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Thermomechanical Modeling of Amorphous Polymers Through the Glass Transition Region

Blome, Thomas (2022)
Thermomechanical Modeling of Amorphous Polymers Through the Glass Transition Region.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00022487
Ph.D. Thesis, Primary publication, Publisher's Version

Abstract

In this thesis, we propose a novel thermodynamically consistent constitutive framework to model amorphous polymers through the glass transition region based on the internal variables approach. The model assumes the thermorheological simplicity hypothesis and covers different relaxation mechanisms related to bulk, shear, thermal stress and entropy relaxation, which are implemented by means of Prony parameters. Although the model is restricted to sufficiently slow processes, it is capable to span a wide range of temperatures of about ±75 °C around a defined reference temperature and predicts finite deformations up to engineering strain levels of 15 %. A key ingredient is the thermoviscoelastic shift function, which is defined in terms of the polymer’s potential internal energy. This allows to capture a variety of material properties intrinsic to amorphous polymers, such as physical aging and pseudo-yielding in tension and compression. In addition, we provide detailed information on the entire algorithmic solution procedure. The spatial discretization is accomplished using the finite element method, while diagonally implicit Runge-Kutta methods serve as the temporal integrator. Finally, we validate the constitutive model on four different polymeric systems, which comprise one thermoplastic (polyvinyl butyral) and three thermosets. The validation includes dilatometric and calorimetric experiments, tension and compression tests at various temperatures as well as three-point and four-point bending tests of laminated glasses with a polyvinyl butyral interlayer.

Item Type: Ph.D. Thesis
Erschienen: 2022
Creators: Blome, Thomas
Type of entry: Primary publication
Title: Thermomechanical Modeling of Amorphous Polymers Through the Glass Transition Region
Language: English
Referees: Gruttmann, Prof. Dr. Friedrich ; Müller, Prof. Dr. Ralf
Date: 2022
Place of Publication: Darmstadt
Collation: xiii, 133, XXXIII Seiten
Refereed: 14 September 2022
DOI: 10.26083/tuprints-00022487
URL / URN: https://tuprints.ulb.tu-darmstadt.de/22487
Abstract:

In this thesis, we propose a novel thermodynamically consistent constitutive framework to model amorphous polymers through the glass transition region based on the internal variables approach. The model assumes the thermorheological simplicity hypothesis and covers different relaxation mechanisms related to bulk, shear, thermal stress and entropy relaxation, which are implemented by means of Prony parameters. Although the model is restricted to sufficiently slow processes, it is capable to span a wide range of temperatures of about ±75 °C around a defined reference temperature and predicts finite deformations up to engineering strain levels of 15 %. A key ingredient is the thermoviscoelastic shift function, which is defined in terms of the polymer’s potential internal energy. This allows to capture a variety of material properties intrinsic to amorphous polymers, such as physical aging and pseudo-yielding in tension and compression. In addition, we provide detailed information on the entire algorithmic solution procedure. The spatial discretization is accomplished using the finite element method, while diagonally implicit Runge-Kutta methods serve as the temporal integrator. Finally, we validate the constitutive model on four different polymeric systems, which comprise one thermoplastic (polyvinyl butyral) and three thermosets. The validation includes dilatometric and calorimetric experiments, tension and compression tests at various temperatures as well as three-point and four-point bending tests of laminated glasses with a polyvinyl butyral interlayer.

Alternative Abstract:
Alternative abstract Language

In dieser Arbeit wird ein neuartiges Materialmodell zur Simulation von thermorheologisch einfachen, amorphen Polymerstrukturen entwickelt, welches auf dem Konzept der internen Variablen beruht. Die thermodynamisch konsistenten Materialgleichungen umfassen unterschiedliche Relaxationsmechanismen, welche sowohl das zeitabhängige Verhalten der Volumen- und Gestaltänderung, als auch die Relaxation der thermischen Spannungen und der Entropie abbildet. Das diskrete Relaxationsspektrum wird mit Hilfe von Prony-Parametern umgesetzt. Das Materialmodell umspannt einen weiten Temperaturbereich von ungefähr ±75 °C um eine definierte Referenztemperatur und ermöglicht die Wiedergabe von nichtlinearen Deformationen bis zu 15 % Ingenieursdehnung, wobei von hinreichend langsamen Deformationsvorgängen ausgegangen wird. Ein besonderes Merkmal stellt der thermoviskoelastische Shiftfaktor dar, welcher über die potentielle innere Energie des Polymers definiert ist. Dies ermöglicht die numerische Vorhersage unterschiedlicher konstitutiver Phänomene, wie beispielsweise physikalische Alterung und fließähnliches Verhalten von amorphen Polymeren unter Zug- als auch Druckbeanspruchung. Darüber hinaus wird eine umfangreiche Darstellung der algorithmischen Umsetzung bereitgestellt. Dies umfasst zum einen die Ortsdiskretisierung mit Hilfe der Methode der finiten Elemente, als auch die Zeitdiskretisierung unter Verwendung von diagonal-impliziten Runge-Kutta Verfahren. Das Modell wird schließlich anhand einer Reihe von experimentellen Versuchen an einem Thermoplast (Polyvinylbutyral) und drei Duroplasten validiert. Hierzu zählen dilatometrische und kalorimetrische Simulationen, die numerische Berechnung von Zug- und Druckversuchen bei unterschiedlichen Temperaturen sowie Drei- und Vierpunktbiegeversuche von Verbundsicherheitsgläsern mit einer Zwischenschicht aus Polyvinylbutyral.

German
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-224876
Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 13 Department of Civil and Environmental Engineering Sciences
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics > Solid Body Mechanics
Date Deposited: 13 Oct 2022 12:02
Last Modified: 14 Oct 2022 05:50
PPN:
Referees: Gruttmann, Prof. Dr. Friedrich ; Müller, Prof. Dr. Ralf
Refereed / Verteidigung / mdl. Prüfung: 14 September 2022
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