Festkörpermechanik

This study presents an approach based on data-driven methods for determining the parameters needed to model time-dependent material behaviour. The time-dependent behaviour of the thermoplastic polymer polybutylene terephthalate is investigated. The material was examined under two conditions, one with and one without the inclusion of reinforcing short fibres. Two modelling approaches are proposed to represent the time-dependent response. The first approach is the generalised Maxwell model formulated through the classical exponential Prony series, and the second approach is a model based on fractional calculus. In order to quantify the comparative capabilities of both models, experimental data from tensile creep tests on fibre-reinforced polybutylene terephthalate and unreinforced polybutylene terephthalate specimens are analysed. A central contribution of this work is the implementation of a machine-learning-ready parameter identification framework that enables the automated extraction of model parameters directly from time-series data. This framework enables the robust fitting of the Prony-based model, which requires multiple characteristic times and stiffness parameters, as well as the fractional model, which achieves high accuracy with significantly fewer parameters. The fractional model benefits from a novel neural solver for fractional differential equations, which not only reduces computational complexity but also permits the interpretation of the fractional order and stiffness coefficient in terms of physical creep resistance. The methodological framework is validated through a comparative assessment of predictive performance, parameter cheapness, and interpretability of each model, thereby providing a comprehensive understanding of their applicability to long-term material behaviour modelling in polymer-based composite materials.

This work examines dynamic models for describing the viscoelastic behaviour of short-fibre reinforced plastics in tensile tests. The creep behaviour of reinforced PBT GF30 compared to unreinforced PBT GF0 is investigated on the basis of experimental data. Two different modelling approaches are compared: a generalised Maxwell model based on the prony series and a model with fractional derivatives. The experimental data show that glass fibres significantly reduce the deformation under constant load, as they stiffen the polymer matrix and inhibit creep deformation. Parameters can be determined for both models using machine learning methods. However, the Prony-Maxwell based model requires three parameters to accurately represent the data, whereas the fractional model only requires two parameters. The results clearly show the advantages of fractional model for the description of the long time series behaviour: on the one hand, fewer parameters are required and on the other hand, additional knowledge can be gained through the interpretation of the parameters obtained. The experimental data as well a the open-source software developed to learn the model is published alongside this work.

In order to enhance Structural Health Monitoring of engineering structures, an appropriate modelling of the underlying structures as e. g. bridges or wings is necessary. Amongst other things this includes relevant (pre-)damages as cracks, delaminations, imperfect bonding, etc. which have to be incorporated at the so-called micro- or mesoscale of the structure. However, given the overall dimensions of typical engineering structures a discrete modelling of these (pre-)damages is not feasible at the macro-/structural scale. Thus, a scale-bridging is necessary to capture the structural behaviour. One promising approach to incorporate (pre-)damages at the microscale while maintaining a numerically manageable model of the overall structure is the sub-structure technique which will be used in the current project. Since a Structural Health Monitoring using the aforementioned numerical models strongly relys on useful measurement data it is of tremendous interest to determine the optimal number and the optimal position of the respective sensors. Hence, this topic is also addressed in the current contribution.

Im Rahmen dieser Arbeit wird das Ausbreitungsverhalten geführter Wellen in vorgespannten und geschichteten Wellenleitern anhand von experimentellen und numerischen Untersuchungen analysiert. Anhand experimenteller Versuchsreihen wird an Aluminiumproben der Einfluss einer Vorspannung in Ausbreitungsrichtung der Wellen auf die Phasengeschwindigkeit untersucht. Darauf aufbauend werden numerische Untersuchungen durchgeführt, um die Eignung verschiedener hyperelastischer Materialmodelle hinsichtlich dieser Einflüsse über große Frequenzbereiche zu bewerten. Im Gegensatz zur einschlägigen Literatur im Bereich technischer Anwendungen wird neben dem häufig verwendeten Materialmodell nach Murnaghan auch das Neo-Hooke-Materialmodell verwendet, um die Anwendbarkeit weniger komplexer Modelle ohne die Verwendung von Materialkonstanten höherer Ordnung zu untersuchen. Im Bereich der geschichteten Wellenleiter wird anhand von experimentellen Versuchsreihen das grundlegende Ausbreitungsverhalten von geführten Wellen in einem Faser-Metall-Laminat aus kohlefaserverstärktem Kunststoff und Stahl untersucht. Anhand von Vergleichen mit numerischen Untersuchungen können analytische und numerische Ansätze, bekannt aus isotropen Materialien und faserverstärkten Kunststoffen für das hier verwendete Werkstoffsystem validiert werden. Der Fokus dieser Vergleiche liegt neben den Dispersionsbeziehungen auf den Verschiebungsfeldern der geführten Wellen.

Due to the capability of mold injecting manufacturing short fiber-reinforced composites are increasingly in use in the aeronautical and automotive industries. However, a crucial aspect is their spatially distributed material properties induced by the probabilistic characteristics of the microstructure. To predict the structural response of components made of short fiber-reinforced composites by numerical simulation correctly the probabilistic information must be included in the modeling approach. Furthermore, commonly used matrix material is characterized by a distinct plastic deformation even at low stress levels. Therefore, in this work, a modeling approach is proposed that utilizes second-order Gaussian random fields for the representation of the spatially distributed material properties on the component level in the elastic and plastic domain. The modeling approach comprises the cross-correlation analysis of the material parameters describing the elastic-ideal plastic material behavior and a subsequent representation of the parameters by second-order Gaussian random fields. The analysis reveals a complex cross-correlation structure of the parameters, which depends on the window size on the mesoscale and requires the use of suitable numerical methods like the multiple correlated Karhunen-Loève expansion to synthesize the representation of the material parameters. The numerical simulations of tensile test specimens in the elastic and plastic domain predict the structural response under uniaxial loading accurately. The localized plastic deformation of the specimen is observable and meets the experimental validation by tensile tests until failure. Furthermore, the experimental data is used to determine the correlation length. Besides this, the modeling approach is validated by nanoindentation tests on the mesoscale, which reveal the spatial distribution of the material properties. Furthermore, it is shown that the area characterized by nanoindentation tests is 25 times larger than the projected area of the used Berkovich tip. In conclusion, the proposed modeling approach utilizing random fields is capable of representing the localized deformation of short fiber-reinforced composites induced by the probabilistic characteristics of the microstructure. Furthermore, the correlation structure can be derived by numerical simulation on the mesoscale, which can be experimentally analyzed by nanoindentation tests. Finally, the correlation length is an independent material parameter, which can be derived from experimental data.

In der vorliegenden Arbeit werden experimentelle und numerische Untersuchungen zum Bruchverhalten von interlaminaren Sensoren durchgeführt. Diese sollen für die strukturelle Zustandsüberwachung von Faser-Kunststoff-Verbunden nutzbar sein und mithilfe eines piezo-gesteuerten Strahldosierers hergestellt werden. Das Ziel ist die Verbesserung der kohäsiven Eigenschaften, der Geometrie und der Position der Sensoren, sodass deren Schädigungswirkung auf das Bauteil minimiert wird. Grundlage für die Herstellung der Sensoren bildet eine Tinte auf Basis von Kohlenstoffnanoröhren und Epoxidharz, wodurch gute elektrische und mechanische Eigenschaften ermöglicht werden sollen. Die Zusammensetzung der Tinte wird unter Nutzung eines statistischen Versuchsplanes optimiert. Bei einem Füllgrad von 0.25 wt% Kohlenstoffnanoröhren wird die Reproduzierbarkeit des Druckprozesses sowie ein geringer elektrischer Schichtwiderstand des entstehenden Komposits sichergestellt. In Doppelkragträger- und endgeschlitzten Dreipunkt-Biegeversuchen werden kohäsive Eigenschaften des Komposits nachgewiesen, welche vergleichbar mit denen von reinen Glasfaser-Kunststoff-Verbunden sind. Numerische Modelle dieser Bruchversuche mit homogenen Kohäsivschichten werden anschließend erstellt. Sie nutzen bewusst grob gewählte finite Elemente sowie Kohäsivzonenmodelle, welche das lokale Risswachstum beschreiben. Zur Validierung werden die numerischen Lösungen mit den analytischen Lösungen der Bruchversuche verglichen. Zu diesem Zweck wird ein Kalibrierungsverfahren für die kohäsive Festigkeit erarbeitet und angewandt. Die Erweiterung der numerischen Modelle auf heterogene Kohäsivschichten ermöglicht in der Folge die Untersuchung des Einflusses von rechteckigen, interlaminaren Sensoren auf das Bruchverhalten. Durch die Variation der kohäsiven Eigenschaften, der Geometrie und der Position der Sensoren werden Designaspekte für eine geringe Schädigungswirkung abgeleitet. Der kumulative Schaden wird als Optimierungskriterium eingeführt. Insbesondere die Fläche und die Orientierung nicht-quadratischer Sensoren unter Beachtung des wirkenden Rissbeanspruchungsmodus bieten großes Optimierungspotenzial. Die abgeleiteten Designaspekte werden anschließend auf interlaminare Sensoren in einem numerischen Faser-Kunststoff-Stringer übertragen und bestätigt. Die Ergebnisse zeigen, dass bereits 87% der Schädigungswirkung durch die Optimierung der Geometrie vermieden werden können. Dies kann zukünftig die interlaminare Integration von Sensormaterialien mit schwächeren kohäsiven Eigenschaften im Vergleich zum Faser-Kunststoff-Verbund ermöglichen.

For the numerical simulation of short fiber-reinforced composites and the correct analysis of the deformation, information about the plastic behavior and its spatial distribution is essential. When using purely deterministic modeling approaches information of the probabilistic microstructure is not included in the simulation process. One possible approach for the integration of stochastic information is the use of random fields, which requires information about the correlation structure of all material input parameters. In this study the correlation structure for finite strain elasto-plastic material behavior of short fiber-reinforced composites is analyzed. This approach combines the use of already established procedures for linear-elastic material behavior with a homogenization method for plasticity. The obtained results reveal a complex correlation structure, which is approximated with triangle and exponential correlation functions influenced by the window size. Due to the dependence of the hyperelastic and plastic material parameters on the fiber mass fraction, the strain-energy density function coefficients are cross-correlated with the yield strength of the composite. With this knowledge at hand, in a subsequent work numerical simulations of tensile tests are conducted that cover the elastic and plastic domain and include spatially distributed material properties.

For the numerical simulation of components made of short fiber-reinforced composites, the correct prediction of the deformation including the elastic and plastic behavior and its spatial distribution is essential. When using purely deterministic modeling approaches, the information of the probabilistic microstructure is not included in the simulation process. One possible approach for the integration of stochastic information is the use of random fields. In this study, numerical simulations of tensile test specimens were conducted utilizing a finite deformation elastic–ideal plastic material model. A selection of the material parameters covering the elastic and plastic domain are represented by cross-correlated second-order Gaussian random fields to incorporate the probabilistic nature of the material parameters. To validate the modeling approach, tensile tests until failure were carried out experimentally, which confirmed the assumption of the spatially distributed material behavior in both the elastic and plastic domain. Since the correlation lengths of the random fields cannot be determined by pure analytic treatments, additionally numerical simulations were performed for different values of the correlation length. The numerical simulations endorsed the influence of the correlation length on the overall behavior. For a correlation length of 5 (Formula presented.) (Formula presented.), a good conformity with the experimental results was obtained. Therefore, it was concluded that the presented modeling approach was suitable to predict the elastic and plastic deformation of a set of tensile test specimens made of short fiber-reinforced composite sufficiently.