Pore-space controlled hardening model in plasticity of porous materials: application to the analysis of indentation experiments

Based on a multi-scale approach comprising a multi-scale material model and a respective finite-element (FE) analysis tool, the indentation response of porous materials is examined in this paper. The considered material is assumed to consist of a homogeneous Drucker-Prager-type matrix-phase and spherical pores. Non-linear homogenization is employed to derive both a strength criterion and a hardening rule at the macroscopic scale without the need of any additional non-physical material parameters. Hereby, the underlying macroscopic hardening is exclusively controlled by the evolution of the porespace during loading. The material model is implemented in a FE program within the framework of elastoplasticity. The so-obtained analysis tool is applied to the analysis of indentation experiments commonly used for characterization and performance-based optimization of materials

Continuum micromechanics-based determination of effective properties of elastoplastic matrix-inclusion materials : application within the finite element analysis of indentation and impact problems

Sowohl natürliche Materialien (z.B. Holz, Knochen, Boden, etc.) als auch technische Materialien (z.B. Beton, Schäume, Composite-Materialien, etc) weisen Inhomogenitäten wie z.B. Poren und Einschlüsse auf. In Herstellungsprozessen von Materialien wird durch Begünstigung oder Behinderung der Ausbildung dieser Inhomogenitäten versucht, die resultierenden Eigenschaften gezielt zu beeinflussen. Dabei ist das Wissen darüber, wie sich Materialinhomogenitäten auf das effektive Materialverhalten auswirken, Grundlage für ein zielorientiertes Vorgehen. Experimentelle Untersuchungen sind hierfür unumgänglich - jedoch nicht immer ausreichend. Theoretische und simulationsbasierte Ansätze ermöglichen einen zusätzlichen Informationsgewinn und tragen zum Verständnis von Zusammenhängen bei. Ziel dieser Dissertation ist es mithilfe der Kontinuummikromechanik und numerischer Simulationen (Finite Elemente Methode) einen Beitrag zum Stand der Wissenschaft über den Einfluss von Materialinhomogenitäten auf die effektiven mechanischen Materialeigenschaften zu leisten. Der Schwerpunkt liegt dabei auf dem nichtlinearen Materialverhalten im Rahmen der Plastizitätstheorie. In Hinblick darauf wird im Rahmen dieser Dissertation eine Weiterentwicklung von Methoden der nichtlinearen Kontinuummikromechanik verfolgt. Numerische Simulationen der Belastung von Materialproben (repräsentative Volumenelemente) dienen zur Validierung dieser analytischen Ansätze und ermöglichen zusätzliche Erkenntnisse. Im Speziellen werden folgende Themen behandelt: Im ersten Teil wird eine Methode zur Bestimmung der effektiven Fließfläche von Matrix-Einschlussmaterialien präsentiert, welche die Berücksichtigung von leeren und flüssigkeitsgefüllten Poren sowie starren Einschlüssen ermöglicht. Die zulässigen Spannungszustände im Matrixmaterial sind dabei durch Fließflächen von zweiter Ordnung definiert (z.B. Mises, Mises-Schleicher, Drucker-Prager und elliptische Fließflächen). Darauf folgend wird der Einfluss der Einschlussform auf die effektiven Materialeigenschaften behandelt. Hierfür wird eine semi-analytische Methode zur Berücksichtigung beliebiger Morphologien vorgestellt, die anschließend auf spezielle Formen (Rotationsellipsoide, Tetraeder und Oktaeder mit gekrümmten Flächen) angewandt wird, um deren charakteristische Auswirkungen gegenüber zu stellen. Thema des dritten Teiles ist das effektive Materialverhalten nach Einsetzen von plastischen Verzerrungen. Dies umfasst einerseits Gesetzmäßigkeiten bezüglich des Fortschreitens der plastischen Verzerrungen ("effektives Fließgesetz") und andererseits die Verfestigung des Materials im Zuge der Verzerrungen. Dazu werden drei Modelle zur Abbildung des Materialverhaltens vorgestellt: (i) für den Fall eines verfestigenden Matrixmaterials, (ii) für die Berücksichtigung des Einflusses der Kompaktion (geometrische Verfestigung) und (iii) für den Fall eines quasi-spröden Matrixmaterials. Die in diesen drei Teilen entwickelten Modelle werden anschließend in numerische Simulationen zur Untersuchung des Verhaltens von porösen Materialien in Indentationsversuchen und unter Impaktbeanspruchung angewandt. Im Zuge dessen werden die Auswirkungen der Variation einzelner Materialparameter diskutiert.Material inhomogeneities such as pores and particles are common constituents of natural materials (e.g., wood, bone, soil, etc.) as well as engineering materials (e.g., concrete, foam materials, different kinds of composites, etc.). In case of the latter, material inhomogeneities may be either provoked on purpose or aimed to be prevented in the production process in order to influence the effective material properties. In this context, knowledge of the potential effects of inhomogeneities is of crucial importance. Substantial experimental studies dedicated to this matter are indispensable - though, sometimes not sufficient for a purposeful development process of materials, as theoretical and computational methods may provide useful additional information. This thesis shall contribute to the state of knowledge on the influence of material inhomogeneities on the effective mechanical material properties using the method of continuum micromechanics on the one hand and numerical simulations (finite element method) on the other hand. The main focus is on the nonlinear behavior of material constituents described in the framework of elastoplasticity. Accordingly, this thesis provides approaches for the advancement of continuum micromechanics in the context of nonlinear behavior. Respective numerical simulations of the loading of material samples (representative elementary volumes) serve as validation of the presented models and give additional insights. The subjects treated in specific are the following: First, a homogenization approach for the determination of an effective yield surface of a matrix-inclusion material is presented. It allows the consideration of empty pores, fluid-filled pores and rigid particles as inclusions and matrix materials whose domains of admissible stress states are defined by second-order yield surfaces comprising, e.g., Mises, Mises-Schleicher, Drucker-Prager and ellipsoidal yield surfaces. Subsequently, the influence of the inclusion shape is addressed. After presenting a semi-analytical methodology allowing the incorporation of arbitrary inclusion shapes into the framework of the aforementioned homogenization scheme, the effect of some selected morphologies is regarded more closely (spheroids, and tetrahedra and octahedra with curved surfaces). In the third part, the post-yield behavior of elastoplastic matrix-inclusion materials is treated, including the effective flow rule as well as the effective hardening behavior. Three models addressing different problems are proposed: (i) for obtaining the effective post-yield behavior in case of strain-hardening matrix materials, (ii) for estimating the contribution of compaction to the effective hardening behavior (geometric hardening), and (iii) the post-yield behavior in case of quasi-brittle matrix material behavior. The developments presented in the aforelisted three parts are then applied within the numerical analysis of indentation experiments and of porous materials subjected to impact loading. In both cases the significance of the involved material parameters is discussed.Roland TraxlZusammenfassung in deutscher SpracheUniversität Innsbruck, Dissertation, 2016OeBB(VLID)138954

Pore-space controlled hardening model in plasticity of porous materials: application to the analysis of indentation experiments

Based on a multi-scale approach comprising a multi-scale material model and a respective finite-element (FE) analysis tool, the indentation response of porous materials is examined in this paper. The considered material is assumed to consist of a homogeneous Drucker-Prager-type matrix-phase and spherical pores. Non-linear homogenization is employed to derive both a strength criterion and a hardening rule at the macroscopic scale without the need of any additional non-physical material parameters. Hereby, the underlying macroscopic hardening is exclusively controlled by the evolution of the porespace during loading. The material model is implemented in a FE program within the framework of elastoplasticity. The so-obtained analysis tool is applied to the analysis of indentation experiments commonly used for characterization and performance-based optimization of materials

Porous Talcum-Based Steatite Ceramics Fabricated by the Admixture of Organic Particles: Experimental Characterization and Effective Medium/Field Modeling of Thermo-Mechanical Properties

In this paper, an experimental campaign, as regards the thermo-mechanical properties (heat capacity, thermal conductivity, Young’s modulus, and tensile (bending) strength) of talcum-based steatite ceramics with artificially introduced porosity, is presented. The latter has been created by adding various amounts of an organic pore-forming agent, almond shell granulate, prior to compaction and sintering of the green bodies. The so-obtained porosity-dependent material parameters have been represented by homogenization schemes from effective medium/effective field theory. As regards the latter, thermal conductivity and elastic properties are well described by the self-consistent estimate, with effective material properties scaling in a linear manner with porosity, with the latter in the range of 1.5 vol-%, representing the intrinsic porosity of the ceramic material, to 30 vol-% in this study. On the other hand, strength properties are, due to the localization of the failure mechanism in the quasi-brittle material, characterized by a higher-order power-law dependency on porosity