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ANALYSIS OF MORPHOLOGY, CRYSTALLIZATION KINETICS,
AND PROPERTIES OF HEAT AFFECTED ZONE
IN HOT PLATE WELDING OF POLYPROPYLENE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree of Philosophy in the Graduate School
of The Ohio State University
By
Jenn-Yeu Nieh, B.S., M.S.
The Ohio State University
1995
Dissertation Committee Approved by
L. J. Lee
K. Koelling
A. Benatar Adviser Department of chemical engineering UHI Number: 9612251
UMI Microform 9612251 Copyright 1996, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized copying under Title 17, United States Code.
UMI 300 North Zeeb Road Ann Arbor, MI 48103 To My Lovely Wife and Two Children ACKNOWLEDGEMENTS
I wish to express my sincere appreciation to Dr. James L. Lee for his guidance
and insight through the study. Under his influnence, I have learned not only how to
handle the project, but also how to sell the ideas. Thanks go to the other members of
my advisory committee, Dr. A. Benatar and Dr. K. Koelling, for their suggestions and comments. I would like to thank Edison Welding Institute for providing technical and
financial supportsiii. I also would like to thank my dear fellow members in polymer group for the discussion and help, especially Dr. C.S. Wu and Dr. J. H. Tsai. Dr.
Wu gave me lots of help while I am developing the computer code. Dr. Tsai walked me through some tough time in the Lab. Gratitude is expressed to Mr. M. Kukalar for his technical assistance.
To my wife, Lillian, it is almost impossible for me to express my appreciation for your encouragement and for all the efforts you made to prepare a warm home for a tired and frustrated heart.
At last I would like to thank my Bible study group members in Columbus
Chinese Christian Church for their praying support At last I would like to thank God for giving me the opportunity to study, learn, and grow in OSU. VITA
Octobor 12,1963 ------Bom, Kaohsiung, Taiwan Republic of China
1985 ------B.S., National Cheng Kung University Tainan
1985-1987 ------Military service
1988-1990 ------Research Associate, Fluidization Lab. The Department of Chemical Engineering The Ohio State University Columbus, Ohio
1990-Present------Research Associate, Polymer Lab. The Department of Chemical Engineering The Ohio State University Columbus, Ohio
FIELDS OF STUDY
Chemical Engineering
Polymer Characterization and Processing LIST OF FIGURES
FIGURES PAGE 1.1 The schematics of pressure and displacement control of the hot plate welding process ...... 3
1.2 The diagram showing the relationship between weld quality and welding factors ...... 7
1.3 Block diagram of methodology ...... 8
2.1 The schematics of joint design ...... 11
2.2 Schematics of different types of misalignment at pipe butt joints ...... 22
2.3 Schematic illustration of three major types of crack causing failure...... 23
2.4 Schematic diagram of the weld with distinctive regions of different microstructres ...... 27
2.5 Disengangement of a chain from its initial tube ...... 37
2.6 Conformation of two chains at the interface before and after diffusion ...... 39
2.7 (a) Average shape and size of a chain’s most probable envelope at the interface before and after healing, (b) Segment density of the chain in (a) before and after healing ...... 39
2.8 The morphology of skin-core zone in an injection molded part ...... 45
2.9 A Hoffman and Week plot to determine the equilibrium melting temperature, T ^ ...... 46
v 2.10 The effects of shear rate on the half time crystallization based on Janeschitz-Kriegl model ...... 59
3.1 Micrographies of type I III and IV spherulites ...... 66
3.2 The DSC heat flux responses during melting and crystallization under different cooling rates ...... 69
3.3 The temperature dependent apparent heat capacity of PP ...... 72
3.4 The isothermal crystallization curve under different crystallization temperatures by DSC ...... 75
3.5 The crystallization peak times under various isothermal conditions ...... 76
3.6 The DSC results of heating to different temperature and then cooling to room temperature to complete the crystallization ...... 77
3.7 The schematic of crystal structure as temperature increases ...... 79
3.8 The DSC results of heating to different temperature zones and holding for 60 min and then cooling at constant rate to complete the crystallization ...... 81
3.9 The setup for microstructure examination during crystallization ...... 82
3.10 The morphological change during melting and crystallization along the DSC curve, case 1, completely melted ...... 84
3.11 The morphological change during melting and crystallization along the DSC curve, case 2, partially melted ...... 87
3.12 The Avrami plot for determining the spherulite growth rate constant and Avrami exponent ...... 93
3.13 The Lauritzen and Hoffman plot for determining KSg parameters...... 94
3.14(A) The comparison of rate constants from model calculation and experimental results under different crystallization temperatures ...... 96
vi 3.14(B) The comparison of rate constants from model calculation and experimental results under different crystallization temperatures ...... 97
3.15 The comparison of model prediction and DSC result of crystallization from zone EU ...... 100
3.16 The comparison of model prediction and DSC result of crystallization from zone I ...... 101
3.17 The simulated crystallization rate versus time under various crystallization temperatures ...... 103
3.18 The typical viscosity rise curve under isothermal crystallization ...... 105
3.19 The shear effect on crystallization induction time ...... 106
3.20 Master curve for the induction time as function of shear rate...... 107
3.21 The shift factor ax is a function of crystallization temperature based on the quiescent crystallization induction time ...... 109
3.22 The comparison of induction times calculated from the modified shear induced crystallization model and from the master curve, at T=140°C ...... 112
3.23 The preshearing effects on the crystallization determined by dynamic oscillation method via R D A II ...... 113
3.24 The simulated crystallization curves at 145°C with various shear rates ...... 115
3.25 The constant steady shear rate effects on nonisothermal crystallization ...... 116
3.26 The measured complex viscosity as a function of frequency ...... 119
3.27 The temperature shift factor, ay, for viscosity based on WLF equation, where To=202°C ...... 121
3.28 The master curve of Carreau model for reduced viscosity ...... 122
3.29 The stress relaxation curve of small strain, 10%. from RDA-700 ...... 123
vii 3.30 The predicted stress relaxation curve from generalized Maxwell model comparing with experimental one at T=161°C...... 125
3.31 The comparison of stress relaxation curves according to generalized Maxwell model based on T=161°C with experimental data ...... 128
3.32 The comparison of stress relaxation curve according to generalized Maxwell model based on T=123°C with experimental data ...... 129
4.1 The temperature profile at joining interface under different welding conditions ...... 133
4.2 Polarizing micrographs of microtomed specimen welded at a heating temperature of 200°C with different heating times ...... 135
4.3 Polarizing micrographs of microtomed specimen welded at a heating time of 10 sec with different heating temperatures...... 137
4.4 Polarizing micrographs of microtomed specimen welded at T=250°C and t=60 sec with a void at interface ...... 138
4.5 The deflection of molten layer due to too large melt length ...... 139
4.6 Micrograph of microtomed welded specimen (T=250°C, t=60 sec) with holding time 10 sec ...... 141
4.7 Tensile strength of weld under various welding conditions ...... 142
4.8 The effects of change-over time on tensile weld factor ...... 145
4.9 The schematics of microstructure in the HAZ...... 146
5.1 DEFORM system flow diagram ...... 149
5.2 The schematics of objects setup for DEFORM ...... 150
5.3 The effect of molten layer size on squeezing-out flash ...... 153
5.4 The simulated temperature profiles after heating from DEFORM ...... 154
viii 5.5 The simulated temperature profiles after squeezing from DEFORM ...... 156
5.6(a) The simulated strain profile after squeezing from DEFORM ...... 157
5.6(b) The micrograph of welded sample at the deflection corner ...... 158
5.7 Control volumes in triangular meshes ...... 161
5.8 A typical two dimensional triangular element ...... 165
5.9 A schematic for exponential shape function ...... 165
5.10 The schematic of the geometry for welding case ...... 168
5.11 The schematic of the element cleavage method ...... 170
5.12 The mesh geometry used in simulation (zoomed in joining interface area) ...... 171
5.13 1-D heat transfer equation and boundary conditions ...... 172
5.12 The measured interface temperature profiles ...... 174
5.15 The schematic of the heating stage as the molten layer built u p ...... 175
5.16(a) Simulated temperature profiles after heating under various heating time ...... 176
5.16(b) Simulated temperature profiles after heating under various heating time ...... 177
5.17(a) Simulated temperature profiles after squeezing under various heating time ...... 179
5.17(b) Simulated temperature profiles after squeezing under various heating time ...... 180
5.18 The averaged simulated cooling temperature profiles at joining interface for different welding displacements (T=250°C, t=30 sec, Usqueeze = 1.6 mm/sec)...... 181
5.19 The average cooling temperature profiles based on different convection heat transfer coefficients at the joining interface (T=200°C, t=60 sec and d=0.7 m m )...... 182
ix 5.20(a) Simulated stress profiles after squeezing under various heating time ...... 184
5.20(b) Simulated stress profiles after squeezing under various heating time ...... 185
5.21 Schematic of a welded sam ple ...... 186
5.22(a)The simulated cooling temperature change with time at the boundary of HAZ under different welding conditions with the same welding displacement, d=0.7 m m ...... 188
5.22(b) Micrographs of microtomed welds ...... 189
5.23(a) The tracer distribution during squeezing under T=250°C and t= 10 sec ...... 191
5.23(b) The micrograph of welded sample at the deflection corner ...... 192
5.24 The schematic layout of the colored later for squeezing visualization ...... 193
5.25 The colored sample (a) before squeezing, (b) after squeezing for 1 mm and (c) after squeezing for 2.5 m m ...... 195
A. 1 Welding flash notches ...... 207
A.2 Mismatch of weld joint ...... 207
A.3 The schematics of hot plate welding processing window ...... 209
A.4 Schematic diagram of the weld with distinctive regions of different microstructres ...... 214
A.5 showing the contributions of microstructure and spherulite boundary effects corresponding to the spherulite size...... 216
A.6 The micrograph of microtomed welded specimen with voids ...... 218
A.7(a) The interface temperature profile at different cooling time,Th=200°C, t=60 sec...... 221
x A.7(b) The interface temperature profile at different cooling time, Th=250°C, t=30 sec...... 222
A.7(c) The interface temperature profile at different cooling time, Th=320°C, t=10 sec...... 223
A.8 The simulated average cooling temperature profiles at joining interface under various welding conditions with same welding displacement, d=0.7mm. All weld factors are above 0.9 ...... 224
A.9 The comparison of estimated and experimental weld factors ...... 228
A. 10 The simulated cooling temperature profiles at joining interface of different welding displacements (T=250°C, t=30 sec)...... 229
A. 11 The estimated weld factors of various welding displacement from simulation ...... 230
A. 12 The estimated weld factors of various welding heating time from simulation ...... 232
xi LIST OF TABLES
TABLES PAGE 2.1 Defect type and possible NDT techniques to detect their occurrence ...... 32
3.1 The parameters used in the differential crystallization model ...... 99
3.2 The Comparison between experimental viscosity rise-up temperature and model prediction ...... 117
3.3 The comparison between experimental and model predicted induction-shifted temperatures based on Xc=0.096, cooling at 3.45°C/min under various shear rates...... 117
3.4 The parameters and constants for the generalized Maxwell model (polymer melt, T=161°C) ...... 126
3.5 The parameters and constants for the generalized Maxwell model, (solid, T=123°C) ...... 126
4.1. The melting temperature and heat of fusion around the weld zo n e ...... 144
A.l The crystallization peak temperature of various welding conditions ...... 224 TABLE OF CONTENTS
ACKNOWLEDGEMENTS...... iii
VTTA...... iv
LIST OF FIGURES...... v
LIST OF TABLES...... vi
CHAPTER ...... PAGE
I. INTRODUCTION...... 1
II. LITERATURE REVIEW
2.1 Introduction ...... 10 2.2 Thermoplastics Welding Technology ...... 10 2.2.1 Hot gas welding ...... 11 2.2.2 Friction welding ...... 12 2.2.3 Ultrasonic welding ...... 13 2.2.4 Induction welding ...... 14 2.2.5 Other welding methods ...... 15 2.2.6 Hot plate welding ...... 15 2.3 Temperature and Pressure Profiles in the Hot Plate Welding Proces ...... 15 2.4 Factors Affecting Joining Strength ...... 18 2.5 Effect of Misalignment ...... 21 2.6 Hot Plate Extension Effect ...... 24 2.7 Weld Bead (Flash ) Effect ...... 24 2.8 Weld Morphology ...... 25 2.9 Failure Mode on Welded Joints ...... 28 2.10 Quality Assessments ...... 29 2.10.1 Destructive testing ...... 29 2.10.2 Nondestructive testing (NDT) ...... 30 2.11 Welding of Dissimilar Materials ...... 35 2.12 Repetation Theory for Welding ...... 36 2.13 Griffith Approach to Brittle Fracture...... 40 2.14 Crystallization Kinetics ...... 43 2.15 Structure of Polymer Crystal ...... 43 2.16 Overall Crystallization Kinetic M odels ...... 49
xiii 2.16.1 Avrami m odel ...... 49 2.16.2 Tobin model ...... 52 2.16.3 Macrokinetic model ...... 53 2.17 Flow-Induced Crystallization ...... 54 2.18 Techniques To Determin Crystallization Kinetics ...... 62 2.18.1 Dilatometric M ethod ...... 62 2.18.2 Calorimetric Method ...... 62 2.18.3 Optical Method ...... 63 2.18.4 Other Analytic Methods ...... 63
III. MATERIAL CHARACTERIZATION 3.1 Introduction ...... 64 3.2 The Molecular Structure And Configuration Of Polypropylene 64 3.3 Thermal Analysis...... 67 3.3.1 DSC experiments...... 67 3.3.2 Melting behavior ...... 68 3.3.3 Apparent heat capacity measurement...... 70 3.3.4 Quiescent crystallization kinetic analysis ...... 73 3.3.5 Crystallization from completely melted polymer ...... 74 3.3.6 Crystallization from partially melted polymer ...... 74 3.4 The Quiescent Crystallization Examination Under Microscope 80 3.5 Proposed Crystallization Model Based On Dsc Curves ...... 89 3.6 Crystallization Kinetics Model For Entire Melting Range ...... 90 3.6.1 Determination of rate constants ...... 91 3.6.2 Differential form crystallization kinetics model ...... 98 3.7 Shear Induced Crystallization Kinetics ...... 102 3.8 The Preshear Effects on the Crystallization Kinetics ...... I l l 3.9 Rheological Characterization ...... 118
IV. HOT PLATE WELDING EXPERIMENTS 4.1 Hot Plate W elder ...... 130 4.2 Welding Sample Preparation ...... 130 4.3 Setup Prior to Welding Operation ...... 131 4.4 Welding Experiments ...... 132 4.5 Results and Discussions ...... 134 4.6 Concluding Remarks ...... 144
V. MODELING AND SIMULATION 5.1 Introduction ...... 147 5.2 DEFORM...... 147 5.2.1 Simulation Results ...... 153 5.3 Control Volume Finite Element Method ...... 155 5.3.1 The continuity equation ...... 159 5.3.2 The equation of motion ...... 159 5.3.3 The energy equation ...... 162 5.3.4 The numerical scheme...... 163 5.3.5 The welding case study ...... 166
xiv 5.3.6 The element cleavage technique ...... 169 5.4 CVFEM Simulation Results ...... 172 5.5 Tracer Method for Material Distribution ...... 187
5.6 Visualization of Colored Layer Molten Plastic Squeezing ...... 190
VI. CONCLUSIONS AND RECOMMANDATIONS...... 196
REFERENCE ...... 200
APPENDIX JOINING STRENGTH CORRELATION A. 1 Correlations of Joining Quality...... 206 A. 1.1 Flash appearance approach...... 206 A. 1.2 Reptation model approach ...... 211 A. 1.3 Dimensionless group approach ...... 212 A. 1.4 Microstmcture approach ...... 213 A.2 Current Approach ...... 217
xv CHAPTER I
INTRODUCTION
For product manufacturing, it is desirable to produce the final part in one piece.
However, in many cases, it is necessary to make joints in the manufacturing of products with complicated geometries. Various joining methods have been applied, such as mechanical fastening, adhesive bonding (gluing), and welding. Welding is an excellent way to make joints without introducing any foreign material into the joint area and with less stress concentration problems[l-2]. Among various welding technologies, hot plate welding has been used extensively in the fabrication of load-supporting structures involving a variety of thermoplastics. It has been used for pipe joints, automobile lamp assemblies, battery sealing, etc. Advantages of hot plate welding include process simplicity, the ability to weld large parts, and the capability of making high strength joints. For dissimilar but compatible polymer joining, the different heating temperature requirements for each polymer can be easily accommodated by using two heated tools in hot plate welding[2-3]. Long cycle times, compared with ultrasonic and vibration welding times, however, are the greatest disadvantage of hot-plate welding. According to different welding control mechanisms, the hot plate welding technique can be divided into two categories; one is by constant pressure control, and the other is by displacement
1 2 control. Figure 1.1. shows the whole process schematically. More detailed descriptions for each phase are given as follows:
Preparation
The hot plate process is very tolerant of contamination and poor fit-up. However, it is recommended that the surfaces of the parts to be welded have to be clean and relatively smooth, and they must match the surface of the heating element. The weld quality may be affected if the surfaces or the hot plate are contaminated by mold release agents or grease[4]. However, sensitivity of the process to contamination depends on several weld parameters and good bonds have been produced even when weld release agents are sprayed on the heated plate.
Heating
In this phase, the parts are heated by a heating element, a hot plate, with a constant matching pressure or with a constant displacement. The hot plate temperature is set so its surface reaches the required temperature. In some cases, the hot plate is covered by PTFE impregnated woven glass fiber to prevent adhering problems[4,5,6]. When such coatings are used, the maximum surface temperature should not exceed 260°C for more than 1 hour continuously[5]. With a constant heating displacement, the heating is carried out in two steps. In the first step, the part surface is brought to contact with the surface of the hot plate with a preset pressure to ensure good contact and to reduce the thermal resistance between the parts and the hot plate surface. This leads to a temperature increase in the parts. Once the parts become soften, the heating displacement can be completed. A small portion of the molten layer between the hot plate and the part may be squeezed out in this stage. Pressure, Pressure, Displacement Displacement A Figure 1.1 The schematics of pressure and displacement control control displacement and pressure of schematics The 1.1 Figure ^Pressure -Heating Displacement Heating Displacement (a) Constant Displacement Control Displacement Constant (a) of the hot plate welding process welding plate hot the of (b) Constant Pressure control control Pressure Constant (b) over Change- over Change Time Time I I
1 I il 1 1
Joining Joining Displacement Pressure Cooling Cooling Displacement Pressure
3 4 With a constant matching pressure of heating, the pressure is maintained constant during the heating phase. The molten layer is developed and begins to flow out. The length of molten layer decreases as the matching pressure increases under the same heating temperature because more molten material is squeezed out by the higher matching pressure.
Change-Over
After the part ends have been heated for a sufficient time, the parts are retracted away from the hot plate and the hot plate is removed quickly and carefully. The interval between the times when the plastics are withdrawn from the hot plate and when the parts are pushed together is called the change-over time. It must be as short as possible to prevent the fall in temperature at the surfaces of the parts from being too large. If the temperature at the surface drops too much, a thin solid film or skin of immobile polymer may form. Change-over time should be kept less than 3 seconds or minimized depending on the mass of polymer involved[5,7]. For some large parts, it might take longer change over time. The cold skin problem would become more severe.
Joining
The parts are contacted by application of desired welding pressure. This forging step can help the intermolecular diffusion that occurs across the interface. The diffusion causes polymer chain entanglement and provides the strength to the weld. Wool et. al.[8] reviewed the studies of strength development at interfaces and related the mechanical properties to the structure of the interface via microscopic deformation mechanisms involving disentanglement and bond rupture on the basis of reptation theory[9,10]. The time dependent structure of the welding interface was determined in terms of the 5 molecular dynamics of the polymer chains, the chemical compatibility, and the nature of
the interfaces. They concluded that the relation between structure and strength is
complex and necessitates the use of new entanglement concepts in microscopic
deformation models. There is still a limited understanding of the relationship between
the entanglement concepts and mechanical properties at the microscopic level.
Although intermolecular diffusion is quite complex, it can be simplified as
follows: for diffusion to occur in amorphous thermoplastics, the diffusion time depends
on the temperature of the material relative to the glass transition temperature. The higher
a temperature is applied, the more mobility of molecular chains can be gained. For the
semicrystalline polymers, the temperature must be greater than the melting temperature
and the time for diffusion is short since the melting temperature is much higher than the
glass transition temperature.
In the joining phase, the joining pressure and forging displacement can be
controlled depending on the type of welding machine used, i.e. hydraulic pressure control
or constant displacement mechanical stop control. Too high a pressure or too large a forging displacement may squeeze out too much molten material from the welded region.
With too low a pressure or too small a displacement, cavities may form at the weld interfaces due to shrinkage during cooling and the entrapped voids.
.Cooling
This is the final step in the process. Here the part cools and resolidifies. The residual stresses and final structure are obtained during cooling. It is important to keep the applied load or pressure throughout the cooling phase to prevent warping due to the residual stresses. With a displacement control mechanism, the applying pressure has already dropped to zero. The stress has changed from compressive mode to tensile mode. 6 The thermal contraction during solidification would affect the joining quality. For semicrystalline polymers, recrystallization occurs and microstructure is developed during this stage. The chemical resistance and mechanical properties will be affected by the microstructure change[ll-13]. The recrystallization behavior depends upon the cooling rates and stress effects.
From the above descriptions, the parameters to be controlled and optimized are heating temperature, matching time (under pressure), heating time ( from pressure to pressureless), matching pressure, matching displacement, change-over time, joining pressure, joining displacement, and cooling time. As shown in Figure 1.2, the governing phenomena, such as thermal history, crystallization kinetics, morphology and stress distribution, are affected by the welding parameters, i.e. heating temperature, heating time and displacement. The governing phenomena have a great influence on the joining quality. Several studies have tried to characterize the joining conditions by determining a joining parameter or several dimensionless groups to correlate the weld quality[5,6].
However, most of these correlations were based on experimental data only. They can be greatly improved if the fundamental aspects of the process are better understood.
The objective of this study is to investigate the microstructure formation during the hot plate welding process. The approach is to fully understand the material characterization related to the hot plate process, such as reheological properties, crystallization kinetics, thermal properties, and to develop a computer simulation in corporate with the those known ploymer to correlate the joining quality, as shown in
Figure 1.3. In this study, a semicrystalline polymer, polypropylene, was used as an example to investigate the microstructure formation in the heat affected zone. The kinetics of crystal melting and recrystallization were studied both experimentally and theoretically. A numerical model was developed to simulate heat transfer and squeezing 7
Controlling Governing Ultimate Parameter Phenomena Property
Heating Temperature Thermal History
Crystallization Joining Heating K in etics Time Strength M orphology
Displacement Stress Distribution
Figure 1.2 The diagram of the relationship between weld quality and welding factor 8
T=T( t, x)
Computer Simulation Parameters Maxwell Model t H. tH- Dw Thermal History Stress Build-up Thermal History ( during welding) Stress Relaxation (during cooling)
DSC Tm, Tc
Flow Induced Crystallization
Figure 1.3 Block diagram of methodology 9 flow during welding and the formation of microstructure in the weld. This model can be used to explain the weld quality in the hot plate welding process.
The flow chart of this study is shown in Figure 1.3. These material properties are then fed into a computer simulation model together with welding parameters such as heating temperature, heating time and displacement. In the heating stage, the temperature distribution in the parts can be calculated by the computer program. The melting temperature curve measured from differential scanning calorimetry can provide the kinetics of crystal melting. The deformation occurred during the squeezing (joining) stage is mostly in the molten layer. The rest of the part is assumed rigid. The stresses in the molten layer are built up during the squeezing stage. The strain rate and the rheological properties of the melt determine the stress distribution inside the molten layer.
As solidification and crystallization take place during the cooling stage, the stress relaxation also occurs. The remaining stresses will be frozen inside the weld zone and will affect the crystal structure. If the crystal structure in the welding zone can be simulated, one may be able to predict the joint strength through a correlation between the weld strength and the microstructure. Chapter II surveys the literatures in hot plate welding, healing theory and crystallization kinetics. Chapter III presents the material characterization including thermal properties, crystallization kinetics and rheological properties. Chapter IV covers the hot plate welding experiments. The computer simulation of the hot plate welding processes is presented in Chapter V. Conclusions and recommendations are drawn in Chapter VI. CHAPTER II
LITERATURE REVIEW
2.1 Introduction
In this chapter, a three-part literature review is conducted: the thermoplastic welding technology, healing theory, and polymer crystallization kinetics. The concepts and information provides the necessary background for the following chapters.
2.2 Thermoplastics Welding Technology
One of the most significant advantages of thermoplastic materials is that by the application of heat the material can exhibit the fluid-like behavior as the temperature reaches above glass transition temperature for amorphous polymers or melting temperature for semicrystalline polymers. The polymer chains between the molten surfaces would be able to diffuse and entangle to each other as the intimate contact is made. The healing process between either similar or dissimilar materials for assembling purpose by ways of heating is the welding process. The welds between parts could be made by different heating methods, such as hot gas, hot plate, vibration, ultrasonic, infrared, induction, microwave, etc. Although the heating mechanisms may be different, the basic concepts, i.e. fusion, diffusion and cooling, are the same. A brief description of some widely used welding techniques is given mentioned in the following sections.
10 11 2.2.1 Hot gas welding
Hot gas welding is widely used in industrial production where manual fabrication is appropriately 14,15]. This method is the most versatile one and is used typically in the fabrication of large plastic tanks, pipe work, and ducts, and in sealing thermoplastic films.
A heating source and a welding rod that assists in fusion of the weld to the parent material are applied. The types of joints used in thermoplastic welding are similar to those in metal welding, namely; butt joints, lap-joints, edge welds, and comer welds, as shown in Figure
2. 1.
Edge Weld Corner Weld
Lap Joint
Butt Joint
Figure 2.1 The schematics of joint design 12 Because of the difference in the physical characteristics of thermoplastics and metals, there are corresponding differences between welding techniques for metals and thermoplastics. In the welding of metals, the welding rod and the parent material become molten and fused into the required bond to form the welded joint. There is a sharply defined melting point in metal welding, which is not the case in thermoplastic welding.
The poor heat conductivity of the thermoplastic material makes the temperature distribution on the rod uneven. It is very likely that the welding rod is partially melted during welding.
Heating with too high a temperature or too long a time, in order to melt the welding rod completely, may degrade and decompose the surface of the plastic welding rod and the parent material. The working temperature range for thermoplastic hot gas welding is narrower than that for metal welding. Applying pressure on the welding rod to force the fusible portion into the joint to create the permanent bond is necessary[16].
2.2.2 Friction welding
In friction welding, two thermoplastic surfaces are rubbed together under friction, to develop sufficient heat for fusion of the two surfaces. Pressure has to be applied at the same time. Spin welding, ultrasonic welding and vibration welding are three major frictional types of welding with different friction mechanisms. Ultrasonic welding would be mentioned in the next section.
Spin welding, which is a rotary friction between two parts, is used extensively for assembling instrument knobs, bottle sections, tool handles, container caps, pipe, pipe fittings, and other similar applications[17-20]. The friction heat for vibration welding was generated by linear oscillations. Once the molten material is produced at the joining interface, vibration is stopped, the parts are aligned and the weld consolidates on 13 cooling[21-24]. The vibration frequency is in the range of 100 - 240 Hz and the amplitude is typically 1 -5 mm.
The advantages of spin welding are the speed at which it can be accomplished and the simplicity of the technique. Due to the poor heat conductivity of thermoplastics, frictional heat required for spin welding is produced almost immediately while the temperature of the material below the surface of the weld remains unchanged. The major disadvantages of spin welding are its limitation to circular areas and the squeezing out of soft material beyond the weld area before the weld is completed. In order to avoid overheating and to maintain proper pressure, the spin-weld cycle should be only long enough to insure complete fusion. The shorter cycle of the welding operation reduces the flash and the resultant internal stresses. The internal stresses would affect the tensile and impact properties of the welded article.
The advantages of vibration welding are: (1) high production rate on welding large complex linear joints, (2) short weld time (about 5 sec), (3) simplicity of tooling, (4) broad suitability for welding almost all thermoplastic materials. The vibration welding has wide applications on automobile parts including front and rear light assemblies, fuel filler doors, spoilers, instrument panels, fan surrounds, and two-part plastic bumpers.
The main disadvantage of the vibration welding is that it is limited to flat-seamed parts only.
2.2.3 Ultrasonic welding
Ultrasonic welding, a high frequency type of vibration welding, is made by holding the parts to be assembled together under pressure and then subjected them to ultrasonic vibrations, usually at 20 or 40 kHz frequency, at right angles to the contact area so that the longitudinal vibrations are transmitted through the component[25-27]. The heat was 14 generated by the alternating high frequency stresses in the plastics. With proper design heat can be selectively produced at the joining interface. The welding performance depends on the design of the welding equipment, the physical properties of the plastics, the design of the components and the welding parameters. The key features of joint design for ultrasonic welding are a slip fit (loose fit) and the provision of an energy director. A slip fit allows the movement between the two parts as well as friction and pressure which is essential for the fusion under the ultrasonic vibration. The energy director, in the simplest form, is a small triangular ridge, about 0.4 - 0.8 mm high, molded on one of the mating parts. The vibration energy is concentrated on the energy director and the material in the director would be melted rapidly. This molten plastic is compressed and spread throughout the joining area to form the weld.
The ultrasonic welding has been applied to assemble valves and filters used in medical equipment, cassette bodies, dash board in automotive, and vacuum cleaner bodies.
The advantages of ultrasonic welding are that it is capable of a high level of automation and can perform at very high production rates. The typical welding times are in the order of 0.5 to 1.5 sec. The disadvantages of ultrasonic welding are: (1) the high cost of the welding equipment, (2) limit on small component welding, for large components, complex and expensive multi-head machine is required.
2.2.4 Induction welding
Induction welding of plastics is fusion of two pieces of plastics by electrically induced heat which is obtained by causing a high frequency electric current to flow in a metallic insert such as a wire screen, a coil of wire, a die-stamped metal foil or a metallic conducting particles intermixed with the base resins near the face of the plastics to be joined together[28-30]. The localized heat around the metallic insert melts the surrounding 15 polymer to the fusion temperature. The joints are made by applying pressure between two joining surfaces. Induction welding is one of the fastest and versatile methods of joining
plastics. The disadvantages of induction welding are: (1) the remaining of the metal insert
in the final product, (2) the high cost of the induction welding equipment, (3) weld strength
not as strong as that by other methods.
2.2.5 Other welding methods
There are some other welding methods under development. They are based on high
efficiency heating schemes, such as microwave, dielectric, infrared, and laser[31]. The
major concern of these new technologies is to develop an automation process which can make high enough joining quality at very short time.
2.2.6 Hot plate welding
Hot plate welding can also be called heated tool welding. It consists of the use of a heated tool to bring the plastic to the fusion temperature by directly contacting the parts to the heated tool. In the hot-plate welding technique, the process can be divided into several phases, such as preparation, heating, change-over, joining, and cooling. The process can be simply described as: the faces to be joined are brought up to a hot plate and heated for some time until a molten layer formed, the hot plate is withdrawn and the two faces are then pressed together. The detailed description of each phase during the welding process has been mentioned in Chapter I. The following sections are focused on the effects of welding controllable parameters on the weld quality. 16 2.3 Temperature and Pressure Profiles in the Hot Plate Welding Process
In hot-plate welding, the typical heating temperature for an amorphous polymer should be at least 100°C higher than its glass transition temperature. For semicrystalline polymers, the heating temperatures should be at least 50°C higher than the melting temperatures. The different temperature setting guideline is due to the temperature dependence of viscosity. Change of viscosity is less sensitive for amorphous polymers in temperatures near the glass transition points than for semicrystalline polymers near the melting points[32].
When the plastic parts contact the hot plate, the temperature at the surface increases rapidly. Due to the thermal resistance between the surfaces of the plastics and the heated tool, the temperature at the plastic surface may be lower than the heating temperature at the tool. The higher matching pressure, which can provide good contact between the parts and the hot plate, results in less thermal resistance. As the time proceeds, the heat transfers from the hot plate surface to the plastic specimens. The molten layer develops from the contact surface to the far end as the temperature rises above the melting temperature. The thickness of the molten layer is affected by the heating temperature and heating time and also depends upon what kind of heating mechanisms is applied.
In the case of heating under a constant force, the molten layer would depend on the competition between the melting rate and the forging velocity, which is a function of the heating pressure. For heating with a constant mechanical stop, the molten layer thickness increases with heating temperature and heating time. Several researchers suggested that the ratio of the molten layer thickness to the part thickness plays an important role in determining the weld quality[5,12]. Since, in general, polymers have low thermal diffusivities, heat transfer through thermal conduction is poor. Most of heat would be localized at the contacting area. The temperature distribution would be broad and the 17 temperature gradient would be large. The matching pressure affects the heating efficiency at low pressure. If the pressure is not high enough, the intimate contact between the hot plate and the parts may not occur and the parts may not be heated properly. However, a higher matching pressure may result in more materials being squeezed out during the heating phase. After completion of matching, the force is reduced to a level at which no more melt is extruded from the joining zone. Heating is continued until the molten layer thickness is large enough to guarantee a good weld quality. During the final joining process, a welding pressure produces a squeezing flow. Thus at constant hot plate temperature and heating time, the joining pressure is the only parameter that affects the joining velocity.
In the change-over period, the part surface temperature may drop a lot due to heat loss by natural heat conduction and convection. The temperature drop is a function of change-over time, ambient conditions, and the molten layer thickness. If the surface temperature drops below the solidification temperature, the surface may form a thin solid skin. Since there is no further heat supplied in the change-over period, the temperature in the part will decrease slightly. For a very short change-over time, the temperature change can be negligible.
In the joining and cooling phases, part of the solidified skin, which is formed on the contact surface due to change-over cooling, and the molten material may be squeezed out like a fountain flow to form flash around welds. The flash acts like an insulation to the weld, so the temperature in the weld gradually cools down.
The amount of squeezed out material is determined by welding pressure and displacement during the joining phase. The more flash around the weld implies that the joining interfaces are at a lower temperature because a lot of hot molten materials have 18 flowed out. In this case the chain diffusion is limited due to low mobility at low temperatures.
2.4 Factors Affecting Joint Strength
The factors affecting the strength of welded joints made by hot plate welding technique have been discussed by many researchers. Bucknall[33] showed how welding displacement, heating time, and hot plate temperature affect the joint strength. Potente[34] proposed a method to improved the processing efficiency by high temperature hot plate welding. John and Lyashenko[35,36] investigated hot plate welding at low ambient temperature. The effects of hot plate stickout[37,38], flash removal[39-41], misalignment[42,43], dissimilar materials[3] on joint strength are also summarized here.
Welding displacement is defined as the inward travel of one of the specimen during the welding stages and is one of the welding parameters. The welding displacement has a great influence on the tensile strength of welded joint. The approach of a normalized welding displacement ( normalized by dividing it by the maximum attainable welding displacement ) was proposed to correlate the weld factor[33]. It was found that the maximum weld factor increases with heating time under the same normalized welding displacement. The weld factor drops abruptly as the welding displacement was out of the optimum range. At small displacements, contact between the mating faces is incomplete, and there may even be trapped air at the interface. At larger displacements, on the other hand, contact between the faces is complete, but a large proportion of the hot melt is squeezed out of the joining interface into the weld flash, leaving a thin layer of highly oriented material in the weld.
A lot of studies revealed that the strength reaches a maximum value at intermediate heating times, while holding the hot plate temperature, the heating displacement, and the 19 welding displacement constant. Increasing the heating time increases the thickness of the molten layer but decreases the normalized welding displacement with a fixed welding displacement. Therefore, the decrease in weld strength at long heating time can be equated with low welding displacements. On the other hand, reducing the heating time also reduces the thermal energy of the molten layer after heating. It results in the diminution of the extent of chain entanglement, so that the degree of chain entanglement is decreased. Both factors lead to a drop in weld strength. The strength reaches a maximum value at intermediate heating time.
Increasing the hot plate temperature, while keeping other conditions constant, has the same effect as increasing the heating time. The weld strength increases to a maximum value and falls rapidly at higher hot plate temperature, as the depth of the melt zone increases beyond the optimum. The reasons for the optimum weld strength are similar to those discussed for heating times. Many polymers would react with oxygen and degrade at high temperatures. The most damaging effect of degradation is the decrease in molecular weight. Consequently, many physical and mechanical properties of the welded parts would change. For example, polyvinyl chloride (PVC) is very vulnerable to the high heating temperature. It was reported that the fracture energy dropped one third as the heating temperature increased 30°C, from 230°C to 260°C[44].
In hot plate welding, either a coating or a sheeting of an anti-adhesive temperature- resistant material is required on the hot plate in order to prevent the molten material from adhesion to the hot plate surface. In practice, these coatings are subject to fast wear due to inherent mechanical and thermal stresses in the process. If sticking does occur and the hot plate and its cover are not cleaned, decomposed particles of material may enter the joining surfaces in the subsequent welding operation and significantly impair the quality of the joints. If the sheet is used, material residues penetrate through the sheet after a period of 20 time onto the hot plate, where they adhere firmly. Considerable cost and time can be
involved in cleaning and replacing these sheets under certain circumstance.
Potente[34] conducted investigations of high-temperature heated tool welding. Hot
plates without coating were used to study the self-cleaning effect with a surface temperature
higher than 300°C during hot plate welding. The concept was that, at a higher hot plate
temperature, the material adhering to the hot plate after welding is decomposed into a low-
molecular fluid substance and finally evaporates. In the subsequent joining process the
deteriorated molten material is pressed out of the weld zone by the joining pressure due to
its lower viscosity. Heating time was as short as possible and the resulting joint strength
reduction must be acceptable. Three materials, PE, PP, and PMMA, have been tested for
the suitability of high-temperature welding. It was reported that materials with thermally
stable additives are not suitable for high-temperature welding. Tests with PE showed that
this material tends to adhere on the hot plate after heating. When the temperature of the hot plate was below 350°C no self-cleaning effect occurred in the case of PP. The critical
temperature for self-cleaning was 410°C for PMMA. The tensile test results revealed that
there is an optimum range of heating time for obtaining good weld quality.
The flow properties of materials may affect the optimum welding process window.
Regarding to this, deCourcy and Atkinson[46] studied the butt welding of PE pipes of different grades with different melt flow index. They found that as the melt flow index decreases, the lower limit of the optimum welding temperature is raised. Hence the available processing range is narrower, so is the welding pressure. Materials of higher melt flow index require less precise welding conditions and thus good welds are easier to produce. 21 2.5 Effect of Misalignment
According to Parmar and Bowman’s definition[42,43], hot plate welded butt joints may have three forms of misalignment; axial misalignment, angular misalignment, and combined axial and angular misalignment, as shown in Figure 2.2. The influence of axial misalignment on the elevated temperature lifetimes of the butt fusion joints has been most extensively explored using fatigue loading.
While the welded pipes were subjected to fatigue tests under either constant or fluctuating pressure loading at elevated temperatures, the joints exhibited three general types of failures, as shown in Figure 2.3[42]. Axial slit mode of pipe cracks occur away from the weld which opened in response to the imposed hoop stresses. This type failure is often associated with random flaws in the pipe. The second type of failure observed was the axial cracking at the butt joint. These cracks always initiated at the disturbances or flaws on the inner weld flash. The cracks propagated through the weld flash, fusion zone, and the adjacent wall appearing to open in response to the applied stresses. The third failure was by circumferential cracks, which initiated at a notch that formed when the internal weld flash rolled toward the bore of the pipe. These notches were both long
(>1100|im) and sharp and the root tip radius was smaller than 6(lm. It was found that in general, 98% of axially misalignment butt fusion joints failed by this type of failure.
The fractional misalignment at the butt joint has a great influence on the performance of the joint. For fractional misalignments up to 0.5, increasing the misalignment progressively reduced performance. Explanation of how misalignment influences performance was given by the additional local or joint axial stress. Parmar and
Bowman[42] also investigated the effects of the existence of the internal or the external flash on the fatigue lifetimes of butt joined pipes. The results clearly demonstrated that the internal weld bead was critical both in determining the fatigue lifetime and in controlling the 22 failure site. Removing the internal bead tripled the lifetime and relocated the failure away from the butt fusion joint to the pipe itself.
(a) axial misalignment
F=r~r~r^ ^
- — — I
(b) angular misalignment
(c) combined angular and axial misalignment
Figure 2.2 Schematics of different types of misalignment at pipe butt joints[42] 23
\ t axial rr^' pipe crack
pipe failure
axial crack initialed at butt joint
axial crack at butt fusion joint external weld flash
circumferential butt joint cracking
circumferential butt joint failure
Figure 2.3 Schematic illustration of three major types of crack causing failure[42] 24 Parmar and Bowman [42,43]concluded that the introduction of axial misalignment in butt joint not only increased the axial stress, but more importantly allowed the notch at the joint to become active and initiate failure. Thus, introducing an axial misalignment induces a stress concentration problem. This stress concentration together with a sharp notch resulted in failure even at very modest axial joint misalignment.
2.6 Hot Plate Extension Effect
In hot plate welding due to the nature of the process, the end surfaces to be welded are subjected to three main heat fluxes during heating: the heat flux from the flash; the heat flux from contacting the hot plate; and the heat flux from the heat-emitting surface of the welding tool extension. Istratov[37,38] paid some attentions to the effects of the extension of the hot plate on the quality of the welded joint. The extension of the hot plate is the portion of the hot plate which does not directly contact the welding component during the heating stage. Of major concern is the heat transfer by radiation from the extension of the hot plate to the parts. In his investigation, he argued that the extension of the hot plate is a technical control parameter for hot plate welding because the increase in the extension alters temperature profile and geometrical dimensions of the shape of the melting zone. He suggested that minimizing the extension effect could have a better control on weld quality.
2.7 Weld Bead( Flash) Effect
The weld bead effect on the joining strength is still inconclusive. Most studies suggested that the existence of flash on the welded part diminished the ultimate tensile strength and the elongation to break[7,41]. Barber and Atkinson[7] claimed that the welded samples with flash on them are less influenced by the hot plate temperature. With a lower hot plate temperature, the increased thickness of the tensile specimen due to the flash 25 enhanced the weld strength. However, for the optimum welding conditions, necking occurred away from the weld, but the failure was initiated by the notch between the welding bead and the gauge length. A similar statement was made by Maksimenko et. al.[41].
Zaitsev et. al.[39] tried to prevent the flash formation by limiting the flow of the molten material from the joint with bevels. They found that blocking of the flow of the molten material made the weld strength even worse, in comparison with the strength of the weld produced without the blocking. They blamed that the blocking piece prevented the occurrence of the essential rheological processes and, consequently, not all ingredients which inhibited the interaction between the polymers of the surfaces being joined were removed from the contact zone.
Removal of the flash after welding can be carried out when it is in either molten or solid status. An investigations[40] showed that after upsetting the joint, there existed certain temperature and time ranges where the flash, in the viscous-flow state, could be removed easily with a cutter. In removal of the flash in the molten state, the cutter must be preheated to a temperature 30-50°C higher than the melting point of the materials.
Experimental results showed that there was no effect on the short-term strength of the welded joint after flash removal.
2.8 Weld Morphology
For semicrystalline materials, the weld morphology can be examined by optical transmition microscopy under polarizing light for microtomed samples and reflective microscopy for etched samples[7,45,46].
Barber and Atkinson[7] defined five zones, remnant of skin, spherulitic with slightly elongated, columnar, boundary nucleation, and spherulitic, around the weld based 26 on their examination of the microstructural features in semicrystalline polymer welding, as
shown in Figure 2.4. These different zones that characterize the butt weld of
semicrystalline polymers were explained on the basis of the flow of materials at the weld
and the consequent temperature variations. The boundary of the molten is at a temperature
less than the melting temperature but greater than the softening point, so the layer may
deform easily and produce a smooth boundary with the colder bulk material. Nucleation
starts to occur all along the boundary layer. The adjacent material, which is near the joining interface, has a large thermal gradient to induce a columnar layer growth towards
the center line of the weld. The columnar structure is revealed easily by chromic acid etching. The relatively cool material will soon crystallize with a slightly elongated spherulitic microstructure due to the temperature gradient. In the flash, the material is hot and much flow has occurred. After the solidification occurs on the surface, the cooling rate will drop and the remaining material in that zone will crystallize with a conventional, spherulitic structure. The microstructure of the skin will be determined by the joining pressure used. At low pressures, the thickness of the slightly elongated spherulitic zone is relatively large since less material is squeezed out and the material adjacent to the skin is relatively hot; hence the skin will melt, nuclei will be destroyed and relatively large spherulites will be formed due to slow cooling. With a high joining pressure, the skin zone will produce a fine-grained structure of spherulites due to rapid cooling.
Gehde, Bevan, and Ehrenstein[47] analyzed the deformation of the interface between the weld and the bulk polymer under a microscope. They examined thin microtomed samples from hot-plate welds under uniaxial tensile stress. They found a steep stress gradient at the junction of the weld flash and the bulk polymer by using the finite element method. Tests on samples without the weld flash showed that the maximum stress occurs within the weld zone. They suggested that low crystallinity polymer is less 27 sensitive to variations in welding parameters. The level of orientation in the deformed spherulites has little influence on the failure behavior. But for a high crystallinity polymer too high a joining pressure may result in a high degree of orientation in the deformed spherulites, resulting in cracks between these spherulites under load.
1: remnant of skin, 2: spherulitic slightly elongated, 3: columnar, 4: boundary nucleation, and 5: spherulite
Figure 2.4 Schematic diagram of the weld with distinctive regions of different
microstructres[7] 28 2.9 Failure Modes on Welded Joints
According to the dislocation theoiy, the most probable zone of the accumulation of
dislocations is the melt boundary in the molten zone, where intense deformation and
orientation occurred. Zaitsev and Kashkovskaya[39] investigated the macromechanism of
the failure of butt joints of HDPE pipes under tensile test. Based on the area of failure initiation, two types of joint failure were observed. One is the failure on one side relative to
the axis of symmetry of the joint and the other is the failure along the fusion line. They
stated that the failure of the melt boundary was the result of stress concentration at the base of the flash. From the microscopic examination, they found microcracks at the base of the flash. These cracks are positioned at an angle 45-60° to the axis of the pipe. However, the short term tensile test is not sensitive enough to detect the presence of these cracks. Under the long term loading in surface-active media, i.e. rain water, the time to failure of the specimens with joints is several time less than that of the parent specimen because of the existence of microcracks.
Parmar and Bowman[42] suggested that the shape and size of these joint induced notches on the weld flash are more important than the effect of microstructure according to failure analysis on butt joined MDPE and HDPE pipes at elevated temperatures under constant and fluctuating internal pressure loading. Cowley and Wylde[48] investigated the behavior of butt joined PE pipes under fatigue loading conditions and examined the microstructure of the fracture surface. They concluded that the crack propagation followed a crack tip blunting model. The fracture surface was characterized by a banded structure consisting of an area of tendrils and a relative smooth area. The fracture surface was modified by material flow during welding, the directional preference of the tendrils followed the direction of material flow. The microstructure of the weld interface did not 29 reveal the same surface tendrils as the fracture. They also found that the crack propagation rate was altered in the heat affected zone due to the microstructure change.
2.10 Quality Assessments
The weakness of a weld joint may be due to one or more of the following factors: incomplete adhesion, thermal degradation, void formation, and narrow or thin molten layers. It is very likely to produce welds that look satisfactory, but fracture easily in a brittle fashion.
Several methods can be applied to evaluate weld quality.
2.10.1 Destructive testing
Tensile Stress Test
The quality of the weld is assessed using two parameters obtained from the tensile test results: (1) the percentage elongation to failure, (2) a welding factor, f, the ratio of the yield strength of the welded material to that of the bulk material. For a satisfactory weld, the test specimen should have a large percentage elongation to failure and a weld factor close to unity. In order to assess weld quality which is not affected by the flash, the flash should be machined off. Recently, the weld factor in tensile test has been widely used to determine weld quality due to its convenience[l 1,45,46,49]. deCourcy and Atkinson[46] suggested that both weld factor and elongation have to be examined in order to evaluate the weld strength for butt welded PE pipes.
Stress Rupture Test
This test is widely applied to predict the long term behavior of the joined pipe under service conditions. The joined pipe is subjected to an internal pressure and the time to 30 failure is measured at a steady ambient temperature. The advantage of the rupture test is that is carried out under conditions similar to service conditions. The disadvantages of the tests are lengthy, expensive, and pipe joints only.
Impact Test
There are several types of impact tests such as Izod and Charpy methods, falling ball or dart tests, and tensile impact test. In general, the energy loss and the type and the location of the failure are recorded to verify the weld quality.
Fatigue Test
The fatigue test is used to examine weld quality by a cyclic stress loading at an elevated temperature to evaluate the lifetime of the welds in the service field. This test has also been applied to investigate the fracture mechanism of crack initiation and propagation [42,43].
2.10.2 Nondestructive testing (NDT)
Developments of nondestructive tests on plastics joints were built on the experiences gained with metals. Of the five methods most frequently used with metals; ultrasonic, radiography, eddy current testing, magnetic particle inspection and die penetrants, only the ultrasonic method and radiography are commonly used to evaluate plastic joints[50]. Eddy currents and magnetic particle inspection are only for the conducting materials and magnetic materials, respectively. Dye penetrants can be used to find surface breaking defects, but it is difficult to remove the penetrant from the defects, which could interfere with subsequent repairs. 31 Alternative methods such as low-frequency vibration and thermography are suitable
for plastics, especially for composites which are sensitive to defects such as delaminations.
Table 2.1 summarizes the most commonly used techniques to inspect defects in either
composites or adhesive joints[50].
Ultrasonic methods:
Ultrasonic testing is carried out either with a single transducer in the pulse-echo mode or with two transducers in the through-transmission mode[50-53]. In either case, it
is essential that transducers are coupled to the structure via a liquid or a solid medium because of the severe impedance mismatch between air and solid materials. This can be achieved by immersing the component or by using a jet probe system. It can be used to detect defects more sensitive than X-radiography without damage to the plastics, but Ewing and Richardson[54] claimed that ultrasonic compression waves of 1.4 and 1.7 MHz cannot detect cold fusion if the defect is less than 100 nm long. Ultrasonic methods are very sensitive, but have the disadvantage of requiring a couplant between the transducer and the test structure. The requirement of the coupling system adds to the expense and inconvenience of testing.
Radiography
X-ray radiography examines the structure based on the absorption characteristics.
The larger defects such as porosity, shrinkage cavities, cracks and inclusions defects could be detected by this method. Since the absorption characteristics of resins and carbon fibers in the reinforced composites are very similar and the overall absorption is low, it is very Table 2.1 Defect type and possible NDT techniques to detect their occurrence Ultrasonic methods Echo Velocity Back- spectro Acousto- Bond amplitude scattering scopy ultrasonic testers Defect type
Voids X X X X
Poor X cohesiveness
Fiber X misalignment
Foreign X X inclusion
Fiber X XX X delamination
Contami X X nation 33
Table 2.1 Defect type and possible NDT techniques to detect their occurrence (continued) ______Eddy Thermo Holo Low Radio currents graphy graphy frequency graphy Defect type vibration
Voids XX
Poor cohesiveness
Fiber X XX misalignment
Foreign XX X inclusion
Fiber XX XX delamination
Contami X X nation 34 unlikely to determine the fiber volume fraction or stacking sequence. The properties of
glass and boron fiber reinforced composites are more suitable for X- radiography.
Thermography
Thermographic methods consist of two types: active, in which heating is produced by applying a cyclic stress to the structure either in a fatigue machine or through resonant vibration: and passive, in which the response of the test structure to an applied heating or cooling transient is monitored[55]. The surface temperature of the structure is measured, usually by an infra-red camera, and the existence of defects is detected by the anomalies in the temperature distribution. Thermographic methods provide a quick way to inspect large areas of structure. However, equipment costs are high and this method is not as sensitive as the ultrasonic methods.
Low Frequency Vibration
Low frequency vibration methods are carried out by using vibrated excitation and measurement to reveal the integrity of the structure. According to the features of the measurement, two techniques, global and local, are included. These methods can be used for composites to quickly distinguish the stacking sequence of multi-layer structures and fiber types of significantly different moduli. However, to detect the local defects, i.e. voids and delaminations, it requires a highly sensitive and low noise testing environment which is isolated from the extraneous vibration, in other words, the equipment cost would be high. 35 2.11 Welding of Dissimilar Materials
The increasing demands of the assembly of different materials in the plastic processing
industry has drawn a great deal of the attention on the dissimilar material welding. A
typical example is the welding of automotive rear lights or indicator lights. The housing of
these lights is mainly made of ABS, whereas the lenses consist of PMMA or
polycarbonate. For the material combinations with very different molten temperature
range, a double hot plate welding technique, i.e. two hot plates mounted in parallel with
different heating temperatures, can be used.
Gabler and Potente[3] carried out welding experiments by using a series of
dissimilar plastic combinations including amorphous polymers; such as PMMA, PVC,
ABS, and PS, and semicrystalline polymers; such as HDPE and PP. They found that the acceptable welds can be made only in semicrystalline v.s. semicrystalline and amorphous v.s. amorphous combinations. In addition to that, they proposed two criteria for weldability of dissimilar thermoplastics. One is the ratio of surface tensions at the solid state and the other is the ratio of thermal expansion coefficients. In overall terms, good strength may be achieved in welding dissimilar plastics for;
— <1.2 (2.1 A) * 2
— <2.0 (2.IB) <*2 where K is the thermal expansion coefficient and c is the surface tension at the solid state.
In some cases, although the welding temperature used at the particular temperature when the surface tensions of two dissimilar polymers are same, the good joining quality still can not achieve. For example, PS and HDPE have the same surface tension at about 36 190°C. However, Gabler and Potente reported that the joints can not be achieved at this
particular temperature[3].
2.12 Reptation Theory for Welding
Mechanical properties of weld joints have been related to the structure of the
interface via microscopic deformation mechanisms involving chain disentanglement and
bond rupture. The extent of chain diffusion at the joining interface is a very important
factor for determining the welding quality, de Gennes and Edwards[9,10] proposed a
reptation theory to model the motion of polymer chains. In the reptation theory the motion
of polymer chains in the melt is analogous to the motion of red wigglers. The polymer chains in the melt can change their shape, and move by local Brownian motion, but can not
intersect each other. In the model, each individual chain is confined to an imaginary tube having a similar shape as the random-coil configuration of the chain. The tube is the constraints to lateral motion of each monomer units which are imposed by the neighboring chains through entanglements. Therefore, the chain as a whole moves one dimensionally but randomly along the tube. According to de Gennes's model, the chain moves back and forth along the tube with a certain diffusion constant. Figure 2.5 illustrates the way a chain disengaging itself from the initial tube[56]. The initial tube is defined as the tube conformation at time zero. As time passes, some end segments of the chains escape from the initial tube. The portion of the chains no longer in the initial tube with time is called the minor chains. The minor chains are the index of the extent of the chains that have lost the memory of their initial conformations. As the minor chains become longer, the new conformations of the initial tubes are gradually formed. The time when the chain has completely escaped from its initial tube is defined as a reptation time, tFj or tube renewal 37
MINOR CHAIN
% _ INITIAL TUBE _
CHAIN
t =• *i
MINOR CHAIN CHAIN
ft. ȣTr
0 < t, < l2 < Tr
Figure 2.5 Disengagement of a chain from its initial tube[56] 38 time. According to de Gennes estimation, tr is proportional to M3, where M is the molecular weight of the linear chains.
Wool and his coworkers[57-60] brought the reptation theory into the polymer healing process. The conformations of two chains at the interface before and after the stages of diffusion and randomization are shown in Figure 2.6. Before diffusion, t=0, the chains are separated by the interface plane and their shape is nonspherical and quite flat.
However, at a time close to tr, the chains have crossed the interface, adopted more spherical configurations, and interpenetrated and made new entanglement with chains on the other side. According to the concept of the minor chains, only portions of the chains, the minor chains, contribute to mass transfer across the interface.
The mean square escape length of the minor chains is:
(l2) = 16Dtt/n (2.2) where D/ is the one-dimensional diffusion coefficient, ~M _1.
In the vicinity of the interface, the minor chains grow at different distances from the interface plane and diffuse across the interface. The evolution of the minor chain Gaussian segment density profiles is shown in Figure 2.7. The minor chains are uniformly distributed and y is a coordinate perpendicular to the interface plane located at y=0. The bell-shaped Gaussian curves of the minor chains eventually grow into the region y<0 on the other side. The distance of interpenetration depth is the average distance of these segments from the interface. According to this definition, the average interpenetration depth, (x) , can be derived as
(2.3) 39
INTERFACE
CHAIN
t•0
Figure 2.6 Conformation of two chains at interface before and after diffusion[57]
(a)
INTERFACE I NON-GAUSSIAN GAUSSIAN
t=0 I > T, (b)
NON-GAUSSIAN .GAUSSIAN
t *0
Figure 2.7 (a) Average shape and size of a chain’s most probably envelope at the interface before and after healing, (b) Segment density, p, of the chain in (a) before and after healing[57]. 40 For the diffusion time less than tr, according to Wool's derivation the interpenetration distance is proportional to t1/4.
However, as the diffusion time is longer than tr, the interpenetration distance will follows the normal Fickian law, which is
(x)2 = 2Dt (2.4)
In other words, the interpenetration distance is proportional to t1/2 for t >Tr.
These theoretical predictions have been evaluated in many experiments; by pulse magnetic field gradient NMR on paraffin and polyethylene[61], by FTIR on polystyrene[62], and by forced Rayleigh scattering[63].
2.13 Griffith Approach to Brittle Fracture
The classical Griffith approach to brittle tensile fracture for a material with a crack is given in terms of the stored strain energy, U, and the surface energy, F , to create a new surface area.
8U>2rSa (2.5)
where da is the crack advanced increment, and 2F<5d is the created surface energy. The fracture energy, or the critical strain energy release rate, Gic, is defined as
(2.6) 41 According this approach, if the surface energy, T , of solid is known, the fracture
energy can be determined by Eq(2.6) However, for high molecular weight entangled
polymers the experimental value are typically of the order Gic ~ 1CP J/m2, and r ~ 10'2
J/m2, which is not acceptable.
The concept of Griffith is still applicable if one can determine how the stored
energy is consumed to form the fracture surface. For the high molecular weight entangled
polymer, A stored strain energy approach to fracture has to consider both chain
disentanglement and chain fracture mechanism.
In a uniaxial stress field, <7, the strain energy is
where E is the Young's modulus.
The number of chains per unit volume, Nv, is
Nv =pNa /M (2.8)
where p is density and Na is Avogadro's number. The strain energy per chain, Uc, is
therefore, written as,
(2.9) c Nv 2EpN a ’
The strain energy associated with a segment of chain length 1, is similarly derived as 42
Uc « o 2l (2 . 10)
The stored strain energy can be used to either pull the chain out from the interface or
fracture the chain. A fracture criterion for chain pullout can be written as
Uc >Up (2.11)
where Up is the energy to pull a chain out of its tube with a force F, and velocity, u.
The pullout force is given by
F = (j)u (2.12)
where
coefficient for the segment is related to the monomer friction coefficient, (j)0 , via so that the energy required to pull a segment out at a constant velocity is written as i Up = Substituting Eqs(2.12) and (2.9) into Eq(2.10), the critical fracture stress for chain disentanglement is obtained as, <7 ~~ (X) (2.14) 43 In the welding process, the interpenetration depth ( x) at the interface, which is 7/O proportional to the (/) , becomes a very important factor to determine the joining strength. Theoretically, the joining strength can be correlated to the processing time when the chain is capable of diffusing through the interface. - = ( - ) m (2.15) tr 2.14 Crystallization Kinetics The properties of semicrystalline polymers are strongly influenced by the crystal microstructure. For analyzing and optimizing the polymer properties in a manufacturing process, it is very important to understand the microstructure formation, i.e. ciystallization kinetics of semicrystalline polymers[13]. Most load bearing materials, such as pipe and automobile bumper are made of semiciystalline thermoplastics because of the superior characteristics of their crystal structure. However, the crystal structure may change in the heat-affected zone due to the welding process. This review covers the basic concepts of the crystallization theory and the available crystallization kinetics models. 2.15 Structure of Polymer Crystal Many polymers, such as polyethylene, polypropylene, and isotactic polyvinyl chloride, are composed of crystalline and amorphous regions. The fraction of crystalline state in a polymer is defined as the degree of crystallinity and it ranges between 0 and close to 1. Several methods have been applied to quantify the degree of crystallinity, 44 including measurements of density and enthalpy of fusion, infrared and Raman spectroscopy[64], X-ray scattering, and NMR spectrometry. The basic principle among these methods is that the responses of the crystalline phase and the amorphous region to the applied input vaiy. The overall responses are considered as a linear combination of the amount of each phase. In general, the degree of crystallinity depends upon the structural regularity of the long chain molecule and the molecular weight. Either by adding dissimilar units to the molecular chain through copolymerization or due to complex side groups on the backbone, the degree of crystallinity decreases. As the molecular weight of certain polymer exceeds the critical or the transition size, the degree of ciystallinity drops with the increase of molecular weight[64]. The polymer crystalline unit can be depicted as the long chain molecule folded back and forth in the amorphous region to form an ordered, packed structure. The crystalline units may form the ordinary laminar spherulite structure, which can be examined under a polarizing microscope, if the crystallization occurs under quiescent conditions from the polymer melt. If the crystallization occurs under stress, either shear or elongation, the level of crystallinity will be enhanced, e.g. in the polyethylene terephthalate stretching experiments the crystallinity increased with the drawing speed[65]. However, the texture of the crystal will be deformed along the stress direction. For example, a micrograph of a microtomed polypropylene part prepared by injection molding reveals that the microstructure of the outer layer (skin) is different from that of the inner layer(core) as shown in Figure 2.8. Since the outer layer experiences a higher stress during the molding process, the crystal texture is more deformed[66,67]. Figure 2.8 The morphology of skin-core zone in an injection molded part The amount of ciystallinity is an important factor for determining the properties of semiciystalline polymers. The extent of crystallinity can be determined by crystallization kinetics. Before the issue of crystallization kinetics is discussed, the crystallization mechanism needs to be understood. The nuclei have to form first, i.e. nucleation, and subsequent crystal growth occurs on the existing nuclei surface. At the beginning of crystallization, nucleation, the long chain molecule starts to fold back and forth to form nuclei in an undercooling condition, i.e. at a temperature below melting but high enough to provide chain mobility. Since the folding and unfolding mechanisms may occur at the same time, the minimum size of nuclei, which are thermodynamically stable, can be determined by minimizing the total free energy including surface energy and energy of crystal formation[68-70]. The folding length of the crystal is temperature dependent. It 46 increases with the crystallization temperature and with the melting temperature. The melting temperature for a semicrystalline polymer is a "temperature range" rather than a "temperature point" under the standard condition. The broad melting temperature range, i.e. varies from 10 to 30 °C depending on the crystallinity distribution, for a polymer is attributed to the distribution of chain folding length. The equilibrium melting temperature is the melting temperature of the crystal with the maximum folding length. Consequently, the equilibrium melting temperature of a semicrystalline polymer, which is used in the growth rate equation, can be determined by the crystallization temperature vs. melting temperature plot, known as the Hoffman and Weeks plot, as shown in Figure 2.9[69]. Equilibrium melting Tm temperature Crystallization temperature Figure 2.9 A Hoffman and Week plot to determine the equilibrium melting temperature, rp O 1 ITT 47 As the nuclei are formed, the crystallization would occur on the surface of the existing nuclei in all directions to build the spherulite. In general, the spherulite growth rate is faster than the nucleation rate because the free energy requirement is lower. If the crystallization occurs under stress, the overall crystallization rate will increase because the stress could orient the molecular chains and make them more packable. The presence of stress during crystallization will cause the crystal texture to be deformed. Even for the solid material, in which the chain mobility is very low, the crystallization may occur under cold drawing. Not only will the ciystal structure transform from an unoriented lamellae to an oriented fibrous structure, but the degree of crystallinity will also increase under the influence of cold drawing[71]. Nucleation & Crystal Growth Theory: The classical nucleation theory assumes that the rate of non-diffusion-controlled crystallization depends upon the overcoming of a nucleation energy barrier by local energy fluctuations in an undercooled system[69,72,73]. The nucleation is the rate-determining step of crystallization. Two types of nucleation are defined. One is the primary nucleation, where a three dimensional crystal is generated; and the other is the secondary nucleation, where the addition of chain segments occurs on the existing crystal surface. Both of them can be expressed as the following equation: t t /“Ea. .—AG. I = IoexP(-j^r)exP(-j^r) (2.16) 48 Where Io is the number of random thermal fluctuations from potential crystallizable entities, Ea is the activation energy of transport of a molecule, AG is the Gibbs free energy of crystal formation, R is the gas constant, and T is the absolute temperature. The above Eq(2.16) consists of three terms to determine the nucleation rate; the first term on the right hand side represents the number of potential crystal units; the second expresses the chain mobility, and the third is the probability of crystal formation from a thermodynamic point of view. The major difference between the primary and the secondary nucleation is the Gibbs free energy. For the secondary nucleation, the total surface generated is less than that from the primary nucleation, since each additional chain removes as much side surface as it creates. Hoffman and Lauritzen[69], based on the classical nucleation theory, derived a linear spherulite growth rate equation on the existing crystal surface as a temperature dependent function after applying surface energy, folding energy, heat of fusion, and the lamellar thickness terms into the Gibbs free energy. The chain mobility term could be modified based on the WLF equation for better agreement between experiment and theory when the greater undercooling condition was applied. The linear growth rate of spherulites is given as follows: — TJ* —K Gcr = Gcro exp(------)exp(------s—) cro ^ R(T_ T / TATE * (2.17) ^£= rj*o— Where GciO is a spherulite growth constant, U* is a temperature independent constant of energy barrier for polymer mobility, T0, which is taken to be Tg-30°C, is the temperature of no chain movement, Kg is a lump temperature independent constant consisting of surface energy, folding energy, and standard heat of fusion terms which is important for 49 determining the rate of polymer chain segment depositing on the existing crystal surface, and £ is a temperature correcting factor for the free energy of crystal formation deviated from the equilibrium melting temperature. The relative rates of nucleation and deposition of chain segments on the crystal surface will affect the crystal growth rate and the spherulite size. Several crystallization regimes are classified. In one extreme case, regime I, the deposition rate is so fast that the crystal unit growing on an existing crystal face is complete before a new layer is initiated. In another case, regime II, where the nucleation rate is fast compared with the deposition rate, the nucleation of new layers could occur before the completion of crystal unit growing on the existing crystal face. In another extreme case, regime III, the nucleation on a given face is so rapid that the subsequent growth along the face can not follow up. As expected, the Kg of different regimes varies. In principle, the magnitudes of Kg,j and Kg,HI are in the same range, and K gji is about half of Kgj[74,75], 2.16 Overall Crystallization Kinetic Models 2.16.1 Avrami model The Avrami type equation is the most widely quoted model for calculating the extent of crystallinity in polymer processing. The equation can determine a relative crystallinity under isothermal crystallization as[76-78]: X r = 1 - exp(-K Atn) (2.18) Where the relative crystallinity, Xr, is defined as the ratio of crystallinity to the final crystallinity, Ka is an Avrami crystallization constant which is highly temperature dependent, and n is an Avrami exponent which is a geometric factor; i.e., n=3, 50 representing the formation of spherulite crystal, n=2, representing the formation of disc like crystal, and n=l, representing the formation of rod-like crystal[79]. Hoffman and Weeks[69] deduced the crystallization constant in the Avrami equation as a function of spherulite growth rate for the spherulite type crystal, i.e. K a = | tcN0G3 (2.19) Where N0 is the nucleation density of spherulite. As shown in Eq.(2.19), the constant KA is a combination of nucleation and spherulite growth. Hence, according to the nucleation theory, the temperature dependence of KA can be expressed as; K‘ = K - exp where Ko is a temperature independent constant, and \|/g is a folding energy constant. These constants can be determined by a series of isothermal crystallization experiments, which will be discussed later. Several generalized Avrami equations have been proposed to model nonisothermal crystallization[80-85]. Nakamura et al.[80,81] assumed the isokinetic condition and the independence of final crystallinity on the cooling process, and led to the following equation; Ln(l — Xr) = —(j^K(T)dt)n (2.21) where K(T) = KA(T)1/n 51 Kamal et al.[82] also used a similar Avrami type equation to simulate the nonisothermal crystallization during the injection molding process. The crystallization equation they used is as follows: Ln(l —Xr j = — J^KA(T)ntn-1dt (2.22) One can note that Nakamura's model and Kamal's model are identical if n=l. However based on Patel and Spruiell's comparison[85], the Nakamura model provided a better prediction when compared to their experimental results. For process modeling, a differential form is more useful than an integral form. The differential form of the Nakamura model can be expressed as: nK(T)(l —Xr) Ln( (2.23) In order to determine the crystallization constant for a given temperature, two methods are commonly used; one is the Avrami plot analysis, and the other is the half-time analysis[85]. The Avrami plot analysis is to measure the relative crystallinity, Xr, under the isothermal condition and to plot Ln(-Ln(l-Xr)) against the logarithm of time, Ln (t). Based on the Avrami equation, the plot should be a straight line. The crystallization constant, Ln(KA), and the Avrami exponent, n, can be obtained from the intercept of the ordinate and the slope of the plot, respectively. The half-time analysis is also based on the Avrami equation. The characteristic time, ti/2, is the time required to complete half of the 52 total ciystallization as measured at several isothermal crystallization conditions. The half time can be converted to the rate constant Ka , if the Avrami exponent is known, i.e. (2.24) 2.16.2 Tobin model Tobin[86,87] took into consideration the effects of spherulite impingement during growth in the crystallization kinetics based on the two dimensional area transformation approach. In this approach, the extent of crystallinity is determined by the ratio of the transformed area to the overall area. He assumed that the formation of nuclei is proportional to the remaining uncrystallized area and the contribution of any growth site to the transformed area is the area of the site without impingement times the overall fractional untransformed area at that time. To describe the homogeneous and heterogeneous nucleation mechanism, the Tobin model can be expressed as: ■r j where Khm is the crystallization rate constant of the homogeneous nucleation, Kht is the crystallization constant of the heterogeneous nucleation, and a is the decaying parameter for nuclei. Tobin claimed that his model is more accurate than the Avrami model in case of relatively large degrees of crystallization. 53 2.16.3 Macrokinetic model Malkin et. al.[88,89] proposed a new approach to study the crystallization kinetics from a macroscopic prospective. The degree of crystallinity was considered as the conversion of chemical reactions. At a given temperature, the crystallization in the polymer melt includes two stages; nucleation and spherulite growth, and the spherulite growth rate is proportional to the existing crystal surface. The overall crystallization rate is the summation of the nucleation rate and the spherulite growth rate. Malkin et. al. assumed that the existing crystal surface is a linear function of crystallinity. The crystallization kinetic equation was written as: ^ ■ = K.fl-X,Xl + C .X ,) (2.26) where Km is the temperature dependent constant for nucleation and Cm is the surface coefficient for the existing crystal. In order to apply this model to the nonisothermal crystallization, Malkin et. al. deduced Km in a temperature dependent form according to the Laurtzin and Hoffman theory; K. - exp(~)exp( - ) (2.27) They applied an inverse method to determine all kinetic constants from the known thermal response of nonisothermal experimental results instead of an isothermal kinetic approach. However, the solutions of these constants are very dependent on the numerical scheme and on the nature and amount of experimental data. 54 2.17 Flow-Induced Crystallization Flow-induced crystallization often occurs during polymer processing, such as injection molding, fiber spinning, blow molding, etc. Not only will the crystallization rate be enhanced by the flow effect, but the microstructure of crystal will change from a spherulite to a fibrous structure, regarded as shish-kebab structure. Flow-induced crystallization depends on the polymer chain extension[90-92]. McHugh[91] conducted a quantitative analysis to reveal the relative effects of extensional and shearing flow on the nucleation rate of polymer solutions. He found that the extensional kinematics are far more effective than shearing kinematics in providing the free energy necessary to overcome the energy barrier for nucleation. In order to make the nucleation from solution possible, the shearing velocity gradient may need to approach infinity. However, the subsequent crystal growth on the existing crystal seed in the shearing flow is much easier. He proposed a nucleation and crystal growth model for flow-induced crystallization from polymer solution. He claimed that the fibrous crystal could only be nucleated under extensional flow and, while the shearing flow field may not be able to make the nucleation possible, it can enhance the opportunity for the crystal growth by forming a continuous backbone through a chain attachment process. Further growth is carried out by the extension and flattening of chains connected to the central backbone and acted upon by the fluid mechanical forces in the shearing flow boundary layer surrounding the growing crystal. Due to energetic constraints, a complete chain extension and crystallization could not occur. The growing crystal thus consists of a chain backbone surrounded by a group of uncrystallized fuzz coils attached to the main backbone. Only the fuzz materials linked to the backbone can remain under a vigorous shearing field. Thus, as the cooling proceeded, the dangling portions would crystallize to form a partly chain folded, partly 55 chain extended bead on the backbone. This explained the formation of the shish-kebab structure. In polymer processing, the polymer melt rheology, heat transfer during processing, and shear-induced crystallization have to be taken into consideration. Janeschitz-Kriegl and coworkers[92-97] have made an extensive effort to model the Stefan problem, which concerns heat transfer with phase change, especially during crystallization. They stressed that the classical Stefan moving boundary problem could not properly depict the characteristics of crystallization in polymer processing. They suggested that the crystallizing region in polymer processing has to be considered as a "crystallization zone" instead of a "crystallization front". Janeschitz-Kriegl and coworkers[97] also proposed a theory to quantitatively determine the kinetics of shear- induced crystallization, based on following experimental observations: i) the crystallization rate increases with the increasing shear rate; ii) a critical shear rate is necessary for the formation of a rod-like or columnar structure; iii) if an Avrami equation is applied to express the crystallization kinetics, the Avrami exponent may change to a higher value, some reported as high as 7, due to the flow- induced crystallization; iv) the number of nuclei is a distinct function of shearing time under a given shear rate before a critical shearing time is reached. The critical shearing time decreases with increasing shear rates; v) the spherulitic (quiescent) and lamellar (shear-induced) crystallizations do not occur in a combined form, they are always distinctly separated. The determination of which mechanism occurs depends on the induction time. The logarithm of induction time is inversely proportional to the logarithm of shear rate; 56 vi) the occurrence of the nucleation for shear-induced crystallization is due to an internal change of the structure of the flowing melt; vii) the flow-induced crystallization can occur during relaxation, after the cessation of flow, if the cooling rate is high enough. Janeschitz-Kriegl et al. assumed that a precursor caused by inhomogeneities in the sheared melt contributes to the shear-induced crystallization. The precursor can only be produced via the shearing condition. The probability for the presence of a precursor, x^ = (_L)2(1_o)-0 (2.28) d t Ya where x is a relaxation time, and y and ya are the applied shear rate and a critical shear rate of activation. The first term on the right hand side describes the creation term, containing the contribution of shearing on the rate of generation of the precursor. The second term expresses the decay of O. In Eq.(2.28) both ya and x are temperature dependent and will vary with time in practice. As <$ goes to unity, the rate of precursor generation plateaus, even though the polymer melt is still under shear. If the polymer melt is sheared for a while, and then quenched to a lower temperature and the flow stopped, the probability for the presence of precursor diminishes as an exponential function of time, divided by the relaxation time. If a linear relation between the probability, Therefore, the unrestricted crystallinity, X r can be written as: 57 Xr = SajN(s) /Gi(Ti)dTi ds = -ln(l-X r) (2.29) 0 Vs where Sa is a geometric parameter of crystal structure. If an isothermal crystallization at constant shear rate is considered, all the rate constants, Kn, Kgi, are constant. Hence, the unrestricted crystallinity becomes; X r =cj f x , y /4 x w or J From Eq.(2.28) can be determined under isothermal and constant shear rate conditions ^Yo.)2 = — h — \ l" expf_[1 + (^ )2]1 (2.31) l + (^ 2 .)2 I v Ya x . Ya Combination of Eqs(2.30B) and (2.31), where ti/2 is the half time of the crystallization, results in the following equations 58 .[l + (Yo.)2]Il/2 l Ya x Ya v . [l + ( io ) 2]2 Ya c (io> 2 (2.32) Ya ln(2) 1/4 C = CQx C is a temperature dependent parameter that decreases with decreasing crystallization temperature. As C becomes smaller, the range of the half time, t\/2, which is inversely proportional to the shear rate, becomes broader, as shown in Figure 2.10. It implies that a critical total strain is responsible for the onset of shear -induced crystallization in this range. This range of "critical total strain" diminishes as the crystallization temperature is raised higher. The effect of shear rate on the half time is very important. If the polymer is crystallized isothermally and sheared for a certain time, and then the flow stopped, the integration of the O function along time, which is larger than the sheared time, results in an equation that contains two terms, a direct shear-affected contribution and a relaxation holding contribution; t t. t + f ^r(t.Yo) = ®(ts. Y0)exp[-(t - ts) / x] where ts is the sheared time. 59 15.00- ■ C=10 • C=1 10.00 - A C=0.1 ♦ C=1 E-3 ▲ □ C=1 E-5 5.00-n ♦ ▲ ■ O C=1 E-9 • L o g ( ^ ) □ ♦ A ■ • O □ ♦ A ■ 0.00 - • o □ ♦ A A A A A o □ ♦ O □ ♦ ♦ O □ ♦ ♦ 4 O □ -5.00- □ □ C - 10.00 . mn-p l j » II I | I I I 1 ■ i ■ ■ ■ ■ r n-p -5 -3 -2 -1 0 1 2 3 4 Log (¥-2-) Ya Figure 2.10 The effects of shear rate on the half time crystallization based on Janeschitz- Kriegl model; C is a temperature dependent constant defined as C in the text. 60 Therefore, based on Eqs(2.31) and (2.33) the half time, ti/2, required in this case can be expressed as: , ('F-l)A -6F2/('F-l)-'FIn(l-A ) tl/2 ts - xln q/A (2.34) where A = 1 - exp[-'P(ts / t)] T ^ l + q2 From Eq.(2.34), one can notice that the shear induced half time can not be reached if the argument of the logarithm at the right hand side is less than zero. In other words, the shear induced crystallization won't occur under this shearing condition. Another possibility is that if the prolonged induction time due to relaxation is longer than the half time of spherulite crystallization (quiescent melt), the crystallization will proceed as a quiescent crystallization. An extreme case is when the polymer is sheared at a temperature well above the equilibrium melting temperature, Tj, for a certain period of time, ts, so that no crystallization can develop. After ts, the polymer melt is quenched to a temperature T 2, which is well below and the shear flow is ceased at the same time. An injection molding process is a typical example. In this case, the shear induced crystallization will depend on the relaxation holding contribution only. Following a similar approach, the relaxation holding time required for the half of completion of crystallization can be written as: 61 where the subscripts, 1 and 2, correspond to temperatures, Ti and T2, respectively. If temperature T2 is so low that the relaxation time %2 is much larger than that of tj/2 - ts, Eq.(2.35) can be rearranged as: (2.36) where l q2 “ *1/2 _ *s The limiting shear rate, below which shear-induced crystallization can not occur, Yu, can be determined as the argument of the logarithm in the Eq.(2.36) approaches to zero. Hence (2.37) where A = & 1 lq2 Replacing the critical shear rate yai by the limiting shear rate Yu, which can be measured by experiments, Eq.(2.36) becomes: 62 -*1 In ( l - A ) [ l - ( ^ - ) 2] (2.38) Yli . Based on this model, it is feasible to quantitatively determine the effects of shear rate on the crystallization. However, the quantitative experimental data for shear induced crystallization is still limited. Good experimental designs for accurately studying shear induced crystallization are necessary. 2.18 Techniques To Determine Crystallization Kinetics[98,99] 2.18.1 Dilatometric Method The crystalline volume is more compact than the amorphous volume since the crystalline structure has an ordered chain arrangement. Therefore, the volume of a polymer melt will decrease while the crystallization is occurring. If the initial volume V i, the final volume Vf, and the volume at any time V(t) are known, the relative crystallinity Xr can be calculated according to the volume change. (2.39) 2.18.2 Calorimetric Method Thermal analytical techniques offer a convenient method of measuring crystallinity. The thermal method based on a two phase model of crystalline regions scattered on an amorphous matrix so that the heat emitted is proportional to the mass 63 fractional content of the crystalline region. In the model, the discrepancies of different size and different morphology on heat of crystallization are neglected. where Q is the amount of heat measured during the occurrence of crystallization, which increase as time proceeds, and AHC is the total heat of crystallization. 2.18.3 Optical Method For polymers with large crystal structure, such as PP, PEEK, the spherulite structure can be observed directly by microscopy. The crystallinity can be determined directly by the measurement of the surface area of the crystal structure. 2.18.4 Other Analytic Methods The x-ray diffraction method can be used to determine the degree of crystallinity if the resolution between crystalline and amorphous structures to the x-ray diffraction pattern is clear enough. This method may also be able to distinguish the contents of different crystal structures. Prior to the analysis, the spectra of the crystalline and amorphous materials have to be known. The infrared absorption is a related analytical technique but using a different emitting source. The method requires that a characteristic wavelength, which can be absorbed either by the amorphous or the crystalline structure, varies clearly and linearly with the amount of a particular structure. CHAPTER III MATERIAL CHARACTERIZATION 3.1 Introduction This study is focused on the effects of welding parameters on the microstructure and properties of the weld. Polypropylene (PP) was used because of its large spherulite crystal structure which provided a clear observation of the effects of thermal and flow induced stresses on the crystalline structure under polarized optical microscopy. Our scope is to better understand the effects of welding parameters on the joining quality, mainly the morphology. This chapter investigates the material characterization experimentally including; thermal analysis, rheological measurement, and crystallization kinetics. The results are used to simulate the welding process in chapter V. 3.2 The Molecular Structure And Configuration Of Polypropylene Polypropylene is a widely used low cost polymer for consumer products such as milk bottles, plastics toys, chemical containers etc. Because of its crystalline structures, it possesses a strong chemical resistance to a lot of solvents. By using stereospecific polymerization invented by Natta to control the structural regularity, three possible 64 65 molecular configurations, isotactic, syndyotactic, and atactic, are present for the polypropylene macromolecule. In the isotactic configuration, all the methylene groups are located on one side of the main chain of polypropylene macromolecule. In the syndyotactic configuration, the methylene groups alternate regularly on both sides of the main chain. The methylene groups randomly position on either side of the main chain in the atactic configuration. These molecular structural arrangements are shown below: Isotactic: CHq H CHq H CHq H CHq H CHq H CHq H / 3 / / 3 / / 3 / / 3 / / 3 / / 3 / c- C- C- C- C- C- C- C- C- C- C- C- \\\ \ \ \\ \ \\\\ HHH HHHH H HHHH Syndyotactic: CHq H H H CHq H H H CHq H H H / o / 3/O / / / 3/ / / / 3/ / 1 I 1 1 1 0 0 C- C- c- c- C- 0 c- c- \ \ \ \ \ \ \ \ \ \ \ \ H H ch3 h H H H ch3 h h H ch3 Atactic: CHq H H H H H CH q H CHq H H H / 3 / / // / / J / / 3 / // 1 1 1 - c- c- C- c- C- 0 0 0 c- c- C- C- \ \ \ \\ \ \ \ \ \ \\ H H ch3 h H ch3 h h H H H ch3 The isotactic polypropylene is the most widely used among these three configurations and its crystal structure can be more easily observed. At the scale of polarized light microscopy, four types of spherulite structures (I, II, III, IV) were suggested by their appearance under cross polars, including sign and nature of the birefringence, as shown in Figure 3.1[100,101]. 66 Type I Type in Type IV Figure 3.1 Micrographs of type I in and IV spherulites; Type H spherulite is very similar to type I spherulite. The differences between type I and type H can only be distinguished on the basis of the birefringence. Type I is positive and Type II is negative! 100]. 67 The macromolecule of i-PP packed helically into a crystalline array. According to the different packing geometries of the three fold helices, three known crystalline structures of PP, depending on crystallization conditions, are classified. They are the monoclinic form (a), the hexagonal form (P), and the triclinic form (y). Among these three crystalline structures, the monoclinic form is the most common and stable one. It could be found in both melt and solution crystallized samples. The rest two (smetic/paracrystalline) are formed under supercool and can be transformed to the monoclinic structure upon heating. These packing geometrical structures were distinguished by the X-ray diffraction[102-104]. It is interesting to note that the quenching process would not be able to produce totally amorphous samples even though the cooling rate is as high as 10,000°C/min. The quenched crystal consisting of very small ciystallites was called smetics or paracrystalline[105-106]. In this study, we are more interested in the crystallization kinetics which can provide useful information for the later computer simulation to analyze and optimize the welding process. The PP used in this study are supplied by Plasticlite. However, not too much information regarding to the grade and type was provided. According to our crystallization study, it might be an isotactic type PP. 3.3 Thermal Analysis 3.3.1 DSC Experiments In order to investigate the crystallization kinetics, the relative crystallinity under different crystallization conditions was measured by differential scanning calorimeter( TA Instrument DSC-10). The PP sample was cut from an injection molded plate to a mass of 3 to 6 mg. The small chopped PP sample was subjected to the DSC in a sealed sample 68 pan. In order to avoid the possibility of unwanted oxidation, dry nitrogen gas was employed into the oven chamber. Every sample was carefully weighed by a balance (Mettler, Model-80) to an accuracy of 0.1 mg. For the investigation of the melting and crystallization behaviors, the heat absorbed and evolved was recorded along the courses of heating and cooling in the DSC. 3.3.2 Melting behavior The samples were heated at the rate of 10°C/min to 220°C which is high enough to melt the sample completely. Due to the existence of crystalline structure, an endothermic peak was observed in the heating mode. The peak of the melting curve is located at 165°C. This melting peak temperature is much lower than the equilibrium melting temperature, 180.9°C. The equilibrium melting temperature was defined as the melting temperature for the crystals with infinite lamellar thickness. The peak size represented the amount of crystalline structure in the sample. The typical melting and recrystallization curves of PP, measured from DSC, are shown in Figure 3.2 The melting peak temperature (~165°C) was higher than the crystallization peak temperature (~120°C). The location of the crystallization peak temperature in Figure 3.2 depended upon the cooling rates. The peak temperature increased as the cooling rate decreased. The change of melting temperature of crystals formed at different cooling rates was not so significant even though the crystal size change, which was observed from the microtomed specimens, depended strongly on the cooling rate. A larger crystal size formed at a lower cooling rate because nuclei are generated at a slower rate and polymer chains have a longer time to grow on an existing nuclei. As shown in Figure 3.2, the melting peak covered quite broad a range, from 140 to 170°C. By comparing the DSC melting peak of PP with that of the similar polymer, HDPE, the temperature range of the PP melting peak is larger, Figure 3.2 The DSC heat flux responses during melting and crystallization under different under crystallization and melting during responses flux heat DSC The 3.2 Figure Heat flow (J/g) Heat flow (J/g) 0.5 14 18 :■ 0 i 11 11- i- 0 10 2 10 4 10 6 10 8 10 200 190 180 170 160 150 140 130 120 110 100 cnig ae 1°C/min rate ^canning heating j cnig ae 5°C/min rate scanning heating i ' ti i 11 11 11 11 i 11 r 11 111 11 11 i Temperature (°C) Temperature cooling rates cooling cooling cooling i T i 11 11 111 i ' i ' i ri i i ri 69 70 the melting peak is located at a higher temperature. From microscopy, one can find that the spherulite size of PP is much larger than that of HDPE and the size distribution is also broader. The broader spherulite size distribution makes the melting peak cover a broader temperature range at the same heating rate. With the existence of a methylene group on each repeated unit, the thermal energy required for the chain mobility is higher for PP than for PE. 3.3.3 Apparent heat capacity measurement The heat capacity is one of the key physical constants for heat transfer modeling. It determines how easy or difficult it is to raise the material temperature. In our heat transfer modeling, the measured apparent heat capacity will be used Since the material used in this study is a semicrystalline polymer, the heat of fusion needs to be counted in the course of melting. An apparent heat capacity is defined to include the heat of fusion term: AH, cnp ,a = c p + — £ rL p V(3.1) / where AHf is the heat of fusion, and AT is the temperature range of the melting peak. The apparent heat capacity was measured by DSC(TA instrument, DSC-2910). The procedures of determining the heat capacity was as follows: 1. In order to stabilize the oven thermally, it is necessary to hold the oven isothermally at the starting temperature for 5 minutes and heat at the desired heating rate to the upper bound temperature. 2. Measure the empty sample pan (without sealed) thermogram as a reference curve. 3. Repeat procedure 2 with a weighed sample in the same empty pan used above. The baseline slope and the signal zero function should not be adjusted. 71 4. Measure the difference of the heat flow between the sample and the blank curves 5. Substitute the difference into the following equation: ,60-E.,AY, cp,a = ( - — )(— ) (3-2) h m where: E =cell calibration coefficient at the temperature of interest /?A=Heating rate in °C/min AY =Difference of heat flow between the sample and the blank curves at the temperature of interest in mW m= sample mass in mg cp a= Heat capacity in J/g°C. Figure 3.3 presents the apparent heat capacity versus temperature. A peak occurred around 165 °C because of melting. Apparent heat capacity (J/g°C) 0 2 3 4 1 5 6 7 8 Figure 3.3 The temperature dependent apparent heat capacity of PP of capacity heat apparent dependent temperature The 3.3 Figure Tempature (°C) Tempature 250 72 73 3.3.4 Quiescent crystallization kinetic analysis Two types of experiments were conducted in this study, for completely melted and partially melted samples. For the completely melted samples, the sample was heated to a maximum heating temperature, higher than the equilibrium melting temperature, to melt all crystalline structures in the sample, then crystallized isothermally under different crystallization temperatures or at a constant cooling rate to room temperature. The results of these experiments provide information that is necessary to determine the constants for the overall crystallization kinetics model. This approach has been used successfully for polymer processing operations, such as injection molding, fiber spinning, and extrusion, to determine the crystallization kinetics. The common feature of these processes is that polymers are crystallized from completely melted status. However, the crystallization kinetics in the welding process are quite different from those in the above mentioned polymer fabrication processes, i.e. injection molding, extrusion, etc. The temperature distribution in the polymer substrate is very broad, ranging from the hot plate temperature which is well above the equilibrium melting temperature, to near room temperature far away from the interface. Crystallization temperatures would vary from well above the melting peak temperature to within the melting peak range, in other words, the molten polymer in the HAZ could crystallize from either completely or partially melted zone. Therefore, the isothermal and nonisothermal crystallization experiments of partially melted polymer need to be conducted. These results reveal more specific information concerning on spherulite growth kinetics which are highly related to the structure formation around the joint interface in welding processes. 74 3.3.5 Crystallization from completely melted polymer In isothermal crystallization experiments on completely melted polymer, PP samples were heated to 185°C, above the melting temperature, and then cooled to the crystallization temperature within 0.5 min and held at that temperature until crystallization was completed. Several DSC runs under isothermal crystallization conditions , from 110 to 150°C, were conducted. In high crystallization temperature runs, the time required for the completion of crystallization was very long and the magnitude of the peak from DSC curve, representing the crystallization rate, was very small. For example, it took more than 4 hrs to complete the crystallization at 145°C. On the other hand, in low crystallization temperature runs, the crystallization peak was sharp and large, and appeared in a very short time, on the order of 10 sec. Figure 3.4 shows two typical crystallization peak thermograms. For the lower temperature case, T=118°C, the crystallization peak occurred at 0.25 min which is much faster than that for the higher temperature one, T=131°C. The crystallization peak time increases exponentially with the crystallization temperature, as shown in Figure 3.5. 3.3.6 Crystallization from partially melted polymer The results of nonisothermal crystallization under a constant cooling rate but different final heating temperatures are shown in Figure 3.6. The thermal history of the sample, within the melting peak temperature range, has a strong influence on the crystallization kinetics. For high final heating temperatures, above 170°C, the influence of thermal history on recrystallization was not significant. The crystallization peak temperatures of these high temperature cases were all around 110°C under the same cooling rate, 2°C/min. The crystallization peak temperature was 60°C below the melting peak temperature and a complete bell shaped curve was observed during crystallization. If Crystallization rate (1/min) Crystallization rate (1/min) 0.5 0.01 0.02 0.03 2.5 3.5 0.04 0.05 0.06 0.07 0.08 1.5 Figure 3.4 The isothermal crystallization curve under different different under curve crystallization isothermal The 3.4 Figure 0.5 crystallization temperatures by DSC by temperatures crystallization Time (min) Time Time (min) Time T=118°C ■ T=131°C 2.5 75 Figure 3.5 The crystallization peak times under various isothermal conditions isothermal various under times peak crystallization The 3.5 Figure Peak time (min) 0 15 110 105 100 rsalzto eprtr (°C) Crystallizationtemperature 2 15 3 15 140 135 130 125 120 76 Figure 3.6 The DSC results of heating to different temperature and then cooling to room room to cooling then and temperature different to heating of results DSC The 3.6 Figure fe S w J3 +4 Heat Flux -0.5 u n n x temperature to complete the crystallization the complete to temperature Time (min) Time (min) Time (min) zone I zone zone zone Hizone 0 3 40 0 g 50 60 l 0 4 50 a a 50 as 70 80 60 h o h O 77 78 the sample was heated to a final heating temperature below the melting peak temperature, the crystallization occurred as soon as the heating stopped. The shape of the crystallization curve was no longer bell-like, instead, it was more like an exponential decay. If the sample was heated to a temperature between the melting peak and the end of the melting temperature, the location of the crystallization temperature was shifted to a higher temperature compared to that of the complete melting case. The shape of the crystallization curve was still the bell shaped but the crystallization peak was broader. The DSC observation suggests that the crystallization kinetics of polymer melt depends on the status of polymer melt. The concept of the crystalline structure change, in terms of spherulites, during melting and crystallization is shown schematically, in Figure 3.7. We can classify the effects of thermal history on crystallization kinetics into three zones, based upon the final heating temperature. Figure 3.6 shows the effect of final heating temperature on the crystallization peak temperature. From Figure 3.6, three zones could be characterized according to the final heating temperature. Zone I and II represented that the sample was partially melted. Zone III indicate that the completely melted status was reached. In zone III, the crystallization peak temperature did not vary too much with final heating temperatures, all around 115°C if the same cooling rate was applied. . In zone n, the crystallization peak temperature was shifted to a higher temperature, around 140 °C, at the same cooling rate. It suggests that the crystallization took place at a faster rate in zone II. In zone I, a small peak was observed right after the cooling initialized. It implies that as soon as the entropy of the partially melted system decreased because of the temperature decreasing, the polymer chains would loose their degree of freedom and immediately recrystallize on the remaining crystal. The effect of the remaining crystalline structure on enhancing the crystallization Crystal size decreases: _ x , crystal number dees not changf0,h crys,al sl2e ancl nu,,,ber chan9s 0 Exo © ® ® ® 0 © ® © e ® Heat Flux k no melting complete melting Endo \ Temperature Figure 3.7 The schematics of crystal structure as temperature increases. Zone It To < T < Tm Zone lit Tjo < T < Tg ZoneIII: T>Te 80 rate in the partially melted sample is the same as the nucleation seeding effect. In another series of experiments on partially melted samples, the samples were heated at 5°C/min to a temperature in the melting peak, and then kept at that temperature for isothermal crystallization. Both melting and crystallization curves were recorded by DSC. The isothermal crystallization of the partially melted sample was conducted under various temperatures, from 150 to 165 °C. The crystallization of partially melted samples in zone I started right after the heating ceased if the melting peak temperature was not reached during heating. If the maximum heating temperature was beyond the melting peak temperature, immediate crystallization could not be observed, as shown in Figure 3.8. 3.4 Quiescent Crystallization Examination Under Microscope A microscopic examination over the crystallization period was made to support the concept proposed in the previous section. The setup was shown in Figure 3.9. The PP sample was heated to 200°C between two cover glasses in a hot stage device. As the sample was completely melted, a compression force was applied on the cover glasses to form a thin film, less than lOpm. In order to monitor the thermal history during crystallization, a small size thermocouple ( K type, gauge 40) was inserted between the cover glasses. The thin film was cooled to completely solidify , around 100 °C, before the microscopy study. A high shutter speed video camera ( Cohu, 4915) and a video recording system ( Panasonic AG-1960, Sony Trinitron) was linked to a polarized microscope (Olympus BH-2) to examine and analyze the morphological change during heating and cooling. Two kinds of heating schemes were used; for case I, the sample was heated to a high enough temperature ( higher than 175°C) where the crystalline structure was 81 F160 ep °) ep °) ep (°C) Temp (°C) Temp LI 50 (°C) Temp L140 1-130 zone I LI 20 LI 10 L100 Time (min) 0.5 j 5 - 0.5 ^ S -1J K-1-5J zone I Time (min) 70 §8 40 30 20 zone II 10 00 Time (min) Figure 3.8 The DSC results of heating to different temperature zones and holding for 60 min and then cooling at constant rate to complete the crystallization Figure 3.9 The setup for microstructure examination during crystallization 83 completely melted, then cooled back; for case II, the samples heated to a temperature in zone I according to the DSC results, then cooled back. In the former case, since the crystalline structure was completely melted, the polarized micrograph shows dark blank background only. As the cooling started, the dark blank background retained until the temperature reached the crystallization temperature (around 120°C). An clear nucleation spotting on the dark blank background, like the flowers blooming in a field, was observed. The crystal growth on nuclei was followed until it impinged to the neighboring crystals. By the comparison of before-melting and after-recrystallization at the same location, the arrangements and the sizes of the spherulites has changed totally. In the latter case, the sample was heated to zone I, the crystalline structure did not disappear but diminished. According to the micrograph, the boundary among the spherulites become blurred. However, the phenomena of shrinking spherulites could not be observed, it might be attributed to the overlapping of several layers of spherulites. The overlapping effects made the view from a single plane blurred. Besides, the thermal expansion might have made the view plane out of focus, which might also contribute to the blurred image. Slight adjustment of the focus was necessary to regain the focus but the blurred boundary among the spherulites still retained. As the cooling started, the blurred boundary among the spherulite regained its sharpness at a higher temperature (around 150°C) compared to the completely melted case. The size and shape of the crystalline structure at the same location is very close to the original one. Figures 3.10 and 3.11 show the micrographs of the important features mentioned above. A schematic DSC thermogram was used to relate the microstructure to the temperatures and thermal responses. Figure 3.10 The morphological change during melting and crystallization crystallization and melting during change morphological The 3.10 Figure Heat Flux along the DSC curve, case 1, completely melted 1, completely case curve, DSC the along heating Temperature Figure 3.10 (continued) Figure 3.10 (continued) Figure 3.11 The morphological change during melting and crystallization crystallization and melting during change morphological The 3.11 Figure Heat Flux along the DSC curve, case 2, partially melted partially 2, case curve, DSC the along heating e perature Tem (a) Figure 3.11 (continued) 89 3.5 Proposed Crystallization Model Based On DSC Curves The DSC observation suggests that the crystallization kinetics of polymer melt depends on the status of the polymer melt. The concept of the crystalline structure change, in terms of spherulites, during melting and crystallization is shown schematically in Figure 3.7. We can classify the effects of thermal history on crystallization kinetics into three zones, based upon the final heating temperature. Zone I: The final heating temperature ranges from where melting just starts to the melting peak temperature. The characteristics of crystallization in this zone are that the partially melted sample will recrystallize immediately after heating and the crystallization rate decreases with increasing crystallinity. In this temperature range, the crystal structure is not completely destroyed and the remaining crystal structure offers sufficient crystal surface for the melted polymer to recrystallize on it (secondary nucleation or spherulite growth). Figure 3.7 shows that the size of the spherulite decreases as temperature is in zone I, but the total number of nuclei may not change. When the temperature stops increasing, the melted material grows directly on the existing crystals. The spherulite crystals grow until they impinge against each other. The decreasing crystallization rate could be attributed to the possibility that adding a new chain onto the existing surfaces decreases because of (1) the diminishing amount of molten polymer, (2) the lower chain mobility, and (3) the impingement effect caused by the higher extent of crystallinity. Zone II: The final heating temperature ranges from the melting peak temperature to that at the end of the melting peak. The characteristics of crystallization in this zone are that the recrystallization of the partially melted polymer occurs at a temperature lower than the final heating temperature, but higher than the crystallization temperature of the completely melted polymer. In this case, there may still be some remaining crystal surfaces in the sample, however, due to the higher temperature, the total number of crystals may be reduced. 90 Therefore, crystallization in zone II includes both homogeneous crystallization, i.e. portion of polymer melt has to go through both nucleation and spherulite growth; and heterogeneous crystallization, i.e. since some crystal surfaces still remain in the polymer melt, crystallization can be induced to occur at a higher temperature. It is very likely that the crystallization rate still follows the bell shaped curve during cooling, as shown in Figure 3.6. Zone HI: As the final heating temperature is beyond the end of the DSC indicated melting zone, the sample is completely melted. No spherulite crystals remain in the melt. In order to initiate the crystallization, the primary nucleation has to start first and then spherulite growth will build upon the nuclei. For a homogeneous primary nucleation, the nuclei won't form until a lower temperature is reached during cooling, in this case, around 115°C.. As soon as the nuclei form, the growth on the nuclei can occur at a faster rate. Hence, the crystallization rate increases while enough nuclei form and then decreases as the extent of crystallinity reaches a high level. 3.6 Crystallization Kinetics Model For the Entire Melting Range An Avrami type crystallization model based on Hoffman theory is proposed to analyze the crystallization kinetics quantitatively. In order to model the crystallization kinetics covering the entire melting range, both the nucleation and the spherulite growth kinetics have to be considered. In our model, the total crystallization rate Xr is considered as the summation of the nucleation rate Xn and the spherulite growth rate Xsg. xr=xn+xsg (3.3) 91 A modified Avrami type equation was adopted here. For the nucleation contribution, the integral form of the equation is: X n = X noo(l- exp(-K nt n")) (3.4) where Xnoo is the final relative crystallinity contributed by nucleation, nn is the Avrami exponent of nucleation, and Kn is the crystallization rate constant of nucleation. As mentioned before, spherulite growth won't occur until the nuclei have been formed, the spherulite growth contribution depends on the nuclei fraction, i.e. Xsg = Xsgoo ^ - ( 1 - exp(-K sgtn'f )) (3.5) A roo whereXSgoo is the final relative crystallinity contributed by spherulite growth, Xroois the final relative crystallinity, K$g is the crystallization rate constant of spherulite growth, and nSg is the Avrami exponent of spherulite growth. These constants are temperature dependent and will be discussed in the following section. 3.6.1 Determination of rate constants The results of isothermal crystallization experiments offered necessary information to determine the rate constants for nucleation and spherulite growth. The crystallization rate of partially melted samples within zone I is assumed to be dominated by the spherulite growth rate. This assumption is based upon the fact that many nuclei are present and the spherulite growth is faster than nuclei formation. The rate of nuclei formation is very low at such high crystallization temperatures. The relative crystallinity, obtained by integrating 92 the peak area under the curve in thermal histogram, represents the contribution from spherulite growth. By using the Avrami analysis, the rate constant and the Avrami exponent for the spherulite growth can be determined from the intercept of the ordinate and the slope of the curve for each crystallization temperature from zone I, as shown in Figure 3.12. The temperature dependence of rate constant, KSg(T), can be written by using Lauritzen -Hoffman theory as follows: (3.6) TATf where U* is the activation energy for the chain mobility in the polymer, \|/sg is the folding energy contribution, Too is the temperature of 30°C below the glass transition temperature, AT is the temperature difference between the crystallization temperature and the equilibrium melting temperature, and f is a correction factor for the decrease of the latent heat as temperature decreases. Since U* is a universal constant for a particular polymer, we can obtain the value of U* directly from literature[107]. Here U* is taken to be 6280 J/mole, and the equilibrium melting temperature from Hoffman and Weeks plot is taken as 180.9°Cfor PP. By taking the logarithm of both sides of Eq(3.6) and rearranging it, we can determine the \|/sg and KSgo from the plot by linear regression analysis as shown in Figure 3.13. To determine the parameters in the nucleation term, the results of the isothermal crystallization of completely melted samples, combined with the known spherulite growth constants, can be used. The sample crystallized from zone III has to form nuclei first, and spherulite growth follows. The overall crystallinity includes contributions from both Figure 3.12 The Avrami plot for determining the spherulite growth rate constant and constant rate growth spherulite the determining for plot Avrami The 3.12 Figure Ln (-Ln(l-X)) Avrami exponent Avrami 93 94 3.5 2.5 cc * z> + c _J 0.5 0.0E+0 2.0E-5 4.0E-5 6.0E-5 8.0E-5 1.0E-4 1.2E-4 1/TATf Figure 3.13 The Lauritzen and Hoffman plot for determining KSg parameters. 95 nucleation and spherulite growth. The spherulite growth contribution can be subtracted from the overall crystallinity. After the spherulite growth contribution has been subtracted, the remaining nucleation contribution can be analyzed following the same procedure, i.e. the rate constants and the Avrami exponents of nucleation at each crystallization temperature are based on an Avrami-type equation. The nucleation rate constant, similar to the spherulite growth rate constant, is temperature dependent and also can be expressed as: * K„ = K„0 exp( ~ Jexp(^) (3.7) ROT-Too) TATf where the activation energy for chain mobility U* is the same as that in the spherulite growth, the differences are Kno and the free energy for chain folding contribution, \|/n. Our experimental results suggested that the folding free energy of nucleation should be larger than that of the spherulite growth. Figures 3.14 (A) and (B) shows the calculated spherulite growth and nucleation rate constants based on Hoffman and Lauritzen theory. By model prediction, a maximum rate constant for both spherulite growth and nucleation exists between the equilibrium melting temperature and the glass transition temperature. Rate constants drop to zero as the temperature approaches to Tg and T^,. Due to the limitation of experimental accuracy for measuring spherulite growth rate at low temperatures, the isothermal crystallization experiments can not cover the low temperature range. However, by comparing the model prediction with the experimental data from nonisothermal crystallization under a constant cooling rate, we can evaluate the applicability of the model over a broad temperature range. 96 Kn — Model • Experiment -50 100 150 200 T(°C ) The nucleation rate constant vs. temperature Figure 3.14(A) The comparison of rate constants from model calculation and experimental results under different crystallization temperatures 97 1.6 1 .4- K(exp) sg 1.2 - K(cal) sg 0.6 - 0 .4 - 0.2 - 100 110 120 130 140 150 160 170 180 190 Temperature (°C) Spherulite growth rate constant vs. temperature Figure 3.14(B) The comparison of rate constants from model calculation and experimental results under different crystallization temperatures 98 3.6.2 Differential form crystallization kinetics model A differential equation is used to simulate the nonisothermal crystallization. Since the cooling rate is constant, the time variable can be replaced by temperature. The differential form model can be written as; Spherulite growth rate: nsg ^^Sg =e- = n .„ - K „ - L n ( ------1 ) gnsg ------•^‘■n H_ + dXn 1^Sg — is . (3.8) dt sg sg i- x sg' Xrco dt X roo Nucleation rate: nn ~ 1 ^ = nn Kn'L" Crystallization rate: dXr dXn dXS2 — i = — 2- + — ^ (3.10) dt dt dt Table 3.1 summarizes all the parameters used in the differential form crystallization model. Since the crystallization model covers quite large a temperature range, from the melting peak temperature to the glass transition temperature, it was suggested to have varied Avrami exponents for different temperature ranges in order to have a better fit[107]. Here a two-temperature-range model was utilized. The two temperature ranges were separated at 127°C for a better fit. 99 Table 3.1 The parameters used in the differential crystallization model Nucleation: Kno Yn nn ForT> 127°C ForT>127°C ForT>127°C 2.5969xl08 3.8468xl05 1.24 For T< 127°C ForT< 127°C ForT< 127°C 5.0366x109 4.1039xl05 1.40 Spherulite growth: Kseo Ysg nse 1.6457xl03 5.5541x10s 1.25 In above equations, Kn and KSg vary with time. By the iteration scheme, the model predicted crystallization rates are shown in Figures 3.15 and 3.16 for zone III and zone I, respectively. This model provides a reasonable prediction for the crystallization in zone I and zone III. We can see that the model prediction for crystallization in zone I occurs right after the heating ceases and the crystallization rate decreases with temperature as in the experimental result. In zone III the model prediction shows a sudden change around 127°C during cooling. This is because different nucleation constants for different temperature ranges are applied, and the temperature transition point is around 127 °C. DSC heat flux, Crystallization rate - 0.5 0 2 3.5 1 . . . 5 5 5 100 iue31 h oprsnofmdlpeito n Cresult SC D and prediction model f o comparison The 3.15 Figure - - - 110 o f crystallization from zone III. zone from crystallization f o 120 Temperature 130 140 Model predicted Model results DSC 150 160 170 100 Crystallization rate 0.05- 0.15- 0.25- 0.35 iue31 h oprsnofmdlpeito n Cresult SC D and prediction model f o comparison The 3.16 Figure 0 0 . . 0 2 1 0 10 2 10 4 10 6 170 160 150 140 130 120 110 100 - - i i i i | i i | "i i i i i | i i i i | i i ii T=160 (model) T=160 ▼ T=160 (exp) T=160 ▼ o f crystallization from zone I zone from crystallization f o Temperature(°C) 1 i | i | i i i s t1 r i^ i i i i i i ft11 ^ i rv | vi ▼ vi 101 102 Figure 3.17 shows simulated crystallization rate versus time of the quiescent isothermal crystallization under various temperatures from the model. The lower temperature crystallization, such as T=135°C, has a larger peak and a shorter crystallization time. The crystallization peak is low and broad for higher temperature cases, such as T=145°C. By comparing the completion time differences between two crystallization temperatures, T=135 and 145°C, one can find the crystallization time of the higher temperature case is hundred times longer than that of the lower one at only a 10°C difference. 3.7 Shear Induced Crystallization Kinetics In the welding process, although the squeezing displacement is not very large, the shear rate may be very significant. In order to model the shear induced effects on the crystallization kinetics, a series of experiment based on a parallel plate type rheolometer (RDAII, Rheometrics) under various shear rates was conducted. The experiments included a constant shear mode and a shear-stop mode to elaborate the strain rate and the preshear effects on the crystallization kinetics, respectively. The preparation of the trial sample is described as follows: Small squares PP samples, about 0.5cm X 0.5cm, were cut from injection molded plates which were used for welding experiments. The small squares were placed in the oven of RDA II using the 63 mm diameter plates at 180 °C to mold thin films of 2 mm thickness. Using a 7 mm in diameter puncher, small round disks were made out of the 2 mm thin films. These small round disks were the sample specimen. The specimen was placed in the RDA II at an elevated temperature, 200°C. The specimen was kept at this temperature for 10 min to avoid any unmelted part. The Figure 3.17 The simulated crystallization rate versus time under various crystallization various under time versus rate crystallization simulated The 3.17 Figure crystallization rate 0.01 0 04- 4 .0 0 0.06 03- 3 .0 0 - 5 .0 0 . 2 0 - - 10 0 30 0 50 0 70 0 90 1000 900 800 700 600 500 400 300 200 100 0 T=138°C T=142°C temperatures time (min) time T=145°C 103 104 specimen thickness was reduced to less than 1 mm in order to have uniform temperature distribution. Then the sample temperature was cooled to a preset crystallization temperature. It took about 9 min for the whole system to reach thermal equilibrium. At high temperatures( higher than 140°C), several hours were necessary for completing the crystallization. Therefore, the 9 min time lag was still acceptable for the high temperature trials. It, however, would be too long for low crystallization temperatures. Two thermal couples were inserted in the sample to monitor the temperature discrepancy. One was around the center of the disk, and the other was at the rim of the sample. The temperature difference between these two locations was less than 1°C as the thermal equilibrium has been reached. A constant shear, ranging from 0.005 to 10 sec1, was applied on the sample as the thermal equilibrium reached. The viscosity would rise as the crystallization took place. A crystallization induction time is defined as the time required for the viscosity jump during crystallization. Figure 3.18 shows a typical viscosity rise curve during the crystallization under shear and the way to determine the crystallization induction time in these experiments. The intersection of two tangential lines was used as the crystallization induction time, indicated by an arrow in Figure 3.18. Figure 3.19 shows that the crystallization induction time decreased as the shear rate increased. After the technique of time-temperature superposition or the method of reduced variables for the rheological properties was applied [108], a master curve was obtained by plotting the reduced induction time versus the reduced shear rate, as shown in Figure 3.20. Here, the reduced induction time is the induction time divided by a temperature shift factor, aj, and the reduced shear rate is the shear rate multiplied by ay. All the induction times and shear rates of different temperatures were shifted to a reference temperature, To=140°C. The shift factor ax used here is determined by the ratio of the quiescent induction time at a Viscosity (c.p.) 100000 Figure 3.18 The typical viscosity rise curve under isothermal crystallization isothermal under curve rise viscosity typical The 3.18 Figure 20000 00 - 40000 -I 70000 00 J 50000 00 - 30000 - 60000 - 90000 00 - 80000 10000 10000 - - under 0.5 sec'1 shear rate shear sec'1 0.5 under 145°C at crystallization Isothermal 0 10 10 20 20 30 30 4000 3500 3000 2500 2000 1500 1000 500 Time (sec) Time 105 Crystallization induction time (sec) 100000 100000 10000 10000 Figure 3.19 The shear effect on crystallization induction time induction crystallization on effect shear The 3.19 Figure 1000 100 0 1 0.001 - - . - -=■ —i—i i o * ♦ A O □ O o ♦ A Temp=140°C Temp=142°C ep10C□ Temp=138°C □ Temp=145°C Temp=150°C 111 0.01 j 11 ----- Shear rate (1/sec) rate Shear — r n r i—i ▼ © A 0.1 1111 * O O ▼ A ♦ Temp=135°C O T ---- * □ 4 ° i—r“ Temp=130°C II 111| 0 1 “I 1 I I I I II I I I I 1 “I ♦ * 10 -s- ln(reduced induction time) Figure 3.20 Master curve for the induction time as function of shear rate shear of function as time induction the for curve Master 3.20 Figure 2 - 4 6 -10 - - • T=142 T=150 T=138 O T=145 T=135 □ T=140 In (reduced shear rate) shear (reduced In Master Curve Master 107 108 temperature T to the quiescent induction time at T0. The quiescent induction time was obtained from the extrapolation to a very low shear rate. The shift factor is written as (3.11) where tk0 is the quiescent induction time. Figure 3.21 shows the shift factor ax versus temperature. The logarithm of temperature shift factor could be modeled by the WLF equation: where Ci=11.9, C2=36.61, and To=140°C. A Carreau type model was used to interpret the master curve of the reduced crystallization induction time. Carreau type equation: In— = ——- In [l + (A/y)" ] (3.13) ko a L -I At high shear rates, i.e. A .y»l, Eq.(3.13) can be reduced to (3.14) So the constants n and X could be determined by the high shear rate data. The parameter a in Eq.(3.13) was determined by a nonlinear regression for the best fit among the experimental data. 109 1.5 f(x) = 3.066898E+0*x + -8.376137E-2 RA2 = 9.991990E-1 0 .5 - 0 - 1 -0 .5 - -1 .5 - 1 T-T, Figure 3.21 The shift factor a j is a function of crystallization temperature based on the quiescent crystallization induction time. 110 Based upon the calculation, the parameter and constants are shown as follows: X, =7.0699 n=0.457 a=0.8 The master curve in Figure 3.20 represents the fit of the Carreau model. The Avrami type crystallization model is written as X = l-expC-kt") (3.15) where k is the crystallization rate constant and X is the relative crystallinity. The induction time is the crystallization time when the relative crystallinity reach a certain level, Xc. The relationship between the crystallization rate constant and the induction time can be rewritten as ln(l —Xc) (3.16) According to Eq.(3.16), the ciystallization rate constant is proportional to By lk comparing the crystallization rate constant with shear and without shear, the sheared crystallization rate constant would be (3.17) I l l where kr and tk are the sheared crystallization rate constant and the induction time, respectively, kro and tk0 are the crystallization rate constant and the induction time without the shear effect, respectively. According to this approach, the sheared crystallization rate c \ n can be determined by multiplying a shear factor, Ksgr=KsgAs and As = ^ko to the v. -k J nonshear crystallization rate constant. In this approach, we assume that shear has same influence on both nucleation and spherulite growth rate constants. The induction time determined from RDA II determined from the modified shear induced crystallization model and from the master curve prediction is compared in Figure 3.22. The agreement is good. It is found that the relative crystallinity, Xc, is 0.096 from model simulation or master curve prediction for all shear rates. 3.8 The Preshear Effects on the Crystallization Kinetics The effects of preshear on crystallization kinetics were studied by a preshearing- then-stopping mode in the rheometer. Figure 3.23 shows the results of preshearing effects. Basically, the sample was sheared isothermally and then cooled under the quiescent condition. Samples were cooled at a rate of 10°C/min after being sheared, 1 and 5 (1/s), respectively, for 100 sec at 145 °C. In order to determine the crystallization induction time during the cooling stage a small strain, 0.5%, and a high frequency, 1 rad/sec, dynamic oscillation on RDA II was applied. As the shear rate increased with the same preshearing time, the induction time reduced. At the higher shear rate, the material would not remain between the parallel plates during the trial because of the Weisenberg effect. As one could observe on (C) in Figure 3.23, the data is not as smooth as (A) and (B). In our model, the preshearing effect was attributed to the increase of the crystallization rate at the shearing stage only, which is the beginning of crystal formation. The 112 2000 O model calc. 1800: + master curve 1600 J 1400 - & 1200 A B ' a iooo C A .2 1 800 A -a C 60 0 -B 400 0 200.: © 0 i i 11 11111) 1111111111 m"i | 111111 itt"] r i i 1111 r 111111 0 5 10 15 20 25 30 35 40 45 50 Shear rate (1/s) Figure 3.22 The comparison of induction times calculated from the modified shear induced crystallization model and from the master curve, at T=140°C Modulus Modulus Modulus 1x10' 1x10- 1x10 1x10 1x10 Figure 3.23 The preshearing effects on the crystallization determined by dynamic by determined crystallization the on effects preshearing The 3.23 Figure 0 15 1 15 2 15 3 15 4 145 140 135 130 125 120 115 110 105 100 0 15 1 15 2 15 3 15 4 145 140 135 130 125 120 115 110 105 100 0 15 1 15 2 15 3 15 4 145 140 135 130 125 120 115 110 105 100 cooling rate :10°C/min rate cooling oln at 10°C/min : te ra Cooling 145°C at 1/s 5 under sec 100 Shear no-shear oscillation method via RDA II RDA via method oscillation Temperature (°C) Temperature cooling rate :10°C/min rate cooling Shear 100 sec under 1 1/s at 145 °C °C 145 at 1/s 1 under sec 100 Shear 113 114 crystallization rate would be enhanced by the existence of larger amount of crystals due to the preshearing, even though the crystallization rate constant is identical for the post-shear period. For this series of experiments, the induction times were determined as the storage modulus crossed over the loss modulus. It implies that the solid behavior started to dominate at that moment. Here, we consider it as a reference to reveal a certain level of crystallinity. By comparing the no shear experiment result with model calculation, the crystallinity at cross-over point is 0.7668. Table 3.2 shows the model predicted cross-over temperature and the experimental cross-over temperature for the preshearing cases. The model gave a good prediction. Figure 3.24 shows the simulated crystallization rate versus time at 145°C with different shear rates. The shearing effects on the sheared crystallization curves is very similar to the temperature effects on the quiescent one based on our approach. A higher shear rate results in an early ciystallization and the crystallization peak becomes sharper and narrower. Figure 3.25 shows the nonisothermal crystallization under various constant steady shear rate, 0.005, 0.5, 1.0, and 1.5 (1/s), at a constant cooling rate, 3.46 °C/min. The critical crystallinity for rapid viscosity rise was assumed to be Xc=0.096, as mentioned earlier. The viscosity rise temperature during cooling was determined by the intersection of two tangential lines from the curve, which is similar to the way of determining the induction time in Section 3.7. Table 3.3 summarizes the comparison between the model predicted viscosity rise temperature based on Xc=0.096 and the experimental one. There are some discrepancies between the model prediction and experimental results, however, it shows correct tendency. The discrepancy may result from (1) over simplifying the relationship between viscosity rise and crystallinity and (2) the shear-thinning effects on the Figure 3.24 The simulated crystallization curves at 145°C with various shear rates shear various with 145°C at curves crystallization simulated The 3.24 Figure Crystallization rate 0.25 0.35 0.15 0.05 0.2 0.1 0.3 0.4 a 7=50 1/s 0 5 = 7 ;a) 1(c) iv (d )7 =0.5 )7 (d iv 7 7 =1.0 1/s =1.0 (e) 7 =0.11/s 7 (e) 1/s. 100 Time (min) Time 150 150 200 250 300 115 Figure 3.25 The constant steady shear rate effects on nonisothermal crystallization nonisothermal on effects rate shear steady constant The 3.25 Figure Viscosity 103 104 -= 105 106 107 1 15 2 15 3 15 4 15 5 15 160 155 150 145 140 135 130 125 120 115 110 ; * • 1 1 rr| 11 11iT~prr| i■ T|'"i11')i 11 11 11i| ■ 11 11 11 11 11 111 11 11 111 % « A * * i + + -P A eprtr °) - (°C) temperature A 1/s =0.005 7 o += r y = y ■ 7 =1.5 0.5 1.0 1 1 1 /s /s /s 116 117 Table 3.2 The Comparison between experimental viscosity rise-up temperature and model prediction ______ experimental model prediction (°C) (Xc=0.7668) (°C) preshear 100 sec with l(l/s) 116.9 116.6 shear rate at 145°C and cool at 10°C/min preshear 100 sec with 5(l/s) 117.6 117.2 shear rate at 145°C and cool at 10°C/min Table 3.3 The comparison between experimental and model predicted induction-shifted temperatures based on Xc=0.096, cooling at 3.45°C/min under various shear rates _____ shear rate (1/s) experimental (°C) model prediction (°C) 0.005 117 117.7 0.5 120 124.5 1.0 125 136.3 1.5 133* 142.9 * ambiguous induction-shifted temperature from the curve 118 viscosity. The Weisenberg effect also contributed to the difficulties at higher shear rate experiments. 3.9 Rheological Characterization The viscoelastic properties of PP were determined using a Rheometrics Dynamic Analyzer (RDA-700) with parallel plates. The complex viscosity was measured at temperatures ranging from 165 °C to 220 °C under the frequency sweep mode with oscillation frequencies ranging from 0.5 to 500 rad/s. Stress relaxation was measured in the same temperature range by recording the response of elastic modulus, G(t), after an instantaneous change in strain. Figure 3.26 shows the measured complex viscosity as a function of frequency. The dynamic complex viscosity was in the 400 to 40000 poise range for temperatures varied from 161 to 235°C. As expected, the polymer melt viscosity is very temperature and shear rate dependent. The complex viscosity decreased as the temperature and shear rate increased. Cox and Merz suggested a way of obtaining an improved relation between the linear viscoelastic properties and the steady shear viscosity. They stated that the magnitude of the complex viscosity is equal to the viscosity at corresponding values of frequency and shear rate[109]. The Cox and Merz rule showed a close approximation for the linear thermoplastics of which the agreement between complex viscosity and steady shear viscosity is within experimental error. In this study, the Cox and Merz rule was assumed to be valid. According to the time-temperature superposition or the method of reduced variables technique, the temperature dependent viscosity could form a master curve by shifting to a reference temperature. The temperature shift factor was defined as V T=161°C % 1E+3- o T=185°C ♦ T=202°C & A T=235°C 1E+2- 0.1 10 100 1000 Frequency (rad/sec) Figure 3.26 The measured complex viscosity as a function of frequency a _ M T)T0p0 (3.18) T ^ 0(T0)Tp where |i0(T) is the zero shear viscosity at T and p is the density. The zero shear viscosity could be determined by extrapolating from the data at the low shear rates to zero shear rate. The WLF equation for ax has been found to hold for a wide variety of polymers.[110] The WLF type equation could be expressed as: —Ci (T —Tp) Ln(aT) = (3.19) C2 + (T —T0) where Q =2.268, 02=151.52, and To=202°C. Figure 3.27 shows the way of determining parameters in the WLF equation. A Carreau model was used to fit the experimental results, as shown in Figure 3.28, where T„ is 202°C. The Carreau viscosity model: (3.21) Po 1 J where |10 =37565, n=0.384, 1=0.656 and a=0.58. The stress relaxation curves for small strain, 10%, are shown in Figure 3.29. The elastic modulus was higher at lower temperatures, however, the difference of relaxation 121 f(x) = -6.681409E+l*x + -4.408899E-1 RA2 = 9.980724E-1 2 » - 1 - - 2 - -l.OE-1 O.OE+O l.OE-1 1 T - T r Figure 3.27 The temperature shift factor, ax, for viscosity based on WLF equation where T o=202°C Figure 3.28 The master curve of Carreau model for reduced viscosity reduced for model Carreau of curve master The 3.28 Figure Viscosity/shift factor (c.p) 10 101 102 103 104 105 ° 10'1 10 T=235°C O ° A T=202°C T=202°C A T=185°C + C T=161 O Shear rate*shift factor (1/s) factor rate*shift Shear Carreau model Carreau 101 102 \& I ill 104 122 123 O T=198°C A T=173°C + T=161°C V T=123°C O ++++ ++++++++^ Time (sec) Figure 3.29 The stress relaxation curve of small strain, 10%. from RDA-700 124 time above melting temperatures was not significant comparing with the variance in its solid state. The stress relaxation curve was characterized based upon the generalized Maxwell model consisting of multiple relaxation modes. Generalized Maxwell Model: G(t) = ^ G ; exp(— —) (3.22) i where G(t) is the elastic modulus at time t, Gj is the i-th initial elastic constant at t=0 before relaxation begins and T; are the i-th relaxation time constants and were determined experimentally at a reference temperature. By knowing these parameters, the percentage of residual stress after a certain length of time can be calculated as % of stress remaining = (3.23) Table 3.4 lists the parameters and constants for the generalized Maxwell model based on T=161°C. The calculation procedures were described in detail by Chen[lll]. Figure 3.30 shows the generalized Maxwell model predicted stress relaxation comparing with experimental one at T=161°C. Same temperature shifting approach used for viscosity was assumed for stress relaxation. The only difference of temperature shift factor for stress relaxation is the reference temperature, T0=161°C. The temperature shift factor, A t, for stress relaxation was modified by 125 1.8x10 1.6x10 O Experimental Model predicted 1.2x10 1.0x10 CD 8.0x104 ^ 6.0x104 -< 4.0x10' 2.0x10' 0.0x10' Time (sec) Figure 3.30 The predicted stress relaxation curve from generalized Maxwell model comparing with experimental one at T=161°C 126 Table 3.4 The parameters and constants for the generalized Maxwell model ( polymer melt, T=161°C) G i=1972.38 dyne/cm 2 Ti =9.56 sec G2=14990.92 dyne/cm 2 12-0.448 sec G3=140224.5 dyne/cm 2 13=0.0892 sec Table 3.5 The parameters and constants for the generalized Maxwell model ( solid, T=123°C) Gi =32048.3 dyne/cm 2 ti=314.5 sec G2=20373.7 dyne/cm 2 t 2= 1.33 sec G3=12268.6 dyne/cm 2 13=0.92 sec G4=7825.9 dyne/cm 2 14=0.75 sec 151.52+(T-202) (3.24) -2.268(161-202) a 161 exp 151.52+(161-202) :) The stress relaxation curves of different temperatures according to the generalized Maxwell model after the temperature shifting are shown in Figure 3.30. The solid state stress relaxation curve could not be well predicted by temperature shift based on the molten stage data, as shown in Figure 3.31. It is necessary to have different parameters and constants of the generalized Maxwell equation to model the solid state stress relaxation. Table 3.5 shows the parameters and constants for the solid state generalized Maxwell model based on 123 °C and Figure 3.32 shows comparison between the model correlation and the experimental result. 128 8.0E+5 7.0E+5 - T=173°C (exp) T=173°C (model) 6.0E+5 - T=123°C(exp) T=123°C(model) 5.0E+5 - O 3.0E+5 2.0E+5 - 1.0E+5 - 0 -0-0 -0 0 nnno q q 0.00 0 0 0 0 q qc O.OE+O M- Time (sec) Figure 3.31 The comparison of stress relaxation curves according to generalized Maxwell model based on T=161°C with experimental data 129 4.5x10s 4.0x10s - 3.5x10s + exp — model 3.0x10s i . 2.5x10s -; O 2.0x10s - ' J . 1.5x10s z . 1.0x10s i \ ; I 5.0xio4-|m 0.0x10° "I— «— I— I— |— I— I— I I | I T I I | I \ T " ‘l ' | I » t » | I I T " T 10 20 30 40 50 60 Time (sec) Figure 3.32 The comparison of stress relaxation curve according to generalized Maxwell model based on T=123°C with experimental data CHAPTER IV HOT PLATE WELDING EXPERIMENTS 4.1 Hot Plate Welder All the welding trials were conducted at the Edison Welding Institute. The hot plate welder used in this work was a Bielomatic HV4806 manufactured by Leuze GMBH. It is a displacement-control type welder. The displacement was controlled by a mechanical stop. The welder could control and monitor the displacement during the heating time and forging operation. The movable parts on the unit, the carriage of the welding sample holder and the heating element, were driven by a pneumatic cylinder. The temperature of the hot plate was controlled by a built-in thermocouple inside the plate and a temperature controller. The change-over time, which is the time from withdrawal of the sample from the hot plate and forging, was at least 3 sec under normal operation. The controllable parameters for this welder are; heating temperature, heating time, heating and welding displacements, and forge pressure. 4.2 Welding Sample Preparation Welding specimens were produced using a Cincinnati Milacron 83 ton electric toggle injection molding machine with a rectangular mold cavity, measuring 15.24 by 10.16 by 0.32 cm. The injection molded samples were cut into 2.54 cm by 15.24 cm welding specimens for use. Prior to the welding process, the welding face of specimens 130 131 were cleaned and wiped by acetone to remove the any possible impurities on the welding surfaces. 4.3 Setup Prior to Welding Operation Alignment of the welding samples: With the machine off, clamp two specimens in the fixtures and manually push two specimens together to check the alignment both vertically and horizontally. Installation of the Teflon impregnated cloth: To avoid the sticking problem during heating and withdrawing the samples from the plate, install a Teflon impregnated woven cloth on the heating plate. Setting of displacements: There are two displacements to set before welding operations; heating displacement and welding displacement. Weld displacement is the amount of polymer melt that being squeezed out from the faying surface during the heating and forging steps of the process. This is adjusted by setting two screws located on the left hand side of the moveable carriage. One screw sets displacement during the heating step and the other sets it during the forging step. The difference of these two settings is the actual welding displacement. To set the displacement screws, the following procedure is recommended. With the heating element in the retracted position and the sample in the holder, manually slide the left side of the carriage until the sample coupons firmly contact. Adjust the bottom screw so that the space between the screw and the small stop plate mounted on the carriage is equal to the amount of desired displacement during the forging step. Next, turn the machine on and move the heating element in the forward position. Turn the machine off and, manually, push the carriage with the sample coupon plus the hot plate until it firmly contacts the other coupon. Adjust the top displacement control screw until the space 132 between the end of the screw and the small stop plate mounted on the carriage is equal to the desired heating displacement. 4.4 Welding Experiments Parameters chosen for study included heating temperature (200 to 320 °C), change over time (1 to 20 sec) and heating time (10 to 60 sec). In order to measure the temperature profile in the specimen, thermocouples were inserted at several different locations: middle of the joint interface, 2 mm and 4 mm away from the interface, for reading the temperature profile. The temperature profiles at the welding interface for different heating temperatures and heating times are shown in Figure 4.1. During the heating stage, the measured temperature at the sample surface was much lower than the set temperature of the hot plate, even though the sample was in intimate contact with the hot plate surface. This is caused by the impregnated woven cloth. For a higher heating temperature and a longer heating time, more heat was absorbed in the sample and the molten layer was larger. Consequently, the cooling rate during the joining stage was lower. Since the crystallization is strongly affected by the cooling rate, both the weld zone morphology and the welding cycle time depend on the selection of heating temperature and heating time. The weld strength was determined by tensile tests using an Instron Tensile Tester (Model 4204) at a cross-head speed of 0.5 cm/min. The flash of the welded samples was removed before performing the tensile tests. Three samples were tested for each welding condition to account for data variations. The microstructure near the joint interface was examined using an Olympus BH12 polarizing microscope. The samples were microtomed to 12 pm thin specimens under -40°C by a microtome machine (Kryostat 1720). The thin microtomed specimen was Figure 4.1 The temperature profile at joining interface under different welding conditions welding different under interface at joining profile temperature The 4.1 Figure V' o a $ Temperature (°Q 1 e 0 200 250 300 100 150 200 50 100 150 200 250 150 50 50 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 120 110 100 90 80 70 60 50 40 30 20 10 0 0 30 20 10 20 (b) Heating temperature was set at 250°C set temperature was Heating (b) (c) Heating temperature was set at 320°C temperature set was Heating (c) (a) Heating temperature was set 200°C at temperatureset was Heating (a) X. 40 0 0 0 0 0 0 0 10 120 110 100 90 80 70 60 50 40 etn ie 10sec time= heating TIME (sec) TIME IE (sec) TIME TIME (sec) TIME 080 60 heating time = 30 sec 30 = time heating heating time=30 sec time=30 heating heating time =30 sec =30 time heating heating time=60 sec time=60 heating heating time= 60 sec 60 time= heating 0 120 100 temperature Crystallization 133 134 mounted between a slide and a cover glass with lubrication oil to keep the sample from curling. The crystalline morphology was examined using the polarizing light microscope. The differences in the degree of crystallinity along the welding zone were investigated by DSC. The microtomed sample of the specimen was carefully cut under microscope to thin slips with specified distances from the weld interface. The thin films were then subjected to DSC. Heat of fusion relating to crystallinity was obtained from the melting curve. 4.5 Results and Discussion The micrographs of the heat affected zone for samples welded at a heating temperature of 200°C and various heating times are shown in Figure 4.2. The microstructure of both cases have similar patterns. There are at least three zones around the joint interface (excluding the flash), i.e. the stressless recrystallization area, the columnar area and the slightly deformed area. The stressless recrystallization area resulted primarily from the reheating and recrystallization of the skin layer and the high temperature molten material near the joint interface. The viscosity and elastic modulus of the molten polymer in this area were smaller due to the higher temperature, hence the material in this area had a lower stress level and had a longer time to relax the stress before resolidification. The temperature profiles in Figure 4.1 show that it took about 15~20 sec for the interface temperature to drop to the crystallization temperature at the joint interface. Hence, the crystals were formed after stress relaxation, which is smaller than 10 sec under the given temperature range as shown in Figure 3.29, had completed. Elongated crystals oriented in the flow direction were found in the columnar area. The viscosity and elastic modulus in this area were high due to the lower temperature. The crystals were formed under flow Figure 4.2 Polarizing micrographs of microtomed specimen welded at heating temperature of 200°C with different heating times. 200X magnification 136 stress so that the shape of the crystals was deformed along the flow direction. The width of the columnar zone across the joining interface was larger at outer part, which is close to the part surface, than at inner part of the joint. The columnar deformed crystals formed under the influences of stresses have less chemical resistance. Several studies have found that the microstructure of the deformed crystal could be attacked easily by the chromic acid after the etching processes. The tensile strength of the deformed structures could be as strong as that of the spherulite ones. However, the deformed crystal may be the initial cracking location under long term service[7,l 1,45,46]. For cases with small molten layer, caused by low heating temperatures and low heating times, the orientation of the deformed crystals is clear and strong. This is caused by the large shear rate for smaller molten layer at the same welding displacement. From Figure 4.2, we can observe that the stressless recrystallization area for the cases with a long heating time (60 sec) was much larger than that for the short heating time (30 sec) because more molten material was at higher temperatures and the cooling rate was lower after joining for the former case. If we compare the size of the Heat Affected Zone ( HAZ) under different heating temperatures at the same heating time, the higher temperature case had a larger HAZ. The difference was significant as shown in Figure 4.3. If too high a heating temperature or too long a heating time was used, there might be a void formed at the joint interface, as shown in Figure 4.4. This might be due to the volume contraction during the cooling stage and the insufficient contact between the samples due to too small joining displacement. Another possibility is that too large a molten layer might have resulted in deflection of the sample and reduce the real welding displacement, as shown in Figure 4.5. In such cases, a larger joining displacement is necessary to avoid the void formation. 137 (a) T =250°C, 100 X (b) T=320°C, 40X m ?< : \ . U y^£ * m £ Figure 4.3 Polarizing micrographs of microtomed specimen welded at heating time of 10 sec with different heating temperatures Figure 4.4 Polarizing micrographs of microtomed welded specimen (T=250°C, t=60 ) 40X The black area is a void. 139 Hot plate molten layer Figure 4.5 The deflection of molten layer due to too large melt length 140 Some cases, as in large pipe joining, require a relatively long change-over time. In this study we prolonged the change-over time to simulate the actual situation in large part welding. The size of the stressless recrystallization area decreased under this condition, however, that of the slightly deformed area increased, as shown in Figure 4.6. Table 4.1 shows the melting temperature and heat of fusion around HAZ for two cases. Variation of the melting temperature was not very large. The heat of fusion, however, changed significantly along the heat affected area, especially for the case of short heating time. This proves that the crystallinity in heat affected area is different from that of the original bulk material. The weld quality of the samples was evaluated by weld factor through tensile tests. The weld factor is defined as the ratio of ultimate tensile strengths between the welded sample and the parent material. Figure 4.7 shows the weld strength of samples under various welding conditions. The tensile strength of virgin material is 8810 psi. In general, at a higher heating temperature, the heating time needs to be selected carefully in order to achieve good weld quality. For the heating temperature of 320 °C (the actual interface temperature was about 275°C), the optimum heating time was 10 sec. Too long or too short a heating time significantly decreased the weld strength. The weld quality was very sensitive to the heating time change. A longer heating time results in a larger molten layer in the parts. With a constant welding displacement, the contact force, which can enhance the chain entanglement, is reduced with increasing molten layer thickness. The volume contraction due to the phase change ( from liquid phase to solid phase) will also be more severe for the case with a larger molten layer. The same was true for the heating temperature of 250°C. For the lower heating temperature(e.g. 200°C), the effects of heating time on weld quality were less significant. For the heating temperature of 250°C and the heating time of 60 sec, it was found that the weld quality improved as the change- 141 Figure 4.6 Polarizing micrographs of microtomed welded specimen with holding time 10 sec (T=250°C, t=60 sec ) 40X •v 142 TABLE 4.1. The melting temperature and heat of fusion around the weld zone (a) Heating temperature=200°C, heating time= 60 sec and weld factor= 0.92 Distance from the joining Melting temperature Heat of fusion interface (±0.2 mm) (°Q (J/g) interface 164.8 73.1 0.5 mm 164.8 83.5 1.0 mm 164.9 84.4 3.0 mm 164.9 81.1 (b) Heating temperature=320°C, heating time= 5 sec and weld factor= 0.65 Distance from the joining Melting temperature Heat of fusion interface (±0.2 mm) (°Q (J/g) interface 164.4 57.9 0.5 mm 164.6 70.8 2.0 mm 164.9 86.3 3.0 mm 164.7 76.8 Weld factor 0.1 0.2 0.3 0.4 0.6 0.5 0.7 0.9 0.8 0 1 Figure 4.7 Tensile strength o f weld under various welding conditions welding various under weld f o strength Tensile 4.7 Figure 0 : t he trend, not for correlation for not trend, t: he : curve for showing for curve : =2 C =5° Q T=200°C Q T=250°C y °C T=320 ^ 10 20 Heating Time (sec) Time Heating 050 30 40 .voir Isfound -a-lctof 60 143 144 over time was increased to 10 sec, as shown in Figure 4.8. The short period of change over time may be able to smooth the uneven temperature distribution in the molten layer, especially for the thin parts. However, a further increase of the change-over time to 20 sec decreased the weld quality because of the formation of a thick solid skin at the joining interface. 4.6 Concluding Remarks The polymer morphology of the heat affected zone around welds had been investigated in this chapter. Based upon observed morphology at weld HAZ, we can conclude that the microstructure at HAZ can be divided into four zones, as shown in Figure 4.9. The influence of HAZ microstructure on the weld strength was conducted by comparing micrographs of microtomed samples and its tensile strength. According to the comparison of moiphology between good weld and poor weld, if no voids formed in the joint, there is no major difference on the morphology. High heating temperatures may be applied to reduce the welding cycle time. However, the heating time should be carefully selected in such cases since the tensile strength was very sensitive to the variation of heating time. 145 0.6 T 0.5 0.4 f U O 40- t rcd ** 0.3 *0 1 0.2 T= 250°C t= 60 sec d= 1.4 mm 0.1 0 i i i i | i" i 'i"'T" | i r “|' i i i 0 5 10 15 20 Change-over time (sec) Figure 4.8 The effects of change-over time on tensile weld factor 146 a: center of the welding interface, larger spherulite b: stressless recrystallation spherulite c: columnar-like deformed crystal d: slightly deformed spherulite Figure 4.9 The schematics of microstructure in the HAZ C H A PT E R V MODELING AND SIMULATION OF THE WELDING PROCESS 5.1 Introduction The temperature distribution, melt displacement profile, and stress contour, which are difficult to measure during the welding process, are the essential factors to determine the weld strength. They are predicted theoretically in this chapter. Two approaches of computer simulation were tried, one is based on a commercial software package, DEFORM, which is widely used in metal forming , and the other a modified control volume finite element method (CVFEM), which has been used for resin transfer molding processes. The welding processes simulated included heating, joining and cooling. 5.2 DEFORM The DEFORM software consists of four major functional modules for simulating the material forming processes. They are pre-processor, simulation engine, post processor, and utility module. A brief description of each module is summarized below. The task of the pre-processor of the DEFORM systems is to assist users in generating finite element mesh for the interested subjects, preparing input data, and also remeshing the old mesh to a new mesh. The density of mesh can be specified according 147 148 to the user's request. A good understanding of the processing characteristics is essential for generating the efficiency mesh and correct input data. The simulation engine is the core of the DEFORM system, which performs the calculation based on FEM. It can handle the deformation analysis of multiple objects with any combination of the following material models: a. Rigid, plastic, and viscoplastic b. Linear thermo-elastic c. Sintered porous preform d. Powder forming coupling with nonlinear heat transfer analysis. The post-processor of the DEFORM system provides output of results numerically and graphically. The output of post-processing can be formatted for SUPTERTAB and PATRAN uses. The utility module offers users the capabilities to setup the system defaults and to maintain the result databases. As shown in Figure 5.1, the logical sequence of using DEFORM system is to: (1) generate FEM mesh using the mesh generator provided by DEFORM; (2) prepare input data (i.e. material properties, processing parameters and characteristics, etc.); (3) perform FEM simulation using the simulation engine; (4) post-process simulation results using post-processing module; (5) perform remeshing using remeshing module if necessary; and (6) repeat the above operations. Object/process description Functional flow Data flow CAD/CAM interface Input preparation Remeshing keyword file necsssary Database Post- FEM simulation processing Interactive graphics Figure 5.1 DEFORM system flow diagram 150 The assumptions and boundary conditions used for welding processes in DEFORM are as follows (a) 2-D heat transfer and squeezing flow (b) quasi steady state at each time increment (c) axial symmetry, considering only 1/4 of the weld (d) constant displacement rate (e) no heat flux and flow velocity in the y-direction flow, as shown in Figure 5.2, at joining interface (f) constant hot plate heating temperature For the rectangular welding specimen, the simulations of heat transfer and squeezing flow could be focused on the thickness and machine displacement directions, if the width of the specimen is much larger than the thickness of the specimen. The whole welding process can be simulated by the following sequence, heating, squeezing, and cooling stages. The characteristics of the objects were treated as a rigid-plastic-rigid combination, as shown in Figure 5.2. x Rigid Object moveable part: grip compressing di recti on P lastic Object deforming part: PP bar ▼ Rigid Object stationary part: Hot plate Figure 5.2 The schematics of objects setup for DEFORM 151 The major feature in the heating stage was simulated as the heat transfer from the constant temperature heated tool to the plastic part. The temperature distribution in the plastic part can be calculated by the program. The heating temperature and time are the input processing parameters. The effects of thermal expansion, the thermal resistance between the hot plate and the plastic part, and the small heating displacement were neglected in the simulation. The material properties, such as heat capacity, viscosity, and thermal conductivity, are functions of temperature, which were determined in Chapter 3. The melting peak temperature, 165°C, from DSC curve was used as a reference temperature for classifying the solid and the molten melt status. The melt portion could flow under the influence of the stress. The solid portion was treated as a material with a very high viscosity. In this case, the magnitude of the solid ‘viscosity’ is 104 times higher than that of the molten layer. After the heating stage, the plastic part consists of solid and melt portions, which was distinguished by the melting peak temperature. The squeezing stage was simulated by a constant velocity moving object, the grip, acting on the plastic object against a rigid wall, which is thermally insulated. The plastic part between the grip and the fixed plane deformed as the grip compressed. However, due to the large differences of viscosity between the solid and the melt, only the melt portion was deformed. In DEFORM, the flow resistance is determined by a flow stress function depending upon strain, strain rate, and temperature , and can be represented as iiik = 'C<,Yi,YpTk) (5.1) where xijk, yi , y;., and Tk are the values of stress, strain, strain rate and temperature. 152 The viscosity model obtained from Chapter 3 was used to calculate the flow stress. The flow stress can be expressed in terms of shear rate and viscosity *yx = lI f T>Tm (5-2) Here, |X follows Carreau viscosity model: - ^ [ l + a y ) 3] ^ (5.3) M'o and |l0 =37565, n=0.384, ^=0.656 and a=0.58. The WLF equation for temperature shifting factor could be expressed as: <54) where Ci=2.268, C2=151.52, and To=202°C. According to this scheme, only the portion with temperature higher than Tm could flow under compression. The flow pattern during squeezing depend strongly on the thickness of the molten layer and the temperature distribution in the molten layer. The x-direction flow driven by the compression in the y- direction would be affected by the thickness of the molten layer. At the same welding displacement rate condition, by the law of conservation of mass, the smaller molten layer one would have a larger flow rate. The flash shape of the welded sample with a smaller molten layer would be sharper than that with a larger 153 molten layer under the same welding displacement. From our experimental results, the flash appearance could be concluded as shown in Figure 5.3. The stress in the molten layer would also be larger for the case with a smaller molten layer. compressing large molten layer flash shape due to squeeze out_____ small molten layer Figure 5.3 The effect of molten layer size on squeezing-out flash 5.2.1 Simulation Results Figure 5.4 shows the temperature profiles after the heating stage. The melt zones in both cases are very small. For T=200°C, t=30 sec case, the melt length is around 0.3 mm, and for T=250°C, t=30 sec case, the melt length is about 0.8 mm. In these small 154 in terface 2.99t T=200°C 2 . 98< t=30 sec 2 .97? 2 .96 Temperature Y (mm) A=150 B=155 C=160 D=165 2 .93* E=170 2 ,92t] F=175 melt boundary G=180 2 .91TJ H=185 2 .90(1 II I------1--1----1 r 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X(m m ) 2 .99t T=250°C 2 .98t t=30 sec 2 .97? 2 .96'C Y (mm) Temperature 2 .9 5 t A=155. 2 . 94t B=165. C=175. 2 .93 D=185 E=195. melt boundary 2 ,92( F=205 2 . 91t G=215. H=225. I.O 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X(m m ) Figure 5.4 The simulated temperature profiles after heating 155 molten layers, the temperature was varied from 200 to 165°C, which is a very large temperature gradient. The temperature contours away from the heating plate is more curvature. The concave curve in the weld during heating was attributed to the convection heat loss from the surface. The radiation heat flux from the extension of the hot plate was ignored, since the welding temperature is not sufficiently high to gain significant radiation heat flux. Figure 5.5 shows temperature profiles after squeezing. The hottest melt was squeezed to the outermost of the flash. If a close examination was made, one could see that the distances between the temperature contours in HAZ decrease because of the melt squeezing-out. The flash shape agrees reasonably with the experimental observation. The lower temperature case, T=200°C, had a sharper shape. Figure 5.6(a) displays the simulated strain profiles after squeezing. The highest strain contour is located at the deflection corner. It implies that the maximum orientation is there too. Similar results were found in the micrograph of microtomed samples shown in Figure 5.6(b). DEFORM, however, can only solve cases with small welding displacements, i.e. d <_0.15 mm, which is not sufficient for real welding cases. Too large a welding displacement resulted in the divergence of computer calculation, even though the remesh procedure had been taken. In order to solve the welding cases with large displacements, the control volume finite element method was used and is discussed in the next section. 5.3 Control Volume Finite Element Method A control volume finite element method, which was developed in our laboratory to simulate the mold filling process for liquid composite molding (LCM), was adopted for 156 3 .0 2 . 99( 2 . 98f 2 .97( Y (mm) 2 . 96< T=200°C Temperature 2 . 95( t=30 secd=0.15mm A=160 2 .94< B=162 C=164 2 .93* D=166 E=168 2 . 92C F=170 2 .9 1 t G=172 H=174 2 . 90C t 1-----1-----1-----1------r 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X (mm) in terface 2 . 99t 2 . 98t Temperature 2 . 97t A=160. B=165. 2 .961 C=170. D=175. 2 . 95t Y (mm) E=180. 2 .94 F=185. G=190. 2 . 93C H=195. 1= 200 . 2 . 92C J=205. T=250°C K=210. 2 .911: t=30 secd=0.15 mm L=215. 2 . 90C 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X(mm) Figure 5.5 The simulated temperature profiles after squeezing 157 2 . 97f 2 . 96f A= 0. 0000 0E+00 B= 0 .3 7 0 7 7 Y (mm) G= 0. 7415 3 F= 1.853 8 2 . 92C G= 2.224 6 H= 2 .5 9 5 4 2 . 90C 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X(mm) 2 .990 2 .9 8 t 2 . 97c 2 . 96t 0 0 0 0 0 0 E+0 0 67965 E-0 1 Y (mm) 2 .95 13593 20389 E= 0 2 7 186 2 . 93C F= 0 33982 2 . 92C 4077 9 47575 2 . 91C 54372 2 .900 i 1-----1-----1-----1-----r 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 X(m m) Figure 5.6(a) The simulated strain profile after squeezing Figure 5.6 (b) The micrograph of welded sample at the deflection comer 159 the welding process. The following section briefly describes how the governing equations are derived[l 12-114]. 5.3.1 The continuity equation For an incompressible fluid, the continuity equation can be written as: Bu Bv Bw (5.5) Bx By Bz or V* v = 0 (5.5a) where v is the velocity vector consisting of three components, u, v and w, in the directions of x, y and z, respectively. 5.3.2 The equation of motion In CVFEM for LCM, Darcy's law for flow through porous media was used for the momentum equation. It is written in the form: Bp (5.6) .Bz. or (5.6a) where ji is the viscosity, k represents the permeability tensor, and p is the pressure. Eq(5.6) also holds for mold filling in a thin gap-wise cavity in injection molding by extending the classical Hele-Shaw approximation for Newtonian fluid under similar 160 conditions[l 15]. From the continuity equation, Eq(5.5), the gap-averaged velocity V along the z direction is written as V = (u ,v )= | + ^ r )dz = J ‘ vdz (5.7) J,2b ox oy J,2b -b -b where 2b is the cavity thickness. With the assumption of neglecting the inertial term, the momentum equation can be reduced to a Darcy-like law in terms of the gap-averaged velocity V(x,y,t) V = -M V p (5.8) b with M = f - —- Shen[115] defined M as the mobility. The mobility M is numerically identical to the k permeability divided by the viscosity, —. The continuity equation can be rewritten as V • M Vp = 0 (5.9) The control volume in the flow domain was established among the meshes, as shown in Figure 5.7. The integration of Eq(5.9) over a control volume facilitates the physical interpretation of mass conservation within the control volume. By using the Divergence theorem, the integration over the volume can be rewritten as jjN * m PdS = 0 (5.10) S Control volume control volume mesh grea boundarV boundary Figure 5.7 Control volumes in triangular meshes 162 where N is the normal vector to the surface S of the control volume. Eq(5.10) is the working equation for solving the flow pattern and is basically a mass balance equation. Although the equation is steady state, the mold filling process is not. The mold filling was regarded as a quasi-steady state process by assuming a steady state at each time step. The transient solution was approached by a sequence of steady state solutions at very small time increment. 5.3.3 The energy equation The energy balance equation is expressed as p cp ^ + (pcp)vr -VT= V -[k-VT] (5.11) where T is the temperature,cp is the apparent heat capacity, and k is the thermal conductivity. The control volume method used here is by integrating the equation over the control volume domain and then applying the Divergence theorem, if possible. It resembles the finite difference method which directly uses the interpolation on the nodal points for integration. Using this approach, the integral form of the energy balance equation over a control volume can be expressed as j J j f p c pTdV + ff[pc„v„T ~k% ldS = 0 (5.12) cv cs 163 5.3.4 The numerical scheme The geometry of the object was discretized into three-node triangular elements. Each nodal point was enclosed by a control volume which was formed by connecting the centroid of each element to the midpoints of the sides of each element, as shown in Figure 5.7. Each element was divided into three sub-elements according to the control volume boundary lines. In order to interpolate pressure in the element, the linear shape functions for a three-node triangular element were applied. For the 2-D case: 3 Y = £ V i N i (5.13) i'= 7 where yr,- is the nodal property ( such as pressure) and Nj is the shape function. Ni = j^ ( 0Ci + pix + Yiy) (5.14) «/ =xjyk -wj A =yj -y/c Yi = xk — xj where iVj ?k, and i, j, and k permute in a natural order, and A is the area of an element. The working equations of mass and energy balances for each control volume were integrated by the summation of all sub-elements. Substituting the partial derivative of shape functions for pressure into Eq(5.10) yields: 164 m Pl>p2’P3 P l1 X \}a clnX’ ny lac ^bc[nx> ny lbc} P2 = 0 (5.15) i=l 7l> 72< 73. P3X where hz is a part thickness, and\ac and lbc are the length between points a and c, and b and c, respectively, as shown in Figure 5.8. The integration of the mass balance along a control volume boundary is the summation of the surrounding m sub-elements. Eq(5.15) can be written for all control volumes in the flow field, which results in a set of linear algebraic equations. By combining with the appropriate boundary conditions, the pressure in the flow field can then be determined. The boundary conditions for the pressure field are p= 0 at flow front p= p0 at inlet gate According to Darcy's law, the average velocity on an element can be easily determined by Eq(5.7). Following the similar approach, the temperature profile can be solved by the discretized form of Eq(5.12) and proper shape functions , i.e. E E d_ (PCPAS t ( dT i * j PV„Tj k > d r e = 0 (5.16) dt Tj I. 1 e=l' ~ 'J e—1f e V Je The solution of one dimensional steady heat transfer equation with conduction and convection terms is an exponential form. Therefore, an exponential shape function may be a more accurate approximation for interpolating the temperature profile in an element. The exponential shape function used in the program is: 1 a 2 Figure 5.8 A typical two dimensional triangular element Figure 5.9 A schematic for exponential shape function 166 (5.17) where £ -rj is a new coordinate system, as shown in Figure 5.9, where E, is the direction of the average velocity over the element, uavg> and p and r are the density and thermal diffusivity over the element. The boundary conditions for the energy equation are T=T0 at inlet gate k ? f = K (T -T air) at flow front where T0 is the initial temperature, Ta;r is the surrounding air temperature hv is the convection heat transfer coefficient. 5.3.5 The welding case study The original CVFEM for LCM is not developed for the welding process. After some modification of the code, it is able to simulate the welding case. The welding case is a two-phase problem. The molten portion is liquid-liked, which can flow and deform. On the other hand, the unmelted solid portion behaves as a rigid body motion. In order to use the LCM program the solid portion was assumed as a very high viscosity liquid comparing to the molten one. And an element cleavage scheme at the solid phase free boundary was used to avoid solid material squeezing out. Therefore, the calculated pressure field would be deviated from the real value because of the high viscosity assumption of the solid. Since the conservation of mass holds, the calculated velocity layer in the molten layer should be reasonable. However, the calculated shear rate and shear stress may not be accurate. 167 Figure 5.10 shows the L-shape computation domain for simulating the welding process. The welding process can be considered as a 2-D case along the thickness ( i.e. x) and the squeezing directions ( i.e. y), if the part width is much larger than the part thickness. The central part of the L-shape represents the plastic bar. For heating, the program assumes that the central part is a filled region without flow. The measured hot plate temperature is assigned at the interface as boundary condition. The time increment for each time step during the heating stage is controlled by confining the maximum temperature change in the time step no greater than 10% of the temperature change in the last time step. The results of the heating simulation is the temperature distribution in the sample. The area where the temperature is higher than or equal to the melting temperature is considered as the molten layer. After the heating stage, the squeezing stage is simulated by fluid flow into the side of the L-shape ( i.e. Region A in Figure 5.10). Since the temperature distribution in the part after heating is known, the molten region can be determined according to the melting temperature. Region A is a computation domain for allowing the polymer melt flow into it during squeezing. For the sake of reducing calculating time, the size of Region A could be adjusted corresponding to the depth of the molten layer and welding displacement. Here the dimension of Region A is 2 mm by 3 mm, which is much larger than the squeezing out flash. Basically, Region A provides a calculation domain for the flash. The size of Region A won’t affect the computation results, as long as it is large enough to accommodate the whole flash. Only the molten material can flow into Region A, as shown in Figure 5.10. The solid portion won’t be able flow into this region. In order to fulfill this requirement, an element cleavage technique (ECT) was applied during the squeezing stage. 168 iot plat e plastic bar heated end (known heating t emperat ure) ( cont act w ith hot plat e) central prefilled region ( plast ic bar) Heating stage Region A Empty before squeezing no heat flux 2 mm Squeezing stage 3 squeezing directi on 9 mm boundary where element cleavage will be considered mm ^ inlet gate during squeezing Figure 5.10 The schematic of the geometry for welding case 169 5.3.6 The element cleavage technique The purpose of the ECT is to avoid the solid material flowing into Region A in Figure 5.10 . Even though a very large viscosity is assigned to the solid part ( i.e.105 times, about 1011 c.p., comparing to the magnitude of the molten material viscosity), the solid part may still move with an unrealistically high pressure field by calculation. In CVFEM, if the connection between the nodal points is cleaved, the program will treat that particular element as mold wall, as shown in Figure 5.11. Based on this algorithm, we may classify the material status at the flow front line into molten or solid status. As long as the temperature of the flow front node is below the melting temperature, the connection between this flow front node and the neighboring unfilled nodes will be cleaved. Consequently, the fluid can not flow in or out of these cleaved solid sub-control volume. The approach can be regarded as changing mold geometry during the squeezing process. Because the welding time is very short (i.e. ~ 1 sec), the squeezing process is assumed to be adiabatic, i.e. the molten status won't change during squeezing. The results of the squeezing simulation include melt distribution, temperature profile after squeezing, and stress distribution. Although the calculated stress values may not be accurate, the calculated stress distribution should be reasonable. The crystallization kinetics are incorporated in the cooling stage with heat transfer. Stress relaxation is also solved based on a generalized Maxwell model, as mentioned in Chapter 3. The amount of residual flow stress depends on the crystallization time. For the long crystallization time, such as in the completely melted region, zone III, the stress will totally relaxed before crystallization. However, the stress won't be able to relax completely if the crystallization time is shorter than the relaxation time. All these calculations are performed in the cooling stage. 9 nodes [ ] Solid flow front Q Liquid flow front ^ Cleaved links after element cleavage Figure 5.11 The schematic of the element cleavage method 171 Figure 5.12 The mesh geometry used in simulation (zoomed in joining interface area) 172 5.4 CVFEM Simulation Results Figure 5.12 shows the mesh, created by IDEAS, used in this study. The height of Region A could be roughly estimated by an analytical solution of 1-D heat transfer to determine the temperature profile and the amount of the molten material. For the 1-D heat transfer of a semi-infinite rectangular bar, as shown Figure 5.13, with constant heating temperature, the analytical solution can be written as: T-T. x 1-erf (5.18) 2-yfat 1- D heat transfer equation ( \ dT_ d2T It dx‘1 I.e . T=T0 at t= 0 B.C. o X T=Th at ii T=T0 at x-» x=0 The boundary condition of the molten layer is at T=Tm (165°C for PP). Figure 5.13 1-D heat transfer equation and boundary conditions 173 Since a Teflon woven cover sheet was used on the hot plate to avoid the problem of the molten plastic sticking on the hot plate surface, the temperature of heated end of the plastic bar was lower than the hot plate set temperature. This temperature difference was attributed to the thermal contact resistance. The thermal contact resistance depends on how good surfaces are contacted. In other words, it is a function of contact surface quality, contact pressure, and heating temperature. In order to measure the actual temperature at the heated end during the heating stage, a thermocouple located at the heated end was used to record the temperature profile during heating. Figure 5.14 shows the measured temperature profile at interface during the heating stage. All the cases showed the similar trend that the temperature raised rapidly at very beginning and reached the plateau then dropped to a lower temperature. This is because that at very beginning the contact between the hot plate and the plastic bar is firm. The contact pressure can be applied on the contacting surface. As the heat transfers from the hot plate to the heated end of the plastic bar, the molten layer starts to build up, which reduces the contact between the hot plate and the plastic bar, as shown in Figure 5.15. At a higher heating temperature, in which the molten layer would be built up faster, the time for the temperature starts to drop also occurs earlier. The measured temperature reading data were used as the heating boundary condition by step-wised fitting at small time intervals. The temperature profiles of various welding conditions after heating is shown in Figure 5.16. According to the temperature profiles, it is easy to determine the length of the molten layer. For easy observation, only the temperature contour above the melting range was shown. At a higher heating temperature, the time needed to achieve the same melt length is shorter and the effect of heating time on heat penetration is also more significant. For example, in Figure 5.16 (a) and (b), the melt length ratio of heating time 30 sec to 10 sec under 250°C welding temperature ( the interface temperature actually is Temperature at interface(°C) Interface temperature (°C) 200 220 220 120 100 4 - - 140 - 160 8 - - 180 100 i 110 120 3 i i 130 i 140 J 150 160 - - J 1 2 3 4 5 60 50 40 30 20 10 0 I I » I | I 1 I I j I I | I 1 I I j I I I I | 1 I I I | » I I » | I I I 1 i— t — Figure 5.14 The measured interface temperature profiles temperature interface measured The 5.14 Figure =60 sec 0 6 t= °C 0 5 2 = T —i —i —i —|"" i i i y i » i | » i i i y » i i i | i " | "T i— i— i— i— |— i— i— 0 0 0 0 0 60 50 40 30 20 10 =60 sec 0 6 t= °C 00 2 = T Heating time (sec) time Heating Heating time(sec) Heating ..... ' I 1' i i i ...... T " " I 175 Hotplate 399999999999 plastic bar teflon cover sheet plastic bar At very beginning 599999999999 teflon cover sheet plastic bar molten material some molten layer built up Figure 5.15 The schematic of the heating stage as the molten layer built up 176 T= 250 °C, t= 10 sec T=250°C t=30 sec o o o o o o o o Q>-. 0 o o o o o 0 o 0 o o. in o in o in o m o © © 03 03 N N (D (D m m o T- r- r - r~ r-T- *— ro ' Figure 5.16(a) Simulated temperature profiles after heating under various heating time 177 T= 320°C t=5sec T=320°C t=10 sec Figure 5.16(b) Simulated temperature profiles after heating under various heating time 178 lower than 250°C) is 1.63. Comparing to the similar melt length ratio at 320°C welding temperature, the heating time difference is from 5 sec to 10 sec. Figure 5.17(a) and (b) show the temperature contours at various welding conditions after squeezing. Here, the welding displacement is 0.75 mm each side. According to the experimental observation, the squeezing velocity was 1.6 mm/sec. The hottest martial was squeezed to the outermost region at the end of the squeezing, and the temperature at the joining plane is less than the set temperature, depending on the amount of welding displacement. Figure 5.18 shows the effect of welding displacement on interface temperature during cooling. An average temperature across the interface, which is the summation of interface nodal temperatures divided by the numbers of the interface nodes, is used here. Apparently, an increase of the welding displacement would decrease the interface temperature because of the melt squeezing-out. The joining quality would be affected by the temperature change at the interface due to over squeezing. In an earlier work, the material in the squeezing-out flash was assumed to be the one close to the interfacefl 16]. By comparing the differences between that assumption and the current approach, it shows that the temperature at interface would be around 170°C based on that assumption and it is around 180°C by the current model, based on the case of T=250°C and t=30 sec (i.e. Figure 5.17(a)). Two major heat fluxes were considered during the cooling stage. One is heat transfer by conduction and the other is heat convection loss from the air-plastic surface. The convection heat transfer coefficient was determined by comparing the simulated cooling temperature profiles at interface under various heat transfer coefficients with the temperature reading from the thermocouple at the joining interface. As shown in Figure 5.19, the convection heat transfer coefficient was chosen as 0.1 J/(m2°C). Figure 5.17(a) Simulated temperature profiles after squeezing under various heating time heating various under squeezing after profiles temperature Simulated 5.17(a) Figure 1 8 0 . OO 179 180 T= 320 °C t= 5 sec T=320°C t= 10 sec o o O OO O o o o o $ o 0 O o O o o o o o t o o O o o o o o o o c in to CM 1 - o (J) CO N (0 ir (M CM (M N CM CM r” r - T-* T“ Figure 5.17(b) Simulated temperature profiles after squeezing under various heating time 181 180 170 - d=0.7 mm d=1.0 mm 160 d= 1.3mm 150 - 120 - 110 - 100 Cooling time (sec) Figure 5.18 The averaged simulated cooling temperature profiles at joining interface for different welding displacements (T=250°C, t=30 sec, Usqueeze =1.6 mm/sec) 182 hv=l. hv=0.1 hv=0. □ experimental data ® 130 1 1 0 - hv=0. ■ i i I | i i i r~] i i i i j i I I I | i i i i | I i i i j i I i r 10 20 30 40 50 60 Cooling time (sec) Figure 5.19 The average cooling temperature profiles based on different convection heat transfer coefficients at the joining interface (T=200°C, t=60 sec and d=0.7 mm) 183 Figures 5.20(a) and (b) show the shear stress distributions after squeezing. The stresses were determined based on shear rate times viscosity. The residual stresses were calculated based on the generalized Maxwell model mentioned in Chapter 3. We assumed that the stress relaxation would stop at the crystallization peak temperature. By the comparison of different cases, the simulated stress level at cases with a larger molten layer is smaller because of a lower shear rate. The residual stress in the completely melted region ( i.e. Zone III mentioned in Chapter 3) was completely relaxed because the completely melted materials have to cool to a lower temperature to initiate the crystallization according to the crystallization kinetics model. However, the partially melted materials (i.e. Zone I and Zone II) would crystallize right after the cooling starts. Hence the stresses would remain in that region where stress-induced crystal zone would form. In the post welding stage, two types of stresses would remain in the weld. One is thermal induced stress caused by thermal contracting during cooling; the other is flow induced residual stress. In the current study, the thermal contraction effect was not considered, the stresses calculated here are only the flow induced stresses from shearing. The direction of the major thermal induced stresses would be perpendicular to that of flow induced stresses. Since the cooling starts after the joint was made, the thermal induced stresses were built up along the moving direction. Hence, the thermal stress would have a strong influence on the orientation in the Y direction instead of the X direction, as shown in Figure 5.21.. However, the orientation of observed elongated spherulites is in the X direction. This implies that although the thermal induced stress exists in HAZ, the major contribution to the orientation of deformed crystal would come from flow induced stresses. 184 T= 250 °C t= 10 sec 1: 1.11E5 2: 2.20E5 3: 3.29E5 4: 4.39E5 5: 5.48E5 T=250°C t=30 sec 1: 0.53E5 2: 1.04E5 ■x- •••>’ 3: 1.54E5 4: 2.05E5 5: 2.56E5 Figure 5.20(a) Simulated stress profiles after squeezing under various heating time 185 T= 320 °C t= 5 sec / ■» —*—*— ;*••••••)► *■...... •V.. 2: 2.01E5 3: 2.91E5 4: 3.81E5 5: 4.71E5 T= 320 C t=10 sec 1: 0.48E5 \-sr-ft /\/\/\ A A A A •’ \ ! / \ A /'■' a /\. AAAA A/\/\ A/ I..:,:! \ Z \ / \ : \ / \ / \ A \ /AZ-k /\ A / \ 2: 0.87E5 \V / \V. A V .A V / \ V / \V 'A'\ // ■’31 A ' ■ ,A - / \ / \v A• >\ \ 3: 1.25E5 ,/ « »/ w V V \/ V\/ V V V V V a ?\7 v t7 \ a / A^tewwOTtAKA 4: 1.64E5 V v v v -/ .vv . v v. .. y \/ -y v .y V . _\Z_y-y. y. v V- , y V. . 7\/\A /m aaaaaaa V v ■/ v v v vV v v v v \/ *■ 5: 2.02E5 -X:-Ar ,* \ / '. . / / • - '. / \ f \ / \ / \ / \ / / £ ■', / •• Figure 5.20(b) Simulated stress profiles after squeezing under various heating time 186 elongated spherulite thermal stress thermal stress direction direction Low temperature Low temperature Fixed end Fixed end High temperature X: Shear stress dominated Y: Thermal stress dominated Figure 5.21 Schematic of a welded sample 187 The stress affected spherulite structure may be avoided by applying high heating temperature, long heating time and short joining displacement. If the thermal energy in the molten layer is high enough to remelt the solid material near the edge of HAZ during cooling, the flow induced residual stresses would be removed. Figure 5.22(a) shows the simulated temperature change with time at the nodes close the melt boundary. All the curves in Figure 5.22(a) show a temperature rise at the beginning of cooling due to the heat flux from the melt zone. For the largest molten layer, curve (a) welded by T= 320°C and t=30 sec. the heat from the melt zone would be able to raise the temperature at HAZ boundary to a temperature higher than the melting peak temperature (165°C). It implies that the flow induced residual stresses would completely relax because of remelting. From the micrograph (a) in Figure 5.22(b), it shows no deformed spherulite at the boundary of HAZ. Curve (b) in Figure 5.22(a) shows the temperature change with time at HAZ boundary welded by T= 250°C and t=10 sec, the smallest molten layer among these cases. The heat from the melt zone only was able to raise the temperature at HAZ boundary to a temperature below melting temperature, 153°C. The remelting behavior won’t occur at this case. The flow induced stresses would not be able to relax at the boundary of HAZ, as shown in micrograph (b) in Figure 5.22(b). 5.5 Tracer Method for Material Distribution A tracer method was implemented in the computer program for better understanding the material distribution during squeezing. Tracers were numerically placed in the interested region, which is the molten layer, after heating. The velocity of the tracer was determined by the velocity of the element where the tracer was. At the end of each time step, the distance of the tracer particle moved was the velocity multiplied by 188 170 160- a: T=320 °C, t=30 sec b: T=250 °C, t=10 sec 150- 140 130- o -120- 110 - 100 - 9 0 - Cooling time (sec) Figure 5.22 The simulated cooling temperature change with time at the boundary of HAZ under different welding conditions with the same welding displacement, d=0.7 mm 189 boundary of HAZ joiniing interface (a) 40X stress induced crystal ■joining interface parent material (b) 100X Figure 5.22(b) Micrographs of micotomed welds (a) T=320°C, t=30 sec The boundary of HAZ is very ambiguous (b) T=250°C, t=10 sec The boundary of HAZ is very clear 190 time. If the tracer moved into a new element, at the next time step the new element velocity of that element was used for this tracer. In some cases, especially close to the flow front and boundary wall, tracer particles might flow out the flow domain and into undefined area, either the unfilled element or the non-mesh area. Those tracers which flowed into a unfilled element with no velocity was stagnant till the element was filled and had a velocity. Those tracers flowing into a non-mesh area would be discarded by the program. The initial location of the tracers is critical for avoiding the missing tracers. If the tracer particle was placed on the line or too close to the line of computation boundary, it may flow out the flow domain. Figure 5.23(a) shows the tracer particle distribution before and after squeezing close to the joining interface under T=250 and t=30 sec. Only the tracers in the molten layer could move in the x-direction. The variation of the x direction velocity along the y direction is not significant. It is due to the small viscosity variation in the y direction, even though the temperature dependent viscosity had been considered. The higher shear rate was found at the corner of the squeezing-out deflection, as shown in Figure 5.23(a) indicated by the dash circle. The micrograph of microtomed sample shows the similar result, as shown in Figure 5.23 (b). 5.6 Visualization of Squeezing Flow Based on Colored Plastic Sample Experiments for observing the squeezing flow pattern layer have been conducted by several researchers based on multiple colored sample[33, 117]. However, most of them placed the colored layers perpendicular to the hot plate, as shown in Figure 5.24(a). According to this result, it can sketch the flow pattern, but it is difficult to distinguish the temperature redistribution after squeezing. In order to verify the feasibility of using the 191 (a) joining interface joining interface 20 □ T IT □ ♦ 19.8 B □ 'r- X □ ♦ □B □ ♦ □ 19.6 □ ♦ □ □ B 19.4 □ □ □ □ □ B 19.2 □ □ B 19 □ □ □ □ forging » □ forging \ □ 18.8 direction ■ □ direct ion □ □ □ 18.6 □ □ □ □ □ □ 18.4 □ □ 18.2 d=0.004mm a □ d=0.412mm ■ □ □ 18 T T 20 B 5------r " □ 19.8 □ 1 • 1 t □ ♦ □ I : i \ 19.6 i ♦ ♦ B ♦ □ " : / \ 19.4 i ♦ P ♦ □ " • * □ □ “■ Il^A v ) 1 a 19.2 -i □ ■ • • □ 19 i □ g □ \) □ □ 18.8 -i □ □ □ ■■ ■ « □ □ 18.6 i forging □ forging direction □ direct ion 18.4 -j ■ □ ■ □ 18.2 i d=0.288mm d=0.67mm 18 i i i i | i i i i iYii i | i i i i | i i ii 4.52 2.5 3.5 4.5 Figure 5.23(a) The tracer distribution during squeezing under T=250°C and t=10 sec Figure 5.23(b) The micrograph of welded sample at the deflection comer 193 (a) method used by other researchers ------Squeezing direction (b) current method Figure 5.24 The schematic layout of the colored later for squeezing visualization 194 modified CVFEM to simulate the hot plate welding process, an experiment of squeezing a multiple colored PP bar, with the colored layers parallel to the hot plate, was conducted. The thickness of the colored tip film was controlled around 0.5 mm for each layer for in the molten layer. The colored films were molded separately then thermally bonded together to form a rectangular bar. This colored bar was heated by a hot plate at 250°C for 60 sec in order to build up a large enough molten layer. After that the plastic bar with the molten layer was squeezed against the hot plate at a reducing temperature, which was cooled by cooling water, to simulate half of the welded sample during squeezing. Figure 5.25 shows the photo before and after squeezing. By comparing the colored pattern, the temperature distribution after squeezing could be traced. It shows that the temperature distribution of the welded sample after squeezing can be simulated reasonably by our computer program. 195 (c) Figure 5.25 The colored sample (a) before squeezing, (b) after squeezing for 1 mm and (c) after squeezing for 2.5 mm CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS In this study, the efforts were made on three aspects; crystallization kinetics, welding process simulation, and welding strength correlation. Crystallization Kinetics A crystallization model which covers the crystallization started from Zone I, Zone II and Zone III, was developed. This semi-empirical model could provide reasonable predictions of crystallization peak temperature and crystallization rate curve under a constant cooling rate condition. This model would be useful for processes of welding and thermal joining of thermoplastic composites, which consists of totally melted and partially melted materials. The shear induced effect was added to the quiescent crystallization model. For the welding process, due to the short welding (squeezing) time, the shear induced effect would be similar to a preshearing phenomenon mentioned in Chapter 3. This preshearing effect would enhance the crystallization rate by the increase of the initial crystallinity. The flow induced effects on crystallization include shearing and elongation. The current model could only solve the cases with shearing condition. For the elongation dominated process, such as fiber spinning, this model might not be adequate. The elongational strain rate would have greater influences than the shear strain rate on 196 197 crystallization rate. For the welding process, the elongational flow is negligible. For the fiber spinning process, the crystallization model with an elongational flow effect should be investigated. In this study, the crystallization model could determine the crystallization peak temperature, crysatllization rate, and relative crystallinity. However, the information of microstructure, such as spherulite size, shape, and crystal orientation can not be predicted by the current approach. If the microstructure information is critical in determining the properties, a more sophisticated crystallization model which can predict the crystal growth and crystal shapes is necessary. Welding Process Simulation The temperature profile, cooling rate, and polymer melt distribution during and after welding could be obtained from CVFEM. This allows us have a better understanding of the effects of the controllable welding parameters on the hot plate welding process. By combining the crystallization model and the joining strength correlation, the simulation results could estimate the size of the HAZ and weld factor. In order to calculate the domain including liquid and solid phases, an element cleavage technique was developed. This method might also be useful for the simulation of molding processes with possible solidification during filling. The tracer methods used in this study only provide the melt distribution after squeezing. The calculations of temperature, velocity, and crystallization kinetics were based on fixed nodes and elements. However, the information of temperature and crystallinity could be carried by tracers. Therefore, the heat transfer and crystallization kinetics calculations can be done by a Lagrange coordinate. It might provide a more accurate computing scheme. 198 The CVFEM was developed for flow through porous medium of which the flow governing equation is Darcy's law. In this study, we adopted the governing equation, Darcy's law, for the squeezing flow in the welding process. Consequently, the simulated flow pattern is reasonable, however, the simulated stress level may not be accurate. For better accuracy, some modification of the flow governing equation or the use of different governing equations ( i.e. Navier-Stokes equation) may be necessary. Other than that, the surface tension in the flow front region and the thermally induced stresses can be added to make the program more sophisticated, and closer to the real case. Welding Strength Correlation The correlation of the welding strength with the processing parameters was based on the healing theory. Since the intimate contact between the joining interface was assumed, the reasonable welding strength can be predicted for the cases with larger welding displacement or shorter heating time. However, due to the neglecting of the thermal contraction, the correlation would not be able to predict the cases with severe thermal stresses. As mentioned before, the weld factor is not the only index to determine the weld quality. The elongation percentage during tensile test, the impact strength, the crack growth rate, the fatigue cycle test, and the chemical resistance test, etc. are other available testing techniques to evaluate the joining quality, which are not discussed in this study. The tensile test may not be sensitive enough to differentiate the difference among various crystalline structures. Further investigations under microscopic scale are necessary in order to make more specific statement on the strength of microstructures in HAZ. According to our observation, the elongation of the welded sample and the non weld sample is quite different. For the non-weld part, the specimen experienced large 199 elongation, about 100 to 200% , depending on the cross head speed of the tensile tester. For the welded sample, even though the joint strength (weld factor) was as good as the parent material, the elongation was hardly beyond 20%, if the failure took place in the weld zone. This is may due to the discontinuity between the spherulite structure and the strongly oriented deformed spherulites. For increasing elongation and the impact properties of welded parts, we suggest that the welding process should provide enough stress relaxation time and to compensate for the thermal shrinkage during cooling. Due to the limit of the constant stop control device, it is very possible to form a weld with voids. There are several approaches to reduce the occurrence of voids, such as; (a) increasing the welding displacement, (b) decreasing the length of molten layer by either decreasing the hot plate temperature or the heating time, (c) releasing the holding mechanics before the weld solidified or applying a small forging pressure to compensate the pulling stress from thermal shrinkage. REFERENCES 1. Stokes, V. J., Polym. Eng. & Sci., 29,19, p l3 10 (1989). 2. Watson, M. N. Joining Plastics In Production. The Welding Institute, (1988). 3. Gabler, K. and Potente, H., J. Adhesion, 11, pl45, (1980). 4. Benatar, A. and Gutowski, T. G., SAMPE Quarterly, 18,1, p34, Oct., (1986) 5. Potente, H. and Tappe P., Polym. Eng. & Sci., 29, 23, p i642, (1989). 6. Potente, H. and Natrop, J., Polym. Eng. & Sci., 29, 23, pl649, (1989). 7. Barber, P. and Atkinson, J. R., J. Mater. Sci., 7, 1131-1136, 1972. 8. Wool, R.P., Yuan, B.-L., and McGarel, O.J., Polym. Eng. & Sci., 29,19, pl340, (1989). 9. de Gennes, P.-G., J. Chem. Phys., 55, p572, (1971). 10. Edwards, S.F., Proc. Phys. Soc., London, 92, p9, (1967). 11. Atkinson, J. R. and DeCourcy, D. R., Plastics & Rubber Processing & Applications, 1,4, p287, (1981). 12. Pimputkar, S. M., Polym. Eng. & Sci., 29,19* pl387, (1989). 13. Van Krevelen, D. W., Chimia, 32, 8, p279, (1978). 14. Henning, A., Autogene Metallbearbeitung, 33, pl28, (1940). 15. Turner, B. and Atkinson, J.R., SPE 47th ANTEC Proceedings, p499, (1989) 16. Kaminsky, SJ. and Williams, J.A., "Welding and Fabricating Thermoplastic Materials", (1964). 17. Pauer, A., ZIS Mitteilungen, 12, p844, (1970). 18. Crawford, R.J. and Tam, J., Journal of Material Science, 16, p3275, (1981). 19. Kulik, E.I. and Lokshin, R.F., Welding Production, 29, p5, (1982). 200 I 201 20. Stokes, V.K., Journal of Material Science, 23, p2772, (1988). 21. Behnefeldt, J. and Bouyoucos, J.V., Revue Generale des Caoutchoucs Plastiques, 59, p41, (1982) 22. Panaswich, J. Automotive Engineering, 92, p40, (1984). 23. Stokes, V.K., Polym. Eng. & Sci., 28, p718, (1988). 24. Stokes, V.K., Polym. Eng. & Sci., 28, p728, (1988). 25. Matsyuk, L.N. and Bogdashevskii, Soviet Plastics, No.2, (1960). 26. Deans, H., Modern Plastics, 38, p95, (1961). 27. Benatar, A. and Gutowski, T.G., SPE 47th ANTEC Proceedings, p507, (1989). 28. Chookazian, M., SPE Journal, 26, p49, (1970). 29. Abele, G.F., Kunststoffe, 61, p676, (1971). 30. Sanders, P., Materials and Design, 8, p41, (1987). 31. Personal communication with Wu, C.Y. in Welding Engineering Dept. 32. Poslinski, A. J. and Stoke, V. ASME winter Meeting, MD-Vol.29, p397, (1990). 33. Bucknall, C. B., Drinkwater, I. C. and Smith, G. R., Polym. Eng. & Sci., 20, 6, p432, (1980). 34. Potene, H., Welding in the World, VI7, 1/2, pl9, (1979). 35. John, P., Welding in the world, V20, 11/12, p222, (1982). 36. Lyashenko, V., Welding Production, 12, p42, (1975). 37. Istratov, I., Welding Production, 11, p30, (1973). 38. Istratov, I., Welding Production, 6, p42, (1975). 39. Zaitsev, K. and Kashkovskaya, E.A., Welding Production, 11, p42, (1975). 40. Zaitsev, K., Vindt, B.F., Lyashenko, V.F., and Lure, I.V., Welding Production, 1, pl4, (1982). 41. Maksimenko, V., "Welding Production, 1, pl6, (1982). 42. Parmar, R., and Bowman, J., Polym. Eng. & Sci., V 29, 19, pl396, (1989). 202 43. Parmar, R., and Bowman, J., Polym. Eng. & Sci., V 29, 19, pl406, (1989). 44. Haworth, B., Law, T.C., Sykes, R.A., and Stephenson, R.C., Plast. & Rubb. Proc. & Appl. 9, p81,(1988). 45. Andrews, J.R.F. and Bevis, M., J. Mater. Sci., 19, p645, (1984). 46. deCourcy, D.R. and Atkison, J.R., J. Mater. Sci., 12, pl535, (1977). 47. Gehde, M., Bevan, L. and Ehrenstein, G. W., Polym. Engr. & Sci., Y32 , 9 , p586, (1992). 48. Cowley, W.E. and Wylde, L.E., Chemistry and Industry, 3, June, p371, (1983). 49. Watson, M. N. and Murch, M. G., Polym. Eng. & Sci., V29, 19, pl382 (1989). 50. Adams, R.D. and Cawley, P., NDT International, 21, p208, (1988). 51. Hagemaier, D.J. and Fassbender, R.H., Material Evaluation, 37, p43, (1979). 52. Speake, J.H., Arridge, R.G.C., and Curtis, G.J., J. Phys. D: Appl. Phys., 7, p412, (1979) 53. Lindrose, A.M., “Experimental Mechanics”, (1978). 54. Ewing, L. and Richardson, W .,,Plastics and Rubber Institute Conference on Jointing and Fabrication of Thermoplastic Pipes and Structures, Bradford, Oct., (1980). 55. Pye, C.J. and Adams, R.D., J. Phys. D: Appl. Phys., 14, p927, (1981). 56. Kim, Y.-H. and Wool, R.-P., Macromolecules, 16, p i 115, (1983). 57. Wool, R.P. and O’Connor, K.M., J. Appl. Phys., 52,10, p5953, (1981). 58. Wool, R.P., ACS Polymer Preprints, 22, 2, p207, (1981). 59. Wool, R.P., ACS Polymer Preprints, 23, 2, p62, (1982). 60. Wool, R.P. and O'Connor, K.M., ACS Polymer Preprints, 21, 2, p40, (1980). 61. Zupancic, I., Lahajnar, G., and Blinc, R., J. Polymer Sci., 23, p387, (1985). 62. Lee, A. and Wool, R.P., Macromolecules, 19, pl063, (1986). 63. Leger, L, Hervet, H., and Rondelez, F., Phys. Rev. Let., 42, pl681, (1979). 64. Mandelkem, L., "The Crystalline State", Physical Properties Of Polymers. 2nd Ed., ACS, (1993). 203 65. Heuvel, H. M. and Huisman, R., J. Applied Polymer Science, 22„ p2229, (1978). 66. Kantz, M. R., Newman, H. D. and Stigale, F. H., J. Appl. Polym. Sci., 16, pl249, (1972). 67. Eder, G. and Janeschitz-Kriegl, H. and Liedauer, S., Prog. Polym. Sci., 15, p629, (1990). 68. Hoffman, J. D. and Lauritzen, J. I. Jr., J. Res. Nat. Bure. Stan.: A. Phys. Chem., 65a, 4, p297, (1961). 69. Hoffman, J. D. and Weeks, J. J., J. Res. Nat. Bure. Stan.: A. Phys. Chem., 66,1, pl3, (1962). 70. Hoffman, J. D. and Weeks, J. J., J. Chem. Phys., 37, 8, pl723, (1962). 71. Peterlin, A., Polym. Eng. & Sci., 17, 3, p i83, (1977). 72. Turnbull, D. and Fisher, J. C„ J. Chem. Phys. 17, p71, (1949). 73. Goldfarb, L., Markromol. Chem., 179, p2297, (1978). 74. Hoffman, J. D., Polymer, 23, p656, (1982). 75. Hoffman, J. D., Polymer, 24, p3, (1983). 76. Avrami, M., J. Chem. Phys., 7, p i 103, (1939). 77. Avrami, M., J. Chem. Phys., 8, p212, (1940). 78. Avrami, M., J. Chem. Phys., 9, p i77, (1941). 79. Anderson, D. P., Air Force Wright Aeronautical Laboratories Report, (1986). 80. Nakamura, K., Watanabe, T., Katayama, K. and Amano, T., Appl. Polym. Sci., 16, p i077, (1972). 81. Kamal, M. R. and Lafleur, P. G., Polym. Eng. & Sci., 24, 9, p692, (1984). 82. Kamal, M. R. and Lafleur, P. G., Polym. Eng. & Sci., 26,1, pl03, (1986). 83. Rein, D. M., Beder, L. M., Baranov, V. G. and Chegolya, A. S., Acta Polymerica, 32, pi, (1981). 84. Velisaris, C. N. and Seferis, J. C., Polym. Eng. & Sci., 26, 22, p i574, (1986). 85. Patel, R. and Spruiell, J. E., Polym. Eng. & Sci., 31,10, p730, (1991). 204 86. Tobin, M. C., J. Polym. Sci., 12, p399, (1974). 87. Tobin, M. C., J. Polym. Sci., 12, p2253, (1976). 88. Malkin, A. Y., Beghishev, V. P., Keapin, I. A. and Bolgov, S. A., Polym. Eng. & Sci., 24,18, p i396, (1984). 89. Malkin, A. Y., Beghishev, V. P., Keapin, I A. and Bolgov, S. A., Polym. Eng. & Sci., 24,18, p i402-1408, (1984). 90. Mackley, M. R., Frank, F. C. and Keller, A., J. Mater. Sci., 10, pl501, (1975). 91. McHugh, A. J. and Forrest, E. H., J. Macromol. Sci.: Phys. B 11, 2, p219, (1975). 92. Eder, G. and Janeschitz-Kriegl, H., Colloid & Polym. Sci., 266, pl087, (1988). 93. Janeschitz-Kriegl ,H. and Eder, G., Plastics & Rubber Processing & Applications, 4, p i45, (1984). 94. Janeschitz-Kriegl, H., Eder, G., Krobath, G. and Liedauer, S., J. Non-Newtonian Fluid Mechanics, 23, pl07, (1987). 95. Janeschitz-Kriegl ,H. and Eder, G., J. Macromol. Sci., A27, 13-14. pl733, (1990). 96. Janeschitz-Kriegl, H., Krobath, G., Roth , W. and Schausberger, A., Eur. Polym. J., 19, 10/11. p893, (1983). 97. Eder, G. and Janeschitz-Kriegl, H. and Liedauer, S., Prog. Polym. Sci., 15, p629, (1990). 98. Mandelkern, L., Crystallization Of Polymers. McGraw-Hill. ("19631. 99. Van Krevelen, Properties Of Polymers. Elsevier. (1990). 100. Keith, H.D., Padden, F.J., Walter, N.M. and Wycoff, M.W., J. Appl, Phys., 30, pl485, (1959). 101. Padden, F.J. and Keith, H.D., J. Appl, Phys., 36, pl479, ( 1959). 102. McAllister, P.E., Carter, T.J. and Hindle, J., J. Polym. Sci., Polym. Phys. Ed., 16, p49, (1978). 103. Gezovich, D.M. and Geil, P.H., Polym. Eng. Sci., 8, p202, (1968). 104. Gailey, J.A. and Ralston, R.H., SPE Trans., 4, p29, (1964). 105. Miller, R.L., Polymer, 1, pl35, (1960). 106. Natta, G. and Corradini, Nuovo Cimento Suppl., 15, pi, (1960). 205 107. Clark, E. J. and Hoffman, J. D., Macromolecules, 17, p878, (1984). 108. Bird, R.B., Armstrong, R.C. and Hassager, O., "Dynamics of Polymeric Liquids - Volume 1 Fluid Mechanics", 2nd Ed., (1987). 109. Cox, W.P. and Mertz, E.H., J. Polym. Sci., 28, p619, (1958). 110. Williams, M.L., Landel, R.F., and Ferry, J.D., J. Am. Chem. Soc., 77, p3701, (1955). 111. Chen, D., The Ohio State University PhD Dissertation, (1988). 112. Yang, W.-B., The Ohio State University PhD Dissertation, (1990). 113. Lin, R.-J., The Ohio State University PhD Dissertation, (1992). 114. Wu, C.-S., The Ohio State University PhD Dissertation, (1995). 115. Thompson et al. edited, Shen, S.F., Numiform 89, p55, (1989). 116. Tirumalai, V.C., The Ohio State University MS Thesis, (1990). 117. Fodor, S., The Ohio State University MS Thesis, (1992). 118. Stacer, R.G. and Schreuder-Stacer, H.L., Int. J. Fracture, 39, p201, (1989). 119. McGarel, O.J. and Wool, R.P., Bull. Am. Phys. Soc. March (1989). 120. Mengs, G, Schmachtenberg, E., and Knausenberger, R. DVS-Berichte, p84, (1983). 121. Bastien, L.J. and Gillespie, J.W., Polym. Eng. & Sci. 31, 24, pl720, (1991). 122. Menges, G. and Zohhren, J., Plastverarbeiter, 18, pl65, (1967). 123. Barber, P. and Atkison, J.R., J. Mater. Sci., 9, pl456, (1974). 124. Way, J.L., Atkinson, J.R., and Nutting, J., J. Mater. Sci., 9, p293, (1974). 125. Friedrich, F., Fracture 1977, ICF4, Waterloo, Canada, June 19-24, (1977). APPENDIX JOINING STRENGTH CORRELATION As mentioned in the previous chapter, the flow pattern, temperature distribution and stress profile after squeezing can be determined by the computer simulation. According to these results and the measured tensile properties of welded samples, a correlation of joining strength with the processing conditions was conducted in this chapter. A.l Correlation of Joining Quality A.1.1 Flash appearance approach The weld quality can be evaluated by both external and internal states of joints[16]. The former can be examined easily after the weld bead formed. It is the minimum criteria for a good weld quality joint. The features of the poor weld joint can be described as: (1) Welding flash notches: The notch between welding flashes is rooted deeper than the parent material, as shown in Figure A.I. It may be caused by insufficient joint pressure, too short a heating time, or too a fast cooling rate. 206 207 — f Y 1------ ^ / Figure A.l Welding flash notches (2) Mismatch of joint planes: Joint planes are misaligned relative to one another, as shown Figure A.2. Figure A.2 Mismatch of weld joint (3) Sharp, excessive welding flash: Too much welding pressure applied during squeezing may result in excessive and sharp-edged welding flash. If any one of the above features was found in the final weld joint, a poor performance may be expected. In addition to these obvious fault features, some poor weld joints may also be formed because of fault internal states of joint, such as: (a) lack of fusion over part or whole of the weld cross-section caused by low heated tool temperature, contaminated joint faces, oxidized or degraded joint faces, or excessive change-over time, (b) cavity in joint planes caused by insufficient joint pressure or cooling time, (c) pores caused by inclusions of foreign matter. 208 To obtain good welded parts, there are several obvious rules of thumb, which are described as follows: (a) large enough molten layer, which allows the polymer chains to have sufficient mobility to diffuse through the joining interface; (b) good alignment between the joined parts, avoiding the unnecessary bend loading on the welded parts; (c) proper joining displacement. If the joining displacement is not sufficient, the poor contact would make the chain diffusion difficult. However, if the joining displacement is too large, the incomplete fusion at interface and too much residual stress may reduce the joining quality; (d) reducing the change-over time as short as possible to avoid the development of frozen layer prior to the joining stage; (e) avoiding extremely high welding temperature for thermal degradation, which may result in some brownish-like material at the joining interface and depreciate the joining quality. From the above description, it is quite obvious that the operating hot plate temperature should be between the plastic melting temperatures and the thermal degradation temperatures of polymers. The higher the heating temperature is, the shorter the heating time requires for building enough molten layer. Figure A.3 demonstrates the schematic processing window for hot plate welding based on controllable parameters. The processing window may increase along with increasing the welding displacement. However, the increase of the welding displacement may result in a large size of squeezing- out flash, which is bad for dimension control. At the same welding displacement condition, the range of acceptable heating time increases as the heating temperature decreases because the tolerance of heating time at lower temperatures is not as sensitive as at higher temperatures. The high viscosity of a low temperature molten layer may result in 209 a large squeezing resistance during welding and it may build up a large contact pressure for better chain diffusion. However, due to the low chain diffusivity at low temperatures, it needs a longer time for the polymer chains to diffuse through or to make enough chain entanglement at the joining plane. If the cooling time is so fast that the molten layer has solidified prior to the chain diffusion may complete, the weld quality would be poor. Degradat ion te mperatu re Thermal degrading time i0) — 13 OS CD Q_ E f m>m> u CD welding displacement cc Q. ■*-* o T. Melt ing t emperatu re Heating time Figure A.3 The schematics of hot plate welding processing window 210 On the contrary, the low viscosity at high temperatures may shorten the diffusion time, but the resultant low squeezing resistance may make the contact insufficient. And a high temperature difference between the molten layer and the cooled solid may induce a high thermal shrinkage, which may result in voids at the joining interface. There is also the bending or even draping problem because of the low mechanical modulus of the high temperature molten layer. These considerations on high temperature operation may confine the processing window. Pressure affects the chain diffusion by decreasing the free volume available for the hopping process necessary for achieving Brownian motion ( i.e. it decreases the self diffusion coefficients. This effect is more pronounced near the glass transition temperature and is important in polymer melt processing where large hydrostatic pressure is encountered[8]. The weld pressure influences the strength development in two ways. One is to promote intimate contact between the joining interface. Stacer and Schreuder- Stacer[l 18] studied the effect of contact pressure on the time dependence of autohesion in polyisobutylene. Their results indicated that as the pressure increases, autohesion data appears to shift to shorter times and the time to achieve equilibrium strength decreases with no discernible effect on equilibrium green strength energy values. They claimed that the high pressure mainly enhance the contact mechanism for bond formation since the diffusion process would be independent of pressure in this pressure range. Mcgarel and Wool[l 19] investigated the welding pressure effects on the fracture energy of polystyrenes at 115°C. The fracture energy of the interface increased with applied pressure. And the fracture energy reached a plateau as the applying pressure was above an optimum welding pressure, 0.4 MPa. The fracture energy at the plateau is no more than 60% of the virgin fracture value. On the other hand, the glass transition temperature will be affected by very high pressures, i.e., the glass transition temperature of PS increases by about 20°C per kilobar. This would have a substantial effect on cases with low weld temperatures. For the hot plate welding process, the heating temperature is often much higher than the glass transition temperature to reduce the processing time. As long as the welding pressure which is large enough to overcome the stresses formed from the thermal contraction and to keep an intimate contact between the joining faces, it will be sufficient. Too large a joining pressure may squeeze out too much molten material, which makes the chain diffusion and entanglement impossible at the joining interfaces. Apparently, the weld quality won't be adequate under extreme joining pressures. Many studies investigating the welding pressure effects on the weld quality showed similar conclusions [5- 7,11,45,46,120], A.1.2 R eptation model approach The intermolecular diffusion between surfaces in intimate contact is essential for the welding or any fusion bonding processes. Wool et al[56-60] postulated a healing theory for the interface of two pieces of polymer brought into contact at a temperature above the glass transition temperature for a very long contact time. The theory analyzed the motion of polymer chains at the interface and calculated the average interpenetrating distance of polymer segments as a function of time and molecular weight. They suggested that the fracture stress is proportional to the average interpenetrating distance and formulate the ratio of stress at healing to the virgin fracture stress as: 212 where o is the fracture stress at time, t, is the virgin fracture stress, % is the average interpenetrating distance at time t, *s the interpenetrating distance at time no less than tr , and tr is the tube renewal time of the reptation theory. Bastien and Gillespie[121] proposed a non-isothermal healing model for the joining strength based on the healing theory. Basically, they divided the thermal history into a very small time intervals. If the time step is sufficiently small to yield converged results, the healing theory can be applied at each time step pseudo-isothermally. According to Eq(A.l), the healing stress of an arbitrary non-isothermal history at the time tp is then: >p , 1/4 _ f+1/4 1/4 I__ & = (A-*) IT o Vt where tr is the tube renewal time at average temperature between t,+i and tj. According to their data reduction scheme, the tube renewal times of varied temperatures were evaluated from the nonisothermal-isothermal approach. The temperature dependence of tube renewal time was represented by an Arrhenius type equation as tr = troeA/T (A.3) A.1.3 Dimensionless group approach Several researchers tried to quantitatively correlate the joining quality with welding parameters by experiments. They all found that the weld qualities were not a monotonic function of any single processing parameter; such as heating temperatures, heating times, welding displacements, and welding pressures. Menges[120] conducted a series of welding experiment on HDPE pipes and suggested that the quality of a weld is mainly 213 determined by the flow out velocity and the shear velocity. The mean flow out velocity was defined as the velocity of polymer melt flowed away from the joining interface. The magnitude of mean flow out velocity depends upon the length of molten layer and squeezing velocity. Potente[2], based on Menges’ assumption of the minimum flow out velocity, deduced some dimensionless groups from one dimensional heat transfer and simplified momentum equations with constant averaged properties. He proposed a semi- empirical correlation between the ultimate breaking stress and processing parameters. No healing or chain diffusion mechanism was mentioned in his approach. He claimed that the shear deformation of polymer melt at the joining interface is the key controlling parameter. According to his observations and analysis, he stated that the optimum ratio of the length of molten layer before squeezing to the length of remaining molten layer after squeezing is the same for a given polymer, no matter how high the heating temperature is, how long the heating time is, or how thick the part is. Potente's correlation for the constant pressure welding process can be written as (A.4) where L0 is the length of the molten layer after the completion of heating, Sp is the welding displacement, Pp is the welding pressure, d is the part thickness, L is the molten layer thickness during joining, and Cj and C 2 are material-specific constants. A.1.4 Microstructure approach From the microstructure of the welds, it is easy to distinguish the heat affected zone form the parent material. For semicrystalline polymers, if the spherulite is not heated above 214 the melting temperature during the welding process, its macro crystalline structure will not change. Generally speaking, the heat affected zone is confined by the deformed spherulite structure. Certain microstructural features of PE , have been characterized by Mengs and Zohren[122] and by Barber and Atkinson[7,123]. Five different microstructural zones in the HAZ were defined: (1) remnant of skin, (2) spherulitic slightly elongated, (3) columnar, (4) boundary nucleation, and (5) spherulite. As shown in Figure A.4, these five zones lay side by side from the joining interface, respectively. The presence of zone 1 usually indicates a poor adhesion at the weld interface, while there is not enough evidence to show the linkage of features in zones 2, 3, 4 and 5 to the joining tensile strength. These authors suspected that the columnar feature of zone 3 would affect the stability of the weld. 1: remnant of skin, 2: spherulitic slightly elongated, 3: columnar, 4: boundary nucleation, and 5: spherulite Figure A.4 Schematic diagram of the weld with distinctive regions of different microstructres 215 By examining the polybutene-1 welds, Barber and Atkinson[123] found that the failure was always initiated at the edge of the junction of zone 3 and zone 2 under optimum welding conditions. The fracture propagated through the weld and failed at the other edge of zone 3. Under non-optimum welding conditions, the fracture would propagate through the weld interface. However, this observation could not be applied to other polymers, such as PE or PP welds. Way, Atkinson, and Nutting[124] investigated the effect of spherulite size on the yield stress of PP. The spherulite size was controlled by varying the cooling temperature. The yield stress increased with increasing the average spherulite size when the radius of the spherulites was below 0.08 mm, and then decreased with an increase of spherulite size. They stated that the yield stress is likely to increase with increasing spherulite size because the crystalline regions are stronger and more rigid than the amorphous regions, however, as the spherulite diameter is relatively large, the voids at the spherulite boundaries and the segregation of impurities at these boundaries may weaken the yield stress and override other effects. The yield stress curve, Figure A.5, is a schematic diagram of two contributions: the microstructure effect, in which slower cooling results in a greater crystal size and so a greater strength; and the spherulite boundary effect, whereby the boundaries become progressively weaker because of impurity segregation and voiding. Friedrich[125] measured the fracture toughness of different spherulite sizes of PP, ranged from 10 to 400 pm, and similar conclusion was drawn. 216 Spherulite boundary Microstructi re Resultant spherulite size Figure A.5 Graph showing the contributions of microstructure and spherulite boundary effects corresponding to the spherulite size[125] 217 A.2 Current Approach Our previous work showed that the deformed spherulites in HAZ result from recrystallization under the presence of flow induced stresses. By examining the weld structure under a polarized microscope, we found that samples with high joining strength all showed the presence of a highly deformed spherulites layer near the boundary of HAZ and a layer of recrystallized small spherulites near the joining interface has been achieved. Due to the limit of the welding machine used, only the welding displacement was regulated by a mechanical stop. The size of HAZ and the presence of residual stresses on the boundary of HAZ can be estimated by our computer program. However, our code can not predict the size and shape of the crystals. The thermal contraction during cooling, especially at very high heating temperatures, would result in voids at the joining interface, as shown in Figure A.6. This indicated that insufficient contact between joining interfaces. The current computer program can not provide the information of thermal stresses. However, the computer simulation can provide the thermal history at the joining interface during the squeezing and the cooling stage. This allows us to predict the joining strength based on the interface chain entanglement with the assumption of no thermal contraction. Bastien and Gillespie's model[121] for non-isothermal healing process was modified in our approach. They generalized the non-isothermal process by a summation of many isothermal subprocesses at each time interval. The strength at interface was found proportional to the processing time to the power of 1/4, i.e. t1/4. However, during the cooling course of the welding process, as shown in Figure 5.19, the temperature at the joining interface decreases rapidly at very beginning and then the cooling rate slows down because of the decrease of temperature gradient. The summation type of approach tends to simplify the cooling rate effect by small time steps in summation. It would be a proper Figure A.6 The micrograph of microtomed welded specimen with voids (T=250°C, t=60 sec) 219 approach for processes with low cooling rates . For cases with high cooling rates, such as welding process, the summation approach may not be adequate. Our approach is to take the differential form of Fickian law and make an integration along the cooling profile at the joining interface. According to Fickian law, the polymer chain penetration length at isothermal conditions can be expressed as {x)2 = 2Dt (A.5) where -E D = D0eRT (A.6) where E is activation energy, R is gas law constant, and T is temperature. In order to reach the virginal strength in the welding process, the penetration length of the polymer at the joining interface has to achieve a certain level, Hence we assume that the chain diffusion would cease at the crystallization peak temperature. From Eq(A.5), the differential form of the penetration length can be rewritten as (x)d(x) = Ddt + tdD (A.7) 220 Substituting Eq(A.5) into Eq(A.7), then d^ The integration of Eq(A.8) along the cooling time combining with Eq(A.7), from the molten polymer temperature at the joining interface to the crystallization peak temperature, represents the diffusion length achieved in the welding process, i.e. -E t=tk -E (x) = dt (A.9) r I RT(ty t=0 where R(t) is the cooling rate, — , and tk is the crystallization peak time. Both T and dt R(t) are functions of time obtained from the computer simulation. Figures A.7(a-c) show the calculated temperature profile at the joining interface. In order to normalize the temperature profile at the joining interface, an average value was taken across the interface. For the low healing temperature case, T=200°C, the temperature variation across the interface is not too much at the beginning of cooling. The temperature at the center of the interface decreases faster than that at the outer edge. Figure A.8 shows the average temperature change with time at the interface during cooling for various good welding condition. The chain diffusion across the interface ceases as the temperature drops to the crystallization peak temperature. The crystallization peak temperatures vary with the cooling profile. The arrows in Figure A.8 indicate the chain diffusion ceasing time. Table A. 1 lists crystallization peak temperatures for different welding conditions from the Figure A.7(a) The interface temperature profile at different cooling time, cooling different at profile temperature interface The A.7(a) Figure Temperature (°C) 100 120 130 140 150 160 170 180 =09 sec t=70.91 t=0.95 sec t=0.95 t=40.38 sec t=40.38 =00 sec t=50.01 t=0.0 sec t=0.0 0.5 sec Th=200°C, t=60 sec t=60 Th=200°C, Distance fron center (mm) center fron Distance t=2.95 sec t=2.95 t=7.27 sec t=7.27 t=l 1.51sec t=l t=23.24 sec t=23.24 sec 2.5 221 Figure A.7(b) The interface temperature profile at different cooling time, cooling different at profile temperature interface The A.7(b) Figure Temperature (°C) 100 120 4 - 140 200 6 _ 160 8 _ 180 - t=4/.80 sec t=4/.80 0.5 t=0.57 sec t=0.57 t=0.0 sec t=0.0 Th=250°C, t=30 sec t=30 Th=250°C, sec Distance from center (mm) center from Distance t=23.70 sec t=23.70 t=l 1.40 sec 1.40 t=l t=40.16 sec t=40.16 t=3.34 sec t=3.34 sec 2.5 222 Figure A.7(c) The interface temperature profile at different cooling time, cooling different at profile temperature interface The A.7(c) Figure Temperature (°C) 210 110 230 130 170 150 250 190 =40.43 sec =40.43 t=23.28 sec t=23.28 t=1.55 sec t=1.55 sec t=0.0 t=0.68 sec t=0.68 t=3.18sec 0.5 t=78.42sec Th=320°C,t=10sec Distance from center (mm) center from Distance 7=15.25 sec 7=15.25 t=6.76 sec t=6.76 t=l 1.49 sec sec 1.49 t=l 2.5 223 224 240 220 - a: T=200°C t= 60 sec b: T=250°C t= 30 sec c: T=320 °C t= 10 sec 200 - U o 1 8 0 - 0 1Uh 1 4 0 - 120 - 100 Cooling time (sec) Figure A.8 The simulated average cooling temperature profiles at joining interface under various welding conditions with same welding displacement, d=0.7mm. All weld factors are above 0.9. Table A.l The crystallization peak temperature of various welding conditions Welding conditions Crystallization peak temperature T=200°C t=60 sec d=0.7mm 114.4°C T=250°C t= 10 sec d=0.7mm 106.6°C T=250°C t=30sec d=0.7mm 112.6°C T=250°C t=30sec d= 1.0mm 113.1°C T=250°C t=30sec d= 1.3mm 119.2°C T=320°C t=5 sec d=0.7mm 104.6°C T=320°C t— 10 sec d=0.7mm 109.1°C 226 crystallization kinetic model. As the weld factor reached 1.0, it suggests that the chain diffusion and entanglement through the joining interface has been completed. According to this concept, the critical diffusion length, In Eq(A.9), the unknown parameters include —(x) at the left-hand side of the equation. With the known cooling temperature profile, crystallization peak time, and maximum weld factor. Here the optimum welding conditions ( i.e. T=200°C, t=60 sec, T=250°C, t=30 sec, and T=320°C, t=10 sec) were used as reference to determine 2/3 (A. 10) (X )o where F is the weld factor. Figure A.9 shows the comparison of estimated and experimental weld factors. The two most discrepancy cases are both welded under T=250°C. It might be due to the thermocouple measured heating temperature, which was used as input boundary condition, is not same as the heating condition of tensile tested sample. The weld factor can be predicted by this semi-empirical model with the information of the cooling temperature history. Figure A. 10 shows the simulated cooling temperature profiles of different welding displacements, from 0.7 to 1.3 mm, under the same heating temperature and heating time, T=250°C and t=30 sec. Since the hot molten material was flowed toward the far end of squeezing-out flash, the starting cooling temperature at the joining interface decreases with the increase of the welding displacement. Consequently, the available chain diffusion time for cases with larger displacements is smaller, which results in a smaller weld factor. Figure A.l 1 displays two sets of estimated weld factor from simulation as a function of welding displacement. Both of them show the similar trends where the weld factors decrease with the increase of welding displacement. The Bucknall’s data[33] displayed similar trend also shown in Figure A.ll. The effect of welding displacement on the weld factor is significant. For example, the weld factor of the higher welding temperature case, T=320°C t=10sec, drops from above 90% to 80% with an increase of 0.5 mm welding displacement. However this correlation model only concerns the chain diffusion (entanglement). The effect of microstructure variation in HAZ and the thermal induced stresses on the joining strength are ignored. According to Figure. A. 11 the highest weld factor is achieved without any welding displacement, which is not correct. For the cases of no welding displacement, the intimate contact between the joining planes could not be established. The chain diffusion theory can not be applied under this circumstance. Figure A.9 The comparison of estimated and experimental weld factors weld experimental and estimated of comparison The A.9 Figure Weld factor (estimated) 0.1 0.2 0.4 0.3 0.5 0.6 0.7 0.8 0.9 0 1 01 . 03 . 05 . 07 . 09 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Weld factor (experimental) factor Weld Figure A. 10 The simulated cooling temperature profiles at joining interface of different different of interface at joining profiles temperature cooling simulated The A. 10 Figure Temperature (°C) 100 110 120 3 - 130 4 - 140 5 - 150 160 7 - 170 180 - - welding displacements (T=250°C, t=30 sec) t=30 (T=250°C, displacements welding Cooling time (sec) time Cooling d= d= 1.3mm d=1.0 mm d=1.0 d=0.7 mm d=0.7 229 230 1 □ 0.9 0.8 0.7 o °-6 o Bucknall's results l l 0.5 2 T=260°C t=30 sec g 0.4 El T=250°C t=30sec 0.3 O T =320°C t=1 Osec 0.2 0.1 0 i i i | i i i | i i i ri i i i i i i i i i i | ii i 0.2 0.4 0.6 0.8 1 1.2 1.4 Welding displacement each side (mm) Figure A.11 The estimated weld factors of various welding displacement from simulation Figure A. 12 shows the effect of heating time on the weld strength. According to our correlation model, the maximum strength would be achieved at 15 sec heating time for the case of T=320°C and d=0.7 mm. For different processing conditions, we can obtain the minimum heating time required to reach the ultimate weld factor. 232 1 0.9 fi 0.8 0.7 1 » o 0.6 ■4—» 2 ° '5 CD £ 0.4 □ model 4) 0.3 -m • experiment 0.2 0.1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 0 5 10 15 20 25 30 Heating time (sec) Figure A. 12 The estimated weld factors of various welding heating time from simulation