Dynamic mechanical analysis : a practical introduction

240 Pages·2008·14.096 MB·English

by  Menard, Kevin P

S e c o n d E d i t i o n
DYNAMIC
MECHANICAL
ANALYSIS
A Practical Introduction
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S e c o n d E d i t i o n
DYNAMIC
MECHANICAL
ANALYSIS
A P r a c t i c a l I n t r o d u c t i o n
Kevin P. Menard
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487‑2742
© 2008 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
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10 9 8 7 6 5 4 3 2 1
International Standard Book Number‑13: 978‑1‑4200‑5312‑8 (Hardcover)
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Library of Congress Cataloging‑in‑Publication Data
Menard, Kevin P.
Dynamic mechanical analysis : a practical introduction / Kevin P. Menard.
p. cm.
Includes bibliographical references and index.
ISBN 978‑1‑4200‑5312‑8 (alk. paper)
1. Materials‑‑Testing. 2. Rheology. I. Title.
TA418.32.M46 2008
620.1’12‑‑dc22 2007048967
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
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Dedication
To my wife, Connie,
Tecum vivere amen,
tecum obeam libens.
—Homer, Epodes, ix
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Contents
Author’s Preface .....................................................................................................xi
Foreword to the First Edition .............................................................................xiii
Foreword to the Second Edition ...........................................................................xv
Acknowledgments ................................................................................................xvii
Author ....................................................................................................................xix
Chapter 1 An Introduction to Dynamic Mechanical Analysis .............................1
1.1 A Brief History of DMA ...................................................................................1
1.2 Basic Principles .................................................................................................2
1.3 Sample Applications ..........................................................................................4
1.4 Creep–Recovery Testing ...................................................................................9
1.5 Aggressive Environments ................................................................................10
Notes ........................................................................................................................12
Chapter 2 Basic Rheological Concepts
Stress, Strain, and Flow .....................................................................15
2.1 Force, Stress, and Deformation .......................................................................15
2.2 Applying the Stress ..........................................................................................17
2.3 Hooke’s Law: Defining the Elastic Response ..................................................20
2.4 Geometry, Sample Shape, and Aspect Ratio ...................................................24
2.5 Liquid-Like Flow or the Viscous Limit...........................................................25
2.6 Another Look at Stress–Strain Curves............................................................28
2.7 Appendix: Conversion Factors ........................................................................32
Notes ........................................................................................................................35
Chapter 3 Rheology Basics
Creep–Recovery and Stress Relaxation ............................................37
3.1 Creep–Recovery Testing .................................................................................37
3.2 Models to Describe Creep–Recovery Behavior ..............................................40
3.3 Analyzing a Creep–Recovery Curve to Fit the Four-Element Model .............41
3.4 Analyzing a Creep Experiment for Practical Use ...........................................44
3.5 Creep Ringing .................................................................................................45
3.6 Other Variations on Creep Tests ......................................................................45
3.7 Superposition: The Boltzmann Principle ........................................................48
3.8 Retardation and Relaxation Times ..................................................................49
3.9 Structure–Property Relationships in Creep–Recovery Tests ..........................50
vii
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viii Contents
3.10 Stress Relaxation Experiments ........................................................................51
3.11 Constant Gauge Length Tests ..........................................................................53
Notes ........................................................................................................................54
Chapter 4 Thermomechanical Analysis ..............................................................57
4.1 Theory of Thermomechanical Analysis ..........................................................57
4.2 Experimental Considerations with TMA Samples ..........................................59
4.3 Expansion and CTE .........................................................................................61
4.4 Flexure and Penetration ...................................................................................64
4.5 Dilatometry and Bulk Measurements .............................................................65
4.6 Mechanical Tests .............................................................................................65
4.7 PVT Relationship Studies ................................................................................67
Notes ........................................................................................................................68
Chapter 5 Dynamic Testing and Instrumentation ...............................................71
5.1 Applying a Dynamic Stress to a Sample .........................................................71
5.2 Calculating Various Dynamic Properties ........................................................74
5.2.1 Calculation from Deformation and Phase Lag ....................................75
5.2.2 Calculating Properties from a Measured Stiffness .............................76
5.3 Instrumentation for DMA Tests ......................................................................76
5.3.1 Forced Resonance Analyzers ..............................................................76
5.3.2 Stress and Strain Control .....................................................................77
5.3.3 Axial and Torsional Deformation ........................................................79
5.3.4 Free Resonance Analyzers ..................................................................79
5.4 Fixtures or Testing Geometries .......................................................................81
5.4.1 Axial ....................................................................................................83
5.4.1.1 Three-Point and Four-Point Bending ....................................84
5.4.1.2 Dual and Single Cantilever ...................................................85
5.4.1.3 Parallel Plate and Variants ....................................................86
5.4.1.4 Bulk .......................................................................................87
5.4.1.5 Extension/Tensile ..................................................................87
5.4.1.6 Shear Plates and Sandwiches ................................................87
5.4.2 Torsional ..............................................................................................88
5.4.2.1 Parallel Plates ........................................................................88
5.4.2.2 Cone-and-Plate ......................................................................89
5.4.2.3 Couette ..................................................................................89
5.4.2.4 Torsional Beam and Braid .....................................................90
5.5 Sample Handling Issues ..................................................................................90
5.6 Calibration Issues ............................................................................................91
5.7 Dynamic Experiments .....................................................................................92
Notes ........................................................................................................................93
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ix Contents
Chapter 6 Time and Temperature Scans Part I
Transitions in Polymers ......................................................................95
6.1 Time and Temperature Scanning in the DMA ................................................95
6.2 Transitions in Polymers: Overview .................................................................98
6.3 Sub-T Transitions ..........................................................................................101
g
6.4 The Glass Transition (T or T) ......................................................................103
g a
6.5 The Rubbery Plateau, T* and T ..................................................................106
a ll
6.6 The Terminal Region .....................................................................................110
6.7 Frequency Dependencies in Transition Studies.............................................112
6.8 Applications ...................................................................................................114
6.9 Time-Based Studies .......................................................................................117
6.10 Conclusions ....................................................................................................118
Notes ......................................................................................................................119
Chapter 7 Time and Temperature Scans Part II
Thermosets .......................................................................................123
7.1 Thermosetting Materials: A Review .............................................................123
7.2 Studying Curing Behavior in the DMA: Cure Profiles .................................127
7.3 Photocuring ...................................................................................................132
7.4 Modeling Cure Cycles ...................................................................................133
7.5 Isothermal Curing Studies .............................................................................133
7.6 Kinetics by DMA: The Roller Model and Other Approaches.......................134
7.7 Mapping Thermoset Behavior: The Gillham–Enns Diagram .......................137
7.8 Quality Control Approaches to Thermoset Characterization .......................138
7.9 Postcure Studies.............................................................................................140
7.10 Conclusions ....................................................................................................141
Notes ......................................................................................................................142
Chapter 8 Frequency Scans ...............................................................................145
8.1 Methods of Performing a Frequency Scan ....................................................145
8.2 Frequency Effects on Materials .....................................................................147
8.3 The Deborah Number ....................................................................................155
8.4 Frequency Effects on Solid Polymers ...........................................................155
8.5 Frequency Effects During Curing Studies ....................................................158
8.6 Frequency Studies on Polymer Melts ............................................................158
8.7 Normal Forces and Elasticity ........................................................................159
8.8 Master Curves and Time–Temperature Superposition ..................................161
8.9 Transformations of Data ................................................................................167
8.10 Molecular Weight and Molecular Weight Distributions ...............................169
8.11 Conclusions ....................................................................................................171
Notes ......................................................................................................................171
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