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Heat transfer analysis of the plasma spray deposition process Wong, Henry Wing-Wo 1997

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HEAT TRANSFER ANALYSIS OF THE PLASMA SPRAY DEPOSITION PROCESS by H E N R Y WING-WO W O N G B.Sc. (Hons), The University of Surrey, 1987 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A January 1997 © Henry Wing-Wo Wong, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly: purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of MSTfrlS M^fjfilS thb/AieeZ/" 6y The University of British Columbia Vancouver; Canada Date Sfe****^  A\tf'V DE-6 (2788) 11 ABSTRACT A novel approach has been used to analyse the flow of heat during the plasma spray coating process. The approach couples heat transfer processes occurring at the micro scale, within the coating, and at the macro scale, in the substrate, using a combination of finite-element and finite-difference based models. One of the key boundary conditions employed in the model has been determined from an inverse heat conduction analysis of data recorded from an array of thermocouples embedded into a copper disk while being sprayed with a stationary gun in the absence of powder deposition. The models have been used to determine the evolution of temperature in 8 wt% yttria partially stabilized zirconia coatings deposited onto AISI-1008 steel for the deposition times of 1, 2 and 3 seconds. The results indicate that the cooling rate of the 7 material deposited initially is of the order of 10 °C/s and that the first splat cools from its -3 melting temperature to room temperature in approximately 10 s. The predictions from the model have been compared qualitatively with the distribution and the shape of pores found in the coating after subsequent metallographic examination. Different size and distribution of pores found at different locations of the zirconia based coating appear consistent with a qualitative understanding of the evolution of temperature in the coatings examined. Pores located at the coating / substrate interface appeared larger and were inter-connected. At the centre near the free surface of the coating, however, pores were closed and isolated. In addition, the same models have been applied for the plasma spray deposition of 17% Co-WC and CP titanium on AISI-1008 steel. The particle temperatures predicted using the model were compared with the temperatures measured in an independent study using a pyrometer-based measurements on the same plasma spray system. The results of the heat flow-based analysis were found to agree with the pyrometer-based measurements to within 10% for the case of 17% Co-WC and to within 16% for CP titanium. i i i TABLE OF CONTENTS Abstract ii Table of Contents i i i List of Tables vi List of Figures vii Nomenclature xii Acknowledgment xv CHAPTER 1 INTRODUCTION 1 1. 1 Background 1 1.2 Description of the Deposition Processes 3 1.2.1 Physical Vapour Deposition of Thermal Barrier Coatings 3 1. 2. 2 Plasma Spray of Thermal Barrier Coatings 5 1. 3 Mechanical and Physical Properties of Thermal Barrier 7 Coating Materials 1.3.1 Thermal Barrier Top Coating 7 1.3.2 Bond Coat 11 1.4 Focus of the Present Study 14 CHAPTER 2 LITERATURE REVIEW 15 2. 1 Plasma Flame 16 2. 1. 1 The Thermal Field of the Plasma Flame 17 2.1.2 The Velocity Field of the Plasma Flame 20 2.1.3 . Plasma Flame - Particle Interaction 20 2.2 Coating - Substrate Interactions 23 2.2. 1 Thermal Interaction 23 2.2.2 Mechanical Interaction 23 2.2.2. 1 Thermal Stresses 23 2. 2. 2. 2 Residual Stresses 24 2.3 Mathematical Modelling 27 2.4 Summary 31 CHAPTER 3 SCOPE A N D OBJECTIVES 32 3. 1 Scope of this Investigation 32 3.2 Objectives of the Investigation 34 CHAPTER 4 E X P E R I M E N T A L 35 4. 1 Temperature Measurements 36 4.1.1 Without Powder Deposition 36 4. 1.2 With Powder Deposition 44 4.1.3 Error Evaluation and Assessment 51 4.2 Powder Deposition Profile 55 iv 4. 3 Microstructure Evaluation 59 4.4 Summary 67 TER 5 M A T H E M A T I C A L M O D E L D E V E L O P M E N T 69 5. 1 Macro Scale Heat Flow Model 70 5. 1. 1 Formulation 72 5. 1. 1. 1 Finite-element Discretization of Spatial Derivatives 73 5. 1. 1. 2 Element Type 74 5. 1. 1. 3 Numerical Integration 75 5. 1. 2 Domain 75 5. 1. 3 Side Boundary Condition 76 5. 1. 4 Symmetry Conditions 76 5. 1. 5 Top Surface Boundary Condition 77 5. 1. 6 Initial Conditions 81 5. 1. 7 Verification of the Macro Finite-element Code 81 5.2 Micro Scale Heat Flow Model 84 5.2. 1 Formulation 84 5.2. 2 Bottom Boundary Condition 87 5. 2. 3 Coupling of Micro Model to Macro Heat Flow Model 87 5. 2. 4 Verification of the Micro Finite-difference Code 88 CHAPTER 6 6. 6. 6. 6. 1 1. 1 1. 2 1. 3 6. 1.4 6. 1. 5 6.2 6. 3 6.4 CHAPTER 7 7. 1 7. 2 7. 3 7. 3. 1 7. 3.2 M A T H E M A T I C A L ANALYSIS OF EXPERIMENT RESULTS Inverse Heat Transfer Analysis Formulation Validation of the Inverse Heat Conduction Calculation Regularization of the Inverse Heat Conduction Calculation Evaluation of the Sensitivity Coefficients Optimal Regularization Parameters for Inverse Heat Conduction Calculation Application to Experimental Results Analysis of Experimental Results Summary 91 91 92 95 98 101 102 106 113 115 117 ANALYSIS OF P L A S M A S P R A Y DEPOSITION PROCESS Application of Macro-Micro Heat Flow Model 117 Sensitivity Analysis 118 Mathematical Analysis of Plasma Spray Deposition 127 Process Analysis of Plasma Spray Deposition of 8wt% Yttria- 127 Zircon i a Analysis of Plasma Spray Deposition of CP titanium and 138 17% Co-WC V 7.4 Summary 144 CHAPTER 8 S U M M A R Y A N D CONCLUSIONS 147 8. 1 Summary and Conclusions 147 8.2 Recommendation of Further Work 151 REFERENCES 152 APPENDIX 1 Dimension, Material and Mesh used in the Finite- 159 Element Model APPENDIX 2 Thermophysical Properties of Materials used in the 160 Models A2. 1 Substrate Materials 160 A2. 1. 1 Pure Copper 160 A2. 1.2 AISI - 1008 Steel 162 A2 .2 Coating Materials 164 A2.2 . 1 Yttria Partially-Stabilized Zirconia 164 A2. 2. 2 17 wt% Cobalt - Tungsten Carbide 167 A2 .2 .3 CP Titanium 170 APPENDIX 3 Algorithm of the Micro Model 174 vi LIST OF TABLES T A B L E I T A B L E II T A B L E III T A B L E IV T A B L E V T A B L E VI T A B L E VII T A B L E VIII T A B L E IX T A B L E X T A B L E X I Spray Parameters for the Estimation of Plasma Torch 40 Power Distribution Spray Parameters and Coating Materials used in the 48 Experiments Thermophysical Properties of Thermocouple and 53 Substrate Materials used in this Investigation Estimated Response Time of Thermocouples used in the 53 Study Estimated Rate of Change of Coating Thickness and 57 Powder Distribution Effects of Regularization Parameter (a) on the Estimated 104 Heat Fluxes and the Predicted Gaussian Distribution Net Total Power, Centre Heat Flux and Distribution 107 Coefficient estimated by the Inverse Heat Conduction Calculation for Tests 1 to 18 Range of Parameters studied in the Sensitivity Analysis 119 of the Thermal Response of Test 20 to Changes in Process Parameters The Sensitivity of Temperature of Test 20 to Changes in 126 the Conditions shown in Table VIII Deposit Temperature, Deposition Power, Power 129 Distribution, Rate of Change of Coating Thickness and Powder Distribution used in the Model Calculations for Tests 19, 20 and 21 Deposit Temperature, Deposition Power, Power 139 Distribution, Rate of Change of Coating Thickness, and Powder Distribution used in the Model Calculations of Tests 22 and 23 V l l FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 FIGURE 8 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 FIGURE 14 FIGURE 15 FIGURE 16 FIGURE 17 FIGURE 18 FIGURE 19 FIGURE 20 FIGURE 21 LIST OF FIGURES a) Schematic cross section of a typical jet engine b) Gas 2 temperature, pressure and velocity profiles across the engine. Schematic of an electron beam evaporation (EB-PVD) 4 system used in the deposition of thermal barrier coatings Schematic of air plasma spraying process 6 Phase diagram of Zr0 2 - rich region of the Zr0 2 - Y 2 0 3 8 system Mole fractions of monoclinic, tetragonal, and cubic 9 phases as a function of composition in plasma sprayed zirconia - yttria The stress - strain behavior of plasma sprayed ZrO^ - 10 Y 2 0 3 coating Ductility / temperature characteristics of various 13 M C r A l Y bond coatings Plasma spray processes a) standard b) Axial III 16 Enthalpy of plasma as a function of temperature 18 Distribution of temperature in an argon / hydrogen 19 plasma flame Radial profiles of WC-Co and Ti particles at 120 mm 22 from the Axial III torch nozzle Predicted variation in the residual stress distribution 26 within a plasma sprayed coating as a function of coating thickness Geometry of the copper disk used for heat flux estimation 38 A typical temperature - time plot for 14 thermocouples 41 obtained from Test 3 Centre temperature - time plots for Test 1 to Test 6 42 Centre temperature - time plots for Test 7 to Test 10 43 Centre temperature - time plots for Test 11 to Test 16 43 Centre temperature - time plots for Test 17 to Test 18 44 Steel disk used for plasma spray deposition 45 Holding fixture for the steel disk 47 Temperature - time plot for 1 second zirconia deposition 49 V l l l (Test 19) FIGURE 22 Temperature - time plot for 2 seconds zirconia deposition 49 (Test 20) FIGURE 23 Temperature - time plot for 3 seconds zirconia deposition 50 (Test 21) FIGURE 24 Temperature -time plot for 17%Co-WC deposition 50 (Test 22) FIGURE 25 Temperature - time plot for CP titanium deposition (Test 51 23) FIGURE 26 Surface topography of 2 seconds zirconia deposition 56 conducted in Test 20 FIGURE 27 Powder distribution of zirconia after 2 seconds direct 58 plasma spray deposition FIGURE 28 Powder distribution of plasma spray deposition of 17% 58 Co-WC after 60 passes at 800 mm/s FIGURE 29 Powder distribution of plasma spray deposition of CP 59 titanium after 134 passes at 800 mm/s FIGURE 30 Micrograph of 1 second deposition of zirconia conducted 60 in Test 19 FIGURE 31 Micrograph of 2 seconds deposition of zirconia 60 conducted in Test 20 FIGURE 32 Micrograph of 3 seconds deposition of zirconia 60 conducted in Test 21 FIGURE 33 Schematic of the locations of pores examined 63 FIGURE 34 S E M photograph of pore found at 150 um from substrate 64 FIGURE 35 S E M photograph of pore found 600 am from the free 65 surface of the coating FIGURE 36 S E M photograph of pore found at 150 am from the free 66 surface of the coating FIGURE 37 Porosity measured at different locations of zirconia 67 coating conducted in Test 20 FIGURE 38 Schematic drawing showing the micro-macro models 71 used in this research program FIGURE 39 Configuration of cylinder used in the F E M model 72 FIGURE 40 Schematic of a Gaussian distributed heat source 80 FIGURE 41 Comparison between the analytical solution for a cylinder 83 IX with a constant heat flux applied to one end and the finite-element solution FIGURE 42 Comparison between the analytical solution for a semi- 90 infinite slab with a constant heat flux applied to one end and the finite-difference solution FIGURE 43 Schematic of heat flux distribution used in inverse heat 92 conduction FIGURE 44 The initial heat flux distribution input for validation of 96 the inverse heat conduction code FIGURE 45 Temperature profile estimated from the direct model 97 FIGURE 46 Comparison of heat fluxes between inverse estimation 98 and original input data FIGURE 47 Temperature data contaminated with ±1°C noise for 99 inverse model verification FIGURE 48 Heat flux estimated from noisy temperature data without 100 regularization FIGURE 49 Heat fluxes estimated from noisy temperature data with 100 regularization parameter of 1 x 10 - 9 FIGURE 50 The optimal regularization parameter of the 12mm thick 105 copper target FIGURE 51 Heat fluxes estimated by inverse heat conduction 108 calculation from temperature data collected in Test 3 FIGURE 52 Comparison of temperature data collected in Test 3 and 108 estimated from inverse heat conduction calculation FIGURE 53 Heat flux distribution estimated from temperature data of 109 Test 3 FIGURE 54 Heat flux distribution of Nozzle 1/2" XS imposed across 110 the substrate surface at different stand-off distances FIGURE 55 Relationship of net total power and the stand-off distance 112 FIGURE 56 Relationship of the distribution coefficient and the stand- 113 off distance FIGURE 57 Sensitivity of the thermal response of Test 20 to changes 122 in thermal conductivity of coating material FIGURE 58 Sensitivity of the thermal response of Test 20 to changes 122 in emissivity of coating material FIGURE 59 Sensitivity of the thermal response of Test 20 to changes 123 in depositing temperature of coating material FIGURE 60 Sensitivity of the thermal response of Test 20 to changes 123 in latent heat of coating material FIGURE 61 Sensitivity of the thermal response of Test 20 to changes 124 in net torch power FIGURE 62 Sensitivity of the thermal response of Test 20 to changes 124 in power distribution of torch power FIGURE 63 Sensitivity of the thermal response of Test 20 to changes 125 in the splat thicknesses of the coating material FIGURE 64 Model predictions and experimental results for Test 20 128 FIGURE 65 Model predictions and experimental results for Test 19 129 FIGURE 66 Model predictions and experimental results for Test 21 130 FIGURE 67 Comparison of model predictions for 1.25 second 131 deposition and experimental results for Test 19 FIGURE 68 Model prediction of the cooling of the first splat 132 FIGURE 69 Model predictions of coating temperature at the centre for 133 Test 20 FIGURE 70 Model predictions of coating temperature at 2 mm from 134 the centre for Test 20 FIGURE 71 Model predictions of coating temperature at 4 mm from 134 the centre for Test 20 FIGURE 72 Model predictions of coating temperature at 6 mm from 135 the centre for Test 20 FIGURE 73 Model prediction of the temperature gradient across the 138 coating for 1, 2 and 3 seconds plasma spray deposition of 8wt% yttria-zirconia FIGURE 74 Model predictions and experimental results for Test 22 140 FIGURE 75 Model predictions and experimental results for Test 23 140 FIGURE 76 Model predictions of coating temperature at coating 142 centre of Test 22 FIGURE 77 Model predictions of coating temperature at coating 143 centre of Test 23 FIGURE 78 Mesh dimensions used in the finite-element model 159 FIGURE 79 The thermal conductivity of pure copper as a function of 161 temperature FIGURE 80 The heat capacity of pure copper as a function of 162 temperature XI FIGURE 81 The thermal conductivity ofAISI-1008 as a function of 163 temperature FIGURE 82 The heat capacity ofAlSI-1008 as a function of 164 temperature FIGURE 83 The heat capacity of zirconia as a function of temperature 165 FIGURE 84 The enthalpy function for zirconia 167 FIGURE 85 The estimated heat capacity of 17% Co-WC as a function 169 of temperature FIGURE 86 The estimated enthalpy function for 17% Co-WC 170 FIGURE 87 The thermal conductivity of titanium as a function of 171 temperature FIGURE 88 The heat capacity of titanium as a function of 172 temperature FIGURE 89 The enthalpy function for titanium 173 xii NOMENCLATURE Latin Symbols Bjk zeroth regularization matrix BiT, Bj matrices of differential operators [C], [C]e global and elemental heat capacitance matrices C heat flux distribution coefficient m Cp heat capacity J / (kg °C) d heat source distribution diameter m D rate of change of coating thickness m /s \f], [f]e global and elemental force vectors H enthalpy J / k g h heat transfer coefficient ' W / ("C m 2) k thermal conductivity W / (m "C) [K], [K]e global and elemental temperature influence matrices m number of integration Gauss points M number of distributed heat flux segments n number of data Ni row vector of interpolation functions for node i Nj column vector of interpolation functions for node j P power W q external heat flux per unit area W / m 2 Q internal heat source per unit volumn (in FEM) W / m 3 Q discretized heat flux per unit area (in IHCP) W / m 2 ' R maximum radius m radial distance m S sum of square of difference t time s At time step used in numerical integration s T model temperature "C u, v local Cartesian coordinate system r xiii w weighting coefficient for Gauss Quadrature integration X sensitivity coefficient ("C m2) / W y axial distance, thickness m Y maximum axial distance m Greek Symbols a thermal diffusivity m 2 / s a* optimal regularization parameter X powder distribution coefficient m 5 diameter of thermocouple wire m 8 emissivity <P root of square error e angular direction (in FEM) e measured thermocouple temperature (in IHCP) °C p density kg / m3 a Botzman constant = 5.67 x l O 8 W / (m 2 °C4) Mathematical Symbols a differential operator V divergence Superscripts modified value ~ approximate value e value within element (in FEM) eff effective value i initial value net net value 0 assumed value Subscripts oo surrounding 1, 2,....M thermocouple location (1, 2,.... M) amb ambient coat coating con convection dep deposition i, j, k nodes i, j, k int substrate / coating interface max maximum value 0 origin, centre location, interface plasma plasma flame r radial coordinate rad radiation sub substrate tc thermocouple torch torch Abbreviation 1-D, 2-D one dimensional, two dimensional CP titanium commercially pure titanium, D.C. direct current D.S. directional dolidification EB-PVD electron beam - physical vapour deposition Eqn. equation F D M finite-difference method F E M finite-element method IHCP inverse heat conduction problem S.X. single crystal sec. second S E M scanning electron microscope T/C thermocouple X V ACKNOWLEDGMENT I would like to express my sincere indebtedness to Dr. Steven Cockcroft for his untiring support and friendship throughout this project. I would also like to express my deep appreciation to Dr. Alec Mitchell for his input and professional advice. Financial assistance from the Science Council of British Columbia is gratefully acknowledged. Many thanks to Mr. Douglas Ross, Alan Burgess and Herbert Tai of Northwest Mettech Corporation for allowing me to use their Axial HI ™ plasma spray system and their agreement to publish the results of experiments we conducted. I would also like to thank Dr. Howard Hawthorne and Mr. Sing Yick of the Institute for Machinery Research, National Research Council of Canada, for their help on the use of the surface profilometer. Finally, I want to acknowledge my wife, Nancy, and my daughter, Hannah. Words do not exist to express how much they mean to me. A l l I can do is to give them my thanks and my love. 1 CHAPTER 1 INTRODUCTION There are many examples where the performance of materials has been extended and expanded through the use of coatings as a means of improving corrosion, erosion and abrasion performance. One such example, are coatings produced by the plasma spray deposition process which are employed to extend the temperature range of components in turbine engines. Referring to Figure 1, which is a schematic diagram illustrating the pressure-temperature relationship in various sections of a modern turbine engine, thermal barrier coatings have been employed in both the combustor and in the turbine to extent the temperature range of the components [1]. The driving force for the development of these coatings and the processes for there deposition has been the substantial improvements in fuel efficiency and performance that can be realized through increasing the turbine inlet temperature [2]. 1.1 Background Presently, nickel based superalloys make-up the majority of the materials used in the hot section of turbines owing to their strength at temperatures up to 80% of their incipient melting point (this capability is derived largely from the y' precipitate). The performance of nickel based superalloys has been improved over the years through the addition of refractory elements to improve corrosion performance (oxidation and sulfidation), by the development of directional casting processes (D.S. and S.X.) and by the use of ducting of relatively cool compressor air through the blades to cool them (the latter method has the disadvantage that it results in a loss of the pressure differential and hence some efficiency). 2 turbine blades air intake C m/s KPa 3000 1000 1000 1500 500 500 0 0 0 compressor turbine vanes turbine discs propelling nozzle V/////7/7A C compression combustion expansion exhaust (a) (b) Figure 1: a) Schematic cross section of a typical jet engine b) Gas temperature, pressure and velocity profiles across the engine. [1] An alternative approach to increasing the high temperature performance of components, and thereby allowing hotter turbine inlet temperatures, is by overlaying an insulating ceramic known as a "Thermal Barrier Coating" onto the surface of the component [2, 3, 4, 5, 6, 7, 8, 9, 10]. Currently, the preferred thermal barrier material is based on zirconia, which has the characteristics of a high melting point, and reasonable thermal shock resistance, coupled with low thermal conductivity [8]. Zirconia has the disadvantage of undergoing a phase transformation during heating and cooling which results in contraction and expansion respectively that, unless suppressed by the addition of stabilizers such as magnesia or yttria, can produce cracking and disintegration of the ceramic [11]. Of the compositions currently available commercially, zirconia 6-8 wt% Y 2 0 3 stabilized Z r 0 2 is preferred [2, 10, 12]. 3 As in other materials, it is clear from the literature that the performance of thermal barrier coatings dependents strongly on microstructure. In addition, it is also evident that there is considerable room for improvement and the tailoring of microstructures for specific applications. For example, the presence of some porosity may be desirable from the standpoint of thermal shock tolerance but objectionable if it becomes too large and interconnected allowing corrosive gas access to the substrate. In order to aid in the development of improved plasma spray processes and optimized coatings for specific applications it is necessary to have a fundamental understanding of the development of plasma spray microstructures. The first step toward this goal begins with an understanding of the heat transfer occurring in the plasma spray deposition process, which is the subject of this thesis. 1. 2 Description of the Deposition Processes There are two processes available for the production of thermal barrier coatings, one is electron beam - physical vapour deposition and the other is plasma spray deposition [6, 8, 10, 13]. The selection of one particular method over the other depends on the requirements with respect to deposition rate, microstructure, surface finish, and cost. 1. 2.1 Physical Vapour Deposition of Thermal Barrier Coatings Ceramic thermal barrier coating deposited via use of an electron beam - physical vapor deposition (EB-PVD) - was first reported in 1982 [14]. This process is a modification of the high rate vapour deposition process for metallic coatings that has been successfully used to coat turbine airfoils. Figure 2 illustrates schematically the EB-PVD 4 process developed jointly by Pratt and Whitney and Temescal as a means of producing overlay coatings for turbine components [8]. Pre-cleaned components (free of absorbed gases, moisture and loose oxides) are mounted in jigs, transferred through a load-lock on rotating shafts and moved through a vacuum lock into a position for pre-heating in the main chamber. After pre-heating, the components are rotated in the vapour cloud above the molten pool of coating alloy, heated by high voltage electron beam. At the processing temperature and vacuum, zirconia exhibits deficiency in oxygen as a result of partial dissociation during evaporation. To minimise any deviations from the stoichiometry of Z r0 2 , a controlled amount of oxygen is bled into the Y 2 0 3 - stabilized Z r 0 2 vapour cloud during coating [10]. Vacuum Chamber Vapour Cloud Over-source heater Pre-heater Components Electron Beam Source Ingot feed Figure 2: Schematic of an electron beam evaporation (EB-PVD) system used in the deposition of thermal barrier coatings [10]. The microstructure of EB-PVD thermal barrier coatings is fundamentally different from that of plasma sprayed thermal barrier coatings. During EB-PVD of thermal barrier 5 coatings, material is deposited and grows in columnar form. Each ceramic column is poorly bonded to adjacent columns, but is tightly bonded to the underlying substrate. Such a columnar structure allows the coating to tolerate much higher thermal strains induced by differential expansion relative to the underlying substrate and within the coating and thus has a longer life under thermal cycling than coatings overlaid by the plasma spray process [10]. 1. 2. 2 Plasma Spraying of Thermal Barrier Coatings Plasma-deposited thermal barrier coatings have been used to extend the durability of aircraft engine combustors for over 20 years. The plasma spray process may be carried out in air, under an argon-shroud, or in a vacuum. The latter is referred to as low-pressure plasma spraying. Figure 3 shows schematically a typical air plasma spraying process. In this process, the plasma gun operates with a gaseous atmosphere of argon, hydrogen, helium or nitrogen. The heat source is a high intensity D.C. arc formed between two electrodes, one of which also serves as the nozzle [4, 8]. The D.C. arc generates temperatures up to 20,000 °C which ionizes the gas when it passes between the electrodes into its plasma state and is ejected at exit velocities of between 200 and 500 m s"1 [8]. To form an air plasma sprayed coating, powder particles are injected into the plasma as the jet emerges from the gun. Within the plasma, the particles are both heated and accelerated. Depending on the material, the particles may be partially or fully melted. These particles are directed at the target surface where they deform into lamellae (often referred to as "splats") 5 to 15 pm thick, and subsequently solidify. The degree of deformation and thus the shape of splat depends on several factors, such as the impact velocity, the viscosity and wettability of the molten particles, the conditions of their cooling, powder granularity, and the character of the substrate surface [15, 16, 17]. Prior to 6 coating, the area of the substrate to be coated is grit blasted to form a clean and rough surface. Contouring of the splats to the uneven surface helps to anchor the depositing droplets and form a strong mechanical bond with the substrate. Figure 3: Schematic of air plasma spraying process [8] During plasma spraying, particles melted in the plasma flame acquire a spherical shape as a result of surface tension. Subsequent impingement of molten particles, one atop the other, results in a lamellar like structure. Consequently, the internal structure of a plasma sprayed coating is not homogenous, generally consisting of grains of different sizes, adhering to each other. Pores are also present in the coating; the porosity being controlled by a suitable selection of the granular powder and the spraying parameters. Coatings made of brittle and hard materials normally exhibit higher porosity. In some cases, high porosity may be desirable, as for example in coatings used in thermal insulation and in filtration. 7 1. 3 Mechanical and Physical Properties of Thermal Barrier Coating Materials The standard plasma-sprayed thermal barrier coating has been developed and refined over a long period of time and is widely accepted in the aircraft industry and elsewhere. In this period, it has evolved in both chemical composition, phase content, microstructure and processing, in to what is described as a "state-of-the-art" coating [5, 18]. A typical thermal barrier coating basically consists of two layers: a M C r A l Y (M = Co, Ni) bond coat, between 75 and 150 pm thick, and a partially stabilized zirconia top coat, between 200 and 400 pm thick. Specifications generally require that the top coat meet some minimum criterion related to microstructure [19]. The major difficulty associated with the use of thermal barrier coatings on metallic substrates relates to in-service thermal cycling, such as arises in a turbine engine. The low thermal expansion coefficient of the ceramic and relatively high expansion coefficient of the metal substrate can result in large differential thermal strains which ultimately lead to delamination or spalling [9]. It has been shown that under certain conditions, the thermal stresses associated with the mismatch of thermal expansion can exceed the tensile strength for bulk zirconia (the calculated thermal stress is 300 N/mm compared with a maximum tensile strength of 120 N/mm 2 for bulk zirconia at 1000 K) [9]. 1. 3.1 Thermal Barrier Top Coating As mentioned previously, yttria partially stabilized zirconia is the most common thermal barrier coating used. Figure 4 shows the modified phase diagram for the zirconia rich portion of the zirconia-yttria system [20]. The stability regimes for non-equilibrium homogeneous phases at room temperature are indicated by the horizontal lines, appearing in the lower portion of the graph. Mole fractions of monoclinic, tetragonal and cubic 8 phases, and coating life cycles, as a function of yttria composition in plasma sprayed yttria stabilized zirconia, are shown in Figure 5 [21]. The maximum tetragonal content of the coating coincides with the 6 - 8 wt % Y 2 0 3 region, which are also the compositions found to have the highest thermal cycle performance. O o <D CD i_ 0) Q. E .0) 3 0 0 0 L i q u i d ( L ) l r~ 2 5 0 0 1 + F 2 0 0 0 C u b i c ( F ) 1500 T e t r a g o n a l ( T ) \ T + F \ 1000 \ K \ \ M \ \ 5 0 0 1 M + F \ 0 M o n o c l i n i c ( M ) , 1 , 1 , 1 C u b i c ( F ) T e t r a g o n a l (T") I " 0 2 4 ZrO, 8 10 12 14 16 18 2 0 wt % Y 2 0 3 Figure 4: Phase diagram of Zr02 - rich region of the Zr02 - Y 20 3 system [redrawn from Reference 20] Increased resistance of plasma sprayed ceramic coatings to cyclic thermal exposure can be achieved by increasing the strain tolerance of the ceramic and by controlling harmful residual stresses [9]. Strain tolerance could be increased by controlling the internal structure to minimize harmful flaws and / or to add favorable discontinuities. Structures with controlled porosity, internal microcracking, and segmentation, have been shown to provide good resistance to thermal cycling [22]. 9 0 2 4 6 8 10 12 14 16 18 20 Zr02 wt % Y 20 3 Figure 5: Mole fractions of monoclinic, tetragonal, and cubic phases as a function of composition in plasma sprayed zirconia - yttria (redrawn from Ref. 21) It has been known that porous materials exhibit lower elastic moduli than dense materials [23]. A porous ceramic coating might then be expected to exhibit lower stresses, for a constant applied mismatch strain, than would be expected for a fully dense ceramic. The improved thermal cycling behavior of porous coatings was believed to result from this factor and from the tendency for cracks to be diverted or arrested by the distributed pores. Figure 6 shows the uniaxial stress-strain behavior of plasma sprayed Z r 0 2 - Y 2 0 3 ceramic coating [24]. The strength of the coating in uniaxial compression is shown to be significantly higher than the strength in tension. The coating also deforms in a non-linear elastic manner in both tension and compression. 10 Percent Strain -2 -1 5 -i | i | i | i | i | 1 1 0.5 / - -10 - -20 CO i—i-(D -30 CO -40 w. -50 -60 Figure 6: The stress - strain behavior of plasma sprayed Zr02 - Y 20 3 coating [24] The integrity of plasma sprayed thermal barrier coatings on metallic substrates, and their performance in high temperature applications, is strongly influenced by the differential thermal expansion behavior of the coating with respect to the substrate, the nature of the coating-substrate bond, and the residual stresses that develop during the application of the coating [25]. In one study, the thermal expansion of Z r 0 2 - 7 wt% Y 2 0 3 over a temperature range 25 to 1100°C was reported to be nearly constant, at approximately 10 x 10~6 / °C [21]. In other more detailed examinations, [26, 27] plasma sprayed zirconia containing 8 wt% yttria was reported to exhibit anisotropic thermal expansion. The coefficient of thermal expansion in the longitudinal direction was found to be 10 x 10-6 / °C and in the transverse directions 2.9 to 23.5 x 10"6 / °C [26, 27]. The anisotropic lamellar structure of the coating and the microcrack network within the coating were considered to contribute to the difference in the thermal expansion coefficient with respect to the longitudinal and transverse directions [27]. 11 The relationship between coating structure and the resulting properties, in plasma sprayed yttria stabilized zirconia coatings, has been examined [18, 22]. In one of the studies, [18] a number of plasma sprayed yttria stabilized zirconia coatings were prepared representing a combination of significantly different starting powders and different plasma torch designs. The coatings had densities in the range of 85% to 91% of the theoretical value. Coating hardness, particle erosion resistance, and cohesive strength, were found to be proportional to the density. In a 1.3 mm thick zirconia coating, the thermal fatigue resistance increased with increasing density. In general, the coatings exhibited a number of properties related to density. No reference was made to the relative roles of the various process parameters examined. In the as-sprayed condition, Y 2 0 3 stabilized Z r 0 2 is characterized by its high content of the non-equilibrium tetragonal phase which can be up to 100% [28]. The tetragonal phase will degrade if the temperature is held at 1600°C for a long period of time [28]. This temperature can be considered as the maximum allowable service temperature for zirconia thermal barrier coatings. 1.3.2 Bond Coat The roles of various M C r A l Y bond coats are : i) to provide an impermeable barrier, thus protecting the substrate from oxidation and sulfidation, and ii) to minimize thermal stresses induced between the substrate and the coating due to thermal expansion mismatch. CoCrAlY bond coat has much better hot corrosion resistance than N i C r A l Y in the temperature range 850 - 900°C [7]. In the low temperature range, 600 - 700°C, N i C r A l Y bond coat is reported to have better oxidation resistance than the CoCrAlY coatings. 12 Yttrium, chromium and aluminum in nickel base bond coats have been found to influence the lifetimes of yttria stabilized zirconia thermal barrier coatings [29]. In a cyclic temperature study, zirconia coatings with no yttrium failed very rapidly. Increasing the concentration of yttrium in the Ni-Cr-Al-Y bond coatings increases the total coating lifetimes. A similar effect is observed with additions of chromium and aluminum. However, the effect is not as great as that due to yttrium. Increased bond coating thickness is also found to increase the lifetimes [29]. In another study, the isothermal oxidation kinetics of Ni-35Cr-6Al-0.95Y, N i -18Cr-12Al-0.3Y and Ni-16Cr-6Al-0.3Y low pressure plasma sprayed bond coat alloys was examined [30]. It was found that the Ni-35Cr-6Al-0.95Y alloy exhibited comparatively high isothermal oxidation weight gains and the longest thermal barrier coating life, whereas the Ni-16Cr-6Al-0.3Y alloy exhibited the lowest weight gains and the lowest thermal barrier coating life. The superiority of the Ni-35Cr-6Al-0.95Y bond coat suggests that factors such as thermal expansion mismatch, bond coat physical and mechanical properties, and bond coat oxide species formed, have a significant influence on the thermal barrier coating life cycle and can even offset the known detrimental effects of bond coat oxidation. Mi ld oxidation of the bond coat has been reported to have a positive effect on coating lifetime of vacuum plasma sprayed Ni-22Cr-10Al-lY bond coat [31]. The oxidation treatments involved heating bond coats for a variety of times and temperatures including 1000°C for 1, 50, 100, and 200 hours, and also at 1100, 1200, and 1300°C for 1 hour to form an oxide scale before subsequent overlaying of a Zr0 2-8wt% Y 2 0 3 top coat. The results showed that bond coat pre-oxidized thermal barrier coatings, when properly processed, generally exhibited lower oxidation rates and longer lifetimes when compared with traditional thermal barrier coated specimens. 13 Apart from their influence on coating lifetime, the aluminum and chromium content has an effect on the brittle / ductile behavior of M C r A l Y coatings. The ductile-brittle transition temperature (DBTT) characteristics of M C r A l Y coatings were reported to be dependent on their composition [32]. In CoCrAlY coatings, the aluminum content was found to have a large effect, with high aluminum contents (-13%) resulting in high values of DBTT. High chromium levels in these coating alloys also favored higher DBTT values, whereas the addition of nickel lowered the DBTT considerably (Figure 7). 0 100 200 300 400 500 600 700 800 900 1000 Temperature (°C) Figure 7: Ductility / temperature characteristics of various MCrAlY bond coatings. [32] As discussed previously, many industrial engine manufacturers seek to improve the performance of the engine by raising the turbine inlet temperature. This may be realized in part through the development of thicker thermal barrier coatings to protect components. Presently there is considerable effort directed towards the development of processes to produce coatings thicker than -1300 pm, which is approximately the current limit in thickness [19, 28]. 14 1. 4 Focus of the Present Study As discussed previously, large thermal stresses associated with the thermal expansion mismatch between the plasma sprayed coating and the substrate may result in coating spallation and delamination during service [9]. Moreover, it has been demonstrated that processing conditions have a bearing on coating performance through their influence on coating microstructure. In light of these factors, an understanding of the thermal history of the coating and the substrate during plasma spray deposition is important. The present investigation focuses on the heat transfer analysis of the plasma spray deposition process. The analysis considers heat transfer processes occurring at both the macro-scale; i.e., the scale of the substrate and of the plasma torch, and at the micro-scale; i.e., the scale of the splats, in order to predict the evolution of temperature within the coating. Once validated, the temperature distributions across the substrate and the coating under different process parameters are predicted with the mathematical model. Harmful thermal and residual stresses are closely related to the thermal history of the coating and the substrate [9]. Thus, the model predictions can yield insights into the optimum process parameters for the production of high quality coatings. CHAPTER 2 LITERATURE REVIEW 15 The plasma spraying process has been in use commercially since the 1950's for the deposition of metals and ceramics [4]. It has been refined considerably since 1970, but the basic design of the plasma torch has changed little. The powder coating material, carried in a stream of gas, such as argon, is conventionally injected radially into the plasma jet either within the nozzle or as it emerges from the outer face of the anode. In 1991, research engineers of the University of British Columbia invented a novel axial reactant powder injection system (see Figure 8) [33]. In this system, powder is carried through the centre powder port and ejects co-axially with the plasma gases. The stated advantages of this system over the standard plasma spray systems, which use radial powder injection are; 1) full entrainment of the powder in the plasma jet which maximises the deposition efficiency and 2) the powder possesses the maximum thermal and kinetic energy, which enhances bonding after impact. A l l the studies in this investigation are directed toward this plasma spray system. Although plasma spray deposition has been used extensively for over four decades, there is only a limited understanding of the process at a fundamental level. The lack of scientific understanding is due to the number and complexity of the parameters that affect the spray process, making the formulation of a comprehensive understanding difficult. Despite its challenges, much work has been done to increase our understanding of the phenomena occurring in the torch, flame and on the substrate. 16 This chapter reviews the current state of scientific knowledge of plasma spray deposition. The review is divided into two sections: the plasma flame and coating / substrate interactions. (a) Standard Plasma Spray (b) Axial III Plasma Spray L_l Figure 8: Plasma spray processes a) standard b) Axial III 2.1 Plasma Flame The original concept of thermal spray deposition was invented and patented by Dr. Ing. Max Ulrich Schoop in 1910. Initially, the depositing materials were mainly in the form of wire as spraying with powder proved more difficult. At that time, an oxyacetylene 17 flame was used as the heat source. As a result, the depositing materials was limited to low melting point metals such as zinc and aluminum. Attempts to extend the temperature range of the heat source resulted in the development of the plasma spraying process in the fifties [34]. The use of an inert plasma gas [34] in the process had the advantage of reducing the oxidation of molten particles during their flight through the flame and subsequent deposition on the substrate. Plasma flame temperatures of over 20,000 K [34], attainable in commercial plasma torches, is considerably higher than the melting and even the evaporation points of most industrial materials. The term "plasma" refers to the highly ionized state of the gas which contains light quanta, neutral atoms, molecules, charged ions, and electrons. When gases pass through a high intensity electric arc, the thermal energy produced from the arc may be high enough to dissociate and to further ionize the gases into their plasma state. This results in a plasma jet possessing a huge amount of thermal and kinetic energy (-23 MJ/kg when using pure Ar or Ar + N 2 mixture on Metco 7MB or 9MB plasma torches [15]) which can be ejected from the torch nozzle at supersonic velocities. 2.1.1 The Thermal Field of the Plasma Flame The temperature of a plasma jet depends primarily on the degree of ionization of the plasma, which is, dependent on the type of plasma gas used and the working parameters of the plasma torch. Figure 9 shows the temperature dependence of the enthalpy of some common plasma gases. As illustrated, the diatomic gases, such as nitrogen and hydrogen, require more energy to effect molecular dissociation prior to ionization. Consequently, these gases possess much larger enthalpies than the monoatomic 18 plasma gases. As a result, for a given amount of electrical energy, the temperature of a plasma produced from a diatonic gas will be lower than that formed from an inert gas. 0 4 8 12 16 20 Temperature (103 K) Figure 9: Enthalpy of plasma as a function of temperature [redrawn from Reference 34] As shown in Figure 9, above 7,000 K a nitrogen plasma contains greater enthalpy than the other gases at the same temperature. Therefore, hard-to-melt materials can be more easily deposited with nitrogen than with argon plasma in the case where the input power of the plasma torch is limited. Hydrogen dissociation requires lower energy than nitrogen. Hydrogen has the highest thermal conductivity of all other plasma gases and requires the highest arc voltage and the highest input power to the arc. However, the dissociation temperature of hydrogen plasma is lower than that of any of the other plasmas. Argon and helium gases require the lowest energy to transfer to plasma state. They provide a stable electric arc and require a lower working voltage. In addition, the temperature of their plasmas is higher than the other plasmas. 19 In order to increase the enthalpy and velocity of the plasma flame, gas mixtures in different proportions are used in plasma spray deposition [15]. For instance, to increase the kinetic energy of the flame and the depositing material, an argon and nitrogen mixture is used [15]. Whereas to ensure environment inertness, a mixture of argon and hydrogen is generally used [15]. A typical temperature isotherm in an argon/hydrogen plasma jet is shown in Figure 10 [35]. Figure 10: Distribution of temperature in an argon / hydrogen plasma flame. (I=452A, V=74V, P=33.4 kW, Ar=75 1/min, H2=15 1/min) [redrawn from Reference 35] Local temperatures in a plasma flame can be measured by means of spectroscopy. Precise determination of temperature is difficult because of abrupt temperature changes and the absorption of radiation by the partially opaque plasma flame [15]. The shape of the plasma flame is a function of plasma gas mixture, torch geometry, working pressure and torch power. Generally, the core temperature of the plasma flame is over 14,000 K. At the outer region of the flame, the plasma temperature drops as a result of turbulent mixing of the plasma with the external environment [35]. 20 2.1. 2 The Velocity Field of the Plasma Flame The velocity of a plasma flame can be calculated approximately by applying the fundamental gas mechanics laws to the condition of a gas flow through a cylindrical tube as it is being heated. Using this approach, Matejka and Benko determined the velocities of plasma flames ranging from 750 to 800 m/s in a torch with a nozzle 3 mm in diameter, 5 kW output and an argon flow rate of 24 l/s [15]. 2.1. 3 Plasma Flame - Particle Interaction The depositing powder is fed by carrier gas (usually argon or nitrogen) through a powder port and cable (tube) to the nozzle exit (see Figure 8). The momentum imparted by the plasma gas stream transports the powder toward the substrate target. The particles are heated by the surrounding plasma and most are melted before they strike the substrate at high velocity. Some of the powder may not be completely melted upon impact and therefore may bounce off of the target; some may be vapourised prior to reaching the target or miss the target entirely. As a result, only a fraction of the powder injected through the torch forms the coating. Once the particles have penetrated the plasma, they are accelerated by the fast flowing plasma gases. The particle trajectory and velocity within the plasma flame are influenced by the mass and the size of the particles and by the velocity distribution within the plasma gas. The residence time of the particle in the plasma stream is important. For example, a particle travelling with a low velocity has more time to absorb heat and become molten. Other factors include the difference in velocity between particle and the plasma which influences the efficiency of heat transfer. 21 Modelling the velocities of particles within the plasma jet is complex as it requires a good prediction of the initial temperature and velocity field of the plasma prior to entrainment of the particles. In addition, accurate modelling requires quantification of the ensuing two-phase flow. There have been numerous experimental studies and mathematical models developed describing the exchange of the thermal and the kinetic energies between the plasma jet and the entrained particles [36, 37, 38, 39, 40, 41]. Further, studies involving measurements suitable for model validation are sparse. In one such study, Moreau, Gougeon, Burgess and Ross used an integrated particle diagnostics system to detect the emitted thermal radiation of tungsten carbide-cobalt and CP titanium particles during air plasma spraying using the Axial HI torch [41] (see Figure 8 for Axial HI torch). In this study, the velocity, temperature and diameter of the particles were determined by the 2-colour pyrometry and time-of-flight method. Some of the results of their study are presented in Figure 11. In the WC-Co system, it was found that the temperature was uniform across the particle stream and that the particle velocity reached 380 m/s near the torch axis [41]. In a separate experiment also reported in Reference 41, the particle velocity of Ti powder was found to approach up to 550 m/s. In addition, there was a significant temperature rise with the stand-off distance found due to the strong exothermic reaction of the titanium particles with entrained air [41]. 22 WC -Co Radial Profile Ti Radial Profile 2750 -15-10 -5 0 5 10 15 •15-10 -5 0 5 10 15 Radial Location (mm) ure 11: Radial profiles of WC-Co and Ti particles at 120 mm from the Axial III torch nozzle [redrawn from Reference 41] 23 2. 2 Coating-Substrate Interactions 2. 2.1 Thermal Interaction When a molten particle impinges against a relatively cold substrate, the spherical particle droplet spreads into a lenticular shaped splat within one micro-second [17, 42]. In so-doing, the hot splat is quenched by the substrate surface. Depending on the prevailing conditions, the solidification time of a splat can be as little as a thousandth of a second. Since the time for the particle droplet to spread and solidify is small compared to the local particle deposition rate, the deposition process can be treated as a series of discrete events. Thus, the successive overlaying of the splats leads to the formation of the deposited coating. 2. 2. 2 Mechanical Interaction The sprayed layer adheres to the substrate surface mainly by mechanical anchoring, with some additional bonding arising due to valency and Van der Waals forces. In metallic coatings sprayed on metal substrates, some diffusion can take place giving rise to strong metallic bonds [15]. 2. 2. 2.1 Thermal Stresses In the plasma spraying process, the coating and the substrate materials undergo disparate thermal histories giving rise to thermal stresses, in that one is being cooled while the other is being heated. In addition, the subsequent deposition of splats; the non-uniform distribution of deposited material; the non-uniform heating of the part due to local 24 variations in the action of the plasma torch; and the difference in thermal expansion between the coating and the substrate; can all interact to cause internal stress to develop across the relatively thin coating. These stresses, if not relieved by micro-cracking, can cause cracking or spalling of the coating during processing and / or can give rise to the development of residual stresses [43]. 2. 2. 2. 2 Residual Stresses Residual stresses have been recognized as one of the most important characteristics in plasma sprayed coatings since they influence, in part, the maximum coating thickness which can be deposited without spallations [44]. In certain circumstances, it can result in the deformation of coated workpieces. In addition, various types of coating performance indicators, such as adhesion strength, [45] resistance to thermal shock, thermal cyclic life [24, 30, 46] and erosion resistance, are strongly influenced by the presence of residual stresses. Residual stresses, their generation and subsequent influence on the performance of mechanical components, have been the subject of several scientific investigations [10, 18, 22, 43, 44, 47]. During the use of the coated system, residual stresses in the coating act as pre-stresses, to which the mechanical or thermal operational loads are added. Residual stresses in excess of the strength of the coating can cause the formation of localized microcracks in the coating which can relax some of the stresses [10, 44]. In thick coatings, residual stresses can be so large that macrocracks form which propagate through the entire coating [18]. Ranking of the thermal fatigue resistance of thick coatings strongly favors the dense, macrocracked coating. It was postulated that the thermal expansion mismatch stresses were uncoupled from the metallic substrate by the long through-thickness cracks [18]. 25 Stress can be generated from three sources during the operation of the plasma spraying process [43]. (1) Stresses resulting from the contraction of individual sprayed splats as they rapidly cool to the substrate temperature. This is the "quenching stress". It is always tensile in the splats. (2) Differential thermal contraction stress. This arises as the substrate and deposit cool together, with or without thermal gradients. It is macroscopic because the bulk of the sprayed deposit can be considered as a continuous solid. Depending on the thermal expansions of the constituents, and the thermal gradient, it can be either tensile or compressive in the deposit. (3) Volume changes associated with solid state phase transformations. There is evidence to suggest that the stress distribution within a coating can vary considerably with changes in the process and material parameters. In one study, a comparison was made of predicted changes in stress distribution which arise as a result of changes in the deposition rate for zirconia (Zr0 2 5% CaO) and tungsten coatings respectively [44]. For plasma sprayed zirconia, a change was predicted to occur in the stress state from compressive to tensile due to a rise in the effective deposition temperature with increasing deposition rate (i.e., rate of heat extracted from zirconia coating was lowered than the rate of heat supplied from the molten particle with increasing deposition rate thus raise the effective deposition temperature). For tungsten coatings, owing to its high thermal conductivity, residual stresses were virtually independent of deposition rate. Also of great importance was the variation in residual stress with coating thickness, since it was often observed in experiments that coatings failed at some critical thickness. The predicted stress distribution in a zirconia coating shifted from being compressive 26 everywhere, for thin deposits, to showing a maximum in compressive stress close to the substrate and large tensile stresses in the outer regions for thicker coatings [44] (Figure 12). 80 ~ 60 o Q. to CO CD i _ to O 40 20 E 0 CD -20 -40 2.5 mm 2.0 mm 1.5 mm / I i 6/ ° ; 8 / 1 ; ° Relative Position 1.0 mm • j 0.5 mm Figure 12: Predicted variation in the residual stress distribution within a plasma sprayed coating as a function of coating thickness [44] The effect of residual stresses on the martensitic transformation from the tetragonal to the monoclinic crystal structure in plasma sprayed Zr0 2 - 8wt% Y 2 0 3 coatings was examined [47]. Indentation tests were used to stress induce tetragonal to monoclinic transformations in the plasma sprayed coatings. Triaxial stresses were obtained from X-ray dispersive analysis, and acoustic signals were recorded during the indentation tests. It was reported that microstructural defects, such as pores and microcracks, had a great influence on the transformation. This finding is questionable since in another study it was concluded that thermal barrier coatings containing 6-8 wt% Y 2 0 3 consisted almost entirely of tetragonal zirconia which does not transform to monoclinic phase under stress [22]. 27 2. 3 Mathematical Modelling The importance of the link between process parameters and coating performance is reflected in the fact that coating properties strongly depend on the spray torch type, nozzle size and spray parameters [48]. Although experimental approaches, such as the statistical Taguchi method [19, 49, 50, 51, 52], can provide insight into the key parameters in thermal spraying, they fail to elucidate the role of these parameters in fundamental terms. Over the last decade, mathematical modeling of the plasma spray process has received increased attention. It allows us to understand the plasma spray deposition process at a fundamental level. In this section, a brief summary on the mathematical models used to investigate the plasma spray process are discussed in chronological order. The low pressure plasma deposition process was examined by a one dimensional finite element method to obtain temperature distributions in the metallic substrate and deposit as a function of time [53]. The calculated temperature distribution in the deposit and substrate was then used to estimate the thermal stresses during the plasma deposition process and during subsequent temperature cycling, also by finite element analysis [54]. The limitation of this study was that the smallest time step used in the model was 1 second and the substrate temperature was assumed to be steady state. In another study, Belashchenko et al. [55] derived analytical equations for the calculation of the temperature fields on the surface of a sheet of finite thickness heated with a normally distributed heat source. The temperature variation along the axis of the plasma jet was analyzed under the assumption that the rear side of the sheet remained isothermal. In another study, Belashchenko [56] calculated the mean temperature field formed on the surface during arrival of the sprayed particles. He concluded that the spray distance had the strongest effect on the variation of the temperature field in the substrate in 28 comparison with other parameters, such as current, voltage, gas flow rates and the amount of sprayed material. El-Kaddah, McKelliget and Szekely [38] developed a mathematical model to describe the plasma spray process in which particular attention was paid to the fluid flow and temperature fields in the plasma jet, the plasma / particle interaction, and the heat transfer phenomena associated with the deposition process. As a result the model was able to predict the particle residence time in the plasma and the temperature history of the particles. In addition, a semi-infinite analytical solution of the one-dimensional problem was used to predict the heat transfer and solidification of particle droplets during plasma spraying. The solidification rate and the different spray rate of the particle droplets were compared and analysed. It was found that the rate of solidification of the particle droplets was solely determined by the rate of heat extraction by the substrate. At high spray rates, where the rate of energy supplied by the particles was greater than the rate of heat extraction by the substrate, the thickness of the solidified layer was less than that of the deposited layer, and the deposit / plasma interface was maintained in a liquid state. In their mathematical calculation, the spray rate and the total output power of the plasma torch were assumed to be distributed uniformly. In practice, the particle distribution and the total output power of the plasma torch were dependent of the radial coordinate. Residual stress in a thin Z r 0 2 - Y 2 0 3 ceramic coating resulting from the plasma spraying operation have been calculated by Mullen et al [45]. The calculations were performed using the two-dimensional bilinear finite element method. The model included the effect of layer size, process time, as well as nonlinear material behavior. The resulting residual stress field was compared to the experimental data [57]. Reasonable agreement between the predicted and measured data was found. Their model was based on the study developed in Reference 53. The substrate temperature was assumed to be maintained in 29 thermal equilibrium at 1090°C and the splat thickness was set to 360 |im, around 40 times thicker than the thickness of a splat normally found in a plasma spray coating. Eckold et al [58] have developed a theoretical analysis of residual stresses in flame sprayed brittle materials. The one dimensional model was able to predict the thermal stress in the coating and substrate during plasma deposition. A sensitivity analysis on coating specific heat capacity, coating latent heat, plasma temperature, coating thermal conductivity, coating expansivity, substrate temperature, deposition rate and coating thickness was performed. The improvement in thermal efficiency and component temperature reduction by using thicker thermal barrier coating was cited. There was, however, no experimental work to validate the model. Detailed studies on finite element thermal stress solutions for thermal barrier coatings were reported by Chang et al [59, 60] and Phucharoen [21]. In their investigations, numerical calculations were used to quantify the stress build-up in a thermal barrier coating with an idealized sinusoidal rough interface between the ceramic (Zr0 2 -Y 2 0 3 ) and bond coat (NiCrAlY). The objective of their work was to determine the stress state in a model thermal barrier coating as it cooled in the air to 600°C from an assumed stress-free state (no residual stress) at 700°C. In their model, materials were assumed to behave elastically. Numerical simulation of the thermo-mechanical behavior of a thick magnesium zirconate thermal barrier coating on 12 % silicon aluminum alloy was studied by Berger et al [61]. The model simulated the deposition of thermal barrier coating onto a piston crown. The calculated stress values represented only the stresses induced in the components due to the thermo-mechanical loading and did not take into account the residual fabrication 30 stresses. The effect due to mechanical and thermal anisotropy of the coating was also excluded. A mathematical study of plasma spray process has been completed in which residual stresses were determined in the as-sprayed coating using a F E M model [62]. The results revealed, that for conditions in which the coefficient of thermal expansion of the coating was smaller than that of the substrate, residual stresses in the coating were influenced by substrate temperature. There existed an optimum substrate temperature above which compressive stresses were induced and below which tensile stresses were induced. The optimum substrate temperature depended on the relative thickness (ratio of coating and substrate thickness). It increased monotonically with the relative thickness. These results showed good agreement with other studies [43, 63]. Residual stresses in plasma sprayed deposits were examined using a numerical model to describe the heat flow and the effects due to thermal contraction [64]. Comparisons were made between predictions and experimental measurements for the substrate / deposit curvatures exhibited during and after spraying of both metallic (FeCrAlY) and ceramic (alumina) deposits. Reasonable agreement (within 30%) was observed between model and experiment with respect to both the thermal and curvature histories. The magnitudes of the stresses were sufficient to cause plastic flow or other relaxation effects such as splat microcracking. The residual stresses in the alumina coating were small and tended to be compressive if deposited on a metallic substrate (Ti alloy), while large tensile stresses readily built up in the FeCrAlY deposit. However, the elemental thickness used in their model was as high as 500 pm and each element was considered isothermal. 31 Elsing et al [65] simulated the thermal behavior of an alumina coating on austenite and ferrite. The objective of their work was to provide an alternative for minimizing the experimental effort required for the development of new plasma spray systems for specific applications. The simulation only concentrated on the temperature profile of the coating and substrate and assumed one-dimensional heat conduction in the coating and the substrate. Latent heat of the coating material was not considered in the model. A two dimensional F E M model was developed for the stress analysis of plasma sprayed thermal barrier coatings by Steffens and Gramlich [66]. The predictions were based on constant material properties and assumed a stress free coating system heated up to 800K. 2.4 Summary The fundamental concepts of the plasma spray deposition process and the interactions between the coating and the substrate have been reviewed. Recent investigation of the plasma spray process has been conducted through mathematical modelling focusing on various aspect of the process. Among these studies, none of them were able to quantify the heat flux, delivered from the plasma torch and / or the sensible heat released from the molten powder onto the coating and the substrate, during plasma spray process at the scale of the splat. This is of utmost importance for the determination of thermal induced stresses in a plasma sprayed coating. In addition, none of the models had included the spatial distribution of the heat flux from the plasma flame and the powder flux. 32 CHAPTER 3 SCOPE AND OBJECTIVES 3.1 Scope of this Investigation The principle direction of this investigation was to develop a heat-flow model of the plasma spray deposition process for the production of the thermal barrier coatings and, using the model, to determine the temperature distribution within the substrate and the thermal barrier coating. The investigation focused on a newly developed 100 kW tri-axial reactant feed plasma torch (US Patent 5,008,511) invented by Mr. Douglas Ross of the Northwest Mettech Corporation [33]. However, the models and experimental techniques developed in this investigation are generally applicable to other plasma spray torches. Heat transfer in the plasma spray process occur on both the macro scale (scale of the substrate) and on the micro scale (scale of the splat). Thus, using a conventional finite element simulation of plasma spray deposition, the size of the elements is necessarily small in order to resolve heat flows occurring at the scale of an individual splat. If applied to the analysis of a component undergoing plasma spray deposition, conventional thermal F E M models, such as the one originally developed by Cockcroft, [67] would be computationally intractable. In order to alleviate this problem, a micro model has been developed to account for the deposition of the sensible heat from individual quenched splats as they impinge on the surface of the substrate or previously deposited coating and the heat conduction within the coating. The micro model is one-dimensional and is incorporated into a macro F E M based heat-flow model which accounts for heat transfer in the substrate. Once formulated, coded and debugged, the micro / macro heat-flow model was validated against the results obtained from the analysis of experimental thermocouple data. 33 To accomplish this, a two dimensional inverse heat conduction model was developed to calculate the spatial distribution of heat deposited on the substrate surface from the plasma flame in the absence of powder deposition. Thermocouples embedded in the substrate were used to obtain thermal histories under a variety of different operating conditions. A data logger with multichannel and analog / digital capabilities was employed to store the temperatures during spraying for post-experimental processing. In addition, analytical solutions to simplified problems were also employed to validate the direct heat conduction formulation and coding for the one-dimensional micro heat transfer model. Having validated the micro / macro heat flow model, computer runs were then made under different operating conditions which fell within the realm of standard practice. The major variables examined were : (1) Heat input due to variation of stand-off distance of the plasma torch. (2) Heat input due to variation in plasma gas flow rates. Secondarily, the effect of torch nozzle was also examined as part of an on going study at the participating company. In addition to the mathematical analysis, the micro and macro cracks formed in the as-sprayed coating as well as porosity are examined carefully and characterized. The results are compared and rationalized against the thermal history of the substrate as well as the plasma sprayed coating, predicted by the mathematical model. 34 3. 2 Objectives of the Investigation The objectives of this investigation can be summarized as follows : (1) To quantify the heat flux distribution resulting from the plasma spray deposition of a thermal barrier coating using the inverse heat transfer procedure. (2) Using the information obtained in (1), to formulate and develop a micro-scale mathematical model to simulate the flow of heat during the deposition of powder droplets on a substrate during plasma spraying. (3) To incorporate the micro-scale thermal deposition model into a macro heat flow model in order to compute the transient thermal field in a coating/substrate system during plasma spraying. (4) Using the model developed in (3), to determine the process parameters that have the greatest influence on the generation of large temperature gradients in plasma sprayed coating. (5) To characterize cracks or pores in the coating, if formed, in terms of the temperature history of both substrate and plasma sprayed thermal barrier coatings predicted by the model. 35 CHAPTER 4 EXPERIMENTAL During plasma spray deposition, heat is transferred from the plasma flame and from the particles to the substrate / coating surface and is removed from the coating via conduction and via convection / radiation at the top surface. In order to investigate the effect of various process parameters on heat transfer during plasma spraying, a number of experiments were conducted. These experiments were divided into two categories; a) measurements of substrate temperature without powder deposition; and b) measurements of substrate temperature with powder deposition. The first series of experiments were conducted to characterize the total transfer power of the plasma torch working under various conditions. This was estimated, using inverse heat transfer methods, from the thermocouple temperature data measured at different locations within the substrate while being heated with the plasma flame. The experiments were performed under different rates of plasma gas flow, different sizes of the nozzle and different stand-off distances between the plasma torch and the substrate in the absence of powder deposition. The parameters used in these experiments encompassed the range of parameters required for the plasma spray deposition of yttria partially stabilized zirconia, CP titanium and cobalt-tungsten carbide. The calculated intensity of the torch transfer power distribution was then used as one of the boundary conditions in the mathematical model. Another series of experiments were aimed at the characterization of heat transfer during deposition as well as the powder deposition profile. The results obtained from these experiments have been employed to validate the overall model as well as to determine the rate of change of coating thickness and powder distribution for input to the mathematical model. 36 Finally, the as-sprayed coatings were examined by microscopy. Specifically, the morphology and distribution of pores and cracks were analysed. The microstructure of the coating was then examined for consistency with the predicted temperature history of the plasma sprayed thermal barrier coating determined using the mathematical model. 4.1 Temperature Measurements 4.1.1 Without Powder Deposition As described in Chapter 2, the total output or transfer power of the plasma torch depends on the input power, the type and the flow rate of plasma gases used, the size of the nozzle, and the stand-off distance between the torch and the substrate. In the current investigation, the total output power and the power distribution of the plasma torch were assumed constant for a given set of operating conditions. In practice, fluctuations of up to 3 % in the input power and the plasma gas flow rates are unavoidable during the experiments. This section describes the experimental procedure for the prediction of the net output power and power distribution of the plasma torch. There is no known direct technique available to measure the power distribution input to the work piece during plasma spraying. Instead, the output power and the power distribution of plasma torch were estimated inversely (see Chapter 6) from the temperature data measured in an object undergoing heating by the plasma torch. In this investigation, temperatures were measured with thermocouples embedded in a disk. The disk was made of commercially pure copper which was 140 mm in diameter and 12 mm thick (for Tests 1 and 2), and 5 mm thick (for Test 3 through Test 18). At the bottom of the copper disk, 14 37 equally spaced 1.17 mm (3/64") diameter holes were drilled in positions radiating from the centre to the circumference. A l l holes were 1.5 mm deep. After the removal of sharp corners, an unsheathed fine gauge 0.25 mm (0.010") diameter, type T (for Test 1 and Test 2) or type K (for Test 3 to Test 18) thermocouple was embedded in each hole and held in place by a 1.0 mm diameter copper rod. The wires were separated by the copper rod in order to ensure that the temperatures were being measured at the base of drilled hole, as shown in Figure 13. This ensured that the temperature recorded was actually that at the back surface and not at some other wire junction as discussed in the literature [68]. The joints were examined carefully under a 10X magnifying glass and electrically tested. A l l thermocouples were calibrated in an ice bath and in boiling water, and were found to deviate within ± 2°C. The thermocouples were further verified using a milli-voltmeter and were found to deviate within 0.01 mV (corresponding to 0.5 °C ) measured at 25°C. Apart from the top surface, which was exposed to the plasma torch heat source, all surfaces of the copper disk were insulated by 6.35 mm (0.25") thick Lytherm® ceramic paper, in order to simplify the subsequent heat transfer analysis. The thermocouples were connected to a digital data logger, sampling at 5 Hz. The setup permitted the plasma torch to be positioned above the centre of the copper disk and to be swung in place and withdrawn from the vicinity of the copper disk quickly either manually (Test 1 to Test 16) or by a robotic arm (Test 17 to Test 18). The robotic arm was programmed to move at the velocity of 800 mm/s. A l l the experiments were performed using a 100 kW tri-axial reactant feed plasma [33]. The whole system, including the 38 copper disk, the data logger and the plasma spray system, was grounded electrically so that the electric noise induced in the thermocouples was kept to a minimum. 12 mm CTests 1 and 2) Thermocouple wires Figure 13: Geometry of the copper disk used for heat flux estimation At the beginning of each test, the stand-off distance was adjusted to the desired range. The plasma torch was positioned and then moved away from the copper disk. The plasma system was ignited and adjusted to the pre-determined parameters (that is; output voltage, output current, and primary and secondary gas flow rate). After the parameters had been selected and the plasma arc was stabilized, the data logger was switched on and the plasma torch swung quickly above the centre of the copper disk for approximately 10 seconds. The heating period was limited in 10 seconds to avoid overheating of the copper substrate. The copper disk was then allowed to cool to room temperature. The experiment was repeated using different process parameters, which included the changes of the different stand-off distance between the plasma torch and the copper 39 disk target, the different setting of the plasma gas flow rate (indicated on the control console), and the different size of the plasma torch nozzle. Table I lists the plasma spray parameters used for the estimation of the power and power distribution of the plasma torch. These tests were conducted at different times throughout the period of this investigation. As part of the ongoing research with the collaborating company, nozzles #6, #3, W'XS, 5/16 and 9/32" were studied (diameter opening of nozzles #6, #3, W'XS, 5/16" and 9/32" are, respectively, 0.5", 0.375", 0.5", 0.313" and 0.283"; due to the confidential agreement with the collaborating company, further details of these nozzles are not available). Plasma spray parameters used in Tests 1 to 11 and Tests 14 to 16 were selected for the study of the relationship between the stand-off distance, net transfer power and power distribution of the plasma torch. The result obtained from Test 11 was further compared with the other experiments having higher hydrogen flow rate (Test 12) and lower hydrogen flow rate (Test 13). Test 15 was the experiment which used the base spray parameters for zirconia. Test 17 and Test 18 were experiments for the plasma spray deposition of tungsten carbide-cobalt composite (WC 17% Co) and CP titanium (Ti), respectively. 40 Table I : Spray Parameters for the Estimation of Plasma Torch Power Distribution Test Nozzle Input Power (kW) Ar / N 2 / H 2 (slm) Stand-off Distance (mm) 1 #6 86 10 /96 /10 85 2 #6 86 10 /96 /10 65 3 #6 86 10/96/10 45 4 #6 86 10 /96 /10 78 5 #6 86 10 /96 /10 120 6 #6 86 10 /96 /10 105 7 #3 86 10 /96 /10 40 8. #3 86 10 /96 /10 55 9 #3 86 10 /96 /10 77 10 - #3 86 10 /96 /10 100 11 1/2" XS 75 10 /96 /10 100 12 1/2" XS 75 11/93/16 100 13 1/2" XS 75 11 / 102/6 100 14 1/2" XS 75 127 96/ 12 120 15 1/2" XS 75 12/96/12 80 16 1/2" XS 75 11/96/11 60 17 5/16" 85 190/25/35 120 18 9/32" 85 190/25/35 120 41 Figure 14 shows a typical time-temperature response measured at the back of the copper substrate as a result of heating from the plasma torch using parameters described in Test 3. In Figure 14, 'Centre of Plate' refers to the position at the centre of the plasma flame distribution and 'Edge of Plate' refers to position furthest away from the flame centre. 42 Since all of the time-temperature curves in this category of experiments are similar in form to that shown in Figure 14, the temperature data from the various runs have been assessed on the basis of the temperature at the centre of the copper disk, designated T/C 1. The results for Tests 1 - 18 are plotted in Figure 15 to Figure 18. Figure 15 shows the temperature measured at different stand-off distances in Test 1 to Test 6 using nozzle #6, and Figure 16 shows the temperature measured in Test 7 to Test 10 using nozzle #3. In Figure 17, the change of temperature with hydrogen gas flow (Test 11 to Test 13) and stand-off distances (Test 11, Test 14 to Test 16) are noted. The temperature - time plots using plasma spray parameters of WC-17% Co and CP Ti are shown in Figure 18. 1000 Test 1 and Test 2 used 12 mm thick copper disk Test 3 to Test 6 used 5 mm thick copper disk ' • • 1 ' 1 • • • • 1 • • • • 1 ' • 1 • 1 1 1 • 1 10 20 30 40 50 Time (second) 60 70 Figure 15: Centre temperature - time plots for Test 1 to Test 6 Figure 16: Centre temperature - time plots for Test 7 to Test 10 600 500 400 O « 300 h Q. E 0) 200 100 Q I , , , , I , . , . I , , , , I 0 10 20 30 40 50 60 70 Time (second) Figure 17: Centre temperature - time plots for Test 11 to Test 16 44 250 200 O 9- 150 0 « Q. 1 1 0 0 r-50 0 0 1 0 20 30 40 50 60 70 Time (second) Figure 18: Centre temperature - time plots for Test 17 and Test 18 Temperature data presented in Figures 15 to 18 will be analysed and discussed in Chapter 6. 4.1. 2 With Powder Deposition As discussed previously, the system used in this investigation is a tri-axial reactant feed plasma torch which uses three distinct electrodes arranged 60° apart from each other. Based on the design of this system, the distribution of powder is not completely axi-symmetric. Thus to make the experiment amenable to subsequent modelling, the substrate being coated was rotated rapidly in order to make the coating axi-symmetric about the axial centre of the torch. The experimental procedure described in the last section for no powder was modified in the following manner. 45 A smaller disk made of AISI-1008 steel, 100 mm (4") in diameter and 6 mm (0.236") thick, was used. Four unsheathed fine gauge type K, 0.25 mm (0.010") diameter thermocouples were resistance welded, with thermocouple wires separated 1 mm (0.04") apart, either at the back (Test 19 to Test 21) or 4.5 mm (0.175") deep from the surface of the back (Test 22, Test 23) at locations shown in Figure 19. Locations for T/Cs ->| | * - 0.04 4— T/C wires are welded on the back flushed with the surface in Tests 19 to 21 0.125 DIA. 0.175 0.079 0,> 0.315 '09 8 / t L — • In Tests 22 & 23, T/C wires are welded 0.175" from the back 1.457 (from Center) surface and hole is then filled up with resin H e o t D i s c AISI - 1008 Steel (All dimensions are in inches) 0.472 C a s t M o u l d ABS Figure 19: Steel disk used for plasma spray deposition The whole assembly was then laid on a acrylonitrile-butadiene-styrene (ABS) mold. A cast slurry mixture was employed to cover all areas of the steel disk except the 46 surface to be plasma sprayed. The slurry was made of 1 mm diameter bubble alumina (hollow alumina granules) and epoxy resin. The cured alumina / epoxy mixture then served as a surface insulator. The surface to be plasma sprayed was cleaned and grit blasted before plasma spraying. During the process, the steel disk assembly was held in a fixture (Figure 20) rotating at 200 revolution per minute. The thermocouples attached at the back of the steel disk were connected electrically via a slip ring assembly, mounted at the centre of the fixture, to a digital data logger sampling at 5 Hz. The coating powder was fed to the plasma jet by carrier gas (argon gas was used) once the plasma torch was ignited and stabilized. The plasma torch was allowed to swing to the centre of the steel disk either manually (Tests 19 through 21) or by a robotic arm moving at a velocity of 800 mm/s (Tests 22 and 23) at the pre-determined stand-off distance above the disk and allowed to deposit the coating material for 1, 2 or 3 seconds. Table U lists the spray parameters and the powder used in Test 19 to Test 23. Powder Zirconia 9204 has the composition of 8 wt% Y 2 0 3 - Z r0 2 . Praxair - WC516 contains 17 wt% Co in W C and Micron Metals Ti is CP titanium. Figures 21 to 25 show the respective time-temperature response, during plasma spray deposition, measured at the back of the substrate from Test 19 to Test 23. These temperature data will be used for the verification of the mathematical model discussed later in Chapter 7. 47 <|> 5.984 0.400 2.963 0.472 2.165 Mill bottom fixture (4 each) and flush with fixture holders <|>0.125x 0.400 Set Screw (Cone Point) 8 each lop Fixture Mild Steel (1 each) 0.120" diameter hole (4 each) on 1.250" pitch circle diameter Bottom Fixture Mild Steel (1 each) 0.438 0.375 375" 2.875 0.375" 0.625 0.500 0.375 2.00 2 each Fixture hblder 0.250 diameter M i l d s t e e , bolts per assembly (4 eacn) Figure 20: Holding fixture for the steel disk 48 Table II: Spray Parameters and Coating Materials used in the Experiments Test Powder Powder Feed rate Deposition Time Spray Parameters 19 Zirconia 9204 * 48 g/min 1 second same as Test 15 20 Zirconia 9204 * 48 g/min 2 seconds same as Test 15 21 Zirconia 9204 * 48 g/min 3 seconds same as Test 15 22 Praxair-WC516 ** 134 g/min 3 seconds same as Test 17 23 Micron Metals Ti *** 27 g/min 3 seconds same as Test 18 Notes : 8% yttria partially stabilised zirconia, powder size (-140+15um), Zircoa Inc., 31503 Solon Road, Solon, OH 44139, USA. 17% Co sintered tungsten carbide, powder size (-270+1 l|im), Praxair Surface Technologies, Inc., 21 Plants Worldwide, Indianapolis, IN 46224, USA. CP titanium, powder size (-90+63u.m), Micron Metals, Inc., 7186 W. Gates Ave., Salt Lake City, UT 84120, USA. 250 200 150 O o <D Z3 « i o Q. .1 100 50 h i i i i i i i i I i i i 1 sec. deposition of 8 wt% Y 2 0 3 - Z r 0 2 T / C 4 • ' ' 1 1 • • ' ' 1 1 1 1 ' 0 10 20 30 40 50 Time (Second) Figure 21: Temperature - time plot for 1 second zirconia deposition (Test 19) 350 300 250 O o 2 200 ns i — CD CL E 150 o> I -100 50 T/C 1 2 sec. deposition of 8 wt% Y 2 0 3 - Z r 0 2 10 20 30 Time (Second) 40 50 Figure 22: Temperature - time plot for 2 seconds zirconia deposition (Test 20) 450 400 350 ^ 300 O O £ 250 to g. 200 E CD 150 100 50 h 0 i i i i i i i i i i i T/C 1 i — • — | i i i — i — | i i 3 sec. deposition of 8 wt% Y 2 0 3 - Z r 0 2 0 10 20 30 40 Time (Second) Figure 23: Temperature - time plot for 3 seconds zirconia deposition (Test 21) 500 400 h 0 - 3 0 0 <D v_ « s 01 Cl E 100 h 3 sec. deposition of - T/C 1 W C - 1 7 % C o Composite -T / C 2 \ \ -- | T / C 3 U > * T/C 4 0 10 20 30 40 50 60 Time (second) Figure 24: Temperature - time plot for 17 % Co-WC deposition (Test 22) 51 Figure 25: Temperature - time plot for CP titanium deposition (Test 23) 4.1. 3 Error Evaluation and Assessment Throughout each of the experiments, a great deal of effort has been made to ensure that the position of the torch was located at the centre of the target. The procedure was as follows: before setting to the determined stand-off distance, the plasma torch was first lowered close to the target. An inspection tool, made of transparent film marked with a series of concentric rings, was used for positioning the torch and for examining the position of the deposit. The robotic arm played an important role here because the position of the arm can be precisely located. The experiments and the subsequent deposits were all examined visually for concentricity. Any test exhibiting an eccentricity greater than 1 mm was discarded. 52 In order to achieve the maximum response time of the thermocouple, intrinsic fine gauge thermocouple wires (i.e., substrate itself acts as one of the materials comprising the thermocouple and forms part of the electrical circuit between thermocouple poles) were attached independently to the metallic substrate (see View " A " of Figure 13). The response time of an intrinsic thermocouple can be determined from the elapsed time (r| 95%) of the thermocouple junction necessary to reach 95% of its steady state voltage. The elapsed time {t I 95%) is expressed in the following equation [69]. 11 95% - ~ 2 5 ( & Y k t c \ (1) \UsubJ \ksubj where 8 is the diameter of the thermocouple wire, a suf, is the thermal diffusivity of the substrate, and ktc and ksui, are the thermal conductivities of the thermocouple wire and substrate, respectively. In the experiment of this investigation (Tests 1 to 23), 0.25 mm fine gauge Type K (nickel-chromium/nickel-aluminum) and Type T (copper/copper-nickel) thermocouples were used. Using Equation (1) and the thermophysical properties listed in Table HI (as reported in the literature [68, 69, 70]), the response times of temperature measurements in this study were estimated and are listed in Table rv. As shown in Table IV, the largest elapsed time necessary for the thermocouple junction to reach 95% of its steady state voltage is 2.4 ms, which is about one one-hundredth of the sampling time employed in this investigation. Thus, the response time of the thermocouple will not introduce a major error. 53 Table III: Thermophysical Properties of Thermocouple and Substrate Materials used in this Investigation [68, 69, 70] Material Temperature (°C) k (cal / sec-cm-°C) a (cm 2 / s) nickel-chromium 20 0.046 0.049 nickel-aluminum 20 0.071 0.066 copper 20 0.934 1.135 copper-nickel 100 0.054 0.061 steel (AISI-1080) 20 0.144 0.164 Table IV : Estimated Response Time of Thermocouples used in the Study Thermocouple wire Substrate H 95% (sec) nickel-chromium steel 1 .6xl0~ 3 nickel-aluminum steel 2.4 x 10 ~3 nickel-chromium copper 2.6 X 10 ~5 nickel-aluminum copper 4 . 1 x l 0 " 5 copper copper 5.5 x 10 " 4 copper-nickel copper 3 . 1 x l 0 ~ 5 54 As mentioned previously, the heat flux delivered from the plasma torch to the substrate target has been estimated by the inverse heat transfer technique. Since the inverse analysis of this process constitutes an ill-posed problem, the heat fluxes calculated from this method can be expected to contain error. To help address this problem, a pure copper target has been employed for heat flux estimation as pure copper has one of the highest thermal diffusivities of the metals and therefore yields large sensitivity coefficients (A77A<2) in the inverse calculation (see Chapter 6). In other words, pure copper yields a high temperature change per unit change of surface heat flux. This result is important from the stand point of heat flux estimation as the inverse calculations become less sensitive to thermocouple noise. The plasma spray deposition of 17% Co-WC composite performed in Test 22 did not exhibit a typical Gaussian profile, as would be expected. Instead, a crater was formed at the centre of the profile. One possible explanation for this is that the spray rate could have been higher than the solidification rate, which could lead to the formation of the crater as reported and discussed in the literature [38]. This condition leads to the occurrence of a liquid phase on top of the solid coating which can be partially blown away by the high velocity plasma jet at the centre of the plasma torch. Detail analysis of the occurrence of a liquid phase on top of the 17% Co-WC plasma spray coating will be discussed in Chapter 7. Finally, the insulator used in the experiments was not perfect as there was heat loss through the insulator. As a consequence, the back of the insulator was warm after each test 55 and the temperature was raised to about 50 °C as measured by an infrared pyrometer, 90 seconds after the plasma torch was removed from the substrate. 4. 2 Powder Deposition Profile During plasma spraying, the deposited material releases its sensible heat to the material it is in contact with via conduction. In order to evaluate the quantity of heat transferred to the relatively cold substrate, knowledge of the rate of change of coating thickness and the coating radial distribution are needed. The rate of change of coating thickness and the coating distribution can be estimated directly from a profile of the deposited coating provided the coating is reasonably thick (> 0.5 mm). Figure 26 shows a typical profile which was obtained in Test 20. This was obtained for 8wt % yttria-zirconia powder sprayed continuously for 2 seconds with the torch held stationary and the sample rotating (maximum coating thickness was approximately 1.25 mm). In cases where the coating material is prone to crater formation, via the mechanisms discussed earlier in Section 4. 1.3, the rate of change of coating thickness and powder deposition distribution must be obtained by analyzing a profile obtained from multiple passes with the plasma torch. This is necessary to avoid crater formation while at the same time obtaining reasonable coating thickness (> 0.5 mm). The dimensions of the multiple-pass profile, combined with the plasma torch velocity and the number of passes, are used to estimate the rate of change of coating thickness and the coating distribution. This method is also suitable for coatings produced from a low powder spray rate. 56 30.0 30.0 20.0 17.5 r > 10 125 *fP 10.0 17.5 Figure 26: Surface topography of 2 seconds zirconia deposition conducted in Test 20 Based on the measured profile, the coating distribution and thus spray distribution can be fitted to Gaussian distribution of the form Dr - D0 exp f \2 r (2) where r is the axial location, Dr is the distributed rate of change of coating thickness, D0 is the maximum rate of change of coating thickness at the torch centre and % is the distribution coefficient. Table V shows the estimated values of DQ and % of 8 wt% Y 2 0 3 - Z r 0 2 sprayed for 2 seconds (obtained in Test 20), for W C - 17% Co after 60 passes of the plasma torch moving at 800 mm/s and for CP titanium after 134 passes at 800 mm/s. These coating contours and their estimated distribution are illustrated, respectively, from Figure 27 to Figure 29. Included in each of the figures is a goodness-of-fit defined as follows : 57 goodness - of - fit = ^ £ (empirical data - fitted data)^ In Variable n in Equation (3) is defined as the total number of data. The goodness-of-fit used in this study bases on the least-squares method. The user-specified fitting function is utilized in such a way as to minimise the sum of squares of distances between the empirical data points and the fitting data. The smaller the number of the goodness-of-fit the better fit is the empirical data to the fitted data. Table V : Estimated Rate of Change of Coating Thickness and Powder Distribution Powder Rate of Change of Distribution Remarks Coating Thickness Coefficient (%) (D0) 8 % Y 2 0 3 - Z r 0 2 6.07 x 10"4 m/s 6.48 x 10"3 m 2 seconds as in Test 20 17% C o - W C 8.49 x lO" 4 m/s 5 .13x l0" 3 m 60 passes at 800 mm/s C P T i 1.39xl0- 4 m/s 9.55 x 10"3 m 134 passes at 800 mm/s 58 Figure 27: Powder distribution of zirconia after 2 seconds direct plasma spray deposition 1.6 1.4 1.2 E 1 ' ° E, | 0.8 Q. 03 Q 0.6 0.4 0.2 0.0 i i I i i i i I i i i i I i i i i I i i i i I i i i i Goodness of Fit Estimated distribution 0.101 mm • Experimental data -15 -10 -5 0 5 10 Radial distance from centre (mm) Figure 28: Powder distribution of plasma spray deposition of 17% Co-WC after 60 passes at 800 mm/s 59 1.0 0.8 f 0.6 E. '55 o Q. CD Q 0.4 0.2 0.0 -10 0 10 Radial distance from centre (mm) Figure 29: Powder distribution of plasma spray deposition of CP titanium after 134 passes at 800 mm/s 4. 3 Microstructure Evaluation The amount of heat delivered to the coating system has influences the coating microstructure [51, 71]. The plasma sprayed zirconia based coatings prepared in Tests 19 through 21 were mounted and polished for microstructure analysis. To insure that the microstructure was representative of the coating, special care was taken during sample preparation. Prior to sectioning of the samples, the relatively porous plasma sprayed zirconia coatings were vacuum pre-impregnated with Struers® (Westlake, Ohio, USA), Epofix cold cured liquid resin. This prevents the coating from mechanical damage during cutting and sectioning. The coating and the substrate backing were then sectioned into 10 mm long by 5 mm wide strips using Buehler® (Lake Bluff, Illinois) Isocut waffering blade 60 rotating at 200 rpm. The coating / substrate strips were vacuum mounted in Epofix resin mold. The surface was ground and polished to 0.1 | im finish. The samples were examined under an optical microscope. Micro-photographs of 1 to 3 seconds deposition of zirconia coatings are shown in Figure 30 through 32. Figure 30: Micrograph of 1 second deposition of zirconia conducted in Test 19 (13X) Figure 31: Micrograph of 2 seconds deposition of zirconia conducted in Test 20 (13X) Figure 32: Micrograph of 3 seconds deposition of zirconia conducted in Test 21 ( 9X) 61 As shown in Figures 30 to 32, multiple cracks along the direction of heat flow appear in the samples examined. These cracks appear to have originated at the free surface of the coating and propagate toward the relatively cold substrate. The cracks being opened up to the free surface of the coating implies that cracks may be initiated after the completion of the deposition process. As can be seen in Figure 30 and 31, the cracks seem to be equally spaced. This phenomenon is similar to that observed by Garrett and Bailey [72] in glass fibre-polyester resin cross-ply laminate in which equally spaced cracks were formed in the relatively weak polyester matrix when the composite was subjected to a tension strain to 1.6%. This implies that the zirconia based coating was subject to a substantial amount of thermal stress during plasma spray. For a 3 second deposition of zirconia based coating, delamination takes place at the coating / substrate interface which appears to be connected with two large cracks across the coating (Figure 32). The temperature gradient across the thick coating was expected to be high in thick zirconia coating which generated an acute level of thermal stress across the coating. The thermal stress was relieved once the coating cracked. Further investigation at higher magnification optical microscope indicated that the zirconia based coating contained a considerable amount of porosity. A closer examination under the scanning electron microscope revealed these pores varied in size and distribution at different locations within the coating. Pores located at the coating / substrate interface appeared larger and were inter-connected. At the centre near the free surface of the coating, however, pores were closed and isolated. Large pores at the coating / substrate interface were expected since zirconia based particles were less likely to spread upon impact on the substrate surface since they are quenched quickly compared with particles 62 deposited further away. As the zirconia based coating is built up, heat loss through the surrounding was less than the heat supplied by the particles and by the plasma flame. The temperature at the free surface of the coating could be well above the melting point of the coating and the material at this region might remain in liquid form for a substantial period. The molten material was likely to flow thus closed up the pores. The variation in pore morphology at different locations within the zirconia based coating is consistent with variations in the thermal history of the coating discussed later in Chapter 7. A general view of the areas of investigation is illustrated schematically in Figure 33. Scanning electron micro-photographs of these areas are shown in Figures 34 through 36. Finally, the 2 second deposition sample of zirconia was examined employing an image analyser to quantify the amount of porosity. It was confirmed that areas close to the substrate / coating interface exhibited a higher porosity than areas near the free surface of the coating, Figure 37. 63 Figure 33: Schematic of the locations of pores examined Figure 34: SEM photograph of pore found at 150 pm from substrate 65 6 3 1 1 9 2 20KV X 3 ! 0 6 K " l S ! S u m Figure 35: S E M photograph of pore found 600 um from the free surface of the coating 66 0 3 1 1 9 1 20KV X 3 ! e e K: " ieiSum Figure 36: SEM photograph of pore found at 150 urn from the free surface of the coating 67 4.6 7.6 17.3 6.0 11.4 17.9 6.8 9.6 12.6 10.5 15.1 9.6 13.2 9.4 15.5 16.3 19.9 13.6 19.0 13.6 12.2 % Porosity Figure 37: Porosity measured at different locations of zirconia coating conducted in Test 20 4.4 Summary In this chapter, the results of experimental tests conducted under various operating conditions have been presented. In addition, the errors associated with the temperature measurements in this investigation were assessed. Metallogfaphic examination of the as-sprayed zirconia based coating indicated that the splats that make-up the coating had experienced a thermal history dependent on proximity to the coating / substrate interface. The equal spaced cracking of the zirconia based coating resembles multiple cracking of composite material under substantial level of 68 thermal stress. Different size and distribution of pores found at different locations of the zirconia based coating appear consistent with a qualitative understanding of the evolution of temperature in the coatings examined. 69 CHAPTER 5 MATHEMATICAL MODEL DEVELOPMENT In order to analyze the various experiments and understand of the temperature evolution in the coating and in the substrate during plasma spray processing, it was necessary to develop a fundamentally based heat flow model of the coating / substrate system. It was intended that this model could be used as part of an overall process model capable of predicting the evolution of stress as well as, ultimately, microstructure in a coating. The simulation and/or calculation of the heat flow conditions prevalent during plasma spray deposition present a number of challenges owing to the fact that heat transfer in the process is occurring over vastly different scales. For example, as a splat impinges on the substrate or on previously deposited coating, heat transfer occurs over a scale of microns, whereas, in the coating conduction may occur on the scale of millimeters, and in the substrate, on the scale centimeters or even meters for large components. In addition, the analysis is further complicated by the fact that there is the incremental addition of material to the domain of the analysis, as deposition takes place, as well as solidification occurring with the associated latent heat release. In order to address the issue of scale, the approach taken in the present investigation was to formulate and couple a "macro model" describing the flow of heat in the substrate with a "micro model" describing the flow in the coating. A general finite element engine is used to calculate the evolution of temperature in the substrate [67]. In order to complete the heat balance, the macro model requires a knowledge of the evolution of temperature or alternatively the heat flux at the interface. This information is provided 70 by the micro model which is a 1-D transient finite difference engine. The domain of the 1-D micro model is perpendicular to the substrate coating interface and changes in length consistent with the incremental addition of material. The 1-D micro model is applied at a series of discrete positions along the substrate / coating interface in accordance with the requirements of the finite element macro model (the macro model requires an interface heat flux at each of the Gauss integration points, as will be defined in Section 5.1.1.3). The nodal spacing employed in the 1-D finite difference model is consistent with the quarter of the average size of a splat (2.5 pm) whereas the element size employed in the macro model is approximately 300X larger. The method used to couple the two models and account for variations in rate of change of coating thickness with distance from the torch axis are discussed in detail later. The basic concept is illustrated schematically in Figure 38. This chapter describes the formulation and verification of the finite element macro model and the finite difference micro model used in this investigation. 5.1 Macro Scale Heat Flow Model For the analysis of heat flow in the substrate, a two dimensional axi-symmetric model was used. The analysis domain, mesh and material type employed in the analyses are listed in Appendix 1. Figure 39 shows the coordinate system adopted for the analysis. The origin was taken to be at the disk centre on the deposition surface. 71 P l a s m a t o r c h H e a t Flux Dis t r ibut ion / / / / X:oat ^ C o a t i n g (0,0) substrate "sub F D M M I C R O q(0 net 10 urn O) c t o sensible ^ Tsub C\(r)\ • substrate 'int F E M M A C R O Q(0 int Tsub^ substrate e l e m e n t 1.5 mm Figure 38: Schematic drawing showing the micro-macro models used in this research program. 72 deposition surface Figure 39: Configuration of cylinder used in the FEM model 5.1.1 Formulation The differential equation describing the flow of heat in a cylinder of a material whose properties are invariant with temperature and there are no gradients in the angular, 0, direction is: ^ r _ i _ a r (4) dr2 r dr dy2 a dt with the applicable boundary conditions. Equation (4) is solved by applying a finite-element discretization of the spatial derivatives. The linear system of ordinary differential equations which results from this approach is then solved using a step-by-step marching technique for integration in time. 73 5.1. 1. 1 Finite-element Discretization of Spatial Derivatives The finite element method is based on the assumption that the variation in temperature V over the domain of the element may be approximated by the following expression. ? e (r ,y ,0) = i/V,.(r,v)7;e(r) ( 5 ) where, N-t are the nodal interpolation functions of a degree which is dependent on the total number of nodes per element, n. Applying the Galerkin criterion [73] to the heat conduction equation with a general set of boundary conditions yields the following system of equations at the elemental level: [cjin+[Kj{T}={fY (6) where, [Kilj = \ v Bj k Bj dV + \A hi Ni Nj dV (7) [Cilj = jvpCP NiNjdV (8) {fihivQNidV-isli N J d S + ishi NJ TambdS (9) In the axi-symmetric case, dV described in Equations (7), (8), and (9) can be defined as dV = 2n r dr dy. In Equation (6), the [K] matrix is recognized as the temperature stiffness 74 or temperature influence matrix which is, in turn, dependent on the B matrix, and the k or thermal conductivity matrix, defined by the following equations, respectively : B (10) Bj = VNj (11) and kr 0 0 ky (12) k = Equation (9) is called the force vector / and includes those terms which drive the system such as internal sources of heat, Q, external sources or sink of heat, q, and heat-transfer coefficients, h, applied to boundaries. The terms required to describe the plasma spray process are discussed in Sections 5. 1. 2 through 5. 1.6. 5.1.1. 2 Element Type Based on a review of the element types available, Cockcroft [67] chose the curve-sided, isoparametric, quadratic temperature elements. An eight node version was used in the two-dimensional axi-symmetric case. For the purpose of this investigation, the isoparametric formulation gives the ability to represent elements of arbitrary shape with good accuracy and with a reasonable amount of computational overhead. The penalty for using this type of element is a slightly increased computational cost as Equation (7) through (9) must be integrated numerically. 75 5. / . / . 3 Numerical Integration There are various procedures for numerical integration over the domain of an element. The Gaussian quadrature technique is well suited to the finite-element techniques since the overall computational effort is kept to a minimum. The general two dimension axi-symmetric form of Gaussian quadrature integration forn sampling points is given by where, W,- and Wj are the weighing coefficients at location / and j respectively, and m is the number of integration Gauss points (Gauss points are sampling points which allow the best possible accuracy for numerical integration in finite element analysis) within the domain of the element. This numerical technique also allows for the convenient handling of temperature dependent material properties and spatially dependent boundary conditions and, thus, is well suited to estimate temperature distribution of a plasma spray system. 5.1.2 Domain Since axi-symmetric analyses have been used in all of the specifications of the finite element models, the physical domain can be described as : (13) 0.0 < r < R, max (14) 0.0 < y < F r max ^max a n c * *max described in Equations (14), (15), (18), (19) and (22) are reported in Appendix 1 as : 76 Rmax = 70 mm for Tests 1 to 18; and 50 mm for Tests 19 to 23. F m a x = 12 mm for Tests 1 & 2; 5 mm for Tests 3 to 18; and 6 mm for Tests 19 to 23. 5.1. 3 Side Boundary Condition In the experimental set-up, the side and the bottom surfaces of the cylindrical target were insulated with a ceramic. Assuming perfect insulation, the boundary condition on these surfaces of the target can be expressed as -k dT sub (15) r=R,r dT Sub d^sub =0 (16) Jsub r^ri 5.1. 4 Symmetry Conditions In the two dimensional axi-symmetric model, it is assumed that there are no temperature gradients in the theta (9) direction allowing for •* - I =0 (17) r=0 5.1. 5 top Surface Boundary Condition The characterization of the top surface boundary condition is one of the primary objectives of this research. In general, there are as many as three heat transfer processes 77 operating at this surface in the absence of powder deposition. These are 1) heat input due to the impingement of the plasma torch, 2) heat loss due to radiation to the surrounding and 3) heat loss due to convection to the surrounding. Mathematically, heat transfer at the top surface boundary during plasma torch heating can be written as Ksub dySub (18) ~ a torch ~^~Qconv ~^"arad ySub=° where qtorch, qconv and qmd are heat fluxes associated with impingement of the plasma from the torch and convection and radiation to the surrounding environment. During heating, all of these transfer mechanisms can be brought together into one positionally dependent term called, qnpfasma, which represents the net total flux transferred to the substrate in the absence of powder deposition. The positional dependence will reflect the temperature and flow distribution arising within the plasma flame. Thus, in the absence of powder, the top surface boundary condition may be expressed as 'Sub 'dy; sub (19) _ net / \ ~y plasma V ' During powder deposition, the mathematical description of the top surface of the substrate becomes more complex as heat is transferred from the hot powder being deposited on the surface and from the plasma flame in those areas not shielded by the coating. Mechanistically, the transport of powder in the flame will result in the transfer of enthalpy and momentum from the plasma to the powder. In general, the powder distribution within the flame will be significantly different than the plasma flame 78 distribution owing to the fact that the powder particles are orders of magnitude more dense than the plasma. In the particular system under investigation, it was observed the plasma flame distribution was approximately 10X wider than the powder distribution. In view of this, during powder deposition, the boundary condition for the surface of the substrate may be expressed as 'Sub sub (20) = <lua(r) + <l"ZLma(r) :v Sub= 0 where qint (r) is the substrate / coating heat flux and qmpelasma{r)is the deposition power transfer from the plasma flame. The first term on the right hand side of Equation (20) represents the heat conducted from the hot coating to the cooler substrate and is non-zero at radial positions where there is a finite deposition rate. This quantity is a function of the temperature distribution within the coating and the conductivity of the coating and, therefore, must be calculated based on a heat balance on the coating. The details of this procedure are discussed in Section 5. 2 on the formulation of the micro model. The second term on the right hand side of Equation (20), q,npe(asma (r) , is non-zero at radial positions where the plasma flame is striking the substrate and the powder deposition rate is zero. In the present investigation it is assumed that the heat flux distribution associated with the plasma flame is unaffected by the presence of powder. The validity of this assumption will be borne out by comparison of the model prediction to measured temperature data. Thus, the heat flux distribution obtained from the analysis of the no-powder experiments can be used. To account for the transfer of enthalpy to the powder the net applied flux is reduced by the amount of heat absorbed by the powder. Hence, the 'prime' in q,np!asma(.r) > distinguishes this term from q"pei'asma. The estimation from qpfasma to 79 q,npiasma(r) requires several steps. Basically it has been done by subtracting the power required to heat the powder up to the plasma spray temperature from the net total power delivered from the plasma flame in the absence of powder, assuming the power distribution remains constant. A review of the literature on modelling plasma spraying and on the characterization of plasma flames suggests that the power distribution within the flame can be represent by a Gaussian or normal distribution as shown in Figure 40 [38, 55, 64]. Thus, based on a review of the literature, the heat flux distribution q"pfasma (r), in Equation (19), can be represented by: (21) r 21 V J where qQ is the net total flux at the centre of the plasma flame (r = 0) and C is the distribution coefficient. Parameters qa and C in Equation (21) are sufficient to describe the power distribution when a circular flame pattern is centred on a cylindrical target (the axi-symmetric case). In these study, these two parameters (q0 and C) could be estimated from the inverse heat transfer analysis of experimental thermocouple data. 80 substrate heat source q( r ) = q 0 e x p { - ( 7 c r ) Figure 40: Schematic of a Gaussian distributed heat source. Once the plasma torch is removed and the target begins to cool, the equation describing heat transfer at the top surface boundary became: dT vsub sub qint (r) + a 8 s u b ( 1 4 - T1)+h (T-Tx) (22) y s u b = ° where the second term on the right-hand side of Equation (20) has been replaced by the heat-loss due to radiation and due to natural or forced convection. In Equation (22) a, e s u b, and T M represent the Boltzmann constant, the emissivity of the substrate, and the ambient temperature, respectively. 81 5.1.6 Initial Conditions The initial temperature of the target in all of the tests was reasonably close to room temperature. Between experiments the targets were cooled to attain an approximately uniform temperature. This was generally confirmed by ensuring that all thermocouples indicated close to the same temperature prior to starting the next experiment. Mathematically, the initial condition may be described as T(r,y)\t = Q = Ti (23) where T' in Equation (23) can be read directly from the thermocouple temperature data at the beginning of each experiment. 5.1. 7 Verification of the Macro Finite-element Code Cockcroft [67] verified his computer code using analytical solutions for various specific conditions. This verification included one-dimensional heat conduction with a heat transfer coefficient boundary condition and one-dimensional heat conduction with a phase change. Tripp, on the other hand, examined and verified Cockcroft's code for a two-dimensional axi-symmetric heat conduction with a heat transfer coefficient boundary condition [74]. Since the plasma spray process involves a heat flux boundary condition in this investigation, an analytical solution for a constant heat flux applied to one plane of a slab was used to verify the two-dimensional axi-symmetric heat conduction problem with heat flux boundary condition. 82 The governing partial differential equation for the simplified problem is given by Equation (4), with the boundary and initial conditions defined as follows : dr dT r = 70 mm ^ s u b (24) dT *"sub ^ s u b y s u b = 3.3 mm 20 kW ySUb=o T(r,y) = 0, t = 0 The analytical solution to the problem defined by Equations 4 and 24 has been obtained from Carslaw and Jaeger [75]. rp ff^max k 3(^ max - v ) 2 - ^ m a x 2 2 ^ (-l)W - k , .2 ±-i „2 6K, e { n n / Y m ^ cos (25) q t Figure 41 shows the comparison between the analytical solution and the finite-element model. The thermophysical properties were set to averages for IN-718, a nickel based superalloy, {k = 11.4 W/m/K, Cp = 435 J/kg/K, p = 8190 kg/m3). The model predictions were output at locations y = 0, 0.5, 1.4, 2.5 and 3.3 mm, for comparison to the analytical solutions. Tripp performed a similar analysis on titanium with different working parameters [74]. Both analyses indicate the formulation of the finite-element model is numerically correct. 83 o 12 "—"•—i— 1 — 1 — 1 — r ~ - i 1 . 1 1 1 1 Goodness of Fit Curve 1 0.0244 °C Curve 2 0.0050 °C yy -< 8 Curve 3 0.0018 °C Curve 4 0.0007 °C /(/// -Curve 5 0.0008 °C 4 7 / S J Analytical Solution • Finite-Element Model 0 I i 1 0 2 4 6 Time (Second) Figure 41: Comparison between the analytical solution for a cylinder with a constant heat flux applied to one end and the finite-element solution. 5.2 Micro Scale Heat Flow Model During plasma spraying, fully or partially molten particles of the average diameter of 60 urn are propelled at subsonic velocity towards the substrate target. Upon impact on the substrate, the particles deform severely and quench rapidly at a rate of the order of 10 7 oC/s. The sensible heat released from the particles is substantial and is approximately 300 times greater than the kinetic energy of the particles (comparison of calculated kinetic energy and heat energy of single particle). The typical thickness of a splat is around 10 u,m as determined from microscopic examination of the coating which is consistent with an aspect ratio of approximate 14. The following section describes the development of a one-84 dimensional micro model, based on the implicit finite-difference method, which has been formulated to quantify the heat transferred from the particles to the substrate. As previously discussed, the advantage of using a micro model is that the temporal and the spatial resolution can be very small compared to that used in the finite-element macro model, to describe heat flow in the substrate, while at the same time yielding a computationally tractable problem. The size of the nodal distance used in the finite-difference model is about 300 times smaller than the size of the element used in the finite-element model, along the heat flow direction. The domain encompassed by the micro model increases with the coating thickness in accordance with the local deposition rate. In essence, a series of micro models are used to determine the heat flux at the Gauss integration points in the macro substrate model along the coating / substrate interface boundary. The heat flux is determined based on the temperature gradient in the coating at the interface. The resulting interfacial heat flux, qmt, is then coupled with the macro finite-element model for macroscopic temperature calculation. The inherent assumption in this approach is that heat transfer in the coating occurs in one-dimensional perpendicular to the substrate / coating interface. 5. 2.1 Formulation The conservation of thermal energy within the coating is governed by the time dependent heat conduction equation which may be expressed in one-dimensional form as: 85 d2T \dT (26) dy2 a dt The origin in the coordinate system used in the analysis is fixed at the substrate coating interface. As previously stated, the domain of the analysis increases with time in accordance with the local deposition rate. This approach is different than that adopted by El-Kaddah et. al. [38] in their study of heat transfer in the plasma flame and in the coating / substrate, in which the conduction equation is expressed in terms of a transformed coordinate x' whose origin corresponds to the surface of the deposit which is moving. Hence, in the present analysis it is not necessary to have the additional term in the conduction equation to account for the bulk flow of heat through the expanding coordinate system [38]. The expansion of the analysis domain is performed by adding the equivalent thickness of a splat, represented by 4 nodes, to the analysis. The integration time step employed in the model is selected to ensure that, at the location of the maximum deposition rate, a maximum of only one splat is added at a time. The initial temperature of the added layer of nodes is set equal to the estimated particle temperature. Using this approach, the sensible heat of the particle is accounted for in a manner analogous to what is actually occurring in the process. The boundary condition describing the flow of heat at the top surface of the coating becomes, dT > net plasma (27) -k, coat coat JcoatW 86 where q,npeiasma(r) is the deposition heat transferred to the target from the plasma flame corrected for the enthalpy loss to the powder, as previously described. Note that in Equation (27), the location of this boundary condition is a function of time consistent with the expanding analysis domain. Once the plasma torch is removed and the coating cools, heat is lost to the environment via radiation and convection as per Equation (28). c^oat dT dy coat 4 4 ( 2 8 ) ^max(r) Equations (26) through (28) have been solved via the finite difference method. The finite difference method has been chosen over the finite element method owing to its computational efficiency. Note that in general, the coating thickness, F m a x , at the end of the deposition will be a function of radial coordinate r. In the micro finite element model, latent heat of the depositing material is treated mathematically as an increase in the apparent heat capacity Cpeff and it is incorporated into the specific heat values. The approach had been reported previously to account for the latent heat released during the solidification of metals [76, 77, 78]. The algebraic equations of the micro model are described in Appendix 3. 87 5. 2. 2 Bottom Boundary Condition Within the macro model time step, the temperature at the bottom boundary of the coating was assumed constant and is evaluated based on the substrate temperature at the appropriate location. Thus, W l ^ ^ W ^ . o (29) where T0 (r) and rsub (r) are the interfacial temperature of the coating and the substrate respectively. 5. 2. 3 Coupling of Micro Model to Macro Heat Flow Model In the micro-model, four equal-spaced nodes are assigned to represent the temperature across a single splat. Thus, the nodal spacing was set to a quarter of the average splat thickness of the depositing material yielding a nominal nodal space of 2.5 pm. The properties of the coating material used in the model are reported in Appendix 2. The macro model calculates the temperature distribution of the substrate with the progression of time in a stepwise manner. In the study, this is defined as the macro time step, which has been set at one thousandth of a second. Within the macro time step, the substrate temperature distribution is assumed constant. The temperature distribution of the coating, however, is up-dated every micro time step from the micro finite difference model. The micro time step varies from the minimum of 10"7 to the maximum of 10 - 4 88 second. The minimum time step prevails when the nodes pass through the freezing range of the coating material in order to account for the latent heat released on solidification. Once the temperature at each node has been calculated, the heat flux across the substrate / coating interface is evaluated using the expression a(r). —k W~T^ (30) y v J i n t - ^coat A AVcoat where T0 (r) and Tj (r) are the first two nodal temperature next to the boundary interface; and A v c o a t is the nodal spacing. q(r\nt then serves as input to the macro heat flow model and is used to describe the flow of heat into the substrate at the coating / substrate interface. 5. 2. 4 Verification of the Micro Finite-difference Code In order to develop confidence in the micro model, it must also be validated. As before a simplified problem was chosen for validation. For this task the heat flow in a semi-infinite domain whose properties are invariant with respect to temperature was selected. The boundary and initial conditions describing the problem and employed in the model are 89 -k, coat dT d 3 W = 0 (31) Jcoat = 0 -k, coat dT ^coat = qnet W / m 2 W =1 m m The analytical solution to the problem defined by Equations (26) and (31) has been obtained from Carslaw and Jaeger [75] as follows. T = q"*y 8<? n e t r m a x £ (-if c-kt\«(2n+mr™)? 3 i n 7ty (2n + l) (32) y A; A:7C2 „=o(2n + l ) 2 2 7 m a x The output for the node at y = 0 was monitored to ensure that it did not change from the initial condition thereby violating the assumption of a semi-infinite domain. Figure 42 shows the comparison of temperature between the analytical solution and the finite-difference model. The thermophysical properties were set to averages for yttria stabilized zirconia alloy (k = 1.0 W/m/K, Cp = 600 J/kg/K, p = 5200 kg/m3). The constant heat flux (g n e t) was set to 1,000 kW/m 2 , which was selected to reflect typical average heat flux from a plasma torch. The output from locations y = 10, 200, 600, 800 and 1,000 pm was selected for comparison. 90 Figure 42: Comparison between the analytical solution for a semi-infinite slab with a constant heat flux applied to one end and the finite-difference solution. 91 CHAPTER 6 MATHEMATICAL ANALYSIS OF EXPERIMENTAL RESULTS Prior to the heat transfer analysis, one of the key boundary conditions must be determined by undertaking an inverse analysis of the measured thermocouple data. 6.1 Inverse Heat Transfer Analysis The inverse heat transfer techniques [74, 79, 80, 81] used in this investigation basically entail the calculation of unknown heat fluxes from known temperatures. In general, the inverse heat conduction problem can be divided into two classes: function estimation [82], and parameter estimation [83]. Function estimation is used for the determination of unknown functions such as the heat flow at the surface of a body or the heat transfer coefficient at the interface between two bodies. Parameter estimation is aimed at the evaluation of intrinsic properties of a material such as the thermal conductivity or the specific heat capacity. In the current investigation, function estimation has been undertaken. The solution technique of function estimation requires the use of a mathematical model which is capable of predicting the temperature distribution in the substrate subject to the heat flux [84]. For this purpose, the macro-model described earlier in Chapter 5.1 has been used. 92 6.1.1 Formulation The unknown heat flux at a given time can be estimated by minimizing a least square function of the difference between the temperature, Qj, measured by thermocouple, and the temperature, Tj, predicted by the model (at a particular location j) using the direct heat conduction method. In the technique employed, the continuous heat flux distribution sought is discretized into a series of constant heat flux segments, Qj, which when determined will approximate the unknown heat flux distribution as shown schematically in Figure 43. If the number of heat flux segments, Qj, are increased, the resolution of the continuous distribution will be improved. However, this will increase the numerical instability of the problem when a large number of parameters is to be estimated. Q Substrate Q Thermocouples Figure 43: Schematic of heat flux distribution used in inverse heat conduction 9 3 The effective sum of square of differences (S) for zeroth-order regularization has been defined as : where M is the number of discretized heat flux segments which, in this study, equals the number of thermocouples employed to measure temperature; 0^  is the temperature measured from the thermocouple; 7y is the temperature predicted by the model; a* is the regularization parameter; and Qj is the discretized heat flux imposed at the surface boundary of the model. The role of the coefficient a* in Equation (33) will be discussed later in this chapter. The minimum least squared error can be found by minimizing the function S in Equation (33) with respect to each variable <2& (k = 1, 2, 3, ... , M), which leads to a system with M equations and M unknown heat fluxes to be estimated. Each k t h equation can be written as follows: S= 1 ( 0 ; - Tj r +a * X Qj (33) 90k dS = - 2 X ( 6 , . - I } ) 7 = 1 M + 2 a I Qj = o (34) where k - 1,2,...,M 94 In the above expression, the derivative of the calculated temperature, 7), with respect to the heat flow, Qk, is called the sensitivity coefficient, Xjk , i.e., xjk -dTj (35) as it represents the change in the j t h temperature resulting from a change in the k t h heat flux segment. In this version of the inverse heat conduction method, an initial heat flux distribution Q°j is assumed resulting in an initial temperature 7°^ predicted by the model. The actual substrate temperature, Tj , in Equations (33) and (34) can be expressed in terms of the approximate temperature in a Taylor series form as: Tj = Tj + Xlj(Ql-Ql) + X2j(Q2-Qi)+...+XMj(QM-Q°M) (36) where Tj depends on the magnitude of ( Q°j , Q°2, , Q°M)-The second term on the right hand side of Equation (34) can be expressed as : * M 3Q, * M j , (37) 2 a J i Q j - ^ - j - = 2 a Z G r G } 7=1 7=1 where k = 1, 2, . . . , M and B:k is the zeroth-order regularization matrix which consists of 95 0 for i*j (38) B j k II f o r / = / Substitute Equations (36) and (37) into Equation (34) and rearranging the like terms, yields an expression of the form where and [A]{AQ}={f} (39) M # (40) Ajk = X Xij Xik + a Bjk i=l (41) M (42) Jj-l(Qj-Tpxij j = i {AQ} in Equation (39) and thus Qj in Equation (41) can be solved using a matrix solver. 6.1. 2 Validation of the Inverse Heat Conduction Calculation In order to validate the inverse heat conduction calculation, a time dependent heat flux distribution containing 14 heat flux segments (Figure 44) was input into the validated finite-element described earlier in Chapter 5.1 as the top surface boundary condition. In Figures 44 to 47, 'Centre of Plate' refers to the position at the centre of the plasma flame 96 distribution and 'Edge of Plate' refers to position furthest away (70 mm) from the flame centre. The thermophysical properties employed in the analysis were those of pure copper (see Appendix 2). In addition, the boundary condition was defined as follows : dT dr dT r — 70 mm = o (43) sub ysub = 5 mm T(r,y) = 25, t = 0 1400 1200 1000 h E 800 I 600 re x 400 h 200 Edge of Plate J i I i L 0 1 2 3 4 5 6 Time (Second) Figure 44: The initial heat flux distribution input to the model for validation of the inverse heat conduction code The output from the finite-element model was a set of temperature data predicted at the 14 locations as shown in Figure 45. This temperature data was then employed as hypothetical thermocouple temperature data and input to the inverse heat conduction model. Figure 46 shows a comparison between the heat fluxes determined from the inverse 97 heat conduction calculation without regularization (i.e., a* = 0) and the original heat flux distribution input to the conduction model. As can be seen, there is excellent agreement between the two heat flux distributions. 14011 i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i 2 0 h 0 f i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i 1 0 1 2 3 4 5 6 7 Time (second) Figure 45: Temperature profile estimated from the direct model. 98 1400 1200 1000 CM | 800 x E 600 <3 x 400 200 0 0 1 2 3 4 5 6 Time (Second) Figure 46: Comparison of heat fluxes between inverse estimation and original input data. 6.1. 3 Regularization of the Inverse Heat Conduction Calculation The estimated heat fluxes shown in Figure 46 have been calculated based on the "clean" ideal temperature data obtained from the thermal model. In practice, the thermocouple temperature data will inevitably include noise. This noise may result in considerable error in the heat flux estimated. To help alleviate this problem, a regularization parameter, introduced earlier in Equations (33), (34), (37) and (40), was employed during the inverse heat conduction calculation. To illustrate the influence of noise and the effectiveness of the regularization parameters, random "white" noise within the range of ± 1°C was superimposed in the temperature data presented in Figure 45, as shown in Figure 47, and input to the inverse heat calculation model with the regularization parameter set to zero and then to l x l O - 9 . " 1 1 • 1 ' Input Heat Flux 99 Without the use of the regularization parameter in the calculation, the estimated heat flux fluctuated dramatically and did not correlate well to the original input heat flux (Figure 48). In contrast, setting the regularization parameter to 1 x 10"9 yields a significant improvement, as illustrated in Figure 49. The use of a large regularization parameter is undesirable because the solution is over-damped and deviates from the exact results. Figure 47: Temperature data contaminated with ±1°C noise for inverse model verification 100 £ i. X 3 12000 10000 8000 6000 4000 — i 1 1 1 1 (- ±1°C Noise Superimposed Regularization Parameter = 0 CO a> X I 1 1 ' Input Heat Flux Inverse Estimation Goodness of Fit 5 _ L J_ 2 3 4 Time (Second) Figure 48: Heat flux estimated from noisy temperature data without regularization 1600 1400 1200 c J - 1000 £ CO CD X 800 600 h 400 200 0 —' 1 ' 1 ' 1 ±1°C Noise Superimposed Regularization Parameter = 1 x 10'9 Goodness of Fit Input Heat Flux Inverse Estimation Goodness of Fit H 2 3 4 Time (Second) Figure 49: Heat fluxes estimated from noisy temperature data with regularization parameter of 1 x 10"9. 101 6.1. 4 Evaluation of the Sensitivity Coefficients The sensitivity coefficients Xj^ defined earlier in Equation (35) can be calculated as follows : a) Using the heat conduction model with the initial heat fluxes imposed at the surface boundary, estimate the nodal temperature at the thermocouple locations. b) Using the same model and the same initial condition employed in step (a), perturb each initial heat flux by 10%, so that a new set of nodal temperatures at the same thermocouple locations is calculated. c) The sensitivity coefficient at a particular thermocouple location is calculated as the change of temperature due to the perturbed heat flux divided by the perturbation of the heat flux. d) Repeat Steps (b) and (c) until all discretized heat fluxes are perturbed. There are 14 thermocouple locations and 14 discretized heat fluxes considered in this investigation. In order to calculate all the sensitivity coefficients, each heat flux is perturbed sequentially and therefore Steps (b) and (c) have to repeat 14 times. Thus, the sensitivity coefficients can be represented by a 14 x 14 square matrix which is symbolized as [A] described in Equation (39). 102 6.1. 5 Optimal Regularization Parameters for Inverse Heat Conduction Calculation Ideally, the regularization parameter for input to the inverse model should be known ahead of time. In practice, however, as this parameter is problem dependent the optimum values for a particular analysis must be determined by trial and error [79]. The optimal regularization method developed by Huang and Ozisik [85] was not suitable for this study. This is probably due to the fact that the initial heat flux and initial temperature have to be considered for the analyses used in this study. To find the optimal regularization parameter for the 12 mm thick copper block, temperature data collected in Test 1 was used. This was done using the following method: First, the discretized heat fluxes along the top surface boundary were estimated using the inverse heat conduction calculation. The optimal regularization parameter was then selected to be the one which produced the minimum difference between the Gaussian heat flux distribution, expressed in Equation (21) and the discretized heat fluxes estimated by the inverse method. The term "net total power" defined in this investigation refers to the power delivered from the plasma torch to the workpiece in the absence of powder deposition. Table VI lists the resulting heat fluxes estimated using different regularization parameters together with the root of squared error of the corresponding predicted Gaussian distributed heat flux. The root of squared error (cp) of M distributed heat flux segments is determined as 103 [M 7 (44) q>=Jz(a--9,o2 where Q and g represent the inverse calculated and the Gaussian distributed heat fluxes, respectively. When the regularization parameter a is set to zero, there is no damping and the estimated heat fluxes are numerically unstable. As can be seen, this leads to negative heat fluxes estimated at certain locations. On the other hand, when a is set at 1 x 10"7, the estimated heat fluxes are over-damped as illustrated by the smaller difference between the peak and the lowest heat fluxes. The optimum regularization parameter was found to be between 10"8 to 1CT9, at which point the root of squared error is at the minimum. The relationship between the regularization parameter and the root of squared error is illustrated graphically in Figure 50. As shown in the figure, a minimum error is found when the regularization parameter lies between 10"8 and 10~9. Hence, a value of 4 x 10"9 was adopted. 104 Table V I : Effects of Regularization Parameter (a) on the Estimated Heat Fluxes and the Predicted Gaussian Distribution a 0.00 1E-11 1E-10 1E-09 4E-09 1E-08 1E-07 root of squared error 8856 138 115 76 64 70 131 Predicted Gaussian Heat Flux Distribution Net total power (kW) 6.75 6.74 6.75 6.77 6.83 6.95 7.7 Distribution Coefficient C (m), defined in Eqn (21) 0.0275 0.0398 0.0400 0.0415 0.0428 0.0441 0.0512 Estimated Heat Fluxes (kW/m2) T/C 1, r = 0 10218 1443 1344 1187 1074 999 733 T/C 2, r = 5 mm -6381 1400 1316 1172 1065 992 731 T/C 3, r= 10 mm 5968 1265 1223 1121 1033 969 722 T/C 4, r = 15 mm 2054 1055 1069 1030 974 925 706 T/C 5, r = 20 mm -6482 834 884 908 890 860 681 T/C 6, r = 25 mm 11956 653 704 769 788 777 648 T/C 7, r = 30 mm - 11855 528 555 632 677 683 609 T/C 8, r = 35 mm 12304 448 447 509 566 584 567 T/C 9, r = 40 mm -10501 397 375 408 462 488 523 T/C 10, r = 45 mm 10581 360 328 332 372 398 481 T/C 11, r = 50 mm -9682 324 295 279 298 321 444 T/C 12, r = 55 mm 9673 281 268 245 241 260 413 T/C 13, r = 60 mm -6767 235 247 224 203 217 391 T/C 14, r = 65 mm 2758 205 234 215 183 194 379 105 200 150 h o i LU "D CD (0 V 100 w "5 o o DC 50 1 1—<-- • -• • • • • '• • • - • • -• -I 10"1 10" 10"1 10"9 10-E 10"' 1 0 ( Regularization Parameter (a) Figure 50: The optimal regularization parameter of the 12mm thick copper target. The same technique was also applied to the 5 mm copper target. Using the temperature data from Test 3, the optimum a was found to be 1 x 10"9, slightly lower than for the 12 mm thick copper block, reflecting the problem sensitivity of the method. Although the trial and error approach in finding the optimum regularization parameter works well in this study, the draw back of this method is that the form of the distribution has to be pre-assumed. As discussed previously, the sensitivity coefficients and the regularization parameter should be defined before the commencement of the inverse calculation. In practice, the sensitivity coefficients do not change substantially if the same target and the same thermocouple locations are considered [85]. 106 6. 2 Application to Experimental Results Temperature data collected from Tests 1 to 18 were processed in order to estimate the heat flux distribution. Table VII lists the results for the net total power, the centre heat flux (q0) and the distribution coefficient ( Q for Tests 1 to 18. For the sake of discussion, the discretized heat flux estimated from the temperature data of Test 3 has been chosen to examine in detail. The resulting heat flux distribution is shown plotted in Figure 51. As can be seen, the heat flux from the plasma torch can be considered to be relatively constant with time. In addition to the heat flux data, the temperatures predicted at particular locations of the target can also be examined. Figure 52 compares the temperatures at the thermocouple locations calculated by the inverse method and from experiment of Test 3. As can be seen, there is good agreement between the two. The heat flux shown in Figure 51 can be fitted to a Gaussian distribution. As discussed earlier, the heat flux is discretized into a number of segments along the heat flux boundary in accordance with the positions of the thermocouples used in the experiment, as shown in Figure 13. Thus, the heat flux distribution can be spatially rearranged as illustrated in Figure 53. As can be seen in Figure 53, the heat fluxes estimated by the inverse model can be approximated adequately with a Gaussian distribution, justifying the original assumption employed in determination of the regularization parameter. 107 Table VI I : Net Total Power, Centre Heat Flux and Distribution Coefficient Estimated by the Inverse Heat Conduction Calculation for Tests 1 to 18. Nozzle Test Net total power (kW) Centre heat flux q0 (kW/m2) Distribution Coefficient C (m) defined in Eqn (21) Stand-off Distance (mm) #6 3 10.75 4364.54 0.028 45 #6 2 8.86 1953.02 0.038 65 #6 4 7.70 1389.43 0.042 78 #6 1 6.83 1175.79 0.043 85 #6 6 7.32 1150.62 0.045 105 #6 5 4.93 827.79 0.044 120 #3 7 8.44 2623.50 0.032 40 #3 8 7.92 1840.52 0.037 55 #3 9 5.55 872.19 0.045 77 #3 10 4.15 597.99 0.047 100 1/2" XS 16 10.67 3316.73 0.032 60 1/2" XS 15 9.09 2363.13 0.035 80 1/2" XS 11 7.36 1267.15 0.043 100 1/2" XS 14 6.37 958.23 0.046 120 1/2" XS 12 7.50 1353.34 0.042 100 1/2" XS 13 7.16 1232.60 0.043 100 5/16" 17 6.56 1031.15 0.045 120 9/32" 18 4.66 617.78 0.049 120 108 6000 I — i — i — i — | i i i | i i — i — | — i i i .•)000 ' ' ' ' ' ' 1 1 ' 1 1 1 ' 1 1 ' 8 12 16 20 24 Time (Second) Figure 51: Heat fluxes estimated by inverse heat conduction calculation from temperature data collected in Test 3. 900 I i | 1 | 1 1 i 1 1 1 r 0 10 20 30 40 50 60 Time (Second) Figure 52: Comparison of temperature data collected in Test 3 and estimated from inverse heat conduction calculation. 109 6000 I i | i i i | i i i | i i i | i i i | i > i | i i i | Distance from center (mm) Figure 53: Heat flux distribution estimated from temperature data of Test 3 In Figure 53, the 2-D Cartesian box plots graph the data in a column as a box representing satistical values predicted by the inverse model. The lower boundary of the box indicates the 25 t h percentile, and the upper boundary of the box indicates the 75 t h percentile. The thin black line and the thick grey line within the box mark the median and the mean, respectively. Error bars above and below the box indicate the 90 t h and 10 t h percentiles. Outlying points are indicated by solid symbols. As discussed previously, the nozzles used in the experiment had a variety of different configurations. In Table VII, the results have been presented for the various nozzle types. The two parameters q0 and C are sufficient to describe the Gaussian heat flux distribution for each nozzle. As the investigation of different nozzle configurations formed part of a confidential investigation undertaken by the cooperating organization (Northwest 110 Mettech Company) and is not related to the objectives of this study, no discussion of the advantages or disadvantages of the various nozzle configurations is presented. Using Equation (21) and the plasma spray parameters of 1/2" XS nozzle, the variation in heat flux distribution across the substrate surface boundary with stand-off distance employed in Tests 11, 14, 15 and 16 were estimated and are presented in Figure 54. 3500 I T " ' | T " r l T - [ l T " T , ! ^ " l " 1 1 " " [•"I"" I I 1 | 1 I1 "I ' ' I ' ' | 1 T " T I " ] I -60 -40 -20 0 20 40 60 Radial coordination (mm) Figure 54: Heat flux distribution of Nozzle 1/2" XS imposed across the substrate surface at different stand-off distances As can be seen in Figure 54, the maximum centre heat flux decreases with increasing stand-off distance. This is due to the fact that cooler ambient air mixes readily with the plasma gases, thus lowering the plasma gas temperature as the stand-off distance. As mentioned earlier in Chapter 2, the stand-off distance, in practice, lies within a certain 111 range. For example, with a short stand-off distance, the residence time of high velocity particles travelling from the plasma torch to the substrate target is small. The heat transfer processes taking place between the plasma gases and the high velocity particles may be limited, and thus the particle may remain solid. Conversely, with a long stand-off distance, the plasma temperature decreases considerably due to the entrainment of the relatively cold ambient air and particles originally molten up-stream in the plasma flame may possibly be cooled down, solidified, or even oxidized as they transit down-stream in the flame. Both situations can result in poor particle adherence efficiencies. In general, the practical range of the stand-off distance in air plasma spray is considered to be within 45 to 150 mm. The net total power delivered from the torch to the substrate in the absence of powder is closely related to the heat flux distribution as shown in Figure 54. Mathematically, the net total power can be determined by the following equation: 7 (45) P= )2nrqrdr The net total power in Equation (45) can be regarded geometrically as the equivalent volume underneath the distribution curve. The net total power listed in Table VII is estimated using Equation (45). The relationship between the net total power and stand-off distance and the distribution coefficient and the stand-off distance are presented in Figures 55 and 56, respectively. Regression lines have been plotted in both figures, together with the data, to better illustrate the trend in the data, (j-axis intercepts and slopes of these regression lines are, respectively, 13.4 kW; -0.0683 kW/mm for 112 Nozzle #6, 11.69kW; -0.0761 kW/mm for Nozzle #3, and 14.956 kW; -0.0731 kW/mm for Nozzle 1/2 XS) 3 I i • * • i • • • • i • • i i i i i i i 30 60 90 120 150 Stand-Off Distance (mm) Figure 55: Relationship of net total power and the stand-off distance. Figures 55 shows the relationship of the net total power delivered from the plasma torch to the substrate and the stand-off distance, using Nozzles #3, #6 and 1/2"XS. In each of the experiments, the torch operating parameters of each nozzle were kept constant. The net total power was found to decrease linearly with increasing stand-off distance. A similar drop of 0.07 kW / mm for all three nozzles was noted. The result may be useful because the net total power of the torch delivered to the target at any particular stand-off distance could be calculated if the net total power at one stand-off distance is known. The relationship between the distribution coefficient and the stand-off distance is presented in Figure 56. As shown in the figure, the distribution coefficients of different 113 type of nozzles do not appear to have a common relationship. Instead, the distribution coefficient in general seems to rise in some relationship with the stand-off distance as indicated by the regression curves in Figure 56. 0.050 0.045 h E 0.040 § 0.035 o I 0.030 0.025 0.020 i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i Goodness of Fit Nozzle # 6 3.39E-04 m Nozzle # 3 2.92E-04 m 1/2"XS Nozzle 14.09E-04 m • Nozzle #6 • Nozzle #3 A 1/2"XS Nozzle i . • • • i • '• , , i 20 40 60 80 100 120 140 160 Stand-Off Distance (mm) Figure 56: Relationship of the distribution coefficient and the stand-off dista nee 6. 3 Analysis of Experimental Results The effects of hydrogen gas flow can be examined by comparing the results of Tests 11, 12 and 13, which have been summarised in Table VII. Recall from Table I, the flow rate of different plasma gases used in Test 11 was 10 slm (standard litre per minute) Ff2, 96 slm N 2 and 10 slm Ar. Increasing hydrogen flow to 16 slm (60%) in Test 12 has increased the net total power and decreased the distribution coefficient by 1.9 % and 2.3%, respectively, as compared to Test 11. As a result, the heat flux and the corresponding 114 plasma flame temperature at the centre of the torch would be higher with increased hydrogen gas flow. Since most of the depositing powder is distributed at the centre of the plasma flame, the consequence of increasing hydrogen gas flow may be to increase the depositing temperature of the coating material. This prediction agrees with the findings reported by Moreau et al. [86]. The decrease in hydrogen flow to 6 slm (-40%) in Test 13 resulted in a decrease in the net total power delivered to the work piece by 2.7%, in spite of a small increase of nitrogen gas flow to 102 slm (6.25%), when compared with Test 11. As the impetus for conducting the inverse heat transfer analysis of the torch was to determine the heat input to the substrate due to the plasma flame, it is important to examine whether the fluxes determined in the absence of powder will be representative of the fluxes prevalent with powder. In order to investigate this issue, we may consider the example of plasma spray deposition of zirconia. Nominally, zirconia has a deposition rate of 48 gram/minute (0.8 gram/second). In order to heat 0.8 gram of zirconia powder from room temperature to the depositing temperature, say 2700°C, in 1 second, requires approximately 2,500 Joules per second (see Appendix 2 for enthalpy of zirconia) or 2,500 W. This is about a quarter of the net total power from the plasma torch estimated from Test 15 (9.09 kW). Consequently, the power loss due to the energy absorbed by the depositing powder must be included. For the purpose of this investigation it has been assumed that the effect of the powder on the plasma flame is to reduce only the net total power of the plasma torch and not the distribution coefficients listed in Table VII. The 115 term "deposition power" used in this investigation refers to the power delivered from the plasma torch to the workpiece in the presence of powder deposition. 6.4 Summary The inverse heat conduction calculation has been applied for the estimation of the surface heat flux and the heat flux at the substrate / coating interface, without and with powder deposition. Apart from the determination of boundary conditions for input to the plasma deposition model, the analysis finds that the net total power of the plasma torch decreases linearly with increasing stand-off distance, in the absence of powder deposition. The term "net total power" defined in this investigation refers to the power delivered from the plasma torch to the workpiece in the absence of powder deposition. In Figure 55, the different nozzle types examined can be seen to have a common negative slope of power loss per unit stand-off distance. The slope is approximately -0.07 kW / mm. Thus, it would appear that for the Axial in plasma torch, the net total power obtained from one test at a particular stand-off distance may be used to predict the net total power delivered to the workpiece at a different distance providing it is within the range of 40 and 120 mm in air plasma spraying, as examined in this study. Although the results obtained in this study are limited to a particular plasma spray system, the experimental approach and the mathematical formulation can be applied to other plasma spraying systems. The power delivered from the torch to the workpiece during powder deposition, defined as "deposition power" in this investigation, may be predicted mathematically by 116 deducting the power necessary to heat up the powder particles to the depositing temperature from the net total power of the plasma torch estimated in the inverse heat transfer calculation. The deposition power will be used as one of the boundary conditions applied in the micro-macro model described in the next chapter. 117 CHAPTER 7 ANALYSIS OF PLASMA SPRAY DEPOSITION PROCESS This chapter describes the heat transfer analysis of the coating and the substrate during plasma spray deposition process. The analysis is accomplished by applying the micro-macro heat flow model, using the rate of change of coating thickness and the heat flux boundary described in Chapters 4 and 6, respectively. The effects of various parameters on the thermal regime in the substrate targets are also analysed. The substrate temperature data collected in Tests 19 to 21 for the plasma spray deposition of 8 wt% yttria-zirconia will be employed to verify the micro-macro model prediction at the thermocouple locations. In addition, the substrate temperature during the plasma spray deposition of 17 wt% cobalt-tungsten carbide and CP titanium predicted by the micro-macro model are compared against the experimental data collected in Tests 22 and 23. 7.1 Application of Micro-Macro Heat Flow Model The novelty contained in this investigation is the analysis of heat transfer of plasma spray deposition process at both microscopic and macroscopic levels, using a validated mathematical model which entails the radial distributed sensible heat released from the deposited powder and the radial distributed heat flux delivered from the plasma torch. The mathematical model consists of a one-dimensional microscopic finite-difference model which has the nodal size equivalent to a quarter of the thickness of a splat, 2.5 pm; couple with a two-dimensional macroscopic axi-symmetric finite-element model utilizing a mesh size 300 times larger than the micro-model. In principle, the micro-macro model can be 118 applied to any plasma spray deposition process as long as the boundary conditions are known. The domain, initial condition and boundary condition for these two models have been defined and specified in Chapter 5. The thermophysical properties of plasma coating used in the micro model are reported in Appendix 2. Since these properties vary considerably with microstructure in the plasma sprayed coating (for example the amount of oxide and porosity), there is a paucity of information published in the literature. In order to estimate the thermophysical properties of the coating, the plasma coating is treated as a composite material comprised of bulk material, pores and oxides which are regarded as different phases with distinct properties. The thermophysical properties of coating are estimated using a rule of mixtures approach. 7. 2 Sensitivity Analysis Prior to applying the model to the experiments (Tests 19 through 23), a sensitivity analysis determined the effect of various parameters on the thermal regime in the substrate target. The parameters chosen for the sensitivity analysis were those parameters which were not well understood (i.e., the thermal conductivity, latent heat, deposition temperature and emissivity of the depositing material) and those which represent possible process control parameters (i.e., the deposition power from the plasma torch, power distribution and the splat thickness). The range of parameters examined is shown in Table V M . The % change in variable parameter bracketed in Table VIII is calculated using the following expression. 119 _ , Base Parameter-New Parameter (46) % change = Base Parameter Table VIII: Range of Parameters studied in the Sensitivity Analysis of the Thermal Response of Test 20 to Changes in Process Parameters Description Parameters Varied Base k = 1.0 W/K/m, e = 0.3, TdeP = 2700°C, H = 662.3 kJ/kg, P = 6.0 kW, C = 0.035 m, Ay = 10 pm k thermal conductivity 0.5 W/K/m (-50%), 1.5 W/K/m (+50%) e emissivity 0.1 (-66.7%), 0.5 (+66.7%) Tdep deposition temperature 2600°C (-3.7%), 3000°C (+11.1%) H heat content 596.076 kJ/kg (-10%), 728.538 kJ/kg (+10%) P torch power 5.0 kW (-16.7%), 7.0 kW (+16.7%) C power distribution coefficient 0.030 m (-14.3%), 0.040 m (+14.3%) Ay splat thickness 5 pm (-50%), 20 pm (+100%) The base parameters and the parameter changes for the sensitivity analysis were selected as follows : The thermal conductivity (k) was chosen from the literature [87]. The k value, however, is known to be dependent on porosity and hence represents a substantial degree of uncertainty. The change in thermal conductivity in the sensitivity analysis was therefore selected to be broad at ± 50%. 120 The emissivity (e) of plasma sprayed zirconia based coating was not documented in the literature. For the first approximation, the emissivity of plasma sprayed alumina, [64] which has a similar texture and appearance compared to plasma spray zirconia, was used. Because of the uncertainty of the emissivity of plasma sprayed zirconia used in the model, a wide range of emissivity was chosen in the sensitivity analysis. The change of emissivity with respect to the base was ± 66.7 % in the analysis. The nominal splat thickness (Ay) of 10 jxm was selected in the micro-macro model. This nominal thickness was chosen from the average splat thickness measured from microstructural examination. The powder size ranges from 45 to 75 \lm. Therefore the splat thickness may be expected to vary considerably. The upper and the lower limit of the splat thickness selected in the sensitivity analysis were set to 20 and 5 (im, which was +100% and -50% of the base parameter, respectively. The deposition temperature of the molten particle (Trfep) was used to fit the model results to the measured data and was the only "adjustable" parameter employed in the model. The base deposition temperature used was 2700 °C as it provided the best agreement between the model predicted temperatures and those measured using the embedded thermocouples. This value was subsequently found to agree with that determined in an independent study [88] using the same plasma spray system and powder composition but narrower sized distribution of zirconia powder (-75+45fim compared to -140+15\im Zirconia 9204). In the sensitivity analysis, the lower limit of the deposition 121 temperature had to be set above 2600 °C — the liquidus of the zirconia powder. The upper limit was set to 3000 °C which was 11.1% above the base deposition temperature. The torch power (P) and the power distribution coefficient ( Q were estimated from the inverse heat transfer model described in Chapter 6. The heat content (H) was calculated from the heat capacity of the zirconia powder reported in Appendix 2. A l l these parameters were reasonably well known and, therefore, the changes to these parameters in the sensitivity analysis were kept small ranging within ± 16.7%. The parameter associated with Test 20 were adopted as the standard run from which the sensitivity analysis was conducted. The sensitivity to the changes in the various parameters were evaluated on the basis of a comparison of temperatures predicted at various locations in the coating as well as at the location of thermocouple T/C 1. The results of the sensitivity analysis are shown graphically in Figure 57 through 63. The temperature at the substrate thermocouple location (T/C 1) and in the coating at locations 2.5 pm, 0.63 mm and 1.25 mm away from the coating / substrate interface, have been output for comparison. A quantitative comparison has been compiled in Table DC on the basis of the predictions after 15 seconds of deposition. 122 Figure 57: Sensitivity of the thermal response of Test 20 to changes in thermal conductivity of coating material 3500 3000 h; + 0 .63 m m y 2 .5 urn 2500 h O 2000 a> i _ £ 1500 CD Q . E £ 1000 500 0 -500 i i i i I i i i i j i i i i I i i i i i + 1.25 m m e m i s s i v i t y - 0 . 5 e m i s s i v i t y - 0 . 3 ( b a s e ) e m i s s i v i t y - 0.1 d i s t a n c e m e a s u r e d f r o m the s u b s t r a t e / c o a t i n g interface (posit ive pos i t ion b e i n g t o w a r d s the coat ing) 1 • 1 1 1 1 • 1 1 • 1 10 15 Time (second) 20 25 Figure 58: Sensitivity of the thermal response of Test 20 to changes in emissivity of coating material 123 Figure 59: Sensitivity of the thermal response of Test 20 to changes in deposition temperature of coating material 3500 3000 h 2500 O 2000 CD | 1500 h a . £ £ 1000 500 h -500 • 1.25 m m l a t e n t h e a t - 7 2 8 5 3 8 J / k g l a t e n t h e a t - 6 6 2 3 0 7 J / k g ( b a s e ) l a t e n t h e a t - 5 9 6 0 7 6 J / k g d i s t a n c e m e a s u r e d f r o m the s u b s t r a t e / c o a t i n g interface (posit ive pos i t ion b e i n g t o w a r d s the coat ing) 1 • 1 1 1 1 • 1 1 1 1 1 • 10 15 20 Time (second) 25 Figure 60: Sensitivity of the thermal response of Test 20 to changes in latent heat of coating material 124 Figure 62: Sensitivity of the thermal response of Test 20 to changes in power distribution of torch power 125 3500 3000 2500 p 2000 | 1500 CD Q . E |2 1000 500 0 -500 5 10 15 20 25 Time (second) Figure 63: Sensitivity of the thermal response of Test 20 to changes in the splat thicknesses of the coating material Based on the results summarized in Table DC, the substrate temperature, measured at the T/C 1 thermocouple location, is most sensitive to the deposition temperature of the molten powder particle, the distribution coefficient and the power of the plasma torch, and is less sensitive to the emissivity and the latent heat of the depositing material. Whereas with regard to the temperature within the coating, it is most sensitive to the thermal conductivity, the deposition temperature of the molten powder particle, the distribution coefficient and the power of the plasma torch, and is less sensitive to the latent heat, the emissivity and the splat thickness of the depositing material. 126 Table IX : The Sensitivity of Temperatures of Test 20 to Changes in the Conditions shown in Table VIII Parameters (refer to Table VIII) T/C 1 in substrate 0.25 pm from coat/sub. interface 0.63 mm from coat/sub. interface 1.25 mm from coat/sub. interface Base 323 °C 242 °C 629 °C 764 °C k (0.5/1.5) 296 / 333 °C 259 / 226 °C 1241 / 393 °C 1253/454 °C ratio of % change* 0.17/0.06 0.14/0.13 1.94/0.75 1.28/0.81 8 (0.1,0.5) 324 / 323 °C 251 /236°C 726 / 574 °C 900 / 686 °C ratio of % change* 0.00 / 0.00 0.06 / 0.04 0.23/0.13 0.27/0.15 Tdep (2600,3000) 332 / 352 °C 245 / 259 °C 618/689 °C 747 / 836 °C ratio of % change* 0.74 / 0.77 0.29/0.65 0.49 / 0.86 0.72/0.85 H (596, 728) 321 /326 °C 239 / 245 °C 612/644 °C 742 / 782 °C ratio of % change* 0.08 / 0.08 0.12/0.10 0.27 / 0.24 0.29/0.24 P (5, 7) 300 / 347 °C 220 / 264 °C 595 / 658 °C 728 / 793 °C ratio of % change* 0.43 / + 0.43 0.55/0.54 0.32 / 0.27 0.29 / 0.22 C (0.03, 0.04) 358 / 287 °C 269 / 212 °C 676 / 579 °C 814/ 710 °C ratio of % change* 0.76 / 0.77 0.78/0.86 0.52 / 0.55 0.45 / 0.50 Ay (5, 20) 301 /339 °C 231 /248 °C 612/ 636 °C 747 / 770 °C ratio of % change* 0.13/0.04 0.09 / 0.03 0.05/0.01 0.05 / 0.01 . X T . P „ . % change of temperature * Note : ratio of % change = % change of parameter The result of the sensitivity analysis indicates that the predictions of the micro-macro model are most sensitive to the particle deposition temperature and that, therefore, it is critical that this parameter is known accurately. However, this is not the case as the 127 accurate measurement of particle temperature within the plasma flame represents a significant challenge, as previously discussed. In lieu of this problem, it was decided to fit the model predictions to the thermocouple data by adjusting the particle deposition temperature. Where possible the resulting "model estimated" deposition temperature would then be compared to measured data. 7. 3 Mathematical Analysis of Plasma Spray Deposition Process 7. 3.1 Analysis of Plasma Spray Deposition of 8wt% Yttria-Zirconia The micro-macro model was used to predict the thermal behaviour arising from each of the plasma spray experiments reported in Chapter 4. The experiments conducted with 8 wt% yttria - zirconia were modelled first. Further, since the conditions surrounding the two second zirconia deposition, designated Test 20, were the most controlled, this experiment was used as the foundation for the analysis. The deposition power from the flame obtained from the inverse heat transfer analysis of Test 15 (less the heat content of the powder) was used to simulate Test 20 as the operating conditions were identical. The remaining parameters, such as power distribution, powder coverage and powder distribution, were estimated using earlier results. The thermophysical properties of substrate and coating material were either available from literature or estimated and reported in Appendix 2. The results of the model predictions were compared to the experimental data. The deposition temperature (Tjep) was then modified until the results shown in Figure 64 were obtained. As can be seen from the figure, the fit to the experimental data is quite good. 128 Table X shows the power, the rate of change of coating thickness, and their distribution utilized in the model to generate the predictions shown in Figure 64. The model results for Test 19 and Test 21 are shown in Figures 65 and 66. These results were obtained using the same model parameters as the ones that generated the Test 20 results. 129 Table X : Deposit Temperature, Deposition Power, Power Distribution, Rate of Change of Coating Thickness and Powder Distribution used in the Model Calculations for Tests 19, 20 and 21 Tests Deposit Temperature (Tdep) Deposition Power (P) Power Distribution (Q Rate of Change of Coating Thickness (Do) Powder Distribution (X) 19, 20,21 2700 °C 6.0 kW* 0.035 m 0.000607 m/s 0.00648 m * Note : Deposition power uses result of Test 15 with the deduction of power loss to the depositing powder 250 200 0 •5- 150 CD i _ to i _ CD Q . 1 100 50 0 0 10 20 30 40 50 Time (Second) Figure 65: Model predictions and experimental results for Test 19 130 450 i i i i I i i i i I i i i i I i i i 400 h \ T/C 1 3 sec. deposition of 8 wt% Y 2 0 3 - Z r 0 2 0 0 • 1 1 • i • • • • i • . • . i . • • • i • • • • 10 20 30 40 50 Time (Second) Figure 66: Model predictions and experimental results for Test 21 As seen in Figures 64 to 66, the model predictions for the one, two and three second deposition experiments of zirconia fit well with the experimental results. However, as can be seen the results for the 2 and 3 second simulations are superior to those obtained for the shorter 1 second simulation. One plausible explanation for this is that the relative error in the deposition time (measured manually in Tests 19 to 21) was substantial in the shorter 1 second experiment. To test this hypothesis the model has been rerun with a 1.25 second deposition time. The result is shown in Figure 67. As can be seen, there is better agreement between the model predictions obtained with the slightly larger deposition time. 131 200 °~ 150 CD ro • CD I 100 r— 50 0 0 10 20 30 40 50 Time (Second) Figure 67: Comparison of model predictions for 1.25 second deposition and experimental results for Test 19 One of the driving forces for the heat transfer analysis is the determination of the temperature distribution across the coating and its evolution with time. For example, the model can be used to examine the thermal history of the first splat as shown in Figure 68. As can be seen in the figure, the first splat cools in less than a milli-second at a cooling rate approaching 107 °C/s, and is then subsequently reheated with the impact of additional splat. i i i i i i i i i i i i i i i i i i i i i i i i ' ' ' ' I • . • • I • • • > I • • • • I • • . • 132 3000 I i i i i I i i i i I i i i i I i i i i | i i i i | i i i i | i i i i Cooling Rate = 107 °C/s 2500 h flrst splat | 2000 h O £ 1500 h Temperature Rise due to Subsequent Deposition E 1000 h 0) Q . 500 h O h 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time after Deposition (Second) Figure 68: Model prediction of the cooling of the first splat Since the powder deposition varies with the radial coordination of the plasma torch, the coating thickness, and consequently the heat transfer processes taking place at the coating / substrate interface, would be expected different from one radial coordination to the other. To examine this, the micro-macro model has been used to predict the substrate and the coating temperature for Test 20, at radial positions 0, 2, 4, and 6 mm away from the centre as shown in Figures 69 through 72. In these figures, it can be seen that the predicted coating temperature exceeds the melting point of the coating material near the flame centre. Whereas, this is not observed further away from the flame centre. This difference arises because at the radial centre of the plasma flame there is more heat input from both the flame and the deposited powder. Further, because the coating is thicker in this region it is more insulating and the heat cannot be as easily conducted away to the substrate. In the 2 second deposition, the surface temperature of the zirconia coating near 133 the torch centre was predicted to reach approximately 500°C (Curves/and g in Figure 69) above the melting temperature. Under the same conditions the temperature gradients in the coating were predicted to exceed 2000 °C/mm. Moreover, after the plasma torch was removed, the surface was predicted to cool faster than the subsurface of the coating and thus a layer of liquid was predicted to persist between two solidified layers, as shown in Figure 69 (just after the 9 t h second). Figure 69: Model predictions of coating temperature at the centre for Test 20 134 3 5 0 0 3 0 0 0 2 5 0 0 P. 2 0 0 0 \ -. | 1 5 0 0 Q _ E CP I - 1 0 0 0 5 0 0 0 a b c c "ii Distance from l ^ N l . . . .?799.!? Substrate Surface (mm) 0 . 0 0 2 5 c u r v e (a) 0 . 2 5 2 5 c u r v e (b) 0 . 5 0 2 5 c u r v e (c) 0 . 7 5 2 5 c u r v e (d) 1 . 0 0 2 5 c u r v e (e) 1 . 2 5 2 5 c u r v e (f) \ \ \ * t e m p e r a t u r e f luc tuat ion d u e to \ \ \ s u b s e q u e n t d e p o s i t i o n of m o l t e n p a r t i c l e s " "•- . . . \ \N, _ L _ L 1 2 1 5 1 8 Time (second) 2 1 2 4 Figure 70: Model predictions of coating temperature at 2 mm from the centre for Test 20 3 5 0 0 r — i — 1 — | — i — 1 — | — i — 1 — | — 1 — 1 — | — 1 — 1 — | — 1 — 1 -3 0 0 0 h a b c d I 2 7 0 0 ° C Distance from Substrate Surface (mm) 0 . 0 0 2 5 c u r v e (a) 0 . 2 5 2 5 c u r v e (b) 0 . 5 0 2 5 c u r v e (c ) 4 0 . 7 5 2 5 c u r v e (d) 1 . 0 0 2 5 c u r v e (e) t e m p e r a t u r e f luc tuat ion d u e to s u b s e q u e n t d e p o s i t i o n of m o l t e n p a r t i c l e s 1 1 1 1 1 1 1 1 2 1 5 1 8 Time (second) 2 1 2 4 Figure 71: Model predictions of coating temperature at 4 mm from the centre of Test 20 135 1 ' ' 1 ' r Distance from Substrate Surface (mm) 0.0025 c u r v e (a) 0.2525 c u r v e (b) 0.5025 c u r v e (c) tuation d u e to j s i t ion of m o l t e n part ic les 1 1 1 1 1 ' ^ 6 9 12 15 18 21 24 Time (second) Figure 72: Model predictions of coating temperature at 6 mm from the centre of Test 20 In view of the radically different thermal behaviour predicted by the model, both in the through-thickness and in the radial direction, it can be anticipated that there may also be an associated variation in microstructure within the coating in terms of the phase content and / or porosity. For example, under the cooling conditions predicted for the first splat (of the order of 107 °C/s as shown in Figure 68) it is likely that non-equilibrium phases dominate consistent with the findings of other studies which have reported the presence of the non-equilibrium tetragonal phase in plasma spray zirconia coating [28]. In addition to cooling rate, coating temperature will also influence porosity formation through its effect on the ability of the splats to flow and deform upon impact. Certainly, in locations where the melting point of zirconia is exceeded a low residual porosity would be expected. As the zirconia based coating is built up during plasma spray, heat supplied by the particles and by the plasma flame was more than the heat loss through the surrounding. 136 The temperature at the free surface of the coating could be well above the melting point of the coating and the material at this region might remain in liquid form for a substantial period, thus resulting in little porosity. Comparing the microstructures found in the 1, 2 and 3 second deposition experiments (Figures 33 to 37, Chapter 4) with the predictions of the model there is a clear and consistent trend to reduced porosity with increasing temperature. In addition to phase content and porosity, the presence of cracks within the coating (Figures 30 to 32) also will have a bearing on its performance. Using the results from the thermal analysis, a crude assessment of the generation of thermal stresses can be made on the basis of the thermal gradient across the coating. To this end, the variation in temperature gradient across the coating with time has been plotted for the 1, 2 and 3 second deposition experiments in Figure 73. The temperature gradient across the coating was calculated from the temperature difference between the coating / substrate interface and the free surface of the coating, divided by the thickness of the coating. The results indicate that at the time of removal of the plasma torch the highest through-thickness gradient is achieved in the 1 second coating followed by the 2 and 3 second coatings. However, with increasing time the gradient in the 1 second coating rapidly decays whereas the gradients in the 2 and 3 second coatings persist and, at times greater than approximately 3 seconds, the 3 second coating has the largest gradient. In comparison to cracks found in the coatings, this result would appear to be inconsistent as the most severe cracking was clearly observed in the 3 second coating. However, before drawing any conclusions, a proper thermal-stress analysis would need to 137 be completed in order to include all of the phenomena in addition to thermal gradient that may have a bearing on the generation of cracks. For example, it would be essential to include the thermal expansion contraction behaviour of the substrate, which is coupled mechanically to the coating. The amount of coating deposited should also be considered because it affects the internal stress and stress distribution of the coating. In addition, on close inspection of the temperature distribution presented in Figure 69, it is apparent that within a few seconds of removal of the plasma torch, the top surface of the coating begins to cool quickly giving rise to a complicate temperature distribution that may include the encapsulation of some liquid just below the coating surface. Further, at the lower cooling rates in the upper layers of the coating (last to be deposited), the tetragonal-to-monoclinic phase transformation in zirconia will likely occur giving rise to an expansion on cooling during the phase transformation which could lead to cracking. From the standpoint of reduction of cracking, it is difficult to apply the thermal model directly to the optimization of the process parameters owing to the complicating factors cited above. There are two approaches that could be used to achieve this goal. One would involve the development of thermal criteria for crack free coatings, which in turn would require numerous experiments; the other would require the development of a fundamental based stress model for the prediction of stresses and strains in the coating as a function of the relevant process parameters. Both are beyond the scope of this thesis. 138 5000 O °— 4000 h « O o 01 co o w O CO 3000 h ~ 2000 h c CD 2 a CO 1000 h CD a . O h ' 1 I 1 1 1 1 I i i i i i i i i i i i Deposition of 8wt% yttria-zirconia on AISI-1008 1 sec deposition 2 sec deposition 3 sec deposition i i i i i i i i 0 1 2 3 4 Time after plasma torch removed (sec) Figure 73: Model prediction of the temperature gradient across the coating for 1, 2 and 3 seconds plasma spray deposition of 8 wt% yttria-zirconia 7. 3. 2 Analysis of Plasma Spray Deposition of CP titanium and 17% Co -WC The application of the micro-macro model is not limited to the yttria-zirconia system. If sound, the model should also be capable of predicting the thermal regime within the coating and substrate during plasma spray deposition of other materials. To verify this capability the model was applied to the plasma spray of CP titanium and 17% Co-WC. The two tests analysed were Tests 22 and 23, respectively. The thermophysical properties of CP titanium and 17% Co-WC are reported in Appendix 2. Since the rate of change of coating thickness of 17% Co-WC is high (134 g/min), the net total power estimated earlier in Test 17 and reported in Table VII has 139 had to be adjusted to account for the heat absorbed by the depositing powder. The parameters used in the model are listed in Table XI. Table X I : Deposit Temperature, Deposition Power, Power Distribution, Rate of Change of Coating Thickness, and Powder Distribution used in the Model Calculations of Tests 22 and 23 Tests Deposit Temperature (Tdep) Deposition Power (P) Power Distribution ( Q Rate of Change of Coating Thickness (D0) Powder Distribution (X) 22 2300°C 4.50 kW* 0.045 m 0.000849 m/s 0.00513 m 23 3200°C 4.66 kW 0.049 m 0.000139 m/s 0.00955 m Note : Deposition power uses result of Test 17 with the deduction of power to the depositing powder Using the parameters listed in Table XI, the model was employed to predict the thermal regime within the substrate target of the samples sprayed with 17% Co-WC and CP titanium. Figures 74 and 75 compare the results predicted by the model and the experimental data for Test 22 and Test 23, respectively. 141 The model predictions have some marginal agreement with the measured data. Comparing Figures 74 and 75, it is clear that the model prediction for the 17% Co-WC in Figure 74 is less successful than the prediction for CP titanium. There are two possible reasons for the poorer agreement in the case of 17% Co-WC. Firstly, the thermophysical properties of 17% Co-WC are not well defined. The thermophysical properties used in the model were based on the incomplete properties for pure cobalt and tungsten carbide. Secondly, the deposition of this material in the experiment was imperfect in that a crater was formed at the centre as reported earlier in Chapter 4, which was neglected in the mathematical analysis. Nevertheless, the deposition temperature used in the model {Tdep = 2300°C) for 17% Co - W C was only 100°C lower than the measured particle temperature for 12% Co -W C reported in the literature [41] (see Figure 11), using the same plasma spray system and spray parameters. In order to achieve the fit shown in Figure 75, the deposition temperature of CP titanium employed in the model was 3200°C, which is around 16% higher than the measured temperature reported in Reference 41 and shown in Figure 8 (Note that the same powder and the same spray parameters have been used in both experiments). As reported in Reference 41, thermal radiation emitted from a hot titanium particle, was collected by an electronic sensor and translated into temperature. However, the temperature detected in this manner may not accurately reflect the deposition temperature of the titanium particle. As discussed in Reference 41, CP titanium was likely to react with entrapped oxygen to form titanium oxide down stream of the plasma flame. The titanium oxide film at the 142 surface might lead to an error in temperature measurement. In addition, the oxide film could act as an insulator and the temperature appearing at the surface may be different from the temperature inside the particle. A l l factors considered, agreement between the measured and predicted temperature is very reasonable. One driving force for the heat transfer analysis is the determination of the temperature distribution across the coating and its evolution with time. The model predictions for the coating temperature of 17% Co-WC and CP titanium, at the plasma torch centre cooling from their deposition temperature, are shown in Figures 76 and 77, respectively. 2500 17% C o - W C 2 3 0 0 C Distance from Substrate Surface (mm) 0.0025 0.2525 0.5025 0.7525 1.0025 1.2525 1.5025 1.7525 2.0025 9 12 Time (second) Figure 76: Model predictions of coating temperature at coating centre of Test 22 143 i i ' i 1 I 1 i • i 1 I 1 i 1 \ a t> C P Ti Powder Deposition ; ] 1 3 2 0 0 ° C Distance from Substrate Surface (mm) 0.0025 c u r v e (a) 0.2525 c u r v e (b) 1 i I i I i I i I i I i I i I i J 5 6 7 8 9 10 11 12 13 14 Time (second) Figure 77: Model predictions of coating temperature at coating centre of Test 23 As mentioned previously in Chapter 4, crater was found at the centre of 17% Co-W C plasma spray coating. One possible explanation for this is that the spray rate could have been higher than the solidification rate, which could lead to the formation of the crater as discussed by other workers [38]. This condition leads to the occurrence of a liquid phase on top of the solid coating which can be partially blown away by the high velocity plasma jet at the centre of the plasma torch. As seen in Figures 76, however, there are no liquid layers formed on the top of 17% Co-WC coatings. An alternative explanation for the formation of the crater in the 17% Co-WC is that tungsten carbide may have been unable to mechanical bond well with the substrate under the high velocity plasma jet at the deposition temperature. The 17% Co-WC consists of a mixture of tungsten carbide and cobalt powders which melt at 2870 ± 50 and 1495 °C, respectively. The typical deposition temperature of 12% Co-WC is 2400 °C [41]. O D U U 3000 h 2500 h O o £ 2000 to i— CD E 1500 CD 1000 500 144 Increasing the deposition temperature up to the melting point of tungsten carbide has no advantage because cobalt starts to boil at 2780 °C. At the deposition temperatures, either the tungsten carbide particles are unable to deform plastically upon impact with the substrate and bounce off under the high velocity plasma jet or the cobalt matrix remelts thus allowing both cobalt and tungsten carbide to be blown away, forming the crater. 7.4 Summary An extensive sensitivity analysis was performed to determine the effects of various model input parameters on the thermal history in the targets. The sensitivity analysis showed that the substrate was most sensitive to the deposition temperature of the molten powder particle, the distribution coefficient and the power of the plasma torch, and was less sensitive to the emissivity and the latent heat of the depositing material. Whereas in the sensitivity analysis of the temperature across the coating, temperature within the coating was most sensitive to the thermal conductivity of the depositing material, the deposition temperature of the molten powder particle, the distribution coefficient and the power of the plasma torch, and was less sensitive to the latent heat, the emissivity and the splat thickness of the depositing material. Because the substrate temperature is most sensitive to the deposition temperature of the molten particle, and this quantity is poorly known, it has been employed to fit the model to the measured data. The coating temperature could influence porosity formation of the coating through its effect on the ability of the splats to flow and deform upon impact. Comparing the 145 microstructures found in the coating with the predictions of the model there was a consistent trend to reduced porosity with increasing temperature. The thermal gradients across the coating on 1,2, and 3 second deposition of 8wt% yttria-zirconia were analysed. The results indicated that the highest through-thickness gradient was achieved in the 1 second coating followed by the 2 and 3 second coatings at the time of removal of the torch. However, the gradient in the 1 second coating rapidly decayed with increasing time whereas the gradients in the 2 and 3 second coatings persisted. This result appeared to be inconsistent in comparison to cracks found in the coatings as the most severe cracking was found in the 3 second coating. In addition, within a few seconds of removal of the plasma torch, the top surface of the coating near the centre began to cool quickly giving rise to a temperature distribution that might include the encapsulation of liquid just below the coating surface. At the upper layers of coating where equilibrium prevailed, the tetragonal-to-monoclinic phase transformation in zirconia would likely occur giving rise to an expansion on cooling during the phase transformation which could lead to cracking. In the application of the micro-macro model, the model fitted very well with the experiment temperature data, except in the modelling of the plasma spray of 17 wt% Co-WC. The deposition temperature of 8 wt% yttria-zirconia, 17 wt% Co-WC and CP titanium were found respectively to be 2700, 2300, 3200 °C. During plasma spray deposition, the plasma torch generally moves at a certain velocity with respect to the target. Consequently, the micro-macro model used in this investigation may not be able to reflect the general situation of the process. However, the 146 model does provide the basic concept of the complicate heat transfer process taking place within the coating and the substrate during plasma spray deposition using a stationary torch. 147 CHAPTER 8 SUMMARY AND CONCLUSIONS 8.1 Summary and Conclusions A series of experiments were conducted to elucidate the heat transfer processes occurring in the plasma spray deposition process. Cylindrical disks of pure copper and AISI-1008 steel have been instrumented with embedded thermocouples to measure the temperature at several locations within the material being heated by a plasma torch, with and without powder deposition. Three powders were examined - 8wt% yttria-zirconia, 17% Co-WC and CP titanium. A l l the experimental tests were conducted on an Axial HI ™ plasma torch. In parallel, a mathematical model of plasma spray deposition process has been developed and used to analyze the experimental results. The model combines a macro-scale (scale of the substrate) finite-element based heat flow model with a micro-scale (scale of the splat) finite-difference based heat flow model in order to simulate heat transfer processes occurring in the substrate and coating, respectively, both during deposition and subsequent cooling. The results of an inverse heat transfer analysis of the thermocouple data with the macro model, recorded in the absence of powder deposition, revealed that the heat flux distribution from the plasma torch (referred to as the net total power) could be described by a Gaussian distribution, with distribution coefficients ranging from 0.028 to 0.049m (Table VII in Chapter 6). Further, the analysis revealed that the net total power varied inversely in proportion with the stand-off distance. Within the range of 40 to 120 mm of 148 the stand-off distance, the net total power was found to vary by 0.07 kW/mm. In another experiment, a 10% change in hydrogen flow was found to have little affect on the net total power transferred from the torch, but was found to alter the distribution of power. The distribution was modified such that the net total flux impinging at the centre was increased with increasing hydrogen flow. Employing the 8wt% yttria-zirconia 2-second experiment as the base case, a comprehensive sensitivity analysis was performed with macro / micro deposition model. In order of decreasing sensitivity, the temperature regime within the substrate was found to be sensitive to the temperature of the depositing material, the distribution and the torch power delivered to the substrate, the thermal conductivity of the coating, the splat thickness, and the latent heat and the emissivity of the coating. As one of the main objectives of the work was to predict the evolution of temperature in the coating and substrate during the plasma spray deposition process the macro / micro model has been used to examine the zirconia based coatings in some detail. For example, from this analysis it was predicted that the initial cooling rate of the first splat approached 107 °C/s. This rapid cooling could limit diffusional processes from occurring and thus a non-equilibrium tetragonal phase is expected to be found within the coating, as reported in the literature [28]. As the deposition process continues, the cooling rate of the overlayed deposits decreases substantially such that the cooling rate drops to 200 °C/s at 0.63 mm from the substrate / coating interface. The consequences of this in terms of the phase content remain to be established. Owing to the fact that the 8wt% yttria-zirconia undergoes a tetragonal-monoclinic phase transformation upon cooling, resulting 149 in a 3% increase in volume, the effect of phase content and distribution could have a significant bearing on the development of stress and, micro and macro crack formation. In addition to the potential variation in phase content, it was found that for the case where the deposition process occurs for two seconds, the surface temperature of the zirconia coating near the torch centre was predicted to reach approximately 500 °C above the melting temperature. Under the same conditions the temperature gradient across the coating was predicted to exceed 2000 °C/mm. Moreover, after the plasma torch was removed, the surface was predicted to cool faster than the subsurface of the coating resulting in a layer of liquid encapsulated between two solidified layers. In addition to the obvious effect on through-coating temperature gradient, the consequences of liquid and solidification on the generation of thermal stresses and micro / macro cracking remains to be established. Likewise, the effect of the liquid on coating porosity and permeability remains to be determined. An examination of the variation in coating porosity with thickness revealed a gradual decrease with increasing distance from the substrate interface consistent with the presence of plastic flow and elevated temperatures. In order to establish the veracity of the model, the macro / micro deposition model was used to analyze the remaining experiments conducted using a stationary torch depositing 8wt% yttria-zirconia, 17% Co-WC and CP titanium. The procedure involved modifying the depositing powder temperature input to the model until good agreement between the experimental thermocouple results and the model predictions was obtained. It was found that particle temperatures of 2700, 2300 and 3200°C yielded the best overall agreement for the 8wt% yttria-zirconia, 17% Co-WC and CP titanium powders, 150 respectively. To assess these results, the particle temperatures predicted using the model were then compared with the temperatures measured in an independent study on the Axial i n torch aimed at determining the particle velocity, temperature and trajectory (refer to Figure 11) [41, 88]. Unfortunately, only the CP titanium powder experiments were done under identical torch operating conditions. Nevertheless, the results of the heat flow-based analysis were found to agree with the pyrometer-based measurements for the case of 8wt% yttria-zirconia and to within 4% for 17% Co-WC and 16% for CP titanium powder, which is remarkable considering the complexity of the process. In summary, based on the agreement between the evolution of temperature predicted by the model in the substrate and that measured with embedded thermocouples, it may be concluded that the macro / micro heat flow model is capable of quantitatively predicting the evolution of temperature within a substrate undergoing plasma spray coating. Further, based on agreement between the particle deposition temperatures predicted by the model and those measured in the independent studies [41, 88], and, on the agreement between the variation in temperature in the coating predicted by the model and variation in porosity found in the coating, it may be concluded that the model is able to qualitatively predict the evolution of temperature within the coating during plasma spray deposition. A corollary result is that a practical means of estimating powder temperatures has also been demonstrated. This research programme, and in particular the model, provides the foundation for understanding in fundamental terms the factors that influence the structure of coatings formed during the plasma spray deposition process. 151 In terms of the impact of the study on the field of plasma spray coating, it was found that micro-pores within the coating could be reduced or potentially eliminated if sufficient heat to cause melting was accumulated in the coating during plasma spraying. Further, based on the results from the model it may be inferred that a number of process parameters are likely to have a significant impact on microstructure in addition to torch power and gas flow rates. These include: deposition rate; traverse velocity of the plasma torch with respect to the substrate; work piece to torch distance (standoff distance); substrate cooling and; thermal mass of substrate (ability to dissipate heat). 8. 2 Recommendations for Future Work More work is needed measuring particle temperatures in the plasma spray deposition process. The formation of macro cracks, discussed earlier, remains to be examined further. Given an understanding of the evolution of temperature, the evolution of stress may also be estimated using a mathematical model. Further work would also be needed on the quantification of the thermomechanical behaviour of plasma sprayed coatings. This investigation has focused on the analysis of a torch stationary with respect to the substrate target. In most applications this is not the case, in that the torch generally moves relative to the substrate. 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[57] McDonald, G. and Hendricks, R. C , "Effect of Thermal Cycling on Zr02 -Y2O3 Thermal Barrier Coatings", Thin Solid Films, Vol. 73, 1980, pp. 491 - 496. [58] Eckold, G.; Golder, B. and Scott, K. T., "A Theoretical Analysis of Residual Stresses in Flame Sprayed Brittle Materials", Second International Conference on Surface Engineering: Stratford-Upon-Avon, England, 16 - 18 June, 1987, pp. 433 - 446. [59] Chang, G. C. and Phucharoen, W., "Behavior of Thermal Barrier Coatings for Advanced Gas Turbine Blades", Surface and Coatings Technology, Vol. 30, 1987, pp. 13 - 28. [60] Chang, G. C. and Phucharoen, W., "Finite Element Thermal Stress Solutions for Thermal Barrier Coatings", Surface and Coatings Technology, Vol. 32, 1987, pp. 307 - 325. [61] Berger, E . ; Perrin, N.; Boussuge, M . and Burlet, H., "Numerical Simulation of the Thermo-Mechanical Behaviour of Thick Ceramic Coatings", Third International Symposium on Ceramic Materials and Components for Engines, (Edited by Tennery, V . J.), Las Vegas, 27 - 30, November, 1988, pp. 528 - 537. [62] Takeuchi, S.; Ito, M . and Takeda, K., "Modelling of Residual Stress in Plasma-Sprayed Coatings: Effect of Substrate Temperature", Surface and Coatings Technology, Vol. 43/44, 1990, pp. 426 - 435. [63] Lu, J. and Flavenot, J. F., "The Residual Stresses Distribution and Microstructure Studies in Advanced Coating Materials", Surface Modification Technologies JU, pp. 101 - 113, (Edited by Sudarshan, T. S. and Bhat, D. G.); Proceedings of the 3r International Conference held in Neuchatel, Switzerland, August 28 - September 1, 1989, The Minerals, Metals & Materials Society, 1990. [64] Gill, S. C. and Clyne, T. W., "Stress Distributions and Material Response in Thermal Spraying of Metallic and Ceramic Deposits", Metallurgical Transactions B, Vol. 21B, April, 1990, pp. 377 - 385. [65] Elsing, R.; Knotek, O. and Baiting, U., "Investigation of Thermal Spraying Processes Using Simulation Methods", Journal of Materials Processing Technology, Vol. 26, 1991, pp. 217-226. • 157 [66] Steffens, H. D. and Gramlich, M . , "FEM-analysis of Plasma Sprayed Thermal Barrier Coatings", Proceedings of the International Thermal Spray Conference & Exposition, Orlando, Florida, USA, 28 May - 5 June, 1992, pp. 531 - 536. [67] Cockcroft, S. L . , "Thermal Stress Analysis of Fused-Cast Monofrax-S Refractories", Ph.D. Thesis, University of British Columbia, Canada, September, 1990. [68] Parker, W. J., Jenkins, R. J., Butler, C. P., and Abbott, G. L . , "Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity", Journal of Applied Physics, Vol. 32, No. 9, September, 1961, pp. 1679 - 1684. [69] Henning, C. D., and Parker, R., "Transient Response of an Intrinsic Thermocouple", Journal of Heat Transfer, Transactions of A S M E , Vol. 146, 1967, pp. 39. [70] Pehlke, R. D., Jeyarajan, A. and Wada, H., "Summary of Thermal Properties for Casting Alloys and Mold Materials", Department of Materials and Metallurgical Engineering, University of Michigan, December, 1982. [71] Pekshev, P. Y. and Murzin, I. G., "Modelling of Porosity of Plasma Sprayed Materials", Surface and Coatings Technology, Vol. 56, 1993, pp. 199 - 208. [72] Garrett, K. W. and Bailey, J. E. , "The effect of resin failure strain on the tensile properties of glass fibre-reinforced polyester cross-ply laminates", Journal of Material Science, Vol. 12, 1977, pp. 2189-2194. [73] Zienkiewicz, O. C , "The Finite Element Method in Structural and Continuum Mechanics", McGraw-Hill, London, England, 1971. [74] Tripp, D. W., "Modelling Power Transfer in Electron Beam Heating of Cylinders", Ph.D. Thesis, University of British Columbia, Canada, April 1994. [75] Carslaw, H. S. and Jaeger, J. C , "Conduction of Heat in Solids", 2nd Edition, Oxford University Press, 1959, p. 112. [76] Eyres, N. R., Hartree, D. R., Ingham, J., Jackson, R., Sarjant, R. J., and Wagstaff, J. B., "The Calculation of Variable Heat Flow in Solids", Philosophical Transactions of the Royal Society of London, 240A, 1946, pp. 1-57. [77] Sarjant, R. J. and Slack, M . R., "Internal Temperature Distribution in the Cooling and Reheating of Steel Ingots", Journal of the Iron and Steel Institute, 177, 1954, pp. 428-444. [78] Adams, C. M . , "Thermal Consideration in Freezing", Liquid Metals and Solidification, American Society of Metals, 1958, pp.187-217. [79] Wong, H. W. W., Cockcroft, S. L. , Mitchell, A., and Ross, D., "Estimation of Heat Flux Distribution by Inverse Problem", Proceedings of the Sixth Inverse Problems in Engineering Seminar, (Edited by Diego A. Murio) University of Cincinnati, June 13-14, 1994. 158 [80] Woodbury, K. A., "Determination of Surface Heat Fluxes During Spray Quenching of Aluminum Using an Inverse Technique", Paper 91-WA-HT-12, The American Society of Mechanical Engineers, December, 1991. [81] Wiskel, J. B., "Thermal Analysis of the Startup Phase for D.C. Casting of an AA5182 Aluminium Ingot", Ph.D. Thesis, University of British Columbia, Canada, July 1995. [82] Beck, J. V.; Blackwell, B. and St. Clair, C. R. Jr., "Inverse Heat Conduction - III posed problems", John Wiley & Sons, New York, 1985. [83] Beck, J. V . and Arnold, K. J., "Parameter Estimation in Engineering and Science", John Wiley & Sons, New York, 1977. [84] Imwinkelried, T., "Modelling of a Single Crystal Turbine Blade Solidification Process", Ph. D. Thesis, Ecole Polytechnique Federale De Lausanne, 1993. [85] Huang, C. H. and Ozisik, M . N , "Optimal Regularization Method to Determine the Strength of a Plane Surface Heat Source", International Journal of Heat and Fluid Flow, Vol. 12, No. 2, June 1991, pp. 173 - 178. [86] Moreau, C , Gougeon, P., Lamontagne, M . , Lascasse, V. , Vaudreuil, G., and Cielo, P., "On-line Control of the Plasma Spraying Process by Monitoring the Temperature, Velocity, and Trajectory of In-flight Particles", Thermal Spray Industrial Applications, (Edited by Berndt, C , C., and Bernecki, T. F.), A S M International, Materials Park, OH, USA, 1994, Proceedings of the 7 t h National Thermal Spray Conference, Boston (MA), USA, 20-24 June, 1994, pp. 431 - 437. [87] Morrell, R., "Handbook of Properties of Technical & Engineering Ceramics", Part 1: An Introduction for the Engineer and Designer, London : H. M . S. O., 1985. [88] Ross, D., "Recent Development in Thermal Spraying", First Joint NRC/UBC/Industry Thermal Spray Day Workshop, University of British Columbia, Vancouver, BC, Canada, 26 July, 1995. [89] "Handbook of Chemistry and Physics", 70th Edition, 1989-1990, CRC Press Inc., Boca Raton, Florida, U.S.A.. [90] Stevens, R., "Zirconia and Zirconia Ceramics", Magnesium Elektron Publication No. 113, 2nd Edition. [91] Yih, S. W. H , and Wang, C. T., "Tungsten, Sources, Metallurgy, Properties, and Applications", Plenum Press, New York, 1979. [92] Betteridge, W., "Cobalt and Its aAlloy", John Wiley & Sons, Ellis Horwood Ltd., 1982. [93] TPRC Data Series : "Thermophysical Properties of Matter", Volume 1, IFI/Plenum Data Co., New York, January, 1981. [94] Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., "Numerical Recipes in Fortran", Second Edition, Cambridge University Press, 1992. 159 APPENDIX 1 DIMENSION, MATERIAL AND MESH USED IN THE FINITE-ELEMENT MODEL The mesh used for the model is shown in Figure 78. A total of 205 nodes in 56 elements were used in Tests 1 to 18 and of 359 nodes in 100 elements were used in Tests 19 to 23. The dimension and the property of mesh used in the finite-element model are defined as follows :-4 (o,o) i *n R max y max Figure 78: Mesh dimensions used in the finite-element model Tests y m a x (mm) y (mm) Rmax (mm) r (mm) material 1,2 12 3 70 5 pure Cu 3 to 18 5 1.25 70 5 pure Cu 19 to 23 6 1.5 50 2 AISI - 1008 160 APPENDIX 2 THERMOPHYSICAL PROPERTIES OF MATERIALS USED IN THE MODELS The mathematical model requires thermal conductivity (k) and heat capacity (C p) as functions of temperature. For materials undergoing a phase change, an enthalpy function is also required. Determination of the enthalpy function requires the determination of heats of transformation. The thermophysical properties of pure copper, AISI 1008 and CP titanium are reasonably well established and available in the literature [70, 74]. In contrast, the thermophysical properties of the 8wt% Y 2 0 3 - Z r 0 2 , 17% Co-WC are not well established in the literature. Consequently, thermophysical properties of these materials are estimated based on a rule of mixtures approach. A2.1 Substrate Materials A2.1.1 Pure Copper Pure copper has been used in Tests 1 through 18 for heat flux estimation. The thermal conductivity, heat capacity and density of pure copper at various temperatures has been obtained in the literature [70]. These values have been used to fit a polynomial to describe pure copper conductivity as a function of temperature. The thermal conductivity can be represented by two polynomials, namely kCu = 399.66 - 0.037259 T- 1.6754 x 10"5 T2, T< 1083 °C ( 4 7 ) kCu = 95.00 + 0.10265 T-2.22963 x 10"5 T2, T> 1083 °C 161 This relationship is shown graphically in Figure 79 . 450 Pure Copper 400 h H 350 F-| 300 f-3 "O c o " 250 V to E i— 200 - -150 - -• j Q Q 1 • I . . . . I . . . . I . . . . I 0 500 1000 1500 Temperature (°C) Figure 79: The thermal conductivity of pure copper as a function of temperature The heat capacity of pure copper is reported as C p = 383.41 +0.09916 T, T< 1083 °C (48) C p = 494.5 T> 1083 °C and is shown graphically in Figure 80. The average density of p = 8,920 kg/m 3 is used for pure copper. 162 550 I i | — i i i 500 O «^  CD « 450 CO O CO cu X Pure Copper 400 350 '—1—1—'—>—J-—•—J- _l I I 1_ - i L 500 1000 Temperature (°C) 1500 Figure 80: The heat capacity of pure copper as a function of temperature A2.1.2 AISI-1008 Steel AISI-1008 steel has been used in Tests 19 through 23 for powder deposition analysis. The thermophysical properties of AISI-1008 were available in the literature [70]. The thermal conductivity of AISI-1008 can be represented by four polynomials, namely kFe= 62.34-0.043971 T, kFc= 58.86 - 0.0384 T, kFe= 16.66 + 0.0113 T, kFe= 242.55-0.1398 T, o°c<r<6oo °c 600 ° C < r < 8 4 9 °C 849 ° C < r < 1495 °C T> 1495 °C (49) The relationship between thermal conductivity of AISI-1008 and temperature is shown graphically as Figure 81. 163 70 60 O JE 50 5 £ 40 o "D c o 2 30 CO E h 2 0 | -10 i i i i i i i i i i i i i i i i i i i i i I 1 1 1 ' I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I AISI-1008 Q r 1 1 1 , \ 1 1 1 1 1 1 1 . 1 1 . . . . i . . . . i . . . . i . . . . i . . . . i 0 200 400 600 800 1000 1200 1400 1600 1800 Temperature (°C) Figure 81: The thermal conductivity of AISI-1008 as a function of temperature The heat capacity of AISI-1008 is reported as C p = 474.79 - 0.37427 T + 7.2679 x 10"4 T2, 0 °C < 7/ < 700 °C (50) C p = -3120.96 + 5.68 T, C p = 3764.00 - 3.5 T, C p = 2199.55- 1.545 T, C p = 605.81 +0.048 T, 700 ° C < T < 7 5 0 °C 750 ° C < T < 8 0 0 °C 800 ° c < r < IOOO °c 1000 °C < T and is shown graphically in Figure 82. 164 1200 i i i i l i i i i l AISI - 1008 400 • 1 ' ' 1 1 ' 0 400 o _ U . 600 800 1000 1200 Temperature (°C) Figure 82: The heat capacity of AISI-1008 as a function of temperature The average density of p = 7,860 kg/m 3 was used for AISI-1008. A2. 2 Coating Materials A2. 2.1 Yttria Partially-Stabilized Zirconia Most of the thermophysical properties of yttria partially-stabilized zirconia are available in the literature [87, 89, 90] and reported as the following. Practical density p = 5,200 kg/m 3 [87] Thermal conductivity k =1.1 W/m/°C [87], Considering the average of 10% porosity appeared in the coating, the thermal conductivity of plasma spray zirconia coating is corrected to 1.0 W/m/°C. The thermal 165 conductivity and the density of yttria partially-stabilized zirconia are assumed to be constant at all temperature. Since the specific heat value for yttria partially-stabilized zirconia is not available, specific heat of zirconia has been used in this investigation. The specific heat of zirconia is reported in the literature [89] as C p = 457.18 + 0.3994 T-2.0373 x 10"47/2, 25°C < 7/< 700°C (51) C p = 533.27 + 0.1522 T- 5.9556 x 10"4 T2, T> 700°C and is shown graphically in Figure 83. Figure 83: The heat capacity of zirconia as a function of temperature 166 As described in Chapter 5, the enthalpy method is used for latent heat evolution associated with a phase change. In this method, an enthalpy function is used to calculate a modified heat capacity for those nodes that above or within a phase transition range. Once through a phase transition range, the enthalpy technique is bypassed to reduce the computational load. Zirconia undergoes three transitions during solidification, namely liquid to cubic; cubic to tetragonal; and tetragonal to monoclinic. Two enthalpy changes associated with the transformation of zirconia are reported in the literature [90]. The monoclinic-tetragonal phase transformation of zirconia takes place from 950 to 1,200°C and the enthalpy change of this transformation is reported as 48,238 J/kg. Zirconia solidifies between 2,500 and 2,600 °C and the associate latent heat of fusion is reported to be 662,307 J/kg. Using 25 °C as the zero reference temperature, the enthalpy of zirconia is estimated as AH25 = -11553.3 + 457.2 T+ 0.19 T2 - 0.67 x 10"4 7/3, 25°C<r<700°C (52) AH2< = - 26864.4 + 533.2 T+ 0.07 7/2 - 1.98 x 10"6 T\ 700°C < T< 950°C AH2* = 21373.5 + 533.3 T + 0.07 T2 - 1.98 x 10"6 T\ 1200°C < T< 2500°C AH 9 s = - 292057.22 + 882.9336 T, 9 5 0 ° C < r < 1200°C A H 2 5 = -16965138 + 7505.71 T, 2500°C<7/<2600°C A# 2s = 683679.9 + 533.27 7+ 0.07 T2 - 1.98 x 10"6 T3, 7/>2600oC The Enthalpy function for the zirconia is illustrated in Figure 84. 167 3000000 oi 2000000 h a. si c UJ 1000000 h 1000 2000 Temperature (°C) 4000 Figure 84: The enthalpy function for zirconia A2. 2. 2 17 wt% Cobalt - Tungsten Carbide The thermophysical properties of 17 wt% Co-WC is not well established in the literature. The thermal conductivity and density of 17 wt% Co-WC are selected as the same values for 16 wt% Co-WC reported in the literature [91]. The thermal conductivity and density of this material are assigned as 175 W/m/°C and 13,600 kg/m 3, respectively. The heat capacity of 17 wt% Co-WC is estimated from the function or value of the heat capacity for individual component (WC and Co). Since the heat capacity of W C is not available, the heat capacity of W is used and reported in the literature [91] as C p (in Cal/g/°C) = 0.032 (1- 4805 7/"2) + 2.17 x 10"6 T+ 5.52 x 10"13 T2, 573 K < T< 3073 K 168 The relationship between the heat capacity of Co and temperature is reported in the literature [92] as The heat capacity of cobalt at various temperature not showing in the list will be interpolated using the data listed above. For the first approximation, the approach of rule of mixtures was used for the calculation of thermophysical properties of powder mixture. The heat capacity of 17 wt% Co-WC is estimated as C p : 400 J/kg/°C (0°C) 480 J/kg/°C (200°C) 520 J/kg/0C (400°C) 600 J/kg/°C (600°C) 680 J/kg/°C (800°C) 800J/kg/°C(1000°C) C p = 177.31 + 0.1 T- 9.05 x 10"5 7/2 + 7.92 x 10"8 T3 25 °C < T< 1497°C C p = 379.18-0.02 T+ 1.38 x 10"5 7/2, T> 1497°C (53) and is presented graphically in Figure 85. 169 500 450 ^ 4 0 0 X 350 o as Q . O 300 15 x 250 200 150 0 500 1000 1500 2000 2500 3000 Temperature (°C) Figure 85: The estimated heat capacity of 17% Co-WC as a function of temperature The melting point of pure cobalt is 1,495°C. To implement the enthalpy method, described earlier in Chapter 5, an artificial melting range between 1,493- 1,497°C has been considered. The latent heat of fusion of cobalt is 280,000 J/kg as reported in the literature [89]. Therefore enthalpy function for 17wt% Co-WC is estimated from the latent heat of cobalt and Equation (53) as AH25 = -4462.3 + 177.31 7+0.05 7/2 - 3.02 x 10"5 T3, + 1.98 x 10"8 TA (54) 2 5 ° C < 7 / < 1493°C A # 2 5 = -17491138+ 11900 T, 1493°C<7/< 1497°C A/f 25 = 90816.74 + 379.18 7/+0.01 T2 - 0.46 x 10"5 7/3, T> 1497°C Enthalpy function for 17% Co-WC expressed Equation (54) is illustrated graphically in Figure 86. i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Estimated heat capacity for 17% Co-WC . • ' ' ' 1 • • • • 1 • • • • 1 • • • 1 1 • • • • 1 • • • • 1 1 * • • 170 1200000 1000000 800000 "55 600000 >> a. ca I 400000 LU 200000 0 0 500 1000 1500 2000 2500 3000 Temperature (°C) Figure 86: The estimated enthalpy function for 17% Co-WC A2. 2. 3 CP Titanium The thermal conductivity of titanium at various temperature has been obtained from the literature [74, 93]. These values have been used to fit a polynomial to describe titanium thermal conductivity as a function of temperature. The thermal conductivity can be represented by one polynomial as k= 21.815-1.441 x 10"2r+2.584 x 10" 5r 2 (55) - 1.323 x 10"8 T 3 + 2.583 x 10"12 T\ 25°C < T< 2500°C This relationship is shown graphically in Figure 87. 120 0 S 100 5 >. 1 80 o T> c o O 60 CD H 40 20 0 0 500 1000 1500 2000 2500 3000 3500 Temperature (°C) Figure 87: The thermal conductivity of titanium as a function of temperature The heat capacity of titanium is reported in the literature [74] as C p = 518.8 + 0.220 T, 0°C<r<882°C C p = 459.3 + 0.165 T, 882 °C < T< 1666°C C p = 720.7, 7/> 1666°C and is shown graphically in Figure 88. 172 750 i i i i I i i i i | i i i i | ' I 1 1 1 1 I 1 1 1 C P Titanium 500 • • • 1 1 1 1 1 • 1 • • • 1 1 • • • 1 1 • • • • 1 • • J_L 0 500 1000 1500 2000 2500 3000 3500 Temperature (°C) Figure 88: The heat capacity of titanium as a function of temperature Titanium goes through two transitions in the temperature range of interest, the ct-P transition at 882°C and the solid to liquid transition at 1,666°C. Since there is no transition gap in a pure material, an artificially small transformation range has been imposed in the system. Thus the melting range of CP titanium is assumed to be from 1,664°C to 1,668°C and the a-P transition is assumed to take place from 880°C to 884°C. The latent heat of the solid-solid transition is reported as 87,680 J/kg and the latent heat of fusion as 307,850 J/kg [74]. Using.the heat capacity function (Equation (56)), heats of transition and the associated temperature ranges, the following enthalpy function for titanium can be determine. AH25 = -13039 + 518.8 7/+0.11 T2, 25 °C<7/<880°C (57) AH25 = -19341629 + 22580 T, 880°C<r<884°C 148231.2 + 459.3 T+ 0.08299 T2, 884°C<7/< 1664°C -128134870 + 77690.6 T, 1664 °C < T< 1668°C 250898.5 + 720.7 T, T> 1668°C The enthalpy function for titanium is shown graphically in Figure 89. 3000000 "S 2000000 2 , _ Q . (0 c m 1000000 0 0 1000 2000 3000 4000 Temperature (°C) Figure 89: The enthalpy function for titanium The density of titanium is set to the average value of 4,540 kg/ m 3 . i 1 1— C P Titanium J i l i L 174 APPENDIX 3 ALGORITHM OF THE MICRO MODEL The finite-difference technique has been used in the micro model. This method involves dividing the solid into a number of nodes. An energy balance is applied to each node, which results in an algebraic equation for the temperature of each node. For surface node n which subjected to a heat flux qmpe{asma(r), (defined in Equation 27) the algebraic equation for an implicit finite-difference method at time interval Ar (or indexed time i to i + 1) is : Jf A v . , ( 5 8 ) Qne.t ' : Ay 1- " _ 1 T n 2 At [ T n Tn> The algebraic equation for interior node m is : ^ [rpi+l r p i + l ] , k \ rpi+l rpi+l] _ [ ,+l , ] — [Tm+l-Tm \+-^[Tm-l-Tm J - — [Tm ~Tm\ For the node adjacent to the substrate / coating interface (m = 1), the substrate temperature is held constant over the macro model time step. The spatial resolution Ay, in Equations (58) and (59), can be set to the size which is comparable to the average thickness of the splat. Latent heat of the depositing material is treated mathematically as an increase in the apparent specific heat capacity Cpeff and it is incorporated into the specific heat values. Equations (58) and (59) can be rearranged into Equations (60) and (61) respectively. 175 2Atk pCfAy2 1+-2Atk PCfAy In In' pCf Ay (60) Atk pCfAy i+-2Affc PCfAy 1 m Atk PCfAy2 rl+ l rpl m+l — 1 m (61) are the only unknown terms in Equations (60) and (61). These two equations can therefore be condensed and written in a matrix notation as [A]{T}={B} (62) [A] is a n x n tridiagonal matrix which contains the known coefficients on the left hand side of Equations (60) and (61). {T} is a column matrix consisting of n unknown temperature P+l. Column matrix {B} includes n known coefficients on the right hand side of Equations (60) and (61). Unknown temperature {T} in Equation (62) can readily be solved by a tridiagonal matrix solver [94]. 

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