CREEP BEHAVIOUR OF WOOD-PLASTIC COMPOSITES
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CREEP BEHAVIOUR OF WOOD-PLASTIC COMPOSITES by Feng-Cheng Chang B.Sc., National Taiwan University, Taiwan, 2000 M.Sc., National Taiwan University, Taiwan, 2002 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Forestry) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2011 © Feng-Cheng Chang, 2011
Transcript of CREEP BEHAVIOUR OF WOOD-PLASTIC COMPOSITES
CREEP BEHAVIOUR OF WOOD-PLASTIC COMPOSITES
by
Feng-Cheng Chang
B.Sc., National Taiwan University, Taiwan, 2000
M.Sc., National Taiwan University, Taiwan, 2002
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
The Faculty of Graduate Studies
(Forestry)
THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)
October 2011
© Feng-Cheng Chang, 2011
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ABSTRACT
In this research, a series of experiments have been conducted, including mountain
pine beetle attacked wood/plastic composite (MPB-WPC) prototype product development,
dynamic mechanical analysis (DMA), short-term creep tests for master curve
construction based on the time-temperature-stress superposition principle (TTSSP), and a
long-term creep test. Moreover, a newly established stress-temperature incorporated
creep (STIC) model, a modified Williams-Landel-Ferry (WLF) equation that incorporates
the variables of temperature and stress, and a newly developed temperature-induced
strain superposition (TISS) method were introduced.
The MPB-WPC products showed definite potential as a value-added product
option for MPB-attacked wood. The formulation affected the MPB-WPC products’
properties. The capacity of the products without a coupling agent was considerably
inferior to the product formulations that included a coupling agent. The surface condition
of the product was also influenced by the formulation.
The dynamic mechanical properties were studied. The mechanical and
viscoelastic behaviours of the MPB-WPC products were considerably influenced by the
formulation of wood and plastic and the presence of a coupling agent, which can be
attributed to modification of the interface property and the internal structure.
The new STIC model smoothly introduced the effect of temperature into a
conventional power law creep equation, and the model can be applied to predict the creep
strain in which the effect of temperature is involved. Moreover, the temperature-stress
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hybrid shift factor and a modified WLF equation were studied; and, the parameters were
successfully calibrated.
Temperature-induced strain was observed in the results of the 220-day creep test.
For a temperature-sensitive material like WPCs, the information obtained from
conventional creep studies is not sufficient to predict long-term performance. The
comparison between the long-term creep data and the master curves showed that master
curves tended to overestimate the creep strain. Generally, the master curves constructed
based on TTSSP cannot precisely predict the long-term creep strain, but can provide
conservative estimations.
To deal with the effect of fluctuating temperatures on the creep strain, the STIC
model and the proposed temperature-induced strain superposition (TISS) method were
established and employed. The additional temperature-induced creep strain and overall
behaviour were successfully simulated.
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PREFACE
A part of chapter 5 has been published. Chang, F.-C., Lam, F. and Englund, K.R.
(2010) Feasibility of using mountain pine beetle attacked wood to produce wood-plastic
composites. Wood and Fiber Science 42(3): 388-397. I organized and conducted all the
testing and wrote the manuscript.
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TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... ii
PREFACE ......................................................................................................................... iv
TABLE OF CONTENTS ................................................................................................. v
LIST OF TABLES ........................................................................................................... ix
LIST OF FIGURES .......................................................................................................... x
ACKNOWLEDGEMENTS .......................................................................................... xiii
DEDICATION................................................................................................................ xiv
CHAPTER 1. INTRODUCTION .................................................................................... 1
1.1 Mountain Pine Beetle Epidemic ................................................................................ 1
1.2 Potential Value-Added Products ............................................................................... 3
1.3 Research Motivation ................................................................................................. 4
1.4 Objectives .................................................................................................................. 7
1.5 Organization of Dissertation ..................................................................................... 7
1.6 Summary ................................................................................................................... 8
CHAPTER 2. BACKGROUND THEORY .................................................................... 9
2.1 Viscoelasticity ........................................................................................................... 9
2.1.1 Linear Viscoelasticity ..................................................................................................... 9
2.1.2 Creep ............................................................................................................................ 11
2.1.3 Analogous Models for Creep ........................................................................................ 13
2.1.4 Boltzmann Superposition Principle .............................................................................. 17
2.2 Dynamic Mechanical Analysis and Time-Temperature Dependence ..................... 18
2.2.1 Dynamic Mechanical Analysis ..................................................................................... 18
2.2.2 Time-Temperature-Stress Superposition ...................................................................... 22
2.2.3 Master Curves ............................................................................................................... 27
2.3 Creep Modelling ...................................................................................................... 29
2.4 Summary ................................................................................................................. 32
CHAPTER 3. LITERATURE REVIEW ...................................................................... 33
3.1 Wood-Plastic Composites ....................................................................................... 33
3.2 Dynamic Mechanical Analysis and Viscoelastic Properties ................................... 38
3.3 Time-Temperature-Stress Superposition Principle for Creep Study....................... 41
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3.4 Creep of Wood-Plastic Composites ........................................................................ 44
3.5 Summary ................................................................................................................. 49
CHAPTER 4. EXPERIMENTAL DESIGN ................................................................. 51
4.1 Materials .................................................................................................................. 51
4.1.1 Raw Materials ............................................................................................................... 51
4.1.2 Product Processing ....................................................................................................... 53
4.2 Mechanical Property Tests ...................................................................................... 54
4.2.1 Experimental Design .................................................................................................... 54
4.2.2 Statistic Analysis .......................................................................................................... 56
4.3 Dynamic Mechanical Analysis................................................................................ 57
4.3.1 Temperature Sweep ...................................................................................................... 58
4.3.2 Deflection Temperature Under Load ............................................................................ 59
4.3.3 The Short-Term Creep Test using DMA ...................................................................... 60
4.3.4 Master Curve Construction ........................................................................................... 61
4.4 Long-Term Creep Test ............................................................................................ 63
4.4.1 Experiment Setup ......................................................................................................... 63
4.4.2 Stress-Strain Analysis ................................................................................................... 65
4.4.3 Corresponding Short-Term Creep Test and the Master Curve ..................................... 67
4.5 Summary ................................................................................................................. 67
CHAPTER 5. MPB-WPC PRODUCTS ....................................................................... 69
5.1 Products ................................................................................................................... 69
5.2 Properties ................................................................................................................. 71
5.2.1 Density .......................................................................................................................... 71
5.2.2 Mechanical Properties .................................................................................................. 71
5.2.3 Characteristic Load-Deformation Behaviours .............................................................. 73
5.2.4 Failure Mode ................................................................................................................ 76
5.2.5 Microscopic Observations ............................................................................................ 77
5.3 Statistical Analysis .................................................................................................. 80
5.3.1 ANOVA ........................................................................................................................ 80
5.3.2 Regression .................................................................................................................... 81
5.3.3 Characteristic Strength ................................................................................................. 83
5.4 Summary ................................................................................................................. 86
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CHAPTER 6. VISCOELASTIC PROPERTIES OF WPCs ....................................... 88
6.1 The Dynamic Mechanical Analysis Spectra ........................................................... 88
6.2 The Effect of Formulation on Transition .............................................................. 100
6.3 Deflection Temperature Under Load .................................................................... 103
6.4 Summary ............................................................................................................... 105
CHAPTER 7. TIME-TEMPERATURE-STRESS SUPERPOSITION AND
MASTER CURVE ........................................................................................................ 107
7.1 Short-Term Creep Tests ........................................................................................ 108
7.1.1 Ten-Minute Creep Tests ............................................................................................. 108
7.1.2 Isochrones ................................................................................................................... 109
7.1.2 Stress-Temperature Incorporated Creep Model.......................................................... 113
7.2 Master Curves ....................................................................................................... 118
7.2.1 Time-Temperature Superposition ............................................................................... 118
7.2.2 Shift Factor ................................................................................................................. 122
7.2.3 Time-Stress Superposition .......................................................................................... 128
7.3 The Modified WLF Equation and the Temperature-Stress Hybrid Shift Factor... 132
7.4 Summary ............................................................................................................... 136
CHAPTER 8. THE LONG-TERM CREEP OF MPB-WPC PRODUCTS ............. 138
8.1 Long-term Creep Test ........................................................................................... 139
8.2 Corresponding Master Curves ............................................................................... 143
8.3 Comparison Between the TTSP Master Curve and Long-Term Creep Tests ....... 148
8.4 Temperature-Induced Strain Superposition Method ............................................. 155
8.5 Summary ............................................................................................................... 165
CHAPTER 9. CONCLUSIONS AND FUTURE WORKS ....................................... 168
9.1 Mountain Pine Beetle Attacked Wood / Plastic Composite Products ................... 168
9.2 Dynamic Mechanical Analysis.............................................................................. 169
9.2.1 Viscoelasticity ............................................................................................................ 169
9.2.2 Time-Temperature-Stress Superposition and Master Curves ..................................... 170
9.3 Creep Behaviour of Mountain Pine Beetle Attacked Wood / Plastic Composites 171
9.4 Recommendations for Future Research ................................................................ 172
BIBLIOGRAPHY ......................................................................................................... 176
APPENDICES ............................................................................................................... 186
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APPENDIX A: SHIFT FACTORS.............................................................................. 186
A.1 Time-Temperature Superposition Shift Factors ................................................... 187
A.2 Time-Stress Superposition Shift Factors .............................................................. 207
APPENDIX B: THE WLF EQUATION FITTING ................................................... 212
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LIST OF TABLES
Table 4-1. Formulations of MPB-WPC Products ............................................................. 53
Table 4-2. Temperature Profile for the Extrusion Process ............................................... 54
Table 4-3. Experimental Conditions for Mechanical Tests .............................................. 55
Table 4-4. Loading Conditions for the Long-Term Creep Test ........................................ 63
Table 5- 1 Properties of MPB-WPC Products .................................................................. 72
Table 5-2. Results of ANOVA for the Effect of Formulations on Product Properties ..... 80
Table 5-3. Results of Regression Analysis ....................................................................... 84
Table 5-4. Parsimonious Results of Regression Analysis ................................................ 85
Table 5-5. Statistical Model Parameters for Flexural MOR of MPB-WPCs .................... 86
Table 6-1. Transition Indices as marked in Figure 6-4 ..................................................... 96
Table 6-2. Comparison of DMA Complex Modulus, Storage Modulus and Traditional
Flexural Modulus .............................................................................................................. 99
Table 6-3. Regression Equations .................................................................................... 102
Table 6-4. Transition of Storage Modulus ...................................................................... 103
Table 6-5. DTUL of MPB-WPC Products and HDPE ................................................... 104
Table 7-1. Parameters for Temperature-Induced Creep Strain Fitting ........................... 116
Table 7- 2. Temperature-Dependent Modulus, ET, Obtained by DMA .......................... 117
Table 7- 3. Parameters for the STIC Model .................................................................... 118
Table 7-4. Horizontal Shift Factors at Various Reference Temperatures At 5 MPa (F2)
......................................................................................................................................... 126
Table 7-5. Coefficients of the WLF Equation for Horizontal Shift Factors (F2) ........... 127
Table 7-6. Shift Factors for the Master Curves in Figure 7-11 ....................................... 131
Table 7-7. Fitted Parameters for the Modified WLF Equation ....................................... 134
Table 8-1. Shift Factors Used to Construct Master Curves ............................................ 145
Table 8-2. The WLF Equation Parameters at Tr = 25°C ................................................ 145
Table 8-3. Standard Error of the Estimate of the STIC Model Prediction ..................... 147
Table 8-4. Parameters of the STIC Model ...................................................................... 148
Table 8-5. Parameters Used for TISS Method ................................................................ 159
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LIST OF FIGURES
Figure 2-1. Scheme of a spring and a dashpot .................................................................. 10
Figure 2-2. Diagram of creep depicting the strain-time relationship ................................ 12
Figure 2-3. Schematic diagram of strain during creep ...................................................... 13
Figure 2-4. Scheme of the Voigt-Kelvin model................................................................ 14
Figure 2-5. Scheme of the Zener model............................................................................ 15
Figure 2-6. Generalized Zener model ............................................................................... 16
Figure 2-7. Scheme of time-temperature shift .................................................................. 23
Figure 4-1. Particle size distribution of MPB wood and AWF pine flours ...................... 52
Figure 4-2. Extrusion processing ...................................................................................... 53
Figure 4-3. The assembly for various mechanical tests: a) flexure, b) compression, c)
hardness, d) nail withdrawal, e) screw withdrawal ........................................................... 55
Figure 4-4. DMA 3-point bending clamp ......................................................................... 58
Figure 4-5. Experimental scheme of the short-term creep test ......................................... 60
Figure 4-6. Loading configuration .................................................................................... 64
Figure 4-7. Long-term creep test fixture and assembly .................................................... 64
Figure 4-8. Scheme of a simply supported beam under a concentrated load ................... 65
Figure 4-9. Scheme of a simply supported beam under symmetric 4-point bending ....... 66
Figure 5-1. MPB-WPC product surfaces. a: mat surface (sharkskin); b: glossy surface.. 70
Figure 5-2. Typical load-deflection/displacement curves from various mechanical tests 74
Figure 5-3(cont). Typical load-deflection/displacement curves from various mechanical
tests ................................................................................................................................... 75
Figure 5-4. Typical failure of MPB-WPCS after mechanical tests .................................. 77
Figure 5-5. Wood encapsulated by HDPE ........................................................................ 78
Figure 5-6. Failure surface – wood not enscapsulated by HDPE ..................................... 78
Figure 5-7. Failure surface of F4, wood was pulled out due to weak bonding between
wood and HDPE ............................................................................................................... 79
Figure 5-8. Failure surface of F1, wood covered by HDPE and ductile failure of HDPE
was observed ..................................................................................................................... 79
Figure 6-1. Storage modulus of MPB-WPCs and HDPE ................................................. 90
Figure 6-2. Loss modulus of MPB-WPCs and HDPE ...................................................... 91
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Figure 6-3. Tan δ of MPB-WPCs and HDPE ................................................................... 93
Figure 6-4. Scheme of transition ....................................................................................... 95
Figure 6-5. DMA spectra of MPB solid wood .................................................................. 97
Figure 6-6. Storage modulus retention.............................................................................. 98
Figure 6-7. Transition of storage modulus ...................................................................... 103
Figure 7-1. A representative result of the 10-minute creep test at various temperatures 109
Figure 7-2. Isochrones taken at 1, 5 and 10 minutes from 10-minute creep tests with
respect to stress at -20, 20 and 45°C (F2) ....................................................................... 110
Figure 7-3. Isochrones taken at 1, 5 and 10 minutes from 10-minutes creep tests with
respect to temperature at 5 MPa (F2) .............................................................................. 111
Figure 7-4. Compliance versus time and temperature (F2) ............................................ 112
Figure 7-5. Creep strain fitted with (a) the power law and (b) the exponential model ... 114
Figure 7-6. Plot of creep strain as a function of time and temperature (F2) ................... 115
Figure 7-7. Master curves at various reference temperatures at 5 MPa (F2) .................. 119
Figure 7-8. Master curves constructed with different temperature ranges (F2) ............. 120
Figure 7-9. Master curves constructed by time-temperature shifting under various stresses
at a reference temperature = 20°C (F2) .......................................................................... 122
Figure 7-10. Shift factor comparison at various stresses at Tr = 20°C (F2). Vertical lines
show the range of the value and boxes show the first quartile (Q1) and the third quartile
(Q3) values, and (+) represent the mean value. .............................................................. 125
Figure 7-11. Comparison between WLF equation and Arrhenius equation fitting (F2 at
Tr= 20°C, under 5 MPa stress) ....................................................................................... 128
Figure 7-12. A master curve construction involving horizontal and vertical shifts........ 130
Figure 7-13. Master curves constructed with the time-stress superposition at 20°C (F2)
......................................................................................................................................... 131
Figure 7-14. The master curve constructed with the time-stress superposition at 20°C
without vertical shift (F2). .............................................................................................. 132
Figure 8-1. Results of the long-term creep test ............................................................... 141
Figure 8-2. The effect of temperature on the long-term creep ........................................ 142
Figure 8-3. Master curves at Tr = 25°C .......................................................................... 144
Figure 8-4. Shift factors used to construct master curves at Tr = 25°C .......................... 144
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Figure 8-5. Comparison between the long-term creep test and the DMA master curve,
with a 95% confidence interval error bar (F4) ................................................................ 150
Figure 8-6. Comparison between the long-term creep test and the DMA master curve,
with a 95% confidence interval error bar (F6) ................................................................ 151
Figure 8-7. Concept scheme of the temperature-induced strain superposition (TISS) ... 158
Figure 8-8. Temperature profile for TISS use ................................................................ 160
Figure 8-9. Model simulation of the temperature-induced strain superposition (F4) ..... 161
Figure 8-10. Model simulation of the temperature-induced strain superposition (F6) ... 162
Figure 8-11. Temperature-induced strain superposition for DMA data ......................... 164
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ACKNOWLEDGEMENTS
I would like to express my gratitude to my research supervisors; Dr. Frank Lam
and Dr. John Kadla, for their academic guidance and financial support through the past
years helped me to develop research skills and finish this dissertation.
Moreover, I would like to extend my appreciation to Dr. Suezone Chow and Dr.
Greg Smith for their service as my research committee members and offering their advice
for my research and this dissertation. As well, a special thank goes to Mr. George Lee,
Mr. George Soong, Dr. Minghao Li, Dr. Far-Ching Lin, Dr. Liheng Chen, Dr. Yueh-Hsin
Lo, and Dr. Juan Blanco for their generosity in sharing their knowledge and offering help
when I need.
In addition, another special thank goes to Mr. Igor Zaturecky from CST
Innovation, New Wesminter, BC, for his offering the facility and collecting MPB fibres
for me. Furthermore, thank Dr. Michael Wolcott, Dr. Karl Englund, Mr. Brent Olsen, Mr.
Derek Tsai, Miss Fang Chen from Composite Materials and Engineering Center,
Washington State University, Pullman, WA, for their considerable helps in MPB-WPC
product manufacture and also for their friendly hospitality during my visiting.
I would also like to thank many previous and present members of Timber
Engineering and Applied Mechanics group and BioMaterials Chemistry Lab for their
friendship as well as assistance for my research and life. In addition, I also like to thank
my teammates in Woody Warriors softball team and fellow musicians in the Vancouver
Concert Band, as well as friends in Taiwanese Graduate Student Association. You made
my life colourful.
Finally, the most sincere appreciation is expressed to my parents; Shyh-Jen Chang
and Lu-Hua Lin, my sister; Yu-Chen Chang, and my dear wife; Xiaoqin Liu, for their
great encouragement and patience. I would have never made it this far without them.
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DEDICATION
To
My parents, Shyh-Jen Chang and Lu-Hua Lin
My wife, Xiaoqin Liu
My sister, Yu-Chen Chang
My daughter, Monica Yong-Han Chang
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CHAPTER 1. INTRODUCTION
This chapter addresses the research background and motivation of this work,
including the issue of the mountain pine beetle (MPB) epidemic, possible value-added
products for the timber from trees attached by MPB, and the critical concern of this
product. Finally, the proposed method and problem statements are also described.
1.1 Mountain Pine Beetle Epidemic
The recent mountain pine beetle (Dendroctonus ponderosae Hopkins) infestation
in British Columbia (B.C.) is the most destructive biotic agent of mature pine forests in
western North America [Safranyik and Carroll 2006]. Outbreaks have been observed in
all pine species; however, they have occurred principally in lodgepole pine (Pinus
contorta var. latifolia). At least 4 large-scale outbreaks have occurred in western Canada
in the past 120 years, as documented in forest survey records or detected in the growth
from tree rings [Safranyik and Carroll 2006; Taylor et al. 2006]. In B.C., lodgepole pine
stands constitute a major commercial resource, comprising 50% of the province’s annual
interior forest harvest [Woo et al. 2005].
During mass attack, MPBs inoculate the tree with blue-staining fungi, primarily
the Ceratocystis species and several species of Europhium [Woo et al. 2005]. The fungi
incursion weakens the trees’ defense mechanisms, interrupts water translocation and
lowers the wood moisture content, eventually leading to tree death [Byrne et al. 2006].
Trees attacked by MPB display distinct signs and symptoms. In the process of
infestation, the trees retain green needles during the first year of attack, which then turn
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red in the following year. Generally, the trees become grey in colour after 3 years [Chow
and Obermajer 2007]. The stages of the damage to the trees are simply termed green, red
and grey. The red-attack stage occurs in the year following the initial attack (green-attack
stage). The beetles have left the tree and the needles have turned red, indicating that the
tree is dead: the fungi carried by the beetles have cut the tree off from its supply of water
and nutrients. In subsequent years, the needles fall off the trees (grey-attack stage).
The volume of blue stain increases as the time increases since the beetle attack,
indicating the need for specific drying schedules employing lower energy levels.
Moreover, the sapwood moisture content of trees drops about 100% from the healthy
stage, while the heartwood moisture drops about 10%, regardless of the stage [Chow and
Obermajer 2007]. The infested trees also develop splits and checks during drying, as
stress is relieved; and, the physical condition of wood is altered [Byrne et al. 2006].
The B.C. Ministry of Forests and Range estimates that the MPB has now killed a
cumulative total of 675 million cubic metres of timber, since the current infestation began;
and, the cumulative area affected is estimated at 16.3 million hectares [B.C. Ministry of
Forests and Range 2010]. According to a recent report [Hamilton 2009], the government
of British Columbia has declared that the MPB epidemic is largely over; however, it is
not because the beetles have been defeated, but because the beetles have run out of trees.
This, in itself, turns out to be another problem of wood supply, since the vast majority of
pine stands have been killed.
Due to MPB, lodgepole pine timber is affected by a blue stain, which occurs in
the sapwood of the attacked trees and appears in products made from stained logs. This
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issue may limit the profit of its wood products [Byrne et al. 2006]. Therefore, several
important tasks need to be carefully considered: finding replacements for solid wood, and
developing value-added products for the low-grade MPB attacked wood.
In addition, processing dry MPB attacked trees can generate more fine material
and residues [Byrne et al. 2006; Watson 2006] compared to healthy, green logs. Thus,
there is a need to investigate alternative products that can make use of these processing
residues.
1.2 Potential Value-Added Products
Wood-plastic composites (WPCs) are being used to create products, such as
landscape timbers, railing, decking, fencing, window and door elements, panels,
moulding, roofing, siding, and even flooring, louvres, indoor furniture, railings in marinas
and bumpers for shipyards. Past research has shown that WPCs have experienced rapid
growth and become a major player in the North American decking market [Clemons 2002;
Winandy et al. 2004; Smith and Wolcott 2006]. This success is primarily attributed to
appropriate performance at a reasonable cost [Smith and Wolcott 2006]. Schneider and
Witt [2004] indicated that the advantages of WPCs can result in increased demands for
value-added WPC products and that the market will increase dramatically in the near
future and continue to grow in the long term.
In the construction community, there is a growing demand for high-performance,
low-maintenance, low-cost building products. Manufacturers of WPCs usually promote
their lower maintenance, lack of cracking or splintering, and high durability. The actual
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lifetime of WPC lumber is currently being debated; however, most manufacturers offer a
10-year warranty. The growing commercial importance of these materials has expanded
efforts for an understanding of their structural properties and for investigation into new
methodologies for producing new materials.
Currently, WPCs are successfully used in non-structural applications [Clemens
2002] and have been recognized as potential choices for use in many light structural
applications [Tajvidi et al. 2010]. More and more research has been undertaken to
improve their mechanical properties for use in structural applications. Comparisons
between WPCs and conventional wood composites have been conducted and indicate that
wood fibre and plastic composite panels have lower bending moduli of elasticity and
rupture than conventional wood based panels; whereas, composite panels performed well
in thickness swell and moisture absorption [Falk et al. 1999; Clemons 2002]. Hence,
these composites are not currently being used in applications that require considerable
structural performance.
1.3 Research Motivation
WPCs can be used for various applications; however, widespread use in structural
applications has been restricted, due to an insufficient understanding of mechanical and
time-dependent behaviours [Kobbe 2005]. The viscoelastic property of WPCs is an
important concern, due to the constitution of the raw materials – plastic and wood.
Failure modes, such as fatigue, creep rupture, excessive deformation and environmental
aging, are all related to the viscoelastic properties of plastic materials [Sain et al. 2000].
Polymers are viscoelastic at all temperatures [McCrum et al. 1997], so that, in
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considering the strains induced in service, not only the stress needs to be taken into
account, but also the time for which it is applied. Furthermore, the viscoelastic properties
are also highly temperature-dependent; therefore, the effect of temperature must also be
taken into consideration.
The examples of viscoelastic behaviours are creep, stress relaxation, fatigue and
dynamic mechanical properties [Deng and Uhrich 2010]. In particular, creep is one of the
most fundamental considerations of the long-term physical properties critical to product
acceptance in many engineering applications [Nkiwane and Mukhopadhyay 1999]. Creep
can lead to unpredicted excessive deformations over a long period of time, which may
cause rupture failures. Therefore, due to the nature of viscoelasticity, static mechanical
tests may not provide sufficient information to predict long-term behaviour.
Creep is not only an important phenomenon in viscoelasticity, but is also of great
significance in the design of plastic based products for load-carrying applications.
Evaluating creep behaviour of a product, however, takes a great deal of time and cost.
Therefore, in order to reduce the expense and time to generate long-term creep
information for design purposes, convenient methods for long-term prediction with
shorter-term experimental data are desired.
Various structural and environmental parameters influence creep behaviour;
however, temperature may be the most important variable, as most polymeric materials
show different behaviours under different temperatures. Consequently, the effect of
temperature is vital in material selection and design of WPCs. However, research
investigating environmental influences (e.g. service temperature) on the mechanical
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performance of WPCs with the goal of assigning structural design values is limited
[Tajvidi et al. 2010].
The dynamic mechanical analysis (DMA) method, which is an accelerated
characterization procedure, can provide a technique to forecast the response of material
and long-term performance. A master curve can be generated based on the time-
temperature superposition principle (TTSP) and can be used to develop a model to
describe long-term performance. This technique provides valuable and practical
information on the time- and temperature-dependent properties, which are essential for
the understanding of long-term behaviour. This knowledge will improve the application
of wood-plastic composites in various uses.
According to past research, the method of DMA and TTSP has certain limits and
some difficulties in its application. Factors, such as stresses, temperatures and types of
material must be taken into careful consideration, and the verification of the master curve
is needed.
Comparisons between the TTSP constructed master curve and the results of a full-
scale creep test have hardly been studied, especially for WPCs, of which formulations
and components may influence the final properties of products, as well as the creep
behaviour. The evaluation of this method was, therefore, investigated by conducting a
long-term creep test in this study, in order to develop an efficient and reasonable method
to study creep behaviour of WPCs. In addition, the viscoelastic properties of WPCs and
their influence on creep behaviours, particularly the effects of temperatures and stresses,
were also studied with the DMA technique.
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1.4 Objectives
The main objectives are summarized as follows:
1. To develop prototypes of mountain pine beetle attacked wood-plastic
composites products and assess the physical and mechanical properties in
terms of formulations.
2. To investigate viscoelastic behaviours of WPCs by means of dynamic
mechanical analysis.
3. To generate the master curves under various stresses and temperatures based
on the time-temperature superposition principle for the prediction of long-term
performance.
4. To study the effects of stresses and temperatures on the creep behaviour of
WPCs.
5. To conduct a long-term creep experiment of WPCs to compare with the
results obtained from short-term DMA tests and study the relationship
between DMA results and long-term test results.
1.5 Organization of Dissertation
This dissertation consists of 9 chapters. In Chapter 1, the issue of the mountain
pine beetle epidemic and potential products for those low-grade materials are pointed out;
and, the major topic of this study is addressed. The fundamental theories of the
approaches adopted in this study are described in Chapter 2; and, the previous research
works that were surveyed are summarized in Chapter 3. Chapter 4 describes the
manufacture of MPB-WPC products and the experimental design. In Chapter 5, the
8
physical and mechanical properties of MPB-WPCs studied by observation and statistical
analysis are presented; and, in Chapter 6, the viscoelastic properties of WPCs are
investigated based on the results of temperature-sweep experiment.
Master curves of WPCs under various stresses and temperatures were generated
and are described in Chapter 7: the influence factors are also discussed. Chapter 8
presents the results from a long-term creep test and a discussion on the comparison
between long-term and short-term data. Conclusions are made in Chapter 9, based on the
overall study; and, future research is suggested.
1.6 Summary
Due to the recent serious MPB epidemic, value-added products for the resulting
low-grade materials are needed. The WPC product is a potential option; however, given
the nature of viscoelasticity, its long-term performance needs to be carefully and
efficiently studied.
In this study, therefore, MPB-WPC products were developed and the effect of the
formulation on properties was investigated. The viscoelastic behaviour, particularly creep,
of WPCs under different temperatures and stresses were studied by dynamic mechanical
analysis and verified with a long-term creep test. This work can improve the
understanding of the time-, temperature- and stress-dependent properties and the
efficiency of the prediction of long-term performance, thereby extending the applications
of wood-plastic composites.
9
CHAPTER 2. BACKGROUND THEORY
Wood-plastic composite (WPC) is a type of polymer based composite with its
behaviour strongly controlled by the characteristics of the polymeric matrix, exhibiting
time-, temperature- and stress-dependent properties. These dependences play important
roles in WPC performance when used in load-bearing applications.
This chapter describes the related fundamental theory applied in this thesis,
including linear viscoelasticity, the dynamic mechanical properties of material, the time-
temperature-stress superposition principle, the behaviour of creep, and related models.
2.1 Viscoelasticity
2.1.1 Linear Viscoelasticity
Most classic materials exhibit either elastic or viscous behaviour in response to
applied stress. Under low stress level, elastic responses are typical in solid materials and
follow Hooke’s Law, which can be shown as an equation: σ = E*ε, where σ is the stress, ε
is the strain, and E is the modulus. This Hookean behaviour can also be observed in
different modes of stress. The response of an elastic system to applied stress is
instantaneous and completely recoverable. A spring can be used as the model for
materials governed by Hooke’ Law.
Viscous behaviour, however, is a characteristic of fluids, in which an applied
stress results in a strain that increases proportionally with time until the stress is removed.
This relationship can be shown in an equation defined by Newton: σ = η*(dε/dt), where σ
10
is the stress, η is the constant of viscosity, and (dε/dt) is the strain rate. In this case, the
strain is not recoverable. A dashpot is usually used as an analogy.
Due to their chain-like structure, the deformation of polymers is accompanied by
a complex series of long- and short-range co-operative molecular rearrangements;
therefore, polymers are not perfectly elastic bodies [Cowie 1973]. Polymers, because of
their viscoelastic nature at all temperatures, display behaviour during deformation that is
both temperature- and time- (frequency-) dependent; and, both time and temperature have
a similar effect on the linear viscoelastic properties, which is based on a
phenomenological theory. Furthermore, due to the viscoelastic properties of a polymeric
matrix, viscoelastic behaviour is dominant in the long-term mechanical behaviour of
polymeric matrix composites.
Figure 2-1. Scheme of a spring and a dashpot
11
2.1.2 Creep
Considering viscoelastic properties, polymer chains slowly rearrange in response
to an applied stress at the structural level. When a constant applied load is maintained, the
resulting strain is not constant, but continues to increase as a function of time. This is
referred to as creep in engineering terms, and it is a manifestation of viscous flow in the
solid polymer. A counterpart to creep is stress relaxation, in which the strain is held as the
constant, and the stress required to maintain the strain decreases as a function of time.
The modulus is defined as the ratio of stress to strain, and the calculation of
modulus in a viscoelastic system should incorporate a time function for both creep and
stress relaxation. If a constant stress is applied to a viscoelastic specimen, the strain is
observed to be time-dependent. To quantify the effect of strain on the material, creep is
normalized as creep compliance, J(t):
( ) ( )
( )
where σ represents a constant applied stress and ε(t) is the time-dependent strain.
For a material in its linear viscoelastic range, the creep compliance is independent
of stress; whereas, the creep compliance is dependent on the stress in the nonlinear range.
The linear viscoelastic range can be determined by an isochrone – plotting strain versus
stress at a specific time. Long-term creep compliance is one performance criteria
commonly used to evaluate composite materials [Lin et al. 2004].
12
By contrast, if a constant strain is maintained on a viscoelastic specimen, the
stress is observed to be time-dependent. To quantify the effect of stress on the material,
stress relaxation is normalized as the stress relaxation modulus:
( ) ( )
( )
A general illustration of elastic and viscous compound behaviour is shown in
Figure 2-2. The material initially responds in an elastic manner and then as a viscous
fluid. When stress is removed, the elastic portion recovers over an extended period of
time.
Figure 2-2. Diagram of creep depicting the strain-time relationship
The general form of a creep curve is shown in Figure 2-3. The curve shows that,
when stress is applied to a material, there is an instantaneous extension followed by rapid
creep. This part is referred to as primary creep. After the primary creep, there is a steady
elongation, referred to as secondary creep, and then an accelerated creep leading to
rupture, known as tertiary creep [Nkiwane and Mukhopadhyay 1999].
13
Figure 2-3. Schematic diagram of strain during creep
To determine the proportion of the elastic and viscous components in a polymer
and the factors that cause the balance to change, it is crucial to understand how the
material will perform in a given application.
2.1.3 Analogous Models for Creep
Using phenomenological approaches to describe creep is very common. The
fundamental idea is the demonstration of behaviour with an analogous system. In this
case, the spring is used to analogize the elastic behaviour (Hookean behaviour), while the
dashpot analogizes the viscous behaviour (time-dependent behaviour). In order to
describe more complex viscoelastic behaviour, many models have been developed that
combine springs and dashpots in parallel, series or both.
One of the basic models is the Voigt-Kelvin model, as shown in Figure 2-4. A
spring and a dashpot are arranged in parallel; therefore, there is the same strain in both
elements, but different stresses. The total stress is equal to the stress in the spring plus the
stress in dashpot, and a differential equation can be made as:
14
( )
During the creep test, stress is constant, but strain is time-dependent; thus, the
time-dependent compliance can be obtained by solving the differential equation:
( ) [ (
)] ( )
Figure 2-4. Scheme of the Voigt-Kelvin model
This model explains the viscous strain well, but not the elastic strain. Thus, one
more spring element can be added for the elastic strain, which is presented as the Zener
model (Figure 2-5):
( ) { [ (
)]} ( )
where τσ is the relaxation time, equal to Jd*η. The first term on the right-hand side
represents the deflection of spring, and the second term is the time-dependent deflection
of the parallel spring-dashpot element. It can be used to fit the isothermal data with three
adjustable parameters, Ju, Jd and τσ, which are valid for creep, stress relaxation and
15
dynamic response [McCrum et al. 1997].
Figure 2-5. Scheme of the Zener model
The Zener model may fail when the observed relaxation times are broader than
the predictions. However, this problem can be fixed by assuming that the mechanism is a
set of relaxation processes with a band of relaxation times that are closely spaced. The
heterogeneity of the polymeric solid causes the relaxation times to occur in a distribution:
all relaxations in polymers are found to be described by distributed relaxation times
[McCrum et al. 1997]. This distribution of relaxation (or retardation) times can be related
to the distribution of molecular mobility, which may be very wide and account for the
protracted nature of the creep phenomenon in a qualitative way [Darlington and Turner
1978].
The generalization of the Zener model (Figure 2-6) to a distribution is a routine
extension with n parallel spring-dashpot elements.
16
( ) ∑ { [ ( ]} ( )
The i-th spring-dashpot element has compliance, Ji, and dashpot coefficient, ηi, and the
relaxation time, τi, and is equal to Ji* ηi. Each element is stressed by the stress, which also
acts on the instantaneous compliance, Ju. The strain in each element is added up to give
the total strain.
Figure 2-6. Generalized Zener model
Consequently, the behaviour of a viscoelastic material can be described in terms
of a distribution function of time constants, which is generally convenient and
informative; and, in principle, such a distribution function is enough to completely
characterize the material. This can be either the distribution of relaxation times
(relaxation spectrum) or, alternatively, the distribution of retardation times (retardation
spectrum) [Dutta et al. 2001].
17
2.1.4 Boltzmann Superposition Principle
The Boltzmann superposition principle (BSP) dates from 1876 and is of great
significant both theoretically and practically. Suppose the time-dependent compliance,
J(t), is known from t0 to tn, the strain, ε0(t), for t0< t< tn resulting from a constant stress, σ0,
applied at t0 = 0 would be:
( ) ( ) ( ) ( )
If there is an additional stress, σ1, applied at time, t1, the resulting strain, ε1(t), for only
itself, according to BSP is:
( ) ( ) ( )
Then, when σ0 and σ1 act together, the total strain at t is:
( ) ( ) ( ) ( ) ( ) ( )
If after time, t1, t2, t3…, the system is subjected to additional stresses, σ1, σ2, σ3…, then
BSP states that the creep response can be predicted simply by summing the individual
responses from each stress increment.
( ) ( ) ( ) ( ) ( ) ( )
Thus, if the stress alters continually, the summation can be replaced by an integral, so that
at time u (0 < u < t), when the stress, σ(u), exists, the strain at time t is given by:
( ) ∫ ( ) ( )
( )
18
For creep loading, σ(t) = σ0H(t), where σ0 is the creep stress and H(t) is the Heaviside
step function. The principle has been successfully applied to the tensile creep of
amorphous and rubber-like polymers, but not when appreciable crystallinity exists in the
sample [Cowie 1973].
2.2 Dynamic Mechanical Analysis and Time-Temperature Dependence
2.2.1 Dynamic Mechanical Analysis
The linear viscoelastic properties of polymers in nature are both time- and
temperature-dependent. Failure modes, such as fatigue, creep rupture, excessive
deformation and environmental aging, are all related to the viscoelastic properties of
plastic materials [Sain et al. 2000]. When considering material for an application, it is
sometimes important to know how the viscoelastic properties will change over a long
period of time and, often, what the viscoelastic properties are under very high-frequency
applications, such as high-speed impact strength.
Dynamic mechanical analysis (DMA) is a method utilized to determine time-
temperature shift factors, by performing dynamic mechanical measurements on solid or
fluid specimens. It has emerged as one of the most powerful tools available for the study
of the behaviour of plastic materials. The understanding of viscoelastic properties
improves the material selection and optimizes the balance between cost and performance
in new and existing products.
The stress function, which is sinusoidal, in a perfectly elastic system results in in-
phase strain. However, in an ideal fluid, the stress leads the strain by 90° (π/2) out of
19
phase. Thus, with viscoelastic materials, the stress function is some hybrid of these two
responses. The stress and strain will be out of phase by some phase angle, δ. A small
phase angle indicates high elasticity, while a large phase angle is associated with high
viscous properties.
The complex response of the material is resolved into the elastic or storage
modulus (E’) and the viscous or loss modulus (E”) in tensile or flexural mode, or G’ and
G” in shear mode. The smaller the phase angle, the closer the elastic modulus is to the
complex modulus. For most conditions at which DMA measurements are made on solid
polymers, the complex modulus and the elastic modulus can be considered equivalent.
The loss modulus is the contribution of the viscous component in the material, i.e. that
portion which flows under stress.
When a specimen is subjected to an oscillatory shear strain of angular frequency,
ω, the strain is generated as:
( )
For a linear viscoelastic material, the stress response is sinusoidal, but out of
phase with the strain by a phase angle, δ:
( ) ( )
From Equation 2-13, σ can be expanded as:
( ) ( ) ( )
20
The stress consists of two components, one in phase with the strain and the other
90° out of phase. The relationship between stress and strain in this dynamic case can be
defined as:
( ) ( )
in which,
( ) = Storage modulus
( ) = Loss modulus
Thus, the component of the stress, E’*γ0, is in-phase with the oscillatory strain; and, the
component, E”* γ0, is 90° (π/2) out of phase.
This formulation is analogous to the relationship between current and voltage in
an electrical circuit, which suggests the use of complex representation [McCrum et al.
1997]. The complex shear modulus is:
( )
The tangent of phase angle is:
( )
For a pure elastic solid, tan δ equals zero, because E” is zero. Since it is
dimensionless, tan δ can be a convenient means for comparing materials, where storage
21
and loss modulus values may be subject to change, due to different formulations,
geometry or processing methods.
The most common graphical presentation of a DMA experiment involves plotting
the storage modulus (E’), the loss modulus (E”), and tan δ as a function of temperature.
The glass transition temperature (Tg) can be measured by the E’ onset point, by the E”
peak, or the peak of tan δ. The Tg may vary according to different indexes; however,
DMA plots provide a comparison of the elastic modulus at different temperatures and
also provide a picture of those temperature regions where material properties are very
stable with temperature and those regions where rapid change may occur.
DMA is widely applied in the characterization of developing material in
laboratory scale, because DMA allows for the use of small sizes of samples in different
forms and various testing functions, as well as various fixtures for different properties of
interests. Furthermore, DMA is a powerful technique that provides quantitative data
regarding the modulus of materials at any temperature of interest [Sepe 1998].
An important aspect of DMA is assurance that the analysis is conducted within
the linear viscoelastic region (LVR). Within the LVR, the response is directly
proportional to the mechanical input; polymer packing is not altered; and, the response
reflects the polymer structure and organization. When the stress/strain response becomes
nonlinear, the mechanical stimulus significantly alters polymer packing. The response
can then reflect other phenomena. However, the quality of the DMA signal is not
satisfactory at very low stresses and strains; consequently, DMA is typically conducted at
22
the highest possible stress/strain within the LVR to optimize the signal quality [Sun et al.
2007].
2.2.2 Time-Temperature-Stress Superposition
A comprehensive creep test is prohibitively expensive and time-consuming;
therefore, it was necessary for methods of interpolation and extrapolation to be developed,
in order to make the most of limited data [Darlington and Turner 1978].
The time-temperature-stress superposition principle (TTSSP), which is an
empirical relationship between the time- and temperature- or stress-dependent properties
of viscoelastic materials, comes from the observation that the time scales of motions of
constituent molecules of a polymer are affected by temperature and stress.
The time-temperature superposition is based on the fact that the viscoelastic
behaviour at one temperature can be related to that at another temperature by a change in
the time or frequency scale only, assuming that the material behaviour is thermo-
rheologically simple [Ferry 1979] and that increasing test temperature accelerates all the
molecular relaxation processes [Darlington and Turner 1978]. This extends the range of
frequencies or times of viscoelastic properties beyond those that are measurable.
In viscoelastic materials, a relaxation process that occurs rapidly at elevated
temperatures (or stresses) occurs to the same degree over longer periods of time at lower
temperatures or stresses; and, the data from creep and stress relaxation experiments
performed at various isothermal temperatures can be superposed to a reference
temperature. These tests may be performed on solid polymer samples using DMA or
23
polymer melts using a rheometer. With creep TTSSP data, the resultant information can
be extended to months, and even years.
This principle is well established for thermoplastics in the LVR. It can provide
qualitative guidance for the extrapolation of creep data for both amorphous and semi-
crystalline thermoplastics, even in the nonlinear region [Darlington and Turner 1978].
Temperature effects are described by altering the time scale of the response (a
horizontal shift, as shown in Figure 2-7), according to:
(
) ( )
where aT is the temperature shift factor and is positive if the curve moves to left of the
reference and negative if the curve moves to right. The shift factor is a function of
temperature only and decreases with increasing temperature [Cowie 1973)]. The creep
compliance at two different temperatures can be related by:
( ) (
) ( )
Figure 2-7. Scheme of time-temperature shift
24
The basis of time-temperature superposition is the free volume theory and
Doolittle’s viscosity equation [Doolittle 1951; Ward 1983; Luo et al. 2001], which is in
the form of:
(
) ( )
(
) ( )
where η is the viscosity of material, A and B are material constants, and f is the free
volume fraction. A linear dependence of the free volume fraction on temperature
variation is:
( ) ( )
where f0 is the free volume fraction at T0, and αT is the thermal expansion coefficient of
free volume fraction.
The shift factor can be defined as:
( )
where η0 and t0 are material viscosity and relaxation time at T0, respectively, likewise for
η and t. Then, the following equation can be derived:
[ (
)] [ (
)]
(
) ( )
25
Since 2.303 log(aT)=ln(aT), Eq.2-24 can be expressed as:
(
) ( )
Substitute Eq.2-22 into Eq.2-24, then yield:
(
) ( )
Define (B/2.303f0) =C1, (f0/αT) = C2, and T0 is the reference temperature, then the
well known Williams-Landel-Ferry (WLF) equation will yield:
( )
( ) ( )
where aT is the time shift factor, Tr is the reference temperature, and T is the temperature
(K) at which the shift factor is desired. The constants C1 and C2 are material dependent
and are based on the slope and intercept of the plot of (T-Tr)/Log(aT) versus (T-Tr). The
WLF equation is typically applied to amorphous polymers in the region from Tg to
Tg+100°C.
A vertical shift factor, which has been evaluated in many research studies, can
also be used to describe the viscoelastic behaviour. Occasionally, a vertical shift is
applied to compensate for the density change of the polymer with temperature:
( )
26
where ρ is the density of the polymer at temperature T, and ρg is the density of the
polymer at the Tg.
The equation is based on the assumption that, above the glass transition
temperature, the fractional free volume increases linearly with respect to temperature
[Ferry 1980]. Banik and Mennig [2006] indicated that free volume plays an important
role in determining the creep behaviour of the semi-crystalline polymers and that a lower
free volume leads to reduced creep strain.
The other model that is commonly used to relate the shift factors with respect to
temperature is the Arrhenius relation:
( )
(
) ( )
where ΔH is the activation energy, R is the gas constant (R = 8.314 J/mole °C), T is the
measurement temperature, Tr is the reference temperature, and aT is the time-based shift
factor.
The Arrhenius equation is typically used to describe viscoelastic events for the
glass transitions associated with semi-crystalline polymers. Frequently, it is used to
obtain the activation energy associated with the glass transition event. However, both
WLF and Arrhenius equations are valid when there is a linear temperature shift in creep
strain due to a change in the temperature [Pramanick and Sain 2006b].
The time-stress superposition is analogous to the time-temperature superposition.
It assumed that the effect of a longer time at a low stress level can be simulated by tests
27
for shorter time at higher stress levels; however, it is on a less firm foundation than the
time-temperature superposition [Darlington and Turner 1978]. The shift factor can be
related to the applied stress by the following equation, which is similar to the WLF
equation:
( )
( ) ( )
where C1 and C2 are material dependent constants, and σr is the reference stress. The
relation between the creep compliance at two stresses can be expressed as:
( ) (
) ( )
where g and aσ are the vertical and horizontal shift factors, respectively.
The vertical shift factor, also called the modulus shift factor, shows the movement
in the vertical direction and depends on the modulus; whereas, the horizontal shift factor,
also called the time shift factor, shows the amount of horizontal movement and depends
on the restraint of viscosity.
2.2.3 Master Curves
As mentioned, the accurate measurement of long-term creep behaviour has always
been difficult. A commonly used test procedure is application of the time-temperature
superposition method, measurement of creep at a number of different elevated
temperatures for a relatively short period of time, and shifting of the results to a reference
temperature to form a master curve for a longer period of time [Gibson et al. 1990].
28
This is accomplished by translating small curves, obtained from creep / stress
relaxation at various temperatures, along the log(t) axis until they are all superimposed to
form a large composite curve. This curve of the modulus/compliance versus time and
temperature provides a useful description of polymer behaviour and allows one to
estimate, among other things, either the relaxation or retardation spectrum [Cowie 1973].
The master curve is of presumed value, since it can be used to calculate the
distribution of retardation or relaxation times and is also often used to predict the
properties of the polymeric material over long time periods beyond the laboratory scale
[Miyase et al. 1993].
A short-term experiment, therefore, can be run under constant or varying stresses
at a constant or increasing temperature. The higher temperature or stress data sets can be
shifted to longer times, until they completely overlap the curve of the reference
temperature or stress. This resulting plot represents the master curve that covers a wide
range of time; therefore, it can serve as a prediction of time-dependent behaviour for
long-term performance.
For a creep master curve, the apparent modulus versus time plot can be converted
into a strain versus time plot by selecting a specific stress. Any temperature and stress can
be used as a reference temperature and stress to construct a master curve. However, the
extent of the projection is limited by the number of tests run at temperatures and stresses
higher than the reference ones. The most reliable predictions can be made for interpolated
temperatures rather than long extrapolations [Cowie 1973]. The curve begins to lose
accuracy, if the selected stresses and strains fall outside the linear elastic region.
29
2.3 Creep Modelling
A number of empirical and theoretical methods have been developed to predict
the time-dependent creep strain. In addition to the above-mentioned creep models, several
commonly used models are summarized in this section.
Findley’s power law model is a simple and widely used model for creep
behaviour. The general form is given as:
( )
where εt is the time-dependent creep strain, ε0 is the instantaneous strain, t is the loading
time, a is the coefficient of the time-dependent strain, and m is the exponential material
constant. This model is simple and easily applied; however, it may not be applicable for
all the situations. The limitation of this approach is that it does not provide a general
representation for creep, recovery and behaviour under complicated loading programs
[Ward 1983].
Findley’s power law can be used to establish the model, which is generally
formed as:
( ) (
) ( )
where ε(t) is the time-dependent strain, ε0 is the instantaneous strain, m is the coefficient
of the time-dependent strain, which is an exponential material constant, t is time after
loading, and t0 is the unit time.
30
The power law equation describes the creep behaviour of a particular material at a
given stress and temperature. Furthermore, to describe the creep behaviour of material at
any stress level, the stress-dependent parameters in the model (ε0 and m) can be replaced
by hyperbolic functions [Findley 1960]:
(
) ( )
(
) ( )
where ε’0 is the instantaneous strain at the reference stress level, σε; σ is the applied stress;
and, m’ is the creep parameter, m, at the reference stress level σm. Equation 2-33 can be
modified with a hyperbolic expression as:
( ) (
) (
) (
)
( )
where constants ε’0, σε, m’ and σm are empirically determined from the data collected at
different stress levels. Values for σε and σm are determined by linearizing the curve for ε0
and m obtained in tests over a range of stresses. Values for ε’0 and m’ are taken as the
slope of the straight-line fit through the respective data with least square procedures. ε’0,
σε, m’ and n are all constants independent of stress, strain and time; however, they still
remain as functions of the material, temperature, humidity and other environmental
factors.
In addition to Findley’s model, many other creep prediction models are
validations of Schapery’s model or Kelvin-Maxwell’s model, where the composite is
31
treated as a single-phase material [Pramanick and Sain 2006a]. However, Martinez-
Guerrero [1998] concluded that wood-plastic lumber does not follow the Kelvin-Maxwell
model. Schapery’s study (1969) takes care of the stress related nonlinearity in creep and
calculates the creep constants for the particular constituents (composites or pure plastics).
Schapery’s single integral constitutive equation is one of the most commonly used
nonlinear viscoelastic models and is derived by using the principles of thermodynamics
of irreversible processes. The time-dependent properties, including the linear viscoelastic
properties and four stress-dependent material parameters, can be determined from
creep/recovery tests. The model is general and can be simplified to other models
[Falahatgar and Salehi 2009]. This model would be a good tool for the validation of any
proposed new creep model, if the material is considered a single-phase material. The
linear viscoelastic power law model is presented by Schapery as:
( ) ( ) ( )
where J0 and J1 are the instantaneous compliance and time-dependent compliance,
respectively, and n is an empirically determined parameter. Schapery also presents a
general form of the time-dependent nonlinear compliance as:
( ) (
) ( )
where J0 is the instantaneous compliance, and ΔJ(t) is the time-dependent compliance.
The equation is nonlinear, because parameters g0, g1, g2 and aσ are stress-dependent and
related to the stress-dependent free energy, but are not time-dependent. When g0 = g1 = g2
= aσ= 1, the model becomes linear and is not stress-dependent.
32
The Bailey-Norton equation is also a power law model that has been used to
describe the viscoelastic response of a material under a constant stress. The primary creep
can be characterized by a monotonic decrease in the rate of creep, and the creep strain can
be described with the Bailey-Norton equation:
( )
where ε is the creep strain, σ is the stress, a, n, and b are temperature-dependent constants
[Betten 2008].
2.4 Summary
In this chapter, previously developed fundamental theories of linear
viscoelasticity, creep behaviour and models, dynamic mechanical analysis, and the time-
temperature-stress superposition principle have been reviewed. This chapter provides the
background knowledge to study the creep behaviours of wood-plastic composites and
develop an efficient methodology for creep prediction based on dynamic mechanical
analysis and the time-temperature-stress superposition principle.
33
CHAPTER 3. LITERATURE REVIEW
Previous researches related to this study are reviewed and summarized in this
chapter, including wood-plastic composites, dynamic mechanical analysis, creep of
wood-plastic composites, and the application of time-temperature-stress superposition
principle to the study of creep for wood-plastic composites.
3.1 Wood-Plastic Composites
Wood-plastic composites (WPCs) are typically made using 30% to 60% wood
filler. Wood flour can be used as a filler to reduce raw material costs and improve
stiffness and dimensional stability over a range of temperatures, with minimal weight
increase [English et al. 1997]. When appropriate coupling agents are added to increase
the fibre matrix compatibility and adhesion, the mechanical properties can be improved
[Lu et al. 2000; English et al. 1996].
Wood flour is made commercially by grinding post-industrial material, such as
planer shavings, chips and sawdust, into a fine, flour-like consistency [Stark 1997]. Wood
fibres are available from both virgin and recycled sources, including pallets, demolition
lumbers and old newsprint [Clemons 2002; Hwang 1997; English et al. 1996]. Wood
from small-diameter trees and underutilized species can also be used.
Various wood species have been used for the manufacture of WPCs; a few
common ones are, pine (Pinus spp.), maple (Acer spp.) and oak (Quercus spp.) [Stark and
Berger 1997; Clemons 2002]. In addition to wood, many particle and fibre types have
been investigated, such as wheat, kenaf, cornstalk, hemp and jute [Rowell 1996;
34
Youngquist et al. 1996; Caulfield et al. 1998; Chow et al. 1999; Bledzki et al. 2004].
English et al. [1997] studied the comparison between wood and mineral fillers in
composites and indicated that wood filler can reduce the specific gravity of composites,
which is an advantage in packaging and transportation applications.
The manufacturing of thermoplastic composites is usually a two-step process. The
raw materials are first mixed together (compounded), and the composite blend is then
formed into products. The combination of these steps is called in-line processing, and the
result is a single processing step that converts raw materials to end products. While still
in its molten state, the compounded material can be immediately pressed or shaped into
an end product or formed into small, regular pellets for future reheating and forming
[Clemons 2002].
Three common forming methods for WPCs are extrusion (forcing molten
composite through a die), injection moulding (forcing molten composite into a cold
mould), and compression moulding (pressing molten composite between mould halves)
Extrusion is, by far, the most common method [Clemons 2002]: the total poundage of
products produced with injection and compression moulding is much less than that
produced with extrusion [English et al. 1996].
Due to the limited thermal stability of wood, only thermoplastics that melt or can
be processed at temperatures below 200°C (392°F) are commonly used in WPCs. The
plastic is often selected based on its inherent properties, product need, availability, cost
and the manufacturer’s familiarity with the material [Clemons 2002]. Currently, most
WPCs are made with polyethylene (PE), low- or high-density, both recycled and virgin.
35
Based on the study of Selke and Wichman [2004], the performance of products made
from recycled high-density PE (HDPE) is at least as good as that from virgin HDPE.
Other thermoplastics have also been used as matrices, such as polypropylene (PP),
polyvinyl chloride (PVC), polystyrene (PS) and acryloni-trile-butadiene-styrene (ABS)
[Clemons 2002], the choice of polymer depending on the intended use of the final
product. A type of biodegradable polymer, poly(lactic acid) (PLA), is getting more and
more attention for its eco-friendliness; therefore, research studies on the applying on PLA
to WPCs have also been done [Ibrahim et al. 2010].
Processing methods affect the performance of WPCs due to different temperatures,
pressures and flows found in the different methods. Clemons and Ibach [2004] indicate
that extruded composites absorb the most moisture, compression moulded composites
absorb less than the extruded composites, and injection moulded composites absorb the
least amount of moisture. The reason may be attributed to the high pressure during
processing used in injection moulding form a thin layer of polymer at the surface [Stark
et al. 2004], and this layer limit the moisture absorption. Stark et al. [2004] also indicated
that the processing method influence the durability of WPCs because of the different
surface conditions, and the retention of flexural properties after weathering is also
influenced. Injection-moulded samples retained higher flexural properties than extruded
samples did.
Wood particle sizes, geometry, and variety of species also influence WPC
properties [Stark and Rowlands 2003; Takatani at al. 2000; Stark 1997]. The affected
properties can include moisture absorption [Wang and Morrell 2004] and decay
36
resistance [Verhey and Laks 2002]. Typical particle sizes for WPCs are 10 to 80 mesh
[Clemons 2002], with smaller particle sizes yielding better material performance
[Takatani at al. 2000]. Based on experimental results, hardwood WPCs exhibit slightly
better tensile and flexural properties and heat deflection temperatures, compared to
softwood WPCs [Stark 1997 and Berger 1997].
The formulation, including the contents of wood, plastic and additives, can
significantly affect WPC properties [Hwang 1997; Stark and Berger 1997; Caulfield et al.
1998; Lu et al. 2000; Stark and Rowlands 2003; Wolcott 2003]. A higher filler content
results in better stiffness properties; however, the modulus of rupture (MOR) and
maximum deflection decrease with increasing wood content and decreasing resin content
of the wood particles [Hwang 1997].
With increasing wood flour content, flexural and tensile modulus, density, heat
deflection temperature, and notched impact energy increase, while flexural and tensile
strength, tensile elongation, mould shrinkage, melt flow index, unnotched impact energy
[Stark and Berger 1997] and heat release rate of WPCs [Stark et al. 1997] decrease. The
reduction is due to the stress concentration effect around the filler particles, which is
produced by weak interaction phenomena of the matrix with the filler, causing weak
adhesion [Crespo et al. 2009].
In fibre reinforced composites, the interaction and adhesion between the fibres
and matrix have a significant effect in determining the mechanical and physical
behaviours of fibre composites [Sanadi et al. 2000; Stark 1999; Caulfield et al. 1998;
Oksman and Clemons 1998; Clemons 1995]. As well, fibre fracture (or lack of it),
37
polymer ductility and fibre polymer bonding all play roles in impact performance
[Clemons 1995].
The key factor in the reinforcement of thermoplastic properties with natural fibre
is the creation of strong bonds that efficiently transfer stress from the matrix to the fibre.
Some maleated copolymers (e.g. maleated anhydride polypropylene/polyethylene) and
silane have been studied and proven useful as compatibilizers or coupling agents for
WPC manufacture [Lu et al. 2000; Herrera-Franco and Valadez-González 2004; Selke
and Wichman 2004; Bengtsson and Oksman 2006; Chowdhury and Wolcott 2007; Lee et
al. 2008; Zhang et al. 2008]. In addition, the effects of different lubricants on WPCs have
also been studied [Harper and Wolcott 2004]. The selection of additives should be
carefully considered for future manufacture, in order to improve the quality of the
product.
WPCs’ decay resistance, due to weather, moisture, temperature, insects or fungi,
has been studied, including laboratory and field tests, [Morris and Cooper 1998; Chow et
al. 1999; Falk et al. 2000a; Falk et al. 2000b; Hwang and Hsiung 2000; Verhey et al.
2001; Clemons and Ibach 2002; Pendleton et al. 2002; Verhey et al. 2003; Lopez et al.
2005; Tajvidi et al. 2010]. WPCs have been shown to possess good dimension stability,
weather resistance, moisture absorption and fungi resistance.
The flexural and tensile properties of WPCs are, however, strongly affected by
temperature. As to freeze-thaw cycling resistance, the effect of cycles is confined to the
first cycle only, the repeated cycling did not exhibit significant effect on mechanical
properties [Tajvidi and Haghdan 2009]. Wang and Morrell (2005) indicate that moisture
38
absorption tends to increase with the number of wet/dry cycles. These composites are
also subject to photodegradation, resulting in a change in appearance and/or mechanical
properties [Stark et al. 2002].
3.2 Dynamic Mechanical Analysis and Viscoelastic Properties
Dynamic mechanical analysis (DMA) is a very powerful technique that allows for
the determination of mechanical properties (modulus and damping), detection of
molecular motions (transitions), and development of morphology relationships [Turi
1997]. DMA has been applied extensively in the study of viscoelastic properties of WPC
materials [Wolcott et al. 2000; Son et al. 2003; Pooler and Smith 2004; Tajvidi et al.
2010].
During the glass transition, the storage modulus exhibits different values for
different heating rates at the same temperature; and, the peak of the curves of the loss
modulus and tan δ show a right shift with increased heating rate. The resulting glass
transition temperature (Tg) and the onset point of glass transition both increase with
increased heating rate. Furthermore, based on thermogravimetric analysis (TGA),
differential scanning calorimetry (DSC), and DMA conducted at different heating rates, it
has been demonstrated that the thermo-physical and thermo-mechanical properties are not
only functions of temperature, but are also functions of time [Bai and Keller 2009].
Sun et al. [2007] used DMA to study the viscoelastic response of various species
(yellow poplar and southern yellow pine) of dry solid wood (moisture < 1%) and found
that the linear viscoelastic region was determined as a function of grain orientation and
temperature.
39
Chartoff et al. (1994) summarized several factors involved with the establishment
of Tg from DMA, including:
1. Instrumental factors: temperature calibration, thermal gradient, sample size,
clamp effect, and sample geometry.
2. Test frequency: increasing the test frequency causes a shift of Tg to a higher
temperature.
3. Material characteristics: the degree of crystallinity, the degree of cross-linking
in thermoset, the specific thermal and mechanical history of the materials, and
possible moisture effects.
4. Choice of Tg criterion: different viscoelastic functions may give different
results.
Son et al. [2003] used DMA to analyze the effect of additives and nucleating
agents on the viscoelastic properties of various extruded wood/polypropylene composites.
The results showed that highly crystalline polypropylene (PP), treated with maleated
anhydride polypropylene (MAPP) as a coupling agent, had a higher storage modulus, but
a lower tan δ. As well, its activation energy for the relaxation process was also higher,
which implies better mechanical performances.
Wolcott et al. [2000] also mentioned that MAPP contributes to the formation of a
transcrystalline layer in the wood/plastic interphase, and this crystallization of
thermoplastics in the presence of wood can be monitored using DMA. Furthermore,
Sanadi and Caufield [2000] found a significant amount of defects in transcrystalline
40
zones in coupled composites using DMA, and suggested that longer molecular chains and
lower anhydride content may result in fewer defects.
Tajvidi et al. [2010] studied hemp-polypropylene composites with DMA and
found that the composite material containing higher hemp fibre content had higher
storage modulus values, indicating that composites with higher fibre content have better
mechanical performance at elevated temperatures. Moreover, the formulation did not
affect the onset of the glass transition.
Deng and Uhrich [2010] investigated ultrahigh molecular weight polyethylene
(PE) using DMA and found that frequency, heating rate and load level affected the
dynamic mechanical properties. Furthermore, they also indicated that the procedure of
isothermal is important. A high storage modulus (E’) value was observed because the
initial response of the experimental specimens to the instant loading was strong. In
addition, it was mentioned that the composite behaved stiffer and more elastically as the
frequency was increased, which also suggests a decrease in toughness and an increase the
tendency of brittle failure.
Swaminathan and Shivakumar [2009] indicated that there are discrepancies in
measuring the storage modulus using DMA device, particularly for high modulus
materials. There was 50% difference between DMA and ASTM D790 results when
testing carbon/epoxy composites. They pointed out that factors that may impact DMA
testing include specimen preparation, geometry, aspect ratio and magnitude of load, were
pointed out; and, guidelines were proposed to accurately measure storage modulus and
tan δ, which were also presented in their study.
41
3.3 Time-Temperature-Stress Superposition Principle for Creep Study
Ferry [1980] summarized several criteria in the application of the time-
temperature-stress superposition principle:
1. The shapes of the adjacent curves at different temperatures must match over a
substantial range of frequencies/time.
2. The same values of shift factors must superpose all the viscoelastic functions.
3. The temperature dependence of the shift factor must have a reasonable form
consistent with experience (e.g. Williams-Landel-Ferry or Arrhenius
equations).
Urzhumtsev and Maksimov (1968) mentioned that, within a reasonable limit of
stresses, the time-stress superposition can be successfully used with the Williams-Landel-
Ferry (WLF) equation. However, Miyase et al. [1993] remarked that the simple time-
temperature superposition principle is generally not applicable to crystalline polymers,
except at low degrees of crystallinity, since there are changes with temperature in the
microcrystalline structure and in the stress bearing mechanisms [Tobolsky and
McLoughlin 1955].
Pooler and Smith [2004] adopted DMA to find the temperature shift factor of
WPCs (58% wood flour) with small specimens. These were loaded in a dual cantilever
fixture. Shift factors were found every 2°C, from -30°C to 65°C, to relate its response to
that observed under ambient conditions. The shift factors were compared to the WLF
equation, and it was found that WLF closely followed the shift factors from -10°C to
65°C.
42
Tajvidi et al. [2005] applied the time-temperature superposition principle (TTSP)
to study creep of a kenaf/HDPE composite; and, the results indicated that the composite
material was thermo-rheologically complex and that a single horizontal shift was not
adequate to predict long-term performance. Thus, they point out that the TTSP can be
applied only to natural fibre / thermoplastic composites with caution.
Dastoorian et al. [2010] studied the creep and stress relaxation for WPCs made
with fir, HDPE and maleated anhydride polyethylene (MAPE), adopting the time-stress
and -strain superposition principle. The results indicated that the studied composite
material was rheologically simple and that a single horizontal shifting along the time axis
was adequate to predict the long-term performance of the material. However, the shift
factors conformed to the Arrhenius equation instead of the WLF equation.
Samarasinghe et al. [1994] applied TTSP to study the creep of southern pine in
compression parallel to the grain and tried to validate the obtained master curves with a
10-month creep test. However, due to the fluctuating environmental conditions, the
geometry of specimens changed and affected the results. Therefore, the conclusion was
made that there was no good comparison between the master curve and long-term data.
Barpanda and Mantena [1998] employed DMA to study a pultruded hybrid
composite for accelerated creep and stress relaxation testing at elevated temperatures and
to also apply TTSP to generate master curves for the prediction of the creep and stress
relaxation properties of the hybrid composites.
Siengchin [2009] conducted a long-term creep test (of about one month) to verify
the DMA short-term creep tests (15 minutes) performed at various temperatures (-50°C to
43
80°C), in order to determine the tensile creep properties of a ternary composite,
consisting of polyoxymethylene, polyurethane and boehmite alumina. Master curves were
constructed by employing TTSP; and, the results showed a significant difference, about
20%, between the long-term data and the model prediction based on the short-term creep.
The results from the master curve were higher than the experimental data, which means
the TTSP method overestimated the practical creep strain. Barbero and Julius [2004] also
applied DMA and TTSP to construct master curves for polymer blends and felt-filled
plastics, and the obtained master curves also overestimated the long-term compliance of
specimens.
One of the difficulties of using the DMA and TTSP method on polymer
composites, which was pointed out by Gibson et al. [1990], is that nonlinearities may be
introduced, because the polymer matrix changes the modulus with respect to the fibre at
the extreme temperatures of the accelerated testing program; and, the master curve may
not reflect the true isothermal linear viscoelastic behaviour of the material at the reference
temperature.
In the study of Tajvidi et al. [2005], a 24-hour creep test was conducted to
validate master curves generated from frequency and temperature sweeps and found that
the actual creep curves and the master curves tended to deviate at longer times. This may
indicate that the effect of temperature on creep is more pronounced than the effect of time.
Barbero and Julius [2004] suggested that the individual TTSP curve must be momentary
to avoid aging effects. In addition, Knauss [2008] pointed out that variation around the
mean temperature may have a measurable effect on the time-temperature superposition
process and lead to imprecise data.
44
Based on Doolittle’s viscosity equation and free volume theory, Luo et al. [2001]
suggested a shift factor that combined temperature and stress, in order to study the time-
temperature-stress equivalence of HDPE. The hybrid shift factor is discussed and the
parameters are validated in Chapter 7.
3.4 Creep of Wood-Plastic Composites
Creep in thermoplastics is a complex phenomenon that depends on material
properties, such as molecular orientation, crystallinity and external factors, i.e. applied
stress, temperature and humidity. The presence of wood fibres introduces additional
variables, including the fibre volume fraction, the fibre aspect ratio, the orientation of
fibres, and the mechanical properties of the fibres, which affect the mechanical and creep
behaviour of the composites [Xu et al. 2001].
In composites, both fibres and matrices contribute to the creep under loads. All
plastic based materials and wood exhibit viscoelastic behaviour and creep under stress.
Tuttle et al. [1995] stated that the polymeric matrix is usually the principle source of the
time-dependent behaviour, although for composites in which fibres are used, the fibre
itself may also be a contributing factor.
It was noted in the study of Sain et al. [2000] that the addition of wood into a PE
matrix significantly retarded the time-dependent strain response, when compared to the
strain response of virgin PE. Wood flours act as discrete particles of high creep resistance
that, when embedded in the plastic matrix, partly retard both the elastic and viscous flow
45
of the polymeric chains under stress. The creep properties of wood flour filled PE are
significantly improved, even at a higher temperature of application.
In the formulation of WPCs, creep decreased slightly with increasing wood
content [Xu et al. 2001]. Likewise, Biswas et al. [2001] reported that, with an increase in
the fibre volume fraction, considerable changes in viscosity occurred; and, the composite
was able to withstand higher temperatures for a longer period of time.
Cyras et al. [2002] also suggested that the creep compliance of natural fibre /
polymer composites increases with decreases in the fibre content. In addition, the
addition of coupling agents or compatibilizers, such silane and MAPP, can improve the
long-term properties of WPCs [Sain et al. 2000; Bengtsson and Oksman 2006].
In regards to the creep test conditions for WPCs, Sain et al. [2000] mentioned that
the instantaneous strain was more dominant than the transient creep strain when lower
stress levels were applied; whereas, time-dependent creep became more significant with
increasing loading levels, which can be attributed to molecular slippage of the structure.
In addition, time-dependent creep was less influenced by temperature than instantaneous
creep. Under a given load, instantaneous creep was more sensitive than transient creep at
low operating temperatures; and, the transient creep strain became more pronounced with
increasing operating temperatures. Cyras et al. [2002] also suggested that the creep
compliance of natural fibre / polymer composites increases with increases in temperature.
Najafi and Najafi [2009] conducted short-term (30 minutes) flexural creep tests
for wood sawdust / HDPE composites with load levels of 10%-40% of maximum bending
load. The creep deflection increased with increasing load levels; and, with the same wood
46
content, composites with recycled HDPE had better creep resistance than did those with
virgin HDPE. Furthermore, at high levels of load, the behaviour of composites became
nonlinear in character.
Najafi et al. [2008] tested the creep properties of medium density fibreboard
(MDF) flour recycled HDPE composites under water immersion and found that water
absorption had a negative effect on creep behaviour and that the creep strain increased
with increasing immersion time. This result is believed to be attributable to the
cumulative effect of the debonding between fibre and matrix caused by the absorbed
water and easier relaxation of polymer molecules at higher moisture contents.
Furthermore, longer immersion resulted in greater irrecoverable creep deflection.
Findley [1987] adopted the power law form to predict tensile creep to 230,000
hours (26 years). Model parameters were determined from the first 1,900 hours of data,
and then were used to predict creep to 230,000 hours. The recovery of the specimen was
also successfully predicted by this equation, associated with the Boltzmann superposition
principle. However, Sain et al. [2000] pointed out that Findley’s power law model
oversimplified the practical situation, and the obtained values from this model cannot be
universally applied due to differences among materials.
In Kobbe’s research (2005), Findley’s power law model was used to describe
nonlinear creep, and it was found that Findley’ power law could accurately predict the
time-dependent creep deformation of polypropylene-based WPCs. Moreover, it was
indicated that this material behaved nonlinearly, even at stress levels as low as 10% of the
ultimate stress.
47
Findley’ power law has also been reported as an adequate model up to about 50%-
60% of the ultimate stress level [Sain et al. 2000; Choi and Yuan 2003]. Najafi and Najafi
[2009] also concluded that the creep behaviour of WPCs followed Findley’s power law.
However, Tajvidi et al. [2005] reported that the Bailey-Norton equation was successfully
used to predict long-term creep of natural fibre / thermoplastic composites.
Pooler and Smith [1999] suggested a modification of the Schapery model – the
Prony series, the general form of which is the same as the generalized Zener model,
which fits the creep behaviour of wood particle-filled plastics well – using 5 elements
over the temperature range of 23°C to 65°C. The Prony series model application calls for
numerical calculations and is very material specific [Pramanick and Sain 2006b].
Moreover, obtaining these data fits can be difficult when the data is spread over a
wide range of time [Chambers 1997].
Teoh et al. [1992] adopted a 3-element spring/dashpot model (i.e. Zener model) to
predict creep rupture and the lower stress level and the upper stress limit, both of which
depend only on the elastic constants and the resilience of the material.
In addition, temperature and moisture can induce nonlinearity [Tuttle et al. 1995].
An issue with temperature is its influence on stress, i.e. whether the combined stress-
temperature effect is additive or interactive [Pramanick and Sain 2006b]. Individual
moisture, temperature and stress related creep issues have been dealt with in the field of
thermosetting based composites [Woo 1994].
In many polymer based materials, creep is nonlinear with respect to stress, in the
sense that compliance is a function of stress. Rangaraj and Smith [1999] developed a
48
nonlinear viscoelastic model, based on the power law model, for wood/thermoplastic
composites and agreed with two-step creep-recovery tests. Walrath [1991] studied
composites containing two viscoelastic phases and found that the Schapery nonlinear
viscoelastic model adequately fit the response to uniaxially applied loads.
Pramanick and Sain [2006a] attempted to develop a generic creep prediction
model to describe the creep behaviour of composites based on the constituents’ creep
behaviours. In different studies that concentrated on creep prediction and characterization
of composites as a single-phase material, the theory of mixture for composites was
applied to describe the creep behaviour of two-phase materials. This is the first model to
describe creep for a two-phase, bio-based composite. The model is generic enough to
extend to varying environmental conditions, such as time and temperature. This study
[Pramanick and Sain 2006a] correlates Schapery’s single-phase model with a two-phase
model, where the same model is validated for step-loading situations.
Pramanick and Sain [2006b] studied the relationship between deformation, time,
temperature, relative humidity and stress. Rice husk / HDPE beams were subjected to
creep and recovery in the flexural mode; and, stress, time and temperature related creep
behaviour was studied. The combined effect of temperature and stress on creep strain was
accommodated in a single analytical function. This means that the stress equivalency of
temperature is possible. This constitutive equation can predict creep over long periods of
time.
49
3.5 Summary
In previous studies, various properties of wood-plastic composite (WPC) products
have been investigated; and, many types of raw materials have been used in their
manufacture. Based on previous successful experiences, the mountain pine beetle
attacked wood may also be a potential raw material for WPC products.
To extend the application of WPC products, the viscoelastic properties,
particularly creep, should be carefully considered. Dynamic mechanical analysis (DMA)
is a powerful technique to study the response of material under different environmental
conditions, particularly temperatures and frequencies, and has been widely applied to
study the viscoelastic properties of a variety of polymer based composite materials.
Moreover, when DMA is accompanied with the time-temperature-stress superposition
principle (TTSSP), creep can be studied more efficiently by constructing a master curve
with short-term data at different temperatures/stresses. This method has also been
extensively applied in the field of material research.
However, since a temperature shift may interfere with a stress shift in creep, there
should be a predictive model that incorporates the relationship between these two shifts.
Furthermore, the master curves obtained in previous research investigations were rarely
validated with a full-scale long-term test; and, to date, the TTSSP and the master curve
have not successfully predicted creep deformation.
Power law models have been widely used in creep studies; however, they cannot
reflect the effect of temperature. Therefore, to extend the application of the power law
model, the effect of temperature needs to be introduced into the model.
50
These issues are studied in this work. The manufacture and mechanical properties
of a prototype mountain pine beetle attacked wood / plastic composite (MPB-WPC)
products are described in Chapters 4 and 5. The viscoelastic properties are covered in
Chapter 6; and, TTSSP and master curves, as well as shifter factors, are discussed in
Chapter 7. Chapter 7 also presents the development of a modified power law model that
introduces the effect of temperature and a modified WLF equation that incorporates the
effects of temperature and stress on the shift factor Furthermore, the validation of master
curves, and the comparison between shot-term and long-term creep data, and the
modelling of WPC products under fluctuating temperatures are studied in Chapter 8.
51
CHAPTER 4. EXPERIMENTAL DESIGN
To study the creep behavior of wood-plastic composite (WPC) products,
particularly the effect of temperature and stress, a series of experiments were conducted.
In addition, a new prototype of a WPC product using mountain pine beetle (MPB)
attacked lodgepole pine and high-density polyethylene (HDPE) was made and various
mechanical properties were tested.
This chapter describes the procedures of MPB-WPC product fabrication and the
experimental design and setups for various mechanical property tests, dynamic
mechanical behaviour analyses, and short- and long-term creep experiments. The results
obtained from the experiments are analyzed and discussed in further chapters.
4.1 Materials
4.1.1 Raw Materials
MPB-attacked lodgepole pine (Pinus contorta var. latifolia Engelm) lumber was
obtained from logs from the Vanderhoof area of British Columbia. The grade is #2 and
better, referring to NLGA standard. The lumber were chipped and refined into flours
using a hammermill (Bliss Industries SF 400HD), without specifically separating
sapwood and heartwood, which means the resultant flours are a mixture of sapwood and
heartwood of MPB-attacked lodgepole pine. A hammermill screen was selected to
provide a particle size distribution similar to commercial wood flour (Figure 4-1). Sixty
mesh pine flours (Pinus spp.), supplied by American Wood Fibers (AWF), were also
52
obtained for use as a reference. The wood flours were dried with a steam tube dryer to a
moisture content of approximately 2% before extrusion.
Figure 4-1. Particle size distribution of MPB wood and AWF pine flours
Specimens were produced with various formulations of wood content and
amounts of plastic by weight. Virgin HDPE (Equistar Petrothene® LB0100-00 with a
density of 950 kg/m3 and a melt index of 0.5 g/10 min) was selected as the plastic matrix
in this study. In addition, to improve the quality and processing capability of the products,
additives, maleated anhydride polypropylene (MAPP, Honeywell A-C® 950P) and a
lubricant (Honeywell OptiPak™ 100) were added in the formulations. The details of the
formulations, selected referring to the study of Slaughter [2004] for polypropylene-based
WPC deck products, are shown in Table 4-1.
53
Table 4-1. Formulations of MPB-WPC Products
Material Formulations (% by weight)
F1 F2 F3 F4 F5 F6
MPB Wood Flour 50.0 58.9 66.7 60.0 − 58.9
60 Mesh AWF Pine − − − − 58.9 −
HDPE 46.7 37.8 30.0 39.0 37.8 33.8
MAPP 2.3 2.3 2.3 0.0 2.3 2.3
Talc 0.0 0.0 0.0 0.0 0.0 4.0
Lubricant 1.0 1.0 1.0 1.0 1.0 1.0
Total 100.0 100.0 100.0 100.0 100.0 100.0
4.1.2 Product Processing
The constituents were dry mixed using a ribbon blender for 10 minutes and then
fed directly through a counter-rotating twin screw extruder (Cincinnati-Milacron TC86)
at a screw speed of 5 rpm, with the temperature profile shown in Table 4-2. MPB-WPC
solid deck boards were produced through a 25 x 140 mm solid profile die and then cooled
down in a water spray cooling system. The extrusion process of the products was
undertaken in the Composite Materials and Engineering Center (CMEC) at Washington
State University (WSU), Pullman, WA, U.S.
Figure 4-2. Extrusion processing
54
Table 4-2. Temperature Profile for the Extrusion Process
Temperature (°C)
Barrel Zone 1 171
2 171
3 171
4 171
Screw 171
Die Zone 1 177
2 177
3 177
4 193
4.2 Mechanical Property Tests
4.2.1 Experimental Design
A series of tests for the products’ properties were conducted, according to the
ASTM D7031 standard, particularly for the evaluation of mechanical and physical
properties of the WPC products and reference to the corresponding standards. The details
and assembly are summarized in Table 4-3 and shown in Figure 4-3. Before the tests
were conducted, the products were conditioned for at least 4 weeks in a constant climate
room with a temperature of 20±1°C and a relative humidity of 65±5%.
The density of the specimens was determined by ratio of the weight to the volume
of the specimen. The volume of the specimen was measured by the water immersion,
method of ASTM D2395 standard method B mode II. The MTS Sintech 30/D and MTS
810 test systems were used to conduct the tests at ambient conditions.
55
Table 4-3. Experimental Conditions for Mechanical Tests
Property ASTM
Sample Size Load
Speed
(mm/min)
Replicates Length
(mm)
Width
(mm)
Thickness
(mm)
Density D 2395* 50 50 22 — 10
Flexure D 4761 406 50 22 10 10
Compression D 4761 102 22 22 0.61 5
Hardness D 1037 150 75 22 6 10
Nail Withdrawal D 1037 150 75 22 1.5 5
Screw Withdrawal D 1037 100 75 22 15 5
* D 2395 was only referred to in order to measure the volume of specimen. The density was
determined by the weight/volume of the specimen.
Figure 4-3. The assembly for various mechanical tests: a) flexure, b) compression, c)
hardness, d) nail withdrawal, e) screw withdrawal
56
The fracture surfaces generated during the flexural tests were examined using an
optical microscope (Nikon Optiphot) and a scanning electron microscope (SEM) (Hitachi
S-3000N). The samples for SEM were sputtered with palladium-gold prior to being
observed in order to prevent charging.
4.2.2 Statistic Analysis
To discuss the effect of the formulations on the properties of the products, an
analysis of variance and multiple comparison and multiple regression analyses for various
properties were conducted.
Comparisons of the different formulations were examined with the analysis of
variance (ANOVA, α = 0.05) to test for significant effects; and, the Tukey test
(confidence level 95%) was conducted to test for significant differences between groups.
Three main explanatory variables, including wood content (WC), HDPE content
(PC) and coupling agent (CA), were examined. CA was deemed a qualitative variable,
since there were only two options in this study – with or without the coupling agent. The
interactions between the variables were also investigated. They were removed, if no
significant effect existed.
Since the true function is unknown, this study adopted the polynomial response
surface method, which is usually approximated by a second-order regression model. The
second-order response function with 4 variables was set up as:
( )
57
where Y = the property of interest
{
{
β0 = interception
β1, β2, β3 and β4 = coefficient for WC, PC, CA and TA, respectively
β12, β13, β14, β23, β24 and β34 = the interaction effect coefficients for interaction
between pairs of variables
εi = error.
4.3 Dynamic Mechanical Analysis
Prototypes of formulations F1-F4 were selected and machined as specimens to
conduct dynamic mechanical analyses (DMAs) with a 3-point bending clamp (Figure 4-
4). The commercial device, a TA Instrument Q 800 Dynamic Mechanical Analyzer
(DMA), was used to study the viscoelastic response of a specimen under constant loads in
creep tests and free resonant oscillatory loads in temperature ramp tests.
The rectangular sample, cut from extruded products, geometry measured
approximately 60 mm in length, 12 mm in width and 3 mm in thickness, and the span of
the test is 50 mm. In order to compare the differences between WPCs and neat HDPE,
and study the effect of the formulation on viscoelastic properties, similar HDPE
specimens were used as references for temperature ramp experiments, which were made
58
with a hot press at a temperature of 180°C. The specimens were conditioned for at least 4
weeks in a constant climate room with a temperature of 20±1°C and a relative humidity
of 65±5% prior to testing.
Figure 4-4. DMA 3-point bending clamp
4.3.1 Temperature Sweep
ASTM D 5023 and E 1640 were referred to in the measurement of the glass
transition region. The storage modulus (E’), loss modulus (E”) and the mechanical loss
factor (tan δ) were measured with a fixed frequency at 1 Hz, in accordance with the
standard. The temperature scan range was -50°C to +120°C, with a heating rate of
1°C/min. The controlled sinusoidal strain of 0.05% was selected for this work. The
specimen was equilibrated at -50°C for 5 minutes before starting the ramp. Five
specimens were tested for each formulation, and the average values of the properties were
utilized for the purpose of discussion.
59
The DMA spectra were assessed, in terms of the formulations, to describe the
behaviour of materials under various temperatures, and discuss the effect of the
formulation on the viscoelastic properties and transition behaviours.
4.3.2 Deflection Temperature Under Load
The deflection temperature under load (DTUL), heat distortion temperature (HDT)
or softening temperature usually denote the highest temperature at which a thermoplastic
polymer may be used as a rigid material. The test was conducted generally in accordance
with ASTM D648. The specimen was subjected to a constant flexural load of 0.455 MPa,
and heated at 2°C/min. The temperature at which a certain modulus, measured by a
deflection of 0.25 mm, is taken as the DTUL.
The DMA specimen was approximately 50 mm in length, 12 mm in width and 3
mm in thickness; however, the required dimensions of the ASTM standard specimen are
127 mm in length, 12 mm in thickness and any width from 3 mm to 13 mm. The
dimensions of the DMA specimens were small compared to the ASTM standard ones.
Transformation for the measured deflection from the DMA Q800 device was made in
order to fit ASTM requirements.
For the test to be valid under the ASTM conditions, this smaller DMA sample
must deform to the same strain induced in the sample at a load of 0.455 MPa as that in
the ASTM sample. Based on the dimensions of the ASTM specimen, 0.25 mm is
equivalent to a specific strain of 0.00121. The equivalent deflection of DMA specimens is
approximately 0.168 mm, which also results in a 0.00121 strain. Therefore, the
60
temperature at which the deflection of 0.168 mm under flexural load was measured was
taken as the DTUL.
4.3.3 The Short-Term Creep Test using DMA
In order to construct master curves for the prediction of long-term behaviours, a
series of 10-minute isothermal creep tests were conducted at various temperatures and
stresses, and the corresponding creep strains were measured. The range of selected
temperatures was from -45°C to +45°C with a 5°C increment. No load was applied
during temperature ramp, and the temperature-equilibrating time was 5 minutes for each
temperature. The schematic procedure is shown in Figure 4-5. Stresses of 1, 3, 5 and 8
MPa were selected for the tests. Three specimens were tested for each stress and
formulation. The mean would be calculated for further discussions.
Figure 4-5. Experimental scheme of the short-term creep test
61
During the tests, the strain of the specimen was recorded to construct the master
curve, and the shift factors were obtained for each temperature. Knauss (2008) indicated
that the environmental control equipment has variations due to the sensitivity of the
device and that the results of the shift factors may be influenced. However, it is
commonly assumed that the average temperature during the period of creep is sufficient
for this type of experiment; therefore, this issue was not considered in this study.
4.3.4 Master Curve Construction
The time-temperature-stress superposition principle was applied for analysis of
the results. The short-term creep test data was processed in the following steps:
1. Take a suitable temperature as the reference temperature and fix the
coordinates of the data curve at this reference temperature.
2. Take the reference temperature as the base and shift the other data curves of
all other temperatures horizontally along the log(t) axis to make one
overlapped smooth curve, using Rheology Advantage Data Analysis software
(TA Instrument)
3. Obtain the master curve by replacing the time, t, of each shifted curve by the
physical time, t’, at the reference temperature, Tr.
4. Investigate the relationship between the temperature and the shift quantity, aTr,
of each data curve while drawing the master curve, thereby calculating the
time-temperature shift factor of that material. The shift factors that were used
to construct the master curves were fitted with the Williams-Landel-Ferry
(WLF) equation, as shown in Equation 2-27:
62
( )
( ) ( )
where aT is the time shift factor, Tr is the reference temperature, and T is the temperature
(K) at which the shift factor is desired. The constants C1 and C2 are material-dependent
and are based on the slope and intercept of the plot of (T-Tr)/Log(aT) versus (T-Tr).
The same procedures were also applied when discussing the effect of stress levels.
The stress-adjusted WLF equation (Equation 2-30) was used to fit shift factors.
( )
( ) ( )
where C1 and C2 are the material-dependent constants, and σr is the reference stress.
In addition, the vertical shift may be adopted if needed, based on the following
relationship:
( ) (
) ( )
where g and aσ are the vertical and horizontal shift factors, respectively. Consequently,
the time-dependent mechanical properties of viscoelastic materials at different
temperatures and stresses can be shifted along the time scale to construct a master curve
of a wider time scale at a given temperature and stress.
63
4.4 Long-Term Creep Test
4.4.1 Experiment Setup
A full-scale, long-term creep test was conducted to validate the master curves
derived from the DMA short-term creep tests. Two formulations, which had the highest
and lowest modulus of elasticity (MOE) values, were selected; and, load levels of 20, 30
and 40% of the maximum flexure load (from the results of flexural tests) were adopted.
The generated stress was calculated based on Equation 4-3 and are summarized in Table
4-4, where P is the load; L is the length of the support span; Li is the length of the inner
span; and, b and d are the width and the depth of the specimen, respectively. There were
6 groups (2 formulations × 3 load levels) in this test; and, 10 specimens, each measured
approximately 406 ×50 × 22 mm3, were tested for each group.
( )
( )
Table 4-4. Loading Conditions for the Long-Term Creep Test
Load levels (%) F4 F6
Load (N) Stress (MPa) Load (N) Stress (MPa)
20 249 1.88 414 3.07
30 373 2.81 618 4.58
40 498 3.75 823 6.10
A bending fixture was used to carry out the measurements (as shown in Figures 4-
6 and 4-7). The deflection of the beams was measured using a linear variable differential
transducer (LVDT) mounted on an aluminum frame and placed at mid-span; and, a data
acquisition system was used to scan and record the deflection, in accordance with the set
64
frequency. Specimens were placed in an ambient environment, and climate conditions
were monitored, particularly the temperature. The period of the test was 220 days.
Figure 4-6. Loading configuration
Figure 4-7. Long-term creep test fixture and assembly
65
In order to make a comparison between the DMA results and those of the long-
term creep test, the deflection obtained from each experiment needed to be converted into
strain. The following section describes the procedures adopted to obtain the strain.
4.4.2 Stress-Strain Analysis
The deflection of a simply supported beam, δ, under concentrated loading, as
shown in Figure 4-8, can be calculated according to Equation 4-4:
[
( ) ( ) ] ( )
where E is the Young’s modulus, and I is the moment of inertia and is equal to (bd3/12), a
is the distance between the left end and the load, x is the distance from the left end and b
= (L-a).
Figure 4-8. Scheme of a simply supported beam under a concentrated load
In this long-term creep study, the WPC specimen was loaded under symmetric
four-point bending, as shown in Figure 4-9; therefore, the deflection can be calculated by
66
superposing two such loads acting simultaneously, as shown in Equation 4-5:
( ) ( )
[
( )( ) ( ( ) ) ]
[
( ( )) ( ) ] ( )
Figure 4-9. Scheme of a simply supported beam under symmetric 4-point bending
The deflection at the mid-point of total span, x = L/2, can be calculated as:
( )
( )
Young’s Modulus can be obtained by rearranging Equation 4-7:
( )
( )
Strain, ε, can be calculated as:
( )
67
Therefore, using Equations 4-3 and 4-7 the strain of the midpoint can be obtained as:
( )
( ) ( )
4.4.3 Corresponding Short-Term Creep Test and the Master Curve
In order to make comparison between long-term creep results and master curves,
10-minute creep tests were conducted using DMA device to generate corresponding
master curves for the 6 groups (2 formulations × 3 load levels, as with the long-term test),
according to the procedure described in Sections 4.3.3 and 4.3.4.
The temperature range was set from 15°C to 70°C with a 5°C increment, and
three specimens were tested for each group. The applied stresses were the same as those
applied in the long-term creep tests (as Table 4-4), and the mid-span strain was recorded
for comparison with the long-term data and for further discussion.
4.5 Summary
The research goals of this study are the development of a new prototype wood-
plastic composite for value-added products for mountain pine beetle attacked wood and
the study of the critical issues that affect the long-term performance of the product.
Series of experiments were conducted in this study, including product
development, mechanical properties evaluation, dynamic mechanical analysis, short-term
creep tests of small specimens and full-scale long-term creep tests.
68
The new MPB-WPC products were manufactured, and various mechanical
properties were tested and discussed based on different formulations and the effect of
components. The dynamic mechanical analysis technique was adopted to study the
viscoelastic properties and perform the short-term creep tests under various temperatures
and stresses. Master curves for the prediction of long-term performance were constructed
based on the time-temperature-stress superposition principle, and comparison of these
master curves was made along with results from long-term test, in order to validate the
application of those master curves.
69
CHAPTER 5. MPB-WPC PRODUCTS
Mountain pine beetle (MPB) attacked lodgepole pine was used to produce wood-
plastic composite (WPC) products, in order to evaluate feasibility and the product
properties. This chapter discusses the properties of the MPB-WPC products and the effect
of formulations on the properties and behaviours through observation and statistical
analysis. These properties also become the references for the subsequent studies on creep
in Chapter 7 and 8.
5.1 Products
The appearance of MPB-WPC products are affected by their formulation. Jam and
Behravesh [2007; 2009] mentioned that a high content of wood may cause some
processing difficulties, owing to the uneven dispersion of wood flours and the low flow
mobility of the composites. In addition, the slip resistance between wood flours may
increase within the melt; thus, when there is an increase in the wood filler percentage, the
shear viscosity of the melt rises as well [Chastagner and Wolcott 2005]. Kumari et al.
[2007] also mentioned that the incorporation of rigid material to polymeric matrices
limits the free mobility and increases the apparent viscosity.
In this study, however, products with lower wood content (formulations F1 and
F2 in Table 4-1) and maleated anhydride polypropylene/polyethylene (MAPP) as the
coupling agent produced edge tearing and mat surfaces (i.e. sharkskin, as shown in Figure
5.1-a), which are caused by the stick-slip phenomenon; whereas, a higher wood content
formulation with MAPP (F3) and without MAPP (F4) (as shown in Figure 5.1-b) resulted
in a glossy surface.
70
Wood flour may deposit on the wall and die surfaces and allow for continuous
slip for the molten WPC mixture; thus, the appearance of sharkskin was decreased in F3
and F4. Li and Wolcott [2004] also mentioned that the addition of wood flours increases
the contribution of wall slip. Partial replacement of wood flour with talc or the addition of
talc to the WPC (as in F6) can decrease the melt viscosity of the WPCs and act as
lubricant to increase the volumetric output through the die [Klyosov 2007], as well
resulting in a smooth and glossy surface.
Other solutions to improve the surface quality may include the addition of a
lubricant, an additive or a processing aid, adjustment of the temperature profile for the die
lips, and modification of the die exit [Vlachopoulos and Strutt 2003].
Figure 5-1. MPB-WPC product surfaces. a: mat surface (sharkskin); b: glossy surface
71
5.2 Properties
5.2.1 Density
The densities of the MBP-WPC products were measured and are summarized in
Table 5-1. If the effect of the lubricant is neglected, a higher wood content resulted in a
slightly higher density. The density of MAPP is 930 kg/m3, close to the 950 kg/m
3 of
high-density polyethylene (HDPE); therefore, MAPP makes approximately the same
contribution as HDPE when product density is considered.
With a greater content of wood flour content, voids may develop, since they are
principally created from the cell lumens of wood and the voids between wood flours that
were not compressed or filled during processing, as well as free space in the polymeric
matrix. However, because the density of wood cell wall substance is approximately 1,500
kg/m3, which is higher than HDPE, assuming the wood structure was completely
compressed or if the polymer filled the lumen and voids in the wood flours during
processing, it is reasonable that the densities of the products became higher with
increasing wood content. In addition, the density of talc is about 2700-2900 kg/m3, much
higher than other components; thus, the F6 product has the highest density value.
5.2.2 Mechanical Properties
Table 5-1 also shows the results of mechanical tests. In general comparison with
the commonly used pine flours, there was no considerable difference between the MPB-
WPC products (F2) and the American Wood Fibers / WPC (AWF-WPC) products (F5)
72
on the basis of the same formulation. This implies that even beetle-infected wood can be
a good raw material for WPCs.
Furthermore, the low coefficients of variation imply that the properties of the
WPC products are consistent. In addition, it is noted that F6 (i.e. the formulation with talc)
turned out a higher modulus of elasticity (MOE) mean value than other groups.
Theoretically, the talc is chemically inert; however, as a filler, talc can improve the
stiffness and strength considerably, particularly stiffness (Klyosov 2007).
The WPC groups with the highest and the lowest MOE values, F6 and F4,
respectively, are selected for long-term creep test in subsequent studies Chapter 8.
Table 5- 1 Properties of MPB-WPC Products
Properties Formulations
F1 F2 F3 F4 F5 F6
Density(kg/m3) 1110
(0.56)
1153
(0.41)
1184
(0.59)
1163
(0.78)
1167
(0.47)
1218
(0.18)
MOE (GPa) 3.91
(3.14)
4.28
(6.60)
5.08
(7.38)
3.39
(15.27)
4.54
(4.01)
6.29
(7.54)
MOR (MPa) 38.26
(4.39)
34.25
(3.06)
30.49
(8.80)
21.89
(6.32)
33.91
(1.33)
35.60
(4.07)
Compression (MPa) 30.82
(3.75)
28.62
(2.38)
27.40
(5.54)
19.41
(1.12)
28.76
(3.29)
28.74
(5.91)
Hardness (kN) 12.55
(1.02)
11.98
(1.75)
10.17
(3.81)
9.57
(2.74)
10.92
(3.69)
10.82
(4.37)
Nail Withdrawal (N) 548.72
(14.20)
542.13
(9.70)
485.06
(7.82)
376.27
(7.06)
485.98
(9.19)
486.89
(7.89)
Screw Withdrawal (N) 3656
(4.04)
3474
(4.32)
3271
(3.83)
2413
(3.84)
3443
(6.80)
3511
(5.42)
Numbers in parentheses are the coefficients of variation (%)
MOE – Modulus of elasticity, based on least square fit over a range of 10–30% of the peak load.
MOR – Modulus of rupture, based on the maximum load
73
5.2.3 Characteristic Load-Deformation Behaviours
Figure 5-2 shows the characteristic load-deformation curves of the WPC products
based on the mechanical tests. Since WPCs are polymer-based materials, all the products
showed a nonlinear load-displacement response and a more or less plastic deformation
during the tests; and, they sustained large elongation before fracture. The mechanical
properties of the uncoupled product (F4) were apparently inferior to the coupled products,
resulting in a lower yielding strength and lower stiffness. It is supposed that poor
interfacial adhesion between the wood and the HDPE may provide a weak area for crack
propagation, thus producing properties with less strength.
The deformation mechanism in heterogeneous polymer-fibre composites is
characterized by fibre pullout, debonding and cavitation of the matrix. Almost all
elongation occurs in the matrix of the composite if the filler is rigid [Hetzer et al. 2009].
The coupling agent may build the interfacial adhesion to improve the properties.
Furthermore, a greater wood content showed relatively less ductile behaviour and failure
at a smaller deformation. The products with a higher HDPE content showed better
strength in all aspects; however, relatively lower stiffness and larger deformation
appeared as well.
Oksman and Clemons [1998] also reported that the addition of a coupling agent in
the WPC formulations decreased the elongation at break. Consequently, depending on
specific formulations, WPCs can show very different responses. An important task when
formulating WPCs products is the consideration of the behaviour of the end product, so
that the formulation matches the application.
74
Figure 5-2. Typical load-deflection/displacement curves from various mechanical tests
75
Figure 5-3(cont). Typical load-deflection/displacement curves from various mechanical
tests
76
5.2.4 Failure Mode
Typical failure modes after various mechanical tests are shown in Figure 5-3. In
the flexure test, brittle failures at the tension side were observed for all the formulations
(Figure 5-3a). A sudden complete split took place as soon as the product failed for all the
coupled groups; whereas, F4, which is the uncoupled group of products still remained
attached, even with a crack at the tension side.
For compression failure, the wedge splitting was identified by the Y shape of the
failure line (Figure 5-3b) for all the groups. However, the hardness test caused two
different types of residual appearances (Figure 5-3c). F1, F2 and F4 resulted in type 1,
which has a smooth apprearance, whereas, F3, F5 and F6 resulted in type 2, which has
splinters The difference may be attributed to formulations with higher wood content and a
coupling agent, which constrain the movement of the internal structure of the product to
reform the shape and remain intact under loading; therefore, splinters as type 2 were
found surrounding the penetration.
In addition, both the nail-penetration-through and screw-withdrawal tests led to
splinters (Figures 5-3d and 5-3e, respectively): these results were different from other
conventional wood composites. Moreover, the screw was still gripped by the WPCs after
withdrawal (Figure 5-3f), which implies that the screw-withdrawal failure occurred
within material instead of the interface between the screw and the material.
77
Figure 5-4. Typical failure of MPB-WPCS after mechanical tests
5.2.5 Microscopic Observations
The failure surface of the product caused by the flexural test was observed with an
optical microscope and a scanning electron microscope. The interfacial properties of
wood-HDPE were investigated. Ideally, wood flours are completely encapsulated in the
matrix to form the product (Figure 5-4); however, it was clearly observed that the
bonding between the wood and the HDPE was not strong. If no coupling agent was added,
the wood was pulled out during mechanical tests, which confirms the poor interfacial
adhesion between the wood and the HDPE.
78
The surface of wood appeared as shown in Figure 5-5, and hollow areas could be
observed as illustrated in Figure 5-6. However, if a coupling agent was added, the ductile
failure happened to the HDPE and the wood was still well encapsulated (Figure 5-7),
which is evidence of improved adhesion between the wood and the HDPE.
Figure 5-5. Wood encapsulated by HDPE
Figure 5-6. Failure surface – wood not enscapsulated by HDPE
79
Figure 5-7. Failure surface of F4, wood was pulled out due to weak bonding between
wood and HDPE
Figure 5-8. Failure surface of F1, wood covered by HDPE and ductile failure of HDPE
was observed
80
5.3 Statistical Analysis
5.3.1 ANOVA
According to the analysis of variance (ANOVA), the formulation of the WPCs
significantly influenced the products’ properties (Table 5-2). The results of the
mechanical tests yielded a general trend that higher wood content has lower strength, but
a higher modulus. The same improvement in the modulus with increasing wood content
was also observed in other studies [Stark and Berger 1997; Selke and Wichman 2004;
Lee et al. 2008]. Moreover, Crespo et al. [2009] mentioned that, when the filler was
increased, the increase in stiffness in the composite material of PVC/sawdust particles
could also be transformed into an increase in hardness.
Table 5-2. Results of ANOVA for the Effect of Formulations on Product Properties
Properties ANOVA Tukey Test
F-value P-value F1 F2 F3 F4 F5 F6
Density 327.00 <0.01** a b c d d e
MOE 80.84 <0.01** a ab c d b e
MOR 128.75 <0.01** a b c d b b
Compression 81.36 <0.01** a b b c b b
Hardness 110.91 <0.01** a b c d e e
Nail Withdrawal 7.98 <0.01** a a a b a a
Screw Withdrawal 37.94 <0.01** a ab b c ab ab
** indicates significant effect
For each property, the same letter means no significant difference between groups.
81
There was no statistically significant difference between F2 and F5, except for
density and hardness. That also indicated that MPB wood can be a good raw material for
WPCs. In addition, the nail-withdrawal property was relatively unaffected by the
different formulations. The critical factor that affected the fastener properties was the
existence of the coupling agent. Falk et al. [2001] also indicated a similar result and
pointed out that the screw-withdrawal capacity of WPC panels was equal to or greater
than that of conventional wood panel products.
In summary, the determinative component is the usage of a coupling agent, with
which WPCs products’ properties can be significantly improved.
5.3.2 Regression
The results of the response function analysis are summarized in Table 5-3. The
interaction and quadratic effects were eliminated if they were found to be highly
correlated with the explanatory variables (i.e. wood content, HDPE content, coupling
agent and talc). The low P-values provide evidence of the existence of regression
relationships between the properties and the formulations. Generally, there was a strong
relationship between the formulation and each property, except nail withdrawal. This
observation agrees with Falk et al. [2001] who found that nail withdrawal was relatively
unaffected by formulation.
According to Table 5-3, for flexural MOE, MOR and hardness, the equations
showed curvilinear responses; and, the quadratic effect of the wood content (WC) may
82
have influenced the final properties. The interaction effect between the WC and the
HDPE content (PC) influenced compression and nail and screw withdrawal.
It should be noted that the estimate of the coefficient for some variables was not
significant (P > α = 0.05) in the presence of the other variables in the equation, i.e. the
interaction between the WC and the PC and the quadratic effect of the WC may appear,
although it is insignificant in the presence of the other 2 variables. Consequently, in
general, the combination and adjustment of wood flour and plastic contents relatively
affect the final properties but not always significant.
Moreover, eliminating the insignificant parameters, the parsimonious results were
summarized in Table 5-4. According to the reduced models, the final properties are
generally governed by the content of each component but not interaction between
components; however, those may also be affected by quadratic effect of the WC for
hardness and screw-withdrawal.
In the study of Zhang et al. [2008], the response surface strategy was adopted to
investigate the effect of the coupling agent content (0-3%), wood fibre content (0-40%)
and wood types on tensile strength, MOE and strain at break. In this study, more wood
content was used, and the matrix content was also taken into consideration. However, the
effect of the coupling agent from various percentages was not studied here (i.e. just with
or without 2.3% MAPP). Thus, different trends were found. Nevertheless, both studies’
results indicate the effect of the formulation on the WPC products’ properties.
83
5.3.3 Characteristic Strength
After estimating the ultimate strength of a group of test specimens, the flexural
strengths of products were fitted with normal, log-normal and 2-parameter Weibull
distribution models. The corresponding parameters and values of the fifth percentile
strength are summarized in Table 5-5. In general, this fifth percentile strength value was
close to the mean value, within differences of approximately 5-15%.
Moreover, the normal distribution model fit well for F1, F2 and F5; whereas, the
2-parameter Weibull model fit better for F3, F4 and F6. It is uncertain if the formulation
influenced the distribution of properties, since the sample size was small. More tests are
required for verification. Nevertheless, this probability fitting implies that the properties
of WPCs are generally uniform and easy to control when developing and using products.
84
Table 5-3. Results of Regression Analysis
Properties Regression Equation SEE* R
2 R
2-adj P
Parameter
Estimate
p-
parameter
Estimate
MOE (MPa) = 61668– 865x1 – 504x2 – 190x3+3.69 x12 381.70 0.887 0.877 <0.01 β1 <0.01
β2 <0.01
β3 0.419
β11 0.091
MOR (MPa) = 76.9– 0.58x1 – 0.34x2 + 11.1x3 – 0.0019x12 1.74 0.922 0.915 <0.01 β1 0.644
β2 0.089
β3 <0.01
β11 0.847
Compression (MPa) = 53.4– 0.87x1 – 0.03x2 + 8.93x3 + 0.0054x12 1.19 0.933 0.919 <0.01 β1 0.483
β2 0.871
β3 <0.01
β11 0.570
Hardness (N) = -44928+ 1324 x1+ 291x2+ 2899x3– 10.1x12 317.19 0.931 0.925 <0.01 β1 <0.01
β2 <0.01
β3 <0.01
β11 <0.01
Nail Withdrawal (N) = -2763+ 74.3x1+ 15.5 x2 + 203x3– 0.533 x12 49.76 0.659 0.590 <0.01 β1 0.159
β2 0.063
β3 <0.01
β11 0.190
Screw Withdrawal (N) = 3608+ 6.0x1– 9.4x2 + 1013x3– 0.33x12 144.85 0.921 0.906 <0.01 β1 0.968
β2 0.685
β3 <0.01
β11 0.776
*Standard error of the estimate, in the same units as each property.
85
Table 5-4. Parsimonious Results of Regression Analysis
Properties Regression Equation SEE* R
2 R
2-adj P
Parameter
Estimate
p-
parameter
Estimate
MOE (MPa) = 45875– 401.80x1 – 470.36x2 386.30 0.879 0.874 <0.01 β1 <0.01
β2 <0.01
MOR (MPa) = 85.38– 0.82x1 – 0.36x2 + 10.94x3 1.72 0.922 0.917 <0.01 β1 <0.01
β2 0.027
β3 <0.01
Compression (MPa) = 31.76– 0.21x1 + 9.20x3 1.14 0.931 0.925 <0.01 β1 <0.01
β3 <0.01
Hardness (N) = -44928+ 1323.60 x1+ 290.94x2+ 2898.60x3– 10.07x12 317.19 0.931 0.925 <0.01 β1 <0.01
β2 <0.01
β3 <0.01
β11 <0.01
Nail Withdrawal (N) = 226.95+ 3.83 x2 + 146.8x3 50.46 0.614 0.579 <0.01 β2 0.047
β3 <0.01
Screw Withdrawal (N) = 3125+ 1039.54x3– 0.20x12 139.34 0.920 0.913 <0.01 β3 <0.01
β11 <0.01
*Standard error of the estimate, in the same units as each property
86
Table 5-5. Statistical Model Parameters for Flexural MOR of MPB-WPCs
Distribution Mean
(MPa)
Std.
Dev.
(MPa)
Weibull
Scale
Weibull
Shape Error
5th
percentile
Value
(MPa)
F1 Normal 38.26 1.81 — — 0.0004 35.34
Log-normal 38.27 1.81 — — 0.0004 35.41
2-p Weibull 38.19 1.83 39.00 26.06 0.0008 34.76
F2 Normal 34.25 1.13 — — 0.0003 32.40
Log-normal 34.25 1.13 — — 0.0003 32.49
2-p Weibull 34.20 1.16 34.71 37.23 0.0004 32.08
F3 Normal 30.39 2.63 — — 0.0161 26.12
Log-normal 30.42 2.62 — — 0.0168 26.35
2-p Weibull 30.32 2.67 31.47 13.90 0.0156 25.50
F4 Normal 21.87 1.43 — — 0.0052 19.55
Log-normal 21.87 1.41 — — 0.0057 19.67
2-p Weibull 21.82 1.48 22.47 18.23 0.0038 19.14
F5 Normal 33.91 0.43 — — 0.0001 33.20
Log-normal 33.91 0.43 — — 0.0001 33.20
2-p Weibull 33.89 0.24 34.11 87.95 0.0002 32.96
F6 Normal 35.60 1.56 — — 0.0010 33.06
Log-normal 35.60 1.55 — — 0.0011 33.15
2-p Weibull 35.54 1.62 36.26 27.45 0.0005 32.57
5.4 Summary
MPB-WPC products were manufactured with various formulations, and their
mechanical properties were evaluated and analyzed. The MPB-WPC products showed no
significant difference from WPC products that were made with healthy pine. This
indicates that WPCs are a great option for value-added products of MPB-killed wood,
since the fine processing residues can be utilized and drying costs would be lower due to
the low moisture content of MPB wood.
87
The test results showed that formulation affected the MPB-WPC products’
properties. A higher wood content resulted in a slightly higher density, lower strength,
but a higher modulus. The quadratic effect of the wood content influenced the flexural
MOE, MOR and hardness, while the interaction between the wood and the HDPE
impacted compression and nail and screw withdrawal. The capacity of the uncoupled
product was significantly inferior to the coupled products; therefore, properties can be
significantly improved when a coupling agent is added. The surface condition of the
product was also influenced by the formulation.
Depending on the formulation, WPCs can show very different behaviours and
appearances. Considering the formulation based on the use of final products is an
important task. Moreover, due to uniform quality, the fifth percentile strength values of
WPCs were close to the mean values, with differences of approximately 5-15%.
88
CHAPTER 6. VISCOELASTIC PROPERTIES OF WPCs
Currently, wood-plastic composite (WPC) products are widely used for outdoor
applications; and, good durability performance has been claimed and supported by many
research studies. It is well known that temperature can have adverse effects on the
performance of WPCs; however, detailed studies on the effect of temperature on the
creep performance of WPCs have rarely been considered. Due to their viscoelastic nature,
the effect of temperature is vital in the application of WPCs. In order to understand the
influence of temperature on the mechanical properties of WPCs, the performance of the
material at various temperatures needs to be studied.
This chapter describes the viscoelastic properties and the influence of the WPC
formulations, based on the spectra of dynamic mechanical analysis (DMA), as a function
of temperature. The deflection temperature under load of WPCs is also discussed.
In order to avoid the influence of the additive talc, only F1 to F4 and neat high-
density polyethylene (HDPE) were considered in this study. In general, the presence of
fillers/fibres in the polymer modify the relaxation processes and produce a more complex
morphology of the composite system. The content of filler/fibres and the use of a
coupling agent can change the morphology of the bulk polymer phase and the interphase.
Thus, the mechanical and viscoelastic properties of the composites are affected.
6.1 The Dynamic Mechanical Analysis Spectra
Typically polymer is in a glassy state before the transition starts, and the modulus
slightly decreases with increasing temperature. However, after a rapid decrease in the
89
storage modulus and an increase in the loss modulus are then observed, corresponding to
the glass-rubber transition of the amorphous domains.
The representative results of DMA of mountain pine beetle (MPB) WPCs are
shown as Figures 6-1 to 6-3, which present the storage modulus, loss modulus and
mechanical loss factor, respectively; and, the dependence of the dynamic mechanical
properties on temperature can be perceived. Typically, the temperature influenced the
polymer behaviour in two ways [Deng and Uhrich 2010]:
1. As the temperature rose, more free volume was generated within the polymer;
thus, it took less time for the polymer chains to relax and thereby respond
quickly to the external load.
2. Higher temperatures softened the polymeric materials and resulted in
decreasing stiffness.
For a semi-crystalline polymer, such as HDPE, usually three relaxation processes
can be found with a decreasing temperature from the crystalline melting point, namely α-,
β- and γ-relaxations from the highest temperature. The α-relaxation is related to the
crystalline fraction; the β-relaxation is related to the amorphous phase and usually
represents the glass transition; and, the γ-relaxation is associated with short-range
motions in the amorphous phase.
For a highly crystalline polymer, the α-transition is the major relaxation below the
melting point [Tajvidi et al. 2003]; and, the glass transition in a highly crystalline
polymer is difficult to identify. Sirotkin et al. [2001] reported that, for HDPE, the β-
90
relaxation is usually absent. The β-relaxation is, therefore, generally attributed to
segmental motions in the non-crystalline phase.
According to Figures 6-1 to 6-3, with an increase in temperature, the storage
modulus (E’) decreased with the elevating temperature, and the loss modulus (E”)
increased up to a certain level and then decreased. However, the mechanical loss factor
(tan δ) increased, indicating an increase in the trend in the viscoelastic response of the
polymer at high temperatures. In addition, there was only an α-transition observed within
the scanned temperature interval.
The MPB-WPC formulations influenced the dynamic mechanical properties,
which were greatly affected by the wood flour content and the presence of a coupling
agent, maleated anhydride polypropylene/polyethylene (MAPP). With MAPP, the
anhydride groups of MAPP reacted chemically with the hydroxyl groups of the wood
flours to form ester bonds (covalent bonds), and the tail of the MAPP entangled with
HDPE, improving the interfacial adhesion between hydrophilic wood and hydrophobic
HDPE.
Figure 6-1. Storage modulus of MPB-WPCs and HDPE
91
In Figure 6-1, the storage moduli as a function of temperature among the various
MPB-WPC formulations and neat HDPE are compared; and, the neat HDPE shows a
considerably lower E’ in all temperature domains. The storage moduli of the WPCs
increased with a higher content of wood flour, indicating enhanced stiffness.
Furthermore, the result that the E’ of F4 was significantly lower than the other
formulations, indicating that the presence of MAPP improved the stiffness and enhances
the interaction between HDPE and wood flours. This is mainly attributable to the
reinforcing effect imparted by the combination of the wood compound / MAPP entangle /
HDPE, which allows for a greater degree of stress transfer from the HDPE to the wood.
In this case, above the onset point of the relaxation transition, no well-developed rubbery
plateau appeared in the course of E’ versus temperature. The decline of E’ associated
with temperature showed different degrees for different formulations.
Figure 6-2. Loss modulus of MPB-WPCs and HDPE
92
Figure 6-2, in which only one peak can be observed within the scanned
temperature range, reveals that the temperature at the peak value of E”, commonly
regarded as the α-transition, associated with the molecular motions of the unrestricted
amorphous polymer chains, shifted towards a higher temperature with the coupling agent
and additional wood flour content.
Since the phase transition is related to the relaxation of amorphous HDPE chains,
this shift indicates that the mobility of HDPE chains decreased with the addition of
MAPP and higher wood flour content. This may be attributed to the restricted motions of
the amorphous HDPE molecule chains at the wood / MAPP / HDPE interface, which is
caused by the covalent interaction between the MAPP and the wood and the
entanglement between the tail of the MAPP and the HDPE. This is an indication that the
formulation changed the morphology of the composite.
Samal et al. [2009] mentioned that the mobility of the macromolecular chains
located in the fibre surface interface is reduced with an increase in the fibre/matrix
interaction, resulting in a shift in the α-transition temperature towards a higher
temperature range. Santos et al. [2009] suggested that the E” increases in filled polymer,
indicating that the fibres turn the dissipation of energy easier, which is probably related to
the increased internal friction between the molecules of polymer and the filled particles.
Jam and Behravesh [2007; 2009] also mentioned that a high content of wood may cause a
low flow mobility of the composites.
In a composite system, tan δ is affected by the incorporation of fibres, due to the
elastic nature of fibres and the shear stress concentrations at the fibre ends, in association
93
with the additional viscoelastic energy dissipation in the matrix material [Samal et al.
2009]. According to Figure 6-3, there are no apparent peaks of tan δ for each formulation,
indicating that the β-transition is not the major relaxation process in neat HDPE or its
composites [Tajvidi et al. 2003].
Chartoff et al. [1994] mentioned that particulate fillers broaden the tan δ peak and
the peak position shifts to a higher temperature. Moreover, the strong adhesion created by
the coupling agent may cause the tan δ peak to narrow and the peak temperature to
decrease. However, this phenomenon was not clearly observed in this study.
Figure 6-3. Tan δ of MPB-WPCs and HDPE
Tan δ changed slowly at temperatures approximately below 15°C; however, it
increased rapidly above 15°C. Moreover, the curves started to deviate into two groups:
one contained F1-F3 and the other consisted of F4 and neat HDPE, which also
represented the coupled (with MAPP) and uncoupled (without MAPP) systems,
94
respectively. Referring to Figures 6-1 and 6-2, the onset of decreasing E’ and increasing
E” started at around the same point.
Since tan δ is equal to E”/E’, the fact that tan δ of F4 and HDPE are remarkably
higher than those of F1-F3 reflects that the addition of MAPP and a higher content of
wood flour changes the mobility of molecular chains at the wood/HDPE interface, as
mentioned above. Higher tan δ values indicate greater degree of molecular mobility. The
difference became even more pronounced at higher temperatures. Furthermore, based on
the lower value of tan δ, better interface adhesion was observed in the formulations that
contained MAPP. A higher tan δ value corresponds to higher impact strength, toughness
and energy dissipation.
When a flexural modulus is measured by traditional methods, it is actually the
complex modulus (E*) of the material, which is a hybrid of both E’ and E” and can be
defined as the slope of the stress-strain curve within the linear region. The DMA resolves
E* into two components. Theoretically, if the phase angle is small, the E’ should be very
close to E*. The tangent of the phase angle (tan δ) is rarely above 0.1 for a solid state
until the material approaches the softening point [Sepe 1998]. In this study, the point at
which tan δ = 0.1 was approximately 43°C for F1 to F3, and 28°C for F4 and HDPE.
The glass transition temperature, at which a material changes from a hard,
glasslike material to a softer, rubberlike material, can be determined from E’, E” or tan δ
curves. However, they may not necessarily give similar values. In this case, the peak of E”
appeared at a higher temperature than the onset point of the decline of E’ did.
95
High-density polyethylene is a type of semi-crystalline polymer with no specific
β-transition (glass transition) temperature; nevertheless, the movement of the amorphous
part, which is associated with the movement of small groups and chains of molecules in
the polymer structure, all of which are initially frozen, still causes a reduction of stiffness.
The transition of the material may be discussed in terms of several transition
points. For E’, the transition points can be taken as the extrapolated onset and endpoint to
the sigmoidal change by constructing tangent lines. The two intersects of three tangent
lines were marked as “onset” and “end”, and the inflection point of the sigmoidal change
was marked as “middle” (as Figure 6-4). For E’, the transition point can be recognized
when peaks were observed.
Figure 6-4. Scheme of transition
The onset of a declining E’ implies that the amorphous parts started to move with
elevated temperature; whereas, a rise of E” indicates an increase in the structural mobility
of the polymer. These circumstances may be explained by Table 6-1; the temperature at
96
which the peak of E” appeared was close to the temperature at which the end point of
relaxation for E’ was pointed
Table 6-1. Transition Indices as marked in Figure 6-4
Formulation Onset (°C) Middle (°C) End (°C) E” Peak (°C)
F1 10.1 (0.99) 20.6 (1.69) 54.0 (1.01) 51.3 (0.72)
F2 13.8 (0.84) 21.1 (0.72) 50.0 (2.89) 51.5 (0.95)
F3 11.0 (1.22) 21.1 (1.13) 54.7 (1.88) 50.4 (1.35)
F4 11.6 (1.00) 21.2 (1.16) 47.8 (3.53) 44.4 (5.22)
HDPE 12.1 (1.81) 20.0 (2.22) 50.5 (1.64) 42.8 (0.61)
Number in parentheses is the standard deviation.
The DMA spectrum of MPB lodgepole pine solid wood was also investigated as a
reference (Figure 6-5). As to E’, no major transition was detected; whereas, clear peaks of
E” and tan δ appeared at around 50°C. This may explain why the peak of E” for the
wood-HDPE composites was located at higher temperature (approximately 50°C) than
that of neat HDPE (42°C). However, it only works when coupling agent is involved.
Since the adhesion between wood and HDPE can be improved with the coupling agent
[Lu et al. 2000; Selke and Wichman 2004; Chowdhury and Wolcott 2007], the behaviour
can be accounted for with a composite instead of two individual components. This point
can be confirmed with the result of F4: without a coupling agent, the temperature at
which the peak of E” appeared was not significantly different from neat HDPE.
97
Figure 6-5. DMA spectra of MPB solid wood
From the viewpoint of mechanical properties and product applications, the change
of E’ with temperature is very important, because E’ directly refers to the stiffness of the
material. Chen and Gardner [2008] also suggest that the glass transition temperature (Tg)
should be determined from E’ for the same reason.
The resistance of WPC products to temperature can be evaluated based on the
storage modulus retention, as shown in Figure 6-6. The E’ at the initial point of the
scanned temperature range was set as 100%. It can clearly be seen that the retention
dramatically decreased with increasing temperature. The mobility of HDPE molecule
chains may be restrained by the presence of wood flours and the coupling agent. The
MAPP coupled products (F1-F3) had better retention, indicating better temperature
resistance than did the uncoupled products (F4). Moreover, the addition of flour also
improved the temperature resistance.
98
Figure 6-6. Storage modulus retention
As previously mentioned, the storage modulus should be very close to the
complex modulus when material is still in its solid state, as well as when tan δ < 0.1.
Moreover, the DMA complex modulus is supposed to be the same as the value from the
traditional method. The modulus of elasticity (MOE) obtained from the flexural test
(Chapter 5), which was conducted at the ambient temperature of approximately 25°C, and
the results of the DMA E* and E’ at various temperatures are summarized in Table 6-2.
Within the common room temperature range of 20-40°C, DMA E* and E’ were
almost the same, since tan δ was still below 0.1, except for F4 where tan δ= 0.1 was at
approximately 28°C. However, the flexural MOE obtained at around 25°C was lower
than the DMA results at the same temperature, but fell between 30 and 35°C for F1 and
F3, 35 and 40°C for F2 and 25 and 30°C for F4. This implied that the DMA may
overestimate the modulus compared to the traditional method.
99
Furthermore, loading frequency may also influence the results since the modulus
of material increase with loading frequency. When applying modulus values obtained by
DMA, this difference should be taken into consideration as the difference between
dynamic loading and static loading may also contribute to this discrepancy.
In addition, for the DMA test, the specimen was isothermally controlled; whereas,
the specimen in the traditional method was conditioned and tested in an ambient
environment. The results of the traditional flexural MOE may not be able to reflect the
real performance of the material at specific temperatures.
Table 6-2. Comparison of DMA Complex Modulus, Storage Modulus and Traditional
Flexural Modulus
F1 F2 F3 F4
T
(°C)
E* E’ MOE E* E’ MOE E* E’ MOE E* E’ MOE
(GPa) (GPa) (GPa) (GPa)
20 4.70
(0.64)
4.70
(0.64) —
5.34
(0.93)
5.34
(0.93) —
6.08
(0.23)
6.07
(0.23) —
3.99
(0.41)
3.98
(0.41) —
25 4.38
(0.61)
4.37
(0.61)
3.91
(0.12)
4.95
(0.87)
4.94
(0.87)
4.28
(0.28)
5.67
(0.26)
5.66
(0.25)
5.08
(0.37)
3.56
(0.36)
3.54
(0.36)
3.39
(0.52)
30 4.12
(0.58)
4.11
(0.58) —
4.67
(0.84)
4.65
(0.84) —
5.34
(0.24)
5.33
(0.24) —
3.24
(0.38)
3.22
(0.37) —
35 3.84
(0.56)
3.83
(0.55) —
4.36
(0.80)
4.34
(0.80) —
4.98
(0.23)
4.96
(0.23) —
2.90
(0.29)
2.87
(0.29) —
40 3.56
(0.53)
3.54
(0.52) —
4.06
(0.74)
4.04
(0.74) —
4.62
(0.22)
4.60
(0.22) —
2.62
(0.24)
2.59
(0.23) —
45 3.28
(0.49)
3.26
(0.49) —
3.75
(0.69)
3.73
(0.69) —
4.27
(0.20)
4.24
(0.20) —
2.36
(0.21)
2.33
(0.20) —
Numbers in parentheses are the standard deviation
Number of specimens for DMA test is 5 and for traditional flexural test is 10.
100
6.2 The Effect of Formulation on Transition
The effect of the formulation on the relaxation transition of WPCs can be
discussed according to the several pointers marked in Figure 6-4. Based on the average
value of 5 specimens for each formulation, the relation transition was affected by
formulations, but not considerably, as indicated in Table 6-1. This may be attributed to
wood flours not affecting the structure characteristics of HDPE. In the research of Tajvidi
et al. [2010], the results of DMA also revealed no change in the Tg when the fibre content
was increased in composites; however, the composite material did have better
temperature resistance at higher fibre content.
The storage modulus as a function of wood content at various temperatures was
plotted as shown in Figure 6-7. In order to eliminate the effect of the coupling agent, the
uncoupled group (F4) was not considered in this comparison. Mahieux and Reifsnider
[2002] suggested that filler can be expected to act similarly to the crystallites, which
impede molecular motion and broaden the distribution of secondary bond (Van-der-
Waals, hydrogen, etc.) strengths. Therefore, the mechanical properties can be enhanced
by the addition of fillers.
According to the results, a higher wood content resulted in a higher E’ value at all
temperatures; however, this effect declined with elevating temperatures. Furthermore, a
higher wood content also resulted in a higher E” value (Figure 6-8); however, this
consequence was more considerable at the temperature around which the α-transition
took place.
101
Figure 6-7. Storage modulus versus wood content at various temperatures
Figure 6-8. Loss modulus versus wood content at various temperatures
102
The predictions of pointers associated with formulations were studied with the
polynomial response surface method, and the results are presented in Table 6-3. As to the
mid-point of the transition, there were no significant differences among the formulations;
whereas, the peak of E” was highly associated and predicable with formulations.
Moreover, the end point of the E’ transition was not very well accounted for by the
formulations.
In this study, unlike a typical semi-crystalline polymer, the E’ versus temperature
spectra did not appear as a clear rubbery plateau region after transition, which may cause
difficulty in determining the end point. However, the end point is close to the peak of E”;
therefore, we can still obtain rough information about the transition of the product with
the prediction of the onset point and the peak of E” with the formulation.
Table 6-3. Regression Equations
Variable Regression R2 Adj-R
2 SEE P
Onset (°C) = -39 + 4.66 x1 + 1.27 x2 – 0.0499 x12 0.878 0.847 0.68 <0.01
Mid (°C) = 1.6 + 0.305 x1 – 0.165 x2 – 0.00129 x12 0.069 0 0.83 0.891
End (°C) = 331 – 9.23 x1 – 0.204 x2 + 0.0776 x12 0.679 0.598 2.19 <0.01
E" peak (°C) = 399 + 2.36 x1 – 4.08 x2 – 0.0156 x12 0.921 0.902 1.32 <0.01
x1 = wood content (%); x2 = HDPE content (%)
If the transition of E’ was considered as a straight line from onset to the end, the
influence of the formulation can be observed in Figure 6-7 and Table 6-4. The greater
slope in absolute value implies a more abrupt transition. The F3 formulation resulted in
the most abrupt transition; however, it still retained the highest E’ after transition.
Furthermore, compared to neat HDPE, the addition of MAPP and higher content of wood
103
flour simply increased the value of modulus, but did not significantly change the range of
transition.
Figure 6-7. Transition of storage modulus
Table 6-4. Transition of Storage Modulus
Formulation Regression R2
F1 y = -58.539x + 6125.2 0.9917
F2 y = -63.854x + 6855.8 0.7335
F3 y = -69.742x + 7376.8 0.9777
F4 y = -62.212x + 5160.8 0.9258
HDPE y= -28.072x + 2297.6 0.9526
6.3 Deflection Temperature Under Load
The deflection temperature under load (DTUL) is considered by many in the
industry to represent the upper limit of safe operating temperatures for products
fabricated from a given resin system. Up to this maximum temperature, a material is able
to support a load for some appreciable time. In the quest for reliable performance at
104
elevated temperatures, this single property is frequently the only criterion used in
determining the fitness for use of a given material.
DTUL is a single-point measurement, which represents a bulk property of the
material rather than one relating to its microscopic structure. For amorphous polymers,
the DTUL is close to the glass transition temperature; whereas, for semi-crystalline
polymers, the DTUL is in the vicinity of the melting temperature.
Table 6-5. DTUL of MPB-WPC Products and HDPE
Formulation DTUL
(°C)
Std. Dev.
(°C)
F1 105.67 2.31
F2 116.00 9.54
F3 108.33 1.15
F4 74.33 2.08
HDPE 58.00 8.19
Table 6-5 shows the DTUL results of the MPB-WPC products, and the neat
HDPE was also tested as a reference. The results reflect the above DMA spectra that the
coupled group and the group with higher wood content had higher DTULs, indicating
better temperature resistance.
Biswas et al. [2001] also reported that, with an increase in fibre volume fraction,
considerable changes in viscosity occurred; and, the composite was able to withstand
higher temperatures for a longer period of time.
105
6.4 Summary
To understand the performance of MPB-WPC products at various temperatures,
dynamic mechanical analysis was adopted to obtain the spectra of the storage modulus
(E’), loss modulus (E”) and mechanical loss factor (tan δ) within a temperature range
from -50 to 120°C. The results showed that the formulations and components have
influences on viscoelastic properties.
In summary, a higher content of wood flour resulted in a higher E’, indicating
better stiffness; whereas, tan δ became lower. Furthermore, the inclusion of a coupling
agent also significantly improved the E’, which is attributed to the enhancement of the
interface property between wood and HDPE, coupled by MAPP.
In addition, the addition of wood and MAPP pushed the transition toward a higher
temperature. The mobility of the macromolecular chains located in the fibre surface
interface reduced with an increase in the fibre/matrix interaction, which resulted in a shift
in the α-transition temperature towards a higher temperature range. This may also imply
that the resistance to temperature was improved. Moreover, based on the modulus
retention ability, the MAPP coupled products had better retention than did uncoupled
products. The results of the DTUL analysis also support this finding.
A higher wood content resulted in a higher E’ value at all temperatures; however,
this effect declined with elevating temperatures. A higher wood content also resulted in a
higher E” value; however, this consequence was more considerable at the temperature
around which the α-transition took place. Also, the addition of MAPP and a higher
106
content of wood flour simply increased the value of modulus, but did not significantly
change the range of transition.
107
CHAPTER 7. TIME-TEMPERATURE-STRESS SUPERPOSITION
AND MASTER CURVE
Due to their viscoelastic nature, wood-plastic composite (WPC) products exhibit
characteristics of both an elastic solid and a viscous material. As a structural material,
WPCs may perform differently under various environmental conditions over a long
period of time. However, direct evaluation of the long-term performances of a product
takes a great deal of time and is costly. Therefore, in order to reduce the expense and time
to generate the long-term information for design purposes, alternative methods for long-
term prediction with shorter-term experimental data are needed.
In addition, whereas various structural and environmental parameters influence
creep behaviour, temperature and stress may be the most important variables in long-term
performance of WPCs, as most polymeric materials show signs of temperature-dependent
and stress-dependent behaviours. In particular, the thermoplastic matrix of WPCs is
susceptible to these two factors; thus, quantification of the long-term performance of a
WPC product is needed. Consequently, the effects of stress and temperature need to be
carefully studied and considered in the application of WPC products.
In Chapter 6, the fundamental viscoelastic properties were studied, based on the
dynamic mechanical analysis (DMA) spectra at various temperatures. For this chapter,
the creep behaviour of mountain pine beetle (MPB) WPC products was studied by
employing the DMA method for accelerating creep strain and the application of the time-
temperature-stress superposition principle (TTSSP) to construct master curves, providing
108
essential information on material behaviour, greatly reducing the time for experiments
and effectively predicting creep strain outside of the available measurement of the device.
Due to the abundance of results, only a portion of them are shown in this chapter
for discussion; and, demonstrations are provided only with the F2 MPB-WPC product,
since the results of other formulations also showed similar trends in all aspects. The rests
of the data are tabulated in the Appendices.
7.1 Short-Term Creep Tests
7.1.1 Ten-Minute Creep Tests
Figure 7-1 shows a representative plot of the creep strain from a series of 10-
minute creep tests at various temperatures from -45 to 45°C with an increment of 5°C.
The effect of temperature can be observed in that the creep strain increased with elevating
temperatures, and the strain increment also increased nonlinearly with respect to
temperature. This may imply that, at a lower temperature, the effect of temperature was
linear; however, with increasing temperature, the effect became nonlinear.
At a lower temperature, the creep strain did not increase considerably; whereas,
the strain increased more and more significantly with elevating temperature. This can be
seen in the graph of the isochrones, in which the creep strains are marked at the same
time point; and, the effect of temperature can be clearly observed in the difference of
strains increasing with elevating temperatures from the same time point.
109
Figure 7-1. A representative result of the 10-minute creep test at various temperatures
7.1.2 Isochrones
Normally, the creep function has two independent variables, time and stress or
strain. The dependence on time can be determined from creep experiments. Isochrones
are useful for determining dependence on stress or strain [Wineman 2009]. If creep strain
is plotted against applied stress after a fixed time and the results are linear, the material
behaves in a linearly viscoelastic manner; on the other hand, isochronous plots of
nonlinear viscoelastic materials are not straight [Burgoyne and Alwis 2008].
Moreover, if temperature has a similar effect as stress does on the creep strain, the
concept of isochrones can be applied to observe the dependence of viscoelastic
behaviours of MPB-WPC products on stress and temperature, as shown in Figures 7-2
110
and 7-3, respectively. The linearity of the response of MPB-WPC products can be
determined based on these isochrones.
Figure 7-2. Isochrones taken at 1, 5 and 10 minutes from 10-minute creep tests with
respect to stress at -20, 20 and 45°C (F2)
111
As to stress, at lower temperatures, the results showed that strain increased nearly
linearly with increasing stress. According to linear viscoelasticity, the results imply that
the product behaved linearly under the selected stresses. However, with increasing
temperature, higher stresses (greater than 5 MPa in this case) appeared to upturn; and,
this was more apparent at higher temperatures. This indicates the effect of temperature on
the viscoelastic behaviour, which may become nonlinear with elevating temperature.
Figure 7-3. Isochrones taken at 1, 5 and 10 minutes from 10-minutes creep tests with
respect to temperature at 5 MPa (F2)
In Figure 7-3, it can be observed that the creep strain increment from 1 minute to
5 minutes was greater than that from 5 to 10 minutes, with respect to temperature. This
observation agrees with Sain et al. [2000] who stated that the temperature influence was
more significant on the instantaneous creep than on the transient creep and that the
transient creep strain became more pronounced with increasing operating temperature.
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
Str
ain
Temperature (°C)
1 min5 min10 min
112
Furthermore, according to Figure 7-3, the material may have behaved nonlinearly when
the temperature was higher than a certain point.
The creep compliance of MPB-WPC as a function time and temperature is
illustrated in a three-dimensional plot in Figure 7-4. Based on the figure, the
instantaneous creep compliances increased with increasing temperatures and the time-
dependent deformations were more pronounced at higher temperatures at the same time
point. This phenomenon may also imply that the behaviours of the material were not
consistent at various temperatures. It should be noted that the knowledge obtained from a
creep test at a certain temperature, as with a conventional creep study, may not be
applicable at other temperatures.
Figure 7-4. Compliance versus time and temperature (F2)
113
7.1.2 Stress-Temperature Incorporated Creep Model
Due to temperature-dependent properties, the ordinary creep test under
conditioned environments may not be sufficient to provide practical information. In order
to introduce the effect of temperature for creep strain prediction, a new empirical model –
creep strain as a function of time, temperature and stress – was developed in this study,
based on the commonly used power law model and introducing the described relationship
between the time-dependent creep strain and the temperature according to isochrones.
First, the common power law model is applied to fit the typical creep strain:
( ) ( )
where t is the time; and, a, b and n are parameters. The representative results are shown
in Figure 7-5a. The graph indicates well-fitted results.
This power law model has been widely used in many previous studies; however,
this model can merely fit the creep curve under simple conditions. Also, the effect of
temperature has not yet been well defined; hence, the application of this power law model
is limited. Therefore, the effect of temperature should be introduced in this model to
extend its application.
Next, the effect of temperature on creep strain is defined by fitting isochrones
with the following exponential equation:
( ) (
) ( )
114
where T is the temperature; and, c, m and d are parameters. The representative results are
shown in Figure 7-5b.
Based on this figure, the effect of temperature can be explained well with this
exponential function; thus, the behaviour of the WPC product at different temperatures at
the same time point can be modeled. This effect can now be introduced into conventional
creep models.
Figure 7-5. Creep strain fitted with (a) the power law and (b) the exponential model
115
As both equations fit the data well; therefore, they can be adapted for building the
governing equation. Then, the effect of temperature is introduced to the creep strain by
multiplying Equations 7-1 and 7-2 as:
( ) ( ) ( (
)) ( )
The preliminary results show that parameters a and c were both statistically
insignificant to the resultant model; therefore, the model was condensed as:
( ) (
) ( )
where t is time; T is temperature; and, b, n, m and d are stress- and material-dependent
parameters. This model was used to fit on experimental data; and, the obtained results,
using F2 as the example, are presented in Figure 7-6. The overall results are summarized
in Table 7-1.
Figure 7-6. Plot of creep strain as a function of time and temperature (F2)
116
Table 7-1. Parameters for Temperature-Induced Creep Strain Fitting
Formulations Stress Parameters
R2 SEE
b m n d
F1
1 3.87E-05 29.9258 0.1519 0.0001 0.9985 3.72E-06
3 0.0001 25.2337 0.1491 0.0005 0.9945 2.93E-05
5 0.0002 27.9546 0.1442 0.0008 0.9984 2.54E-05
8 0.0004 26.5967 0.1486 0.0012 0.9989 3.85E-05
F2
1 3.73E-05 33.7424 0.1345 0.0001 0.9985 2.82E-06
3 0.0001 32.5904 0.1333 0.0004 0.9987 8.89E-06
5 0.0002 23.3039 0.1472 0.0006 0.9986 1.53E-05
8 0.0003 28.9737 0.1338 0.0010 0.9980 2.81E-05
F3
1 3.20E-05 30.4366 0.1546 0.0001 0.9982 3.38E-05
3 9.42E-05 28.9728 0.1405 0.0004 0.9983 9.79E-05
5 0.0002 27.9655 0.1408 0.0007 0.9982 1.87E-05
8 0.0003 26.0500 0.1460 0.0012 0.9985 3.70E-05
F4
1 3.18E-05 23.9935 0.1849 0.0002 0.9982 5.75E-06
3 0.0001 22.3473 0.1686 0.0006 0.9984 1.99E-05
5 0.0001 21.2893 0.1753 0.0006 0.9985 2.27E-05
8 0.0002 16.0565 0.1897 0.0015 0.9977 9.51E-05
F6
1 2.21E-05 29.7368 0.1530 0.0001 0.9964 3.39E-06
3 5.75E-05 27.4813 0.1423 0.0004 0.9962 9.79E-06
5 0.0001 24.7183 0.1522 0.0009 0.9960 2.85E-05
8 0.0002 23.1081 0.1503 0.0011 0.9963 3.86E-05 R
2: Coefficient of determination
SEE: Standard error of the estimate
Based on the results, Equation 7-4 successfully agreed with the experimental data,
indicating that the effect of temperature on WPC creep can be introduced in the
prediction of creep strain of WPC products.
In order to improve the convenience of the model and extend its application to
various stresses and temperatures, the effect of stress should be introduced in this
equation. Referring to the Bailey-Norton equation (Equation 2-39), the primary creep can
be characterized as a monotonic decrease in the rate of creep, which could introduce the
effect of stress to this model. The instantaneous strain and the effect of temperature on
the instantaneous strain should also be taken into account; therefore, the temperature-
117
dependent modulus, ET, which is obtained by the DMA temperature sweep, is included in
the model. Therefore, this new stress-temperature incorporated creep (STIC) model can
be represented as:
( )
(
) ( )
where σ is stress; t is time; T is temperature; ET is the temperature-dependent modulus
(storage modulus, E’) obtained by the DMA temperature sweep, as shown in Table 7- 2;
and, b, u, n and m are material parameters. The parameters were obtained by fitting the
models to experimental data using the Marquardt-Levenberg nonlinear algorithm.
Table 7- 2. Temperature-Dependent Modulus, ET, Obtained by DMA
Temperature
(°C)
Temperature-Dependent Modulus, ET (MPa)
F1 F2 F3 F4 F6
-45 6672 7578 8500 5607 9546
-40 6630 7521 8445 5572 9493
-35 6552 7423 8348 5507 9394
-30 6453 7299 8226 5429 9271
-25 6340 7158 8085 5343 9134
-20 6214 7004 7931 5250 8985
-15 6078 6838 7761 5151 8824
-10 5929 6662 7579 5042 8651
-5 5770 6479 7386 4922 8464
0 5600 6288 7181 4790 8262
5 5419 6086 6963 4639 8044
10 5227 5878 6731 4468 7807
15 5025 5661 6456 4270 7552
20 4703 5344 6080 3987 7186
25 4380 4948 5674 3557 6704
30 4123 4669 5342 3243 6352
35 3842 4359 4978 2898 5953
40 3562 4061 4619 2618 5549
45 3282 3754 4266 2365 5138
118
Based on the results that are presented in Table 7-3, this model fits very well with
the experimental data. It is also the first model that incorporates the effect of temperature
and stress on creep in one simple equation. However, the model was developed based on
the 10-minute short-term creep experiment: a long-term creep experiment is needed to
verify the application of the model. Moreover, the temperature range was limited, from -
45 to +45°C in this case; thus, the applicability of this model to temperatures outside of
this range also needs to be verified.
Table 7- 3. Parameters for the STIC Model
Formulations Parameters
R2 SEE
b u m n
F1 1.78E-05 1.1882 28.6396 0.2172 0.9976 5.05E-05
F2 7.43E-06 0.8599 25.7969 0.3092 0.9946 4.82E-05
F3 8.48E-06 1.7418 35.5365 0.1770 0.9947 6.49E-05
F4 2.64E-08 3.7216 14.4137 0.2882 0.9727 0.0002
F6 3.66E-05 1.0388 45.7410 0.1511 0.9589 0.0001
R2: Coefficient of determination
SEE: Standard error of the estimate
7.2 Master Curves
7.2.1 Time-Temperature Superposition
The effect of time and temperature on a composite material can be determined
using the time-temperature superposition principle, the basis of which is the equivalency
of time and temperature [Ferry 1980]. According to this principle, the effect of a constant
temperature change on all time-dependent response functions, such as compliance and
modulus, is equivalent to a uniform shift in the logarithmic time scale.
119
In this case, the manifestation of the principle is the collection of viscoelastic data
at higher temperatures and their superimposition at a lower temperature by shifting the
data with respect to the time axis. Shifting the high temperature data to lower
temperatures has the effect of making the data appear to have been collected at a lower
temperature, thus increases the corresponding time scale [Barpanda and Mantena 1998].
One can obtain a series of strain versus time curves by conducting the 10-minute
short-term creep experiment at different temperatures. Applying the time-temperature
superposition in which only horizontal shifts were made and using various reference
temperatures, smooth master curves were obtained covering several decades of time, as
shown in Figure 7-7. In addition, the resultant master curves can still be shifted along the
time axis as typical horizontal shift processing.
Figure 7-7. Master curves at various reference temperatures at 5 MPa (F2)
120
This successful time-temperature superposition implies that WPCs may be a
thermo-rheologically simple material. The results, however, did not agree with Tajvidi et
al. [2005] who suggested that a single horizontal shift is not adequate and that a two-
dimensional superposition method is preferable for a similar composite.
A trend can be observed where a lower reference temperature resulted in a longer
extrapolation of time and where a longer time is needed to reach the same strain. This
may indicate that the WPC product can endure longer in a low-temperature environment.
It may also imply that the selection of the reference temperature and the testing
temperature range should be carefully considered.
Figure 7-8. Master curves constructed with different temperature ranges (F2)
121
Based on the previous observation, the temperature influenced the creep strain
nonlinearly; and, WPCs, which are a temperature sensitive material, may behave
unpredictably at higher temperature and result in different master curves at the same
reference temperature. Figure 7-8 shows comparisons between two master curves
constructed at a reference temperature of 35°C, but with different temperature ranges.
According to the figure, the curve of the 35-75°C range resulted in a higher strain
than the one of the -45-45°C range, indicating that the temperature range influenced the
resultant master curve. Moreover, for the same reference temperature, the master curve
constructed with higher temperatures tended to result in a higher strain than with lower
temperatures.
The master curve may lose accuracy when extrapolating the curve to a
temperature outside of the selected range. The selection of the reference temperature
close to the temperature of interest would be an appropriate choice. As well, a
temperature range that starts from the temperature of interest may ensure valid and longer
extrapolation of data.
In some cases, master curves can be made by using a vertical shift of the
experimental curves, in addition to or instead of a horizontal shift. However, in this study,
the application of a simple horizontal shift seems to be good enough to construct a
smooth master curve for the time-temperature superposition. Figure 7-9 shows the master
curves obtained from the time-temperature shifting process for various stresses at a
reference temperature of 20°C. Within the same period of time, greater stress caused
greater strain.
122
Figure 7-9. Master curves constructed by time-temperature shifting under various stresses
at a reference temperature = 20°C (F2)
7.2.2 Shift Factor
When generating a master curve, the data at higher temperatures is shifted and
superimposed at a lower temperature. This shifting of a curve can be horizontal, vertical
or both. Shifting a curve along the log time axis corresponds to multiplying every value
of its abscissa by a constant factor, called the horizontal shift factor; whereas, the
constant for the shifting of a curve along the log strain axis is called the vertical shift
factor.
The shift factors required to achieve master curves at various reference
temperatures for various stresses are summarized in Appendix I. Table 7-4 is an example
of the results, presenting the shift factors used to construct the master curves for the F2
MPB-WPC product under a stress of 5 MPa. (The numbers are shown in logarithm base.)
The leftmost column shows the temperatures at which the 10-minute creep tests were
conducted.
123
Temperature effects are described by altering the time scale of the response (a
horizontal shift) according to the time-temperature superposition principle. The creep
strain at two different temperatures, similar to creep compliance at two different
temperatures, can be related by:
( ) (
( ) ) ( )
( ) ( )
where t* is referred to as the shifted time, and Ta (T) is the temperature shift factor at
temperature T, which is the leftmost column in Table 7-4.
For example, when T0 (reference temperature) is -35°C, the creep strain curves at
other temperatures can be shifted by using the shifted time, t*, which is obtained by
converting the original time using the numbers shown in the column under the reference
temperature of -35°C, to change their time scale, so that they overlap each other. A
master curve with a wider time range can then be formed as shown in previous sections.
Furthermore, the master curve can also be shifted to different temperatures based on the
shift factors.
It should be noted that the number in Table 7-4 is presented in logarithm base;
therefore, the actual shift factor should be 10 raised to the power of the tabular numbers.
If, in the log-scale time axis, the tabular number is the shift factor; and, a negative value
indicates a right shift, whereas a positive value indicates a left shift. Furthermore, the
shift factor would vary when different reference temperatures are selected.
124
The shift factors were also fitted with the Williams-Landel-Ferry (WLF) equation,
and two parameters, C1 and C2, were obtained and are listed in Table 7-5. The WLF
equation can be represented as in Equation 2-27:
( )
( ) ( )
where aT is the time shift factor, Tr is the reference temperature, and T is the temperature
(K) at which the shift factor is desired.
The results showed that the WLF model provided a great fit in this study. The
parameters would vary with different reference temperatures, since the shift factors also
vary with different reference temperatures.
Stress, however, does not seem to significantly influence the horizontal shift
factor. According to Figure 7-10, which is a summary of shift factors under different
stresses and various reference temperatures, the logarithm values of the shift factors
decreased with an increasing reference temperature; however, no significant difference
was observed among the different stresses. This may imply that, within certain limits, the
horizontal shift factor is independent of stress.
Previous research has indicated that the WLF equation is typically applied to
amorphous polymers in the region from the glass transition temperature (Tg) to Tg+100°C,
and the Arrhenius equations is used outside of this range [Pooler and Smith 2004]. The Tg
of the MPB-WPC product, however, cannot be defined in this study (refer to the DMA
spectra in Chapter 6). Hence, this criterion is not applicable.
125
In other research, the Arrhenius equation was regarded as a better explanation for
the temperature dependence of the shift factors than the WLF equation for nature fibre /
thermoplastic composites [Tajvidi et al. 2005]. However, this statement is not confirmed
in this study. The results of fitting show that the WLF equation works better than
Arrhenius equation for MPB-WPC products. Figure 7-11 shows an example of
comparison.
Figure 7-10. Shift factor comparison at various stresses at Tr = 20°C (F2). Vertical lines
show the range of the value and boxes show the first quartile (Q1) and the third quartile
(Q3) values, and (+) represent the mean value.
126
Table 7-4. Horizontal Shift Factors at Various Reference Temperatures At 5 MPa (F2)
T (°C) Reference Temperature (°C)
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.363 0.776 1.238 1.700 2.124 2.549 2.982 3.426 3.864 4.298 4.737 5.184 5.641 6.116 6.656 7.209 7.701 8.197
-40 -0.398 0 0.394 0.850 1.319 1.754 2.166 2.597 3.036 3.478 3.909 4.353 4.795 5.253 5.727 6.266 6.823 7.314 7.811
-35 -0.851 -0.439 0 0.424 0.899 1.344 1.766 2.191 2.643 3.073 3.504 3.956 4.395 4.855 5.330 5.871 6.429 6.916 7.405
-30 -1.294 -0.923 -0.465 0 0.450 0.889 1.317 1.758 2.189 2.628 3.055 3.496 3.940 4.397 4.876 5.414 5.973 6.458 6.963
-25 -1.787 -1.398 -0.955 -0.476 0 0.419 0.848 1.288 1.728 2.164 2.592 3.039 3.478 3.938 4.410 4.955 5.513 5.998 6.495
-20 -2.255 -1.860 -1.374 -0.954 -0.484 0 0.412 0.849 1.297 1.734 2.163 2.612 3.047 3.510 3.980 4.526 5.080 5.569 6.065
-15 -2.671 -2.282 -1.832 -1.409 -0.951 -0.481 0 0.422 0.866 1.317 1.750 2.189 2.624 3.091 3.568 4.107 4.665 5.150 5.650
-10 -3.104 -2.732 -2.241 -1.817 -1.358 -0.899 -0.462 0 0.429 0.879 1.327 1.772 2.206 2.655 3.143 3.675 4.237 4.726 5.223
-5 -3.545 -3.176 -2.688 -2.278 -1.811 -1.358 -0.869 -0.471 0 0.444 0.883 1.339 1.782 2.226 2.710 3.249 3.806 4.297 4.794
0 -3.978 -3.610 -3.155 -2.736 -2.246 -1.813 -1.348 -0.913 -0.467 0 0.437 0.890 1.344 1.801 2.270 2.811 3.367 3.855 4.353
5 -4.451 -4.079 -3.577 -3.194 -2.719 -2.278 -1.795 -1.351 -0.927 -0.448 0 0.445 0.898 1.360 1.838 2.376 2.941 3.426 3.928
10 -4.869 -4.535 -4.044 -3.634 -3.172 -2.733 -2.248 -1.803 -1.365 -0.923 -0.430 0 0.446 0.915 1.396 1.929 2.486 2.981 3.476
15 -5.335 -4.989 -4.499 -4.085 -3.638 -3.190 -2.676 -2.290 -1.792 -1.360 -0.892 -0.439 0 0.461 0.947 1.493 2.047 2.530 3.032
20 -5.808 -5.480 -4.956 -4.583 -4.095 -3.665 -3.143 -2.730 -2.277 -1.825 -1.368 -0.891 -0.488 0 0.481 1.030 1.601 2.083 2.572
25 -6.318 -5.941 -5.440 -5.047 -4.555 -4.142 -3.655 -3.244 -2.757 -2.318 -1.829 -1.372 -0.945 -0.450 0 0.545 1.124 1.613 2.103
30 -6.849 -6.548 -5.987 -5.589 -5.127 -4.679 -4.171 -3.756 -3.315 -2.847 -2.385 -1.934 -1.516 -1.007 -0.527 0 0.569 1.076 1.569
35 -7.418 -7.086 -6.531 -6.166 -5.710 -5.244 -4.726 -4.334 -3.894 -3.405 -2.955 -2.459 -2.067 -1.609 -1.136 -0.598 0 0.501 1.002
40 -7.937 -7.582 -7.030 -6.642 -6.224 -5.793 -5.242 -4.813 -4.382 -3.904 -3.428 -2.966 -2.552 -2.100 -1.618 -1.058 -0.498 0 0.488
45 -8.440 -8.133 -7.507 -7.148 -6.698 -6.253 -5.737 -5.342 -4.883 -4.411 -3.944 -3.499 -3.046 -2.608 -2.089 -1.537 -1.000 -0.486 0
The numbers in the table were presented as log(shift factor)
127
Table 7-5. Coefficients of the WLF Equation for Horizontal Shift Factors (F2)
F2
Tr
(°C)
1 MPa 3 MPa 5 MPa 8 MPa
C1 C2 SEE C1 C2 SEE C1 C2 SEE C1 C2 SEE
-45 1.37E+08 1.619E9 0.238 1.25E+08 1.387E9 0.144 1.52E+08 1.665E9 0.112 7.39E+07 7.868E8 0.206
-40 1.41E+08 1.586E9 0.138 1.26E+08 1.380E9 0.104 4.14E+07 4.448E8 0.104 6.57E+07 6.623E8 0.142
-35 1.47E+08 1.610E9 0.127 1.37E+08 1.475E9 0.107 4.41E+08 4.797E9 0.089 6.16E+07 6.284E8 0.163
-30 8.92E+07 9.651E8 0.149 9.09E+07 9.706E8 0.110 4.78E+07 5.124E8 0.088 2.13E+08 2.109E9 0.163
-25 8.16E+06 8.788E7 0.165 1.69E+08 1.813E9 0.117 9.54E+07 1.022E9 0.098 9.35E+07 9.453E8 0.160
-20 1.39E+08 1.498E9 0.181 1.74E+08 1.853E9 0.133 8.78E+06 9.365E7 0.101 7.61E+07 7.689E8 0.157
-15 1.01E+08 1.084E9 0.220 9.78E+07 1.048E9 0.148 1.38E+08 1.491E9 0.107 1.42E+08 1.420E9 0.207
-10 1.67E+08 1.847E9 0.196 7.58E+07 8.120E8 0.147 7.96E+07 8.553E8 0.127 1.89E+06 1.921E7 0.181
-5 1.23E+08 1.366E9 0.209 1.08E+08 1.175E9 0.151 2.11E+08 2.274E9 0.142 2.57E+08 2.606E9 0.229
0 2.68E+07 3.000E8 0.225 1.53E+08 1.677E9 0.177 9.02E+07 9.854E8 0.145 1.38E+08 1.419E9 0.235
5 1.72E+08 1.939E9 0.218 9.62E+07 1.063E9 0.187 1.95E+08 2.156E9 0.149 5.31E+07 5.520E8 0.216
10 6.08E+07 6.969E8 0.209 1.50E+08 1.685E9 0.141 2.29E+08 2.561E9 0.146 1.12E+08 1.187E9 0.242
15 9.90E+07 1.138E9 0.187 9.16E+07 1.032E9 0.169 8.96E+07 1.006E9 0.158 1.98E+08 2.108E9 0.220
20 9.16E+07 1.045E9 0.155 1.06E+08 1.185E9 0.129 1.02E+08 1.148E9 0.149 7.93E+06 8.436E7 0.202
25 9.09E+07 1.042E9 0.149 7.10E+07 7.986E8 0.129 1.53E+08 1.715E9 0.128 6.78E+07 7.166E8 0.210
30 4.84E+07 5.446E8 0.148 1.01E+08 1.120E9 0.111 1.52E+08 1.674E9 0.106 5.40E+07 5.638E8 0.169
35 6.74E+06 7.510E7 0.158 7.89E+07 8.644E8 0.125 2.51E+08 2.715E9 0.131 1.54E+07 1.558E8 0.187
40 1.13E+08 1.246E9 0.177 8.83E+07 9.531E8 0.150 1.11E+08 1.195E9 0.140 4.24E+07 4.205E8 0.227
45 9.04E+07 9.919E8 0.184 9.28E+07 9.941E8 0.165 7.55E+07 8.055E8 0.142 8.05E+07 7.894E8 0.256
128
Figure 7-11. Comparison between WLF equation and Arrhenius equation fitting (F2 at
Tr= 20°C, under 5 MPa stress)
7.2.3 Time-Stress Superposition
In a previous study, the time-stress superposition has also been proven applicable
[Dastoorian et al. 2010]. Based on the graphs of the isochrones, the behaviour of the
product would be within the linear region at lower temperatures. Referring to mechanical
tests, the product strength of F2 is, on average, 34.25 MPa. This indicated that the MPB-
WPC product F2 behaves linearly at least up to approximately 25% of the ultimate stress
at lower temperatures and lessens with elevating temperatures.
Kobbe [2005] suggested that the wood-polypropylene composites behaved
nonlinearly at even 10% of the ultimate stress. The difference from this study may be
attributed to a different polymer matrix, since the molecule structures of semi-crystalline
polymer, particularly the amount of amorphous and crystalline phases, determine the
linear viscoelastic behaviour. Nevertheless, a similar wood-HDPE product in Dastoorian
129
et al. [2010] behaved linearly up to 50% of the ultimate stress, which may imply the
potential for this type of product.
In addition, during the shifting process, the horizontal shift was not adequate to
construct a master curve; therefore, a proper vertical shifting was needed as well to make
a smooth curve. This observation does not agree with that of Dastoorain et al. [2010].
Nevertheless, this vertical shifting for time-stress superposition has been mentioned in
other research [Tajvidi et al. 2005].
The horizontal shift factor for time-stress superposition can be related to the
applied stress as in Equation 2-30:
( )
( ) ( )
where C1 and C2 are parameters, and σr is the reference stress.
The typical horizontal shift may only be applicable to shifting short-term creep
curves to overlap at the time axis; however, the creep strain may not necessarily overlap
without vertical shifting. The vertical shifting process, therefore, may be needed in order
to obtain a smooth master curve in such a case.
The shift factors for horizontal shifts can conform to the WLF equation, Equation
2-30; and, the relation between the creep strains at two stresses can be expressed with
Equation 7-8:
( ) (
) ( )
130
where g and aσ are the vertical and horizontal shift factors, respectively. The graphical
demonstration of a time-stress superimposed master curve construction, involving both
horizontal and vertical shift processing, is shown in Figure 7-11.
Figure 7-12. A master curve construction involving horizontal and vertical shifts
131
In this study, the generated master curves based on time-stress shifting at various
reference stresses are shown as Figure 7-12, at a temperature of 20°C. The horizontal and
vertical shift factors are summarized in Table 7-6.
Figure 7-13. Master curves constructed with the time-stress superposition at 20°C (F2)
Table 7-6. Shift Factors for the Master Curves in Figure 7-11
σr (MPa) Stress (Mpa) H Shift* V Shift*
1
1 0 0
3 -1.578 0.4024
5 -3.682 0.4106
8 -5.787 0.4755
3
1 1.039 -0.443
3 0 0
5 -2.104 0
8 -4.199 0.07237
5
1 2.898 -0.439
3 2.105 0
5 0 0
8 -2.071 0.06761
8
1 5.003 -0.5576
3 4.21 -0.08525
5 2.105 -0.06761
8 0 0
* The number is presented as log(shift factor), the
positive value means a shift left for a horizontal shift
and a shift up for a vertical shift.
132
If vertical shift was not considered time-stress superposition, the resultant master
curve may show some gap between those shifted short-term curves, shown as Figure 7-14
(the same series of short-term curves in Figure 7-12). In order to avoid the uncertainty
and make a continuously smooth master curve, the vertical shift is recommended for
time-stress superposition in this study.
Figure 7-14. The master curve constructed with the time-stress superposition at 20°C
without vertical shift (F2).
7.3 The Modified WLF Equation and the Temperature-Stress Hybrid Shift Factor
The data from short-term creep tests at various temperatures and stresses were
integrated as an interface between the temperature and the stress factor. The relationships
among temperature, stress and shift factor were developed based on the theory of free
volume, which is void space allowing for motion of the polymer chain, and on the
equivalence of time, temperature and stress.
Since temperature shift may interfere with stress shift in creep, there should be a
model that incorporates the relationship between these two shifts. Luo et al. [2001]
133
proposed that the free volume fraction can be expressed with temperature and stress
simultaneously in the form of:
( ) ( ) ( ) ( )
where ασ is the stress-induced expansion coefficient of the free volume fraction. Then,
assume that there is a temperature-stress hybrid shift factor, aTσ, which satisfies:
( )
( ) ( )
Take the natural logarithm for both sides:
( )
( ) ( ) ( ) ( )
Based on Doolittle’s equation as in Equation 2-21, Equation 7-10 can be
converted as:
[ (
( ) )] [ (
)] (
( )
) ( )
Since 2.303*log(aTσ) = ln(aTσ), Equation 7-12 can be transferred as:
(
( )
) ( )
Then, substitute f with Equation 7-8:
(
( ) ( )
) ( )
134
Equation 7-14 can be rearranged as:
(
( ) ( )
[ ( ) ( )]
) ( )
Define (B/2.303f0) = C1, (f0/αT) = C2 and (f0/ασ) = C3, and then Equation 7-15 can be
transferred as a modified WLF equation, which covers both effects of temperature and
stress as:
( ) [ ( ) ( )
( ) ( )] ( )
In this study, a series of experiments considering the stress and temperatures were
organized based on this model. The horizontal shift factors obtained from short-term
creep tests were employed to verify Equation 7-16, using the Marquardt-Levenberg
nonlinear algorithm, and the results are summarized in Table 7-7.
Based on the results, the modified WLF equation fitted the data very well. The
application of the conventional WLF model can be extended to incorporate 2 variables –
temperature and stress.
Table 7-7. Fitted Parameters for the Modified WLF Equation
Formulations Parameters
R2 SEE
C1 C2 C3
F1 -347.5444 3775.1184 -497.8436 0.9878 0.3875
F2 -316.6602 3414.7100 -468.1292 0.9896 0.3588
F3 -410.1868 4247.9461 -638.7846 0.9838 0.4642
F4 -314.2968 3313.0659 -600.6259 0.9772 0.5372
F6 -235.5687 -2610.5140 -397.9588 0.9731 0.5621
*The unit for stress is MPa and for temperature is K, when deriving parameters
135
The relationship of creep compliance of materials at different conditions can be
expressed as:
( ) (
) (
) (
) ( )
where aσT is the stress shift factor at a constant temperature, and aT
σ is the temperature
shift factor at a constant stress, both of which can be shown, respectively, as:
( )
( )
[ ( )
( ) ( )] ( )
( )
( )
[ ( )
( ) ( )] ( )
Consequently, the time-dependent mechanical properties of viscoelastic materials
at different temperatures and stresses can be shifted along the time scale to construct a
master curve of a wider time scale at a given temperature and stress. The shift factor
under the conditions of interest can be described by the modified WLF model and applied
to original data to construct the desired master curve; and, the resultant master curve can
be shifted to the condition of interest.
If a vertical shift is necessary, the vertical shift factor, g, can be introduced in the
relationship:
( ) (
) ( )
136
7.4 Summary
In this study, short-term creep tests were conducted at various temperatures; and,
the time-temperature-stress superposition principle was successfully applied to the
construction of smooth master curves for the prediction of long-term creep strain.
Based on the results, creep strain increased with elevating temperatures and
stresses at the same time point. At lower temperatures, the results showed that strain
increased linearly with increasing stress, but may become nonlinear with elevating
temperature. Moreover, the temperature had significantly more influence on
instantaneous creep than on transient creep. Isochrones were also discussed, and the
effect of temperature on creep was found to be an exponential increase with temperature.
A new creep model, STIC model, which incorporates the effects of temperature and
stress, was established.
As to master curve construction, the selection of a reference temperature and the
testing temperature range should be carefully considered. For the same reference
temperature, the master curve constructed with higher temperatures tended to result in
higher strain than with lower temperatures.
The WPC product is a rheologically simple material, only horizontal shifting is
needed for the time-temperature superposition; however, vertical shifting would be
needed for the time-stress superposition. Moreover, the shift factor is independent of the
stress for horizontal shift within certain limits. In addition, temperature- and stress-shift
factors used to construct master curves were fitted with the WLF equation. The results
137
showed that the WLF equation works better than the Arrhenius equation for MPB-WPC
products.
To extend the application, a temperature-stress hybrid shift factor fitted a
modified WLF equation, which incorporates stress and temperature for fitting of the shift
factors, and was verified using short-term creep tests under various temperature and
stresses; and, the parameters were successfully calibrated. The application of the
conventional WLF model can be extended to incorporate 2 variables – temperature and
stress. The application of the time-temperature-stress superposition method can be
extended to various conditions.
Comparisons between master curves from short-term creep tests and full-scale
long-term creep data are made in Chapter 8.
138
CHAPTER 8. THE LONG-TERM CREEP OF MPB-WPC
PRODUCTS
To model the time-, temperature- and stress- dependent phenomena of
viscoelastic materials, there are two important aspects. The first is the development of a
constitutive equation that can accurately describe the mechanical response of the material;
and, the second is the development of methods for using constitutive equations in
conjunction with the governing equations of thermo-mechanics to determine stresses and
deformations in structures made of these materials [Wineman 2009].
In Chapter 7, the time-temperature-stress superposition principle was smoothly
applied for mountain pine beetle wood / plastic composites (MPB-WPCs) to generate
master curves under various temperature and stress conditions. However, the resultant
master curves need to be validated by a full-scale long-term creep experiment, since the
data obtained from the accelerated method may not reflect the real long-term behaviour
of the materials.
In many previous studies, creep tests were conducted to compare with master
curves obtained from short-term tests; however, the period of the creep experiments was
usually relatively short (about several hours to a week). Typically, the short-term creep
data was modeled and then extrapolation to a longer period of time. However, it is
unclear what the effectiveness and robustness of such extrapolation procedure as the
model may lose accuracy in actual long-term performance. Consequently, the validation
of the master curves is vital prior to the practical application.
139
Furthermore, the use of wood-plastic composites (WPC) for load bearing products
is continually increasing, particularly in outdoor applications. However, during the
service of products, the temperature or stress may change with elapsed time. The creep
data obtained from a conditioned environment may not reflect practical situations, since
the products are sensitive to stress and temperature. In most of the previous research
investigations, the creep tests were usually conducted in a conditioned climate; whereas
in this study, the creep test was performed in an unconditioned ambient room. The results
may reflect what might happen to the WPCs under ambient conditions.
8.1 Long-term Creep Test
To validate the application of master curves obtained from short-term creep tests,
a full-scale long-term creep test was conducted for 220 days, in an ambient environment
without temperature or relative humidity control, which should be able to reflect the
practical application of the product. Two formulations were selected, based on the lowest
and the highest average values for the modulus of elasticity (MOE). As such, F4 and F6
were chosen (refer to Table 5-1). Load levels of 20, 30 and 40% were selected based on
the maximum load obtained from the flexural test. The details of the experimental setup
are described in Chapter 4.
In order to eliminate differences in specimen sizes, the comparison between long-
term creep data of large specimens and dynamic mechanical analysis (DMA) master
curves of small specimens were based on stress and strain, instead of load and deflection.
The loading levels were converted to stress according to Equation 4-3 and are
summarized in Table 4-4. The data of mid-span deflection collected from the data
140
acquisition system for the long-term creep test were converted into strain, according to
Equation 4-9. The results of long-term creep test are presented in Figure 8-1, in which the
presented curves are the mean value of 10 replications for each group.
Under the same load level, F4, which is the uncoupled group of MPB-WPC
products, resulted in a higher strain than did F6, the coupled group. This indicates that the
improved stiffness enhanced the creep resistance for the MPB-WPC products. This result
agrees with previous findings.
Since the environmental conditions were not fixed during the period of testing,
the temperature changed with elapsed time. The temperature was recorded daily and
attached to the experimental creep curves, as shown Figure 8-2, in order to provide
evidence for the effect of temperature. A short period of a sudden temperature rising
caused an abrupt increment of strain on the roughly 50-55th day, which indicates the
effect of temperature on the MPB-WPC products and also implies that the change of
environmental conditions may cause unexpected deformation, even failure.
The conventional creep test usually under a conditioned environment, therefore,
may not provide sufficient information for practical use. This phenomenon was first
depicted in the creep study, since previous studies were usually conducted in a
conditioned environment; thus, this temperature-induced creep increment has not been
observed. For future use, a model applicable for a fluctuating environment will be needed.
A new superposition approach based on Boltzmann superposition and hereditary method
is proposed in this study and is discussed in Section 8.4.
141
Figure 8-1. Results of the long-term creep test
142
Figure 8-2. The effect of temperature on the long-term creep
143
8.2 Corresponding Master Curves
Based on the same stresses, the corresponding master curves were constructed by
superimposing creep curves obtained from a series of 10-minute creep tests at a
temperature range from 15-70°C, increasing at an increment of 5°C. The results are
presented in Figure 8-3, and the corresponding shift factors are presented in Figure 8-4.
The Williams-Landel-Ferry (WLF) equation was used to fit the shift factors, and the
obtained parameters are summarized in Table 8-1.
In this case, as previously mentioned, the MPB-WPC products are rheological
simple, and only a horizontal shift was needed for the time-temperature superposition.
The obtained master curves displayed different trends from the long-term creep test
results. Unlike the results of the long-term creep test, the master curves of all the groups
of F6 specimens resulted in a lower creep strain than the groups of the F4 specimens.
This phenomenon may be attributable to the inferior temperature resistance of the
uncoupled material.
144
Figure 8-3. Master curves at Tr = 25°C
Figure 8-4. Shift factors used to construct master curves at Tr = 25°C
145
Table 8-1. Shift Factors Used to Construct Master Curves
Temperature
(°C)
F4 F6
20% 30% 40% 20% 30% 40%
15 1.192(2.10) 1.180(2.59) 1.255(4.85) 1.042(5.30) 1.027(0.65) 1.061(2.72)
20 0.622(3.27) 0.611(2.13) 0.655(5.67) 0.576(8.89) 0.526(4.37) 0.558(2.09)
25 0 0 0 0 0 0
30 -0.684(5.83) -0.705(2.46) -0.726(1.26) -0.600(3.20) -0.644(2.52) -0.626(10.8)
35 -1.433(3.60) -1.484(2.50) -1.574(7.28) -1.259(3.38) -1.348(4.10) -1.313(1.42)
40 -2.042(2.15) -2.102(2.76) -2.267(0.22) -1.834(6.95) -2.031(3.77) -1.998(4.03)
45 -2.536(1.76) -2.695(2.21) -2.905(2.07) -2.440(7.07) -2.621(2.52) -2.652(1.69)
50 -2.978(1.84) -3.215(2.24) -3.402(1.68) -3.013(7.36) -3.187(2.25) -3.172(1.42)
55 -3.401(2.09) -3.664(2.47) -3.925(1.44) -3.472(6.97) -3.683(2.67) -3.689(1.64)
60 -3.784(1.70) -4.100(3.54) -4.420(2.01) -3.899(6.32) -4.110(1.80) -4.178(1.84)
65 -4.173(2.73) -4.544(2.67) -4.928(1.41) -4.270(5.92) -4.493(2.36) -4.612(0.93)
70 -4.555(2.92) -5.001(3.07) -5.433(0.79) -4.619(5.60) -4.876(3.51) -5.008(0.86)
*The numbers in the table are presented as log(shift factor)
** Numbers in parentheses are the |coefficients of variation| (%)
Table 8-2. The WLF Equation Parameters at Tr = 25°C
Formulations
Load
Levels
(%)
WLF Parameters
C1 C2 (K) SEE
F4
20 18.87 138.20 0.0999
30 25.98 185.30 0.1051
40 30.75 206.80 0.1468
F6
20 29.81 236.30 0.1277
30 32.01 240.50 0.1296
40 38.61 292.10 0.1421 SEE the standard error of the estimate
The right tails of the master curves (as shown in Figure 8-3) are comprised of the
short-term creep curves obtained at higher temperatures. The inferior temperature
resistance may cause additional strain to the original strain, which is caused by stress
only. Thus, at the same temperature, the uncoupled group (F4) produced higher strains
than the coupled groups (F6). Furthermore, a higher stress resulted in a higher strain. Due
to the inferior temperature resistance, as well as the simultaneous effect of stress and
temperature, the 40% group of F4 specimens produced a considerably higher strain than
146
other groups did in each short-term creep test, finally resulting in a master curve with a
considerably higher strain.
The concept of the time-temperature-stress superposition principle (TTSSP) is
that the viscoelastic behaviour at one temperature can be related to that at another
temperature by a change in the time scale only. However, as determined in Chapter 6, due
to their temperature-sensitive nature, the stiffness (storage modulus) of the MPB-WPC
products decreased with elevating temperature; and, the modulus retention was
influenced by the existence of a coupling agent. The uncoupled products resulted in
higher strains at each applied temperature under the same load level, eventually leading
to master curves with higher strains.
Moreover, as mentioned in Chapter 7, the effect of temperature on creep appeared
to be nonlinear, i.e. an exponential increase with elevating temperature instead of a linear
increase. This may imply that the effect of temperature on creep is more pronounced than
the effect of time. The higher the temperature, the more significant is the effect.
Therefore, if the higher end of the chosen temperature range for short-term creep tests is
too high, the master curve may lose its ability for accurate prediction at the tail of a
longer time scale.
One of the limitations of TTSSP is that the curve begins to lose accuracy if the
selected stresses fall outside the linear region. Likewise, the nonlinear behaviour caused
by temperature may also influence the application of the master curve. Consequently, the
selection of the temperature range in this method is important and should be considered
carefully.
147
The short-term creep data were predicted with the newly developed stress-
temperature incorporated creep (STIC) model, as shown in Equation 7-5 and described in
Chapter 7, and were compared with the experimental data. The results of the standard
error of the estimate (SEE) are summarized in Table 8-3.
Table 8-3. Standard Error of the Estimate of the STIC Model Prediction
Temperature F4 F6
1.88 2.81 3.75 3.07 4.58 6.10
15 0.00045 0.00041 0.00042 0.00009 0.00027 0.00033
20 0.00053 0.00047 0.00050 0.00011 0.00031 0.00038
25 0.00062 0.00055 0.00059 0.00013 0.00036 0.00043
30 0.00078 0.00071 0.00068 0.00013 0.00038 0.00044
35 0.00105 0.00097 0.00101 0.00011 0.00037 0.00042
40 0.00130 0.00127 0.00134 0.00009 0.00034 0.00039
45 0.00157 0.00161 0.00173 0.00007 0.00031 0.00031
50 0.00183 0.00193 0.00209 0.00008 0.00026 0.00026
55 0.00209 0.00224 0.00247 0.00011 0.00024 0.00023
60 0.00237 0.00257 0.00284 0.00015 0.00024 0.00023
65 0.00265 0.00290 0.00316 0.00016 0.00025 0.00025
70 0.00295 0.00324 0.00341 0.00016 0.00027 0.00027
According to Table 8-4, the STIC model can smoothly explain the short-term
creep data. However, the STIC model was developed based on the temperature range of -
45 to 45°C; whereas, the data in this section were obtained for a temperature range of 15
to 70°C. The parameters are not universal for the data obtained from the two different
temperature ranges; and, SEE increased with increasing temperature, which also indicates
the effect of temperature. The reason may be attributed to the fact that an adjustment
needs to be made to compare the data from the different temperature ranges.
Consequently, the parameters need to be obtained based on experimental results and may
not be applied universally, in order to retain the accuracy.
148
Table 8-4. Parameters of the STIC Model
Formulations Parameters
R2 SEE
b u m n
F615-70 1.28E-05 0.9461 29.3976 0.2334 0.9898 8.70E-05
F6-45-45 3.66E-05 1.0388 45.7410 0.1511 0.9589 0.0001
F415-70 5.02E-05 0.6563 26.0764 0.2179 0.9870 0.0002
F4-45-45 2.64E-08 3.7216 14.4137 0.2882 0.9727 0.0002
As well, since the size of the specimen for DMA is relatively small, compared to
the bulk product, the properties may not be uniform among specimens; and, variation
may also cause this difference. Hence, a set of universal parameters cannot be obtained.
However, according to the low SEE value in Table 8-3, the error of the model prediction
is very small, perhaps indicating that the new STIC model is applicable at temperatures
up to 70°C.
8.3 Comparison Between the TTSP Master Curve and Long-Term Creep Tests
Comparisons between the TTSP master curves and the long-term creep tests are
shown in Figures 8-5 and 8-6, in which the error bar represents a 95% confidence interval.
The results of 3 groups (3 load levels ) of F6 specimens showed good agreement between
the master curves and the long-term creep; whereas, the master curves overestimate the
long-term creep strain for F4 specimens, particularly at the 20% load level, showing a
considerably overestimation, and the deviation increased with time. This agrees with the
previous observation that the effect of temperature caused additional strain to the original
stress-induced strain, particularly for material of inferior temperature resistance; therefore,
the master curve tended to over predict the creep strain. However, for the stiffness-
149
enhanced product (i.e. coupled MPB-WPC products), the effect of temperature may not
be so substantial; thus, the prediction of the master curve agreed more reasonably with
the long-term data.
In previous studies, Tajvidi et al. [2005] also indicated that the effect of
temperature on the viscoelastic response of WPCs is much more significant than the
effect of time; and, so the conventional time-temperature superposition (TTS) method
would overestimate longer-term creep. In addition, Dastoorian et al. [2010] studied a fir-
HDPE composite using a power law to fit the creep test data and then extrapolated the
creep data to compare with the corresponding master curve; and, based on the difference
between the slope of the extrapolated data and the master curve, concluded that the
overestimation observed in the case of the master curve is statistically significant.
Moreover, Siengchin [2009] also found that the master curve constructed from
DMA short-term creep tests overestimated practical results and that the reason could be
attributed to the progressive decreasing of the material stiffness with time during long-
term loading, as well as physical aging.
In addition, the variation among master curves was great and resulted in a wider
confidence interval. The reason may be attributable to the selection of specimens. The
small-sized DMA specimens were cut and randomly selected from MPB-WPC products
of a larger size, and variation within the product may have caused the experimental
differences. However, this variation was still relatively small compared to that of solid
wood products.
150
Figure 8-5. Comparison between the long-term creep test and the DMA master curve,
with a 95% confidence interval error bar (F4)
151
Figure 8-6. Comparison between the long-term creep test and the DMA master curve,
with a 95% confidence interval error bar (F6)
152
Furthermore, the master curves consisted of several short-term creep curves at
various temperatures, and variation existed between samples at the same temperature;
therefore, the construction of the master curve may result in large variations. However,
this confidence interval overlapped and even covered the long-term creep result. Thus,
the master curves may be used to give a conservative estimate for the creep behaviour of
a product for which no other long-term test results are available.
AS to the tested formulated groups, F4 and F6, the material properties are fairly
different. As mentioned before, the formulation without coupling agent showed lower
modulus value, producing greater deformation in long-term behaviour; whereas, the
coupling agent improve the stiffness and showed better resistance on creep. That can be
discussed based on the ratio of modulus of elasticity (MOE) to modulus of rupture
(MOR). According to testing result (Table 5-1), the MOE/MOR is 154.87 for F4 inferior
to 176.69 for F6. These numbers showed that F4 is less stiff and tend to deform more
greatly under long-term loading under the same loading condition. In other words, the
properties of the testing materials may also affect the feasibility of experimental and
modeling methods. The results of comparison in this study implied that the TTSSP
method may not be suitable for materials of low MOE to MOR ratio since the resultant
strain may be greater than expectation.
Furthermore, the loading history in short-term creep tests under various
temperatures may affect the resultant master curves. Based on the testing program of
DMA device, the sequence of creep tests is continuous and merely stopped when
changing temperature. The time between tests may not be sufficient for the specimen to
recover; therefore, the overall strain may accumulate from each test because the results of
153
the sequential tests may be influenced by the previous conditions, and resulted in a
master curve of overestimation after superimposing all of those curves from short-term
creep tests. Particularly for F4, a less stiff material, since the non-recovered strain is
supposed to be greater than F6 if no sufficient recovery time, the accumulation of those
strains would produce a highly overestimated master curve as seen in Figure 8-5. As to
F6, this issue may be relatively less influential owing to better stiffness; therefore, the
master curve prediction and long-term test results were agreed more reasonably.
The different testing fixtures and configurations between the DMA and the long-
term creep test should also be discussed. For the long-term creep test, in order to obtain
the deflection from pure bending at the mid-span of the specimen, a 4-point bending
fixture was used; whereas, a 3-point bending fixture was used in the DMA, due to the
small size of the specimen. The volume of the specimen under maximum stress was
different for these 2 tests; the 4-point bending would have a greater stressed volume than
3-point bending, thereby resulting in a larger strain under the same stress. According to
the comparisons, F6 specimens at 30 and 40% load levels agreed with this suggestion. As
to F4, the overestimation of the DMA was caused by the temperature, resulting in a strain
greater than the expected original strain. Therefore, the application of DMA at high stress
levels and high temperatures simultaneously is not recommended.
As well, the different testing fixture between the 3-point and 4-point bending
resulted in different shear diagrams on the specimen. In the case of flexural test, the
deflection of specimen is caused by a combination of internal transverse shear force and
bending moment. For the 4-point bending, the center area between loading points is shear
free; whereas, the shear force may influence the overall deflection of 3-point bending.
154
Therefore, the DMA 3-point bending test may result in a greater creep strain than the
long-term test with 4-point bending due to shear force in this case. Moreover, the
transverse shear force may cause greater deformation when the bonding between wood
and matrix is not strong. The improvement on shear strength by the treating with
coupling agent has been mentioned in previous study [Herrera-Franco and Valadez-
González 2004]. The inferior property of shear resistance of F4 to that of F6 may be
assumed in this case. Consequently, due to the contribution of shear force, the master
curve may vastly over predict the overall strain particularly for F4 but not for F6.
However, a further investigation will be needed to find more evidences.
Another difficulty of using the DMA master curve is that the construction of the
master curve must be based on only one reference temperature; whereas, a real
environment is not consistent. The master curve cannot characterize the situation of an
initial high reference temperature with the real temperature decreasing afterward; instead,
the master curve would follow the initial trend, causing an overestimation.
Likewise, if the initial reference temperature was low and the real temperature
increased afterward, the master curve cannot characterize this situation either. Therefore,
the conventional single-phase master curve may mislead the prediction and cannot reflect
the real information. An approach that can deal with the effect of fluctuating temperatures
is required.
155
8.4 Temperature-Induced Strain Superposition Method
In this study, in order to model the effect of temperature directly applied on the
creep strain of a WPC product, a modified superposition approach – the temperature-
induced strain superposition (TISS) – is proposed in this thesis. Based on the concept of
the Boltzmann superposition principle, the additional stress causes the additional strain,
and the creep response can then be predicted simply by summing the individual responses
from each stress increment [McCrum et al. 1997]. This concept was employed in this
case, so that the increase of the temperature would also result in additional strain.
In conventional creep study, the experiment is usually conducted in a conditioned
environment; therefore, the typical curve of strain looks very similar in all related
research. In a practical situation, however, the temperature changes over time, and may
increase or decrease unpredictably. It was shown in the previous section that this change
of temperature may cause additional strain to the curve expected under original
conditions. In order to determine a more realistic behaviour, the TISS was developed to
simulate the additional strain caused by changing temperature and to attach the additional
strain to the base curve, which represents the expected creep strain.
The concept is similar to hereditary integral method and the difference is that
temperature changing instead of a multiple loading process was considered in this case,
which was illustrated in Figure 8-7. Based on the figure, the following steps describe the
development of the method.
156
1. Section t-t1: Assuming that there is a temperature function, T(t), that represents the
fluctuating temperature and that T(0) = T0 at t = 0, which is the initial temperature,
the resulting strain from the initial condition can be represented as:
( ) ( )
where σ0 is the applied stress, which remains constant during the period of the test;
T0 is the initial temperature; and, t is the global time. If the temperature remains
constant as T0, the result should be similar to the conventional creep strain curve,
such strain (1) in Figure 8-7. The additional temperature-induced strain is considered
based on this value.
2. Section t1-t2: Assuming the temperature increased from T0 to T1 at t1 (i.e. T(t1) = T1)
and the stress remained at σ0, the effect of T1 alone on the creep strain is:
( ) ( ) ( )
Like the conventional superposition principle, this increase in temperature caused an
additional strain; and, the total strain (2) in Figure 8-7 is equal to the strain under the
initial temperature plus the additional strain:
( ) ( ) [ ( ) ( )] ( )
The temperature-induced additional strain is:
( ) ( ) ( )
157
3. Section t2-t3: Assume that another temperature increment occurs at t = t2 (i.e.
T(t2)=T2). The effect of T2 alone on the creep strain is:
( ) ( ) ( )
However, not only should the second additional strain from the effect of changing
the temperature from T1 to T2 be considered, but the effect of the change from T2 to
T0 should be taken into account as well. Once the temperature increased, all the
additional strain should be accumulated; therefore, the total strain (3) in Figure 8-7 is:
( ) ( ) [ ( ) ( ] [ ( )
( )] ( )
This indicates that, after t2, the additional strain is:
[ ( ) ( ]
[ ( ) ( )] ( )
4. If there is a sequence of increases in temperature, the total strain is:
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
158
Figure 8-7. Concept scheme of the temperature-induced strain superposition (TISS)
For the conventional superposition principle, removing stresses also cause
changes in the strain. In this case, however, the specimen was still under loading, even
when the temperatures decreased. Moreover, unlike removing stress, the effect of
decreasing temperature may not result in a prompt recovery, since the specimen is still
under loading; instead, the effect of decreasing temperature may merely change the creep
rate of the material. Therefore, the basic assumption of this method is that only the
increase of temperature is considered to cause change in the creep strain. In other words,
the effect of decreasing temperatures is neglected.
In summary, therefore, three basic assumptions were made when conducting this
superposition:
159
1. There is a base curve at the initial temperature and under a constant load. The effect
of changing the temperature induces additional strains to this curve.
2. The effect of temperature is considered only when temperature is increased.
Decreasing temperature does not result in any increment or recovery.
3. Increasing temperature influences not only the last temperature, but also on the
previous temperature history. The effect of temperature should be considered for all
previous temperatures.
To verify the proposed method, the 40% load level groups of F4 and F6
specimens were used as examples. The developed STIC model (Equation 7-5) was
employed to fit the long-term creep strain of the first 50 days, with the corresponding
recorded temperatures to obtain the proper set of parameters using the Marquardt-
Levenberg nonlinear algorithm for further simulation, as shown in Table 8-5.
In addition, the temperature profile for TISS use, as shown in Figure 8-8,
considered only temperature increases. Following the proposed method, the sequent
additional strains were obtained and superimposed accordingly. The results of the
simulation are shown in Figures 8-9 and 8-10.
Table 8-5. Parameters Used for TISS Method
Formulations Parameters
R2 SEE
b u m n
F4-20% 0.0692 -11.3729 13632.15 0.1965 0.9529 7.32E-05
F4-30% 1.70E-05 1.9955 785.45 0.1762 0.9591 0.0001
F4-40% 4.04E-05 1.1133 33654.85 0.1761 0.9644 0.0002
F6-20% 2.06E-05 1.4369 144.13 0.1349 0.9868 8.91E-05
F6-30% 8.93E-06 1.9131 124.77 0.1418 0.9547 9.96E-05
F6-40% 8.10E-06 1.9643 126.98 0.1316 0.9844 8.05E-05
R2: coefficient of determination
160
Figure 8-8. Temperature profile for TISS use
The effect of temperature can clearly be observed in Figures 8-9 and 8-10. If the
temperature remained at the initial temperature of 25°C, as it would in conventional creep
studies, there would be no unexpected increment of strain. These figures also verify that
the STIC model can be valid for relatively long-term creep prediction, particularly for
fitting fluctuating temperatures. The additional strain induced by increasing temperatures
can be successfully simulated with the TISS method. This approach can be applied to
other comparable studies. Moreover, the assumption for this method that only increases
in temperature should be considered is confirmed.
It should be noted that, in this case, the measurement of the daily temperature was
made only once a day. More details, such as the hourly temperature, were not available.
The acquisition of a sufficient temperature profile may be able to improve the accuracy of
this simulation.
161
Figure 8-9. Model simulation of the temperature-induced strain superposition (F4)
162
Figure 8-10. Model simulation of the temperature-induced strain superposition (F6)
163
In addition, this long-term creep test was conducted in an ambient indoor
environment; hence, the temperature range was relatively narrow and steady. Since
changes in an outdoor environment are more complicated, in order to extend this method
to an environment of wider temperature ranges and test the real capacity of WPC
products, a field experiment of creep for WPC products is recommended.
An attempt was made to apply TISS in the simulation of long-term behaviour
using the short-term data obtained from the DMA 10-minute creep tests. The short-term
creep strain in the temperature range of 15 to 35°C was fitted with the STIC model, and
the parameters were calibrated. The corresponding long-term creep curves were then
simulated and are shown in Figure 8-11.
As previously discussed, the DMA master curve tends to overestimate the real
creep strain. In this case, the base curve was also the result of overestimation; therefore,
the overall result of simulation also considerably overestimated the real strain.
Consequently, the TISS method is limited to practical data, instead of that from short-
term and accelerated tests like DMA.
164
Figure 8-11. Temperature-induced strain superposition for DMA data
In general, the nonlinear constitutive equation was for isothermal conditions and
independent of temperature. In principle those isothermal constitutive equation is
applicable for describing creep behaviour under all isothermal states, but the kernel
functions at each temperature are different [Findley at al. 1989]. In previous studies, the
reduced time with the temperature shift factor and the theory of activation energy were
165
employed to deal with issue of varying temperatures [Findley et al. 1989; Pramanick and
Sain 2006b]. Their methods may also be possible solutions for this issue. However, the
temperature may not be a direct variable but an indirect adjustment for time. In this study,
effect of temperature was regarded as a direct variable to account for creep stain. By
applying the newly developed empirical STIC model, which was discussed in Chapter 7,
the temperature can be introduced into the creep strain prediction without additional
adjustments for the time. The temperature issue may be processed more efficiently.
Another potential solution may be to apply temperature shift factor obtained from
short-term creep test and TTSSP to shift all the segments at various temperatures to the
selected reference temperature, treating it as an isothermal condition and then modeling it
using conventional creep models such as power law model or Prony series. This
suggestion was not covered in this study; however, the future investigation is
recommended.
8.5 Summary
The validation of the master curves is a vital task prior to the practical application.
In this chapter, a 220-day creep experiment for the selected 6 groups of MPB-WPC
products, consisting of 2 formulations and 3 load levels, was conducted. The
corresponding master curves were constructed for comparison.
An unconditioned environment, particularly for temperature, caused unexpected
increases in strain. For temperature-sensitive material such as MPB-WPCs, the
166
information obtained from the conventional creep study method may be insufficient to
reflect practical applications.
The newly developed stress-temperature incorporated creep (STIC) model was
verified in this chapter with DMA creep tests at a temperature range of 15 to 70°C. The
equation was smoothly applied; however, the parameters obtained from different
temperature ranges cannot be universal.
The comparison between the long-term creep data and the DMA master curves
showed that DMA master curves tend to overestimate the real creep strain of a large
specimen. For the groups of the coupled MPC-WPC products (F6), the prediction of the
master curve agreed more reasonably with the long-term creep data; whereas, the master
curves showed considerable overestimation for the uncoupled products (F4). The testing
fixture and configuration and the properties of the material may affect the feasibility of
the TTSSP method and the prediction of master curves, and the loading history may also
influence the resultant master curves. Moreover, the TTSSP method using small
specimens resulted in relatively great variations; however, the confidence interval
overlapped with the long-term experimental data. Consequently, this method can be used
for a relatively conservative prediction.
To simulate the effect of fluctuating temperatures on the creep strain, the STIC
model and the proposed temperature-induced strain superposition (TISS) method were
employed in combination. The temperature-induced additional strain was successfully
simulated, indicating that the creep test under an ambient environment could successfully
simulate long-term creep, even with fluctuating temperatures. This approach and the
167
concept can be applied to comparable future studies. However, the TISS method is
limited to practical data, instead of that from short-term and accelerated tests like DMA.
168
CHAPTER 9. CONCLUSIONS AND FUTURE WORKS
In this research, a series of experiments have been conducted, including mountain
pine beetle attacked wood / plastic composite (MPB-WPC) prototype product
development, dynamic mechanical analysis (DMA), short-term creep tests for master
curve construction based on time-temperature-stress superposition principle (TTSSP),
and a long-term creep test. A newly established stress-temperature incorporated creep
(STIC) model, a modified Williams-Landel-Ferry (WLF) equation that incorporates the
variables of temperature and stress, and a newly developed temperature-induced strain
superposition (TISS) method have been introduced in this study.
The details of data analyses and discussions were presented in the previous
chapters. This chapter summarizes the important outcomes and findings of this research
and suggests potential future research works.
9.1 Mountain Pine Beetle Attacked Wood / Plastic Composite Products
MPB-WPC products were manufactured with various formulations, and their
mechanical properties were evaluated and analyzed. The MPB-WPC products showed
definite potential to be a value-added option for MPB-attacked wood.
The test results showed that the formulation affected the MPB-WPC products’
properties. A higher wood content resulted in a slightly higher density, lower strength,
but higher modulus. The performance of the uncoupled product was significantly inferior
to the coupled products; therefore, the properties of MPB-WPC products can be
significantly improved when a coupling agent, such as maleic anhydride polypropylene
169
(MAPP) is added. The surface condition of the product was also influenced by the
formulation. Moreover, depending on the formulation, WPCs can show very different
behaviours and appearances. Consideration of the formulation based on the use of the
final products is an important task.
9.2 Dynamic Mechanical Analysis
9.2.1 Viscoelasticity
The dynamic mechanical properties, including the storage modulus (E’), loss
modulus (E”) and mechanical loss factor (tan δ), based on the dynamic mechanical
analysis (DMA) spectra as a function of temperature, were investigated. The presence of
fillers in the polymer produced a more complex morphology of the composite system.
The content of filler/fibres and the use of a coupling agent can change the morphology of
the bulk polymer phase and that of the interphase, thus influencing the mechanical and
viscoelastic properties of the composites.
In summary, a higher content of wood flour resulted in higher E’, indicating better
stiffness; whereas, tan δ became lower. Furthermore, the existence of a coupling agent
also significantly improved E’, which can be attributed to the enhancement of the
interface property between the wood and the high-density polyethylene (HDPE), coupled
with MAPP. Furthermore, the addition of MAPP and a higher content of wood caused the
point of the transition to move toward a higher temperature.
170
Based on the modulus retention ability, the MAPP coupled products had better
modulus retention at elevated temperatures than did uncoupled products. A higher
content of wood flour and the addition of MAPP simply increased the value of modulus,
but did not significantly change the range of transition.
9.2.2 Time-Temperature-Stress Superposition and Master Curves
A series of short-term creep tests were conducted at various temperatures, and the
TTTSP was successfully applied in the construction of smooth master curves for the
prediction of long-term creep strain.
Based on the isochronal graphs, the creep strain of MPB-WPCs increased with
elevating temperatures and stresses at the same time point; in particular, the effect of
temperature on creep strain can be modeled with an exponential function. At lower
temperatures, the results showed that the strain increased linearly with increasing stress,
but may become nonlinear with elevating temperature. Moreover, the temperature had a
more significant influence on instantaneous creep than on transient creep.
According to this finding, a new creep model – the stress-temperature
incorporated creep (STIC) model – was established. This model smoothly introduced the
effect of temperature into the conventional power law creep equation, and the model can
be applied to predict the creep strain in which the effect of temperature is involved.
The MPB-WPC products were rheologically simple materials, and merely a
horizontal shift was needed for the time-temperature superposition; however, vertical
shifting would be needed for the time-stress superposition. The shift factor was
171
independent of the stress for horizontal shifts. In addition, the temperature- and stress-
shift factors used to construct master curves were fitted with the Williams-Landel-Ferry
(WLF equation); and, the results showed that the WLF equation is more suitable than the
Arrhenius equation for MPB-WPC products.
A temperature-stress hybrid shift factor and a modified WLF equation, which
incorporated variables of stress and temperature for the shift factor fitting, were studied;
and, the parameters were successfully calibrated. The application of this method can be
extended to curve shifting that involves the effects of both temperature and stress
simultaneously.
9.3 Creep Behaviour of Mountain Pine Beetle Attacked Wood / Plastic Composites
A 220-day long-term creep test was conducted under an unconditioned
environment. The results showed that the effect of elevating temperature caused
unexpected additional increases in creep strain. For temperature-sensitive materials such
as MPB-WPCs, the information obtained from the conventional creep study method may
be insufficient to reflect the practical application.
Comparisons between the long-term creep data and the DMA master curves
showed that the DMA master curves tended to overestimate the real creep strain of large
specimens and that the deviation increased with time. For the groups of coupled MPC-
WPC products, the prediction of the master curve agreed more reasonably with the long-
term data, whereas the master curves showed considerable overestimation for the
uncoupled products. The testing configuration and the properties of the material may
172
affect the feasibility of the TTSSP method and master curve prediction, and the loading
history may also influence the resultant master curves. In general, however, the master
curves constructed based on TTSSP cannot precisely predict the long-term creep strain,
but merely provide conservative under estimations.
To deal with the effect of fluctuating temperatures on the creep strain, the STIC
model and the proposed temperature-induced strain superposition (TISS) method were
established and employed. The additional temperature-induced strain and the overall
behaviour were successfully simulated with this combined methodology (STIC and TISS).
This indicates that, based on the TISS method, the creep test under an ambient
environment could successfully simulate the long-term creep strain, even under
fluctuating temperatures. This approach and concept may be applied to comparable future
studies. However, the TISS method is limited to practical data, instead of that from short-
term and accelerated tests like DMA.
9.4 Recommendations for Future Research
This work extended the research of creep behaviour from conventional constant
stress and temperature methods to introducing the effect of temperature into the creep
model and to dealing with the condition of fluctuating temperatures. However, there are
various potential topics that can be recommended for future research.
According to the fitting results, the newly developed STIC model can smoothly
predict creep strain under various stresses and temperatures. In this study, however, the
selected stresses were relatively small, in order to make sure that the products behaved
173
linearly. As well, the temperature range was chosen based on the practical environment
condition. Employing the model for higher load/stress levels and wider temperature
ranges would be an important task in the extension of the application of the model.
Furthermore, the nonlinear behaviour of the MPB-WPC products, which was not covered
in this study, also needs to be studied carefully in the future.
In order to limit the variables on creep behaviour, the effect of the formulation
was not considered in the model. It is suggested that incorporation of the effect of the
formulation into the model could improve the convenience and efficiency of product
development and evaluation.
It was found that master curves constructed using conventional DMA and TTSSP
tended to overestimate the creep strain. However, reasonable agreement was also
observed for the coupled WPC products, implying that there is the potential to apply this
method as long as an appropriate adjustment, such as multiplication by a factor of
correction, can be made. The accuracy of the master curve may be improved.
Furthermore, the application of temperature shift factor to make the environmental
condition of varying temperature as an isothermal one may be another possible solution
for the varying temperature issue, and then the master curve, in this case, may become a
comparable reference after a proper adjustment.
The STIC model was developed by incorporating the exponential effect of
temperature into a power law model. The power law model has been widely used in
various materials; however, the effect of temperature may be material dependent and may
174
have different influences on materials. Validation for the application of the STIC model
on other materials is needed, in order to extend its application.
Due to the nature of viscoelasticity and the sensitivity of WPCs to stress and
temperature, the combined effect of stress and temperature is a critical concern for the
application of WPC products, as was confirmed in this study. However, in practical
situations, instead of simple constant loading, cyclic loading and fluctuating temperatures
may influence the product simultaneously. This complex but vital topic has not yet been
studied.
Currently, there is no standard testing method to properly evaluate the creep
behaviour of WPC products. ASTM D7031 is the only available one, and it addresses the
testing method for the creep rupture for WPC products. It is not, however, sufficient to
deal with the temperature effect, since values obtained at one temperature cannot be
applied to other temperatures. It is important to establish an appropriate method to
evaluate this critical property.
In the TISS study, only the effect of increasing temperatures was considered;
therefore, the effect of decreasing temperatures could be a topic for future research.
Furthermore, the temperature was measured only once days; and, more details, such as
the hourly temperatures, were not available. More temperature details could be included
in future studies.
In addition, this long-term creep test was conducted under an ambient indoor
environment; hence, the fluctuation of temperatures was not severe and the range was
relatively narrow, which made it relatively simple to model and predict. Changes in an
175
outdoor environment are more complicated; and, in order to extend this method to an
environment with a wider temperature range and to test the real capacity of the WPC
product, a field experiment of creep is recommended. Knowledge from practical usage
will be invaluable in the verification of the models and methods established in this work.
176
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APPENDICES
APPENDIX A: SHIFT FACTORS
Shift factors, based on time-temperature-stress superposition, obtained from 10-min creep test for master curves constructing
introduced and discussed in Chapter 7, were summarized in this appendix. The numbers were presented as log (shift factor) in tables.
This appendix was divided into two parts:
A.1 Time-Temperature Superposition Shift Factors:
The first row presented the reference temperature, and the tabulated number presented the log (shift factor) for the
corresponding temperatures listed in the first column.
A.2 Time-Stress Superposition Shift Factors:
The time-stress superposition may require doubly shifts, horizontal and vertical. The first row presented the reference stress,
and the tabulated number presented the horizontal (H) and vertical (V) log (shift factor) for the corresponding stresses
listed in the second row and the corresponding temperatures listed in the first column.
187
A.1 Time-Temperature Superposition Shift Factors
F1- 1MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 -0.030 0.177 0.985 0.971 1.447 1.826 2.260 2.647 3.110 3.553 3.997 4.434 4.893 5.324 5.793 6.324 6.847 7.300
-40 0.021 0 0.193 0.976 0.980 1.433 1.832 2.230 2.630 3.120 3.579 3.976 4.459 4.903 5.349 5.821 6.310 6.877 7.330
-35 -0.223 -0.233 0 0.742 0.704 1.173 1.568 1.994 2.373 2.823 3.281 3.724 4.157 4.608 5.047 5.519 6.053 6.580 7.037
-30 -1.010 -1.053 -0.831 0 -0.003 0.459 0.890 1.313 1.723 2.180 2.640 3.092 3.518 3.967 4.405 4.879 5.413 5.942 6.394
-25 -1.021 -1.035 -0.811 -0.007 0 0.415 0.814 1.252 1.658 2.099 2.550 2.987 3.426 3.882 4.325 4.796 5.325 5.854 6.309
-20 -1.487 -1.494 -1.318 -0.494 -0.517 0 0.381 0.818 1.223 1.672 2.123 2.559 2.996 3.453 3.898 4.366 4.897 5.427 5.881
-15 -1.909 -1.896 -1.715 -0.927 -0.930 -0.431 0 0.428 0.823 1.277 1.736 2.166 2.599 3.056 3.502 3.974 4.503 5.029 5.487
-10 -2.333 -2.352 -2.174 -1.351 -1.332 -0.847 -0.472 0 0.379 0.830 1.282 1.720 2.148 2.604 3.051 3.520 4.055 4.579 5.035
-5 -2.753 -2.788 -2.588 -1.796 -1.803 -1.267 -0.897 -0.423 0 0.443 0.901 1.349 1.786 2.233 2.679 3.152 3.684 4.208 4.663
0 -3.206 -3.253 -3.056 -2.234 -2.265 -1.745 -1.327 -0.882 -0.492 0 0.447 0.898 1.342 1.800 2.239 2.705 3.242 3.771 4.224
5 -3.672 -3.724 -3.519 -2.682 -2.713 -2.189 -1.803 -1.331 -0.945 -0.468 0 0.443 0.887 1.350 1.796 2.261 2.798 3.325 3.779
10 -4.106 -4.141 -3.950 -3.136 -3.167 -2.619 -2.255 -1.777 -1.389 -0.913 -0.477 0 0.437 0.900 1.352 1.829 2.357 2.884 3.331
15 -4.577 -4.623 -4.382 -3.583 -3.631 -3.091 -2.722 -2.172 -1.829 -1.360 -0.901 -0.452 0 0.459 0.913 1.394 1.932 2.451 2.898
20 -5.014 -5.053 -4.822 -4.030 -4.081 -3.568 -3.141 -2.660 -2.272 -1.809 -1.376 -0.907 -0.460 0 0.450 0.935 1.479 2.003 2.448
25 -5.455 -5.524 -5.279 -4.456 -4.527 -3.994 -3.618 -3.133 -2.776 -2.306 -1.850 -1.356 -0.906 -0.469 0 0.480 1.026 1.554 2.010
30 -5.954 -5.983 -5.792 -4.946 -5.031 -4.490 -4.090 -3.622 -3.223 -2.795 -2.309 -1.843 -1.363 -0.961 -0.477 0 0.537 1.071 1.526
35 -6.520 -6.548 -6.354 -5.496 -5.567 -5.048 -4.655 -4.137 -3.775 -3.327 -2.867 -2.425 -1.918 -1.493 -1.016 -0.578 0 0.522 0.977
40 -7.053 -7.103 -6.896 -6.039 -6.149 -5.585 -5.200 -4.672 -4.339 -3.873 -3.419 -2.945 -2.459 -2.042 -1.594 -1.127 -0.563 0 0.444
45 -7.521 -7.534 -7.383 -6.493 -6.595 -6.075 -5.665 -5.140 -4.760 -4.355 -3.891 -3.444 -2.937 -2.506 -2.050 -1.593 -1.002 -0.493 0
188
F1- 3MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.256 0.582 1.015 1.465 1.908 2.323 2.788 3.190 3.650 4.087 4.554 4.995 5.464 5.949 6.455 6.953 7.460 7.961
-40 -0.314 0 0.306 0.717 1.161 1.614 2.033 2.479 2.900 3.360 3.803 4.268 4.712 5.182 5.665 6.165 6.667 7.174 7.679
-35 -0.657 -0.367 0 0.388 0.829 1.272 1.700 2.153 2.565 3.022 3.466 3.937 4.375 4.844 5.326 5.825 6.331 6.836 7.342
-30 -1.084 -0.774 -0.419 0 0.416 0.851 1.282 1.739 2.144 2.609 3.058 3.511 3.963 4.435 4.914 5.415 5.918 6.424 6.932
-25 -1.564 -1.242 -0.869 -0.526 0 0.418 0.837 1.301 1.720 2.174 2.621 3.084 3.530 4.004 4.482 4.977 5.483 5.991 6.498
-20 -2.021 -1.694 -1.371 -0.968 -0.488 0 0.399 0.856 1.286 1.753 2.191 2.652 3.094 3.569 4.050 4.549 5.052 5.560 6.067
-15 -2.476 -2.173 -1.813 -1.395 -0.917 -0.496 0 0.441 0.869 1.342 1.787 2.244 2.691 3.166 3.647 4.142 4.645 5.157 5.658
-10 -2.911 -2.599 -2.269 -1.858 -1.409 -0.952 -0.485 0 0.412 0.882 1.334 1.798 2.235 2.706 3.188 3.687 4.187 4.698 5.204
-5 -3.330 -3.012 -2.699 -2.269 -1.813 -1.361 -0.911 -0.470 0 0.457 0.912 1.379 1.832 2.297 2.782 3.274 3.780 4.290 4.795
0 -3.824 -3.492 -3.211 -2.770 -2.289 -1.853 -1.363 -0.912 -0.487 0 0.439 0.919 1.371 1.842 2.320 2.815 3.318 3.830 4.335
5 -4.323 -3.943 -3.626 -3.205 -2.735 -2.305 -1.813 -1.362 -0.959 -0.465 0 0.472 0.926 1.404 1.886 2.390 2.878 3.387 3.892
10 -4.811 -4.420 -4.088 -3.676 -3.246 -2.813 -2.288 -1.825 -1.400 -0.965 -0.487 0 0.445 0.925 1.413 1.900 2.408 2.923 3.429
15 -5.244 -4.894 -4.576 -4.117 -3.661 -3.247 -2.780 -2.298 -1.837 -1.423 -0.927 -0.465 0 0.475 0.971 1.461 1.969 2.484 2.989
20 -5.712 -5.369 -5.041 -4.590 -4.132 -3.724 -3.214 -2.772 -2.321 -1.891 -1.429 -0.931 -0.465 0 0.489 0.984 1.506 2.010 2.515
25 -6.219 -5.830 -5.516 -5.089 -4.642 -4.178 -3.713 -3.259 -2.835 -2.363 -1.902 -1.381 -0.954 -0.502 0 0.494 1.030 1.544 2.050
30 -6.687 -6.331 -6.017 -5.573 -5.149 -4.688 -4.191 -3.756 -3.277 -2.858 -2.378 -1.899 -1.430 -0.970 -0.479 0 0.526 1.041 1.548
35 -7.197 -6.848 -6.517 -6.081 -5.670 -5.198 -4.723 -4.252 -3.831 -3.398 -2.910 -2.399 -1.963 -1.502 -1.002 -0.534 0 0.514 1.022
40 -7.707 -7.357 -7.040 -6.604 -6.178 -5.716 -5.224 -4.802 -4.320 -3.911 -3.463 -2.926 -2.486 -1.990 -1.578 -1.016 -0.518 0 0.505
45 -8.215 -7.892 -7.566 -7.099 -6.691 -6.213 -5.733 -5.267 -4.832 -4.416 -3.953 -3.430 -2.997 -2.482 -2.037 -1.541 -1.003 -0.493 0
189
F1- 5MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.271 0.648 1.095 1.566 1.998 2.434 2.894 3.316 3.788 4.223 4.734 5.153 5.639 6.135 6.654 7.232 7.785 8.300
-40 -0.310 0 0.358 0.786 1.274 1.711 2.135 2.583 3.010 3.481 3.923 4.432 4.857 5.335 5.831 6.348 6.928 7.480 7.997
-35 -0.694 -0.451 0 0.415 0.894 1.330 1.758 2.206 2.640 3.112 3.552 4.052 4.485 4.958 5.454 5.970 6.551 7.104 7.620
-30 -1.178 -0.895 -0.463 0 0.457 0.888 1.323 1.781 2.204 2.669 3.114 3.613 4.051 4.520 5.021 5.537 6.118 6.671 7.187
-25 -1.700 -1.393 -0.945 -0.515 0 0.418 0.856 1.312 1.760 2.220 2.653 3.152 3.591 4.062 4.556 5.073 5.653 6.206 6.722
-20 -2.120 -1.810 -1.391 -0.995 -0.492 0 0.425 0.885 1.337 1.801 2.228 2.729 3.173 3.643 4.139 4.654 5.237 5.789 6.304
-15 -2.618 -2.281 -1.847 -1.410 -0.913 -0.448 0 0.451 0.894 1.365 1.810 2.304 2.740 3.213 3.710 4.226 4.807 5.360 5.877
-10 -3.046 -2.753 -2.313 -1.866 -1.410 -0.939 -0.509 0 0.437 0.905 1.359 1.857 2.292 2.756 3.258 3.775 4.354 4.906 5.424
-5 -3.525 -3.198 -2.778 -2.313 -1.859 -1.380 -0.947 -0.491 0 0.458 0.913 1.417 1.859 2.320 2.817 3.333 3.916 4.468 4.986
0 -3.978 -3.628 -3.246 -2.783 -2.332 -1.851 -1.393 -0.972 -0.458 0 0.449 0.955 1.407 1.877 2.373 2.890 3.470 4.022 4.539
5 -4.456 -4.104 -3.692 -3.252 -2.768 -2.300 -1.874 -1.441 -0.927 -0.470 0 0.496 0.949 1.423 1.914 2.432 3.010 3.562 4.081
10 -4.956 -4.580 -4.182 -3.737 -3.250 -2.799 -2.354 -1.951 -1.423 -0.982 -0.490 0 0.451 0.932 1.428 1.947 2.527 3.080 3.593
15 -5.412 -5.063 -4.658 -4.237 -3.724 -3.267 -2.834 -2.395 -1.848 -1.452 -0.966 -0.477 0 0.469 0.976 1.502 2.075 2.627 3.145
20 -5.877 -5.508 -5.144 -4.708 -4.232 -3.737 -3.318 -2.881 -2.348 -1.923 -1.443 -0.922 -0.482 0 0.495 1.030 1.609 2.158 2.675
25 -6.382 -6.031 -5.619 -5.214 -4.682 -4.224 -3.801 -3.394 -2.848 -2.423 -1.936 -1.430 -0.978 -0.487 0 0.528 1.115 1.670 2.187
30 -6.912 -6.524 -6.110 -5.740 -5.214 -4.738 -4.325 -3.908 -3.367 -2.958 -2.448 -1.961 -1.448 -1.029 -0.530 0 0.577 1.151 1.669
35 -7.491 -7.083 -6.742 -6.346 -5.821 -5.329 -4.901 -4.477 -3.937 -3.514 -3.066 -2.534 -2.045 -1.618 -1.116 -0.561 0 0.572 1.111
40 -8.047 -7.668 -7.336 -6.891 -6.355 -5.878 -5.480 -5.036 -4.495 -4.101 -3.639 -3.115 -2.597 -2.166 -1.687 -1.188 -0.526 0 0.534
45 -8.566 -8.207 -7.830 -7.457 -6.884 -6.394 -6.037 -5.584 -5.036 -4.615 -4.135 -3.653 -3.129 -2.734 -2.224 -1.700 -1.058 -0.548 0
190
F1- 8MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.292 0.708 1.174 1.643 2.096 2.543 3.003 3.481 3.958 4.437 4.906 5.400 5.892 6.398 6.960 7.554 8.117 8.648
-40 -0.354 0 0.393 0.840 1.305 1.764 2.225 2.683 3.164 3.630 4.128 4.578 5.082 5.566 6.081 6.633 7.231 7.789 8.332
-35 -0.781 -0.443 0 0.419 0.880 1.357 1.812 2.270 2.747 3.216 3.705 4.169 4.667 5.151 5.668 6.221 6.817 7.374 7.917
-30 -1.230 -0.909 -0.465 0 0.445 0.907 1.379 1.833 2.318 2.785 3.274 3.741 4.233 4.720 5.232 5.789 6.385 6.938 7.486
-25 -1.680 -1.407 -0.966 -0.508 0 0.447 0.918 1.383 1.852 2.320 2.806 3.280 3.775 4.256 4.773 5.330 5.925 6.480 7.025
-20 -2.139 -1.905 -1.415 -1.024 -0.492 0 0.455 0.917 1.401 1.863 2.346 2.819 3.311 3.800 4.314 4.871 5.463 6.021 6.566
-15 -2.640 -2.387 -1.891 -1.492 -0.941 -0.503 0 0.457 0.935 1.401 1.884 2.355 2.854 3.335 3.848 4.409 5.005 5.560 6.105
-10 -3.106 -2.858 -2.387 -1.971 -1.403 -0.979 -0.469 0 0.467 0.935 1.429 1.894 2.388 2.873 3.382 3.944 4.543 5.094 5.644
-5 -3.575 -3.328 -2.879 -2.434 -1.880 -1.459 -0.943 -0.485 0 0.462 0.957 1.430 1.925 2.402 2.919 3.481 4.076 4.631 5.176
0 -4.042 -3.826 -3.346 -2.939 -2.368 -1.924 -1.409 -0.944 -0.479 0 0.487 0.966 1.465 1.944 2.461 3.018 3.611 4.169 4.712
5 -4.529 -4.314 -3.826 -3.426 -2.875 -2.428 -1.903 -1.433 -0.967 -0.478 0 0.476 0.981 1.473 1.975 2.543 3.141 3.693 4.242
10 -5.021 -4.779 -4.321 -3.929 -3.355 -2.900 -2.399 -1.927 -1.450 -0.975 -0.480 0 0.495 0.987 1.508 2.061 2.652 3.208 3.752
15 -5.534 -5.291 -4.797 -4.419 -3.849 -3.397 -2.876 -2.405 -1.959 -1.477 -0.989 -0.488 0 0.491 1.013 1.575 2.165 2.719 3.260
20 -6.003 -5.792 -5.284 -4.919 -4.355 -3.898 -3.385 -2.907 -2.440 -1.949 -1.487 -0.967 -0.510 0 0.520 1.084 1.693 2.230 2.779
25 -6.530 -6.309 -5.798 -5.435 -4.862 -4.408 -3.861 -3.426 -2.967 -2.461 -1.975 -1.486 -1.006 -0.506 0 0.562 1.175 1.721 2.263
30 -7.065 -6.875 -6.372 -6.016 -5.427 -4.951 -4.450 -4.002 -3.518 -3.044 -2.525 -2.043 -1.554 -1.086 -0.520 0 0.609 1.173 1.722
35 -7.693 -7.482 -6.994 -6.598 -6.054 -5.560 -5.063 -4.605 -4.147 -3.628 -3.171 -2.645 -2.167 -1.721 -1.145 -0.608 0 0.563 1.116
40 -8.257 -8.048 -7.539 -7.150 -6.612 -6.143 -5.583 -5.183 -4.741 -4.209 -3.754 -3.246 -2.699 -2.266 -1.724 -1.180 -0.583 0 0.544
45 -8.781 -8.593 -8.119 -7.666 -7.116 -6.721 -6.152 -5.718 -5.263 -4.740 -4.270 -3.772 -3.236 -2.824 -2.271 -1.720 -1.108 -0.540 0
191
F2- 1MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.128 0.514 0.897 1.323 1.745 2.138 2.597 3.027 3.463 3.923 4.361 4.812 5.327 5.745 6.274 6.769 7.276 7.737
-40 -0.187 0 0.329 0.696 1.123 1.551 1.952 2.407 2.848 3.295 3.744 4.175 4.650 5.133 5.567 6.086 6.574 7.090 7.552
-35 -0.557 -0.426 0 0.314 0.731 1.168 1.577 2.025 2.462 2.901 3.367 3.795 4.256 4.754 5.175 5.709 6.195 6.710 7.172
-30 -0.952 -0.787 -0.403 0 0.393 0.816 1.229 1.693 2.116 2.567 3.036 3.460 3.917 4.421 4.846 5.378 5.863 6.377 6.839
-25 -1.397 -1.225 -0.883 -0.485 0 0.397 0.789 1.257 1.707 2.131 2.591 3.021 3.482 3.978 4.407 4.935 5.422 5.934 6.398
-20 -1.824 -1.693 -1.339 -0.963 -0.499 0 0.366 0.813 1.259 1.701 2.155 2.576 3.058 3.536 3.962 4.492 4.980 5.488 5.956
-15 -2.214 -2.128 -1.746 -1.350 -0.927 -0.496 0 0.417 0.862 1.307 1.782 2.206 2.663 3.161 3.585 4.114 4.601 5.119 5.577
-10 -2.696 -2.540 -2.197 -1.773 -1.382 -0.914 -0.501 0 0.434 0.877 1.357 1.789 2.241 2.733 3.154 3.691 4.177 4.688 5.159
-5 -3.192 -2.974 -2.646 -2.263 -1.837 -1.372 -0.953 -0.459 0 0.430 0.909 1.351 1.814 2.294 2.720 3.254 3.745 4.256 4.727
0 -3.601 -3.425 -3.101 -2.694 -2.278 -1.814 -1.383 -0.899 -0.441 0 0.469 0.913 1.386 1.865 2.294 2.828 3.320 3.834 4.303
5 -4.101 -3.913 -3.592 -3.171 -2.763 -2.300 -1.870 -1.400 -0.915 -0.497 0 0.430 0.898 1.397 1.820 2.349 2.839 3.345 3.814
10 -4.535 -4.340 -4.070 -3.649 -3.207 -2.757 -2.352 -1.819 -1.370 -0.935 -0.443 0 0.464 0.969 1.390 1.920 2.416 2.920 3.387
15 -4.988 -4.805 -4.514 -4.113 -3.672 -3.222 -2.784 -2.291 -1.833 -1.409 -0.937 -0.449 0 0.488 0.928 1.463 1.951 2.469 2.933
20 -5.476 -5.313 -4.998 -4.621 -4.173 -3.738 -3.281 -2.752 -2.329 -1.910 -1.434 -0.976 -0.503 0 0.436 0.976 1.469 1.980 2.461
25 -5.937 -5.753 -5.414 -5.046 -4.604 -4.205 -3.740 -3.181 -2.765 -2.326 -1.883 -1.445 -0.935 -0.444 0 0.529 1.026 1.546 2.014
30 -6.436 -6.289 -5.966 -5.602 -5.133 -4.690 -4.274 -3.737 -3.285 -2.909 -2.440 -1.975 -1.527 -0.956 -0.496 0 0.489 1.010 1.485
35 -6.960 -6.757 -6.483 -6.049 -5.642 -5.181 -4.789 -4.228 -3.767 -3.372 -2.932 -2.467 -1.974 -1.482 -1.018 -0.477 0 0.522 0.996
40 -7.465 -7.308 -6.961 -6.570 -6.150 -5.702 -5.294 -4.707 -4.320 -3.890 -3.446 -2.978 -2.504 -1.994 -1.557 -1.011 -0.510 0 0.475
45 -7.978 -7.793 -7.469 -7.063 -6.660 -6.207 -5.805 -5.223 -4.802 -4.386 -3.966 -3.489 -3.008 -2.495 -2.031 -1.492 -1.013 -0.488 0
192
F2- 3MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.258 0.642 1.083 1.522 1.958 2.382 2.853 3.300 3.704 4.146 4.611 5.044 5.546 5.973 6.491 7.007 7.540 8.040
-40 -0.322 0 0.362 0.787 1.228 1.671 2.087 2.579 3.015 3.416 3.869 4.325 4.760 5.266 5.701 6.212 6.731 7.263 7.765
-35 -0.726 -0.401 0 0.401 0.832 1.279 1.708 2.177 2.625 3.027 3.476 3.929 4.365 4.869 5.303 5.815 6.334 6.864 7.364
-30 -1.172 -0.825 -0.479 0 0.417 0.854 1.292 1.780 2.206 2.610 3.064 3.521 3.948 4.461 4.895 5.407 5.921 6.453 6.954
-25 -1.652 -1.331 -0.939 -0.469 0 0.422 0.855 1.341 1.783 2.182 2.634 3.085 3.520 4.029 4.465 4.975 5.498 6.030 6.531
-20 -2.136 -1.800 -1.403 -0.930 -0.457 0 0.419 0.904 1.352 1.761 2.200 2.656 3.090 3.594 4.026 4.539 5.061 5.593 6.094
-15 -2.567 -2.220 -1.820 -1.393 -0.897 -0.464 0 0.468 0.919 1.323 1.781 2.220 2.663 3.172 3.605 4.110 4.633 5.165 5.666
-10 -3.044 -2.675 -2.309 -1.857 -1.388 -0.959 -0.510 0 0.443 0.856 1.316 1.768 2.200 2.708 3.141 3.654 4.175 4.707 5.208
-5 -3.496 -3.127 -2.762 -2.318 -1.825 -1.415 -0.961 -0.510 0 0.407 0.867 1.329 1.762 2.262 2.700 3.209 3.731 4.265 4.764
0 -3.915 -3.558 -3.183 -2.766 -2.247 -1.845 -1.416 -0.910 -0.404 0 0.450 0.910 1.353 1.859 2.283 2.795 3.320 3.851 4.354
5 -4.389 -4.028 -3.611 -3.222 -2.729 -2.305 -1.840 -1.352 -0.888 -0.452 0 0.456 0.896 1.413 1.846 2.355 2.872 3.404 3.905
10 -4.871 -4.477 -4.103 -3.664 -3.189 -2.789 -2.297 -1.858 -1.351 -0.915 -0.478 0 0.444 0.958 1.405 1.914 2.433 2.965 3.465
15 -5.319 -4.929 -4.565 -4.142 -3.660 -3.192 -2.746 -2.297 -1.818 -1.365 -0.953 -0.465 0 0.509 0.951 1.465 1.988 2.523 3.027
20 -5.848 -5.438 -5.036 -4.635 -4.175 -3.728 -3.252 -2.812 -2.309 -1.864 -1.453 -0.929 -0.530 0 0.449 0.965 1.494 2.019 2.528
25 -6.276 -5.862 -5.519 -5.095 -4.645 -4.183 -3.726 -3.288 -2.786 -2.338 -1.935 -1.395 -0.963 -0.451 0 0.515 1.048 1.580 2.078
30 -6.813 -6.361 -6.043 -5.579 -5.124 -4.671 -4.214 -3.773 -3.304 -2.842 -2.424 -1.871 -1.480 -0.954 -0.504 0 0.535 1.070 1.578
35 -7.326 -6.955 -6.547 -6.141 -5.632 -5.266 -4.770 -4.315 -3.799 -3.386 -2.969 -2.423 -2.021 -1.493 -1.055 -0.513 0 0.524 1.045
40 -7.887 -7.428 -7.114 -6.697 -6.185 -5.764 -5.294 -4.844 -4.381 -3.912 -3.493 -2.929 -2.575 -2.030 -1.572 -1.045 -0.523 0 0.514
45 -8.385 -7.984 -7.632 -7.185 -6.699 -6.290 -5.809 -5.361 -4.886 -4.455 -3.993 -3.448 -3.063 -2.543 -2.098 -1.552 -1.033 -0.519 0
193
F2- 5MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.363 0.776 1.238 1.700 2.124 2.549 2.982 3.426 3.864 4.298 4.737 5.184 5.641 6.116 6.656 7.209 7.701 8.197
-40 -0.398 0 0.394 0.850 1.319 1.754 2.166 2.597 3.036 3.478 3.909 4.353 4.795 5.253 5.727 6.266 6.823 7.314 7.811
-35 -0.851 -0.439 0 0.424 0.899 1.344 1.766 2.191 2.643 3.073 3.504 3.956 4.395 4.855 5.330 5.871 6.429 6.916 7.405
-30 -1.294 -0.923 -0.465 0 0.450 0.889 1.317 1.758 2.189 2.628 3.055 3.496 3.940 4.397 4.876 5.414 5.973 6.458 6.963
-25 -1.787 -1.398 -0.955 -0.476 0 0.419 0.848 1.288 1.728 2.164 2.592 3.039 3.478 3.938 4.410 4.955 5.513 5.998 6.495
-20 -2.255 -1.860 -1.374 -0.954 -0.484 0 0.412 0.849 1.297 1.734 2.163 2.612 3.047 3.510 3.980 4.526 5.080 5.569 6.065
-15 -2.671 -2.282 -1.832 -1.409 -0.951 -0.481 0 0.422 0.866 1.317 1.750 2.189 2.624 3.091 3.568 4.107 4.665 5.150 5.650
-10 -3.104 -2.732 -2.241 -1.817 -1.358 -0.899 -0.462 0 0.429 0.879 1.327 1.772 2.206 2.655 3.143 3.675 4.237 4.726 5.223
-5 -3.545 -3.176 -2.688 -2.278 -1.811 -1.358 -0.869 -0.471 0 0.444 0.883 1.339 1.782 2.226 2.710 3.249 3.806 4.297 4.794
0 -3.978 -3.610 -3.155 -2.736 -2.246 -1.813 -1.348 -0.913 -0.467 0 0.437 0.890 1.344 1.801 2.270 2.811 3.367 3.855 4.353
5 -4.451 -4.079 -3.577 -3.194 -2.719 -2.278 -1.795 -1.351 -0.927 -0.448 0 0.445 0.898 1.360 1.838 2.376 2.941 3.426 3.928
10 -4.869 -4.535 -4.044 -3.634 -3.172 -2.733 -2.248 -1.803 -1.365 -0.923 -0.430 0 0.446 0.915 1.396 1.929 2.486 2.981 3.476
15 -5.335 -4.989 -4.499 -4.085 -3.638 -3.190 -2.676 -2.290 -1.792 -1.360 -0.892 -0.439 0 0.461 0.947 1.493 2.047 2.530 3.032
20 -5.808 -5.480 -4.956 -4.583 -4.095 -3.665 -3.143 -2.730 -2.277 -1.825 -1.368 -0.891 -0.488 0 0.481 1.030 1.601 2.083 2.572
25 -6.318 -5.941 -5.440 -5.047 -4.555 -4.142 -3.655 -3.244 -2.757 -2.318 -1.829 -1.372 -0.945 -0.450 0 0.545 1.124 1.613 2.103
30 -6.849 -6.548 -5.987 -5.589 -5.127 -4.679 -4.171 -3.756 -3.315 -2.847 -2.385 -1.934 -1.516 -1.007 -0.527 0 0.569 1.076 1.569
35 -7.418 -7.086 -6.531 -6.166 -5.710 -5.244 -4.726 -4.334 -3.894 -3.405 -2.955 -2.459 -2.067 -1.609 -1.136 -0.598 0 0.501 1.002
40 -7.937 -7.582 -7.030 -6.642 -6.224 -5.793 -5.242 -4.813 -4.382 -3.904 -3.428 -2.966 -2.552 -2.100 -1.618 -1.058 -0.498 0 0.488
45 -8.440 -8.133 -7.507 -7.148 -6.698 -6.253 -5.737 -5.342 -4.883 -4.411 -3.944 -3.499 -3.046 -2.608 -2.089 -1.537 -1.000 -0.486 0
194
F2- 8MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.172 0.677 1.056 1.574 2.058 2.441 2.978 3.377 3.839 4.360 4.767 5.273 5.764 6.280 6.836 7.470 8.082 8.662
-40 -0.235 0 0.486 0.872 1.390 1.871 2.236 2.783 3.187 3.647 4.169 4.574 5.080 5.576 6.090 6.644 7.278 7.886 8.469
-35 -0.789 -0.573 0 0.352 0.869 1.373 1.764 2.284 2.698 3.149 3.670 4.095 4.584 5.077 5.596 6.145 6.779 7.395 7.970
-30 -1.150 -0.969 -0.364 0 0.498 0.995 1.386 1.909 2.324 2.771 3.285 3.710 4.200 4.700 5.221 5.768 6.403 7.025 7.593
-25 -1.689 -1.477 -0.930 -0.555 0 0.482 0.874 1.418 1.829 2.276 2.798 3.215 3.713 4.209 4.725 5.275 5.907 6.523 7.098
-20 -2.235 -2.003 -1.435 -1.045 -0.544 0 0.380 0.925 1.351 1.802 2.318 2.739 3.222 3.727 4.245 4.792 5.425 6.041 6.615
-15 -2.613 -2.389 -1.842 -1.460 -0.925 -0.429 0 0.527 0.952 1.412 1.917 2.340 2.841 3.339 3.853 4.403 5.036 5.653 6.226
-10 -3.149 -2.948 -2.374 -2.008 -1.462 -0.964 -0.557 0 0.420 0.883 1.393 1.831 2.315 2.839 3.335 3.884 4.531 5.146 5.726
-5 -3.588 -3.373 -2.829 -2.456 -1.882 -1.411 -1.014 -0.467 0 0.456 0.968 1.417 1.904 2.394 2.915 3.460 4.088 4.706 5.283
0 -4.042 -3.857 -3.272 -2.919 -2.357 -1.888 -1.476 -0.914 -0.462 0 0.504 0.951 1.452 1.943 2.458 3.007 3.635 4.253 4.834
5 -4.523 -4.360 -3.786 -3.443 -2.891 -2.371 -1.954 -1.403 -0.998 -0.542 0 0.451 0.954 1.458 1.974 2.518 3.149 3.766 4.340
10 -4.986 -4.826 -4.285 -3.924 -3.370 -2.843 -2.451 -1.890 -1.472 -0.986 -0.429 0 0.502 1.004 1.527 2.058 2.689 3.305 3.881
15 -5.484 -5.310 -4.750 -4.436 -3.833 -3.359 -2.928 -2.383 -1.944 -1.459 -0.920 -0.497 0 0.498 1.026 1.581 2.198 2.812 3.391
20 -5.996 -5.826 -5.240 -4.933 -4.327 -3.846 -3.395 -2.872 -2.430 -1.942 -1.437 -0.995 -0.460 0 0.519 1.074 1.703 2.317 2.900
25 -6.511 -6.344 -5.774 -5.477 -4.825 -4.347 -3.942 -3.391 -2.975 -2.469 -1.958 -1.509 -0.977 -0.505 0 0.556 1.186 1.800 2.385
30 -7.040 -6.898 -6.317 -6.040 -5.353 -4.935 -4.518 -3.952 -3.517 -3.016 -2.500 -2.072 -1.571 -1.059 -0.535 0 0.632 1.258 1.826
35 -7.673 -7.534 -6.955 -6.649 -6.051 -5.519 -5.120 -4.537 -4.157 -3.644 -3.165 -2.670 -2.192 -1.707 -1.231 -0.637 0 0.618 1.212
40 -8.288 -8.118 -7.601 -7.290 -6.623 -6.118 -5.782 -5.196 -4.790 -4.266 -3.764 -3.331 -2.800 -2.284 -1.835 -1.218 -0.642 0 0.589
45 -8.879 -8.708 -8.180 -7.828 -7.236 -6.749 -6.343 -5.794 -5.360 -4.855 -4.357 -3.899 -3.388 -2.875 -2.454 -1.817 -1.201 -0.572 0
195
F3-1MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.162 0.335 0.657 1.174 1.596 2.002 2.417 2.840 3.292 3.731 4.205 4.641 5.095 5.549 6.042 6.566 7.023 7.451
-40 -0.143 0 0.200 0.481 1.018 1.443 1.840 2.233 2.671 3.129 3.552 4.040 4.487 4.928 5.381 5.878 6.380 6.855 7.292
-35 -0.369 -0.237 0 0.239 0.725 1.160 1.561 1.961 2.384 2.862 3.317 3.770 4.205 4.662 5.111 5.607 6.141 6.584 7.032
-30 -0.744 -0.598 -0.403 0 0.415 0.818 1.248 1.683 2.094 2.528 2.969 3.455 3.900 4.345 4.793 5.290 5.807 6.266 6.707
-25 -1.235 -1.113 -0.885 -0.603 0 0.369 0.770 1.190 1.634 2.067 2.490 2.974 3.424 3.866 4.315 4.813 5.321 5.794 6.222
-20 -1.688 -1.523 -1.311 -1.012 -0.470 0 0.388 0.800 1.249 1.700 2.130 2.602 3.049 3.497 3.940 4.444 4.957 5.411 5.862
-15 -2.050 -1.932 -1.717 -1.386 -0.852 -0.457 0 0.387 0.842 1.293 1.742 2.189 2.641 3.096 3.539 4.036 4.557 5.012 5.462
-10 -2.451 -2.379 -2.162 -1.807 -1.275 -0.887 -0.479 0 0.432 0.885 1.339 1.800 2.241 2.690 3.145 3.637 4.157 4.610 5.061
-5 -2.923 -2.795 -2.618 -2.280 -1.728 -1.323 -0.917 -0.453 0 0.438 0.888 1.365 1.804 2.254 2.706 3.198 3.713 4.169 4.618
0 -3.368 -3.261 -3.059 -2.757 -2.188 -1.766 -1.353 -0.924 -0.477 0 0.446 0.915 1.371 1.823 2.264 2.757 3.274 3.730 4.179
5 -3.794 -3.697 -3.523 -3.191 -2.639 -2.231 -1.822 -1.354 -0.909 -0.466 0 0.456 0.914 1.373 1.822 2.313 2.831 3.282 3.737
10 -4.263 -4.192 -3.983 -3.677 -3.131 -2.707 -2.313 -1.840 -1.392 -0.965 -0.480 0 0.452 0.915 1.380 1.875 2.384 2.844 3.297
15 -4.712 -4.644 -4.414 -4.142 -3.584 -3.180 -2.765 -2.292 -1.819 -1.392 -0.941 -0.460 0 0.454 0.918 1.423 1.947 2.393 2.848
20 -5.210 -5.118 -4.895 -4.597 -4.040 -3.654 -3.218 -2.774 -2.286 -1.895 -1.420 -0.955 -0.455 0 0.457 0.963 1.495 1.949 2.399
25 -5.664 -5.558 -5.347 -5.106 -4.515 -4.092 -3.666 -3.228 -2.750 -2.342 -1.865 -1.406 -0.939 -0.462 0 0.508 1.037 1.505 1.951
30 -6.161 -6.036 -5.852 -5.570 -4.997 -4.606 -4.177 -3.708 -3.257 -2.837 -2.371 -1.899 -1.424 -0.960 -0.512 0 0.520 0.988 1.442
35 -6.652 -6.599 -6.425 -6.095 -5.539 -5.126 -4.725 -4.278 -3.773 -3.356 -2.920 -2.428 -1.964 -1.518 -1.012 -0.519 0 0.456 0.908
40 -7.137 -7.089 -6.884 -6.592 -6.016 -5.608 -5.207 -4.729 -4.270 -3.841 -3.414 -2.923 -2.441 -1.994 -1.498 -1.011 -0.504 0 0.436
45 -7.635 -7.516 -7.350 -7.039 -6.454 -6.080 -5.644 -5.202 -4.746 -4.319 -3.880 -3.362 -2.901 -2.448 -1.945 -1.462 -0.934 -0.485 0
196
F3- 3 MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.230 0.760 1.171 1.645 2.131 2.567 3.045 3.475 3.957 4.423 4.894 5.332 5.852 6.386 6.952 7.557 8.098 8.620
-40 -0.471 0 0.272 0.681 1.165 1.656 2.077 2.538 2.985 3.478 3.946 4.407 4.845 5.375 5.898 6.465 7.070 7.611 8.133
-35 -0.812 -0.291 0 0.380 0.855 1.340 1.790 2.257 2.685 3.178 3.655 4.116 4.554 5.085 5.608 6.174 6.778 7.320 7.842
-30 -1.269 -0.789 -0.441 0 0.444 0.934 1.375 1.858 2.281 2.756 3.232 3.698 4.136 4.664 5.187 5.750 6.356 6.899 7.419
-25 -1.727 -1.237 -0.924 -0.526 0 0.477 0.910 1.395 1.817 2.305 2.774 3.240 3.678 4.201 4.726 5.294 5.903 6.439 6.967
-20 -2.238 -1.773 -1.481 -1.064 -0.547 0 0.417 0.905 1.344 1.837 2.312 2.773 3.210 3.740 4.265 4.834 5.436 5.979 6.499
-15 -2.712 -2.214 -1.891 -1.444 -0.950 -0.450 0 0.472 0.911 1.410 1.890 2.350 2.788 3.320 3.841 4.408 5.011 5.554 6.075
-10 -3.193 -2.668 -2.364 -1.935 -1.408 -0.951 -0.503 0 0.432 0.933 1.416 1.884 2.316 2.847 3.369 3.931 4.539 5.081 5.602
-5 -3.631 -3.171 -2.790 -2.407 -1.903 -1.398 -0.925 -0.445 0 0.485 0.975 1.451 1.882 2.410 2.940 3.510 4.109 4.652 5.172
0 -4.109 -3.650 -3.312 -2.886 -2.382 -1.924 -1.423 -0.967 -0.522 0 0.479 0.957 1.405 1.933 2.458 3.028 3.628 4.171 4.692
5 -4.595 -4.181 -3.789 -3.390 -2.908 -2.421 -1.928 -1.436 -1.032 -0.491 0 0.467 0.917 1.453 1.971 2.534 3.146 3.689 4.205
10 -5.064 -4.640 -4.261 -3.876 -3.375 -2.920 -2.354 -1.906 -1.491 -0.995 -0.492 0 0.448 0.988 1.509 2.061 2.668 3.211 3.733
15 -5.530 -5.119 -4.726 -4.326 -3.821 -3.365 -2.817 -2.363 -1.921 -1.432 -0.929 -0.420 0 0.536 1.060 1.628 2.238 2.771 3.290
20 -6.075 -5.649 -5.247 -4.868 -4.387 -3.912 -3.364 -2.909 -2.447 -1.950 -1.489 -0.965 -0.552 0 0.516 1.091 1.693 2.234 2.754
25 -6.600 -6.168 -5.757 -5.372 -4.906 -4.406 -3.875 -3.422 -2.983 -2.493 -2.002 -1.447 -1.054 -0.514 0 0.573 1.177 1.725 2.244
30 -7.210 -6.710 -6.329 -5.973 -5.445 -5.010 -4.426 -3.973 -3.548 -3.053 -2.597 -2.031 -1.656 -1.061 -0.588 0 0.603 1.165 1.685
35 -7.841 -7.312 -6.920 -6.532 -6.077 -5.613 -5.050 -4.586 -4.187 -3.650 -3.223 -2.632 -2.273 -1.681 -1.194 -0.614 0 0.554 1.073
40 -8.354 -7.837 -7.494 -7.092 -6.617 -6.178 -5.583 -5.107 -4.729 -4.248 -3.740 -3.164 -2.810 -2.232 -1.802 -1.164 -0.530 0 0.526
45 -8.921 -8.405 -8.004 -7.609 -7.143 -6.690 -6.154 -5.651 -5.294 -4.733 -4.272 -3.699 -3.333 -2.767 -2.324 -1.677 -1.120 -0.513 0
197
F3- 5MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.289 0.732 1.197 1.666 2.110 2.581 3.060 3.517 3.980 4.424 4.923 5.437 5.904 6.542 7.098 7.694 8.287 8.806
-40 -0.340 0 0.401 0.866 1.347 1.801 2.257 2.722 3.188 3.650 4.108 4.593 5.110 5.566 6.202 6.758 7.364 7.947 8.478
-35 -0.786 -0.454 0 0.433 0.910 1.379 1.852 2.293 2.757 3.215 3.673 4.160 4.677 5.133 5.769 6.326 6.932 7.514 8.043
-30 -1.290 -0.942 -0.514 0 0.443 0.917 1.397 1.854 2.310 2.775 3.225 3.721 4.240 4.696 5.332 5.886 6.484 7.077 7.595
-25 -1.785 -1.420 -0.992 -0.513 0 0.453 0.928 1.398 1.862 2.319 2.777 3.265 3.795 4.251 4.888 5.446 6.042 6.633 7.154
-20 -2.293 -1.901 -1.478 -0.983 -0.513 0 0.459 0.929 1.400 1.867 2.322 2.804 3.320 3.773 4.409 4.976 5.583 6.163 6.694
-15 -2.744 -2.387 -1.956 -1.449 -0.945 -0.514 0 0.458 0.931 1.406 1.870 2.341 2.860 3.324 3.960 4.508 5.113 5.695 6.224
-10 -3.203 -2.879 -2.422 -1.942 -1.464 -0.978 -0.466 0 0.465 0.935 1.407 1.886 2.388 2.855 3.487 4.045 4.644 5.226 5.754
-5 -3.689 -3.341 -2.905 -2.395 -1.937 -1.478 -0.956 -0.501 0 0.468 0.941 1.427 1.916 2.376 3.010 3.566 4.171 4.753 5.282
0 -4.184 -3.829 -3.372 -2.891 -2.394 -1.936 -1.418 -0.965 -0.510 0 0.468 0.956 1.457 1.908 2.562 3.095 3.703 4.285 4.814
5 -4.671 -4.290 -3.869 -3.368 -2.871 -2.441 -1.916 -1.458 -0.961 -0.500 0 0.478 0.981 1.448 2.069 2.623 3.231 3.813 4.342
10 -5.169 -4.803 -4.367 -3.864 -3.325 -2.919 -2.418 -1.963 -1.426 -0.985 -0.481 0 0.494 0.961 1.597 2.143 2.753 3.335 3.864
15 -5.678 -5.297 -4.862 -4.361 -3.831 -3.431 -2.897 -2.481 -1.949 -1.475 -0.975 -0.480 0 0.462 1.098 1.660 2.262 2.844 3.373
20 -6.176 -5.760 -5.318 -4.841 -4.304 -3.874 -3.317 -2.948 -2.417 -1.970 -1.452 -0.970 -0.500 0 0.633 1.200 1.801 2.381 2.910
25 -6.765 -6.386 -5.965 -5.440 -4.902 -4.504 -3.950 -3.550 -3.019 -2.582 -2.049 -1.570 -1.110 -0.620 0 0.573 1.181 1.769 2.291
30 -7.325 -6.970 -6.526 -5.997 -5.475 -5.073 -4.511 -4.117 -3.644 -3.158 -2.625 -2.133 -1.714 -1.184 -0.536 0 0.621 1.212 1.731
35 -7.941 -7.598 -7.199 -6.630 -6.070 -5.683 -5.105 -4.734 -4.228 -3.779 -3.286 -2.757 -2.351 -1.772 -1.183 -0.586 0 0.580 1.123
40 -8.518 -8.149 -7.736 -7.260 -6.663 -6.268 -5.714 -5.361 -4.833 -4.368 -3.839 -3.347 -2.911 -2.385 -1.763 -1.170 -0.596 0 0.543
45 -9.058 -8.697 -8.286 -7.765 -7.196 -6.812 -6.244 -5.883 -5.375 -4.881 -4.372 -3.856 -3.453 -2.913 -2.320 -1.742 -1.106 -0.522 0
198
F3- 8MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.321 0.796 1.280 1.757 2.228 2.711 3.186 3.665 4.148 4.687 5.168 5.696 6.211 6.810 7.400 8.023 8.597 9.146
-40 -0.339 0 0.442 0.910 1.400 1.889 2.359 2.827 3.309 3.798 4.334 4.828 5.357 5.873 6.472 7.059 7.682 8.256 8.809
-35 -0.821 -0.503 0 0.453 0.939 1.430 1.909 2.363 2.855 3.337 3.888 4.364 4.890 5.407 6.009 6.592 7.216 7.790 8.342
-30 -1.308 -0.989 -0.520 0 0.458 0.949 1.434 1.899 2.381 2.869 3.403 3.897 4.411 4.921 5.530 6.109 6.729 7.304 7.864
-25 -1.820 -1.469 -1.011 -0.503 0 0.461 0.951 1.434 1.901 2.399 2.923 3.421 3.925 4.450 5.050 5.641 6.263 6.836 7.386
-20 -2.331 -1.955 -1.533 -0.977 -0.513 0 0.462 0.946 1.426 1.918 2.429 2.928 3.453 3.968 4.564 5.154 5.775 6.348 6.899
-15 -2.811 -2.432 -1.996 -1.468 -0.996 -0.516 0 0.467 0.955 1.447 1.938 2.437 2.963 3.481 4.084 4.664 5.287 5.860 6.408
-10 -3.316 -2.929 -2.509 -1.956 -1.453 -0.985 -0.509 0 0.472 0.972 1.471 1.955 2.484 3.002 3.612 4.183 4.806 5.380 5.927
-5 -3.789 -3.438 -2.970 -2.461 -1.944 -1.478 -1.010 -0.482 0 0.490 0.991 1.496 1.999 2.502 3.111 3.710 4.331 4.904 5.454
0 -4.268 -3.914 -3.492 -2.938 -2.418 -1.991 -1.504 -0.994 -0.519 0 0.491 1.000 1.520 2.021 2.625 3.225 3.844 4.418 4.970
5 -4.745 -4.393 -3.974 -3.435 -2.927 -2.488 -1.993 -1.497 -0.996 -0.507 0 0.505 1.028 1.545 2.132 2.735 3.355 3.927 4.479
10 -5.251 -4.936 -4.484 -3.940 -3.443 -2.996 -2.491 -1.988 -1.498 -0.979 -0.517 0 0.515 1.033 1.639 2.231 2.849 3.423 3.976
15 -5.754 -5.445 -4.987 -4.460 -3.951 -3.494 -2.997 -2.502 -2.022 -1.484 -1.035 -0.499 0 0.515 1.128 1.726 2.343 2.917 3.469
20 -6.251 -5.948 -5.494 -4.967 -4.477 -3.998 -3.505 -3.001 -2.497 -2.010 -1.521 -1.014 -0.522 0 0.614 1.223 1.839 2.411 2.962
25 -6.882 -6.557 -6.106 -5.581 -5.093 -4.613 -4.113 -3.617 -3.135 -2.651 -2.155 -1.655 -1.064 -0.580 0 0.603 1.244 1.813 2.364
30 -7.460 -7.203 -6.723 -6.198 -5.689 -5.220 -4.674 -4.201 -3.743 -3.253 -2.751 -2.227 -1.679 -1.208 -0.592 0 0.635 1.229 1.781
35 -8.168 -7.804 -7.353 -6.831 -6.328 -5.825 -5.298 -4.852 -4.382 -3.896 -3.365 -2.878 -2.326 -1.844 -1.240 -0.655 0 0.590 1.150
40 -8.700 -8.420 -7.922 -7.422 -6.922 -6.419 -5.900 -5.439 -4.973 -4.483 -3.976 -3.453 -2.901 -2.444 -1.817 -1.236 -0.628 0 0.556
45 -9.275 -8.987 -8.479 -7.968 -7.476 -7.019 -6.455 -6.014 -5.489 -5.068 -4.550 -3.992 -3.486 -3.002 -2.350 -1.793 -1.151 -0.547 0
199
F4- 1MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.212 0.266 0.703 1.039 1.469 1.748 2.190 2.576 2.985 3.530 3.903 4.395 4.838 5.327 5.836 6.436 6.931 7.378
-40 -0.178 0 0.106 0.523 0.854 1.291 1.571 2.017 2.397 2.807 3.343 3.733 4.215 4.661 5.136 5.657 6.262 6.754 7.191
-35 -0.343 -0.154 0 0.387 0.718 1.148 1.432 1.866 2.251 2.674 3.216 3.591 4.084 4.527 5.013 5.522 6.126 6.627 7.062
-30 -0.812 -0.591 -0.481 0 0.269 0.711 0.995 1.440 1.826 2.244 2.784 3.139 3.630 4.072 4.556 5.086 5.677 6.166 6.613
-25 -1.106 -0.958 -0.812 -0.404 0 0.397 0.676 1.121 1.500 1.932 2.474 2.838 3.316 3.758 4.253 4.785 5.362 5.857 6.298
-20 -1.588 -1.422 -1.295 -0.889 -0.497 0 0.271 0.716 1.084 1.531 2.074 2.428 2.912 3.357 3.852 4.380 4.963 5.455 5.896
-15 -1.856 -1.687 -1.553 -1.151 -0.790 -0.343 0 0.425 0.806 1.253 1.797 2.145 2.634 3.078 3.573 4.100 4.677 5.168 5.618
-10 -2.312 -2.143 -2.003 -1.572 -1.263 -0.771 -0.467 0 0.371 0.808 1.368 1.728 2.201 2.637 3.133 3.670 4.245 4.733 5.178
-5 -2.690 -2.560 -2.365 -1.965 -1.636 -1.160 -0.869 -0.400 0 0.432 0.979 1.346 1.823 2.263 2.759 3.295 3.859 4.352 4.803
0 -3.179 -3.014 -2.847 -2.400 -2.100 -1.609 -1.341 -0.868 -0.466 0 0.535 0.899 1.383 1.835 2.316 2.860 3.428 3.919 4.366
5 -3.716 -3.530 -3.390 -2.977 -2.642 -2.142 -1.913 -1.431 -1.013 -0.572 0 0.367 0.853 1.317 1.814 2.344 2.915 3.407 3.851
10 -4.107 -3.897 -3.760 -3.351 -3.032 -2.520 -2.233 -1.779 -1.415 -0.944 -0.374 0 0.478 0.932 1.436 1.967 2.546 3.037 3.480
15 -4.588 -4.409 -4.226 -3.836 -3.488 -3.006 -2.728 -2.274 -1.875 -1.442 -0.864 -0.485 0 0.454 0.957 1.502 2.070 2.562 3.006
20 -5.057 -4.855 -4.682 -4.322 -3.939 -3.457 -3.235 -2.747 -2.345 -1.896 -1.301 -0.929 -0.450 0 0.497 1.044 1.618 2.105 2.548
25 -5.541 -5.358 -5.203 -4.815 -4.458 -3.948 -3.713 -3.250 -2.844 -2.399 -1.805 -1.433 -0.962 -0.513 0 0.542 1.122 1.617 2.062
30 -6.049 -5.892 -5.711 -5.351 -5.001 -4.483 -4.261 -3.778 -3.376 -2.909 -2.351 -1.950 -1.499 -1.016 -0.539 0 0.574 1.071 1.523
35 -6.635 -6.470 -6.280 -5.934 -5.571 -5.077 -4.821 -4.351 -3.938 -3.510 -2.906 -2.539 -2.069 -1.623 -1.128 -0.547 0 0.488 0.936
40 -7.129 -6.978 -6.795 -6.425 -6.076 -5.564 -5.322 -4.855 -4.410 -3.995 -3.433 -3.045 -2.557 -2.100 -1.619 -1.045 -0.513 0 0.439
45 -7.597 -7.426 -7.253 -6.892 -6.516 -6.011 -5.792 -5.337 -4.875 -4.453 -3.885 -3.495 -3.009 -2.576 -2.086 -1.518 -0.983 -0.459 0
200
F4- 3MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.193 0.469 0.915 1.267 1.737 2.099 2.532 2.972 3.428 3.893 4.405 4.816 5.306 5.960 6.550 7.188 7.764 8.274
-40 -0.219 0 0.280 0.716 1.066 1.550 1.907 2.320 2.764 3.214 3.684 4.198 4.617 5.115 5.777 6.356 6.988 7.571 8.085
-35 -0.561 -0.351 0 0.402 0.752 1.221 1.585 2.024 2.443 2.895 3.362 3.878 4.312 4.805 5.469 6.049 6.688 7.262 7.776
-30 -0.962 -0.823 -0.509 0 0.326 0.792 1.165 1.606 2.031 2.485 2.951 3.470 3.893 4.379 5.042 5.623 6.265 6.843 7.349
-25 -1.331 -1.157 -0.857 -0.377 0 0.443 0.808 1.249 1.677 2.129 2.598 3.111 3.546 4.035 4.697 5.285 5.923 6.495 7.004
-20 -1.814 -1.650 -1.359 -0.888 -0.524 0 0.353 0.789 1.243 1.696 2.157 2.674 3.106 3.599 4.262 4.844 5.484 6.060 6.567
-15 -2.164 -2.011 -1.707 -1.229 -0.895 -0.420 0 0.425 0.868 1.328 1.800 2.303 2.738 3.228 3.892 4.470 5.112 5.689 6.198
-10 -2.659 -2.433 -2.137 -1.698 -1.340 -0.884 -0.466 0 0.433 0.899 1.372 1.880 2.307 2.802 3.466 4.048 4.682 5.266 5.772
-5 -3.066 -2.893 -2.610 -2.122 -1.777 -1.309 -0.942 -0.463 0 0.454 0.926 1.446 1.878 2.372 3.033 3.622 4.257 4.833 5.339
0 -3.538 -3.388 -3.062 -2.606 -2.262 -1.783 -1.397 -0.932 -0.489 0 0.466 0.990 1.423 1.914 2.576 3.163 3.803 4.377 4.883
5 -4.012 -3.841 -3.538 -3.091 -2.708 -2.251 -1.874 -1.402 -0.950 -0.474 0 0.516 0.953 1.449 2.106 2.691 3.332 3.904 4.413
10 -4.504 -4.362 -4.038 -3.595 -3.200 -2.776 -2.367 -1.908 -1.441 -0.990 -0.524 0 0.433 0.933 1.595 2.178 2.819 3.390 3.897
15 -4.962 -4.799 -4.471 -4.049 -3.666 -3.209 -2.796 -2.353 -1.861 -1.424 -0.964 -0.431 0 0.486 1.156 1.741 2.379 2.952 3.463
20 -5.452 -5.315 -4.969 -4.511 -4.161 -3.668 -3.298 -2.824 -2.362 -1.904 -1.437 -0.920 -0.498 0 0.671 1.263 1.896 2.468 2.973
25 -6.174 -5.956 -5.634 -5.220 -4.790 -4.360 -3.973 -3.493 -3.039 -2.601 -2.136 -1.606 -1.157 -0.693 0 0.601 1.254 1.826 2.331
30 -6.733 -6.535 -6.259 -5.770 -5.404 -4.958 -4.589 -4.062 -3.622 -3.185 -2.721 -2.183 -1.778 -1.292 -0.633 0 0.649 1.234 1.745
35 -7.423 -7.205 -6.891 -6.428 -6.045 -5.617 -5.272 -4.742 -4.277 -3.836 -3.407 -2.859 -2.434 -1.937 -1.255 -0.664 0 0.580 1.098
40 -7.994 -7.782 -7.461 -7.043 -6.649 -6.170 -5.834 -5.284 -4.897 -4.411 -4.000 -3.436 -3.017 -2.546 -1.834 -1.235 -0.569 0 0.516
45 -8.494 -8.308 -7.968 -7.561 -7.151 -6.733 -6.369 -5.811 -5.389 -4.935 -4.501 -3.959 -3.539 -3.068 -2.334 -1.773 -1.093 -0.515 0
201
F4-5MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.190 0.503 0.915 1.283 1.689 2.126 2.440 2.858 3.285 3.749 4.192 4.708 5.241 5.779 6.365 7.001 7.571 8.104
-40 -0.216 0 0.303 0.690 1.066 1.474 1.924 2.245 2.646 3.075 3.556 3.984 4.513 5.016 5.574 6.168 6.798 7.375 7.902
-35 -0.550 -0.377 0 0.359 0.725 1.139 1.596 1.915 2.326 2.756 3.232 3.669 4.179 4.706 5.259 5.845 6.482 7.044 7.572
-30 -1.002 -0.799 -0.404 0 0.342 0.749 1.210 1.538 1.938 2.368 2.844 3.283 3.803 4.321 4.872 5.461 6.101 6.666 7.195
-25 -1.372 -1.149 -0.834 -0.398 0 0.379 0.834 1.163 1.582 2.004 2.486 2.923 3.439 3.951 4.511 5.095 5.733 6.296 6.825
-20 -1.774 -1.588 -1.218 -0.837 -0.449 0 0.432 0.760 1.186 1.614 2.087 2.524 3.034 3.553 4.103 4.700 5.336 5.899 6.427
-15 -2.256 -2.057 -1.725 -1.294 -0.931 -0.487 0 0.314 0.741 1.180 1.652 2.092 2.596 3.116 3.670 4.259 4.901 5.465 5.993
-10 -2.557 -2.374 -2.032 -1.631 -1.240 -0.831 -0.361 0 0.413 0.846 1.332 1.775 2.295 2.816 3.361 3.947 4.583 5.145 5.674
-5 -2.997 -2.787 -2.468 -2.083 -1.675 -1.229 -0.773 -0.430 0 0.425 0.910 1.359 1.858 2.377 2.937 3.529 4.178 4.736 5.265
0 -3.448 -3.199 -2.927 -2.495 -2.099 -1.668 -1.241 -0.865 -0.447 0 0.474 0.923 1.433 1.945 2.497 3.099 3.737 4.300 4.829
5 -3.942 -3.685 -3.383 -2.962 -2.591 -2.142 -1.685 -1.357 -0.912 -0.457 0 0.441 0.950 1.477 2.028 2.624 3.273 3.830 4.358
10 -4.379 -4.143 -3.848 -3.436 -3.018 -2.590 -2.162 -1.816 -1.371 -0.945 -0.469 0 0.495 1.028 1.590 2.175 2.821 3.380 3.908
15 -4.874 -4.635 -4.358 -3.940 -3.510 -3.085 -2.653 -2.305 -1.853 -1.408 -0.945 -0.513 0 0.528 1.093 1.683 2.327 2.885 3.413
20 -5.380 -5.152 -4.893 -4.459 -4.063 -3.573 -3.157 -2.888 -2.407 -1.964 -1.468 -1.049 -0.519 0 0.569 1.179 1.826 2.383 2.912
25 -5.944 -5.706 -5.453 -5.019 -4.606 -4.163 -3.753 -3.403 -2.962 -2.474 -2.046 -1.614 -1.096 -0.584 0 0.603 1.268 1.813 2.341
30 -6.566 -6.322 -6.087 -5.658 -5.195 -4.729 -4.322 -4.075 -3.563 -3.155 -2.677 -2.217 -1.682 -1.183 -0.586 0 0.651 1.219 1.748
35 -7.237 -6.980 -6.756 -6.315 -5.846 -5.443 -5.005 -4.708 -4.225 -3.778 -3.323 -2.908 -2.330 -1.869 -1.250 -0.608 0 0.567 1.096
40 -7.793 -7.574 -7.333 -6.876 -6.424 -6.005 -5.560 -5.275 -4.796 -4.370 -3.892 -3.444 -2.900 -2.426 -1.820 -1.221 -0.600 0 0.521
45 -8.332 -8.110 -7.872 -7.400 -6.952 -6.529 -6.126 -5.823 -5.344 -4.879 -4.447 -3.966 -3.465 -2.978 -2.336 -1.728 -1.114 -0.533 0
202
F4-8MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 0.242 0.528 0.941 1.383 1.828 2.257 2.756 3.215 3.718 4.203 4.752 5.304 5.917 6.547 7.249 7.988 8.731 9.467
-40 -0.220 0 0.343 0.759 1.212 1.649 2.079 2.580 3.043 3.539 4.033 4.590 5.133 5.744 6.376 7.077 7.816 8.560 9.295
-35 -0.601 -0.362 0 0.395 0.835 1.286 1.734 2.191 2.679 3.174 3.656 4.213 4.756 5.363 5.995 6.696 7.433 8.182 8.917
-30 -1.029 -0.811 -0.457 0 0.417 0.854 1.308 1.799 2.255 2.770 3.252 3.806 4.353 4.951 5.587 6.287 7.026 7.777 8.514
-25 -1.498 -1.272 -0.937 -0.480 0 0.426 0.878 1.377 1.853 2.342 2.832 3.386 3.927 4.524 5.154 5.855 6.594 7.343 8.080
-20 -1.942 -1.720 -1.385 -0.950 -0.470 0 0.432 0.932 1.416 1.917 2.403 2.953 3.502 4.106 4.737 5.437 6.174 6.931 7.665
-15 -2.367 -2.191 -1.830 -1.376 -0.941 -0.444 0 0.484 0.966 1.481 1.953 2.511 3.058 3.662 4.295 4.996 5.735 6.484 7.221
-10 -2.864 -2.690 -2.324 -1.875 -1.415 -0.947 -0.467 0 0.473 0.989 1.472 2.020 2.563 3.161 3.798 4.499 5.235 5.981 6.716
-5 -3.382 -3.189 -2.820 -2.363 -1.918 -1.435 -0.975 -0.473 0 0.504 0.989 1.545 2.084 2.688 3.322 4.023 4.757 5.508 6.240
0 -3.853 -3.653 -3.318 -2.845 -2.398 -1.937 -1.459 -0.994 -0.500 0 0.486 1.045 1.598 2.187 2.831 3.532 4.266 5.020 5.752
5 -4.334 -4.164 -3.824 -3.369 -2.885 -2.424 -1.952 -1.487 -1.022 -0.472 0 0.545 1.099 1.706 2.337 3.037 3.777 4.527 5.265
10 -4.902 -4.706 -4.365 -3.922 -3.467 -2.970 -2.513 -2.030 -1.579 -1.059 -0.554 0 0.551 1.161 1.788 2.489 3.235 3.981 4.724
15 -5.452 -5.290 -4.940 -4.503 -3.994 -3.516 -3.044 -2.568 -2.124 -1.608 -1.102 -0.547 0 0.604 1.262 1.963 2.708 3.435 4.176
20 -6.043 -5.877 -5.512 -5.040 -4.618 -4.108 -3.672 -3.149 -2.724 -2.216 -1.703 -1.147 -0.594 0 0.661 1.378 2.104 2.853 3.593
25 -6.711 -6.564 -6.172 -5.729 -5.323 -4.762 -4.312 -3.847 -3.368 -2.896 -2.404 -1.812 -1.273 -0.645 0 0.721 1.479 2.201 2.946
30 -7.451 -7.264 -6.904 -6.434 -6.041 -5.467 -5.031 -4.592 -4.108 -3.644 -3.109 -2.570 -1.962 -1.409 -0.727 0 0.754 1.502 2.241
35 -8.204 -8.036 -7.672 -7.200 -6.811 -6.250 -5.791 -5.363 -4.864 -4.400 -3.861 -3.323 -2.735 -2.144 -1.478 -0.758 0 0.742 1.496
40 -8.966 -8.787 -8.393 -7.943 -7.568 -7.009 -6.523 -6.128 -5.610 -5.161 -4.641 -4.076 -3.483 -2.892 -2.250 -1.488 -0.766 0 0.753
45 -9.726 -9.562 -9.169 -8.713 -8.326 -7.761 -7.280 -6.911 -6.375 -5.936 -5.379 -4.854 -4.259 -3.661 -3.002 -2.271 -1.540 -0.763 0
203
F6-1MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 -0.090 0.070 0.278 0.559 0.978 1.378 1.678 2.039 2.535 2.903 3.339 3.708 4.160 4.570 5.116 5.684 6.192 6.705
-40 -0.016 0 0.132 0.347 0.658 1.042 1.433 1.753 2.123 2.610 2.978 3.420 3.796 4.235 4.656 5.181 5.761 6.261 6.774
-35 -0.143 -0.156 0 0.202 0.461 0.844 1.237 1.559 1.936 2.461 2.815 3.256 3.605 4.038 4.466 4.990 5.563 6.069 6.582
-30 -0.370 -0.384 -0.259 0 0.185 0.568 0.957 1.258 1.674 2.123 2.492 2.930 3.335 3.766 4.195 4.719 5.291 5.802 6.314
-25 -0.701 -0.692 -0.585 -0.387 0 0.330 0.703 1.007 1.435 1.894 2.248 2.675 3.076 3.511 3.934 4.464 5.043 5.547 6.058
-20 -1.094 -1.136 -1.083 -0.776 -0.499 0 0.312 0.616 1.026 1.500 1.857 2.284 2.685 3.120 3.543 4.071 4.652 5.156 5.664
-15 -1.488 -1.496 -1.362 -1.137 -0.879 -0.493 0 0.269 0.671 1.147 1.514 1.956 2.344 2.772 3.203 3.726 4.304 4.810 5.319
-10 -1.818 -1.839 -1.687 -1.463 -1.208 -0.787 -0.382 0 0.391 0.851 1.226 1.674 2.080 2.501 2.931 3.461 4.036 4.543 5.049
-5 -2.130 -2.152 -2.081 -1.854 -1.536 -1.174 -0.774 -0.393 0 0.452 0.815 1.271 1.689 2.097 2.526 3.067 3.639 4.132 4.640
0 -2.640 -2.678 -2.539 -2.314 -2.030 -1.685 -1.281 -0.859 -0.516 0 0.342 0.794 1.216 1.651 2.080 2.607 3.178 3.687 4.195
5 -2.966 -3.044 -2.933 -2.642 -2.421 -2.045 -1.670 -1.252 -0.853 -0.386 0 0.448 0.870 1.304 1.733 2.253 2.829 3.338 3.846
10 -3.467 -3.530 -3.390 -3.098 -2.930 -2.557 -2.095 -1.712 -1.330 -0.896 -0.462 0 0.422 0.859 1.289 1.818 2.385 2.894 3.402
15 -3.862 -3.923 -3.851 -3.516 -3.309 -3.067 -2.540 -2.107 -1.759 -1.253 -0.919 -0.428 0 0.431 0.861 1.391 1.971 2.479 2.988
20 -4.320 -4.383 -4.238 -3.976 -3.775 -3.394 -2.992 -2.565 -2.269 -1.732 -1.309 -0.937 -0.516 0 0.421 0.956 1.535 2.043 2.552
25 -4.762 -4.758 -4.712 -4.400 -4.120 -3.919 -3.362 -2.960 -2.629 -2.169 -1.723 -1.330 -0.919 -0.462 0 0.526 1.106 1.616 2.124
30 -5.255 -5.350 -5.282 -4.987 -4.707 -4.428 -3.913 -3.483 -3.138 -2.673 -2.249 -1.849 -1.442 -1.002 -0.591 0 0.580 1.090 1.598
35 -5.814 -5.876 -5.838 -5.480 -5.233 -5.018 -4.505 -4.130 -3.770 -3.289 -2.868 -2.480 -2.015 -1.607 -1.229 -0.515 0 0.506 1.017
40 -6.340 -6.352 -6.360 -5.976 -5.759 -5.528 -5.031 -4.588 -4.288 -3.782 -3.319 -2.955 -2.541 -2.101 -1.689 -1.042 -0.526 0 0.500
45 -6.809 -6.850 -6.883 -6.451 -6.285 -6.042 -5.503 -5.077 -4.779 -4.290 -3.808 -3.481 -3.060 -2.624 -2.188 -1.533 -1.044 -0.475 0
204
F6-3MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 -0.037 0.178 0.591 0.959 1.378 1.784 2.205 2.589 3.044 3.490 3.930 4.426 4.867 5.501 6.038 6.666 7.237 7.854
-40 -0.034 0 0.214 0.623 1.007 1.413 1.830 2.255 2.661 3.105 3.545 4.023 4.477 4.940 5.531 6.085 6.718 7.292 7.895
-35 -0.302 -0.272 0 0.362 0.744 1.133 1.567 1.984 2.400 2.825 3.279 3.761 4.214 4.670 5.300 5.814 6.455 7.028 7.632
-30 -0.702 -0.633 -0.391 0 0.358 0.763 1.164 1.606 1.997 2.422 2.917 3.349 3.803 4.316 4.902 5.395 6.045 6.649 7.222
-25 -1.086 -1.010 -0.884 -0.493 0 0.376 0.788 1.217 1.626 2.065 2.535 2.985 3.437 3.924 4.523 5.064 5.684 6.266 6.860
-20 -1.511 -1.498 -1.345 -0.850 -0.493 0 0.386 0.839 1.244 1.678 2.125 2.603 3.057 3.513 4.145 4.693 5.281 5.896 6.457
-15 -1.873 -1.831 -1.738 -1.278 -1.015 -0.516 0 0.430 0.833 1.291 1.744 2.217 2.671 3.131 3.759 4.270 4.893 5.477 6.071
-10 -2.383 -2.222 -2.253 -1.738 -1.344 -0.867 -0.505 0 0.378 0.830 1.292 1.767 2.218 2.675 3.303 3.825 4.432 5.049 5.610
-5 -2.806 -2.746 -2.711 -2.105 -1.765 -1.324 -0.900 -0.411 0 0.444 0.906 1.389 1.840 2.297 2.925 3.446 4.070 4.683 5.245
0 -3.299 -3.102 -3.104 -2.582 -2.268 -1.793 -1.363 -0.906 -0.507 0 0.453 0.937 1.392 1.856 2.487 3.035 3.643 4.257 4.818
5 -3.710 -3.624 -3.628 -3.058 -2.783 -2.287 -1.856 -1.367 -0.974 -0.460 0 0.468 0.940 1.396 2.018 2.573 3.149 3.763 4.324
10 -4.236 -4.117 -4.025 -3.566 -3.255 -2.698 -2.310 -1.870 -1.480 -0.921 -0.454 0 0.447 0.918 1.549 2.080 2.687 3.301 3.863
15 -4.759 -4.618 -4.484 -4.060 -3.742 -3.222 -2.787 -2.326 -1.940 -1.443 -0.908 -0.494 0 0.461 1.097 1.640 2.239 2.854 3.417
20 -5.221 -5.045 -5.010 -4.551 -4.252 -3.705 -3.277 -2.786 -2.450 -1.936 -1.356 -0.921 -0.458 0 0.629 1.184 1.783 2.396 2.957
25 -5.977 -5.713 -5.601 -5.185 -4.827 -4.457 -4.015 -3.449 -3.023 -2.563 -2.079 -1.610 -1.152 -0.657 0 0.526 1.155 1.768 2.328
30 -6.437 -6.177 -6.120 -5.709 -5.353 -4.904 -4.494 -3.948 -3.609 -3.089 -2.596 -2.131 -1.612 -1.159 -0.497 0 0.629 1.250 1.827
35 -7.124 -6.867 -6.720 -6.443 -5.977 -5.545 -5.161 -4.603 -4.328 -3.678 -3.345 -2.785 -2.270 -1.816 -1.148 -0.672 0 0.621 1.198
40 -7.754 -7.477 -7.361 -6.955 -6.627 -6.200 -5.817 -5.244 -4.917 -4.278 -3.931 -3.416 -2.807 -2.405 -1.792 -1.304 -0.556 0 0.574
45 -8.264 -8.084 -7.888 -7.53 -7.169 -6.786 -6.338 -5.762 -5.444 -4.927 -4.471 -3.879 -3.369 -3.001 -2.381 -1.820 -1.140 -0.592 0
205
F6-5MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 -0.016 0.419 0.748 1.112 1.506 1.870 2.257 2.705 3.125 3.596 4.030 4.544 5.021 5.593 6.111 6.738 7.349 7.952
-40 -0.131 0 0.288 0.608 0.972 1.382 1.730 2.129 2.574 3.018 3.481 3.898 4.413 4.889 5.470 5.979 6.606 7.217 7.829
-35 -0.436 -0.339 0 0.304 0.672 1.077 1.430 1.833 2.253 2.689 3.152 3.600 4.117 4.589 5.141 5.681 6.308 6.921 7.500
-30 -0.821 -0.800 -0.296 0 0.343 0.734 1.101 1.504 1.949 2.344 2.815 3.269 3.756 4.240 4.812 5.350 5.977 6.560 7.171
-25 -1.206 -1.112 -0.672 -0.384 0 0.373 0.740 1.143 1.589 1.994 2.474 2.936 3.431 3.934 4.479 5.019 5.646 6.237 6.838
-20 -1.530 -1.505 -1.090 -0.844 -0.510 0 0.361 0.765 1.211 1.653 2.108 2.557 3.045 3.547 4.101 4.639 5.266 5.849 6.460
-15 -1.923 -1.896 -1.482 -1.221 -0.839 -0.438 0 0.386 0.835 1.283 1.731 2.171 2.658 3.161 3.723 4.252 4.880 5.462 6.082
-10 -2.351 -2.354 -1.941 -1.714 -1.295 -0.931 -0.510 0 0.424 0.871 1.343 1.803 2.288 2.774 3.324 3.887 4.514 5.099 5.685
-5 -2.808 -2.794 -2.399 -2.109 -1.689 -1.325 -0.890 -0.460 0 0.440 0.908 1.384 1.869 2.342 2.909 3.460 4.087 4.671 5.272
0 -3.269 -3.218 -2.827 -2.535 -2.180 -1.816 -1.287 -0.936 -0.483 0 0.458 0.935 1.425 1.929 2.489 3.039 3.663 4.244 4.853
5 -3.703 -3.736 -3.315 -3.041 -2.637 -2.243 -1.761 -1.404 -0.905 -0.409 0 0.467 0.956 1.469 1.996 2.545 3.178 3.767 4.359
10 -4.159 -4.208 -3.776 -3.501 -3.146 -2.759 -2.279 -1.904 -1.413 -0.933 -0.500 0 0.493 1.000 1.551 2.081 2.715 3.305 3.911
15 -4.685 -4.666 -4.260 -3.980 -3.607 -3.279 -2.723 -2.398 -1.898 -1.458 -1.011 -0.505 0 0.493 1.044 1.618 2.222 2.811 3.405
20 -5.145 -5.187 -4.744 -4.473 -4.098 -3.679 -3.249 -2.921 -2.424 -1.910 -1.521 -1.027 -0.526 0 0.551 1.125 1.729 2.302 2.936
25 -5.742 -5.773 -5.303 -4.975 -4.651 -4.320 -3.740 -3.446 -2.948 -2.434 -2.014 -1.561 -0.994 -0.499 0 0.551 1.203 1.776 2.364
30 -6.243 -6.279 -5.829 -5.561 -5.240 -4.844 -4.303 -3.972 -3.471 -2.952 -2.595 -2.077 -1.545 -1.031 -0.587 0 0.629 1.253 1.846
35 -6.967 -6.937 -6.574 -6.267 -5.826 -5.530 -4.964 -4.623 -4.090 -3.590 -3.349 -2.843 -2.232 -1.816 -1.179 -0.657 0 0.625 1.217
40 -7.587 -7.578 -7.068 -6.847 -6.451 -6.153 -5.597 -5.270 -4.748 -4.175 -3.941 -3.434 -2.857 -2.411 -1.899 -1.296 -0.625 0 0.588
45 -8.179 -8.167 -7.734 -7.489 -7.043 -6.712 -6.221 -5.830 -5.320 -4.816 -4.584 -4.059 -3.438 -3.036 -2.487 -1.918 -1.248 -0.592 0
206
F6-8MPa
°C -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
-45 0 -0.034 0.285 0.700 1.209 1.629 2.064 2.486 2.960 3.418 3.872 4.383 4.814 5.444 5.946 6.621 7.320 7.972 8.604
-40 -0.099 0 0.304 0.711 1.127 1.562 1.973 2.354 2.861 3.286 3.740 4.251 4.732 5.362 5.867 6.521 7.219 7.872 8.503
-35 -0.491 -0.436 0 0.378 0.765 1.200 1.644 2.050 2.499 2.986 3.407 3.947 4.428 5.057 5.563 6.176 6.874 7.526 8.158
-30 -0.992 -0.827 -0.506 0 0.378 0.789 1.217 1.663 2.113 2.575 3.028 3.544 4.025 4.654 5.160 5.789 6.487 7.140 7.771
-25 -1.480 -1.187 -0.905 -0.510 0 0.411 0.851 1.298 1.747 2.205 2.630 3.158 3.639 4.268 4.773 5.403 6.101 6.753 7.385
-20 -1.873 -1.701 -1.399 -0.905 -0.458 0 0.427 0.871 1.336 1.788 2.234 2.759 3.240 3.869 4.375 4.999 5.697 6.350 6.981
-15 -2.378 -2.096 -1.857 -1.297 -0.853 -0.510 0 0.435 0.895 1.369 1.836 2.331 2.816 3.446 3.951 4.579 5.277 5.931 6.562
-10 -2.769 -2.585 -2.297 -1.789 -1.365 -0.970 -0.497 0 0.448 0.923 1.389 1.916 2.403 3.032 3.538 4.135 4.833 5.487 6.132
-5 -3.271 -2.982 -2.755 -2.272 -1.727 -1.477 -1.004 -0.498 0 0.462 0.937 1.461 1.943 2.572 3.078 3.707 4.405 5.058 5.689
0 -3.766 -3.508 -3.209 -2.732 -2.250 -1.888 -1.462 -0.956 -0.516 0 0.469 0.997 1.474 2.103 2.609 3.238 3.936 4.589 5.220
5 -4.224 -3.909 -3.732 -3.242 -2.775 -2.348 -1.968 -1.478 -1.021 -0.462 0 0.508 1.011 1.642 2.140 2.770 3.467 4.120 4.751
10 -4.750 -4.432 -4.188 -3.760 -3.286 -2.849 -2.494 -1.994 -1.534 -0.955 -0.521 0 0.493 1.130 1.641 2.264 2.962 3.615 4.237
15 -5.252 -4.954 -4.712 -4.229 -3.800 -3.375 -2.954 -2.510 -2.049 -1.482 -1.015 -0.524 0 0.629 1.139 1.773 2.470 3.123 3.769
20 -5.906 -5.604 -5.313 -4.822 -4.449 -4.023 -3.677 -3.129 -2.739 -2.136 -1.633 -1.113 -0.592 0 0.510 1.149 1.841 2.494 3.120
25 -6.364 -6.123 -5.823 -5.315 -4.843 -4.451 -4.170 -3.619 -3.195 -2.537 -2.154 -1.638 -1.107 -0.526 0 0.629 1.340 1.993 2.618
30 -7.087 -6.715 -6.477 -5.966 -5.534 -5.141 -4.820 -4.274 -3.857 -3.202 -2.808 -2.295 -1.773 -1.115 -0.564 0 0.711 1.369 1.994
35 -7.778 -7.483 -7.201 -6.686 -6.283 -5.837 -5.545 -5.030 -4.560 -3.968 -3.458 -2.987 -2.501 -1.888 -1.346 -0.754 0 0.658 1.295
40 -8.405 -8.154 -7.860 -7.467 -6.931 -6.561 -6.137 -5.681 -5.176 -4.573 -4.165 -3.704 -3.163 -2.542 -2.001 -1.407 -0.623 0 0.629
45 -9.043 -8.779 -8.512 -8.063 -7.588 -7.202 -6.811 -6.338 -5.798 -5.197 -4.787 -4.296 -3.920 -3.151 -2.646 -2.067 -1.289 -0.608 0
207
A.2 Time-Stress Superposition Shift Factors F1
T(°C) σr 1 3 5 8
σ 3 5 8 1 5 8 1 3 8 1 3 5
-45 H -0.279 -2.265 -3.588 0.067 -0.274 -2.369 0.534 0.468 -2.056 2.704 2.573 0.469
V 0.491 0.653 0.829 -0.507 0.202 0.354 -0.700 -0.193 0.161 -0.858 -0.358 -0.194
-40 H -0.279 -2.265 -3.843 0.066 -0.655 -2.562 0.535 0.468 -2.056 2.975 2.647 0.789
V 0.499 0.668 0.846 -0.492 0.201 0.363 -0.701 -0.193 0.161 -0.850 -0.347 -0.185
-35 H -0.551 -2.655 -4.233 0.067 -0.264 -0.253 0.856 0.789 -1.908 2.975 2.647 0.789
V 0.499 0.660 0.922 -0.507 0.201 0.411 -0.693 -0.185 0.161 -0.862 -0.354 -0.185
-30 H -0.551 -2.655 -4.237 0.066 -0.558 -2.663 0.859 0.793 -1.908 3.119 2.651 0.794
V 0.495 0.648 0.809 -0.499 0.193 0.330 -0.685 -0.185 0.145 -0.837 -0.346 -0.185
-25 H -0.647 -2.750 -4.821 0.067 -0.563 -2.668 1.512 1.216 -2.105 3.633 3.165 1.390
V 0.499 0.645 0.781 -0.523 0.193 0.330 -0.692 -0.177 0.137 -0.813 -0.315 -0.161
-20 H -0.645 -2.750 -4.821 0.140 -1.060 -3.036 2.498 1.972 -2.105 4.472 3.946 1.974
V 0.491 0.620 0.749 -0.507 0.177 0.306 -0.644 -0.145 0.121 -0.765 -0.266 -0.129
-15 H -1.036 -3.015 -5.000 0.296 7.32E-5 -2.172 2.515 1.989 -2.105 4.620 4.094 2.105
V 0.483 0.612 0.741 -0.507 0.2178 0.323 -0.620 -0.129 0.113 -0.733 -0.242 -0.112
-10 H -1.060 -3.122 -4.755 0.470 -2.068 -4.204 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.467 0.580 0.685 -0.499 0.113 0.218 -0.612 -0.113 0.104 -0.717 -0.218 -0.105
-5 H -1.060 -3.122 -4.755 0.470 -2.068 -4.204 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.467 0.572 0.700 -0.491 0.104 0.193 -0.580 -0.104 0.097 -0.668 -0.185 -0.089
0 H -1.317 -3.411 -5.472 0.794 -2.066 -3.974 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.451 0.548 0.636 -0.475 0.096 0.193 -0.563 -0.081 0.097 -0.668 -0.177 -0.089
5 H -1.578 -3.682 -5.787 0.873 -2.066 -3.924 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.435 0.524 0.596 -0.484 0.081 0.177 -0.548 -0.072 0.072 -0.628 -0.145 -0.065
10 H -1.578 -3.682 -5.787 1.044 -2.104 -3.917 2.897 2.104 -2.105 5.002 4.209 2.105
V 0.427 0.507 0.572 -0.459 0.077 0.165 -0.540 -0.064 0.064 -0.596 -0.120 -0.056
15 H -1.578 -3.682 -5.787 1.151 -2.054 -3.976 2.897 2.104 -2.105 5.002 4.209 2.105
V 0.435 0.499 0.556 -0.454 0.059 0.135 -0.540 -0.065 0.065 -0.612 -0.137 -0.064
20 H -1.585 -3.689 -5.794 1.102 -2.066 -4.213 2.975 2.104 -2.105 5.080 4.209 2.105
V 0.419 0.467 0.524 -0.451 0.064 0.112 -0.524 -0.056 0.056 -0.588 -0.120 -0.056
25 H -1.585 -3.689 -5.674 1.220 -2.084 -4.223 3.320 2.104 -2.105 5.425 4.209 2.105
V 0.419 0.476 0.532 -0.443 0.048 0.081 -0.483 -0.033 0.041 -0.540 -0.089 -0.032
30 H -1.976 -4.070 -6.165 1.572 -2.084 -4.230 3.494 2.105 -2.071 5.599 4.210 2.105
V 0.370 0.411 0.451 -0.411 0.049 0.081 -0.457 -0.034 0.034 -0.473 -0.050 -0.017
35 H -1.976 -4.070 -6.175 1.865 -2.104 -4.226 3.957 2.100 -2.071 6.062 4.205 2.105
V 0.363 0.386 0.419 -0.370 0.024 0.049 -0.371 0.000 0.034 -0.371 0.000 0.000
40 H -1.977 -3.916 -6.021 1.857 -1.973 -4.068 3.781 1.923 -2.105 5.887 4.029 2.105
V 0.379 0.378 0.394 -0.389 0.000 0.000 -0.402 0.000 0.016 -0.406 0.000 0.000
45 H -1.977 -3.850 -5.935 1.996 -1.989 -4.094 3.814 1.841 -2.105 5.901 3.929 2.087
V 0.386 0.394 0.402 -0.379 0.000 0.000 -0.378 0.000 0.000 -0.372 0.000 0.000
208
F2
T(°C) σr 1 3 5 8
σ 3 5 8 1 5 8 1 3 8 1 3 5
-45 H -0.270 -2.265 -3.588 0.066 -0.558 -2.539 1.282 1.216 -1.661 2.640 2.574 0.469
V 0.475 0.572 0.781 -0.475 0.129 0.322 -0.588 -0.113 0.202 -0.801 -0.314 -0.220
-40 H -0.279 -2.265 -3.588 0.066 -0.558 -2.539 2.038 1.971 -1.055 2.574 2.574 0.469
V 0.484 0.572 0.772 -0.483 0.125 0.306 -0.580 -0.097 0.202 -0.794 -0.304 -0.220
-35 H -0.279 -2.265 -3.843 0.067 -0.655 -2.582 2.172 2.105 -1.238 2.894 2.894 0.789
V 0.476 0.563 0.758 -0.483 0.121 0.306 -0.558 -0.084 0.186 -0.795 -0.305 -0.220
-30 H -0.551 -2.655 -4.233 0.067 -0.563 -2.668 2.172 2.105 -1.499 2.894 2.894 0.789
V 0.471 0.551 0.729 -0.491 0.129 0.298 -0.564 -0.082 0.180 -0.772 -0.282 -0.200
-25 H -0.647 -2.750 -4.821 0.066 -0.641 -2.617 2.172 2.105 -1.710 2.965 2.898 0.793
V 0.471 0.542 0.695 -0.484 0.121 0.281 -0.558 -0.068 0.186 -0.760 -0.287 -0.203
-20 H -0.647 -2.750 -4.821 0.140 -1.060 -3.036 2.244 2.104 -2.105 3.461 3.321 1.217
V 0.459 0.531 0.683 -0.484 0.106 0.265 -0.548 -0.071 0.153 -0.731 -0.248 -0.177
-15 H -1.060 -3.164 -5.152 0.147 -1.315 -3.290 2.245 2.105 -1.971 3.963 3.963 1.858
V 0.448 0.507 0.648 -0.480 0.094 0.242 -0.547 -0.064 0.145 -0.692 -0.202 -0.145
-10 H -1.060 -3.164 -4.621 0.147 -2.104 -4.159 2.245 2.105 -1.971 4.218 4.078 1.973
V 0.454 0.506 0.666 -0.486 0.052 0.189 -0.541 -0.051 0.135 -0.659 -0.185 -0.135
-5 H -1.060 -3.164 -4.621 0.147 -2.104 -4.199 2.401 2.105 -1.971 4.276 4.210 2.105
V 0.442 0.489 0.648 -0.477 0.042 0.165 -0.523 -0.050 0.135 -0.659 -0.186 -0.135
0 H -1.060 -3.164 -4.876 0.470 -2.104 -4.199 2.574 2.105 1.4E-4 4.679 4.210 2.105
V 0.442 0.484 0.620 -0.465 0.035 0.142 -0.506 -0.033 0.220 -0.609 -0.135 -0.102
5 H -1.578 -3.682 -5.787 0.794 -2.066 -4.170 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.411 0.435 0.539 -0.459 0.040 0.137 -0.484 -0.033 0.105 -0.580 -0.129 -0.104
10 H -1.578 -3.682 -5.787 0.871 -2.104 -4.006 2.894 2.105 1.5E-4 4.679 4.210 2.105
V 0.403 0.427 0.515 -0.442 0.032 0.137 -0.457 0.000 0.236 -0.558 -0.085 -0.068
15 H -1.578 -3.682 -5.787 0.957 -2.062 -4.042 2.894 2.105 1.5E-4 4.999 4.210 2.105
V 0.402 0.419 0.499 -0.442 0.024 0.112 -0.439 0.000 0.220 -0.558 -0.101 -0.068
20 H -1.578 -3.682 -5.787 1.039 -2.104 -4.199 2.898 2.105 -2.071 5.003 4.210 2.105
V 0.402 0.411 0.476 -0.443 0.000 0.072 -0.439 0.000 0.068 -0.558 -0.085 -0.068
25 H -1.578 -3.682 -5.787 1.121 -2.104 -4.199 2.898 2.105 -2.071 5.003 4.210 2.105
V 0.403 0.411 0.475 -0.427 0.000 0.064 -0.439 0.000 0.068 -0.506 -0.051 -0.051
30 H -1.582 -3.656 -5.721 1.133 -2.084 -4.192 2.939 2.085 -2.105 5.046 4.191 2.105
V 0.394 0.411 0.451 -0.419 0.000 0.048 -0.443 0.000 0.040 -0.490 -0.051 -0.033
35 H -1.582 -3.656 -5.721 1.220 -2.098 -4.203 3.255 2.038 -2.105 5.361 4.144 2.105
V 0.394 0.402 0.435 -0.418 0.000 0.030 -0.418 0.000 0.030 -0.406 0.000 0.000
40 H -1.977 -3.965 -6.060 1.775 -1.995 -4.100 3.748 1.973 1.8E-4 5.854 4.079 2.105
V 0.342 0.348 0.371 -0.360 0.000 0.000 -0.355 0.000 0.220 -0.355 0.000 0.000
45 H -1.977 -3.916 -6.021 1.972 -1.973 -4.068 3.880 1.908 1.8E-4 5.952 3.979 2.072
V 0.336 0.342 0.342 -0.337 0.000 0.000 -0.338 0.000 0.254 -0.337 0.000 0.000
209
F3
T(°C) σr 1 3 5 8
σ 3 5 8 1 5 8 1 3 8 1 3 5
-45 H -0.279 -2.270 -3.580 0.067 -0.278 -2.383 0.037 -6.4E-5 -0.286 0.333 0.296 0.296
V 0.471 0.671 0.884 -0.490 0.236 0.430 -0.725 -0.236 0.230 -0.948 -0.465 -0.230
-40 H -0.279 -2.270 -3.588 0.067 -0.278 -2.383 0.535 0.468 -2.056 3.033 2.573 0.469
V 0.489 0.672 0.884 -0.489 0.230 0.418 -0.719 -0.224 0.195 -0.896 -0.415 -0.233
-35 H -0.551 -2.527 -3.566 0.068 -0.279 -0.279 0.535 0.468 -2.056 3.041 2.573 0.469
V 0.477 0.672 0.896 -0.483 0.242 0.477 -0.716 -0.224 0.195 -0.896 -0.412 -0.230
-30 H -0.551 -2.527 -3.566 0.066 -0.655 -2.563 0.535 0.468 -2.056 3.115 2.647 0.789
V 0.474 0.660 0.878 -0.491 0.218 0.402 -0.717 -0.217 0.185 -0.878 -0.407 -0.224
-25 H -0.641 -2.680 -4.262 0.067 -0.658 -2.565 0.856 0.789 -1.908 3.115 2.647 0.789
V 0.467 0.645 0.846 -0.483 0.218 0.407 -0.693 -0.218 0.193 -0.885 -0.411 -0.225
-20 H -0.641 -2.680 -4.266 0.066 -0.655 -2.628 0.933 0.793 -1.908 3.119 2.651 0.794
V 0.467 0.637 0.829 -0.483 0.210 0.394 -0.693 -0.209 0.185 -0.854 -0.386 -0.217
-15 H -1.036 -3.020 -4.594 0.140 -1.046 -2.870 2.009 1.216 -1.908 3.683 2.894 1.217
V 0.451 0.620 0.821 -0.475 0.210 0.403 -0.652 -0.193 0.177 -0.846 -0.394 -0.210
-10 H -1.036 -3.020 -4.660 0.469 7.9E-5 -2.136 2.178 1.389 -2.105 3.954 3.165 1.390
V 0.443 0.604 0.789 -0.459 0.234 0.394 -0.645 -0.185 0.169 -0.822 -0.363 -0.193
-5 H -1.036 -3.015 -4.995 0.469 7.9E-5 -2.136 2.646 1.857 -2.105 4.503 3.714 1.858
V 0.443 0.604 0.773 -0.468 0.242 0.394 -0.611 -0.161 0.154 -0.781 -0.338 -0.169
0 H -1.317 -3.296 -5.391 0.469 7.8E-5 2.136 2.778 1.989 -2.105 4.767 3.978 1.990
V 0.419 0.563 0.724 -0.460 0.242 0.395 -0.588 -0.153 0.153 -0.757 -0.306 -0.161
5 H -1.578 -3.682 -5.657 0.789 3.5E-4 -1.907 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.402 0.539 0.693 -0.443 0.233 0.402 -0.572 -0.137 0.145 -0.708 -0.273 -0.145
10 H -1.578 -3.682 -5.787 0.789 3.5E-4 0.005 2.893 2.104 -2.105 4.998 4.209 2.105
V 0.394 0.524 0.668 -0.442 0.242 0.507 -0.555 -0.121 0.145 -0.693 -0.257 -0.136
15 H -1.578 -3.682 -5.787 0.793 3.5E-4 -1.905 2.897 2.104 -2.105 5.002 4.209 2.105
V 0.379 0.507 0.644 -0.435 0.242 0.394 -0.555 -0.121 0.137 -0.676 -0.250 -0.137
20 H -1.584 -3.650 -5.712 1.130 -2.104 -3.921 2.897 2.104 -2.105 5.002 4.209 2.105
V 0.386 0.499 0.637 -0.403 0.113 0.266 -0.532 -0.105 0.137 -0.668 -0.215 -0.129
25 H -1.584 -3.650 -5.712 1.220 -2.104 -4.199 2.859 2.070 -2.105 5.425 4.209 2.105
V 0.371 0.475 0.604 -0.386 0.105 0.225 -0.539 -0.105 0.129 -0.628 -0.234 -0.129
30 H -1.976 -4.070 -5.955 1.571 -2.084 -3.902 3.493 2.104 -2.105 5.598 4.209 2.105
V 0.330 0.4423 0.580 -0.354 0.097 0.242 -0.467 -0.097 0.121 -0.588 -0.201 -0.121
35 H -1.976 -4.070 -6.175 1.989 -2.104 -4.218 4.076 2.104 -2.105 6.181 4.209 2.105
V 0.315 0.394 0.492 -0.315 0.089 0.193 -0.394 -0.081 0.113 -0.507 -0.193 -0.112
40 H -1.964 -4.070 -6.165 2.000 -2.104 -4.161 4.093 2.104 -2.105 6.205 4.209 2.105
V 0.290 0.363 0.467 -0.298 0.064 0.161 -0.346 -0.056 0.089 -0.459 -0.177 -0.105
45 H -2.104 -4.172 -6.277 2.104 -2.034 -4.181 4.208 2.104 -2.105 6.313 4.209 2.105
V 0.236 0.322 0.411 -0.274 0.064 0.145 -0.322 -0.049 0.089 -0.402 -0.129 -0.081
210
F4
T(°C) σr 1 3 5 8
σ 3 5 8 1 5 8 1 3 8 1 3 5
-45 H -0.279 -2.270 -3.383 0.067 -0.655 -2.461 2.170 2.104 -1.055 0.103 0.067 0.067
V 0.451 0.467 0.781 -0.459 0.041 0.330 -0.459 0.000 0.314 -0.829 -0.379 -0.330
-40 H -0.279 -2.270 -3.383 0.067 -0.655 -2.461 2.170 2.104 -1.055 0.103 0.067 0.067
V 0.451 0.475 0.789 -0.459 0.041 0.338 -0.451 0.000 0.306 -0.837 -0.394 -0.330
-35 H -0.551 -2.665 -2.918 0.066 -0.558 -2.441 2.170 2.104 -1.055 0.177 0.140 0.140
V 0.442 0.451 0.773 -0.459 0.0399 0.330 -0.459 0.000 0.314 -0.846 -0.379 -0.322
-30 H -0.641 -2.683 -3.736 0.066 -0.641 -2.615 2.038 1.972 -1.055 0.831 0.765 0.296
V 0.442 0.443 0.757 -0.455 0.040 0.322 -0.459 0.000 0.310 -0.821 -0.363 -0.314
-25 H -0.641 -2.580 -3.561 0.140 -1.060 -2.647 1.695 1.816 -1.055 2.574 2.507 0.469
V 0.437 0.436 0.742 -0.460 0.021 0.304 -0.468 0.000 0.300 -0.763 -0.303 -0.312
-20 H -0.641 -2.480 -3.534 2.104 -1.529 -2.116 1.645 1.578 -1.055 2.697 2.631 0.789
V 0.436 0.430 0.731 -0.389 0.000 0.312 -0.466 0.000 0.295 -0.754 -0.295 -0.306
-15 H -1.036 -2.640 -4.102 0.469 -2.088 -3.543 1.641 1.574 -1.521 2.762 2.631 0.789
V 0.425 0.419 0.695 -0.442 -0.024 0.253 -0.468 0.000 0.277 -0.742 -0.277 -0.295
-10 H -1.036 -2.610 -4.251 0.469 -2.088 -3.543 1.111 1.044 -1.661 2.766 2.635 0.794
V 0.424 0.407 0.678 -0.448 -0.036 0.248 -0.477 0.000 0.265 -0.725 -0.265 -0.300
-5 H -1.317 -2.896 -4.720 0.789 -1.841 -3.486 1.356 1.052 -1.727 2.992 2.795 1.217
V 0.407 0.389 0.642 -0.430 -0.030 0.230 -0.460 0.000 0.265 -0.725 -0.265 -0.283
0 H -1.578 -2.631 -4.674 0.789 -1.841 -3.815 1.430 0.970 -2.056 3.165 2.705 1.390
V 0.395 0.401 0.631 -0.436 -0.047 0.195 -0.454 0.000 0.230 -0.713 -0.259 -0.277
5 H -1.578 -2.645 -4.618 0.793 -1.841 -3.815 1.676 0.887 -2.105 3.534 2.745 1.858
V 0.383 0.371 0.595 -0.424 -0.059 0.165 -0.430 0.000 0.218 -0.654 -0.230 -0.230
10 H -1.582 -2.619 -4.674 0.793 -1.956 -4.051 1.534 0.745 -2.105 3.523 2.734 1.990
V 0.383 0.359 0.566 -0.436 -0.082 0.124 -0.430 0.000 0.212 -0.654 -0.212 -0.218
15 H -1.582 -2.619 -4.674 1.220 -1.578 -3.683 1.551 0.762 -2.105 3.651 2.862 2.105
V 0.371 0.354 0.566 -0.389 -0.064 0.142 -0.424 0.000 0.206 -0.625 -0.200 -0.200
20 H -1.645 -2.537 -4.642 1.568 -1.004 -3.109 1.683 0.763 -2.105 3.789 2.868 2.105
V 0.359 0.354 0.542 -0.359 -0.023 0.171 -0.418 0.000 0.189 -0.613 -0.197 -0.195
25 H -1.984 -2.602 -4.655 1.775 -0.744 -2.849 1.728 0.602 -2.105 3.833 2.707 2.105
V 0.330 0.324 0.513 -0.360 0.000 0.183 -0.418 0.000 0.183 -0.583 -0.183 -0.183
30 H -1.976 -2.609 -4.659 1.996 -0.597 -2.702 2.140 0.578 -2.105 4.244 2.683 2.105
V 0.318 0.312 0.495 -0.312 0.000 0.171 -0.359 0.000 0.177 -0.531 -0.177 -0.177
35 H -2.104 -2.655 -4.726 2.104 -0.542 -2.627 2.433 0.526 -2.105 4.550 2.643 2.105
V 0.283 0.277 0.466 -0.289 0.000 0.183 -0.312 0.000 0.183 -0.477 -0.176 -0.174
40 H -2.104 -2.655 -4.726 2.104 -0.528 -2.623 2.423 0.517 -2.105 4.538 2.631 2.105
V 0.271 0.271 0.466 -0.265 0.000 0.183 -0.301 0.000 0.177 -0.489 -0.189 -0.189
45 H -2.104 -2.655 -4.726 2.104 -0.542 -2.627 2.433 0.526 -2.105 4.545 2.638 2.105
V 0.247 0.212 0.415 -0.274 0.000 0.194 -0.292 0.000 0.203 -0.495 -0.195 -0.203
211
F6
T(°C) σr 1 3 5 8
σ 3 5 8 1 5 8 1 3 8 1 3 5
-45 H -0.283 -0.846 -2.834 0.076 -0.279 -2.374 0.062 -0.023 -0.289 2.291 2.064 1.968
V 0.395 0.743 0.828 -0.390 0.367 0.442 -0.761 -0.357 0.113 -0.828 -0.442 -0.085
-40 H -0.283 -0.846 -2.834 0.067 -0.274 -2.369 0.067 0.000 -0.289 2.235 2.169 2.105
V 0.405 0.743 0.818 -0.395 0.358 0.433 -0.767 -0.367 0.108 -0.837 -0.433 -0.075
-35 H -0.284 -0.858 -2.813 0.067 -0.275 -2.370 0.066 0.000 -0.287 2.233 2.172 2.105
V 0.395 0.752 0.837 -0.405 0.358 0.433 -0.757 -0.367 0.113 -0.828 -0.423 -0.066
-30 H -0.587 -2.494 -4.378 0.067 -0.281 -2.385 0.067 0.000 -0.288 2.214 2.172 2.105
V 0.395 0.720 0.790 -0.395 0.366 0.433 -0.757 -0.358 0.113 -0.818 -0.423 -0.066
-25 H -0.669 -2.474 -4.579 0.067 -0.274 -2.369 0.067 0.000 -0.287 2.320 2.252 2.105
V 0.385 0.706 0.762 -0.405 0.358 0.405 -0.771 -0.367 0.103 -0.800 -0.414 -0.056
-20 H -0.647 -2.465 -4.570 0.067 -0.274 -2.369 0.067 0.000 -0.287 2.463 2.252 2.105
V 0.386 0.705 0.771 -0.405 0.358 0.423 -0.771 -0.376 0.094 -0.809 -0.405 -0.047
-15 H -1.044 -2.604 -4.664 0.146 -0.574 -2.679 0.067 0.000 -0.289 2.479 2.322 2.105
V 0.376 0.686 0.734 -0.395 0.348 0.395 -0.771 -0.367 0.103 -0.800 -0.405 -0.038
-10 H -1.044 -2.604 -4.664 0.147 -0.568 -2.663 2.574 0.470 -2.105 4.679 2.575 2.105
V 0.376 0.696 0.733 -0.405 0.348 0.386 -0.687 -0.348 0.038 -0.715 -0.386 -0.038
-5 H -1.063 -2.548 -4.653 0.389 -2.104 -4.199 2.574 0.470 -2.105 4.679 2.575 2.105
V 0.367 0.686 0.733 -0.395 0.282 0.311 -0.686 -0.358 0.038 -0.706 -0.386 -0.028
0 H -1.044 -2.604 -4.664 0.389 -2.104 -4.199 2.616 0.871 -2.105 4.671 2.976 2.105
V 0.367 0.668 0.687 -0.395 0.292 0.320 -0.677 -0.339 0.028 -0.687 -0.358 -0.019
5 H -1.412 -2.988 -5.093 0.794 -1.907 -4.002 2.600 1.036 -2.105 4.831 3.141 2.105
V 0.348 0.659 0.678 -0.376 0.292 0.306 -0.659 -0.329 0.019 -0.668 -0.329 0.000
10 H -1.582 -2.881 -4.986 0.871 -1.907 -4.012 2.607 1.044 -2.105 4.839 3.149 2.105
V 0.339 0.658 0.668 -0.367 0.282 0.292 -0.649 -0.320 0.019 -0.659 -0.320 0.009
15 H -1.584 -3.248 -5.344 0.957 -1.715 -3.800 2.697 1.128 -2.105 4.656 3.189 2.068
V 0.339 0.640 0.649 -0.358 0.301 0.301 -0.659 -0.329 0.000 -0.668 -0.329 -0.009
20 H -1.578 -3.223 -5.326 0.955 -1.907 -3.992 2.665 1.102 -2.104 4.577 3.189 2.072
V 0.329 0.640 0.649 -0.358 0.282 0.282 -0.659 -0.329 0.000 -0.678 -0.339 0.000
25 H -1.828 -3.802 -5.798 1.128 -1.974 -3.887 2.616 1.220 -1.921 4.479 3.085 1.866
V 0.329 0.611 0.602 -0.358 0.282 0.272 -0.668 -0.320 0.000 -0.665 -0.323 -0.007
30 H -1.585 -3.331 -5.222 1.125 -1.566 -3.527 2.702 1.570 -1.941 4.563 3.346 1.774
V 0.329 0.620 0.611 -0.348 0.292 0.282 -0.649 -0.292 -0.009 -0.659 -0.311 0.000
35 H -1.663 -3.724 -5.425 1.571 -1.827 -3.592 3.440 1.868 -1.739 4.933 3.544 1.572
V 0.310 0.574 0.583 -0.320 0.273 0.272 -0.583 -0.264 0.000 -0.593 -0.264 0.000
40 H -1.976 -3.958 -5.502 1.865 -1.948 -3.540 3.800 2.104 -1.618 5.533 3.668 1.564
V 0.272 0.517 0.518 -0.282 0.244 0.245 -0.527 -0.235 -0.009 -0.508 -0.226 0.000
45 H -1.976 -4.070 -5.561 1.995 -2.068 -3.535 4.100 2.104 -1.457 5.550 3.555 1.451
V 0.263 0.480 0.480 -0.254 0.225 0.226 -0.470 -0.217 0.000 -0.489 -0.225 0.000
212
APPENDIX B: THE WLF EQUATION FITTING
The obtained shift factors from time-temperature superposition master curve constructing were fitted with the Williams-
Landel-Ferry (WLF) equation, and the results were summarized as the following tables.
F1
Tr (°C) 1 MPa 3MPa 5 MPa 8 MPa
C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE
-45 3.38E07 4.343E08 0.361 1.41E08 1.589E09 0.168 2.83E07 3.082E08 0.168 5.32E07 5.670E08 0.184
-40 1.04E08 1.223E09 0.214 9.01E07 9.991E08 0.121 1.33E08 1.423E09 0.113 6.48E07 6.594E08 0.123
-35 7.96E07 8.898E08 0.229 1.47E08 1.588E09 0.113 8.10E07 8.518E08 0.128 9.22E07 9.378E08 0.129
-30 5.27E07 6.403E08 0.250 8.87E07 9.541E08 0.120 1.38E08 1.438E09 0.139 1.99E08 1.988E09 0.118
-25 2.30E08 2.520E09 0.271 8.76E07 9.384E08 0.132 1.02E08 1.069E09 0.126 7.37E07 7.455E08 0.138
-20 5.67E07 6.348E08 0.257 3.30E07 3.537E08 0.137 2.05E08 2.156E09 0.135 5.06E07 5.088E08 0.148
-15 1.76E08 1.960E09 0.285 1.95E08 2.115E09 0.153 6.87E07 7.151E08 0.166 1.60E08 1.629E09 0.154
-10 4.57E07 5.238E08 0.277 9.21E07 1.001E09 0.157 9.42E07 9.784E08 0.183 1.05E08 1.061E09 0.180
-5 2.12E08 2.436E09 0.315 1.40E08 1.531E09 0.180 3.59E07 3.823E08 0.185 3.46E08 3.513E09 0.195
0 7.67E07 8.943E08 0.297 8.02E07 8.830E08 0.188 2.09E08 2.219E09 0.204 2.18E08 2.246E09 0.192
5 2.27E08 2.688E09 0.275 8.72E07 9.734E08 0.183 1.01E08 1.097E09 0.210 1.38E08 1.431E09 0.195
10 7.47E07 8.940E08 0.257 1.22E07 1.376E08 0.149 1.34E08 1.460E09 0.179 2.03E08 2.133E09 0.189
15 7.80E07 9.388E08 0.225 6.71E07 7.600E08 0.150 4.35E06 4.787E07 0.164 2.05E08 2.166E09 0.166
20 6.92E07 8.287E08 0.222 1.23E08 1.392E09 0.131 1.39E08 1.531E09 0.174 9.21E07 9.711E08 0.180
25 2.90E07 3.468E08 0.215 5.93E07 6.650E08 0.132 1.88E08 2.059E09 0.158 1.00E08 1.054E09 0.149
30 3.55E07 4.192E08 0.214 1.76E08 1.950E09 0.124 3.04E07 3.294E08 0.146 8.97E07 9.285E08 0.142
35 1.24E08 1.432E09 0.224 2.11E08 2.319E09 0.134 1.44E08 1.523E09 0.151 1.75E08 1.778E09 0.160
40 6.11E07 6.930E08 0.249 1.29E08 1.405E09 0.153 3.71E07 3.866E08 0.182 6.77E07 6.789E08 0.177
45 6.58E07 7.427E08 0.252 4.93E07 5.314E08 0.170 7.06E07 7.310E08 0.196 6.09E07 6.060E08 0.197
213
(continued)
F2
Tr
(°C)
1 MPa 3MPa 5 MPa 8 MPa
C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE
-45 1.37E08 1.619E09 0.238 1.25E08 1.387E09 0.144 1.52E08 1.665E09 0.112 7.39E07 7.868E08 0.206
-40 1.41E08 1.586E09 0.138 1.26E08 1.380E09 0.104 4.14E07 4.448E08 0.104 6.57E07 6.623E08 0.142
-35 1.47E08 1.610E09 0.127 1.37E08 1.475E09 0.107 4.41E08 4.797E09 0.089 6.16E07 6.284E08 0.163
-30 8.92E07 9.651E08 0.149 9.09E07 9.706E08 0.110 4.78E07 5.124E08 0.088 2.13E08 2.109E09 0.163
-25 8.16E06 8.788E07 0.165 1.69E08 1.813E09 0.117 9.54E07 1.022E09 0.098 9.35E07 9.453E08 0.160
-20 1.39E08 1.498E09 0.181 1.74E08 1.853E09 0.133 8.78E06 9.365E07 0.101 7.61E07 7.689E08 0.157
-15 1.01E08 1.084E09 0.220 9.78E07 1.048E09 0.148 1.38E08 1.491E09 0.107 1.42E08 1.420E09 0.207
-10 1.67E08 1.847E09 0.196 7.58E07 8.120E08 0.147 7.96E07 8.553E08 0.127 1.89E06 1.921E07 0.181
-5 1.23E08 1.366E09 0.209 1.08E08 1.175E09 0.151 2.11E08 2.274E09 0.142 2.57E08 2.606E09 0.229
0 2.68E07 3.000E08 0.225 1.53E08 1.677E09 0.177 9.02E07 9.854E08 0.145 1.38E08 1.419E09 0.235
5 1.72E08 1.939E09 0.218 9.62E07 1.063E09 0.187 1.95E08 2.156E09 0.149 5.31E07 5.520E08 0.216
10 6.08E07 6.969E08 0.209 1.50E08 1.685E09 0.141 2.29E08 2.561E09 0.146 1.12E08 1.187E09 0.242
15 9.90E07 1.138E09 0.187 9.16E07 1.032E09 0.169 8.96E07 1.006E09 0.158 1.98E08 2.108E09 0.220
20 9.16E07 1.045E09 0.155 1.06E08 1.185E09 0.129 1.02E08 1.148E09 0.149 7.93E06 8.436E07 0.202
25 9.09E07 1.042E09 0.149 7.10E07 7.986E08 0.129 1.53E08 1.715E09 0.128 6.78E07 7.166E08 0.210
30 4.84E07 5.446E08 0.148 1.01E08 1.120E09 0.111 1.52E08 1.674E09 0.106 5.40E07 5.638E08 0.169
35 6.74E06 7.510E07 0.158 7.89E07 8.644E08 0.125 2.51E08 2.715E09 0.131 1.54E07 1.558E08 0.187
40 1.13E08 1.246E09 0.177 8.83E07 9.531E08 0.150 1.11E08 1.195E09 0.140 4.24E07 4.205E08 0.227
45 9.04E07 9.919E08 0.184 9.28E07 9.941E08 0.165 7.55E07 8.055E08 0.142 8.05E07 7.894E08 0.256
214
(continued)
F3
Tr (°C) 1 MPa 3MPa 5 MPa 8 MPa
C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE
-45 7.43E07 9.266E08 0.301 3.63E07 3.807E08 0.181 1.46E08 1.504E09 0.184 4.97E07 5.023E08 0.199
-40 9.16E07 1.068E09 0.184 4.12E06 4.317E07 0.174 4.20E07 4.237E08 0.149 6.44E07 6.314E08 0.163
-35 3.01E08 3.346E09 0.171 1.12E08 1.152E09 0.131 7.09E07 7.061E08 0.150 7.65E07 7.426E08 0.137
-30 9.78E07 1.057E09 0.224 1.25E08 1.266E09 0.142 1.22E08 1.221E09 0.150 7.85E07 7.640E08 0.153
-25 1.20E08 1.327E09 0.193 1.21E08 1.220E09 0.153 7.28E07 7.330E08 0.144 1.23E08 1.194E09 0.159
-20 1.34E08 1.479E09 0.209 2.57E08 2.583E09 0.159 1.13E08 1.118E09 0.161 1.57E08 1.509E09 0.156
-15 1.20E08 1.324E09 0.236 2.29E08 2.343E09 0.172 1.11E08 1.117E09 0.164 8.66E07 8.381E08 0.157
-10 1.52E08 1.697E09 0.253 1.15E08 1.180E09 0.177 2.18E08 2.154E09 0.202 2.29E08 2.215E09 0.191
-5 3.53E07 4.011E08 0.252 6.62E06 6.752E07 0.229 1.11E08 1.114E09 0.218 6.44E07 6.251E08 0.213
0 3.38E08 3.865E09 0.253 9.74E07 1.008E09 0.216 2.61E07 2.642E08 0.239 1.80E08 1.756E09 0.239
5 8.91E07 1.034E09 0.245 1.55E08 1.618E09 0.223 2.17E06 2.236E07 0.241 1.51E08 1.484E09 0.227
10 1.49E08 1.740E09 0.210 1.03E08 1.101E09 0.185 4.00E07 4.170E08 0.229 1.21E08 1.203E09 0.225
15 4.09E07 4.796E08 0.193 1.50E08 1.607E09 0.236 1.92E08 2.001E09 0.247 9.66E06 9.690E07 0.200
20 4.71E07 5.517E08 0.184 1.62E08 1.735E09 0.179 1.98E08 2.089E09 0.220 1.34E08 1.345E09 0.208
25 1.41E08 1.654E09 0.167 1.63E08 1.723E09 0.186 1.20E08 1.227E09 0.168 2.61E08 2.584E09 0.157
30 5.25E07 6.055E08 0.171 1.21E08 1.256E09 0.155 5.87E07 5.957E08 0.157 1.30E08 1.267E09 0.159
35 8.27E07 9.363E08 0.190 7.75E07 7.896E08 0.182 8.07E07 8.027E08 0.183 1.16E08 1.112E09 0.179
40 6.14E07 6.926E08 0.192 4.35E07 4.391E08 0.200 6.47E07 6.335E08 0.210 4.11E07 3.897E08 0.196
45 1.12E08 1.259E09 0.199 1.44E08 1.448E09 0.208 6.87E07 6.703E08 0.217 1.28E08 1.209E09 0.205
215
(continued)
F4
Tr (°C) 1 MPa 3MPa 5 MPa 8 MPa
C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE
-45 3.15E08 4.010E09 0.364 2.12E08 2.427E09 0.390 1.44E08 1.689E09 0.366 5.81E07 5.997E08 0.505
-40 1.15E08 1.391E09 0.272 1.44E08 1.566E09 0.281 3.12E07 3.504E08 0.289 5.49E07 5.357E08 0.402
-35 9.56E07 1.096E09 0.230 7.71E07 8.131E08 0.253 7.23E07 7.821E08 0.278 6.83E07 6.478E08 0.358
-30 1.99E08 2.259E09 0.238 1.65E08 1.726E09 0.261 7.64E07 8.210E08 0.265 6.43E07 6.018E08 0.356
-25 5.53E06 6.166E07 0.259 2.35E08 2.423E09 0.269 7.37E07 7.870E08 0.263 1.59E08 1.460E09 0.380
-20 1.25E08 1.415E09 0.259 1.96E07 2.012E08 0.276 1.88E08 2.000E09 0.284 1.53E08 1.407E09 0.384
-15 1.10E08 1.208E09 0.358 1.97E08 1.990E09 0.339 1.69E08 1.791E09 0.295 1.79E08 1.635E09 0.420
-10 8.56E07 9.579E08 0.358 1.71E08 1.761E09 0.349 4.83E07 5.035E08 0.387 2.21E08 2.004E09 0.472
-5 1.29E08 1.468E09 0.390 4.47E08 4.659E09 0.386 4.78E07 5.102E08 0.412 9.29E07 8.546E08 0.508
0 4.62E08 5.408E09 0.395 6.57E06 6.970E07 0.401 9.97E07 1.089E09 0.434 9.41E07 8.791E08 0.552
5 2.12E08 2.524E09 0.297 1.07E08 1.155E09 0.413 1.02E08 1.132E09 0.423 1.41E08 1.353E09 0.563
10 1.04E08 1.262E09 0.317 3.18E06 3.475E07 0.362 9.42E07 1.071E09 0.424 1.62E08 1.589E09 0.539
15 1.06E08 1.279E09 0.278 1.71E08 1.903E09 0.382 6.17E07 7.047E08 0.363 6.89E07 6.840E08 0.493
20 2.00E08 2.421E09 0.264 1.91E08 2.125E09 0.364 1.38E08 1.560E09 0.337 1.88E08 1.851E09 0.444
25 1.82E08 2.167E09 0.251 1.16E08 1.249E09 0.281 1.24E07 1.386E08 0.282 6.34E07 6.156E08 0.393
30 1.66E06 1.937E07 0.252 7.61E07 8.007E08 0.284 2.07E08 2.244E09 0.279 1.55E08 1.463E09 0.366
35 1.12E08 1.270E09 0.284 7.68E07 7.837E08 0.321 1.87E06 1.958E07 0.329 7.76E07 7.068E08 0.402
40 2.99E08 3.337E09 0.298 7.27E07 7.291E08 0.350 4.99E07 5.139E08 0.353 8.03E07 7.084E08 0.460
45 9.51E07 1.061E09 0.298 2.73E07 2.732E08 0.352 4.00E07 4.082E08 0.367 1.41E08 1.210E09 0.525
216
(continued)
F6
Tr (°C) 1 MPa 3MPa 5 MPa 8 MPa
C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE C1 C2 (K) SEE
-45 6.50E07 9.640E08 0.485 5.46E07 6.573E08 0.498 3.78E06 4.638E07 0.448 7.23E07 7.877E08 0.414
-40 1.25E06 1.675E07 0.341 2.70E07 3.087E08 0.342 6.60E07 7.444E08 0.316 6.43E07 6.757E08 0.345
-35 2.74E07 3.418E08 0.306 1.32E08 1.404E09 0.258 1.69E08 1.897E09 0.307 1.48E08 1.498E09 0.308
-30 8.69E07 1.067E09 0.304 3.31E06 3.508E07 0.303 2.24E08 2.424E09 0.292 1.41E08 1.420E09 0.334
-25 6.55E07 7.748E08 0.356 8.41E07 8.710E08 0.311 4.35E07 4.647E08 0.297 7.40E06 7.409E07 0.331
-20 8.40E07 9.686E08 0.390 1.20E08 1.246E09 0.353 7.88E06 8.247E07 0.334 8.18E07 8.056E08 0.348
-15 5.23E07 6.200E08 0.388 1.58E08 1.625E09 0.387 1.85E08 1.983E09 0.369 4.94E07 4.768E08 0.387
-10 8.75E07 1.064E09 0.435 1.24E08 1.317E09 0.386 2.03E08 2.155E09 0.418 1.49E08 1.460E09 0.435
-5 1.36E08 1.666E09 0.476 1.61E08 1.700E09 0.460 9.96E07 1.087E09 0.415 1.36E08 1.351E09 0.451
0 1.77E08 2.228E09 0.409 2.65E08 2.915E09 0.430 2.58E08 2.915E09 0.402 2.02E08 2.097E09 0.429
5 4.15E07 5.414E08 0.395 1.61E08 1.805E09 0.442 1.83E08 2.060E09 0.461 1.53E08 1.619E09 0.456
10 1.84E08 2.411E09 0.387 5.61E07 6.424E08 0.400 4.49E07 5.180E08 0.431 1.27E08 1.349E09 0.438
15 1.47E08 1.949E09 0.373 7.06E07 8.196E08 0.351 7.41E07 8.624E08 0.355 1.36E06 1.471E07 0.446
20 6.58E07 8.708E08 0.345 1.79E08 2.078E09 0.364 1.77E07 2.106E08 0.410 1.52E08 1.657E09 0.402
25 1.05E08 1.381E09 0.339 7.36E07 8.409E08 0.321 8.38E07 9.728E08 0.357 8.67E07 9.364E08 0.367
30 8.91E06 1.140E08 0.295 3.52E07 3.939E08 0.314 1.26E08 1.424E09 0.328 1.08E08 1.127E09 0.340
35 1.09E08 1.337E09 0.339 1.08E08 1.160E09 0.322 7.66E07 8.240E08 0.353 5.44E07 5.404E08 0.366
40 8.92E07 1.068E09 0.370 3.26E07 3.406E08 0.388 8.82E07 9.220E08 0.390 1.24E08 1.195E09 0.425
45 1.30E08 1.522E09 0.401 5.95E07 6.140E08 0.420 1.50E08 1.532E09 0.437 4.33E07 4.085E08 0.469
