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Creep behaviour of wood-plastic composites Chang, Feng-Cheng 2011

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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  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  ii  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.  iii  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.  iv  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 v  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 vi  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 vii  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  viii  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  ix  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 x  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 xi  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  xii  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.  xiii  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  xiv  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 1  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  2  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  3  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  4  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  5  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 timetemperature 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 fullscale 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.  6  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  7  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.  8  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 timetemperature-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  9  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  10  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].  11  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].  12  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:  13  (  )  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  14  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.  15  ( )  ∑ {  [ (  ]}  (  )  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].  16  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:  ( )  ∫ (  )  ( )  (  )  17  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 timetemperature 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 inphase strain. However, in an ideal fluid, the stress leads the strain by 90° (π/2) out of 18  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: (  )  (  )  19  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  20  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  21  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 thermorheologically 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  22  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 semicrystalline 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 23  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: [ (  )  (  )]  [  (  )] (  )  24  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:  (  )  25  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  26  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]. 27  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.  28  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.  29  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  30  treated as a single-phase material [Pramanick and Sain 2006a]. However, MartinezGuerrero [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. 31  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 timetemperature-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.  32  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;  33  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.  34  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  35  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),  36  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  37  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. 38  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  39  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.  40  3.3 Time-Temperature-Stress Superposition Principle for Creep Study Ferry [1980] summarized several criteria in the application of the timetemperature-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-LandelFerry (WLF) equation. However, Miyase et al. [1993] remarked that the simple timetemperature 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. 41  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 42  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. 43  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 timetemperature-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  44  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 45  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.  46  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 stresstemperature 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 47  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.  48  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. 49  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.  50  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  51  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.  52  Table 4-1. Formulations of MPB-WPC Products Formulations (% by weight) Material F1 F2 F3 F4 F5 − MPB Wood Flour 50.0 58.9 66.7 60.0 − − − − 60 Mesh AWF Pine 58.9 HDPE 46.7 37.8 30.0 39.0 37.8 MAPP 2.3 2.3 2.3 0.0 2.3 Talc 0.0 0.0 0.0 0.0 0.0 Lubricant 1.0 1.0 1.0 1.0 1.0 100.0 100.0 100.0 100.0 100.0 Total  F6 58.9 − 33.8 2.3 4.0 1.0 100.0  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 53  Table 4-2. Temperature Profile for the Extrusion Process Temperature (°C) Barrel Zone 1 2 3 4 Screw Die Zone 1 2 3  171 171 171 171 171 177 177 177  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.  54  Table 4-3. Experimental Conditions for Mechanical Tests Sample Size Load Property  ASTM  Length  Width  Thickness  Speed  (mm)  (mm)  (mm)  (mm/min)  Replicates  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 55  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:  (  ) 56  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 44). 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  57  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.  58  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  59  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  60  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:  61  ( (  ) )  (  )  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.  62  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 F4 F6 Load levels (%) 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 46 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  63  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 64  In order to make a comparison between the DMA results and those of the longterm 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  65  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:  66  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 woodplastic 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.  67  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.  68  CHAPTER 5. MPB-WPC PRODUCTS Mountain pine beetle (MPB) attacked lodgepole pine was used to produce woodplastic 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. 69  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  70  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/m3 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 MPBWPC products (F2) and the American Wood Fibers / WPC (AWF-WPC) products (F5)  71  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 Formulations  Properties 3  Density(kg/m ) MOE (GPa) MOR (MPa) Compression (MPa) Hardness (kN) Nail Withdrawal (N) Screw Withdrawal (N)  F1  F2  F3  F4  F5  F6  1110 (0.56) 3.91 (3.14) 38.26 (4.39) 30.82 (3.75) 12.55 (1.02) 548.72 (14.20) 3656 (4.04)  1153 (0.41) 4.28 (6.60) 34.25 (3.06) 28.62 (2.38) 11.98 (1.75) 542.13 (9.70) 3474 (4.32)  1184 (0.59) 5.08 (7.38) 30.49 (8.80) 27.40 (5.54) 10.17 (3.81) 485.06 (7.82) 3271 (3.83)  1163 (0.78) 3.39 (15.27) 21.89 (6.32) 19.41 (1.12) 9.57 (2.74) 376.27 (7.06) 2413 (3.84)  1167 (0.47) 4.54 (4.01) 33.91 (1.33) 28.76 (3.29) 10.92 (3.69) 485.98 (9.19) 3443 (6.80)  1218 (0.18) 6.29 (7.54) 35.60 (4.07) 28.74 (5.91) 10.82 (4.37) 486.89 (7.89) 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  72  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.  73  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  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.  76  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.  77  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 78  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  79  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 ANOVA  Tukey Test  Properties 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.  80  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  81  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.  82  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.  83  Table 5-3. Results of Regression Analysis SEE*  R2  R2-adj  P  381.70  0.887  0.877  <0.01  MOR (MPa) = 76.9– 0.58x1 – 0.34x2 + 11.1x3 – 0.0019x12  1.74  0.922  0.915  <0.01  Compression (MPa) = 53.4– 0.87x1 – 0.03x2 + 8.93x3 + 0.0054x12  1.19  0.933  0.919  <0.01  Hardness (N) = -44928+ 1324 x1+ 291x2+ 2899x3– 10.1x12  317.19  0.931  0.925  <0.01  Nail Withdrawal (N) = -2763+ 74.3x1+ 15.5 x2 + 203x3– 0.533 x12  49.76  0.659  0.590  <0.01  144.85  0.921  0.906  <0.01  Properties  Regression Equation  MOE (MPa) = 61668– 865x1 – 504x2 – 190x3+3.69 x12  Screw Withdrawal (N) = 3608+ 6.0x1– 9.4x2 + 1013x3– 0.33x12  β1 β2 β3 β11 β1 β2 β3 β11 β1 β2 β3 β11 β1 β2 β3 β11 β1 β2 β3 β11 β1  pparameter Estimate <0.01 <0.01 0.419 0.091 0.644 0.089 <0.01 0.847 0.483 0.871 <0.01 0.570 <0.01 <0.01 <0.01 <0.01 0.159 0.063 <0.01 0.190 0.968  β2  0.685  β3  <0.01  β11  0.776  Parameter Estimate  *Standard error of the estimate, in the same units as each property. 84  Table 5-4. Parsimonious Results of Regression Analysis SEE*  R2  R2-adj  P  386.30  0.879  0.874  <0.01  1.72  0.922  0.917  <0.01  1.14  0.931  0.925  <0.01  317.19  0.931  0.925  <0.01  Nail Withdrawal (N) = 226.95+ 3.83 x2 + 146.8x3  50.46  0.614  0.579  <0.01  Screw Withdrawal (N) = 3125+ 1039.54x3– 0.20x12  139.34  0.920  0.913  <0.01  Properties  Regression Equation  MOE (MPa) = 45875– 401.80x1 – 470.36x2 MOR (MPa) = 85.38– 0.82x1 – 0.36x2 + 10.94x3  Compression (MPa) = 31.76– 0.21x1 + 9.20x3 Hardness (N) = -44928+ 1323.60 x1+ 290.94x2+ 2898.60x3– 10.07x12  Parameter Estimate β1 β2 β1 β2 β3 β1 β3 β1 β2 β3 β11 β2 β3 β3 β11  pparameter Estimate <0.01 <0.01 <0.01 0.027 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 0.047 <0.01 <0.01 <0.01  *Standard error of the estimate, in the same units as each property  85  F1  F2  F3  F4  F5  F6  Table 5-5. Statistical Model Parameters for Flexural MOR of MPB-WPCs 5th Std. Mean Weibull Weibull percentile Distribution Dev. Error (MPa) Scale Shape Value (MPa) (MPa) Normal 38.26 1.81 — — 0.0004 35.34 Log-normal 2-p Weibull Normal Log-normal 2-p Weibull Normal  38.27 38.19 34.25 34.25 34.20 30.39  1.81 1.83 1.13 1.13 1.16 2.63  — 39.00 — — 34.71 —  — 26.06 — — 37.23 —  0.0004 0.0008 0.0003 0.0003 0.0004 0.0161  35.41 34.76 32.40 32.49 32.08 26.12  Log-normal  30.42  2.62  —  —  0.0168  26.35  2-p Weibull Normal Log-normal 2-p Weibull  30.32 21.87 21.87 21.82  2.67 1.43 1.41 1.48  31.47 — — 22.47  13.90 — — 18.23  0.0156 0.0052 0.0057 0.0038  25.50 19.55 19.67 19.14  Normal  33.91  0.43  —  —  0.0001  33.20  Log-normal 2-p Weibull  33.91 33.89  0.43 0.24  — 34.11  — 87.95  0.0001 0.0002  33.20 32.96  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. 86  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%.  87  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 highdensity 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 88  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-  89  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 90  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  91  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  92  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,  93  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.  94  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  95  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.  96  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.  97  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.  98  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 E* E’ MOE E* E’ MOE E* E’ MOE E* E’ MOE T (°C) (GPa) (GPa) (GPa) (GPa) 20 4.70 4.70 5.34 5.34 6.08 6.07 3.99 3.98 — — — — (0.64) (0.64) (0.93) (0.93) (0.23) (0.23) (0.41) (0.41) 25 4.38 4.37 3.91 4.95 4.94 4.28 5.67 5.66 5.08 3.56 3.54 3.39 (0.61) (0.61) (0.12) (0.87) (0.87) (0.28) (0.26) (0.25) (0.37) (0.36) (0.36) (0.52) 30 4.12 4.11 4.67 4.65 5.34 5.33 3.24 3.22 — — — — (0.58) (0.58) (0.84) (0.84) (0.24) (0.24) (0.38) (0.37) 35 3.84 3.83 4.36 4.34 4.98 4.96 2.90 2.87 — — — — (0.56) (0.55) (0.80) (0.80) (0.23) (0.23) (0.29) (0.29) 40 3.56 3.54 4.06 4.04 4.62 4.60 2.62 2.59 — — — — (0.53) (0.52) (0.74) (0.74) (0.22) (0.22) (0.24) (0.23) 45 3.28 3.26 3.75 3.73 4.27 4.24 2.36 2.33 — — — — (0.49) (0.49) (0.69) (0.69) (0.20) (0.20) (0.21) (0.20) Numbers in parentheses are the standard deviation Number of specimens for DMA test is 5 and for traditional flexural test is 10.  99  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 T g 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-derWaals, 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.  100  Figure 6-7. Storage modulus versus wood content at various temperatures  Figure 6-8. Loss modulus versus wood content at various temperatures  101  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.  Variable  Table 6-3. Regression Equations Regression R2  Onset (°C) = -39 + 4.66 x1 + 1.27 x2 – 0.0499 x12  Adj-R2  SEE  P  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 102  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 F2 F3 F4 HDPE  y = -58.539x + 6125.2 y = -63.854x + 6855.8 y = -69.742x + 7376.8 y = -62.212x + 5160.8 y= -28.072x + 2297.6  0.9917 0.7335 0.9777 0.9258 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  103  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 DTUL Std. Dev. Formulation (°C) (°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.  104  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  105  content of wood flour simply increased the value of modulus, but did not significantly change the range of transition.  106  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 longterm 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 timetemperature-stress superposition principle (TTSSP) to construct master curves, providing  107  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 10minute 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.  108  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 7-2 109  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) 110  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.  2.0E-03 1 min 5 min 10 min  Strain  1.5E-03  1.0E-03  5.0E-04  0.0E+00 -45 -40 -35 -30 -25 -20 -15 -10 -5 0  5 10 15 20 25 30 35 40 45  Temperature (°C)  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. 111  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 timedependent 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)  112  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:  ( )  ( )  (  )  113  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  114  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) 115  Table 7-1. Parameters for Temperature-Induced Creep Strain Fitting Parameters Formulations Stress R2 SEE d b m n 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 F1 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 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 F2 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 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 F3 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 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 F4 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 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 F6 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 R2: 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 temperature116  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-Dependent Modulus, ET (MPa) Temperature (°C) F1 F2 F3 F4 -45 6672 7578 8500 5607 -40 6630 7521 8445 5572 -35 6552 7423 8348 5507 -30 6453 7299 8226 5429 -25 6340 7158 8085 5343 -20 6214 7004 7931 5250 -15 6078 6838 7761 5151 -10 5929 6662 7579 5042 -5 5770 6479 7386 4922 0 5600 6288 7181 4790 5 5419 6086 6963 4639 10 5227 5878 6731 4468 15 5025 5661 6456 4270 20 4703 5344 6080 3987 25 4380 4948 5674 3557 30 4123 4669 5342 3243 35 3842 4359 4978 2898 40 3562 4061 4619 2618 45 3282 3754 4266 2365  F6 9546 9493 9394 9271 9134 8985 8824 8651 8464 8262 8044 7807 7552 7186 6704 6352 5953 5549 5138  117  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 Parameters Formulations 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  2  R : 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.  118  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) 119  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 twodimensional 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)  120  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.  121  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. 122  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 aT (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. 123  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.  124  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.  125  T (°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  Table 7-4. Horizontal Shift Factors at Various Reference Temperatures At 5 MPa (F2) Reference Temperature (°C) -45 0 -0.398 -0.851 -1.294 -1.787 -2.255 -2.671 -3.104 -3.545 -3.978 -4.451 -4.869 -5.335 -5.808 -6.318 -6.849 -7.418 -7.937 -8.440  -40 0.363 0 -0.439 -0.923 -1.398 -1.860 -2.282 -2.732 -3.176 -3.610 -4.079 -4.535 -4.989 -5.480 -5.941 -6.548 -7.086 -7.582 -8.133  -35 0.776 0.394 0 -0.465 -0.955 -1.374 -1.832 -2.241 -2.688 -3.155 -3.577 -4.044 -4.499 -4.956 -5.440 -5.987 -6.531 -7.030 -7.507  -30 1.238 0.850 0.424 0 -0.476 -0.954 -1.409 -1.817 -2.278 -2.736 -3.194 -3.634 -4.085 -4.583 -5.047 -5.589 -6.166 -6.642 -7.148  -25 1.700 1.319 0.899 0.450 0 -0.484 -0.951 -1.358 -1.811 -2.246 -2.719 -3.172 -3.638 -4.095 -4.555 -5.127 -5.710 -6.224 -6.698  -20 2.124 1.754 1.344 0.889 0.419 0 -0.481 -0.899 -1.358 -1.813 -2.278 -2.733 -3.190 -3.665 -4.142 -4.679 -5.244 -5.793 -6.253  -15 2.549 2.166 1.766 1.317 0.848 0.412 0 -0.462 -0.869 -1.348 -1.795 -2.248 -2.676 -3.143 -3.655 -4.171 -4.726 -5.242 -5.737  -10 2.982 2.597 2.191 1.758 1.288 0.849 0.422 0 -0.471 -0.913 -1.351 -1.803 -2.290 -2.730 -3.244 -3.756 -4.334 -4.813 -5.342  -5 3.426 3.036 2.643 2.189 1.728 1.297 0.866 0.429 0 -0.467 -0.927 -1.365 -1.792 -2.277 -2.757 -3.315 -3.894 -4.382 -4.883  0 3.864 3.478 3.073 2.628 2.164 1.734 1.317 0.879 0.444 0 -0.448 -0.923 -1.360 -1.825 -2.318 -2.847 -3.405 -3.904 -4.411  5 4.298 3.909 3.504 3.055 2.592 2.163 1.750 1.327 0.883 0.437 0 -0.430 -0.892 -1.368 -1.829 -2.385 -2.955 -3.428 -3.944  10 4.737 4.353 3.956 3.496 3.039 2.612 2.189 1.772 1.339 0.890 0.445 0 -0.439 -0.891 -1.372 -1.934 -2.459 -2.966 -3.499  15 5.184 4.795 4.395 3.940 3.478 3.047 2.624 2.206 1.782 1.344 0.898 0.446 0 -0.488 -0.945 -1.516 -2.067 -2.552 -3.046  20 5.641 5.253 4.855 4.397 3.938 3.510 3.091 2.655 2.226 1.801 1.360 0.915 0.461 0 -0.450 -1.007 -1.609 -2.100 -2.608  25 6.116 5.727 5.330 4.876 4.410 3.980 3.568 3.143 2.710 2.270 1.838 1.396 0.947 0.481 0 -0.527 -1.136 -1.618 -2.089  30 6.656 6.266 5.871 5.414 4.955 4.526 4.107 3.675 3.249 2.811 2.376 1.929 1.493 1.030 0.545 0 -0.598 -1.058 -1.537  35 7.209 6.823 6.429 5.973 5.513 5.080 4.665 4.237 3.806 3.367 2.941 2.486 2.047 1.601 1.124 0.569 0 -0.498 -1.000  40 7.701 7.314 6.916 6.458 5.998 5.569 5.150 4.726 4.297 3.855 3.426 2.981 2.530 2.083 1.613 1.076 0.501 0 -0.486  45 8.197 7.811 7.405 6.963 6.495 6.065 5.650 5.223 4.794 4.353 3.928 3.476 3.032 2.572 2.103 1.569 1.002 0.488 0  The numbers in the table were presented as log(shift factor)  126  Table 7-5. Coefficients of the WLF Equation for Horizontal Shift Factors (F2) F2  -45  C1 1.37E+08  1 MPa C2 1.619E9  SEE 0.238  C1 1.25E+08  3 MPa C2 1.387E9  SEE 0.144  C1 1.52E+08  5 MPa C2 1.665E9  SEE 0.112  C1 7.39E+07  8 MPa C2 7.868E8  SEE 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  Tr (°C)  127  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 MPBWPC 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  128  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:  (  )  (  )  (  )  129  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  130  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 0 0 3 -1.578 0.4024 1 5 -3.682 0.4106 8 -5.787 0.4755 1 1.039 -0.443 3 0 0 3 5 -2.104 0 8 -4.199 0.07237 1 2.898 -0.439 3 2.105 0 5 5 0 0 8 -2.071 0.06761 1 5.003 -0.5576 3 4.21 -0.08525 8 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. 131  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]  132  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:  (  (  )  (  )  )  133  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 Parameters Formulations 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  134  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 aTσ 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:  (  )  (  )  (  )  135  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  136  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.  137  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.  138  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 longterm 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 139  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.  140  Figure 8-1. Results of the long-term creep test  141  Figure 8-2. The effect of temperature on the long-term creep  142  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.  143  Figure 8-3. Master curves at Tr = 25°C  Figure 8-4. Shift factors used to construct master curves at Tr = 25°C  144  Temperature (°C) 15 20 25 30 35 40 45 50 55 60 65 70  Table 8-1. Shift Factors Used to Construct Master Curves F4 F6 20% 30% 40% 20% 30% 1.192(2.10) 0.622(3.27) 0 -0.684(5.83) -1.433(3.60) -2.042(2.15) -2.536(1.76) -2.978(1.84) -3.401(2.09) -3.784(1.70) -4.173(2.73) -4.555(2.92)  1.180(2.59) 0.611(2.13) 0 -0.705(2.46) -1.484(2.50) -2.102(2.76) -2.695(2.21) -3.215(2.24) -3.664(2.47) -4.100(3.54) -4.544(2.67) -5.001(3.07)  1.255(4.85) 0.655(5.67) 0 -0.726(1.26) -1.574(7.28) -2.267(0.22) -2.905(2.07) -3.402(1.68) -3.925(1.44) -4.420(2.01) -4.928(1.41) -5.433(0.79)  1.042(5.30) 0.576(8.89) 0 -0.600(3.20) -1.259(3.38) -1.834(6.95) -2.440(7.07) -3.013(7.36) -3.472(6.97) -3.899(6.32) -4.270(5.92) -4.619(5.60)  1.027(0.65) 0.526(4.37) 0 -0.644(2.52) -1.348(4.10) -2.031(3.77) -2.621(2.52) -3.187(2.25) -3.683(2.67) -4.110(1.80) -4.493(2.36) -4.876(3.51)  40% 1.061(2.72) 0.558(2.09) 0 -0.626(10.8) -1.313(1.42) -1.998(4.03) -2.652(1.69) -3.172(1.42) -3.689(1.64) -4.178(1.84) -4.612(0.93) -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 WLF Parameters Load Formulations Levels C1 C2 (K) SEE (%) 20 18.87 138.20 0.0999 F4 30 25.98 185.30 0.1051 40 30.75 206.80 0.1468 20 29.81 236.30 0.1277 30 32.01 240.50 0.1296 F6 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 145  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.  146  The short-term creep data were predicted with the newly developed stresstemperature 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 F4 F6 Temperature 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.  147  Table 8-4. Parameters of the STIC Model Parameters Formulations 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-  148  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 firHDPE 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 longterm 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.  149  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  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 152  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 longterm 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. 153  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 ValadezGonzález 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.  154  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 temperatureinduced 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.  155  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: (  )  (  )  156  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: ( )  (  )  (  )  (  )  ( )  (  )  (  )  157  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:  158  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 MarquardtLevenberg 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 Parameters Formulations R2 b u m n F4-20% 0.0692 -11.3729 13632.15 0.1965 0.9529 F4-30% 1.70E-05 1.9955 785.45 0.1762 0.9591 F4-40% 4.04E-05 1.1133 33654.85 0.1761 0.9644 F6-20% 2.06E-05 1.4369 144.13 0.1349 0.9868 F6-30% 8.93E-06 1.9131 124.77 0.1418 0.9547 F6-40% 8.10E-06 1.9643 126.98 0.1316 0.9844  SEE 7.32E-05 0.0001 0.0002 8.91E-05 9.96E-05 8.05E-05  R2: coefficient of determination 159  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.  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  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 shortterm and accelerated tests like DMA.  163  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  164  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  165  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  166  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.  167  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 168  (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.  169  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 170  independent of the stress for horizontal shifts. In addition, the temperature- and stressshift 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 MPCWPC products, the prediction of the master curve agreed more reasonably with the longterm data, whereas the master curves showed considerable overestimation for the uncoupled products. The testing configuration and the properties of the material may  171  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 shortterm 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  172  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  173  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. 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Holz Roh Werkst 66: 267-274. 185  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.  186  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  0.379  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  0  187  F1- 3MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  188  F1- 5MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  189  F1- 8MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  190  F2- 1MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  191  F2- 3MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  192  F2- 5MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  193  F2- 8MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  194  F3-1MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  195  F3- 3 MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  196  F3- 5MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  197  F3- 8MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  198  F4- 1MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  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-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  199  F4- 3MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  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  -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  -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  -45  0  -40 -35  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  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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  202  F6-1MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  -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  -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  -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  -45  0  -40 -35  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  203  F6-3MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  -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  -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  -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  -45  0  -40 -35  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  204  F6-5MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  -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  -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  -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  -45  0  -40 -35  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  205  F6-8MPa °C  -45  -40  -35  -30  -25  -20  -15  -10  -5  0  5  10  15  20  25  30  35  40  45  -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  -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  -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  -45  0  -40 -35  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  206  A.2 Time-Stress Superposition Shift Factors F1 T(°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  σr σ H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V  3 -0.279 0.491 -0.279 0.499 -0.551 0.499 -0.551 0.495 -0.647 0.499 -0.645 0.491 -1.036 0.483 -1.060 0.467 -1.060 0.467 -1.317 0.451 -1.578 0.435 -1.578 0.427 -1.578 0.435 -1.585 0.419 -1.585 0.419 -1.976 0.370 -1.976 0.363 -1.977 0.379 -1.977 0.386  1 5 -2.265 0.653 -2.265 0.668 -2.655 0.660 -2.655 0.648 -2.750 0.645 -2.750 0.620 -3.015 0.612 -3.122 0.580 -3.122 0.572 -3.411 0.548 -3.682 0.524 -3.682 0.507 -3.682 0.499 -3.689 0.467 -3.689 0.476 -4.070 0.411 -4.070 0.386 -3.916 0.378 -3.850 0.394  8 -3.588 0.829 -3.843 0.846 -4.233 0.922 -4.237 0.809 -4.821 0.781 -4.821 0.749 -5.000 0.741 -4.755 0.685 -4.755 0.700 -5.472 0.636 -5.787 0.596 -5.787 0.572 -5.787 0.556 -5.794 0.524 -5.674 0.532 -6.165 0.451 -6.175 0.419 -6.021 0.394 -5.935 0.402  1 0.067 -0.507 0.066 -0.492 0.067 -0.507 0.066 -0.499 0.067 -0.523 0.140 -0.507 0.296 -0.507 0.470 -0.499 0.470 -0.491 0.794 -0.475 0.873 -0.484 1.044 -0.459 1.151 -0.454 1.102 -0.451 1.220 -0.443 1.572 -0.411 1.865 -0.370 1.857 -0.389 1.996 -0.379  3 5 -0.274 0.202 -0.655 0.201 -0.264 0.201 -0.558 0.193 -0.563 0.193 -1.060 0.177 7.32E-5 0.2178 -2.068 0.113 -2.068 0.104 -2.066 0.096 -2.066 0.081 -2.104 0.077 -2.054 0.059 -2.066 0.064 -2.084 0.048 -2.084 0.049 -2.104 0.024 -1.973 0.000 -1.989 0.000  8 -2.369 0.354 -2.562 0.363 -0.253 0.411 -2.663 0.330 -2.668 0.330 -3.036 0.306 -2.172 0.323 -4.204 0.218 -4.204 0.193 -3.974 0.193 -3.924 0.177 -3.917 0.165 -3.976 0.135 -4.213 0.112 -4.223 0.081 -4.230 0.081 -4.226 0.049 -4.068 0.000 -4.094 0.000  1 0.534 -0.700 0.535 -0.701 0.856 -0.693 0.859 -0.685 1.512 -0.692 2.498 -0.644 2.515 -0.620 2.893 -0.612 2.893 -0.580 2.893 -0.563 2.893 -0.548 2.897 -0.540 2.897 -0.540 2.975 -0.524 3.320 -0.483 3.494 -0.457 3.957 -0.371 3.781 -0.402 3.814 -0.378  5 3 0.468 -0.193 0.468 -0.193 0.789 -0.185 0.793 -0.185 1.216 -0.177 1.972 -0.145 1.989 -0.129 2.104 -0.113 2.104 -0.104 2.104 -0.081 2.104 -0.072 2.104 -0.064 2.104 -0.065 2.104 -0.056 2.104 -0.033 2.105 -0.034 2.100 0.000 1.923 0.000 1.841 0.000  8 -2.056 0.161 -2.056 0.161 -1.908 0.161 -1.908 0.145 -2.105 0.137 -2.105 0.121 -2.105 0.113 -2.105 0.104 -2.105 0.097 -2.105 0.097 -2.105 0.072 -2.105 0.064 -2.105 0.065 -2.105 0.056 -2.105 0.041 -2.071 0.034 -2.071 0.034 -2.105 0.016 -2.105 0.000  1 2.704 -0.858 2.975 -0.850 2.975 -0.862 3.119 -0.837 3.633 -0.813 4.472 -0.765 4.620 -0.733 4.998 -0.717 4.998 -0.668 4.998 -0.668 4.998 -0.628 5.002 -0.596 5.002 -0.612 5.080 -0.588 5.425 -0.540 5.599 -0.473 6.062 -0.371 5.887 -0.406 5.901 -0.372  8 3 2.573 -0.358 2.647 -0.347 2.647 -0.354 2.651 -0.346 3.165 -0.315 3.946 -0.266 4.094 -0.242 4.209 -0.218 4.209 -0.185 4.209 -0.177 4.209 -0.145 4.209 -0.120 4.209 -0.137 4.209 -0.120 4.209 -0.089 4.210 -0.050 4.205 0.000 4.029 0.000 3.929 0.000  5 0.469 -0.194 0.789 -0.185 0.789 -0.185 0.794 -0.185 1.390 -0.161 1.974 -0.129 2.105 -0.112 2.105 -0.105 2.105 -0.089 2.105 -0.089 2.105 -0.065 2.105 -0.056 2.105 -0.064 2.105 -0.056 2.105 -0.032 2.105 -0.017 2.105 0.000 2.105 0.000 2.087 0.000  207  F2 T(°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  σr σ H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V  3 -0.270 0.475 -0.279 0.484 -0.279 0.476 -0.551 0.471 -0.647 0.471 -0.647 0.459 -1.060 0.448 -1.060 0.454 -1.060 0.442 -1.060 0.442 -1.578 0.411 -1.578 0.403 -1.578 0.402 -1.578 0.402 -1.578 0.403 -1.582 0.394 -1.582 0.394 -1.977 0.342 -1.977 0.336  1 5 -2.265 0.572 -2.265 0.572 -2.265 0.563 -2.655 0.551 -2.750 0.542 -2.750 0.531 -3.164 0.507 -3.164 0.506 -3.164 0.489 -3.164 0.484 -3.682 0.435 -3.682 0.427 -3.682 0.419 -3.682 0.411 -3.682 0.411 -3.656 0.411 -3.656 0.402 -3.965 0.348 -3.916 0.342  8 -3.588 0.781 -3.588 0.772 -3.843 0.758 -4.233 0.729 -4.821 0.695 -4.821 0.683 -5.152 0.648 -4.621 0.666 -4.621 0.648 -4.876 0.620 -5.787 0.539 -5.787 0.515 -5.787 0.499 -5.787 0.476 -5.787 0.475 -5.721 0.451 -5.721 0.435 -6.060 0.371 -6.021 0.342  1 0.066 -0.475 0.066 -0.483 0.067 -0.483 0.067 -0.491 0.066 -0.484 0.140 -0.484 0.147 -0.480 0.147 -0.486 0.147 -0.477 0.470 -0.465 0.794 -0.459 0.871 -0.442 0.957 -0.442 1.039 -0.443 1.121 -0.427 1.133 -0.419 1.220 -0.418 1.775 -0.360 1.972 -0.337  3 5 -0.558 0.129 -0.558 0.125 -0.655 0.121 -0.563 0.129 -0.641 0.121 -1.060 0.106 -1.315 0.094 -2.104 0.052 -2.104 0.042 -2.104 0.035 -2.066 0.040 -2.104 0.032 -2.062 0.024 -2.104 0.000 -2.104 0.000 -2.084 0.000 -2.098 0.000 -1.995 0.000 -1.973 0.000  8 -2.539 0.322 -2.539 0.306 -2.582 0.306 -2.668 0.298 -2.617 0.281 -3.036 0.265 -3.290 0.242 -4.159 0.189 -4.199 0.165 -4.199 0.142 -4.170 0.137 -4.006 0.137 -4.042 0.112 -4.199 0.072 -4.199 0.064 -4.192 0.048 -4.203 0.030 -4.100 0.000 -4.068 0.000  1 1.282 -0.588 2.038 -0.580 2.172 -0.558 2.172 -0.564 2.172 -0.558 2.244 -0.548 2.245 -0.547 2.245 -0.541 2.401 -0.523 2.574 -0.506 2.893 -0.484 2.894 -0.457 2.894 -0.439 2.898 -0.439 2.898 -0.439 2.939 -0.443 3.255 -0.418 3.748 -0.355 3.880 -0.338  5 3 1.216 -0.113 1.971 -0.097 2.105 -0.084 2.105 -0.082 2.105 -0.068 2.104 -0.071 2.105 -0.064 2.105 -0.051 2.105 -0.050 2.105 -0.033 2.104 -0.033 2.105 0.000 2.105 0.000 2.105 0.000 2.105 0.000 2.085 0.000 2.038 0.000 1.973 0.000 1.908 0.000  8 -1.661 0.202 -1.055 0.202 -1.238 0.186 -1.499 0.180 -1.710 0.186 -2.105 0.153 -1.971 0.145 -1.971 0.135 -1.971 0.135 1.4E-4 0.220 -2.105 0.105 1.5E-4 0.236 1.5E-4 0.220 -2.071 0.068 -2.071 0.068 -2.105 0.040 -2.105 0.030 1.8E-4 0.220 1.8E-4 0.254  1 2.640 -0.801 2.574 -0.794 2.894 -0.795 2.894 -0.772 2.965 -0.760 3.461 -0.731 3.963 -0.692 4.218 -0.659 4.276 -0.659 4.679 -0.609 4.998 -0.580 4.679 -0.558 4.999 -0.558 5.003 -0.558 5.003 -0.506 5.046 -0.490 5.361 -0.406 5.854 -0.355 5.952 -0.337  8 3 2.574 -0.314 2.574 -0.304 2.894 -0.305 2.894 -0.282 2.898 -0.287 3.321 -0.248 3.963 -0.202 4.078 -0.185 4.210 -0.186 4.210 -0.135 4.209 -0.129 4.210 -0.085 4.210 -0.101 4.210 -0.085 4.210 -0.051 4.191 -0.051 4.144 0.000 4.079 0.000 3.979 0.000  5 0.469 -0.220 0.469 -0.220 0.789 -0.220 0.789 -0.200 0.793 -0.203 1.217 -0.177 1.858 -0.145 1.973 -0.135 2.105 -0.135 2.105 -0.102 2.105 -0.104 2.105 -0.068 2.105 -0.068 2.105 -0.068 2.105 -0.051 2.105 -0.033 2.105 0.000 2.105 0.000 2.072 0.000  208  F3 T(°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  σr σ H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V  3 -0.279 0.471 -0.279 0.489 -0.551 0.477 -0.551 0.474 -0.641 0.467 -0.641 0.467 -1.036 0.451 -1.036 0.443 -1.036 0.443 -1.317 0.419 -1.578 0.402 -1.578 0.394 -1.578 0.379 -1.584 0.386 -1.584 0.371 -1.976 0.330 -1.976 0.315 -1.964 0.290 -2.104 0.236  1 5 -2.270 0.671 -2.270 0.672 -2.527 0.672 -2.527 0.660 -2.680 0.645 -2.680 0.637 -3.020 0.620 -3.020 0.604 -3.015 0.604 -3.296 0.563 -3.682 0.539 -3.682 0.524 -3.682 0.507 -3.650 0.499 -3.650 0.475 -4.070 0.4423 -4.070 0.394 -4.070 0.363 -4.172 0.322  8 -3.580 0.884 -3.588 0.884 -3.566 0.896 -3.566 0.878 -4.262 0.846 -4.266 0.829 -4.594 0.821 -4.660 0.789 -4.995 0.773 -5.391 0.724 -5.657 0.693 -5.787 0.668 -5.787 0.644 -5.712 0.637 -5.712 0.604 -5.955 0.580 -6.175 0.492 -6.165 0.467 -6.277 0.411  1 0.067 -0.490 0.067 -0.489 0.068 -0.483 0.066 -0.491 0.067 -0.483 0.066 -0.483 0.140 -0.475 0.469 -0.459 0.469 -0.468 0.469 -0.460 0.789 -0.443 0.789 -0.442 0.793 -0.435 1.130 -0.403 1.220 -0.386 1.571 -0.354 1.989 -0.315 2.000 -0.298 2.104 -0.274  3 5 -0.278 0.236 -0.278 0.230 -0.279 0.242 -0.655 0.218 -0.658 0.218 -0.655 0.210 -1.046 0.210 7.9E-5 0.234 7.9E-5 0.242 7.8E-5 0.242 3.5E-4 0.233 3.5E-4 0.242 3.5E-4 0.242 -2.104 0.113 -2.104 0.105 -2.084 0.097 -2.104 0.089 -2.104 0.064 -2.034 0.064  8 -2.383 0.430 -2.383 0.418 -0.279 0.477 -2.563 0.402 -2.565 0.407 -2.628 0.394 -2.870 0.403 -2.136 0.394 -2.136 0.394 2.136 0.395 -1.907 0.402 0.005 0.507 -1.905 0.394 -3.921 0.266 -4.199 0.225 -3.902 0.242 -4.218 0.193 -4.161 0.161 -4.181 0.145  1 0.037 -0.725 0.535 -0.719 0.535 -0.716 0.535 -0.717 0.856 -0.693 0.933 -0.693 2.009 -0.652 2.178 -0.645 2.646 -0.611 2.778 -0.588 2.893 -0.572 2.893 -0.555 2.897 -0.555 2.897 -0.532 2.859 -0.539 3.493 -0.467 4.076 -0.394 4.093 -0.346 4.208 -0.322  5 3 -6.4E-5 -0.236 0.468 -0.224 0.468 -0.224 0.468 -0.217 0.789 -0.218 0.793 -0.209 1.216 -0.193 1.389 -0.185 1.857 -0.161 1.989 -0.153 2.104 -0.137 2.104 -0.121 2.104 -0.121 2.104 -0.105 2.070 -0.105 2.104 -0.097 2.104 -0.081 2.104 -0.056 2.104 -0.049  8 -0.286 0.230 -2.056 0.195 -2.056 0.195 -2.056 0.185 -1.908 0.193 -1.908 0.185 -1.908 0.177 -2.105 0.169 -2.105 0.154 -2.105 0.153 -2.105 0.145 -2.105 0.145 -2.105 0.137 -2.105 0.137 -2.105 0.129 -2.105 0.121 -2.105 0.113 -2.105 0.089 -2.105 0.089  1 0.333 -0.948 3.033 -0.896 3.041 -0.896 3.115 -0.878 3.115 -0.885 3.119 -0.854 3.683 -0.846 3.954 -0.822 4.503 -0.781 4.767 -0.757 4.998 -0.708 4.998 -0.693 5.002 -0.676 5.002 -0.668 5.425 -0.628 5.598 -0.588 6.181 -0.507 6.205 -0.459 6.313 -0.402  8 3 0.296 -0.465 2.573 -0.415 2.573 -0.412 2.647 -0.407 2.647 -0.411 2.651 -0.386 2.894 -0.394 3.165 -0.363 3.714 -0.338 3.978 -0.306 4.209 -0.273 4.209 -0.257 4.209 -0.250 4.209 -0.215 4.209 -0.234 4.209 -0.201 4.209 -0.193 4.209 -0.177 4.209 -0.129  5 0.296 -0.230 0.469 -0.233 0.469 -0.230 0.789 -0.224 0.789 -0.225 0.794 -0.217 1.217 -0.210 1.390 -0.193 1.858 -0.169 1.990 -0.161 2.105 -0.145 2.105 -0.136 2.105 -0.137 2.105 -0.129 2.105 -0.129 2.105 -0.121 2.105 -0.112 2.105 -0.105 2.105 -0.081  209  F4 T(°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  σr σ H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V  3 -0.279 0.451 -0.279 0.451 -0.551 0.442 -0.641 0.442 -0.641 0.437 -0.641 0.436 -1.036 0.425 -1.036 0.424 -1.317 0.407 -1.578 0.395 -1.578 0.383 -1.582 0.383 -1.582 0.371 -1.645 0.359 -1.984 0.330 -1.976 0.318 -2.104 0.283 -2.104 0.271 -2.104 0.247  1 5 -2.270 0.467 -2.270 0.475 -2.665 0.451 -2.683 0.443 -2.580 0.436 -2.480 0.430 -2.640 0.419 -2.610 0.407 -2.896 0.389 -2.631 0.401 -2.645 0.371 -2.619 0.359 -2.619 0.354 -2.537 0.354 -2.602 0.324 -2.609 0.312 -2.655 0.277 -2.655 0.271 -2.655 0.212  8 -3.383 0.781 -3.383 0.789 -2.918 0.773 -3.736 0.757 -3.561 0.742 -3.534 0.731 -4.102 0.695 -4.251 0.678 -4.720 0.642 -4.674 0.631 -4.618 0.595 -4.674 0.566 -4.674 0.566 -4.642 0.542 -4.655 0.513 -4.659 0.495 -4.726 0.466 -4.726 0.466 -4.726 0.415  1 0.067 -0.459 0.067 -0.459 0.066 -0.459 0.066 -0.455 0.140 -0.460 2.104 -0.389 0.469 -0.442 0.469 -0.448 0.789 -0.430 0.789 -0.436 0.793 -0.424 0.793 -0.436 1.220 -0.389 1.568 -0.359 1.775 -0.360 1.996 -0.312 2.104 -0.289 2.104 -0.265 2.104 -0.274  3 5 -0.655 0.041 -0.655 0.041 -0.558 0.0399 -0.641 0.040 -1.060 0.021 -1.529 0.000 -2.088 -0.024 -2.088 -0.036 -1.841 -0.030 -1.841 -0.047 -1.841 -0.059 -1.956 -0.082 -1.578 -0.064 -1.004 -0.023 -0.744 0.000 -0.597 0.000 -0.542 0.000 -0.528 0.000 -0.542 0.000  8 -2.461 0.330 -2.461 0.338 -2.441 0.330 -2.615 0.322 -2.647 0.304 -2.116 0.312 -3.543 0.253 -3.543 0.248 -3.486 0.230 -3.815 0.195 -3.815 0.165 -4.051 0.124 -3.683 0.142 -3.109 0.171 -2.849 0.183 -2.702 0.171 -2.627 0.183 -2.623 0.183 -2.627 0.194  1 2.170 -0.459 2.170 -0.451 2.170 -0.459 2.038 -0.459 1.695 -0.468 1.645 -0.466 1.641 -0.468 1.111 -0.477 1.356 -0.460 1.430 -0.454 1.676 -0.430 1.534 -0.430 1.551 -0.424 1.683 -0.418 1.728 -0.418 2.140 -0.359 2.433 -0.312 2.423 -0.301 2.433 -0.292  5 3 2.104 0.000 2.104 0.000 2.104 0.000 1.972 0.000 1.816 0.000 1.578 0.000 1.574 0.000 1.044 0.000 1.052 0.000 0.970 0.000 0.887 0.000 0.745 0.000 0.762 0.000 0.763 0.000 0.602 0.000 0.578 0.000 0.526 0.000 0.517 0.000 0.526 0.000  8 -1.055 0.314 -1.055 0.306 -1.055 0.314 -1.055 0.310 -1.055 0.300 -1.055 0.295 -1.521 0.277 -1.661 0.265 -1.727 0.265 -2.056 0.230 -2.105 0.218 -2.105 0.212 -2.105 0.206 -2.105 0.189 -2.105 0.183 -2.105 0.177 -2.105 0.183 -2.105 0.177 -2.105 0.203  1 0.103 -0.829 0.103 -0.837 0.177 -0.846 0.831 -0.821 2.574 -0.763 2.697 -0.754 2.762 -0.742 2.766 -0.725 2.992 -0.725 3.165 -0.713 3.534 -0.654 3.523 -0.654 3.651 -0.625 3.789 -0.613 3.833 -0.583 4.244 -0.531 4.550 -0.477 4.538 -0.489 4.545 -0.495  8 3 0.067 -0.379 0.067 -0.394 0.140 -0.379 0.765 -0.363 2.507 -0.303 2.631 -0.295 2.631 -0.277 2.635 -0.265 2.795 -0.265 2.705 -0.259 2.745 -0.230 2.734 -0.212 2.862 -0.200 2.868 -0.197 2.707 -0.183 2.683 -0.177 2.643 -0.176 2.631 -0.189 2.638 -0.195  5 0.067 -0.330 0.067 -0.330 0.140 -0.322 0.296 -0.314 0.469 -0.312 0.789 -0.306 0.789 -0.295 0.794 -0.300 1.217 -0.283 1.390 -0.277 1.858 -0.230 1.990 -0.218 2.105 -0.200 2.105 -0.195 2.105 -0.183 2.105 -0.177 2.105 -0.174 2.105 -0.189 2.105 -0.203  210  F6 T(°C) -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45  σr σ H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V H V  3 -0.283 0.395 -0.283 0.405 -0.284 0.395 -0.587 0.395 -0.669 0.385 -0.647 0.386 -1.044 0.376 -1.044 0.376 -1.063 0.367 -1.044 0.367 -1.412 0.348 -1.582 0.339 -1.584 0.339 -1.578 0.329 -1.828 0.329 -1.585 0.329 -1.663 0.310 -1.976 0.272 -1.976 0.263  1 5 -0.846 0.743 -0.846 0.743 -0.858 0.752 -2.494 0.720 -2.474 0.706 -2.465 0.705 -2.604 0.686 -2.604 0.696 -2.548 0.686 -2.604 0.668 -2.988 0.659 -2.881 0.658 -3.248 0.640 -3.223 0.640 -3.802 0.611 -3.331 0.620 -3.724 0.574 -3.958 0.517 -4.070 0.480  8 -2.834 0.828 -2.834 0.818 -2.813 0.837 -4.378 0.790 -4.579 0.762 -4.570 0.771 -4.664 0.734 -4.664 0.733 -4.653 0.733 -4.664 0.687 -5.093 0.678 -4.986 0.668 -5.344 0.649 -5.326 0.649 -5.798 0.602 -5.222 0.611 -5.425 0.583 -5.502 0.518 -5.561 0.480  1 0.076 -0.390 0.067 -0.395 0.067 -0.405 0.067 -0.395 0.067 -0.405 0.067 -0.405 0.146 -0.395 0.147 -0.405 0.389 -0.395 0.389 -0.395 0.794 -0.376 0.871 -0.367 0.957 -0.358 0.955 -0.358 1.128 -0.358 1.125 -0.348 1.571 -0.320 1.865 -0.282 1.995 -0.254  3 5 -0.279 0.367 -0.274 0.358 -0.275 0.358 -0.281 0.366 -0.274 0.358 -0.274 0.358 -0.574 0.348 -0.568 0.348 -2.104 0.282 -2.104 0.292 -1.907 0.292 -1.907 0.282 -1.715 0.301 -1.907 0.282 -1.974 0.282 -1.566 0.292 -1.827 0.273 -1.948 0.244 -2.068 0.225  8 -2.374 0.442 -2.369 0.433 -2.370 0.433 -2.385 0.433 -2.369 0.405 -2.369 0.423 -2.679 0.395 -2.663 0.386 -4.199 0.311 -4.199 0.320 -4.002 0.306 -4.012 0.292 -3.800 0.301 -3.992 0.282 -3.887 0.272 -3.527 0.282 -3.592 0.272 -3.540 0.245 -3.535 0.226  1 0.062 -0.761 0.067 -0.767 0.066 -0.757 0.067 -0.757 0.067 -0.771 0.067 -0.771 0.067 -0.771 2.574 -0.687 2.574 -0.686 2.616 -0.677 2.600 -0.659 2.607 -0.649 2.697 -0.659 2.665 -0.659 2.616 -0.668 2.702 -0.649 3.440 -0.583 3.800 -0.527 4.100 -0.470  5 3 -0.023 -0.357 0.000 -0.367 0.000 -0.367 0.000 -0.358 0.000 -0.367 0.000 -0.376 0.000 -0.367 0.470 -0.348 0.470 -0.358 0.871 -0.339 1.036 -0.329 1.044 -0.320 1.128 -0.329 1.102 -0.329 1.220 -0.320 1.570 -0.292 1.868 -0.264 2.104 -0.235 2.104 -0.217  8 -0.289 0.113 -0.289 0.108 -0.287 0.113 -0.288 0.113 -0.287 0.103 -0.287 0.094 -0.289 0.103 -2.105 0.038 -2.105 0.038 -2.105 0.028 -2.105 0.019 -2.105 0.019 -2.105 0.000 -2.104 0.000 -1.921 0.000 -1.941 -0.009 -1.739 0.000 -1.618 -0.009 -1.457 0.000  1 2.291 -0.828 2.235 -0.837 2.233 -0.828 2.214 -0.818 2.320 -0.800 2.463 -0.809 2.479 -0.800 4.679 -0.715 4.679 -0.706 4.671 -0.687 4.831 -0.668 4.839 -0.659 4.656 -0.668 4.577 -0.678 4.479 -0.665 4.563 -0.659 4.933 -0.593 5.533 -0.508 5.550 -0.489  8 3 2.064 -0.442 2.169 -0.433 2.172 -0.423 2.172 -0.423 2.252 -0.414 2.252 -0.405 2.322 -0.405 2.575 -0.386 2.575 -0.386 2.976 -0.358 3.141 -0.329 3.149 -0.320 3.189 -0.329 3.189 -0.339 3.085 -0.323 3.346 -0.311 3.544 -0.264 3.668 -0.226 3.555 -0.225  5 1.968 -0.085 2.105 -0.075 2.105 -0.066 2.105 -0.066 2.105 -0.056 2.105 -0.047 2.105 -0.038 2.105 -0.038 2.105 -0.028 2.105 -0.019 2.105 0.000 2.105 0.009 2.068 -0.009 2.072 0.000 1.866 -0.007 1.774 0.000 1.572 0.000 1.564 0.000 1.451 0.000  211  APPENDIX B: THE WLF EQUATION FITTING The obtained shift factors from time-temperature superposition master curve constructing were fitted with the WilliamsLandel-Ferry (WLF) equation, and the results were summarized as the following tables. F1  -45  C1 3.38E07  1 MPa C2 (K) 4.343E08  -40 -35 -30 -25 -20 -15 -10 -5 0  1.04E08 7.96E07 5.27E07 2.30E08 5.67E07 1.76E08 4.57E07 2.12E08 7.67E07  1.223E09 8.898E08 6.403E08 2.520E09 6.348E08 1.960E09 5.238E08 2.436E09 8.943E08  0.214 0.229 0.250 0.271 0.257 0.285 0.277 0.315 0.297  9.01E07 1.47E08 8.87E07 8.76E07 3.30E07 1.95E08 9.21E07 1.40E08 8.02E07  9.991E08 1.588E09 9.541E08 9.384E08 3.537E08 2.115E09 1.001E09 1.531E09 8.830E08  0.121 0.113 0.120 0.132 0.137 0.153 0.157 0.180 0.188  1.33E08 8.10E07 1.38E08 1.02E08 2.05E08 6.87E07 9.42E07 3.59E07 2.09E08  1.423E09 8.518E08 1.438E09 1.069E09 2.156E09 7.151E08 9.784E08 3.823E08 2.219E09  0.113 0.128 0.139 0.126 0.135 0.166 0.183 0.185 0.204  6.48E07 9.22E07 1.99E08 7.37E07 5.06E07 1.60E08 1.05E08 3.46E08 2.18E08  6.594E08 9.378E08 1.988E09 7.455E08 5.088E08 1.629E09 1.061E09 3.513E09 2.246E09  0.123 0.129 0.118 0.138 0.148 0.154 0.180 0.195 0.192  5 10 15 20 25 30 35 40 45  2.27E08 7.47E07 7.80E07 6.92E07 2.90E07 3.55E07 1.24E08 6.11E07 6.58E07  2.688E09 8.940E08 9.388E08 8.287E08 3.468E08 4.192E08 1.432E09 6.930E08 7.427E08  0.275 0.257 0.225 0.222 0.215 0.214 0.224 0.249 0.252  8.72E07 1.22E07 6.71E07 1.23E08 5.93E07 1.76E08 2.11E08 1.29E08 4.93E07  9.734E08 1.376E08 7.600E08 1.392E09 6.650E08 1.950E09 2.319E09 1.405E09 5.314E08  0.183 0.149 0.150 0.131 0.132 0.124 0.134 0.153 0.170  1.01E08 1.34E08 4.35E06 1.39E08 1.88E08 3.04E07 1.44E08 3.71E07 7.06E07  1.097E09 1.460E09 4.787E07 1.531E09 2.059E09 3.294E08 1.523E09 3.866E08 7.310E08  0.210 0.179 0.164 0.174 0.158 0.146 0.151 0.182 0.196  1.38E08 2.03E08 2.05E08 9.21E07 1.00E08 8.97E07 1.75E08 6.77E07 6.09E07  1.431E09 2.133E09 2.166E09 9.711E08 1.054E09 9.285E08 1.778E09 6.789E08 6.060E08  0.195 0.189 0.166 0.180 0.149 0.142 0.160 0.177 0.197  Tr (°C)  SEE 0.361  C1 1.41E08  3MPa C2 (K) 1.589E09  SEE 0.168  C1 2.83E07  5 MPa C2 (K) 3.082E08  SEE 0.168  C1 5.32E07  8 MPa C2 (K) 5.670E08  SEE 0.184  212  (continued) F2  -45  C1 1.37E08  1 MPa C2 (K) 1.619E09  -40 -35 -30 -25 -20 -15 -10 -5  1.41E08 1.47E08 8.92E07 8.16E06 1.39E08 1.01E08 1.67E08 1.23E08  1.586E09 1.610E09 9.651E08 8.788E07 1.498E09 1.084E09 1.847E09 1.366E09  0  2.68E07  3.000E08  5 10 15 20 25 30 35  1.72E08 6.08E07 9.90E07 9.16E07 9.09E07 4.84E07 6.74E06  1.939E09 6.969E08 1.138E09 1.045E09 1.042E09 5.446E08 7.510E07  40 45  1.13E08 9.04E07  1.246E09 9.919E08  Tr (°C)  SEE  0.238 0.138 0.127 0.149 0.165 0.181 0.220 0.196 0.209 0.225 0.218 0.209 0.187 0.155 0.149 0.148 0.158 0.177 0.184  C1 1.25E08  3MPa C2 (K) 1.387E09  1.26E08 1.37E08 9.09E07 1.69E08 1.74E08 9.78E07 7.58E07 1.08E08  1.380E09 1.475E09 9.706E08 1.813E09 1.853E09 1.048E09 8.120E08 1.175E09  1.53E08  1.677E09  9.62E07 1.50E08 9.16E07 1.06E08 7.10E07 1.01E08 7.89E07  1.063E09 1.685E09 1.032E09 1.185E09 7.986E08 1.120E09 8.644E08  8.83E07 9.28E07  9.531E08 9.941E08  SEE  0.144 0.104 0.107 0.110 0.117 0.133 0.148 0.147 0.151 0.177 0.187 0.141 0.169 0.129 0.129 0.111 0.125 0.150 0.165  C1 1.52E08  5 MPa C2 (K) 1.665E09  4.14E07 4.41E08 4.78E07 9.54E07 8.78E06 1.38E08 7.96E07 2.11E08  4.448E08 4.797E09 5.124E08 1.022E09 9.365E07 1.491E09 8.553E08 2.274E09  9.02E07  9.854E08  1.95E08 2.29E08 8.96E07 1.02E08 1.53E08 1.52E08 2.51E08  2.156E09 2.561E09 1.006E09 1.148E09 1.715E09 1.674E09 2.715E09  1.11E08 7.55E07  1.195E09 8.055E08  SEE  0.112 0.104 0.089 0.088 0.098 0.101 0.107 0.127 0.142 0.145 0.149 0.146 0.158 0.149 0.128 0.106 0.131 0.140 0.142  C1 7.39E07  8 MPa C2 (K) 7.868E08  6.57E07 6.16E07 2.13E08 9.35E07 7.61E07 1.42E08 1.89E06 2.57E08  6.623E08 6.284E08 2.109E09 9.453E08 7.689E08 1.420E09 1.921E07 2.606E09  1.38E08  1.419E09  5.31E07 1.12E08 1.98E08 7.93E06 6.78E07 5.40E07 1.54E07  5.520E08 1.187E09 2.108E09 8.436E07 7.166E08 5.638E08 1.558E08  4.24E07 8.05E07  4.205E08 7.894E08  SEE  0.206 0.142 0.163 0.163 0.160 0.157 0.207 0.181 0.229 0.235 0.216 0.242 0.220 0.202 0.210 0.169 0.187 0.227 0.256  213  (continued) F3  -45  C1 7.43E07  1 MPa C2 (K) 9.266E08  SEE 0.301  C1 3.63E07  3MPa C2 (K) 3.807E08  SEE 0.181  C1 1.46E08  5 MPa C2 (K) 1.504E09  SEE 0.184  C1 4.97E07  8 MPa C2 (K) 5.023E08  SEE 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  Tr (°C)  214  (continued) F4  -45  C1 3.15E08  1 MPa C2 (K) 4.010E09  -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  Tr (°C)  SEE 0.364  C1 2.12E08  3MPa C2 (K) 2.427E09  SEE 0.390  C1 1.44E08  5 MPa C2 (K) 1.689E09  SEE 0.366  C1 5.81E07  8 MPa C2 (K) 5.997E08  SEE 0.505  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  215  (continued) F6  -45  C1 6.50E07  1 MPa C2 (K) 9.640E08  SEE 0.485  C1 5.46E07  3MPa C2 (K) 6.573E08  SEE 0.498  C1 3.78E06  5 MPa C2 (K) 4.638E07  SEE 0.448  C1 7.23E07  8 MPa C2 (K) 7.877E08  SEE 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  Tr (°C)  216  

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