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Thermodynamically Consistent Formulation of Induced Anisotropy in Polar Ice Accounting for Grain Rotation, Grain-size Evolution and Recrystallization.

Abstract

In this thesis we present a general theory able to comprehend important phenomena related to the dynamics of a polycrystalline material such as the ice of an ice sheet. The theoretical framework is founded upon the Theory of Mixtures with Continuous Diversity, for which the second law of thermodynamics is exploited to get a complete set of restrictions on the constitutive equations. The main goal of such an exploitation is to provide a theoretical tool to investigate the effects of the micostructure on the mechanical behaviour of polycrystalline materials. An explicit anisotropic constitutive law is given for the stretching tensor of an incompressible polycrystalline material in terms of its deviatoric stress tensor and of the distribution (Orientation Distribution Function or ODF) of the lattice orientations of the crystallites belonging to the polycrystal. Such a law is able to comprehend the mechanical response for any state of deformation, it is objective and its validity is checked by some remarkable examples. The evolution of the anisotropy is modelled with the aid of the evolution of the ODF, and it is not postulated ab initio. The balance of mass, as it is given in the form of the presented mixture with continuous diversity, provides such an evolution equation, that contains two constitutive functions. They are able to model the grain rotation and the Grain Boundary Migation (GBM) and recrystallization, respectively. We provide also a proposal for the explicit form of these two functions. From the balance of mass in the form of the presented mixture with continuous diversity, we have also derived a general evolution equation of the distribution of grain sizes. Two constitutive functions are present in this new equation. They are able to model the effects of grain growth and polygonization, respectively, on the evolution of the distribution of grain sizes. Even in this case, we give our proposal for the explicit form of these two functions. Results about the evolution of the dislocation density is also given.

Item Type: Ph.D. Thesis
Erschienen: 2005
Creators: Placidi, Luca
Title: Thermodynamically Consistent Formulation of Induced Anisotropy in Polar Ice Accounting for Grain Rotation, Grain-size Evolution and Recrystallization.
Language: English
Abstract:

In this thesis we present a general theory able to comprehend important phenomena related to the dynamics of a polycrystalline material such as the ice of an ice sheet. The theoretical framework is founded upon the Theory of Mixtures with Continuous Diversity, for which the second law of thermodynamics is exploited to get a complete set of restrictions on the constitutive equations. The main goal of such an exploitation is to provide a theoretical tool to investigate the effects of the micostructure on the mechanical behaviour of polycrystalline materials. An explicit anisotropic constitutive law is given for the stretching tensor of an incompressible polycrystalline material in terms of its deviatoric stress tensor and of the distribution (Orientation Distribution Function or ODF) of the lattice orientations of the crystallites belonging to the polycrystal. Such a law is able to comprehend the mechanical response for any state of deformation, it is objective and its validity is checked by some remarkable examples. The evolution of the anisotropy is modelled with the aid of the evolution of the ODF, and it is not postulated ab initio. The balance of mass, as it is given in the form of the presented mixture with continuous diversity, provides such an evolution equation, that contains two constitutive functions. They are able to model the grain rotation and the Grain Boundary Migation (GBM) and recrystallization, respectively. We provide also a proposal for the explicit form of these two functions. From the balance of mass in the form of the presented mixture with continuous diversity, we have also derived a general evolution equation of the distribution of grain sizes. Two constitutive functions are present in this new equation. They are able to model the effects of grain growth and polygonization, respectively, on the evolution of the distribution of grain sizes. Even in this case, we give our proposal for the explicit form of these two functions. Results about the evolution of the dislocation density is also given.

Publisher: Technische Universität
Uncontrolled Keywords: Grain Boundary Migration, Continuous Diversity, Lagrange Multipliers, Ice cores
Divisions: Study Areas
Study Areas > Study Area Mechanic
Date Deposited: 17 Oct 2008 09:22
Official URL: urn:nbn:de:tuda-tuprints-6145
License: only the rights of use according to UrhG
Referees: Hutter, Ph. D. Kolumban; Prof. ; Svendsen, Prof. Dr. Bob
Refereed / Verteidigung / mdl. Prüfung: 17 November 2004
Alternative Abstract:
Alternative abstract Language

In this thesis we present a general theory able to comprehend important phenomena related to the dynamics of a polycrystalline material such as the ice of an ice sheet. The theoretical framework is founded upon the Theory of Mixtures with Continuous Diversity, for which the second law of thermodynamics is exploited to get a complete set of restrictions on the constitutive equations. The main goal of such an exploitation is to provide a theoretical tool to investigate the effects of the micostructure on the mechanical behaviour of polycrystalline materials. An explicit anisotropic constitutive law is given for the stretching tensor of an incompressible polycrystalline material in terms of its deviatoric stress tensor and of the distribution (Orientation Distribution Function or ODF) of the lattice orientations of the crystallites belonging to the polycrystal. Such a law is able to comprehend the mechanical response for any state of deformation, it is objective and its validity is checked by some remarkable examples. The evolution of the anisotropy is modelled with the aid of the evolution of the ODF, and it is not postulated ab initio. The balance of mass, as it is given in the form of the presented mixture with continuous diversity, provides such an evolution equation, that contains two constitutive functions. They are able to model the grain rotation and the Grain Boundary Migation (GBM) and recrystallization, respectively. We provide also a proposal for the explicit form of these two functions. From the balance of mass in the form of the presented mixture with continuous diversity, we have also derived a general evolution equation of the distribution of grain sizes. Two constitutive functions are present in this new equation. They are able to model the effects of grain growth and polygonization, respectively, on the evolution of the distribution of grain sizes. Even in this case, we give our proposal for the explicit form of these two functions. Results about the evolution of the dislocation density is also given.

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