Lecture Notes in Engineering

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1 Lecture Notes in Engineering The Springer-Verlag Lecture Notes provide rapid (approximately six months), refereed publication of topical items, longer than ordinary journal articles but shorter and less formal than most monographs and textbooks. They are published in an attractive yet economical format; authors or editors provide manuscripts typed to specifications, ready for photo-reproduction. The Editorial Board Managing Editors C. A Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton S04 2AA (UK) S.AOrszag Applied and Computational Mathematics 218 Fine Hall Princeton, NJ (USA) Consulting Editors Chemical Engineering: J. H. Seinfeld Dept. of Chemical Engg., Spaulding Bldg. Calif. Inst. of Technology Pasadena, CA (USA) Dynamics and Vibrations: P'Spanos Department of Mechanical and Civil Engineering, Rice University P. O. Box 1892 Houston, Texas (USA) Earthquake Engineering: AS. Cakmak Dept. of Civil Engineering, Princeton University Princeton, NJ (USA) Electrical Engineering: P. Silvester Dept. of Electrical Engg., McGill University 3480 University Street Montreal, PO H3A 2A7 (Canada) Geotechnical Engineering and Geomechanics: C.S. Desai College of Engineering Dept. of Civil Engg. and Engg. Mechanics The University of Arizona Tucson, AZ (USA) Hydrology: G.Pinder School of Engineering, Dept. of Civil Engg. Princeton University Princeton, NJ (USA) Laser Fusion - Plasma: R. McCrory Lab. for Laser Energetics, University of Rochester Rochester, NY (USA) Materials Science and Computer Simulation: S. Yip Dept. of Nuclear Engg., MIT Cambridge, MA (USA) Mechanics of Materials: FA Leckie Dept. of Mechanical Engineering Univ. of California Santa Barbara, CA (USA) A R. S. Po nter Dept. of Engineering, The University Leicester LEl 7RH (UK) Fluid Mechanics: K.-P. Holz Inst. fur Stromungsmechanik, Universitat Hannover, Callinstr Hannover 1 (FRG) Nonlinear Mechanics: K.-J. Bathe Dept. of Mechanical Engg., MIT Cambridge, MA (USA) Structural Engineering: J. Connor Dept. of Civil Engineering, MIT Cambridge, MA (USA) w. Wunderlich Inst. fur Konstruktiven Ingenieurbau Ruhr-Universitat Bochum Universitatsstr.150, Bochum-Ouerenburg (FRG) Structural Engineering, Fluids and Thermodynamics: J. Argyris Inst. fur Statik und Dynamik der Luft- und Raumfahrtkonstruktion Pfaffenwaldring 27 D-7000 Stuttgart 80 (FRG)

2 Lecture Notes in Engineering Edited by C. A. Brebbia and S. A. Orszag 59 K. P. Herrmann Z. S. Olesiak (Eds.) NO LONGER THE PROPERTY OF THE UNIVERSITY OF DELAWARE LIBRARY Thermal Effects in Fracture of Multiphase Materials Proceedings of the Euromech Colloquium 255 October 31 - November 2, 1989, Paderborn, FRG Spri nger-verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona

3 Series Editors C. A. Brebbia. S. A. Orszag Consulting Editors J. Argyris. K.-J. Bathe' A. S. Cakmak. J. Connor; R. McCrory C. S. Desai' K.-P. Holz. F. A. Leckie' G. Pinder' A. R. S. Pont J. H. Seinfeld. P. Silvester' P. Spanos' W. Wunderlich' S. Yip Editors Klaus P. Herrmann Laboratory of Technical Mechanics University of Paderborn Pohlweg Paderborn FRG Zbigniew S. Olesiak Department of Mathematics, Informatics and Mechanics University of Warsaw Palace of Culture and Science Warsaw Poland ISBN ISBN (ebook) / This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication 'or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. Springer-Verlag Berlin, Heidelberg 1990 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

4 PREFACE This book contains a selection of the lectures presented at the Euromech Colloquium 255, held at the Liborianum, Paderborn, from 31 October to 2 November The subject of the Colloquium "Thermal Effects in Fracture of Multiphase Materials" attracted about 50 scientists from 13 countries. Several well known scientists who are active in research on thermal effects in fracture processes were present at the Colloquium as lecturers (29 lectures were delivered) as well as valuable participants of the intensive discussions which took part during the sessions, coffe breaks and lunch times. The closing session of the Colloquium was devoted to a general discussion on the trends in the development of the research in the field, the prospects of the theoretical research, new materials (composites, ceramics etc.), and the trends in technological applications. Over twenty comments and remarks have been made during this final general discussion, showing the interest of the auditorium in such an exchange of viewpoints. However, this discussion is not reflected in this volume. The Colloquium has been subdivided into six sessions: I II. III IV-VI "Thermodynamics of Fracture Processes" "Fracture of Nonhomogeneous Solids" "Thermal Cracking of Heterogeneous Materials" "Fracture Phenomena in Composite Systems I-III" One of the main topics in session I consisted in the description of the influence of thermal effects on shear band localization failure. Thereby shear bands nucleate due. to the presence of local inhomogeneities causing enhanced local deformation and local heating where thermal effects influence especially the microdamage process. Further, the localization of plastic deformation w ~ t h i n shear bands under the consideration of thermal effects and induced anisotropy on the localisation phenomenon was modelled by a thermoelastoplastic material model for the first stage of the flow process and by a thermoejastic-viscoplastic material model including an advanced micro-damage process for the postcritical behaviour within shear bands. Moreover, fracture processes in thermoelastoplastic materials were studied by a specialization of the thermodynamic energy balance equations leading to the establishment of a fracture criterion for thermal cracking of nomhomogeneous materials. This criterion also delivers information concerning the prospective crack path of a propagating crack. Further investigations reported in the sessions IT and III concerned fracture mechanisms at free surfaces of heterogeneous materials as well as thermal cracking of solids with local inhomogeneities and microcracks. Thereby discontinuous thermal strains cause microcracking at the surfaces of

5 IV structures, particularly under cyclic thermal load. By considering a model of a bimaterial interface intersecting a free surface the component of the stress tensor which is parallel to the free surface has a discontinuity at the crossing point, resulting in a very high stress variation under cyclic thermal load which should be the origin for the initiation of edge cracks. Furthermore, discontinuous plastic strains are also the cause of very high stresses at the crossing point where a jump relation between' plastic strains and some stress components can be derived which has an analogue in the jump relation for thermal stresses. Special studies dealt with the influence of the cooling rate on the stress intensity factors in thermal shock problems of thwo-phase cracked composite structures. Results were given for a surface crack, a crack terminating at or intersecting the material interface and a crack initiating from the interface. Besides, the sessions IV-VI of the Colloquium concerned especially thermal cracking of fibrous composites, CFRP-Iaminates as well as of shape memory alloys and damaged particle strengthened ceramics. Thereby the methods of the micromechanical and the macromechanical approach in composite mechanics, respectively, were applied in order to reach an understanding of the complicated cracking mechanisms under the essential influence of thermal effects. The solutions of the associated boundary value problems of thermoelasticity as well as thermoviscoplasticity were obtained by using modem methods of continuum mechanics, for instance finite element and integral equation methods. The conference gave an overview about the important influence of thermal effects on the fracture behaviour of multiphase materials. It can be further stated that the scientific and social success of the conference represented a confirmation of the basic idea of Euromech-Colloquia to discuss particular topics in science in small working parties of specialists. Finally, the two organizers are grateful to the Euromech Committee for approving this Colloquium as well as to the Stiftung Volkswagenwerk, the DAAD, the Nixdorf Computer AG, and the Universitiitsgesellschaft Paderborn for some financial support. The help of the administrative staff of the Laboratorium fur Technische Mechanik at Paderborn University during the planning phase of the Colloquium and during the Colloquium itself was indispensable. K. 'Po Herrmann Z.Olesiak

6 CONTENTS H. P. Stiiwe SOME CONSIDERATIONS ON THE THERMODYNAMICS OF FRACTURE 1 E. Stein, M. K. Duszek-Perzyna, P. Perzyna INFLUENCE OF THERMAL EFFECTS ON SHEAR BAND LOCALIZATION IN ELASTIC-PLASTIC DAMAGED SOLIDS 10 B. Kaempf, K. P. Herrmann SPECIALIZATION OF THE THERMODYNAMIC ENERGY BALANCE EQUATIONS TO FRACTURE PROCESSES IN THERMOELASTOPLASTIC MATERIALS 25 H. D. Bui, S. Taheri STRESS SINGULARITIES AND DISCONTINUITIES ON THE FREE SURFACE OF A THERMOELASTOPLASTIC BIMATERIAL BODY 36 H. Rauh STRESS-DRIVEN SOLUTE SEGREGATION NEAR CRACK TIPS: THEORETICAL MODELLING AND APPLICATIONS TO THE INTERGRANULAR FRACTURE OF HETEROGENEOUS MATERIALS 46 L. V. Berka CONTINUUM MECHANICS OF MEDIA WITH INTERFACES 57 F. Erdogan, A. A. Rizk FRACTURE OF COATED PLATES AND SHELLS UNDER THERMAL SHOCK 66 Z. S. Olesiak DEBONDING OF THIN SURFACE LAYERS GENERATED BY THERMAL AND DIFFUSIVE FLUXES 76 A. Bettin, D. Gross CRACK PROPAGATION IN MATERIALS WITH LOCAL INHOMOGENEffiES UNDER THERMAL LOAD 85 E. Steck CRACK EXTENSION IN INHOMOGENEOUS MATERIALS 94

7 VI C. T. Herakovich, J. M. Duva THERMAL CRACKING IN FIBROUS COMPOSITES USING THE NORMAL. STRESS RATIO los Y. Q. Wang, K. P. Herrmann THE EFFECT OF A PLASTIC ZONE AROUND A FIBER ON THE FRACTURE RESISTANCE OF A FIBER REINFORCED COMPOSITE 114 K. Friedrich FAILURE MECHANISMS AND FRACTURE TOUGHNESS OF DIFFERENT POLYMER COMPOSITE SYSTEMS 123 A. E. Giannakopoulos, K. Breder MODELLING OF TOUGHENING AND ITS TEMPERATURE DEPENDENCY IN WHISKER-REINFORCED CERAMICS 136 W. H. MUller THEORETICAL MODELS FOR THE EXPLANATION OF TOUGHENING MECHANISMS IN HEAVY-DUTY CERAMICS 146 E. Hombogen THERMO-MECHANICAL FATIGUE OF SHAPE MEMORY ALLOYS 156 H. Eggers, H. C. Goetting, W. Hartung, H. Twardy MATRIX CRACKING OF CROSS-PLY LAMINATES UNDER T-FATIGUE AND THERMAL LOADING 168 K. Schulte, H. Neubert, H. Harig LOAD AND DAMAGE DEPENDENT THERMAL EFFECTS IN CFRP-LAMINATES 178 D. Wei, D. Baptiste, Ph. Bompard, D. Francois A STATISTICAL APPROACH TO THERMAL SHOCK BEHAVIOUR OF SYNTACTIC FOAM 188 I. MUller, W. Milller, P. Villaggio STATIC AND DYNAMIC PULL-OUT OF AN ELASTIC ROD FROM A RIGID WALL 195

8 VII K. P. Herrmann, I. Mihovsky, M. Usunova AN EXTERNAL RADIAL CRACK IN A UNIT CELL OF A FIBRE-REINFORCED COMPOSITE 203 P. Mazilu, G. Ondracek ON THE EFFECTIVE YOUNG'S MODULUS OF ELASTICITY FOR POROUS MATERIALS PART 1: THE GENERAL MODEL EQUATION 214 F. E. Buresch THE CRACK DRIVING FORCE IN DAMAGED PARTICLE STRENGTHENED CERAMICS 227 P. Lipinski, M. Berveiller STRESS CONCENTRATION IN MICROINHOMOGENEOUS INELASTIC MATERIALS 239