films is much lower than that of silicon bulk, due to phonon confinement and boundary scattering. All these aspects cause severe self–heating effects, that detrimentally impact the carrier mobility and therefore the saturation drive current for high–performance transistors; as a consequence, thermal device design is becoming a fundamental part of integrated circuit engineering. The second part of this thesis discusses the problem of self–heating in SOI transistors. Chapter 5 describes the causes of heat generation and dissipation in SOI devices, and it provides a brief overview on the methods that have been proposed in order to model these phenomena. In order to understand how this problem impacts the performance of different SOI architectures, three–dimensional electro–thermal simulations have been applied to the analysis of SHE in planar single and double–gate SOI transistors as well as FinFET, featuring the same isothermal electrical characteristics. In chapter 6 the same simulation approach is extensively employed to study the impact of SHE on the performance of a FinFET representative of the high–performance transistor of the 45 nm technology node. Its effects on the ON–current, the maximum temperatures reached inside the device and the thermal resistance associated to the device itself, as well as the dependence of SHE on the main geometrical parameters have been analyzed. Furthermore, the consequences on self–heating of technological solutions such as raised S/D extensions regions or reduction of fin height are explored as well. Finally, conclusions are drawn in chapter 7.

Higher-Order Concurrency: Expressiveness and Decidability Results

Higher-order process calculi are formalisms for concurrency in which processes can be passed around in communications. Higher-order (or process-passing) concurrency is often presented as an alternative paradigm to the first order (or name-passing) concurrency of the pi-calculus for the description of mobile systems. These calculi are inspired by, and formally close to, the lambda-calculus, whose basic computational step ---beta-reduction--- involves term instantiation. The theory of higher-order process calculi is more complex than that of first-order process calculi. This shows up in, for instance, the definition of behavioral equivalences. A long-standing approach to overcome this burden is to define encodings of higher-order processes into a first-order setting, so as to transfer the theory of the first-order paradigm to the higher-order one. While satisfactory in the case of calculi with basic (higher-order) primitives, this indirect approach falls short in the case of higher-order process calculi featuring constructs for phenomena such as, e.g., localities and dynamic system reconfiguration, which are frequent in modern distributed systems. Indeed, for higher-order process calculi involving little more than traditional process communication, encodings into some first-order language are difficult to handle or do not exist. We then observe that foundational studies for higher-order process calculi must be carried out directly on them and exploit their peculiarities. This dissertation contributes to such foundational studies for higher-order process calculi. We concentrate on two closely interwoven issues in process calculi: expressiveness and decidability. Surprisingly, these issues have been little explored in the higher-order setting. Our research is centered around a core calculus for higher-order concurrency in which only the operators strictly necessary to obtain higher-order communication are retained. We develop the basic theory of this core calculus and rely on it to study the expressive power of issues universally accepted as basic in process calculi, namely synchrony, forwarding, and polyadic communication.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Tecniche MonteCarlo per l'analisi di sistemi a rete

The assessment of the RAMS (Reliability, Availability, Maintainability and Safety) performances of system generally includes the evaluations of the “Importance” of its components and/or of the basic parameters of the model through the use of the Importance Measures. The analytical equations proposed in this study allow the estimation of the first order Differential Importance Measure on the basis of the Birnbaum measures of components, under the hypothesis of uniform percentage changes of parameters. The aging phenomena are introduced into the model by assuming exponential-linear or Weibull distributions for the failure probabilities. An algorithm based on a combination of MonteCarlo simulation and Cellular Automata is applied in order to evaluate the performance of a networked system, made up of source nodes, user nodes and directed edges subjected to failure and repair. Importance Sampling techniques are used for the estimation of the first and total order Differential Importance Measures through only one simulation of the system “operational life”. All the output variables are computed contemporaneously on the basis of the same sequence of the involved components, event types (failure or repair) and transition times. The failure/repair probabilities are forced to be the same for all components; the transition times are sampled from the unbiased probability distributions or it can be also forced, for instance, by assuring the occurrence of at least a failure within the system operational life. The algorithm allows considering different types of maintenance actions: corrective maintenance that can be performed either immediately upon the component failure or upon finding that the component has failed for hidden failures that are not detected until an inspection; and preventive maintenance, that can be performed upon a fixed interval. It is possible to use a restoration factor to determine the age of the component after a repair or any other maintenance action.

Numerical modeling of the Alto Tiberina low angle normal fault

The aim of this Thesis is to obtain a better understanding of the mechanical behavior of the active Alto Tiberina normal fault (ATF). Integrating geological, geodetic and seismological data, we perform 2D and 3D quasi-static and dynamic mechanical models to simulate the interseismic phase and rupture dynamic of the ATF. Effects of ATF locking depth, synthetic and antithetic fault activity, lithology and realistic fault geometries are taken in account. The 2D and 3D quasi-static model results suggest that the deformation pattern inferred by GPS data is consistent with a very compliant ATF zone (from 5 to 15 km) and Gubbio fault activity. The presence of the ATF compliant zone is a first order condition to redistribute the stress in the Umbria-Marche region; the stress bipartition between hanging wall (high values) and footwall (low values) inferred by the ATF zone activity could explain the microseismicity rates that are higher in the hanging wall respect to the footwall. The interseismic stress build-up is mainly located along the Gubbio fault zone and near ATF patches with higher dip (30°models demonstrate that the magnitude expected, after that an event is simulated on the ATF, can decrease if we consider the fault plane roughness.