Challenges in developing a general constitutive relation for cyclic loading*

Fernand Ellyin; Zihui Xia

doi:10.3139/120.100705

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Challenges in developing a general constitutive relation for cyclic loading*

Fernand Ellyin und Zihui Xia

Veröffentlicht/Copyright: 28. Mai 2013

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Abstract

Deformation of most metals and alloys is time-dependent and this dependency becomes more pronounced at temperatures exceeding a third of the material's melting point. Furthermore, the deformation response of a material to cyclic loading involves transients prior to stabilization. Some manifestations of the transient responses are: strain hardening or softening, loading sequence effect, strain-rate and strain-path history dependency, creep-plasticity interaction, strain ratcheting, among others. In addition, a constitutive model formulated in terms of macroscopic parameters must have a certain underlying microscopic rationalization. In this paper rate-dependent constitutive relations for an inelastic material are presented. This constitutive model is of a coupled nature, in the sense that the effect of prior creep on the subsequent plastic deformation and vice versa, are taken into account. Thus, the framework for these constitutive relations is based on the concept that any loading sequence can be predicted by two separate (elastoplastic and creep) but coupled models. A number of examples covering a wide range of cyclic loading types are presented.

Kurzfassung

Die Verformung der meisten Metalle und ihrer Legierungen ist zeitabhängig und diese Abhängigkeit wird umso deutlicher bei Temperaturen, die ein Drittel des Schmelzpunktes des jeweiligen Werkstoffes überschreiten. Darüber hinaus weist die Verformung eines Werkstoffes infolge einer zyklischen Beanspruchung Transienten vor der Stabilisierung auf. Einige Ursachen für diese Transienten sind unter anderen Verfestigungs- oder Entfestigungseffekte (bekannt als strain hardening oder softening), Effekte der Belastungsfolge, Abhängigkeiten von der Dehnrate oder der Verformungshistorie oder Interaktionen zwischen Kriechen und Plastifizierung. Ein konstitutives Modell, das mittels makroskopischer Parameter formuliert wird, muss weiterhin mit einer bestimmten mikroskopischen Überlegung unterlegt sein. Im vorliegenden Beitrag werden geschwindigkeitsabhängige konstitutive Beziehungen für ein inelastisches Material abgeleitet. Dieses constitutive Modell hat einen gekoppelten Aufbau in dem Sinn, dass die Wirkung vorherigen Kriechens auf die nachfolgende plastische Verformung und umgekehrt berücksichtigt wird. Somit basiert das Rahmenwerk für diese konstitutiven Beziehungen auf dem Konzept, dass alle Belastungsfolgen durch zwei separate (elastoplastische Verformung und Kriechen), aber gekoppelte Modelle vorhergesagt werden können. Eine Anzahl von Beispielen, die ein weites Feld zyklischer Beanspruchungsarten abdeckt, wird außerdem präsentiert.

Professor Fernand Ellyin's current research activities are the investigation of micro and macro behaviour of composite systems using extensive and unique experimental and numerical techniques. Two primary categories of materials being studied are: (1) Polymers and Fiber Reinforced Polymer Composites, (2) Metals and Metal Matrix Composites. Professor Ellyin was the NOVA (TCPL)/NSERC Senior Industrial Research Chair holder from 1996– 2003 and prior to that Professor of Mechanical engineering since 1981. He is now Professor Emeritus at the University of Alberta and Adjunct professor at the University of British Columbia. In recognition of his contributions, Professor Ellyin has been awarded the McCalla and Killam professorships by the University of Alberta, the Robert Angus Medal, and George H. Duggan Medal by the Canadian Society for Mechanical Engineering and senior fellowships by the Japan Society for the Promotion of Science and SFB Germany, among others. He was made an Honorary Fellow of the DVM, in 2004. He is the author of two books, five book chapters, more than 300 papers, and has edited 5 volumes of proceedings and participated in the writing of five volumes of standards for the Candu Nuclear Power Plants.

Dr. Zihui Xia graduated from Department of Engineering Mechanics, Tsinghua University, Beijing, China and obtained Master and Ph. D. Degrees there in 1981 and 1984, respectively. He worked in the Shanghai Ship and Shipping Research Institute as a senior Research Engineer and Vice Director from 1981–1987. In 1987 he moved to Canada and worked in the Department of Mechanical Engineering, University of Alberta as Post Doctoral Fellow, Senior Research Associate, and Assistant Professor and is currently a tenured Associate Professor. In recent years, his research has been focused on advanced composite materials. He has published more than 50 papers in major international journals and about 50 papers in international conference proceedings.

Contribution to the 7^th International Conference on Biaxial/Multiaxial Fatigue and Fracture (7ICBMFF)

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Published Online: 2013-05-28

Published in Print: 2006-02-01

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https://doi.org/10.3139/120.100705