Table Of ContentDynamic Mechanical
Analysis
Dynamic Mechanical
Analysis
Third Edition
Kevin P. Menard
Noah R. Menard
Third edition published 2020
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
© 2020 Taylor & Francis Group, LLC
First edition published by CRC Press 2002
Second edition published by CRC Press 2008
CRC Press is an imprint of Taylor & Francis Group, LLC
Reasonable efforts have been made to publish reliable data and information, but the author and pub-
lisher cannot assume responsibility for the validity of all materials or the consequences of their use.
The authors and publishers have attempted to trace the copyright holders of all material reproduced
in this publication and apologize to copyright holders if permission to publish in this form has not
been obtained. If any copyright material has not been acknowledged please write and let us know so
we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known
or hereafter invented, including photocopying, microfilming, and recording, or in any information
storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.
com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.
co.uk
Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
ISBN: 9781482255515 (hbk)
ISBN: 9780429190308 (ebk)
Typeset in Palatino
by Deanta Global Publishing Services, Chennai, India
eResource material is available for this title at https://www.crcpress.com/9781482255515.
To my wife, Connie,
Tecum vivere amem, tecum obeam libens.
—Quintus Horacius Flaccus
—Kevin
To my family and friends, who have kept me going through the years.
—Noah
Contents
Foreword .................................................................................................................xi
Preface to the First Edition ................................................................................. xiii
Preface to the Second Edition ..............................................................................xv
Preface to the Third Edition ............................................................................. xvii
Authors ................................................................................................................. xix
1 An Introduction to Dynamic Mechanical Analysis ................................1
1.1 A Brief History of DMA .......................................................................1
1.2 B asic Principles ......................................................................................2
1.3 S ample Applications .............................................................................5
1.4 C reep-Recovery Testing ..................................................................... 10
1.5 A ggressive Environments .................................................................. 11
1.6 S pecifc Applications .......................................................................... 13
1.7 A Bit of Material Science .................................................................... 14
1.7.1 T he Solid State ........................................................................ 14
1.7.2 T he Liquid State ..................................................................... 15
1.7.3 T ransitions............................................................................... 16
1.8 S tudy Questions .................................................................................. 16
Notes................................................................................................................16
2 Basic Rheological Concepts: Stress, Strain, and Flow .......................... 19
2.1 Force, Stress, and Deformation ......................................................... 19
2.2 A pplying the Stress ............................................................................. 21
2.3 H ooke’s Law: Defning the Elastic Response ..................................24
2.4 G eometry, Sample Shape, and Aspect Ratio ...................................29
2.5 L iquid-Like Flow or the Viscous Limit ............................................30
2.6 A nother Look at Stress–Strain Curves.............................................35
2.7 S tudy Questions ..................................................................................39
2.8 A ppendix: Conversion Factors ..........................................................40
Notes................................................................................................................43
3 Rheology Basic: Creep-Recovery and Stress Relaxation ......................45
3.1 C reep-Recovery Testing .....................................................................45
3.2 M odels to Describe Creep-Recovery Behavior ...............................48
3.3 A nalyzing a Creep-Recovery Curve to Fit the Four-Element
Model....................................................................................................50
3.4 A nalyzing a Creep Experiment for Practical Use .......................... 52
3.5 C reep Ringing .....................................................................................53
3.6 O ther Variations on Creep Tests .......................................................54
3.7 S uperposition: The Boltzmann Principle .........................................57
3.8 Retardation and Relaxation Times ...................................................59
vii
viii Contents
3.9 S tructure–Property Relationships in Creep-Recovery Tests ........59
3.10 S tress-Relaxation Experiments .........................................................60
3.11 C onstant Gauge Length Tests ............................................................ 62
3.12 S tudy Questions ..................................................................................64
Notes ................................................................................................................64
4 Thermomechanical Analysis .....................................................................69
4.1 T heory of Thermomechanical Analysis ..........................................70
4.2 Experimental Considerations with TMA Samples ........................71
4.3 Expansion and CTE ............................................................................73
4.4 Flexure and Penetration .....................................................................76
4.5 Dilatometry and Bulk Measurements ..............................................78
4.6 Mechanical Tests .................................................................................79
4.7 PVT Relationship Studies ..................................................................80
4.8 Study Questions .................................................................................. 81
Notes ................................................................................................................82
5 Dynamic Testing and Instrumentation ...................................................85
5.1 Applying a Dynamic Stress to a Sample .........................................85
5.2 Calculating Various Dynamic Properties........................................88
5.2.1 Calculation from Deformation and Phase Lag ..................88
5.2.2 Calculating Properties from a Measured Stiffness ...........90
5.3 Instrumentation for DMA Tests ........................................................90
5.3.1 Forced Resonance Analyzers ...............................................90
5.3.2 Stress and Strain Control ......................................................92
5.3.3 Axial and Torsional Deformation ........................................93
5.3.4 Free Resonance Analyzers ....................................................94
5.4 Fixtures or Testing Geometries .........................................................96
5.4.1 Axial .........................................................................................98
5.4.1.1 Three-Point and Four-Point Bending ..................98
5.4.1.2 Dual and Single Cantilever ................................. 100
5.4.1.3 Parallel Plate and Variants .................................. 101
5.4.1.4 Bulk ........................................................................ 102
5.4.1.5 Extension/Tensile ................................................. 102
5.4.1.6 Shear Plates and Sandwiches ............................. 103
5.4.2 Torsional ................................................................................103
5.4.2.1 P arallel Plates ........................................................103
5.4.2.2 C one-and-Plate ..................................................... 104
5.4.2.3 Couette ...................................................................104
5.4.2.4 Torsional Beam and Braid ...................................105
5.5 Sample Handling Issues .................................................................. 105
5.6 Calibration Issues .............................................................................. 106
5.7 Dynamic Experiments ...................................................................... 107
5.8 Study Questions ................................................................................ 109
Notes .............................................................................................................. 109
Contents ix
6 Time and Temperature Scans Part I: Transitions in Polymers .......... 111
6.1 T ime and Temperature Scanning in the DMA ............................. 111
6.2 T ransitions in Polymers: Overview ................................................ 114
6.3 S ub-T Transitions.............................................................................. 117
g
6.4 T he Glass Transition (T or T) ......................................................... 119
g α
6.5 T he Rubbery Plateau, T* And T ....................................................123
α ll
6.6 The Terminal Region ........................................................................ 128
6.7 Frequency Dependencies in Transition Studies ........................... 129
6.8 Applications ....................................................................................... 131
6.9 Time-Based Studies .......................................................................... 135
6.10 Conclusions ........................................................................................136
6.11 Study Questions ................................................................................ 136
Notes..............................................................................................................137
7 Time and Temperature Scans Part II: Thermosets .............................. 143
7.1 Thermosetting Materials: A Review .............................................. 143
7.2 Studying Curing Behavior in the DMA: Cure Profles ................ 148
7.3 Photocuring ....................................................................................... 153
7.4 Modeling Cure Cycles ...................................................................... 155
7.5 Isothermal Curing Studies .............................................................. 155
7.6 Kinetics by DMA: The Roller Model and Other Approaches..... 157
7.7 Mapping Thermoset Behavior: The Gillham–Enns Diagram .... 159
7.8 Quality Control Approaches to Thermoset Characterization .... 160
7.9 PostCure Studies ............................................................................... 163
7.10 Conclusions ........................................................................................164
7.11 Study Questions ................................................................................ 164
Notes..............................................................................................................164
8 Frequency Scans ......................................................................................... 167
8.1 Methods of Performing a Frequency Scan .................................... 167
8.2 Frequency Effects on Materials ....................................................... 170
8.3 The Deborah Number ...................................................................... 178
8.4 Frequency Effects on Solid Polymers .............................................179
8.5 Frequency Effects during Curing Studies .....................................180
8.6 Frequency Studies on Polymer Melts ............................................. 183
8.7 Normal Forces and Elasticity .......................................................... 183
8.8 Master-Curves and Time–Temperature Superposition ...............186
8.9 Transformations of Data .................................................................. 193
8.10 M olecular Weight and Molecular Weight Distributions ............. 195
8.11 V an Gurp–Palmen Plots and Long Chain Branching .................. 198
8.12 C onclusions ........................................................................................199
8.13 S tudy Questions ................................................................................200
Notes ..............................................................................................................200
