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AD-A268 427

international Union of Theoreticaland Applied Mechanics

George J. Dvorak (Ed.)

Inelastic Deformationof Composite Materials

IUTAM Symposiu m, Troy, New YorkMay 29-June 1, 1990

With 101 Illustrations

Sprinqer VerlagNew Yrk Berlin Heidelberg LondonParis -o ,io Hong Kong Barcelona

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IUTAM Symposium on Inelastic Deformation of Composite PE 6.1102FMaterials Task 2302/B2

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George J Dvorak (Editor)

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Department of Civil Engineering REPORT NUMBER

Center for Composite Materials and StructuresRensselaer Polytechnic InstituteTroy, NY 12180-3590 40)RT- 9

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Published by Springer-Verlag New York Inc. 1991ISBN # 0-387-52011-2/1991

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This volume contains a selection of recent work by leading researchers inmicromechanics that was presented at the IUTAM Symposium on Inelastic Deformationof Composite Materials at Rensselaer. The Symposium was made possible by thegenerous support of AFOSR, ARO, NSF, IUTAM and RPI. Thanks are due to the sponsorsand to the local organizing committee for their support and work on behalf of theSymposium.

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Composite Materials, Inelastic :)cformation, Micromechanics 11

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UNCLASSIFIED IUNCLAcSIFIED UNCLASSIFIED UL

George J. DvorakDepartment of Civil EngineeringCenter for Composite Materials and StructuresRensselaer Polytechnic InstituteTroy. New York 12180-3590USA

Printed on acid-tree paper.

• 1991 Springer-Verlag New York Inc.All rights reserved. This work may not be translated or copied in whole or in part without thewritten permission of the publisher (Springer-Verlag New York, Inc.. 175 Fifth Avenue. NewYork, NY 10010, USA), except for brief excerpts in connection with reviews or scholarlyanalysis. Use in connection with any form of information storage and retrieval, electronicadaptation, computer software, or by similar or dissimilar methodology now known or here-after developed is forbidden.The use of general descriptive names, trade names, trademarks. etc., in this publication,even if the former are not especially identified, is not to be taken as a sign that such names.as understood by the Trade Marks and Merchandise Act, may accordingly be used freely byanyone.Permission to photocopy for internal or personal use, or the internal or personal use ofspecific clients, is granted by Springer-Verlag New York, Inc. for libraries registered with theCopyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $0.20per page is paid directly to CCC, 21 Congress St., Salem, MA 01970, USA. Special re-quests should be addressed directly to Spnnger-Verlag New York, 175 Fifth Avenue, NewYork, NY 10010, USAISBN 0-387-52011-2/1991 $0 00 + 020

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Preface

In the last 25 years, the science and technology of composite materials haveexperienced a period of substantial development. The initial goal was toprovide light, strong, and stiff materials for the aerospace industry. That wasmet by the introduction of polymer matrix composites with continuous fiberreinforcement, and with certain discontinuous reinforcements. Such mate-rials are now routinley used not only in aerospace, but also in numerousother applications, e.g., in automobile and construction industries.

Meanwhile, composite materials have been introduced, or are expected toserve, in many other functions which cannot be fulfilled by conventionalmaterials, particularly in extreme environments. Accordingly, the researchfocus has been broadened to include not only new polymer systems, but alsometal, intermetallic, and ceramic matrix materials. This has brought fortha number of new problems in fabrication and processing, and in analysis ofcomposite material behavior and properties.The latter set of problems is usually approached by various micromechani-

cal techniques. In recent years, their scope has been expanded fromprediction of overall properties of elastic, perfectly bonded systems, toinclude problems associated with inelastic deformation of the phases,debonding at interfaces, and growth of distributed damage. Many familiaraspects of mechanical behavior, such as fracture, fatigue, compressivestrength and buckling have been reexamined and adapted for application tothe new material systems.

This volume contains a selection of recent work by leading researchers inmicromechanics that was presented at the IUTAM Symposium on InelasticDeformation of Composite Materials at Rensselaer. The Symposium wasmade possible by the generous support of AFOSR, ARO, NSF, IUTAM andRPI. Thanks are due to the sponsors, and to the local organizing committeefor their support and work on behalf of the Symposium. Special thanks aredue to Christine Stephenson for her coordination of the local arrangements,and for her contribution to the preparation of this volume.

George J. Dvorak

Troy, New York

June 1990

Sponsors of the IUTAM Symposium on

Inelastic Deformation of Composite Materials

International Union of Theoretical and Applied Mechanics (IUTAM)

National Science FoundationSolid Mechanics and Geomechanics ProgramDr. Oscar W. Dillon, Program Director

Department of the Air ForceAir Force Office of Scientific ResearchDivision of Aerospace SciencesLt. Colonel George K. Haritos, Acting Director

Department of the ArmyArmy Research OfficeMaterials Science DivisionDr. Edward S. Chen

The Civil Engineering Department andThe Institute Center for Composite Materials and StructuresRensselaer Polytechnic Institute

International Scientific Committee of the SymposiumProfessor George J. Dvorak (USA), ChairmanProfessor Z. Hashin (USA-Israel)Professor J. Backlund (Sweden)Professor T. Hayashi (Japan)Professor J.P. Boehler (France)Professor T. Lehmann (FRG)Professor R.M. Christensen (USA)Professor A.J.M. Spencer (UK)Professor D.C. Drucker (USA)Professor V.V. Vasiliev (USSR)Professor S.S. Wang (USA)

Local ArrangementsChristine StephensonJudy BrownellJanet PertierraJo Ann GregaMichelle Peattie

List of Participants

Ahzi, S., Massachusetts Institute of Technology, USAAllen, David H., Texas A&M University, USAAlpa. Giovanni, University of Genova, Italy

Argon, Ali S., Massachusetts Institute of Technology, USABassani, John L. University of Pennsylvania, USABahei-EI-Din, Yehia, Rensselaer Polytechnic Institute, USABathias, Claude, C.N.A.M.. Paris, FranceBenveniste, Yakov, Tel-Aviv University, IsraelBerveiller. Marcel, Laboratoire P.M.M.. Metz. FranceBudiansky, Bernard. Harvard University. USACardon. Albert H., Vrije Universiteit Brussel. Belgium(Chen. Peter. Department of the Army, LISAChen, Tungyang, Rensselaer Polytechnic Institute. LISAChristensen, Richard M.. Lawrence Livermore Labs. USAde Buhan, Patrick, Ecole Polytechnique Palaiseau, FranceDvorak. George J., Rensselaer Polytechnic Institute, USAEggleston, Michael. General Electric'Corporation, USAFares. Nabil F., Rensselaer Polytechnic Institute, USAFleck, Norman A., Cambridge University. EnglandGambarotta, Luigi. University of Genova, ItalyGosz, Michael R.. Northwestern University. USAGupta, Vijay. Dartmouth College. USA

Hall. Richard, Rensselaer Polytechnic Institute, USAHaritos, George K., Department of the Air Force, USAHashin, Zvi, University of Pennsylvania, USA: Tel-Aviv Univeristy, Israel"Herakovich, Carl T.. University of Virginia. USA

Herrmann. Klaus, Gesamthochschule Paderborn. FRGHluang, Chien-Ming, Rensselaer Polytechnic Institute, USAHui, C.Y. Herbert, Cornell University, USAIkegami, Kozo, Tokyo Institute of Technology, Japan

Krempl, Erhard. Rensselaer Polytechnic Institute, USAKuo, Wen-Shyong, University of Delaware, USALadeveze, Pierre. E.N.S. de Cachan. France

Lagoudas. Dimitris C., Rensselaer Polytechnic Institute. USALaws, Norman, Universits ot Pittsburgh. USALlorca. Javier. Brown Uniersily. USAMallon, Patrick J., UniversN. ('College Galway, IrelandMoran. Brian. Northwkestcrn t mnersity, LISAMura, Toshio. Norlhvestern t mscrsity. LISA

viii

Murakami, Sumio, Nagoya University, JapanNakajo. Yuichi, Ashikaga Institute of Technology, JapanNeedleman, Alan. Brown University, USANemat-Nasser. Sia. University of California, San Diego, USANigam, Himanshu. Ren".elaer Polytechnic Institute, USAOrtiz, Michael, Brown University. USAParks, David M., Massachusetts Institute of Technology, USAPindera, Marek-Jerzy. University of Virginia. USAPipes, R. Byron. University of Delaware, USAPonte Castaneda. Pedro, Johns Hopkins University, USAPyrz, Ryszard, University of Aalborg, DenmarkRajapakse, Yapa D.S.. Office of Naval Research, USAReddy, J.N., Virginia Polytechnic Institute, USARogers, Tryfan G.. University of Nottingham, EnglandSaleh, Ahmed, Rensselaer Polytechnic Institute. USASantare, Michael |I., University of Delaware, USASchapery. Richard A., Texas A&M University, USASelvadurai, A.P.S. Patrick. Carlton University. USAShah, Rahul S., Rensselaer Polytechnic Institute, USASham, T.L. Sam, Rensselaer Polytechnic Insitute, USAShephard, Mark S., Rensselaer Polytechnic Institute, USASpencer, Anthony J.M., University of Nottingham, EnglandSteif, Paul S.. Carnegie-Mellon University. USASternstein, Sanford S.. Rensselaer Polytechnic Institute. USAStorakers, Bertil. The Royal Institute of Technology, SwedenSuresh, Sabra, Brown University, USATaggart, David, University of Rhode Island, USATalbot. David R.S., Coventry Polytechnic, Englandten Busschen. Albert. Delft University of Technology, HollandTeply, Jan L.. Aluminum Company of America, USATvergaard, Viggo, Technical University of Denmark, DenmarkWafa. Amr, Rensselaer Polytechnic Institute. USAWalker, Kevin. Engineering Science Software. Inc., USAWeitsman. Y. Jack. University of Tennessee, USAWeng, George J.. Rutgers University, USAWillis, John R.. Baih I Iniversity. EnglandWisnom, Michael. I 1niersity of Bristol, EnglandWu, Jer-Fang. Rensclaer Polytechnic Institute, USA

Xu, Simon W.. ( Im -.-crsit ý of Cincinnati, USAZarzour. Joseph. Re'schlcr Polytechnic Institute, USAZbib. Hussein M.., Aahington State University, USA

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Contents

P re fac e ...................................................................................................... vS p o n so rs ................................................................................................... v iL ist o f P articipants .................................................................................. v ii

Session I. Interfaces I Chairman: J.R. Willis

Composite Materials with Interphase: Thermoelastic andInelastic E ffects ................................................................................... 3Z. Hashin

Effect of a Viscoelastic Interfacial Zone on the Mechanical Behaviorand Failure of Fiber-Reinforced Composites ..................................... 35B. Moran. M. Gows and J.). Achenhach

Measurement of Strength of Thin Film Interfaces by LaserSpallation Experim ent ....................................................................... 5 I1". Gupta and A.S. Argom

Session 2. Interfaces If Chairman: A.S. Argon

On a Correspondence Between Mechanical and Thermal Fields inComposites with Slipping Interfaces ................................................. 77Y. Benveniste and G.J. Dvorak

Micromechanical Modelling of Fibre Debonding in a MetalReinforced by Short Fibres ..................................................................... 99V Tvergaard

Session 3. Damage Chainnan: Y. Raiqaakse

Fiber Stress Enhancement Due to Initial Matrix Cracking .................. 115A. Dollar and P.S. Steif

Fracture Toughness Enhantcement Due to Particle Transformation ..... 125Z. Gao and T. Mura

Cracks at the Extremiltc,' ,, ("l lindrical Fibre Inclusion. ................... 147A P.S. Selhad•hrai

xii

Session 4. Inelastic Behavior I Chairman: B. Budianskv

Bounos for the Creep Behavior of Polycrystalline Materials ............... 175R Lendievel. G. Bonnet und J.R. Willis

Simplifications in the Behavior of Viscoelastic Composites withG row ing D am age .................................................................................. 193R.A. Sc•haperv

The Effective Properties of Brittle/Ductile IncompressibleC o m po sites ............................................................................................ 2 15P. Ponte Castaneda

Session 5. Inelastic Behavior 11 Chairman: Z. Hashin

Compressive Failure of Fibre Composites Due to Microbuckling ...... 235N.A. Fleck and B. Budianskv

A Critical Evaluation for a Class of Micro-Mechanics Models ........... 275R.M. Christensen

Experiments and Modeling in Plasticity of Fibrous Composites ......... 283G.J. Dvorak. Y.A. Ba/wi-EI-Din, R.S. Shah and H. Nigam

Session 6. Computational Methods Chairman: George K. Haritos

The Effect of Superposed Hydrostatic Stress on the MechanicalResponse of Metal-M atrix Composites ................................................ 309T. Christmnan..1. Lhorca. S. Suresh and A. Needleman

Micromechanical Modeling of Plasticity Texture Evolution inSem i-C rystalline Polym ers ................................................................... 325D.M. Parks and S. Ahz:i

A Unified Formulation of Micromechanics Models ofFiber-Reinforced Com posites ............................................................... 341J.L. Teph%, and J.N. Reddv

Session 7. Inelastic Behavior Ill Chairman: R.A. Sc'haperv

A Micromechanical Composite Yield Model Accounting forR esid ual S tresses .................................................................................. 37 3C. 1. th'rako~n.I.1hl',,1lh and .I.L. Bea/h..Ir.

The [Ifects of Thcrml. I'lastic and IElastic Stress Concentrationson the Overall Beha% mor of Metal Matrix Composiles ......................... 3X9F. Corvasce. P. l.ipot ,onI . Berveilh'r

xiii

Session 8. Inelastic Behavior IV Chairman: R.M. Christensen

Residual Stresses in Fibrous Metal Matrix Composites:A Therm oviscoplastic Analysis ............................................................ 411E. Krernpl and N.M. Yeh

Elasto-Plastic Analysis for Cracked Fibrous Composites under Axialand T herm al Loads ............................................................................... 445K.P. Herrmann and Y Q. Wang

Incremental Elastoplastic Behavior of Metal Matrix CompositesBased on Averaging Schem es .............................................................. 465D.C. Lagiodas and A.C, Gvaz::i

Session 9. Inelastic Behavior V Chairman: E. Krenmpl

Global and Internal Time Dependent Behaviour of PolymerM atrix C om posites ................................................................................ 489A,.t Cardmn

A Local-Field Theory for the Overall Creep of Fiber-ReinforcedM etal M atrix C om posites ..................................................................... 50 1Y.M. Wang and G.J. Weng

The Overall Behaviour of a Nonlinear Fibre ReinforcedC om po zite ............................................................................................ 527D.R.S. Talbot and J.R. Willis

Session 10. Damage and Failure Chairman: P. Ladeveze

A Continuum Model for Damage Evolution in LaminatedC o m po sites ............................................................................................ 549D.C. Lo, D.H. Allen and C.E. Harris

Lower and Upper Bound Estimates for the Macroscopic StrengthCriterion of Fiber Composite M aterials ................................................ 563P. de Buhan, J. Salenmon and A. Tuliercio

Static and Fatigue Biaxial Testing of Fiber Composites Using ThinW alled Tubular Specim ens ................................................................... 581T.P. Soemardi. 1). Lai and C. Bathias

xiv

Session 11. Fracture Chairman: D.H. Allen

Mesomodeling of Damage for Laminate Composites: Applicationto D elam ination ..................................................................................... 607P. Ladeve:e, 0. Alfix and L. Daudeville

Constitutive Relaiions of Hybrid Fiber Reinforced Plastics ofGFRP/CFRP and GFRP/AFRP under Combined Stress State ............. 623K. Ikegami and M. Yoshida

Predictions of the Critical Strain for Matrix Cracking of CeramicM atrix C om posites ................................................................................ 639W.S. Kuo and T.W. Chou

Session 12. Inelastic Behavior VI Chairman: C.T. Herakovi'h

Shear Characterisation and Inelastic Torsion of Fibre-ReinforcedM aterials ............................................................................................... 6 5 3T.G. Rogers

Inelastic Deformation and Fatigue Damage of Composites underM ultiaxial Loading ............................................................................... 675S. Murakarni. Y. Kanagawa. T. Ishida and E. Tsushima

A Hybrid Model for Nonlinear Characterization of CompositeM aterials ............................................................................................... 69 5R. Pyrz

Session 13. Inelastic Behavior VII Chairman: K. Herrmann

Admissible Deformations in Diaphragm Forming of ContinuousFibre Reinforced Therm oplastics ......................................................... 709PJ. Mallon, C.M. O'Bradaigh, M.R. Monaghan and R.B. Pipes

Viscoelastic Creep Post Buckling Behavior of AS4/J IThermoplastic-Matrix Composite Laminates ....................................... 727Y. Nakajo

Asymmetrical Growth of Edge Delaminations in CFRP TensileS pecim en s ............................................................................................. 741P.A. Klurnpp and E .S hmuak

Matrix Mean-Field and l..cal-Field Approaches in the Analysis ofM etal M atrix C oim po,,itc ...................................................................... 76 1J. Atoudi and MI tmdnh