Low density cellular plastics

Transcription

1 Low density cellular plastics

2 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 n I SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

3 First edition Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1994 Softcover reprint ofthe hardcover Ist edition 1994 ISBN ISBN (ebook) DOI / 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 Z (Permanence of Paper).

4 Contents List of contributors Preface IX xiii 1 Physical behaviour of polymeric foams - an overview 1 A. Cunningham and N.C. Hilyard 1.1 General Foam formation Cell structure Matrix polymer morphology Thermal behaviour Stress-strain behaviour Energy management Final comments 19 References 20 2 Polyurethane flexible foam formation 22 Luis D. Artavia and Christopher W Macosko 2.1 Introduction Reaction chemistry Morphology development The cell opening mechanism Conclusions 51 Acknowledgements 51 References 52 3 Characterizations of polymeric cellular structures 56 M. B. Rhodes 3.1 Introduction Background Quantitative characterization Stereology 64

5 vi Contents 3.5 Difficulties associated with measurement Optical microscopy 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 The dynamics of phase separation The morphological characterization of foams Summary 101 Acknowledgements 101 References Heat transfer in foams 104 Leon R. Glicksman 5.1 Introduction Conduction heat transfer Radiative heat transfer Gas conduction Overall conductivity 139 Acknowledgements 143 Appendix A: Lower limit analysis 144 Appendix B: List of symbols 148 References Thermal ageing 153 C. J. Hoogendoorn 6.1 Introduction Theory and modelling Experimental methods Different testing methods 181 Appendix: List of symbols 184 References The elastic behavior of low-density cellular plastics 187 Andrew M. Kraynik and William E. Warren 7.1 Introduction Elastic behavior of perfectly ordered two-dimensional foams Elastic behavior of three-dimensional foams Future directions 220 Acknowledgements 223 References 223

6 Contents Vll 8 Hysteresis and energy loss in flexible polyurethane foams 226 N. C. Hilyard 8.1 Introduction Mechanical response Definitions and relationships Mechanisms Static hysteresis Dynamics hysteresis Ball rebound resilience Conclusions 264 Appendix: List of symbols 267 References Impact response 270 N. J. Mills 9.1 Introduction Macroscopic deformation geometry Cell geometry and deformation mechanisms Impact properties Relation of impact properties to microstructure Packaging design Complex impacts Discussion 316 References Acoustic characteristics of low density foams 319 Walter Lauriks 10.1 Introduction Single-wave approximation for foams with a low flow resistivity Acoustic properties of foams of medium and high flow resistivity Matrix representation of layered porous materials Conclusion 353 Appendix A: Matrix elements 354 References 359 Index 362

7 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 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

8 x Andrew M. Kraynik Sandia National Laboratories Albuquerque New Mexico Contributors 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 N. J. Mills School of Metallurgy and Materials University of Birmingham Birmingham B15 2TT UK R. D. Priester PUjTPU Product Research, B1470D Dow Chemical Freeport Texas M. B. Rhodes Chemistry Department University of Massachusetts Amhurst Massachusetts MA R. B. Turner PUjTPU Product Research, B1470D Dow Chemical Freeport Texas 77541

9 William E. Warren Department of Civil Engineering Texas A&M University College Station Texas Contributors Xl

10 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 commercialdriving 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 relationships 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.

11 XIV Preface This book brings together a worldwide group of authors from industry and academia who are at the forefront of research into the physics of low-density solid polymer foams. They report, explain and quantify, using empirical data, phenomenological modelling and mathematical analysis the current understanding of fundamental issues concerning foam formation and physical behaviour, and in so doing bring to the readers' attention the many new and exciting possibilities in foam development which have potential for commercial exploitation. Unlike other books on polymeric foams, which concentrate on the chemistry and process technology of foams, it focuses on the essential material science issues of the quantification and mathematical modelling of physical behaviour whether it be mechanical, pneumatic, thermal or acoustic. The book addresses fundamental issues concerning the physics of lowdensity cellular plastics and is intended for any researcher, whether they be chemist, physicist, material scientist or advanced postgraduate student majoring in cellular materials, who may be involved in the development or application of new low-density cellular polymer products. It deals for the most part, but not exclusively, with polyurethane foams and includes chapters by Cunningham (ICI Polyurethanes, Belgium, the Overview), Artavia and Macosko (University of Minnesota,, although Artavia is now based at Cindad Universtaria Rodrigo Facio, Costa Rica), foam formation; Rhodes (University of Massachusetts, ), cell structure characterization; Priester and Turner (Dow Chemical ), morphology of flexible polyurethane matrix polymers; Glicksman (Massachussets Institute of Technology, ), heat transfer; Hoogendoorn (Delft University, the Netherlands), thermal ageing; Kraynik and Warren (Sandia National Laboratories,, although Warren is now based at Texas A&M), elastic behaviour; Hilyard (Sheffield Hallam University, UK), hysteresis and energy loss; Mills (University of Birmingham, UK) impact response; Lauriks (University of Leuven, Belgium) acoustic absorption and insulation. Editorial change has been kept to the minimum required and the editors would wish to thank contributors for their forebearance over the prolonged time the book has been in preparation. N.C. Hilyard A. Cunningham SheffieldjEverberg, January 1994