Table Of ContentLow 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
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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.
