Low density cellular plastics: Physical basis of behaviour PDF
Preview Low density cellular plastics: Physical basis of behaviour
Low density cellular plastics Low density cellular plastics Physical basis of behaviour Edited by N. C. Hilyard Honorary Research Fellow, Materials Research Institute, Division of Applied Physics, Sheffield Hallam University, UK and A. Cunningham Company Science and Technology Associate, International R&T Centre, ICI Polyurethanes, Everberg, Belgium ID nI SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. First edition 1994 © 1994 Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1994 Softcover reprint ofthe hardcover Ist edition 1994 ISBN 978-94-010-4547-6 ISBN 978-94-011-1256-7 (eBook) DOI 10.1007/978-94-011-1256-7 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms oflicences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A catalogue record for this book is available from the British Library §Printed on acid-free text paper, manufactured in accordance with ANSI/NISO Z39.48-1992 (Permanence of Paper). Contents List of contributors IX Preface xiii 1 Physical behaviour of polymeric foams - an overview 1 A. Cunningham and N.C. Hilyard 1.1 General 1 1.2 Foam formation 3 1.3 Cell structure 4 1.4 Matrix polymer morphology 7 1.5 Thermal behaviour 9 1.6 Stress-strain behaviour 11 1.7 Energy management 14 1.8 Final comments 19 References 20 2 Polyurethane flexible foam formation 22 Luis D. Artavia and Christopher W Macosko 2.1 Introduction 22 2.2 Reaction chemistry 23 2.3 Morphology development 33 2.4 The cell opening mechanism 47 2.5 Conclusions 51 Acknowledgements 51 References 52 3 Characterizations of polymeric cellular structures 56 M. B. Rhodes 3.1 Introduction 56 3.2 Background 57 3.3 Quantitative characterization 60 3.4 Stereology 64 vi Contents 3.5 Difficulties associated with measurement 67 3.6 Optical microscopy 70 3.7 Final comments 75 Acknowledgements 76 References 76 4 The morphology of flexible polyurethane matrix polymers 78 R. D. Priester, Jr and R. B. Turner 4.1 Introduction 78 4.2 The dynamics of phase separation 78 4.3 The morphological characterization of foams 84 4.4 Summary 101 Acknowledgements 101 References 102 5 Heat transfer in foams 104 Leon R. Glicksman 5.1 Introduction 104 5.2 Conduction heat transfer 106 5.3 Radiative heat transfer 121 5.4 Gas conduction 135 5.5 Overall conductivity 139 Acknowledgements 143 Appendix A: Lower limit analysis 144 Appendix B: List of symbols 148 References 150 6 Thermal ageing 153 C. J. Hoogendoorn 6.1 Introduction 153 6.2 Theory and modelling 155 6.3 Experimental methods 169 6.4 Different testing methods 181 Appendix: List of symbols 184 References 185 7 The elastic behavior of low-density cellular plastics 187 Andrew M. Kraynik and William E. Warren 7.1 Introduction 187 7.2 Elastic behavior of perfectly ordered two-dimensional foams 190 7.3 Elastic behavior of three-dimensional foams 210 7.4 Future directions 220 Acknowledgements 223 References 223 Contents Vll 8 Hysteresis and energy loss in flexible polyurethane foams 226 N. C. Hilyard 8.1 Introduction 226 8.2 Mechanical response 227 8.3 Definitions and relationships 230 8.4 Mechanisms 238 8.5 Static hysteresis 251 8.6 Dynamics hysteresis 257 8.7 Ball rebound resilience 261 8.8 Conclusions 264 Appendix: List of symbols 267 References 268 9 Impact response 270 N. J. Mills 9.1 Introduction 270 9.2 Macroscopic deformation geometry 272 9.3 Cell geometry and deformation mechanisms 276 9.4 Impact properties 283 9.5 Relation of impact properties to microstructure 291 9.6 Packaging design 300 9.7 Complex impacts 307 9.8 Discussion 316 References 317 10 Acoustic characteristics of low density foams 319 Walter Lauriks 10.1 Introduction 319 10.2 Single-wave approximation for foams with a low flow resistivity 321 10.3 Acoustic properties of foams of medium and high flow resistivity 331 10.4 Matrix representation of layered porous materials 339 10.5 Conclusion 353 Appendix A: Matrix elements 354 References 359 Index 362 Contributors Luis D. Artavia Escuela de Ingenieria Quimica Universidad de Costa Rica Ciudad Universtaria Rodrigo Facio San Jose Costa Rica A. Cunningham ICI Polyurethanes Everslaan 45 B-3078 Everberg Belgium Leon R. Glicksman Massachusetts Institute of Technology Cambridge Massachusetts MA 082139 USA N.C. Hilyard Materials Research Institute Division of Applied Physics Sheffield Hallam University Sheffield SI 1WB UK C. 1. Hoogendoorn Heat Transfer Group Applied Physics Department Delft University of Technology Delft The Netherlands x Contributors Andrew M. Kraynik Sandia National Laboratories Albuquerque New Mexico 87185-0834 USA Walter Lauriks Laboratorium voor Akoestic en Warmtegeieiding Departement Natuurkunde K.U. Leuven Celestijnenlaan 200 D B-3001 Heverlee Belgium Christopher W. Macosko Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis MN 55455-0132 USA N. J. Mills School of Metallurgy and Materials University of Birmingham Birmingham B15 2TT UK R. D. Priester PUjTPU Product Research, B1470D Dow Chemical USA Freeport Texas 77541 USA M. B. Rhodes Chemistry Department University of Massachusetts Amhurst Massachusetts MA 01003-0035 USA R. B. Turner PUjTPU Product Research, B1470D Dow Chemical USA Freeport Texas 77541 USA Contributors Xl William E. Warren Department of Civil Engineering Texas A&M University College Station Texas 77843-3136 USA Preface Foams are gas filled integral structures in which the gas is finely dispersed throughout a continuously connected solid phase. The bulk density is usually substantially lower than that of the solid component, and for the foams which form the focus for this book the volume fraction of the gas phase is considerably greater than 0.5 and in most instances in excess of 0.9. Many of the materials encountered in every day experience, such as bread, plants and trees, structural materials for buildings, comfort materials for domestic and automotive seating, shock absorbers or car bumpers and materials for noise control, have one thing in common - the cellular nature of their physical structure. Why are these structures so important in the natural and man-made world? The reasons are both technical and commercial. From a technical viewpoint cellular materials offer: 1. high specific stiffness and strength - making them suitable for structural applications; 2. close to ideal energy management - hence their use in thermal and acoustic insulation, vibration damping, acoustic absorption and shock mitigation; and 3. comfort - hence their use for domestic and automotive seating. The commercial driving force is cost reduction and legislation, such as weight saving and noise reduction in the automotive and industrial sectors. Density reduction can be converted directly to cost savings and it is this reason which ensures that commercially produced foams are inexorably being driven towards their lowest possible density for a given application. As densities become ever lower the control and optimisation of the cellular structure and physical properties becomes more complex. To facilitate progress in this respect there is a need for a better understanding of the fundamental relation- ships between composition, cellular structure, matrix morphology and the physical properties. This will facilitate the identification of key factors that control behaviour and performance in use and thereby enable the selection of appropriate chemical and processing variables.
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