Silicon photovoltaics: experimental testing and modelling of fracture across scales

The study of the properties of materials can be addressed through a multi-scale approach, in order to have the possibility to grasp at each of the levels of analysis the peculiar aspects. Tracing a path inside the state-of-the-art in the available bibliography, historically in the field of mechanics s are found in which the material is studied through nonlocal theories based on continuous or discrete local approaches. More recently, with the advent of great computatio- nal power computers, analytical methodologies based on theories also very complex deriving from the field of chemistry and physics have been developed, capable to discretize at the ato- mic scale the material and study its behavior by applying energy approaches. Starting from the analysis of some of these theories at the nano- and micro-scales, it is possible to investi- gate the separation mechanisms at the molecular level, which may be considered as cracking processes within the material according to the adopted scale of analysis. The application of theories of this kind to large portions of material, in which there are up to some millions of particles involved is reasonably not an applicable solution, since it would require a huge effort in terms of computation time. To work around this problem and find a method suitable for the study of cracking mechanisms, a mixed method (MDFEM) was byconjugating pure molecu- lar dynamics (MD) and the finite element method (FEM), in which the material is discretized by means of one-dimensional elements whose mechanical characteristics are derived from MD. This approach is based on the application of a nonlocal theory in which the contribution of a portion of material placed within a certain distance from the point of fracture is taken into account by means of a parameter of non-locality. Moreover, the study of the evolution of cracking is addressed at the meso-scale by the application of a cohesive non-linear model. Towards the analysis of the macroscale, the theories put forward so far have been ap- plied to the study of phenomena of breakage inside Silicon cells embedded into rigid or semi-flexible photovoltaic modules. By performing various laboratory tests, useful for the characterization of the material and for understating the evolution of cracking process due to multiple causes, a study on the main issues that may compromise the durability and mainte- nance of the expected service levels of photovoltaic panels has been conducted. Experimen- tally results have been interpreted by using appropriate macro-scopic continuum models. The research carried out had the purpose to provide an introduction to a correct design of these systems of energy production in order to increase their durability and resistance to cracking

Computational Modeling of Discrete Mechanical Systems and Complex Networks: Where We are and Where We are Going

WHERE WE ARE IN MODELING MECHANICAL, TRAFFIC, AND SOCIO-ECONOMICAL DISCRETE SYSTEMS Discrete systems have been firstly introduced in physics (Fisher and Wiodm, 1969; Noor and Nemeth, 1980; Adhikari et al., 1996; Kornyak, 2009) to simulate materials at the microand nano-scales where a continuum description of matter breaks down. The constituents can be atoms or molecules and their interactions are usually modeled by force fields resulting from chemical potentials or weak van der Waals interactions, depending on the type of bonding. These models have been further exploited in mechanics with the aim of predicting macroscopic properties such as strength and toughness from the non-linear interactions taking place between the constituents at the different scales. Pioneering attempts in mechanics to model discrete mechanical systems are those using lattice models (van Mier et al., 1995; Schlangen and Garboczi, 1997) characterized by a network of nodes connected by links modeled by beams. Although proven to suffer from meshdependency, they have been broadly used for studying the non-linear fracture behavior of concrete at the meso-scale. Another line of research regards the generalizedBorn approach (Pellegrini and Field, 2002; Marenich et al., 2013), firstly used in chemistry to model a solute represented as a set of three-dimensional spheres into a continuum medium solvent, then applied in molecular mechanics (called MM/GBSA) to investigate contact and fracture of bodies at the micro-scale. The high-computational power and the development of powerful open source software allow nowadays the design of wide discrete scalable models composed of up to millions of particles or molecules whose equations of motions and mutual interactions are described by highly nonlinear interatomic potential laws. This is the field of molecular dynamics (MD), which led to the development of specific explicit time integration schemes (like the velocity-verlet integration scheme) to solve large systems of equations with a reduced computational cost. Car and Parrinello (1985) proposed a minimization of the total energy of the system by applying a dynamical simulated annealing based on MD. MD computations can also be coupled with continuum simulations by multi-scale methods. Among the many strategies available in the literature, (Shenoy et al., 1999; Knap and Ortiz, 2001) developed an approach based on the Tadmor's quasi-continuum method (Tadmor et al., 1996) operating on a representative atomistic zone with a reduced number of degrees of freedom. Local minima of the whole system potential energy are determined via the total energy from a cluster of atoms, avoiding the complete calculation of the full atomistic force field. The MD enriched continuum method by Belytschko and Xiao (2003) and Xiao and Belytschko (2003) was also another pioneering approach to couple a potential energy Hamiltonian calculation conducted on a fine scale MD domain with a Lagrangian calculation on a coarse scale continuum domain with an overlapped bridging domain among the two representations. Recently, an implementation of interatomic potential laws within a displacement-based finite element (FE) formulation has also been proposed in Nasdala et al. (2010), with a rigorous implicit solution scheme, aiming at generating models where non-linear discrete and continuous systems can be suitably combined. Discrete systems made of nodes and links are also used in other disciplines than mechanics to model transport or socio-economical networks (Caldarelli and Vespignani, 2007; Whrittle, 2012). Based on a continuum version of traffic conservation along a link, Lighthill and Whitham (1955) and Whitham (1974) and independently Richards (1956) proposed the LWR model where the governing equation describing the dependency of the traffic flux on time and on location along a link is a nonlinear hyperbolic partial differential equation (PDE) analogous to that describing the propagation of the front of a wave inside a medium. For a homogenous link where the velocity of traffic is the same at any location and no shocks on the traffic flow are present, the integration of the LWR PDE leads to a non-linear relation between the traffic flow and the density of vehicles, which fully represents the traffic state. Also, in economics, it is of great interest to quantify the effect of breaking a link over the whole network response by simulating the dynamics of flow redistribution. Again a flow model can be used as suggested in Zhou et al. (2010) to decode a huge human crowd without distinction betwee

Simulated hail impacts on flexible photovoltaic laminates: testing and modelling

The problem of simulated low-velocity hail impacts on flexible photovoltaic (PV) modules resting on a substrate with variable stiffness is investigated. For this type of PV module it is shown that the prescriptions of the IEC 61215 International Standard for quality control used for rigid (glass-covered) PV modules should be augmented by taking into account their real mounting condition and the stiffness of the substrate in the simulated hail impact tests. Moreover, electroluminescence inspection of the crack pattern should be made in addition to electric power output measurements.An implicit finite element simulation of the contact problem in dynamics is also proposed, with two different degrees of accuracy, to interpret the experimentally observed extension of cracking. Results pinpoint the important role of stress wave propagation and reflection in the case of soft substrates

Experimental and numerical investigation on the stress field induced by impact loadings in semi-flexible photovoltaic modules

In the present work, the effects of impacts on silicon (Si) cells embedded in semi-flexible photovoltaic (PV) modules are investigated from both the experimental and the numerical point of views. Semi-flexible PV modules, frequently installed on curved surfaces, such as on sailing boat decks, mountain refuge roofs, motorhomes and innovative electrical cars, are in fact particularly sensitive to the impact of hailstones, due to the fact that they are entirely made of soft polymeric layers. In order to simulate the hailstone impact, a polyamide sphere with a radius of 20 mm has been shot with a compressed-air apparatus against the PV module at different velocities, up to a maximum value of 10m/s. The effects of the impact load on the Si cells, invisible by the naked eye, have been analyzed through pictures taken with the electroluminescence (EL) technique [1]. Different typologies of substrates on which the panels are laid on have been considered, in order to identify the configuration that minimizes the extension of the zone around the impact point characterized by a high stress level. In the case of a rigid substrate, the damage is localized in a narrow circular area, where the Si cell is completely destroyed, whereas a completely different damage pattern is occurring in the case of a soft substrate, showing several concentric cracks developed around the point of impact. As regards the numerical modelling, an axisymmetric finite element model of the laminate has been proposed using the finite element analysis program FEAP. Linear elastic constitutive laws have been adopted for the materials composing the layers, except for the epoxy material encapsulating the Si cells for which a neo-Hookean constitutive behavior has been considered. An implicit integration scheme has been used to solve the contact problem, using the node-to-segment contact strategy [2] and the penalty method to model the contacting interfaces. Different values of the penalty parameter have been used along the contact interface between the PV module and the substrate, to simulate different substrate stiffnesses. Numerical predictions regarding the extension of the damaged areas are in good agreement with our own experimental results obtained in the laboratory

Image analysis of polycrystalline solar cells and modeling of intergranular and transgranular cracking

An innovative image analysis technique is proposed to process real solar cell pictures, identify grains and grain boundaries in polycrystalline silicon, and finally generate finite element meshes. Using a modified intrinsic cohesive zone model approach to avoid mesh dependency, nonlinear finite element simulations show how grain boundaries and silicon bulk properties influence the crack pattern. Numerical results demonstrate a prevalence of transgranular over intergranular cracking for similar interface fracture properties of grains and grain boundaries, in general agreement with the experimental observatio

Electrical recovery and fatigue degradation phenomena in cracked silicon cells

An experimental study based on the electroluminescence technique is herein proposed to demonstrate the existence of coupling between mechanical deformations and the intensity of the electric field due to cracks in monocrystalline Silicon cells embedded in photovoltaic modules. In spite of the very brittle nature of Silicon, due to the action of the encapsulating polymer and residual compressive stresses resulting from the lamination stage, cracks experience crack closure and contact during mechanical unloading, partially recovering their original electric response. Crack propagation in case of cyclic loading, as, e.g., in case of vibrations due to transportation and use, have also been reported for the very first time. The research results pinpoint the need of improving electric predictions based on the estimation of inactive cell areas, since worst case scenarios not accounting for electro-mechanical coupling are too conservative

Tuberculose : place de la vaccination dans la maîtrise de la maladie

La tuberculose, important problème de santé publique dans le monde, aconduit l’OMS à inciter les gouvernements à promouvoir un programmenational de lutte contre cette maladie. Dans les pays en développement, où ily a une forte endémie de tuberculose, la vaccination des nouveau-nés par leBCG est une action déterminante de ce programme, l’amélioration de l’efficacitédu vaccin est considérée comme une priorité mondiale.Dans les pays industrialisés, l’existence d’une politique vaccinale au sein duprogramme est variable. Certains pays ont en effet privilégié la détectionprécoce des cas, le traitement des cas contagieux et la thérapie préventive despersonnes infectées plutôt que la vaccination. En France, pays de forte traditionvaccinale, la vaccination par le BCG est obligatoire pour l’entrée encollectivité des enfants et la couverture vaccinale est élevée (95 % à 6 ans).En application d’un décret et d’un arrêté publiés en juillet 2004, une seulevaccination est désormais préconisée et les tests tuberculiniques ne sont pluseffectués pour contrôler la vaccination.Il est difficile de distinguer le rôle spécifique de la vaccination dans l’impactglobal des programmes sur le contrôle de la tuberculose. Il est cependantuniversellement admis que la vaccination protège les jeunes enfants contreles formes sévères de tuberculose (méningite et miliaire). Par ailleurs, l’efficacitéde la vaccination par le BCG a pu être évaluée dans certains pays oùl’interruption des programmes de vaccination s’est traduite par une augmentationdu nombre de cas de tuberculose.Plusieurs pays d’Europe à faible incidence de tuberculose ont arrêté la primovaccinationou pratiquent une vaccination ciblée sur des groupes à risque.L’efficacité de la stratégie de vaccination sélective est dépendante de lacouverture vaccinale obtenue dans ces groupes cibles et donc de la capacité àles identifier et à les vacciner.En France, l’incidence moyenne des cas déclarés, de l’ordre de 11 pour100 000, est équivalente à l’incidence moyenne en Europe occidentale. Cechiffre global cache une disparité importante, géographique mais surtoutentre les populations natives et étrangères. À Paris, l’incidence des casdéclarés est 5 fois plus forte que l’incidence moyenne nationale. En France,dans les populations étrangères issues de pays à forte endémie, l’incidence,environ 10 fois supérieure à celle des populations autochtones, est enaugmentation (de près de 20 % par an pour la population des 15-24 ans)