Fatigue Crack Propagation in Pressurized metallic Fuselages

On the basis of well-known literature, an analytical tool named LEAF (Linear Elastic Analysis of Fracture) was developed to predict the Damage Tolerance (DT) proprieties of aeronautical stiffened panels. The tool is based on the linear elastic fracture mechanics and the displacement compatibility method. By means of LEAF, an extensive parametric analysis of stiffened panels, representative of typical aeronautical constructions, was performed to provide meaningful design guidelines. The effects of riveted, integral and adhesively bonded stringers on the fatigue crack propagation performances of stiffened panels were investigated, as well as the crack retarder contribution using metallic straps (named doublers) bonded in the middle of the stringers bays. The effect of both perfectly bonded and partially debonded doublers was investigated as well. Adhesively bonded stiffeners showed the best DT properties in comparison with riveted and integral ones. A great reduction of the skin crack growth propagation rate can be achieved with the adoption of additional doublers bonded between the stringers.

Effect of Laser Shock Peening on Fatigue Crack Propagation of Aeronautical Structures

Laser Shock Peening (LSP) is a surface enhancement treatment which induces a significant layer of beneficial compressive residual stresses up to several mm underneath the surface of metal components in order to improve the detrimental effects of crack growth behavior rate in it. The aim of this thesis is to predict the crack growth behavior of thin Aluminum specimens with one or more LSP stripes defining a compressive residual stress area. The LSP treatment has been applied as crack retardation stripes perpendicular to the crack growing direction, with the objective of slowing down the crack when approaching the LSP patterns. Different finite element approaches have been implemented to predict the residual stress field left by the laser treatment, mostly by means of the commercial software Abaqus/Explicit. The Afgrow software has been used to predict the crack growth behavior of the component following the laser peening treatment and to detect the improvement in fatigue life comparing to the specimen baseline. Furthermore, an analytical model has been implemented on the Matlab software to make more accurate predictions on fatigue life of the treated components. An educational internship at the Research and Technologies Germany- Hamburg department of Airbus helped to achieve knowledge and experience to write this thesis. The main tasks of the thesis are the following: -To up to date Literature Survey related to laser shock peening in metallic structures -To validate the FE models developed against experimental measurements at coupon level -To develop design of crack growth slow down in centered and edge cracked tension specimens based on residual stress engineering approach using laser peened patterns transversal to the crack path -To predict crack growth behavior of thin aluminum panels -To validate numerical and analytical results by means of experimental tests.

Fault detection in rotating machines by vibration signal processing techniques

Machines with moving parts give rise to vibrations and consequently noise. The setting up and the status of each machine yield to a peculiar vibration signature. Therefore, a change in the vibration signature, due to a change in the machine state, can be used to detect incipient defects before they become critical. This is the goal of condition monitoring, in which the informations obtained from a machine signature are used in order to detect faults at an early stage. There are a large number of signal processing techniques that can be used in order to extract interesting information from a measured vibration signal. This study seeks to detect rotating machine defects using a range of techniques including synchronous time averaging, Hilbert transform-based demodulation, continuous wavelet transform, Wigner-Ville distribution and spectral correlation density function. The detection and the diagnostic capability of these techniques are discussed and compared on the basis of experimental results concerning gear tooth faults, i.e. fatigue crack at the tooth root and tooth spalls of different sizes, as well as assembly faults in diesel engine. Moreover, the sensitivity to fault severity is assessed by the application of these signal processing techniques to gear tooth faults of different sizes.

Studio del comportamento meccanico di smalti porcellanati per substrati metallici

Composite porcelain enamels are inorganic coatings for metallic components based on a special ceramic-vitreous matrix in which specific additives are randomly dispersed. The ceramic-vitreous matrix is made by a mixture of various raw materials and elements and in particular it is based on boron-silicate glass added with metal oxides(1) of titanium, zinc, tin, zirconia, alumina, ecc. These additions are often used to improve and enhance some important performances such as corrosion(2) and wear resistance, mechanical strength, fracture toughness and also aesthetic functions. The coating process, called enamelling, depends on the nature of the surface, but also on the kind of the used porcelain enamel. For metal sheets coatings two industrial processes are actually used: one based on a wet porcelain enamel and another based on a dry-silicone porcelain enamel. During the firing process, that is performed at about 870°C in the case of a steel substrate, the enamel raw material melts and interacts with the metal substrate so enabling the formation of a continuous varying structure. The interface domain between the substrate and the external layer is made of a complex material system where the ceramic vitreous and the metal constituents are mixed. In particular four main regions can be identified, (i) the pure metal region, (ii) the region where the metal constituents are dominant compared with the ceramic vitreous components, (iii) the region where the ceramic vitreous constituents are dominant compared with the metal ones, and the fourth region (iv) composed by the pure ceramic vitreous material. It has also to be noticed the presence of metallic dendrites that hinder the substrate and the external layer passing through the interphase region. Each region of the final composite structure plays a specific role: the metal substrate has mainly the structural function, the interphase region and the embedded dendrites guarantee the adhesion of the external vitreous layer to the substrate and the external vitreous layer is characterized by an high tribological, corrosion and thermal shock resistance. Such material, due to its internal composition, functionalization and architecture can be considered as a functionally graded composite material. The knowledge of the mechanical, tribological and chemical behavior of such composites is not well established and the research is still in progress. In particular the mechanical performances data about the composite coating are not jet established. In the present work the Residual Stresses, the Young modulus and the First Crack Failure of the composite porcelain enamel coating are studied. Due to the differences of the porcelain composite enamel and steel thermal properties the enamelled steel sheets have residual stresses: compressive residual stress acts on the coating and tensile residual stress acts on the steel sheet. The residual stresses estimation has been performed by measuring the curvature of rectangular one-side coated specimens. The Young modulus and the First Crack Failure (FCF) of the coating have been estimated by four point bending tests (3-7) monitored by means of the Acoustic Emission (AE) technique(5,6). In particular the AE information has been used to identify, during the bending tests, the displacement domain over which no coating failure occurs (Free Failure Zone, FFZ). In the FFZ domain, the Young modulus has been estimated according to ASTM D6272-02. The FCF has been calculated as the ratio between the displacement at the first crack of the coating and the coating thickness on the cracked side. The mechanical performances of the tested coated specimens have also been related and discussed to respective microstructure and surface characteristics by double entry charts.

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

Bonded structures for enhanced damage tolerant pressurized fuselages

Adhesive bonding provides solutions to realize cost effective and low weight aircraft fuselage structures, in particular where the Damage Tolerance (DT) is the design criterion. Bonded structures that combine Metal Laminates (MLs) and eventually Selective Reinforcements can guarantee slow crack propagation, crack arrest and large damage capability. To optimize the design exploiting the benefit of bonded structures incorporating selective reinforcement requires reliable analysis tools. The effect of bonded doublers / selective reinforcements is very difficult to be predicted numerically or analytically due to the complexity of the underlying mechanisms and failures modes acting. Reliable predictions of crack growth and residual strength can only be based on sound empirical and phenomenological considerations strictly related to the specific structural concept. Large flat stiffened panels that combine MLs and selective reinforcements have been tested with the purpose of investigating solutions applicable to pressurized fuselages. The large test campaign (for a total of 35 stiffened panels) has quantitatively investigated the role of the different metallic skin concepts (monolithic vs. MLs) of the aluminum, titanium and glass-fiber reinforcements, of the stringers material and cross sections and of the geometry and location of doublers / selective reinforcements. Bonded doublers and selective reinforcements confirmed to be outstanding tools to improve the DT properties of structural elements with a minor weight increase. However the choice of proper materials for the skin and the stringers must be not underestimated since they play an important role as well. A fuselage structural concept has been developed to exploit the benefit of a metal laminate design concept in terms of high Fatigue and Damage Tolerance (F&DT) performances. The structure used laminated skin (0.8mm thick), bonded stringers, two different splicing solutions and selective reinforcements (glass prepreg embedded in the laminate) under the circumferential frames. To validate the design concept a curved panel was manufactured and tested under loading conditions representative of a single aisle fuselage: cyclic internal pressurization plus longitudinal loads. The geometry of the panel, design and loading conditions were tailored for the requirements of the upper front fuselage. The curved panel has been fatigue tested for 60 000 cycles before the introduction of artificial damages (cracks in longitudinal and circumferential directions). The crack growth of the artificial damages has been investigated for about 85 000 cycles. At the end a residual strength test has been performed with a “2 bay over broken frame” longitudinal crack. The reparability of this innovative concept has been taken into account during design and demonstrated with the use of an external riveted repair. The F&DT curved panel test has confirmed that a long fatigue life and high damage tolerance can be achieved with a hybrid metal laminate low weight configuration. The superior fatigue life from metal laminates and the high damage tolerance characteristics provided by integrated selective reinforcements are the key concepts that provided the excellent performances. The weight comparison between the innovative bonded concept and a conventional monolithic riveted design solution showed a significant potential weight saving but the weight advantages shall be traded off with the additional costs.

Multilaminati piezoelettrici a gradiente funzionale

Aim of this thesis was the production of porosity-graded piezoelectric ceramics for ultrasonic applications by tape casting and screen printing. The study and optimization of each single step of the tape casting process allowed to produce flat and crack-free multilayers of Pb0.988(Zr0.52Ti0.48)0.976Nb0.024O3 (PZTN) of uniform and graded porosity. The multilayers of thickness ranging between 400 and 800 µm were produced stacking optimized green layers with different amount of pore former. The functionally graded materials showed porosity ranging between 10 and 30% with piezoelectric properties suitable for the specific ultrasonic applications. Screen printing inks of PZTN for deposition onto four different substrates were studied and optimized. Thick films with thickness ranging between 4 and 20 µm were produced tailoring the screen printing parameters and number of depositions.

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.

Modelli semplificati per valutazione di vulnerabilità sismica di strutture in muratura

L'obiettivo della tesi è stato quello di indagare il complesso problema della vulnerabilità sismica dei ponte in muratura ad arco utilizzando modelli semplificati. Dopo una descrizione dei materiali da costruzione impiegati nella realizzazione e dei principali elementi dei un ponti in muratura, si è indirizzato lo studio di un ponte ad arco situato nel comune di San Marcello Pistoiese. Viene mostrato un modello numerico che permette di descrivere il comportamento strutturale del ponte sotto azione sismica e di valutare la capacità di carico del ponte sottoposto ad una azione trasversale. In un secondo momento viene descritta la realizzazione di un modello in scala del ponte, che è stato sottoposto a prove distruttive effettuate per valutare la capacità di carico del ponte rispetto ad un ipotetica azione orizzontale. Si è cercato poi di inquadrare il problema in un modello teorico che faccia riferimento all'analisi limite. Esso descrive un cinematismo di collasso a telaio che prende spunto dal quadro fessurativo del modello in muratura. Infine sono stati presentati modelli FEM numerici in ordine di complessità crescente, cercando di inquadrare il comportamento meccanico del prototipo del ponte. Tre tipi di modelli sono rappresentati: un telaio incernierato alle estremità costituito da elementi beam con resistenza alla flessione . Il secondo tipo è costituito da una reticolare equivalente che mima lo schema del ponte ed è formato solo da bielle. Infine, il terzo tipo cerca di descrivere l'intero modello con elementi tridimensionali.

Fracture Mechanics Investigation of Structures with Defects

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities. This dissertation, concentrates on some of the fractural aspects of shaft and composite which have being increasingly used in modern structures, consists four chapters within two parts. Chapters 1 to 4 are included in part 1. In the first chapter, the basic knowledge about the stress and displacement fields in the vicinity of a crack tip is introduced. A review involves the general methods of calculating stress intensity factors are presented. In Chapter 2, two simple engineering methods for a fast and close approximation of stress intensity factors of cracked or notched beams under tension, bending moment, shear force, as well as torque are presented. New formulae for calculating the stress intensity factors are proposed. One of the methods named Section Method is improved and applied to the three dimensional analysis of cracked circular section for calculating stress intensity factors. The comparisons between the present results and the solutions calculated by ABAQUS for single mode and mixed mode are studied. In chapter 3, fracture criteria for a crack subjected to mixed mode loading of two-dimension and three-dimension are reviewed. The crack extension angle for single mode and mixed mode, and the critical loading domain obtained by SEDF and MTS are compared. The effects of the crack depth and the applied force ratio on the crack propagation angle and the critical loading are investigated. Three different methods calculating the crack initiation angle for three-dimension analysis of various crack depth and crack position are compared. It should be noted that the stress intensity factors used in the criteria are calculated in section 2.1.

Toward a Magnitude Scale for Low Frequency Seismicity The LP energy for Campi Flegrei caldera

The energy released during a seismic crisis in volcanic areas is strictly related to the physical processes in the volcanic structure. In particular Long Period seismicity, that seems to be related to the oscillation of a fluid-filled crack (Chouet , 1996, Chouet, 2003, McNutt, 2005), can precedes or accompanies an eruption. The present doctoral thesis is focused on the study of the LP seismicity recorded in the Campi Flegrei volcano (Campania, Italy) during the October 2006 crisis. Campi Flegrei Caldera is an active caldera; the combination of an active magmatic system and a dense populated area make the Campi Flegrei a critical volcano. The source dynamic of LP seismicity is thought to be very different from the other kind of seismicity ( Tectonic or Volcano Tectonic): it’s characterized by a time sustained source and a low content in frequency. This features implies that the duration–magnitude, that is commonly used for VT events and sometimes for LPs as well, is unadapted for LP magnitude evaluation. The main goal of this doctoral work was to develop a method for the determination of the magnitude for the LP seismicity; it’s based on the comparison of the energy of VT event and LP event, linking the energy to the VT moment magnitude. So the magnitude of the LP event would be the moment magnitude of a VT event with the same energy of the LP. We applied this method to the LP data-set recorded at Campi Flegrei caldera in 2006, to an LP data-set of Colima volcano recorded in 2005 – 2006 and for an event recorded at Etna volcano. Experimenting this method to lots of waveforms recorded at different volcanoes we tested its easy applicability and consequently its usefulness in the routinely and in the quasi-real time work of a volcanological observatory.