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Anisotropic Plasticity and Viscoplasticity

Schick, David (2004):
Anisotropic Plasticity and Viscoplasticity.
Darmstadt, Technische Universität, TU Darmstadt,
[Ph.D. Thesis]

Abstract

Plastic anisotropy effects may be described in a phenomenological model by employing in the constitutive theory a set of internal variables, which are defined suitably. These variables have to model the hardening response of the material under consideration to describe e.g. the rotation of some symmetry axes. Such axes are imagined to be related with the development of the material substructure assumed, or, correspondingly, with the state variables characterizing this development. The objective of the first part of this work is to develop the constitutive equations governing the material response for the case of orthotropic and cubic anisotropy. Therefore the thermodynamically consistent theory for plasticity (and viscoplasticity), recently published by Tsakmakis (2004), which accounts for anisotropy effects is presented and extended for the aforementioned cases of anisotropy. Important features of the theory are the use of the multiplicative decomposition of the deformation gradient tensor as well as the assumption of the validity of Il'iushin's postulate in the case of plasticity. For simplicity, apart from kinematic hardening effects, only orientational evolution of the underlying substructure is regarded. Care is taken that the theory is invariant with respect to rigid body rotations superposed to both, the current and the so-called plastic intermediate configuration. Anisotropy effects are elaborated in the free energy and the yield function by means of structural tensors. For the case of cubic material symmetry a Brinell hardness indentation test has been simulated and is compared qualitatively with the experiment for a commercially available single-crystal nickel-based superalloy (CMSX4). Inelastic deformations induce anisotropy in the material response, even if this is initially isotropic. For metallic materials, deformation induced anisotropy is reflected, above all, by translation, rotation and distortion of the yield surface. This has been confirmed by several experimental investigations independent of the way the yield point is defined. In the second part of this work a simple, thermodynamically consistent model is proposed, describing the evolving anisotropy of the yield surface. The model is first theoretically established, based on a sufficient condition for the dissipation inequality to be satisfied. Then, it is applied to predict the subsequent yield surfaces, after various prestressings, which have been observed experimentally by Ishikawa for SUS 304 stainless steel.

Item Type: Ph.D. Thesis
Erschienen: 2004
Creators: Schick, David
Title: Anisotropic Plasticity and Viscoplasticity
Language: English
Abstract:

Plastic anisotropy effects may be described in a phenomenological model by employing in the constitutive theory a set of internal variables, which are defined suitably. These variables have to model the hardening response of the material under consideration to describe e.g. the rotation of some symmetry axes. Such axes are imagined to be related with the development of the material substructure assumed, or, correspondingly, with the state variables characterizing this development. The objective of the first part of this work is to develop the constitutive equations governing the material response for the case of orthotropic and cubic anisotropy. Therefore the thermodynamically consistent theory for plasticity (and viscoplasticity), recently published by Tsakmakis (2004), which accounts for anisotropy effects is presented and extended for the aforementioned cases of anisotropy. Important features of the theory are the use of the multiplicative decomposition of the deformation gradient tensor as well as the assumption of the validity of Il'iushin's postulate in the case of plasticity. For simplicity, apart from kinematic hardening effects, only orientational evolution of the underlying substructure is regarded. Care is taken that the theory is invariant with respect to rigid body rotations superposed to both, the current and the so-called plastic intermediate configuration. Anisotropy effects are elaborated in the free energy and the yield function by means of structural tensors. For the case of cubic material symmetry a Brinell hardness indentation test has been simulated and is compared qualitatively with the experiment for a commercially available single-crystal nickel-based superalloy (CMSX4). Inelastic deformations induce anisotropy in the material response, even if this is initially isotropic. For metallic materials, deformation induced anisotropy is reflected, above all, by translation, rotation and distortion of the yield surface. This has been confirmed by several experimental investigations independent of the way the yield point is defined. In the second part of this work a simple, thermodynamically consistent model is proposed, describing the evolving anisotropy of the yield surface. The model is first theoretically established, based on a sufficient condition for the dissipation inequality to be satisfied. Then, it is applied to predict the subsequent yield surfaces, after various prestressings, which have been observed experimentally by Ishikawa for SUS 304 stainless steel.

Place of Publication: Darmstadt
Publisher: Technische Universität
Uncontrolled Keywords: formative Verfestigung, kinematische Verfestigung, thermodynamische Konsistenz der Theorie, Evolution der Anisotropie, Postulat von Iliushin, Orthotropie, kubische Anisotropie, einkristalline Nickelbasislegierung, CMSX-4
Divisions: Study Areas
Study Areas > Study Area Mechanic
Date Deposited: 17 Oct 2008 09:21
Official URL: urn:nbn:de:tuda-tuprints-3922
License: only the rights of use according to UrhG
Referees: Gruttmann, Prof. Dr.- Friedrich
Refereed / Verteidigung / mdl. Prüfung: 7 January 2004
Alternative keywords:
Alternative keywordsLanguage
Distortional hardening, orientational hardening, kinematic hardening, thermodynamic consitency of the theory, evolution of anisotropy, postulate of Iliushin, orthotropy, cubic anisotropy, single-crystal nickel-base alloy, CMSX-4English
Alternative Abstract:
Alternative abstract Language
Anisotropie, gekoppelt mit inelastischem Fließen spielt in vielen Bereichen der Materialtheorie eine wichtige Rolle. Beispiele dafür sind Stoffgesetze zur Kristallplastizität, zur Beschreibung von Texturen in Blechen usw. Im ersten Teil der vorliegenden Arbeit werden die konstitutiven Materialgleichungen für die Materialantwort bei Orthotropie und kubischer Anisotropie entwickelt. Zu diesem Zweck wird das in Tsakmakis (2004) vorgestellte thermodynamisch konsistente konstitutive Materialmodell für Plastizität und Viskoplastizität bei großen Deformationen für diese beiden Fälle der Anisotropie weiter ausgeführt. Wichtige Bestandteile der Theorie sind die multiplikative Zerlegung des Deformationsgradienten in einen elastischen und inelastischen Anteil sowie die Annahme der Gültigkeit des sogenannten Postulats von Il'iushin für Plastizität. Es wird sowohl eine anisotrope kinematische Verfestigung als auch eine allgemeine Gestaltänderung der Fließfläche berücksichtigt. Die Theorie ist phänomenologisch formuliert und invariant gegenüber beliebigen überlagerten Starrkörperrotationen in der plastischen Zwischenkonfiguration und der Momentankonfiguration. Die Anisotropie wird mit Hilfe sogenannter Strukturtensoren in der freien Energiefunktion und der Fließfunktion formuliert. Für den Fall der kubischen Anisotropie wurde ein Brinell Kugeleindruckversuch simuliert und qualitativ mit dem Experiment an einer einkristallinen Nickelbasislegierung (CMSX4) verglichen. Bei einem anfänglich isotropen Material kann durch die plastische Deformation eine Anisotropie induziert werden, was sich insbesondere bei Metallen durch eine Verschiebung, Rotation und Verzerrung (formative Verfestigung) der Fließfläche ausdrückt. Dies wurde auch durch verschiedene experimentelle Untersuchungen unabhängig von der Definition des Fließbeginns bestätigt. Im zweiten Teil der Arbeit wird ein einfaches, thermodynamisch konsistentes Materialmodell für kleine Deformationen entwickelt, das die Evolution der Anisotropie in der Fließfläche beschreibt. Das Modell erfüllt hinreichende Bedingungen für die sogennante Dissipationsungleichung. Abschließend wird die Evolution der Fließfläche für verschiedene Vorbelastungen simuliert und mit den Experimenten von Ishikawa an SUS 304 Edelstahl Rohrproben qualitativ verglichen.German
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