A stochastic failure investigation of composites under combined compression-shear loads

Because of their excellent specific strength and stiffness properties, fiber-reinforced polymers (FRPs) have become increasingly material of choice for advanced industries such as aerospace and wind turbines. One of the design limiting factors in FRPs is their lower compression strength in comparison to their tensile strength. Microbuckling (MB) is the dominant failure mode in unidirectional FRPs under predominant compression loads. The main factors dictating failure under compression dominated loads are the fiber misalignment and the nonlinear material behavior. Because of high sensitivity of MB failure to the fiber misalignment, the MB strength shows uncertainty. To enable reliable failure prediction, a quantification of the strength uncertainty is required. The current investigation aims for a probabilistic prediction of MB failure under axial compression and combined compression-shear loads. Using a newly in-house developed combined loading fixture, a statistically significant number of specimens was tested under aforementioned load cases. Using the experimental strain measurements, a probabilistic failure envelope in strain space is presented. Results of the axial compression load case are interpreted in the context of the notion of the effective misalignment angle using an analytical model. A failure envelope in stress space is derived using an analytical solution for the combined compression-shear load cases and the effective global misalignment angle calculated from the measurements. Other experimental aspects of the problem are also investigated such as the material characterization and measurements of the fiber misalignment. To represent the fiber misalignment in numerical models for the prediction of MB strength while preserving the spatial correlation information, the spectral representation method is employed in this investigation. A large number of realizations were developed based on spectral densities calculated from the measurements of the fiber misalignment. The numerically determined probabilistic failure envelopes in stress and strain spaces are presented with lower percentiles of distributions of failure. The failure enveloped are also compared against classical failure criteria from the literature to highlight the limitations of the classical criteria. Since the sizes of the model and the experimental specimen were different, a comparison of numerically predicted strengths against experimentally obtained results under the axial compression loads was performed on the basis of a scaling law. A discussion on differences in the shape of the failure envelopes is provided. Conclusions are drawn at the end and an outlook for further research on the topic is given.Faserverstärkte Verbundwerkstoffe (CFK/GFK) sind aufgrund ihrer ausgezeichneten spezifischen Festigkeits- und Steifigkeitseigenschaften zunehmend zum bevorzugten Material für hochentwickelte Industrien wie die Luft- und Raumfahrt und Windkraftanlagen geworden. Einer der konstruktionsbegrenzenden Faktoren bei CFK/GFK ist ihre geringere Druckfestigkeit im Vergleich zu ihrer Zugfestigkeit. Microbuckling (MB) ist die vorherrschende Versagensart bei unidirektionalen CFK/GFK unter vorherrschenden Druckbelastungen. Die Hauptfaktoren, die das Versagen bei Druckbelastungen diktieren, sind die Faserimperfektionen und das nichtlineare Materialverhalten. Aufgrund der hohen Empfindlichkeit des MB-Versagens gegenüber der Faserimperfektionen ist die MB-Festigkeit mit Unsicherheit behaftet. Um eine zuverlässige Versagensvorhersage zu ermöglichen, ist eine Quantifizierung der Festigkeitsunsicherheit erforderlich. Die aktuelle Studie zielt auf eine probabilistische Vorhersage des Versagens von MB unter axialer Druck- und kombinierter Druck-Schub-Belastung ab. Unter Verwendung einer neu entwickelten kombinierten Prüfvorrichtung wurde eine statistisch signifikante Anzahl von Proben unter den vorgenannten Lastfällen geprüft. Anhand der experimentellen Dehnungsmessungen wird eine probabilistische Versagenskurve im Dehnungsraum dargestellt. Die Ergebnisse des axialen Druckbelastungsfalls werden im Zusammenhang mit dem Begriff des effektiven Versatzwinkels anhand eines analytischen Modells interpretiert. Unter Verwendung einer analytischen Lösung für den kombinierten Druck-Schub-Lastfall und des aus den Messungen berechneten effektiven globalen Versatzwinkels wird eine Versagenshüllkurve im Spannungsraum abgeleitet. Andere experimentelle Aspekte des Problems werden ebenfalls untersucht, wie z. B. die Materialcharakterisierung und Messungen der Faserimperfektionen. Um die Faserimperfektionen mit Berücksichtigung auf räumliche Korrelationsinformation in numerischen Modellen zur Vorhersage der MB-Festigkeit darzustellen, wird in dieser Untersuchung die Methode der spektralen Darstellung verwendet. Auf der Grundlage von Spektraldichten, die aus den Messungen der Faserverschiebung berechnet wurden, wurde eine große Anzahl von Realisierungen erstellt. Die numerisch ermittelten probabilistischen Versagenskurven in Spannungs- und Dehnungsräumen werden mit unteren Perzentilen der Versagensverteilungen dargestellt. Die probabilistische Versagenskurven werden auch mit klassischen Versagenskriterien aus der Literatur verglichen, um die Grenzen der klassischen Kriterien aufzuzeigen. Da die Größen des Modells und der experimentellen Probe unterschiedlich waren, wurde ein Vergleich der numerisch vorhergesagten Festigkeiten mit den experimentell ermittelten Ergebnissen unter den axialen Druckbelastungen auf der Grundlage eines Skalierungsgesetzes durchgeführt. Es wird eine Diskussion über die Unterschiede in der Form der Versagenskurven geführt. Anschließend werden Schlussfolgerungen gezogen und ein Ausblick auf weitere Forschungsaktivitäten zu diesem Thema gegeben

Etude multi-échelle du couplage matériau-procédé pour l'identification et la modélisation des variabilités au sein d'une structure composite

Une des problématiques liées à l'utilisation des matériaux composites dans les structures tient à la difficulté de prévoir l'effet des variabilités inhérentes à ce type de matériau sur le comportement mécanique. Les propriétés d'une structure composite dépendent non seulement du procédé, mais aussi des matières premières et des choix de conception. Dans le but d'introduire des variabilités géométriques dans le calcul numérique des pièces composites, on part dans ce travail de l'hypothèse que les variations des grandeurs géométriques ne sont pas distribuées totalement aléatoirement, mais que celles-ci suivent des évolutions spatiales continues. Pour que les valeurs d'entrée qui nourrissent le modèle numérique soient basées sur la réalité du matériau, l'identification et la quantification des plages de variabilités et de leurs évolutions sont réalisées sur la période de la fabrication de plaques composites CFRP comptant ici 16 plis avec une stratification quasi isotrope et polymérisées en autoclave. Parmi les sources de variabilité identifiées et quantifiées, l'étude de la répartition des désalignements des fibres dans le plan et de l'évolution des variations des épaisseurs des plis a mené à la proposition de lois mathématiques d'évolution spatiale basées sur la réalité du matériau dans la pièce. Ces lois mathématiques sont ensuite utilisées pour récréer numériquement plusieurs structures composites différentes de la structure observée mais qui possèdent des valeurs de dispersions des propriétés similaires aux plaques réelles. Enfin, les structures numériques sont analysées dans un modèle éléments finis pour évaluer l'impact des dites variabilités géométriques et matériaux sur les propriétés mécaniques de la structure finale au travers de plusieurs études de cas.One of the major challenges related to the use of composite materials in structural applications is the difficulty to predict the effect of their inherent variabilities on the mechanical behaviour for such materials. The structural properties do not only depend on the fabrication process, but also depend on the raw materials and design considerations. The major goal of this thesis is the introduction of geometrical variabilities into a finite element (FE) model starting from the hypothesis that geometrical variations are not completely randomly distributed, but they maintain a spatial continuous evolution. To guarantee that the input parameters of the FE model are based on the reality of the material, the identification and quantification of the variability distributions together with their spatial evolutions are performed during the fabrication of CFRP composite plates. These plates have a 16 ply quasi-isotropic stratification and are cured in autoclave. Among the identified and quantified variability sources, the study of the in plane fibre misalignments and the evolution of the ply thickness variations has conducted to the proposition of mathematical representations of the spatial evolution of these variables based on the material reality. These mathematical representations are used to recreate different sets of virtual composites structures maintaining dispersion values similar to the real plates. Finally, the virtual structures are analysed in the FE model to evaluate the impact of such geometrical and material variabilities on the mechanical properties of the final structure

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

The Public Service Media and Public Service Internet Manifesto

This book presents the collectively authored Public Service Media and Public Service Internet Manifesto and accompanying materials.The Internet and the media landscape are broken. The dominant commercial Internet platforms endanger democracy. They have created a communications landscape overwhelmed by surveillance, advertising, fake news, hate speech, conspiracy theories, and algorithmic politics. Commercial Internet platforms have harmed citizens, users, everyday life, and society. Democracy and digital democracy require Public Service Media. A democracy-enhancing Internet requires Public Service Media becoming Public Service Internet platforms – an Internet of the public, by the public, and for the public; an Internet that advances instead of threatens democracy and the public sphere. The Public Service Internet is based on Internet platforms operated by a variety of Public Service Media, taking the public service remit into the digital age. The Public Service Internet provides opportunities for public debate, participation, and the advancement of social cohesion. Accompanying the Manifesto are materials that informed its creation: Christian Fuchs’ report of the results of the Public Service Media/Internet Survey, the written version of Graham Murdock’s online talk on public service media today, and a summary of an ecomitee.com discussion of the Manifesto’s foundations

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This open access book presents established methods of structural health monitoring (SHM) and discusses their technological merit in the current aerospace environment. While the aerospace industry aims for weight reduction to improve fuel efficiency, reduce environmental impact, and to decrease maintenance time and operating costs, aircraft structures are often designed and built heavier than required in order to accommodate unpredictable failure. A way to overcome this approach is the use of SHM systems to detect the presence of defects. This book covers all major contemporary aerospace-relevant SHM methods, from the basics of each method to the various defect types that SHM is required to detect to discussion of signal processing developments alongside considerations of aerospace safety requirements. It will be of interest to professionals in industry and academic researchers alike, as well as engineering students. This article/publication is based upon work from COST Action CA18203 (ODIN - http://odin-cost.com/), supported by COST (European Cooperation in Science and Technology). COST (European Cooperation in Science and Technology) is a funding agency for research and innovation networks. Our Actions help connect research initiatives across Europe and enable scientists to grow their ideas by sharing them with their peers. This boosts their research, career and innovation