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  • Upsetting and Viscoelasticity of Vitreous SiO2: Experiments, Interpretation and

    Simulation

    vorgelegt von

    Diplom Ingenieur

    Frank Richter

    von der Fakultt III Prozesswissenschaften

    der Technischen Universitt Berlin

    zur Erlangung des akademischen Grades

    Doktor der Ingenieurwissenschaften

    Dr.-Ing.

    genehmigte Dissertation

    Promotionsausschuss:

    Vorsitzende: Prof. Dr.-Ing. C. Fleck

    Berichter: Prof. Dr. rer. nat. H.-J. Hoffmann

    Berichter: Prof. Dr.-Ing. M. H. Wagner

    Tag der wissenschaftlichen Aussprache: 14. Juli 2005

    Berlin 2006

    D 83

  • I

    Dedicated to my parents.

  • II

    Acknowledgement

    The author would like to thank first of all his advisor, Prof. H.-J. Hoffmann, for this very

    rewarding topic. His contagious enthusiasm is gratefully acknowledged and was the basis for

    pushing this thesis far beyond the original expectations. Lengthy and useful conversations

    with him expressed individuality and the entailing enthusiasm contributed greatly to fully

    exploit the data, inspiring the author to broaden his experiences in experimental, numerical

    and computational skills.

    The execution of this work would not have been conceivable without the assistance from

    colleagues and coworkers to whom I wish to indicate my sincere appreciation. Feeling unable

    to put all these in an order of importance the only listing that hopefully does not do injustice

    to anyone must be alphabeticala. In particular I am indebted to

    Dr.-Ing. C. Alexandru to whom the author feels deepest gratitude for procuring the constitutive equation for a Zener-Maxwell-body in three-dimensional space in tensor

    notation which seems impossible to come by in the literature

    Dr.-Ing. W. Baumann from the Konrad-Zuse-Zentrum fr Informationstechnik Berlin who advised the author on the many pitfalls of ABAQUS and its implementation in an

    effort to master the finite-element simulations without ever feeling pestered (didnt

    say so at least)

    Practitioner and Dipl.-Min. B. Bchtemann for inspirational nutritional facts Prof. Dr.-Ing. C. Fleck for serving as chairwoman Mr T. Hamfler to whom a special note of appreciation is dedicated for machining

    specimens from glass blocks and bizarre talk

    Prof. U. Hildebrandt for distracting chats every now and then garnished with occasional revelations from long-time experience

    Dipl.-Ing. K. Jirka for providing moral support in long office nights that had a positive impact

    Dipl.-Phys. B. Khn, Heraeus Quarzglas GmbH & Co. KG Hanau, for generously donating the specimen material

    the machine shop staff G. Hautmann, P. Schneppmller, M. Ziehe and W. Eisermann a All persons listed are affiliated with the Technical University of Berlin if not stated otherwise.

  • III

    who were eager to fulfill the large and the many smaller requests before they were

    approached with them

    Prof. D. M. Martin, retired professor at the Iowa State University, Department of Materials Science and Engineering, Ames, USA, who developed a theory that sheds

    light on a previous explanation for the phenomenon of bollarding that came out after

    many valuable suggestions were proposed

    Dr. rer. nat. S. Nzahumunyurwa for essential programming of an image recording program and interfacing with the hardware

    Dipl.-Ing. F. G. Osthues from W. Haldenwanger, Technische Keramik GmbH & Co KG, for machining of and valuable suggestions on alumina pistons

    Mrs I. Sauer for electron microscope investigations allowing insight into the surface topography of samples after completion of an experiment

    Dr. rer. nat. C. Schrder for x-raying samples providing evidence of crystallization the secretaries Mrs B. Gunkler-Steinhoff, C. Braatz and I. Speicher for coping with the

    administration

    Prof. Dr.-Ing. M. Wagner for acting as second reviewer Dipl.-Ing. (FH) K. Weisser whose ingenuity in wiring and understanding data

    acquisition hardware, in mastering computer problems and in beefing up hardware to

    be interfaced with the MTS was indispensable.

    Each individual contribution is sincerely acknowledged and will be remembered with thanks.

    The joy of graduating from this institute is dimmed by the grim outlook of leaving behind the

    friendly atmosphere among the group that helped to ease the course of this research. My

    gratitude is likewise extended to faculty and staff of the ceramics department with whom the

    lab was shared.

    The author would be glad to respond if interested readers contacted him for details. A good

    starting point would be to type in Master Frank in some internet search engine.

  • IV

    Legal notices

    Suprasil is a registered trademark of Heraeus Quarzglas GmbH, Germany.

    MTS is a registered trademark of MTS Systems Corporation, USA.

    MATHEMATICA is a registered trademark of Wolfram Research, USA.

    ABAQUS is a registered trademark of Hibbitt, Karlsson & Sorensen, Inc., USA.

  • V

    Abstract

    The task of the present study was the axial compression of and subsequent stress relaxation in

    glass cylinders made of the vitreous silica type Suprasil 1 at temperatures ranging from

    1000C to 1375C and at nominal strain rates from -10-5 to -10-2 per second in a servo-

    hydraulic press. Earlier, the method had been applied thoroughly at the Technical University

    of Berlin while it did not find wide appreciation elsewhere. An overall critical review of

    published work, however, reveals many areas of deficiencies in glass upsetting and comes up

    with a reinterpretation of the reported nonlinear viscosity. The former experimental and

    analytical approaches are proven untenable. The present procedure embraces experimental

    studies stringently analyzed by a dual analytical and numerical approach along rational

    guidelines which in the end clearly reveal consistency, but firmly contradict hitherto

    uncontested research. Building upon a few previous studies glass upsetting is shown to be an

    accurate and reliable method. The present study relies to a minor extent on literature data, but

    these are not critical for the technique.

    A persuasive case is built to demonstrate that the previously reported distinct 'stress

    generation modulus' is not physical. This modulus does not markedly develop if provisions

    are made to establish firm interface contact between the specimen and the pistons.

    The different analytical approaches for upsetting purely viscous substances suggested in the

    literature are reviewed. The consequences radial friction restraint on the interface has on the

    inner stress field in upset samples is discussed. A theory of Nadai on the inner stress state in

    axially compressed viscous bodies while bulging must be rejected.

    Instead, the concept of viscoelasticity is accepted and closed-form solutions are derived to

    demonstrate that the interpretation as a single-element Maxwell model renders Young's

    modulus readily measurable along with the viscosity. This concept had been applied in a few

    earlier studies, but is here extended to measure the Young's modulus and the viscosity as a

    function of temperature and stress. Thus, the deformation resistance in glass is not exclusively

    determined by viscosity. The significant contribution of elasticity, found to be inherent in

    glass even at elevated temperatures, can not be neglected. This very distinct behavior does not

    appear to have received widespread explicit recognition. The interpretation as a single-

  • VI

    element Maxwell model is capable of adequately describing glass behavior to a sufficient

    approximation and opens up the possibility to compute both Young's modulus and the tensile

    viscosity. The condition of a homogeneous deformation occurring under perfect interface

    slippage is shown not to be a strong one if the degree of compression is small.

    The analysis reveals that the Young's modulus decreases with a rise in temperature when the

    nominal strain rate is held fixed and with a reduction in nominal strain rate at constant

    temperature. The Young's modulus has been neglected in the majority of earlier studies on

    glass upsetting. The viscosity can be characterized either by a VFT-fit or by an Arrhenian fit

    where one parameter is load-dependent. Thus, nonlinearities are manifested by a non-

    Hookean elasticity and a non-Newtonian viscosity. Both nonlinear coefficients Youngs

    modulus and viscosity are fitted by linear functions to the stress as the simplest approach to

    nonlinearity. This procedure may be revised if theoretical fit formulas become available.

    The analytical treatment implicitly assumes that the deformation can be taken as isothermal.

    A heat balance between the internally generated heat and heat losses was carried out

    demonstrating that the assumption of an isothermal state is justified. The applicability of this

    algorithm is proven with reference to an earlier study.

    The stress relaxation behavior has also been analyzed without reference to the interpretation

    as a Maxwell model and found to be load-dependent. The relaxation ability is influenced by

    the temperature and the stress attained. All stress relaxation functions normalized to the initial

    stress can be superposed by renormalizing the time scale depending on the temperature and

    the stress. A statement on wheth