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Transient Liquid Phase bonding in the nickel base superalloy CM 247 LC Cheng, Jacky Man-Lam 2005

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TRANSIENT LIQUID PHASE BONDING IN THE NICKEL BASE SUPERALLOY C M 247 L C By JACKY MAN-LAM CHENG B . A . S c , The University of British Columbia, 2003  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF M A S T E R OF A P P L I E D  SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES (Materials Engineering)  T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A  November 2005  © Jacky M a n - L a m Cheng, 2005  Abstract In this work, the effects o f temperature and time were investigated on the microstructure and properties o f Transient Liquid Phase bonds in the directionally solidified superalloy C M 247 L C with a commercial braze filler material M B F - 8 0 ( N i - C r - B - C ) .  Specimens  were bonded at 1070°C, 1125°C and 1170°C for durations o f 15 minutes, 1 hour and 4 hours.  The resultant microstructures were then examined metallographically using  optical and scanning electron microscopes. The mechanical properties were determined by micro-hardness and tensile tests.  The microstructure o f bonded joints contained blocky and acicular precipitates in the base material. The chemical compositions o f these precipitates were found to be similar and were nickel depleted and tungsten rich compared to the base metal.  Mechanical tests  made it evident that completion o f the isothermal solidification in a T L P bond joint does not guarantee satisfactory joint properties.  Extensive precipitation o f hard and brittle  phases and chemical inhomogeneity in the joint microstructure warrants further postbond heat treatment.  Models o f the T L P bonding process, available in the literature, were applied i n this work. The apparent activation energy for the diffusion o f boron i n C M 247 L C was found to be 219 kJ/mol.  Analytical models predicted isothermal solidification times i n close  agreement with experimental observations.  Two numerical models were developed in this work included a moving boundary model based on diffusion coefficients and equilibrium compositions and a phenomenological model coupled to thermodynamic and atomic mobility databases. The moving boundary model predicted satisfactory isothermal solidification times.  The phenomenological  model predicted times which were generally lower than those found experimentally. From this work, it is apparent that the mobility data available for boron is insufficient for the current system.  ii  Table of Contents Abstract  ii  Table of Contents  iii  List of Tables  v  List of Figures  vi  List of Symbols  ix  Acknowledgement  xiii  Chapter 1 - Introduction  1  Chapter 2 - Literature Review 2.1  .  The Metallurgy o f Superalloys  4 4  2.1.1  Superalloy Microstructures  4  2.1.2  Superalloy Chemistry  8  2.2  Component Repair Technologies for Superalloys  2.2.1  Fusion Welding  2.2.2  High Temperature Brazing  10  2.2.3  Transient L i q u i d Phase Bonding  15  2.3  .-  9  Evolution o f Microstructure in T L P Bonded Joints  9  19  2.3.1  Ideal Joints  19  2.3.2  Real Joints  20  Chapter 3 - Experimental Methods  26  3.1  Casting  27  3.2  D T A Analysis o f the Interlayer Material  32  3.3  Brazing  34  3.4  Metallography  36  3.5  Mechanical Testing  37  Chapter 4 - Results and Discussion 4.1 4.1.1  39  Microstructure o f T L P Bonded Joints Centerline Eutectic  39 42  iii  4.1.2  Isothermal Solidification Zone  47  4.1.3  Precipitation Zone  48  4.2  H i g h Temperature Tensile Properties  52  4.3  Hardness Properties  56  4.4  Diffusion of A l l o y i n g Elements  60  Chapter 5 - Modeling Predictions 5.1  64  Analytical Models for T L P Bonding  64  5.1.1  Heat U p  65  5.1.2  Liquid Dissolution  66  5.1.3  Widening  68  5.1.4  Isothermal Solidification  70  5.1.5  Homogenization  71  5.2  Predictions from the Analytical Models  72  5.2.1  Thermodynamic Data of the N i - B System  72  5.2.2  Diffusion Coefficient of Boron in N i c k e l  74  5.2.3  Analytical M o d e l Predictions  78  5.3  Numerical Models for T L P Bonding  84  5.3.1  M o v i n g Boundary Models  86  5.3.2  Predictions from the M o v i n g Boundary M o d e l  89  5.3.3  Phenomenological M o d e l  93  5.3.4  Predictions from the Phenomenological M o d e l  96  Chapter 6 - Conclusions  101  6.1  Summary  101  6.2  Recommendations for Future Work  104  References  106  Appendices.....  112  Appendix A - Analytical Solution for the Interlayer Dissolution Stage  112  Appendix B - Analytical Solution for the Widening and Homogenization Stage  115  Appendix C - Analytical Solution of the Isothermal Solidification Stage  118  iv  List of Tables Table 1 - Composition o f common Ni-base superalloys, i n weight percent  8  Table 2 - Compositions o f common nickel-base braze fillers i n weight percent  12  Table 3 - N o m i n a l chemical composition for C M 247 L C in weight percent  26  Table 4 - E D S Analysis o f globular and acicular precipitates adjacent to the braze/substrate interface and i n the precipitation zone o f the substrate material i n a joint bonded at 1125°C for 1 hour  50  Table 5 - H i g h temperature tensile properties o f T L P bonded C M 247 L C joints at 850°C  53  Table 6 - Equilibrium compositions obtained from the N i - D A T A Superalloy Database, Kaufman Binary A l l o y Database and A S M Phase Diagram i n atomic fraction Table 7 - Diffusion coefficients for boron i n nickel at 1170°C  74 74  Table 8 - Apparent diffusion coefficients for boron i n nickel-base superalloys at 1170°C. -.  78  Table 9 - Predicted dissolution width using the analytical model vs. average experimentally observed widths (microns)  83  Table 10 - Dimensionless solidification rate constants, K , calculated using the analytical model outlined by Ramirez et al. for equilibrium compositions defined by various sources at 1070°C, 1125°C and 1170°C  83  Table 11 - The predicted solidification time using analytical models proposed by Ramirez et al. and Gale et al. vs. experimentally observed times (hours)  84  Table 12 - Predicted dissolution width using the moving boundary model vs. experimentally observed widths (microns)  92  Table 13 - Predicted solidification times using the moving boundary model vs. experimentally observed times (hours)  92  Table 14 - Predicted dissolution width using the coupled phenomenological model vs. experimentally observed widths (microns)  99  Table 15 - Predicted solidification time using the coupled phenomenological model vs. experimentally observed times (hours)  99  v  List of Figures Figure 1 - Cut away diagram o f the internals o f a modern high-bypass gas turbine aeroengine (Rolls-Royce Trent 1000) [2]  2  Figure 2 - Increases in temperature capability o f superalloys over their historical development [9]  5  Figure 3 - The evolution o f Superalloy microstructures, showing beneficial phases above and deleterious phases below the diagram [12]  7  Figure 4 - Discretized stages o f the T L P bonding process showing composition variation with distance x. ( A ) Initial composition prior to T L P bonding (B) Dissolution o f the interlayer, (C) Widening and homogenization o f the liquid, (D) Isothermal solidification  16  Figure 5 - (a) N i - B phase diagram [46] (b) Schematic diagram o f the evolved microstructure found in an incompletely isothermal solidified binary alloy joint A ) Eutectic phase formed from the thermal solidification o f residual liquid B ) Solidsolution pro-eutectic phase formed during isothermal solidification C ) Base material  20  Figure 6 - Directional solidification furnace used for casting C M 247 L C substrates  27  Figure 7 - Schematic diagram o f the hot zone o f the directional solidification furnace used for casting C M 247 L C substrates  28  Figure 8 - Longitudinal section o f a cast and heat treated C M 247 L C nickel-base superalloy specimen (2.25 cm long x 3.55 c m diameter)  30  Figure 9 - Cast and heat treated C M 247 L C microstructure consisting o f fine cuboidal gamma prime precipitates in a nickel-solid solution gamma matrix and globular carbides  31  Figure 10 - E D S scan o f a typical carbide precipitate in the cast and heat treated C M 247 L C base material  31  Figure 11 - D T A curve for M B F - 8 0 braze foil during the cooling regime  33  Figure 12 - ( A ) Molybdenum brazing support loaded with a specimen for the processing o f tensile specimens i n a butt-joint configuration. (B) Schematic diagram Figure 13 - Vacuum furnace used for the T L P bonding experiments  vi  34 35  Figure 14 - A test specimen loaded on the Electro-Thermo-Mechanical Tester [69]  38  Figure 15 - Typical microstructures o f T L P bonds in C M 247 L C processed at various temperatures and times  40  Figure 16 - E D S scans o f the centerline phases in a joint produced by holding at 1070°C for 1 hour ( A ) N i c k e l rich eutectic (B) Chromium rich eutectic  44  Figure 17 - E D S scans o f the centerline phases in a joint produced by holding at 1125°C for 1 hour ( A ) N i c k e l rich eutectic (B) Chromium rich eutectic  45  Figure 18 - E D S scans o f the centerline phases in a joint produced by holding at 1170°C for 1 hour ( A ) N i c k e l rich eutectic (B) Chromium rich eutectic  46  Figure 19 - Typical E D S scan o f the isothermal solidification zone in a joint held at 1070°Cfor4hours  47  Figure 20 - ( A ) Precipitation in the isothermal solidification zone o f a joint bonded at 1170°C for 15 minutes. (B) Magnified image o f the region indicated in ( A )  48  Figure 21 - Diffusion induced precipitation zone in the base material o f a joints bonded at 1070°C, 1125°C and 1170°C for 1 Hour  49  Figure 22 - Typical E D S scan o f precipitates bonded at 1125°C for 1 hour detecting the presence o f boron  51  Figure 23 - E D S map scan o f precipitates adjacent to the braze/substrate interface on a sample bonded at 1170°C for 1 hour  51  Figure 24 - E D S map scan o f the diffusion induced precipitation zone in the base material o f a sample bonded at 1170°C for 1 hour  52  Figure 25 - Microstructure o f a joint produced at 1170°C for 4 hours with joint loading. 53 Figure 26 - Fracture surface o f a tensile specimen bonded at 1170°C for 4 hours and tested at 850°C  54  Figure 27 - E D S point scan o f precipitates found i n the fracture surface o f a joint bonded at 1170°C for 4 hours and tested at 850°C  55  Figure 28 - Schematic diagram o f micro-hardness testing locations  56  Figure 29 - Hardness data for samples bonded without joint loading  57  Figure 30 - Hardness data for E T M T tensile samples processed with joint loading  58  vii  Figure 31 - Element concentration profile o f a joint held at various temperatures and times  62  Figure 32 - Schematic o f the interlayer dissolution mechanism  67  Figure 33 - Nickel-Boron phase diagrams generated using Thermo-Calc and (A) N i D A T A Superalloys Database [77] (B) Kaufman Binary A l l o y Database [76] (C) Nickel-Boron phase diagram [46]  73  Figure 34 - Residual liquid measurement of samples processed at 1070°C, 1125°C and 1170°C  76  Figure 35 - The linear relationship between In (m) and i / r u s e d to measure the apparent diffusion coefficient from T L P bonding experiments in C M 247 L C specimens.... 77 Figure 36 - Increase i n liquid width with varying isothermal holding temperature and initial gap widths  79  Figure 37 - Effect of saturation of M P D in the substrate and supersaturation in the liquid filler metal on solidification time  80  Figure 38 - Change in the dimensionless solidification rate constant with temperature.. 81 Figure 39 - Required processing time with initial gap sizes at varying temperatures  82  Figure 40 - Schematic diagram of interface node. The liquid/solid interface is shown by the dashed line and is located in sub-system Sk=X=  S2  87  Figure 41 - Validation o f the moving boundary model against other M B M (Zhou & North and Illingworth) and experimental data from Zhou & North [74, 85]  90  Figure 42 - M o v i n g Boundary M o d e l simulations of T L P bonds at 107Q°C, 1125°C and 1170°C with Ni-0.078 at% B substrates and Ni-18.1 at% B filler material  91  Figure 43 - Phenomenological model simulation o f T L P bonding at 1070°C, 1125°C and 1170°C with Ni-0.078 at% B substrates and Ni-18.1 at% B filler material  viii  98  List of Symbols Analytical Model Symbols  C ° ° , C*  Initial solute concentration o f species / in a specific phase, m o l / m  Cf ,  Equilibrium solidus and liquidus concentrations for species i respectively,  ,L  5  L  Cf  s  mol/m  3  3  D f , Df  Diffusion coefficient o f the solute atom in a specified phase, m /s  D  Effective diffusion coefficient proposed by Shewmon, m /s  D  Pre-exponential term for the diffusivity o f a solute atom, m /s  h  Half-liquid thickness, m  2  2  eff  o  K" , K , p  K  Dimensionless growth constants  Q  Activation energy o f diffusion, J/mol  R  Universal Gas Constant = 8.3144 J mol" K "  T  Temperature, K  t  Time, s  x  Thickness o f the copper interlayer lost through diffusion during the heat-  1  1  up stage as proposed by Niemann and Garrett, m W  Theoretical maximum width o f the liquid, m  Z  Interface displacement by widening v i a dissolution o f the base material, m  m  p  Density o f the solid substrate, kg, m  p  Density o f the liquid interlayer, kg/m  s  L  ix  Moving Boundary Model Symbols ,s c  t  Concentration o f species i i n sub-system Sk at time t, m o l / m  f  L i q u i d phase fraction  h  Interface k  L  Flux o f solute species / across interface  s  Vector denoting sub-system k  At  Time step, s  k  3  mol/m s 2  X  Vector indicating sub-system containing the solid liquid interface  K  M o l a r volume, m / m o l  X,  M o l a r fraction o f solute species /'  Az  Sub-system width, m  3  X  Phenomenological Model Symbols g  Gibbs energy o f a phase, J/mol  g  ref  g'  d jx  Reference Gibbs energy, J/mol Gibbs energy o f ideal mixing, J/mol  g  Excess Gibbs energy, J/mol  g°  Reference Gibbs energy o f species i in a specific phase, J/mol  L  Interaction parameter for the calculation o f the excess energy  AG*  Activation energy for the diffusion o f species i, J/mol  G / , Gf  Interaction parameters for the species p and j  L*  Phenomenological parameter evaluated at the interface k, m o l m J" s  Ly  Phenomenological parameter evaluated at a subsystem  ex  jk  2  , llij  1  1  Phenomenological parameters evaluated at the equilibrium concentrations 9  1  1  1  as defined by local equilibrium in the specified phase, m o l m" J" s"  2  11  Mj, M  Atomic mobility o f species j, m o l m J" s" Product o f the atomic jump distance squared and jump frequency, m Is  Pj"  Chemical potential o f species j i n sub-system  Vp'l  Chemical potential gradient o f species j across the interface I , J/mol  a  J/mol k  xi  Nomenclature ADB  Activated Diffusion Brazing  ADH  Activated Diffusion Healing  CALPHAD  C A L c u l a t i o n o f P H A s e Diagrams  DFB  Diffusion Brazing  DS  Directional Solidified  DTA  Differential Thermal Analysis  EDM  Electro Discharge Machining  EDS  Energy Dispersive Spectrography  ETMT  Electro Thermo Mechanical Tester  EBW  Electron Beam Welding  GTAW  Gas Tungsten A r c Welding  HAZ  Heat Affected Zone  LBW  Laser Beam Welding  LIPIB  L i q u i d Infiltrated Powder Interlayer Bonding  LPM  Liburdi Powder Metallurgy ™  MBM  M o v i n g Boundary M o d e l  MPD  Melting Point Depressant  PAW  Plasma A r c Welding  PWHT  Post W e l d Heat Treatment  SEM  Scanning Electron Microscope  SX  Single Crystal  TLIM  Transient Insert Liquid Metal  TLP  Transient Liquid Phase  TLPS  Transient Liquid Phase Sintering  xii  Acknowledgement The author would like to thank his supervisors, Dr. Roger C . Reed and Dr. A i n u l Ahktar for their invaluable guidance and encouragement throughout this work. I am grateful for the financial support and helpful discussions with Dr. Prakash Patnaik o f the I A R N R C .  A s a considerable amount o f equipment was created for this study, a great many thanks go out to the technical support staff at U B C for their assistance with special mention to Rudy Cardeno, Ross M c C l e o d , Carl N g , Dave Torok and M a r y Mager. In addition, I would like to acknowledge the invaluable aid provided by Matt Brooks o f the N P L , U K for assistance on the E T M T .  I would also like to thank my family and friends for their encouragement over the years and I would like to dedicate this thesis to them.  xiii  Chapter 1  Introduction  A high bypass gas-turbine engine (Figure 1) is composed o f four sections. A fan located at the front o f the engine accelerates the incoming air producing thrust. A portion o f the incoming air is passed through the core o f the engine which is passed through a compressor, compressing it into a high pressure stream that is mixed and combusted with fuel in the combustion chamber located in the midsection. The hot, high pressure off-gas stream is passed through the end section consisting o f a series o f turbine blades which extract energy from the gas to power the compressor and fan sections. But long before gas-turbines were envisioned for use as jet engines, they were being developed for use as superchargers i n aircraft internal combustion engines to provide a pressurized air/fuel mixture, because o f the lower air pressure at higher altitudes [1].  In the 1940s major advances in the gas turbine prompted a need for high strength alloys capable o f being operated at elevated temperatures.  It was found that the compressor  outlet and turbine inlet temperatures are direct factors for engine efficiencies prompting the development o f materials with superior properties.  The term "Superalloy" was  coined for a group o f materials that were designed for this purpose and encompasses a range o f materials including nickel, nickel-iron, cobalt and titanium base alloys.  1  While the history o f the development o f the jet turbine engine is intertwined with the advances i n superalloys, there have been many other applications where these materials with superior strength, high temperature capability and resistance to corrosion and oxidation have found a home including land-based turbines, helium reactors, heat exchangers, furnaces and sour gas equipment.  Figure 1 - Cut away diagram of the internals of a modern high-bypass gas turbine aeroengine (Rolls-Royce Trent 1000) [2]. Superalloys are created from carefully tailored microstructures  from  which these  materials inherit their properties. However, due to the harsh operating environment, the resulting damage accumulated by superalloy components limit their operating life. In the case o f high performance components, the high cost o f their fabrication makes it economical to repair damaged components even though complicated repairs may cost up to 2/3 o f the cost o f a new component [3].  2  A number o f repair techniques are available for revitalizing hot engine  components  including fusion welding, brazing and more recently Transient L i q u i d Phase ( T L P ) bonding.  The T L P bonding process is a repair process that is derived from high  temperature brazing. However, unlike brazing, T L P bonding depends on the diffusion o f melting point depressants ( M P D ) out o f the liquid, subsequently raising the melting temperature o f the liquid which induces solidification isothermally.  W i t h sufficient  homogenization time, this allows a joint to be produced that has properties similar to those o f the base material and avoids unwanted precipitation o f secondary phases [4]. The creation o f successful joints however requires the optimization o f processing parameters as  insufficient processing  time  or temperature results  i n poor joint  microstructures, whereas excessive processing time results in poor economics. development  The  o f repair technologies has traditionally been empirically based w i t h  emphasis only on process modeling in recent years [5].  W i t h process modeling, the  optimal processing conditions can be estimated without excessive experimentation thus resulting in cost and time savings.  The purpose o f this work is to examine the T L P bonding process and develop a coupled thermodynamic/phenomenological diffusion model for determining the effect o f bonding parameters on the nickel-base superalloy C M 247 L C . This alloy is a modified version o f the popular polycrystalline superalloy M A R - M 247 which was created in the early 1970s by Danesi & Lund at Martin Metals Corporation (now Lockheed-Martin, U S A ) . Modifications were made for improved directional solidification castability i n thin walled structures such as gas turbine blades.  Further modifications o f the composition o f C M  247 L C * have led to the series o f nickel-base single crystal superalloys designated by the C M S X * name which are also used i n turbine blade applications [6]. Experiments were performed in parallel to validate the model and to assess the quality o f the joints produced by T L P bonding using various processing parameters.  What follows is an  overview o f the metallurgy o f superalloys, their repair techniques and T L P bonding.  * C M 247 L C and C M S X is the trademark of Cannon Muskegon Corporation (Muskegon, MI, USA)  3  Chapter 2  Literature Review  2.1 The Metallurgy of Superalloys The critical role that superalloys played i n the development o f the gas turbine engine has been such that the limits o f the materials properties have become the limits o f the engine. The role o f a turbine blade is to extract power from a hot stream o f gas which generally imparts immense stresses on components. Higher operation temperatures are pursued to bring about  increased efficiency  which brings about  reduced  fuel  consumption.  Impurities i n the fuel cause hot corrosion and the hot gas stream quickly oxidizes unprotected surfaces [7]. A t the high temperatures and stresses employed by gas turbine engines, most materials tend to creep over time making them dimensionally unsuitable for the task. Since the materials operate i n a temperature range from room temperature up to near their melting temperature, the issue o f phase stability is critical. The reasons for the remarkable properties o f superalloys can be found in their microstructure.  2.1.1 Superalloy Microstructures The desired microstructure o f a superalloy component is dependant on the role o f that component.  In turbine disc applications, the low-cycle fatigue from high loads during  take-off and landing operations and l o w centrifugal forces experienced by these  4  components prompts the use o f a fine grain equiaxed microstructure.  Such a  microstructure has superior fatigue resistance but relatively low resistance to temperature and environment.  Whereas, in stationary turbine vanes and rotating turbine blades,  components are typically made o f high temperature resistant alloys which can be equiaxed or columnar grained or even have a single crystal structure depending on the proximity to the gas inlet. These components have superior creep resistance and stress rupture properties in addition to high temperature strength, corrosion, and oxidation resistance.  The elimination o f transverse grain boundaries in columnar grain structures  and the elimination o f all grain boundaries with single crystal technology resulted i n improved high temperature creep properties because o f the elimination o f grain boundary sliding.  Because o f the high temperature and centrifugal stresses placed on these  components, turbine blade alloys are compared to each other by their stress rupture properties. Figure 2 shows the increase in temperature capability with the development o f better alloys and structures. C M 247 L C has similar temperature capability as M A R M 2 0 0 H f D S [8].  Mechanical alloying Columnar grain directional structures  Cast alloys  C  1000  900  W  HastelloyB  m  Nl^aso & « [ o co-base Cast a OS and SC P/M A ODS NHiase  1980  -fir.  Year Introduced  Figure 2 - Increases in temperature capability of superalloys over their historical development [9].  5  The primary constituent phases o f most modern nickel-base superalloys are:  1) y phase, F C C austenitic 2) y' phase, ordered L l intermetallic 2  3) carbides  The  y phase is the continuous austenitic matrix comprised primarily o f N i with solid  solution strengthening provided by C o , Cr, M o , W .  While the alloy obtains a large  portion o f its strength from the y phase which is a solid solution, the majority o f the strengthening is gained from the ordered y' precipitates found within the y grains.  The  y' phase is an intermetallic with an ordered LI2 structure represented by an A3B  compound where relatively electronegative elements, such as N i or C o fill the ' A ' position, and electropositive elements like A l , T i or T a fill the ' B ' position. Thus, typically i n a nickel-base superalloy, y' could have the chemical formula (Ni, Co)3(Al, T i , Ta)  [10].  The y' phase has a primitive cubic LI2 crystal structure with the A l atoms  forming the cubic crystal and the N i atoms located at the face centers. The morphology of the precipitate is governed by the degree o f lattice mismatch between the y and y' phases. Hagel and Beattie observed that for small mismatches o f < 0.05%, y ' precipitates are spherical, between 0.5% -1.0% they have a cubic morphology and at those > 1.25%, plates are formed [11].  Carbides are found in polycrystalline equiaxed grain and columnar grain microstructures. In both these alloys, carbon is added to form grain-boundary strengthening carbides which improve the strength by pinning dislocations at the grain boundaries and inhibiting grain boundary sliding [10].  6  Figure 3 shows the history o f evolution o f microstructures in typical superalloys showing the beneficial and the detrimental phases.  1940  1950  1960  1970  1980  Figure 3 - The evolution of Superalloy microstructures, showing beneficial phases above and deleterious phases below the diagram [12].  In precipitation hardened alloys, the high strength properties are derived from interactions between the ordered y' precipitates and the motion o f dislocations.  In order for a  dislocation to cut through a y' precipitate it must travel i n pairs (superdislocations) due to a high energy penalty incurred by traveling through an ordered phase. A superdislocation is formed by the coupling o f two dislocations linked by an anti-phase boundary [11].  The effectiveness o f precipitates is influenced by the particle size and volume fraction. In the case o f large precipitates, dislocations find it easier to bow between them and loop around them. W i t h small precipitates, it requires less energy for dislocations to climb and bypass them rather than cutting through.  The mechanical synergy between these two  phases has been optimized in modern alloys that contain around 70% by volume y' [13].  7  2.1.2 Superalloy Chemistry Superalloy compositions are carefully tailored to produce a microstructure with specific properties.  Modern nickel-based superalloys are composed o f a complex chemical  system comprised o f as many as ten elements all o f which are tailored for an alloy. Table 1 shows the variations in chemistry between different types o f superalloys. IN-738 L C is a polycrystalline equiaxed grain superalloy, C M 247 L C is a directionally solidified (DS) superalloy that later was used to develop single crystal ( S X ) superalloys such as C M S X - 2 (1 generation) and C M S X - 4 ( 2 st  nd  generation) [14].  Table 1 - Composition of common Ni-base superalloys, in weight percent. Alloy  Co  Cr  Mo  Al  Ti  Ta  W  Re  Hf  B  c  Zr  Nb  Ni  Inconel 738 LC  8.5  16.0  1.7  3.4  3.4  1.7  2.6  -  -  0.01  0.11  0.05  0.9  Bal  CM 247 LC  9.2  8.1  0.5  5.6  0.7  3.2  9.5  -  1.4  0.015  0.07  0.07  -  Bal  CMSX-2  4.6  8.0  0.6  5.6  0.9  5.8  7.9  -  -  -  -  -  -  Bal  CMSX-4  9  6.5  0.5  5.6  1  6.4  6  3  -  -  -  -  -  Bal  Elements used in alloying nickel-base superalloys can be categorized into four types. The first type o f elements is called y formers which segregate preferentially into the disordered  Ni  strengthening.  matrix,  stabilizing and  strengthening  it  through  Examples o f such elements are C o , M o , W , and Re.  solid  solution  In the second  category, elements preferentially segregate to the y' precipitates and serve to stabilize and strengthen that phase. A l , T i , N b and T a are examples o f y' formers.  Grain boundary  strengtheners form the  grain  third class o f elements used.  Typical  boundary  strengtheners found i n polycrystalline superalloys are C , B , N b , Zr, and Hf.  These  elements are added because they preferentially migrate to grain boundaries forming carbides which add strength to polycrystalline superalloys. H f is a notable addition in D S alloys because it assists in strengthening the grain boundaries and avoids grain boundary cracking [14]. A l and C r are also added because o f their tendency to form oxide scales that provide environmental protection from oxidation and corrosion.  8  2.2 Component Repair Technologies for Superalloys In cyclical duty engines such as those used i n aero-engines, the primary modes o f failure are thermal mechanical fatigue, high-cycle fatigue, rubs/wear and foreign object damage [15].  Aero-engine components are complicated cast components with specifically  tailored microstructures, have a limited service life with expensive overhaul and replacement costs.  The refurbishment o f these components is complex; often this  involves many steps including cleaning, pre-repair heat treatment, brazing or welding, machining, coating and post-repair heat treatment. However, due to the high costs o f replacement  it is economical to perform limited repairs to increase the life o f  components.  For the repair o f hot section components, the most common techniques  used are fusion welding and brazing.  2.2.1 Fusion Welding Typical blade repairs include restoration o f blade tip or tip shroud dimensions to strict tolerances using weld overlay processes.  Manual gas tungsten arc welding ( G T A W ) is  commonly used for these tasks but plasma arc welding ( P A W ) [16], laser beam welding ( L B W ) [17] and electron beam welding ( E B W ) [18] are finding increased usage i n overhaul processes.  W e l d filler compositions are derived from lean solid solution  strengthened or gamma-prime precipitate strengthened alloys with modifications for component  coating compatibility and joint strength.  Consequently weld  fillers  commonly have small amounts o f aluminum to increase coating compatibility with aluminide coatings by pack cementation and alloy additions which increase the strength o f the joint [15]. However, repairs by fusion welding o f superalloys with high aluminum and titanium content (> 6 wt. % A l + T i ) are complicated by micro-fissuring i n the heat affected zone ( H A Z ) during welding and/or during post weld heat treatment ( P W H T ) . Micro-fissuring in these alloys is attributed to the residual stresses induced by the rapid dissolution and reprecipitation o f y' in the weld joint [19,20]. Ojo has reported that a high volume fraction o f y' precipitates also contributes to the microfissuring during  9  welding by constitutionally liquidating the H A Z [21]. To avoid these problems long preweld and post-weld heat treatments are often employed and the chemistry o f the filler material is carefully selected to create consequently weaker but more ductile joints than the base material [3]. A s such, weld repairs are generally not made in highly stressed areas o f engine components.  Large microstructural changes are also induced i n  components repaired by fusion welding which are undesirable i n D S and S X components. M a n y modern superalloys such as IN-617, IN-738 and M A R - M 247 are not easily weldable because o f these problems.  2.2.2 High Temperature Brazing Due to the limitations o f fusion welds, high temperature brazing was developed as an alternative repair technique and is widely used for the repair o f many engine components. Brazing techniques offer advantages such as l o w thermal exposures with little or no dissolution o f the base material, low mechanical stresses and the ability to j o i n complicated  geometries,  dissimilar materials  and  create joints  with temperature  capabilities approaching that o f the base material(s) [22].  In high temperature brazing, a lower melting filler material is inserted between two base material surfaces.  The assembly is heated above the liquidus o f the filler material but  below the melting temperature o f the base material. The liquid filler material flows into the gap between the surfaces o f the joint by capillary action and solutes from the joint and base material interdiffuse forming a metallurgical bond.  The component is held for  sufficient time such that the liquid flows and fills the gap.  Solidification o f the joint  occurs during cooling. Following solidification, a post bonding heat treatment is often employed to homogenize the joint and dissolve unwanted secondary phases. Flux-less high temperature brazing is performed in vacuum using pressures in the order o f ICT 4  10" torr on nickel-base superalloys due to their affinity for oxygen at high temperatures. 6  In the  aerospace industry, high temperature brazing is used to repair  components  such as vanes, stators and combustion liners.  stationary  Critical, highly stressed  locations on components are not permitted to be repaired by brazing methods because it  10  is considered unreliable due to the uncertainty that a crack is completely healed by the repair process [23]. Obtaining a sound brazed joint requires careful consideration o f the following:  •  Base material characteristics  •  Filler material characteristics  •  Surface preparation  •  Gap design  •  Temperature  •  Time  2.2.2.1 Filler Alloy Selection The following characteristics are considered in selecting a braze filler material: wetting o f the substrate, flow characteristics, high stability to prevent reactions with the base material, and the ability to alloy with the base material to form a composition having a remelt temperature higher than the bonding temperature.  Wettability can be defined as the degree o f local equilibrium established at the solid/liquid interface [22].  It can be measured by the contact angle between a liquid  braze filler and the base material. However, adequate wetting does not imply good flow characteristics.  The viscosity o f a braze filler is also important for flow.  Braze filler  materials with narrow melting ranges close to eutectic compositions generally have lower viscosities resulting in better flow characteristics than those with wider melting ranges i.e. far from eutectic compositions [22].  A special class o f commercial braze fillers called diffusion braze fillers are classified as braze fillers with fast diffusing melting point depressant ( M P D ) . For example a N i - B - C r braze filler material is considered a diffusion braze filler because it contains boron as the only melting point depressant which is a fast diffusing interstitial atom. However, N i - B Si filler alloys are not considered diffusion alloys because i n addition to boron, they  11  contain silicon which is a slow diffusing substitutional atom. However, all braze alloys have M P D s that diffuse to some degree.  Diffusion brazing takes advantage o f the  diffusivity o f these elements to drive the melting temperature o f the joint up and dissolve brittle intermetallic phase that form upon resolidification. This can be extremely useful i n high temperature joints for aero-engine applications.  The compositions o f a range o f  typical nickel-base brazes is shown in Table 2.  Table 2 - Compositions of common nickel-base braze fillers in weight percent. Chemical System  Trade Name*  C  Cr  B  Si  Ni  Other  Ni-B-Si  MBF 30  0.06  -  3.2  4.5  bal  984  1054  Ni-B-Si-Cr  MBF 50  0.08  19  1.5  7.3  bal  -  1052  1144  Ni-P  MBF 60  0.1  -  -  11 P  883  921  MBF 80  0.06  15.2  4  -  bal  Ni-B-Cr  bal  -  1048  1091  Solidus Liquidus °C •°C  "Metglas Inc. (Conway, SC, USA) [24].  2.2.2.2 Surface Preparation Braze flow is facilitated by capillary action which results from surface energy effects. The braze alloy contact angle is a measure o f the surface free energy between the liquid/vapor, solid/vapor and liquid/solid interfaces.  A low surface free energy at the  solid/liquid interface results i n a small contact angle and better spreading o f the liquid over the solid.  The presence o f surface oxides increases the surface free energy and  prevents wetting. Therefore, surface preparation is vital to the quality o f a brazed joint. A n excellent review on the theory o f the wetting o f surfaces by liquids i n brazing can be found by Gale & Butts [25].  In practice components are chemically stripped to remove coatings, oils and greases followed by mechanical cleaning o f the surface by grit blasting to eliminate persistent oxides. For narrow cracks, reactive gas treatments are commonly used [26]. In alloys with low T i and A l contents hydrogen gas cleaning is deemed sufficient to clean the surface.  A l l o y s with high T i and A l , contents contain more persistent aluminum and  titanium oxides which cannot be broken down i n hydrogen gas. Hydrogen fluoride has  12  proven to be effective for removing stable aluminum and titanium oxides that form on nickel-base superalloy surfaces [27].  The following chemical reactions take place to  remove the oxides from the surface [28].  6 H F + AI2O3 4HF + T i 0  2  6HF + C r 0 2  ->  2A1F + 3 H 0 2  (1)  TiF + 2H 0  (2)  3  4  ->  3  2  3 H 0 + 2CrF + F 2  2  (3)  2  In addition to removal o f the oxides on the surface and within cracks, surface depletion o f elements such as titanium and aluminum also occurs which enhances wettability by removing oxide formers.  3 H F + A1  -»  A l F + 3/2H  3HF + T i  -»•  T i F + 3/2H  3  3  (4)  2  (5)  2  2.2.2.3 Gap Size Gap tolerances must be created such that they are narrow enough for the braze filler material to flow through them by capillary flow.  In the extreme case, i f a joint is too  narrow then the alloy w i l l be "sluggish" at the braze temperature and w i l l not flow into the gap thus forming voids. O n the other extreme, i f the gap is too large, then the filler flows out o f the joint because o f a lack o f capillary forces to hold the liquid i n place. Moreover, wide gaps have a tendency to form voids due to shrinkage effects.  Another  drawback o f large gaps is the formation o f a large amount o f eutectic due to insufficient diffusion and solubility o f the melting point depressant contained in the braze filler alloy. Typically, narrow gap brazing clearances that range from 0.03 to 0.08 m m (0.001 to 0.003 in.) result in superior capillary action and greatest joint strength [22].  Wide gap joints are needed i n applications such as the rebuilding o f missing sections o f an airfoil or building up the thickness in a section o f a component. Wide gap braze fillers are formulated with a mixture o f two types o f materials often referred to as composite  13  braze filler materials. The mixture consists o f some ratio o f the base alloy and a hightemperature braze alloy powder with M P D s mixed i n desired proportions. This modified filler material has a desirably inferior flow characteristic to that o f conventional braze fillers since not all o f the filler is molten at the brazing temperature [23].  2.2.2.4 Brazing Temperature and Holding Time The brazing temperature is chosen such that it remains above the liquidus o f the braze filler but below the solidus o f the base material.  Excessively high temperatures may  cause undesirable changes in the base-material such as annealing, grain growth or warpage.  However, higher temperatures also improve wetting, fluid flow and enhance  the mobility o f melting point depressants resulting in higher remelt temperatures.  To  avoid heat induced changes, the processing time is chosen to allow sufficient time for complete melting o f the braze filler in the joint(s) and to achieve capillary flow and limited to avoid excessive thermal exposure. In a typical brazing cycle, a soak time o f 15 - 30 minutes is usually employed.  Heating rates are initially kept low to prevent thermal shock and the possibility o f spalling or distortion o f the braze filler on the substrate. After a soak at a temperature below the filler material solidus, a fast heating rate to the brazing temperature is employed to prevent the liquidation o f the braze filler where the lower melting point constituents melt separately from the bulk. Rapid cooling is usually employed to reduce thermal exposure but it is controlled to avoid cracking or distortion o f the part.  2.2.2.5 Brazing Defects In the event that insufficient time is provided for post bond heat treatment, the brazed joint would have a melt-back temperature lower than expected, especially i f unwanted stable l o w melting phases are formed. Improper surface preparation, excessive gap sizes, entrapped gas or improper fixturing can lead to porosity or cavities within a joint. This can be catastrophic unless detected through non-destructive evaluation. Through visual inspection the exterior would appear sound while damage could exist  14  underneath.  Another limitation o f high temperature brazing is the formation o f brittle eutectics upon cooling from the bonding temperature.  This is caused by insufficient diffusion o f the  M P D s from the bond region and result i n a joint having poor ductility.  A n alternative to high temperature brazing is diffusion brazing also known as Transient L i q u i d Phase ( T L P ) bonding.  Joints in T L P bonding are prepared similarly to high  temperature braze joints and share all the same processing equipment.  T L P bonding  shares many o f the advantages o f high temperature brazing such as being a capillary joining process which allows for multiple joints to be performed at the same time and a higher degree o f geometrical freedom and has the added advantages o f avoiding secondary phase precipitation and joint properties similar to the base material.  2.2.3 Transient Liquid Phase Bonding Transient liquid phase bonding, a derivative o f high-temperature  fluxless vacuum  brazing, is widely used in aerospace, land-based power generation and other industries for primary fabrication and post-service repairs. In common with brazing T L P bonding depends upon the use o f a thin liquid-forming interlayer (typically less than 50 urn thick), with a melting-point (initially) below that o f the substrate material [25,29,30]. However, unlike i n brazing, extensive interdiffusion between the interlayer and the substrate occurs resulting in isothermal solidification during processing and a joint results that has composition and mechanical properties similar to those o f the base material. Because o f the similarities, furnaces used to perform vacuum brazing, materials such as commercial brazing foils and fundamentals regarding wetting and joint design can be shared.  In the T L P bonding processes, a thin interlayer containing M P D s is placed i n between two mating surfaces.  The assembly is then heated to the bonding temperature under an  inert atmosphere or vacuum.  A s the assembly is held at the joining temperature, the  quickly diffusing M P D components diffuse into the substrate, locally increasing the melting point o f the interlayer adjacent to the substrate [4].  In this way, a joint is  produced by isothermal solidification without the precipitation o f unwanted phases [30].  15  The solidified structure can be homogenized to reduce the solute gradient at the joint to produce composition, microstructure and mechanical properties similar to those o f the substrate [31].  Figure 4 is a schematic diagram o f the bonding process. The T L P process is described as consisting o f five stages consisting o f heat-up, dissolution, widening, isothermal solidification, and homogenization [29]. These can be divided into four distinct phases as follows.  -CoL  c o  E  •CLS  C  <u o  c  o O  o O  -*-CSL  ~ 0) o c o O  -«-CLS  ~  -CLS  -CSL  O  o^-CSL  COS  (B)  (A)  (D)  (C)  Figure 4 - Discretized stages of the T L P bonding process showing composition variation with distance x. (A) Initial composition prior to T L P bonding (B) Dissolution of the interlayer, ( C ) Widening and homogenization of the liquid, (D) Isothermal solidification.  Phase I is referred to as the 0  th  Stage or heat-up. In this phase, the assembly is heated up  from room temperature to the brazing temperature.  Diffusion o f solute from the  interlayer into the substrate consequently must be accounted for, especially for thin interlayers where a portion o f the interlayer can be consumed during heating.  Phase II consists o f two stages: dissolution o f the interlayer (if it is not already molten at the processing temperature) and widening o f the liquid through dissolution o f the base material.  These two stages are  combined into one phase because they  occur  simultaneously during bonding. A t the bonding temperature, an interlayer can initially be in the liquid or solid state depending on its composition and the chemical system. In the case o f a solid interlayer at the bonding temperature, Stage I - Dissolution w i l l occur. In Stage I, M P D s  from the interlayer diffuse  into the parent material which w i l l  simultaneously lower the equilibrium solidus and liquidus temperatures o f the substrate  16  and interlayer materials. This results in the formation o f liquid regions at the interfaces between the interlayer and the substrate. In this model it is assumed that discrete solidliquid interfaces exist between the substrate and liquid and the liquid and the interlayer with two-phase regions that are infinitely narrow. A s the assembly is held at the bonding temperature the liquid regions grow and the interlayer is consumed. Stage II - Widening is the widening o f the liquid which is shared by T L P bonding with both o f the types o f interlayers described above. In this stage the M P D continues to diffuse into the substrate material further dissolving the parent material. A t the completion o f Phase II - Stage II Widening, the liquid region is assumed to have reached its maximum width which corresponds to when the composition o f the liquid has reached a value where its liquidus temperature is equal to that o f the bonding temperature. Similarly, the substrate material immediately adjacent to the solid-liquid interface would have a composition equal to a value where its solidus temperature is equal to the bonding temperature.  Phase III is called isothermal solidification. This is the most time consuming phase since it depends on the width o f the liquid created by the dissolution and widening o f the joint and the relatively slow rate o f diffusion o f the M P D through the solid substrate. During this stage, the M P D continues to diffuse into the base material, decreasing the solute concentration i n the liquid region driving isothermal solidification. During the isothermal solidification o f a binary alloy system, the compositions on either side o f the solid/liquid interface are respectively equal to the solidus and liquidus compositions as defined by the equilibrium tie lines according to the local equilibrium assumption.  In Phase I V the solute concentration peaks are reduced i n the assembly i n the so-called homogenization stage. This process occurs similarly to homogenization processes i n a conventional heat treatment. Normally, this stage is continued until the concentration peaks are reduced to a predetermined maximum level. This theoretically w i l l improve the mechanical properties and increase the melt-back temperature o f the joint.  17  2.2.3.1 Variants and Applications of TLP Bonding Transient liquid phase bonding is a term that has been used interchangeably i n the literature with diffusion brazing ( D F B ) and Transient Liquid Insert Metal ( T L I M ) bonding.  In many cases the authors have not distinguished it from high temperature  brazing because there are many similarities between both processes.  A l s o , there have  been many patents obtained on similar technologies which utilize common solidification mechanisms but different configurations such as Activated Diffusion Healing ( A D H ) [32], Liburdi Powder Metallurgy™ ( L P M ) [33] Transient Liquid Insert Metal ( T L I M ) [34], Transient L i q u i d Phase Sintering ( T L P S ) [35] and L i q u i d Infiltrated Powder Interlayer Bonding (LIPIB) [36]. Activated Diffusion Braze/Bonding ( A D B ) [37] is also commonly confused with T L P bonding.  In A D B a bond is created by conventional  brazing methods, it is then heat-treated to dissolve precipitates that form upon thermal solidification.  T L P bonding can be used to join a variety o f material systems including nickel-base superalloys, titanium, boron-aluminum composites and semiconductor materials.  The  process can also be potentially expanded to include any class o f materials where the diffusion o f a M P D from an additive interlayer leads to the creation o f a liquid and further diffusion o f the M P D leads to solidification.  Over the last 30 years, several  variants o f T L P bonding have been produced by various companies and research groups for different materials systems [30] including joining o f ceramics [38], intermetallics [3941] and fabrication o f ceramic fiber reinforced metal matrix composites [42].  There are three general classifications o f T L P interlayers which have been used i n the literature. In Type I processes, the interlayer is a pure metal which is the M P D . It either melts and diffuses into the base material or interacts with the base material to create a lower melting liquid.  This type o f interlayer exhibits extensive widening o f the liquid  region [43]. Type II processes use an interlayer composition close to that o f the parent and thus the widening/homogenization stage is reduced or avoided.  Composite  interlayers form the third type. The interlayers comprise o f a lower melting constituent  18  and a higher melting constituent, the latter with a higher level o f alloying [34].  These  interlayers are particularly useful in filling wide gap T L P bond joints [36].  2.3 Evolution of Microstructure in TLP Bonded Joints In common with conventional brazing, the quality o f the microstructure created i n T L P bonding depends on the processing parameters employed.  The chemical system, gap  size, processing temperature, joint loading, and the microstructure o f the base material can all have considerable influence on the final microstructure.  2.3.1 Ideal Joints In a binary chemical system, an ideal joint that has completely solidified by isothermal solidification would not precipitate secondary phases. In the special case o f the bonding o f two single crystals, an epitaxial growth mechanism would produce a joint with no grain boundaries [44]. It has been shown that with post-bond solution heat treatment and aging heat treatments it is possible to eliminate all traces o f an interface, however, this can take several days o f heat treatment [45].  In the event o f incomplete isothermal solidification, the residual liquid would solidify in the same way as i n a brazed joint. For example, in the case o f a binary N i - 4 wt% B alloy, a M 3 B eutectic would form from the solidification o f the residual liquid (Figure 5).  19  Weight Percent Boron  (a)  (b)  Figure 5 - (a) Ni-B phase diagram [46] (b) Schematic diagram of the evolved microstructure found in an incompletely isothermal solidified binary alloy joint A) Eutectic phase formed from the thermal solidification of residual liquid B) Solid-solution proeutectic phase formed during isothermal solidification C) Base material.  2.3.2 Real Joints In contrast to the chemical systems used in the ideal binary alloy model, real commercial systems consist o f complex, highly alloyed base materials and filler materials.  This  creates complicated chemical systems where deviations from the conventional model may occur.  Gap widths which are carefully controlled can still vary slightly and  processing parameters such as bonding temperature and joint loading have significant influence over the final microstructure. There is also evidence obtained recently that base material grain boundaries andfast diffusing, low solubility M P D s such as boron can also cause deviations from ideal models o f T L P bonding [47].  2.3.2.1 Effect of Composition The addition o f alloying elements i n the filler material or substrate increases the complexities o f chemical interactions in the bonding system.  Although there is limited  work reported in the literature on the effects o f a change in the chemistry o f the base  20  material, variations in filler material chemistry have been quite extensively researched for brazing nickel-base superalloys [48,49].  In commercial nickel-base braze fillers, boron, silicon, phosphorous or combinations o f these are commonly used as M P D s . In T L P bonding, boron is preferred because it has the highest diffusivity amongst the M P D s mentioned and very little boron is needed to depress the melting point o f nickel [50]. However, its low solubility in nickel can lead to the formation o f brittle intermetallic boride phases decreasing the mechanical properties o f the component. Boron also has a strong driving force for combining with chromium to form  0364  and O3B5 which results the adjacent regions becoming chromium depleted  and decreased corrosion resistance [51]. However, W u argues that boron segregation is not entirely detrimental to the mechanical properties o f the joint since the tensile properties o f some boron containing stainless steels have similar tensile properties to other  stainless  steels with similar compositions without boron  [52,53].  Boron  preferentially segregates to grain boundaries [51] forming borides which provide grain boundary pinning resulting in favorable stress rupture properties as it decreases the tendency for grain boundary sliding during high temperature creep.  Borides on grain  boundaries also inhibit grain growth resulting in smaller grains adjacent to the joint interface than further away from the joint [52].  In single crystal superalloys, the grain boundary strengthening elements are removed because they lead to lower melting temperature structures which can result i n nonoptimal heat treatment. However, when T L P bonding these alloys, a small misorientation o f the crystal structures can lead to the creation o f a grain boundary.  Since these joints  would not have the required grain boundary strengtheners to pin the grain boundaries, the joints would exhibit poor mechanical properties [54]. In properly aligned T L P bonded specimens, mechanical tests performed on single crystal C M S X - 2  showed tensile  strengths and low cycle fatigue properties similar to base material properties.  However,  the elongation was notably lower than in the base material, this being attributed to the possibility o f borides pinning low angle grain boundaries [31].  21  A s with high temperature braze fillers, the composition o f T L P bond fillers benefits from the addition o f chromium to increase the corrosion resistance o f the joint. This alloying addition however has an impact on the chemical system o f the joint.  For example,  Ohsasa [55] observed that the solidification products o f a N i - C r - B residual liquid precipitated a ternary eutectic made up o f a nickel solid solution, M 3 B and C r B upon cooling from 1100°C.  A l l o y i n g additions present i n the base material can enter the joint v i a a mixing o f the dissolved base material with the liquid filler and through diffusion during bonding and the following heat treatment. The degree o f interdiffusion increases with temperature but is relatively slow compared to that during isothermal solidification due to the sluggish diffusion o f heavy alloying elements [56]. The interdiffusion o f these elements is the primary goal o f the homogenization stage following completed bonding, because the braze filler often does not contain vital strengthening additions as they can slow the rate o f isothermal solidification [45].  2.3.2.2 Effect of Gap Size For very narrow gaps, it is important to increase the heating rate o f the bonding process to ensure proper melting and flow o f the filler material. When slow heating rates are used, M P D s are lost to the base material during heating and can prevent the proper formation o f a joint due to premature solidification [57].  In wide gaps the need for longer processing times to complete isothermal solidification arises.  If a conventional filler material were used i n wide gap applications, the total  quantity o f M P D can quickly saturate the base material, especially in the case o f boron where the solubility in nickel is low. This results in long bonding times for large gaps. It is observed that for a given processing time and temperature, an increase in gap size results in an increased volume o f eutectic [58].  22  Composite interlayers have been found to be better for wide gaps than conventional filler materials and are similar i n composition to wide-gap braze  fillers.  T L P bonding with  wide gap braze fillers are performed at temperatures above the lower melting point constituent which contains M P D s but below the higher melting point constituent which is highly alloyed but does not contain M P D [34].  A s with wide-gap braze fillers, it is  intended that the composite filler material have poor flow properties during bonding and thus become useful for filling wide gaps or building up surfaces that have been worn away. The rate o f solidification o f a wide gap joint is increased when using composite filler  materials because o f the lower total amount o f M P D as well as a decreased  diffusion distance since the higher melting constituent acts as a sponge for the M P D [49].  2.3.2.3 Effect of Bonding Temperature The diffusivity o f M P D s increases with temperature, promoting a shorter isothermal solidification stage. A n increased bonding temperature also increases the dissolution o f the base material due to lower solubility o f M P D at the base material-liquid interface. But raising the temperature is generally restricted to avoid damaging the base material microstructure by excessive thermal exposure during long bonding cycles. There has been evidence that elevated temperatures can also influence the rate o f isothermal solidification negatively. Idowu observed that the wide-gap T L P bonding o f PW 738 L C with a N i - C r - B filler material resulted i n a slower isothermal solidification rate when bonding at temperatures o f 1160°C and 1175°C as opposed to 1130°C and 1145°C due to enrichment o f the liquid with solutes from the base material [59].  Slower diffusing  M P D s such as T i , Z r and N b were suspected to have diffused from the base material into the liquid and influenced the solidification path o f the joint.  2.3.2.4 Effect of Joint Loading Rabinkin reported that a slight load on braze joints improved the microstructure and subsequent mechanical properties o f high temperature braze joints due to the so-called "ejection model" [51].  In this model, it is postulated that an increase i n joint loading  assists in reducing the amount o f eutectic by squeezing out liquid from the joint. This  23  also decreases the time for complete isothermal solidification.  A reduction in gap size  also reduces the diffusion distances required for heat treatment thus reducing the processing time required to produce a joint with similar structure to that o f the base material. Similar observations were made in T L P joints in polycrystalline M A R - M 247 [60] and single crystal C M S X - 2 [31].  2.3.2.5 Effect of Grain Boundaries The existence o f grain boundaries i n the base material can assist i n the breakdown o f planar interfaces by liquid penetration along the grain boundaries.  Small atoms such as  boron are known to segregate to grain boundaries and move quickly along them. It has been suggested that the grain boundaries facilitate liquid penetration into the substrate past the primary joint interface resulting i n non-planar interfaces [52]. Grain boundaries have also been shown to accelerate the isothermal solidification rate by increasing the interfacial area [61]. The grain boundary effect was noted by Saida who observed that single crystal materials had the slowest rate o f solidification when compared to coarse grain and fine grain materials, with the fine grain material having the highest rate o f solidification [62].  2.3.2.6 Deviations from Local Equilibrium Most models o f T L P bonding assume that a state o f local equilibrium is reached at the solid-liquid interface.  A l l stages o f the bonding process are also assumed to remain  sequential and do not occur i n parallel. Because o f these assumptions, the formation o f secondary phases cannot occur i f the joint is allowed to completely solidify by isothermal solidification.  However, there is recent evidence that deviations from local equilibrium  occur in real systems.  Ojo observed a deviation from local equilibrium i n T L P bonded  IN-738 L C with a N i - C r - B filler alloy which contained intragranular and intergranular precipitation o f C r and N i rich boride precipitates in regions adjacent to the braze joint interface at temperatures below the N i - B eutectic temperature (1080°C) and just C r rich borides above the N i - B eutectic temperature (1140°C) but below the C r - B eutectic temperature (1500°C) [63]. Gale also reported similar evidence i n N i joints made with  24  N i - S i - B filler alloys [47]. Ni-rich borides were observed adjacent to bond-lines after 1 minute at 1065°C and remained stable even after completion o f isothermal solidification. A t 1150°C extensive liquidation o f the substrate was observed especially at the substrate grain boundaries. In the experiments performed by Ojo and Gale the concentration o f the boron exceeded the solubility limit in the base material resulting i n anomalous precipitation o f borides.  This is counter to conventional T L P bonding models which  assume local equilibrium would have taken place and would not account for these precipitates.  Gale postulated that this deviation might occur only when fast diffusing  M P D s are used and that the unexpected precipitation i n the isothermal solidification region occurred prior to the establishment o f local equilibrium at the solid liquid interface [25].  25  Chapter 3  Experimental Methods  The experiments were conducted with two objectives i n mind.  First, the effect o f  bonding parameters on the T L P bonding o f the superalloy C M 247 L C was examined. This information is currently lacking i n the literature. Secondly, quantitative evaluation was made o f the microstructures so as to compare the results with the predictions o f the modeling work conducted in this work.  Table 3 shows the nominal chemical composition for C M 247 L C . Cast C M 247 L C is a precipitation hardened nickel-base superalloy yielding a 65-68 volume percent fine coherent y' precipitates [14].  Table 3 - Nominal chemical composition for CM 247 LC in weight percent. Co  Cr  Mo  Al  Ti  Ta  W  Hf  B .  9.2  8.1  0.5  5.6  0.7  3.2  9.5  1.4  0.015  C  Zr  Ni  0.07  0.015  Bal  The braze filler material used i n this study is MJ3F-80, a quaternary N i - C r - B - C nickelbase diffusion braze filler.  The nominal composition o f M B F - 8 0 by weight percent is  26  15.2 Cr, 4 B , 0.06 C , balance N i and has a solidus and liquidus o f 1048°C and 1091°C respectively as listed in Table 2.  3.1 Casting Specimens were cast into columnar grain structures with a directional solidification furnace.  The casting furnace is shown below in Figures 6 and 7.  The raw sample  material was obtained from a 7.6 cm diameter x 15 cm long polycrystalline cylindrical charge.  This charge contained solidification shrinkage along the cylinder axis and  exhibited a large degree o f chemical segregation inherent in castings o f this type.  The  charge was divided longitudinally using wire-feed electric discharge machining ( E D M ) to form  uniform  wedge  shaped  charges  for  subsequent  remelting  and  directional  solidification.  Figure 6 - Directional solidification furnace used for casting CM 247 LC substrates.  27  :  o  o  o  o  o  o  o  o  o  o  o  o  Quartz Tube  Induction C o i l s  Ceramic M o u l d Support  M o t o r i z e d Stainless Steel P i s t o n  Figure 7 - Schematic diagram of the hot zone of the directional solidification furnace used for casting C M 247 L C substrates.  28  The directional solidification furnace was constructed by using a 58 c m long x 6.35 cm O D fused quartz process tube to form the hot zone o f the furnace.  The hot zone was  created using a high frequency induction heater and a molybdenum susceptor fixed to the ceramic mould. A stainless steel chamber at the base o f the furnace was used to load and unload castings.  Melting was carried out i n a controlled atmosphere.  The following  procedure was used. First, a diffusion pump and roughing pump combination produced a vacuum o f better than l x l 0 " torr. Then,-the furnace was back-filled with a static argon 5  atmosphere during casting. Oxidation was further reduced by employing titanium wire as a getter. A titanium wire was heated using a Variac transformer i n the cold zone o f the furnace during the entire melting and solidification process. In addition, a titanium wire was wrapped around the susceptor and heated v i a induction heating to prevent oxidation i n the hot zone o f the furnace.  To effect the translation o f the solid/liquid interface across the sample and promote directional growth, the furnace employs a motorized stainless steel platform on which sits a non-cooled ceramic mould support which acts to insulate the stainless steel platform from the high processing temperature.  This support is sealed from the surrounding  environment by a double o-ring seal located at the base o f the furnace. A withdrawal rate o f 0.6 cm/min was used for all castings.  The cylindrical castings produced by this  furnace were approximately 5 cm long x 3.55 c m i n diameter.  Heat treatment o f the C M 247 L C substrates was performed according to Harris [14]. The treatment consists o f solutionizing o f the eutectic y' for reprecipitation as a fine uniform y/y' structure and to reduce chemical segregation acquired during casting [64,65]. The solution heat treatment and cooling was performed in an atmospheric superkanthal^ furnace at 1232°C for 2 hours/1243°C for 2 hours/then quenched by air cooling.  The subsequent oxidation layer formed by the lack o f a protective atmosphere was removed v i a sandblasting. E D M cutting was employed to remove the top o f the casting where defects i n the casting are more likely and the bottom o f the casting where an f  Kanthal Super® is a registered trademark of Kanthal (AB, Sweden) 29  equiaxed grain structure would exist. The top and bottom o f each sample was surface ground to produce flat surfaces that were at right angles to the casting direction. The final dimensions o f the semi-cylindrical substrates are 2.25 cm long x 3.55 cm diameter.  The microstructure o f the cast and heat treated C M 247 L C substrates consists o f large columnar grains oriented along the casting direction o f the casting. Figure 8 shows the longitudinal section o f a directionally cast and heat treated specimen that was polished and etched with aqua regia (1 H N O 3 : 3 HC1). A t a higher magnification under an S E M , a finely distributed, coherent y/y' precipitation strengthened structure with inter and intragranular carbides was observed (Figure 9). A s C M 247 L C is a D S superalloy, the composition is engineered to produce a favorable distribution o f carbides.  3.55 cm Figure 8 - Longitudinal section of a cast and heat treated CM 247 LC nickel-base superalloy specimen (2.25 cm long x 3.55 cm diameter).  30  5 ™  (A)  (B)  Figure 9 - Cast and heat treated CM 247 LC microstructure consisting of fine cuboidal gamma prime precipitates in a nickel-solid solution gamma matrix and globular carbides. E D S analysis o f the carbide showed them to be titanium, tantalum, tungsten and hafnium rich (Figure 10).  These microstructural features were similar to those reported in the  literature [14].  Figure 10 - EDS scan of a typical carbide precipitate in the cast and heat treated CM 247 LC base material.  31  3.2 DTA Analysis of the Interlayer Material Differential Thermal Analysis ( D T A ) was performed on the M B F - 8 0 braze filler to determine the solidus and liquidus temperatures o f the braze filler. This information was then used to select suitable temperatures for the brazing experiments.  D T A was performed with a Linseis L81/1750 thermo gravimetric/differential thermal analysis apparatus under an inert flowing argon atmosphere to limit oxidation. D T A analysis involves the measurement o f the temperature difference between the specimen and an inert reference during controlled heating or cooling.  During cooling there w i l l  always be a slight thermal lag due to differences in thermal properties between the sample and reference.  This results in a roughly linear D T A signal.  However, large  differences i n the temperature between the sample and the reference can indicate a change in state i n the specimen due to the release o f energy during such transformations [66]. In the case o f exothermic reactions the D T A signal would result i n a peak whereas an endothermic reaction results in a trough. Changes in heating rate can also result in a D T A signal due to the thermal lag produced by differences in heat capacity between the sample and reference.  It is important to properly interpret a D T A curve when  determining the start and finish points o f a phase transformation.  For an exothermic  phase transformation during the cooling regime, the start o f the phase transformation is defined as the onset temperature. This temperature is the point on the D T A signal curve where deviation occurs from linear behavior. The finish o f the phase transformation is the point on the D T A signal curve where linear behavior is re-established.  In the present work a 0.1 g sample o f the brazing foil was used i n the measurement. A l u m i n a crucibles were used because they are inert towards the sample alloy. A n empty alumina crucible was utilized for the reference.  The sample was heated at a rate o f  15°C/min to a temperature, o f 1200°C and held for 30 minutes. A controlled cooling rate o f 3°C/min was used to cool the specimen to 800°C whereupon the sample was furnace cooled to room temperature. Figure 11 shows the D T A curve through the liquid to solid phase transformation during the cooling regime.  32  The data obtained in the present work show that the solidus and liquidus temperatures are 992°C and 999°C respectively, which is a significant difference from the values o f 1048°C and 1091°C reported by the manufacturer [24].  The solidus and liquidus  temperatures for a N i - 4 wt% B binary alloy are 1090°C and 1130°C respectively according to the N i - B phase diagram. A l l bonding temperatures were selected above the liquidus temperature o f the braze filler but were also either below, in-between, or above the solidus and liquidus temperatures o f the N i - 4 wt% B binary alloy as suggested by Gale [47]. Bonding temperatures o f 1070°C, 1125°C and 1170°C were selected.  33  3.3 Brazing  Butt joints were created by placing a 40 micron thick foil in between two 5 m m thick x 15 m m x 15 m m C M 247 L C substrates cut from the recast and heat treated bars. Spot welding was used to keep the gap width fixed throughout the brazing operation.  To evaluate the tensile properties o f the resultant T L P bonds 45 m m long tensile samples were bonded in butt joint configurations as follows. The cylindrical C M 247 L C castings were cut longitudinally using E D M cutting. The ends o f each semi-cylinder were then surface ground to a uniform length.  This created two equal 22.5 mm long x 35.5 m m  diameter semi-cylindrical specimens.  A 40 micron thick braze foil was placed between  the two substrates and fixed in place by spot welding and placed in a molybdenum brazing support. This configuration resulted in a small load being applied during bonding due to the difference in thermal expansion between molybdenum and C M 247 L C . The bonding configuration is shown in Figure 12.  Braze foil  MBF-80 Braze Foil  \  CM 247 LC Substrates  /  CM 247 LC Substrates  (A)  (B)  Figure 12 - (A) Molybdenum brazing support loaded with a specimen for the processing of tensile specimens in a butt-joint configuration. (B) Schematic diagram.  Prior to joining, all bond faces were polished flat using 1200 grit silicon carbide paper and ultrasonically cleaned in acetone to leave a flat surface without surface oxides. U p o n fixing the braze foil to the substrates by spot welding, the assembly was then loaded into  34  a  tube-type  resistance  heating  vacuum  furnace.  thermocouple was positioned close to the joint.  A  K-type  (chromel-alumel)  H i g h vacuum was achieved by  employing a diffusion pump-roughing pump combination on a fused quartz process tube. The process tube was sealed on both ends with water-cooled brass end-caps with o-ring seals. The vacuum brazing furnace is shown in Figure 13.  Figure 13 - Vacuum furnace used for the T L P bonding experiments.  Brazing was performed in vacuum at better than 10" torr to reduce oxidation during 5  processing. Samples were bonded by heating the specimen to the bonding temperature, holding for a specified time and cooled in vacuum by shutting down the furnace.  The  heating and initial cooling rates employed were measured to be approximately 5°C/min and 9°C/min respectively. Post-bonding heat treatment which is commonly employed in industrial practice to improve joint properties was not used in this work.  35  3.4 Metallography Metallographic samples were sectioned perpendicular to the joint interface after joining by an abrasive cut-off wheel to reveal the internal structure o f the bond. Samples were polished to a 1 micron diamond finish and etched using Pratt & Whitney Etch #17 (150 m L H 0 + 100 m L HC1 + 100 m L H N 0 2  preferentially [67].  3  + 3 g M0O3) which dissolves y' precipitates  Tensile specimens were machined into 1 m m x 2 m m x 40 m m  tensile bars using wire-fed E D M .  Eight samples from each brazing condition were  created and one specimen from each brazing condition was polished to a 1 micron diamond finish, etched and examined to determine the quality o f the bonded joint. These samples were taken to be representative for the other test specimens i n the group.  The joint microstructures were examined by optical microscopy using a N i k o n Epiphot 300 inverted optical microscope with C L E M E X vision image processing software. Scanning electron microscopy was performed under an accelerating voltage o f 20 k V on a Hitachi S-3000N scanning electron microscope. A 5 k V accelerating voltage was used to detect boron.  The system is equipped with a Quartz X O n e Energy Dispersive  Spectroscopy ( E D S ) system which was used to semi-quantitatively measure the change i n chemical composition across the joint. The Quartz X O n e software package applies Z A F correction factors to account for the effects fluorescence on the resulting E D S spectrum.  o f atomic number,  absorption  and  Selected area E D S scans were performed  on regions up to 300 microns away from the joint interface on polished but not etched samples to obtain the change in the average chemical composition across the joint.  The E D S analysis o f superalloy materials warrants a few points that one must keep i n mind.  In general, E D S quantification o f light elements requires large Z A F correction  factors which limit the reliability o f these measurements [68]. Thus the boron and carbon content i n these structures can only be determined qualitatively. In the same regard, aluminum is also considered a light element in this alloy due to the heavy matrix in which it resides.  This also results in large correction factors which can result i n large errors.  Furthermore, the analysis o f cobalt and nickel can lead to some errors as they reside i n  36  similar peaks. A similar argument also exists for the quantification o f tungsten, tantalum and hafnium.  3.5 Mechanical Testing Hardness measurements were made on the various phases contained i n the bonded microstructures. Tests were performed on a microhardness tester with a 25 g load.  3  measurements were taken per zone in 5 zones across the joint interface and an average value is reported.  H i g h temperature tensile tests were performed on an Electro-Thermo-Mechanical-Tester ( E T M T ) designed by the National Physical Laboratory ( N P L , Teddington, U K ) [69]. The E T M T enables high temperature tensile tests as well as creep and stress rupture tests to be carried out. Heating to the desired temperature is achieved by the E T M T through resistance heating. A n R-type 0.1 m m diameter thermocouple (Pt/Pt-13%Rh) was spot welded to the joint interface to measure and control the temperature o f the specimen. The strain on the specimen may be obtained i n the E T M T either through a measurement o f the displacement o f the grips by capacitance measurements or through the change i n resistance o f the specimen.  Resistance measurements across the gauge length o f the  specimen were made by spot welding 0.1 m m diameter platinum 1 m m to each side o f the thermocouple. Samples were tested at 850°C with a strain rate o f 5x10" /s. Tests were 4  performed twice for each bonding condition.  37  Figure 14 - A test specimen loaded on the Electro-Thermo-Mechanical Tester [69].  38  Chapter 4  Results and Discussion The objective o f the experiments was to determine the effects o f bonding time and temperature on the quality o f the T L P bonds produced in the superalloy C M 247 L C . In these experiments, the exposure times selected at a given temperature to produce conditions which would result in partial and complete isothermal solidified joints. Samples in the butt-joint configuration were held at 1070°C, 1125°C and 1170°C each for durations o f 15 minutes, 1 hour and 4 hours.  4.1 Microstructure of TLP Bonded Joints The microstructures as observed on the transverse section are shown in Figure 15. The microstructure o f the completely bonded joints consisted o f a single solid solution phase. B y contrast, incompletely eutectic phases were observed at the joint centerline when isothermal solidification had not progressed to completion. The centerline structure is indicated by L .  The centerline eutectic phases are bordered by an isothermal  solidification zone comprised o f a proeutectic solid-solution region which fills the remainder o f the joint.  Bordering the joint region in both completely and incompletely  isothermal solidified joints is a precipitation zone containing globular and acicular precipitates indicated by P . Further away from the center o f the joint is the unaffected base metal indicated by B . The dissolution width is also indicated in the micrographs by arrows. Each o f these regions is discussed in the following sections.  39  15 Minutes  1 Hour  40  15 Minutes  1 Hour  41  4 Hours  4.1.1 Centerline Eutectic The centerline eutectic structures are formed as a result o f the solidification o f the residual liquid in the joint during the cooling o f the specimen to room temperature.  In  Figure 15, the centerline eutectic is indicated by L and is typically found i n the center o f the joint microstructure.  The width o f the residual liquid in the joint was observed to  decrease with increasing holding time.  In the joint produced at 1070°C, the lower  bonding temperature resulted i n slower diffusion rates for the M P D .  A t the end o f 4  hours o f processing, the joint still contained a centerline eutectic structure with a width only slightly narrower than the joint produced after 1 hour holding time.  In joints  produced at higher temperatures, the isothermal solidification rate was higher resulting in a shorter processing time for the completion o f the bond. For example, joints held at 1170°C were nearly solidified after only 1 hour holding due to the higher diffusion rate o f the M P D .  E D S scans o f the solidified structures in the residual liquid revealed two eutectic phases: a nickel rich phase and a chromium rich phase.  In the microstructures observed, the  nickel rich phases were present in large volumes in the form o f a continuous chain running the length o f the joint. The chromium rich phase was present i n discrete islands. E D S point scans o f these phases detect the presence o f boron concentrations i n these phases. Using E D S mapping, regions o f high chromium content can be detected i n the centerline eutectic phases which correspond to chromium borides. Figures 1 6 - 1 8 show regions o f high chromium content within the braze microstructures produced at 1070°C, 1125°C and 1170°C and the presence o f boron in both eutectic phases.  These observations are similar to those o f Ohsasa who explored the solidification behavior o f residual liquid in the T L P bonding o f a pure nickel substrate using a N i - C r - B filler material [55]. It was shown that at the processing temperature o f 1100°C, a nickel rich solid solution phase was formed by isothermal solidification.  U p o n cooling, a  eutectic reaction producing N i solid-solution and M 3 B resulted at 1042 C. A ternary P  eutectic reaction would follow at 997°C which produced N i solid-solution, N13B and  42  CrB.  Since these phases have lower solidus temperatures than the base material, the  presence o f these eutectic phases can have deleterious consequences on the operation temperature these materials can be used at. Furthermore, as these phases form brittle and continuous chains along the length o f the joint, the existence o f these phases would result in poor mechanical properties.  43  44  45  46  4.1.2 Isothermal Solidification Zone The isothermal solidified region is located adjacent to the centerline eutectic in incompletely isothermal solidified joints.  The isothermally solidified microstructure is  composed o f a proeutectic nickel rich phase and contained a level o f chromium initially close to the braze filler composition (Figure 19). In a completely bonded joint, the entire joint would be comprised o f this phase. The width o f the joint was observed to widen during bonding due to base material dissolution. The final width was found to be a function o f the bonding temperature. The widest joint width was found at the highest processing temperature and the narrowest joint was found i n the lowest bonding temperature.  Ni  Al  Ti Cr Co  Ni Ta W  C r  i  1 0  ii  M  i  1  Li  o  y  at%  3.2 0.4 12.7 5.5 72.5 2.5 3.2  14.1 0.8 6.8 1.0 71.4 0.5 5.4  Ni  C o  C  wt%  T a  w  1  Ta  W  Figure 19 - Typical E D S scan of the isothermal solidification zone in a joint held at 1 0 7 0 ° C  for 4 hours.  Cuboidal precipitates were found i n the isothermal solidification region in the T L P joints processed at 1170°C for all times and in 1125°C after an exposure o f 4 hours.  The  average size o f the precipitates closest to the substrate/filler material interface was approximately 0.5 microns and decreases towards the center o f the joint.  A s w i l l be  shown later (Figure 34), in joints that were held at the processing temperature for longer times, E D S analysis detected alloying elements not initially present i n the filler material in this region due to diffusion from the substrate material.  47  These precipitates  are  suspected to be y' precipitates although this could not be confirmed in the present work. The formation o f these precipitates may be the result o f the diffusion o f y' forming alloying elements from the base material into the joint. For samples bonded at longer times and higher temperatures, precipitates were found to be larger and extended further into the joint. The longer processing time and higher temperature increase the diffusion distances  for the  alloying  elements  in the  substrate into the joint, leading to  homogenization o f the joint. Figure 20 shows the typical morphology o f the precipitates observed in the isothermal solidification zone.  (B)  (A)  Figure 20 - (A) Precipitation in the isothermal solidification zone of a joint bonded at 1170°C for 15 minutes. (B) Magnified image of the region indicated in (A).  4.1.3 Precipitation Zone A mixture o f blocky and acicular precipitates were detected on the filler material side o f the liquid/substrate interface. Further away from the joint centerline were zones o f fine precipitates which grew in size with distance from the center o f the joint as indicated on Figure 15 by P. These zones were composed o f fine precipitates that were observed to have precipitated in the same orientation as acicular precipitates adjacent to the joint interface.  In some samples, it was observed that coarser precipitates that were further  from the joint centerline coalesced and formed long acicular structures.  Comparative  photographs are shown in Figure 21 o f the precipitation zones i n samples bonded at 1070°C, 1125°C and 1170°C for 1 hour.  48  Figure 21 - Diffusion induced precipitation zone in the base material of a joints bonded at 1070°C, 1125°C and 1170°C for 1 Hour. 49  In the sample bonded at 1170°C for 1 hour (Figure 21 - C ) , blocky precipitates adjacent to the filler material/substrate interface were approximately 1-2 microns i n diameter. Adjacent to this region, smaller densely packed blocky precipitates were present. They coarsened with distance from the center o f the joint and reached a maximum size o f 0.5 microns i n diameter.  Still further from these precipitates, acicular precipitates on the  order o f 10-20 microns long and 1 micron wide were present. Similar observations were made i n joints produced at the other two temperatures and other bonding times. These precipitates were also found in the samples that had undergone complete isothermal solidification.  Therefore, they could not have formed from the solidification o f the  residual liquid. The only mechanism for their formation is due to the exceeding o f the solubility limit o f the surrounding material.  E D S scans o f the globular and acicular precipitates showed that they have similar compositions (Table 4). These compositions were similar i n all samples. Both phases were found to be tungsten rich and slightly nickel depleted despite having very different morphologies.  Boron was also detected in these precipitates indicating that the  precipitates may be nickel-borides (Figure 22).  The tungsten rich and slightly nickel  depleted structures were identified by E D S M a p scans.  Figure 23 and Figure 24  respectively show E D S map scans o f the precipitates adjacent to the  filler/substrate  interface and in the precipitation zone.  Table 4 - E D S Analysis of globular and acicular precipitates adjacent to the braze/substrate interface and in the precipitation zone of the substrate material in a joint bonded at 1 1 2 5 ° C for 1 hour. Element Al Ti Cr Co Ni Hf Ta W  Joint/Substrate Interface Blocky Acicular wt% at% wt% at% 6.0 14.7 3.8 10.7 1.0 1.4 0.8 1.3 6.7 8.5 10.8 15.6 6.6 7.4 5.0 6.4 51.3 57.4 36.7 47.4 1.6 0.6 0.0 0.0 3.3 1.2 2.4 1.0 21.9 7.8 38.1 15.7  50  Precipitation Zone Blocky Acicular wt% at% wt% at% 6.1 14.9 3.9 10.9 1.0 1.4 0.8 1.3 6.8 8.6 11.0 15.9 6.7 7.5 5.1 6.5 52.0 57.9 37.6 48.3 1.7 1.6 0.0 0.0 3.4 1.2 2.6 1.1 22.2 7.9 • 39.0 16.0  Figure 22 - Typical EDS scan of precipitates bonded at 1125°C for 1 hour detecting the presence of boron.  Figure 23 - EDS map scan of precipitates adjacent to the braze/substrate interface on a sample bonded at 1170°C for 1 hour. 51  Figure 24 - E D S map scan of the diffusion induced precipitation zone in the base material of a sample bonded at 1170°C for 1 hour.  4.2 High Temperature Tensile Properties H i g h temperature tensile tests were conducted at 850°C. Joint loading was present in the fabrication o f these joints as noted earlier.  Nakahashi [60] has reported that loading  during brazing improves tensile and stress rupture properties.  In the tensile samples  produced i n this work, the microstructures contained considerably lower volume o f residual liquid than in samples produced without loading.  For example, a sample  produced at 1170°C did not exhibit any eutectic structures even when processed for 15 minutes whereas the specimen bonded without load contained a 20 micron wide centerline eutectic structure. The typical joint width was also found to be approximately 30 microns from an initial width o f 40 microns. This indicates the expulsion o f liquid  52  from the joint which would accelerate the solidification process. Precipitation products in the substrate were found to be similar in morphology to those observed in samples processed for longer periods o f time without bond loading (Figure 25). H i g h temperature properties are reported in Table 5 and compared to values found in the literature [14].  Figure 25 - Microstructure of a joint produced at 1170°C for 4 hours with joint loading.  Table 5 - High temperature tensile properties of T L P bonded C M 247 L C joints at 8 5 0 ° C .  Temperature CM 247 LC [141. 1070°C 1070°C 1070°C 1125°C  Residual Liquid Present  Time (h)  -  -  Yes Yes No  0.25 1 4  Yes No  Yield Strength (MPa) 819 313  Ultimate Tensile Strength (MPa)  % Elongation 10.5 0  468 321  830 313 468 321  30* 567  30* 567  0 0  0 0  1125°C  No  0.25 1 4  512  512  0  1170°C  No  0.25  450  450  0  1170°C  No  1  390  390  0  1170°C  No  4  380  380  0  1125°C  * Defects in bonded joint resulted in poor properties  53  In all samples, a brittle joint was observed with poor elongation measured. Necking in the samples was not observed and all joints broke suddenly. While this was expected in joints with residual liquid where brittle eutectic phases form, joints that completed isothermal solidification also exhibited poor properties. The fracture surfaces o f tensile specimens revealed particles which were rich in refractory elements and slightly depleted in nickel (Figure 26). A n E D S point scan o f these particles showed they also contained a significant amount o f boron (Figure 27).  Figure 26 - Fracture surface of a tensile specimen bonded at 1170°C for 4 hours and tested at 850°C.  54  <  G  toy  oo  01  o:  Figure 27 - EDS point scan of precipitates found in the fracture surface of a joint bonded at 1170°C for 4 hours and tested at 850°C. The brittle centerline eutectic is detrimental to the properties o f a joint because it forms a continuous fracture path and results in poor tensile properties. A possible reason for the poor properties in the completed joints is the presence o f unwanted precipitation in the precipitation zone and the anomalous precipitation that occurred adjacent to the filler material/substrate interface.  These precipitates could potentially reduce the ductility in  the joint and result in poor properties.  Furthermore, the lack o f solid-solution  strengthening elements in the filler alloy due to the lack o f a proper post bond heat treatment can lead to a weak joint regardless o f unwanted precipitation.  55  In the sample bonded at 1125°C for 15 minutes, the joint exhibited particularly poor properties.  It is suspected that bonding defects that arose from contamination o f the  sample prevented proper bonding o f this specimen.  4.3 Hardness Properties Hardness testing was performed at 6 locations across the joint interface (Figure 28). These locations were chosen to represent ( A ) The centerline eutectic, (B) isothermally solidified solid-solution hardened phase, ( C - D - E ) diffusion induced precipitation zone, and (F) base material. Differences in sample widths due to processing are avoided using this selective zone hardness testing method.  A  B CD  E  F  Figure 28 - Schematic diagram of micro-hardness testing locations.  Two sets o f samples were examined: microstructural specimens processed without joint loading and samples taken from the E T M T tensile samples which were bonded with a compressive load. Figure 29 and Figure 30 show the hardness data obtained for samples with and without joint loading respectively.  56  Average Hardness (Hv)  1070°C  1125°C  Figure 30 - Hardness data for E T M T tensile samples processed with joint loading.  58  1170°C  In samples created without the joint loading, a hard centerline eutectic was found i n incompletely isothermal solidified joints with an average  micro-hardness  o f 850  HV0.0025 which is significantly higher than the base material that was found to have a micro-hardness o f 450 HV0.0025. The high level o f hardness in these phases suggests an embrittling effect which can allow propagation o f a crack along its continuous length.  In the isothermal solidified region adjacent to the centerline eutectic was the proeutectic nickel solid-solution which had hardness levels o f around 400 H V 0 . 0 0 2 5 .  In samples  that had completed isothermal solidification, the centerline hardness was equal to the isothermal solidified region, both o f which are slightly less than that o f the base material. This indicates that the absence o f strengthening alloy additions i n the filler material results in the need for a longer post-bonding heat treatment.  A longer exposure time  would permit the diffusion o f the desired elements from the base material into the region occupied by the filler, thus improving the properties o f the joint.  The region adjacent to the joint was found to be harder than the base material in all cases with hardness levels decreasing with increased holding time and temperature.  Average  values adjacent to the joint were 600 HV0.0025 indicating that a large amount o f brittle precipitates had formed in this region. A s observed in this work, short holding times promoted the creation o f the precipitates in the precipitation zone and longer holding times resulted i n their dissolution due to homogenization.  The difference i n thermal expansion between the brazing support and the superalloy substrate resulted i n a load being applied during the preparation o f the tensile specimen. This load squeezed liquid out o f the joint during joining and resulted i n liquid widths that were significantly narrower than in samples created without load. Since the gaps were narrower, the completion o f isothermal solidification occurs sooner i n these joints and less residual eutectic remained. Consequently, the peak hardness was lower in the tensile specimens as compared with that o f specimens bonded without loading for an equivalent processing temperature and time (Figure 30). However, the joint loading did not have an  59  effect on the average hardness o f the residual liquid that existed in samples that were incompletely isothermal solidified joints.  4.4 Diffusion of Alloying Elements Due to the lack o f strengthening alloy additions in the braze filler, the diffusion o f chemical elements from the base material into the braze joint is vital for producing a high quality joint. A n advantage o f T L P bonding is that the homogenization o f the bond can be performed in the same processing stage as the bonding by protracting the holding time. Selected area E D S analysis was used to map the composition gradient across the T L P bonded interfaces and the affected base material composition.  The analyzed elements were selected due to their role i n the strengthening o f the superalloy.  A l , T i and Ta are strongly partitioned into the y' phase from which  precipitation hardened superalloys derive their strength.  C o and W are important solid  solution strengthening additions for the y phase. Due to the high concentration o f C r i n the braze filler, it was also prudent to observe the changes i n this element.  While  measurements were made up to 300 microns away from the center o f the joint, only a distance o f 150 microns is reported as no significant change was observed beyond this distance. The results o f the scans are shown below i n Figure 31.  Homogenization o f a higher degree was observed i n joints that had undergone completed isothermal solidification and in joints processed at higher temperatures and longer times. In specimens having undergone incomplete solidification during the isothermal treatment, steep chemical gradients remained between regions containing residual liquid and the isothermally solidified proeutectic region. joints.  A l was the quickest to homogenize i n the  In the sample held at 1170°C for 4 hours, only a slight gradient was observed  between the joint and the base material.  The A l atom is among the smallest i n the  superalloy chemical system and has a relatively high diffusivity.  A t the higher  processing temperature and longer holding times, the emergence  o f the cuboidal  precipitates in the isothermal solidification zone is a product o f the diffusion o f this  60  element into the joint. C o atoms were observed to have diffused into the joint nearly as fast as A l atoms despite being larger than the A l atom.  The C o concentration despite  quickly diffusing into the joint was still deficient i n the joint due to the high concentration normally present i n the base metal.  After 4 hours at 1170°C, the joint  contained only 7 at% C o compared to the 11 at% in the base material. Conversely, the concentration o f T a and T i were relatively low in the substrate but they quickly homogenized i n the joint during the same processing time. A s the joint was rich i n C r atoms due to the alloying o f the filler material, it is interesting to note that the C r concentration i n the joint remained high even after the completion o f solidification. The joint was also found to be W deficient and remained so even i n samples held for 4 hours at 1170°C. This is expected since the diffusion o f W i n N i is amongst the slowest i n all the platinum-group metals [70].  61  15 Minutes  1 Hour  62  4 Hours  15 Minutes  1 Hour  4 Hours  Chapter 5  Modeling Predictions  One o f the advantages o f the T L P bonding is the elimination o f unwanted eutectic phases. However, as noted i n the previous chapter, insufficient processing time leads to incompletely isothermal solidified joints that contain brittle intermetallic structures which can be detrimental to joint strength.  Since there are many processing variables such as  the bonding time and temperature, process modeling is a useful tool for the prediction o f a final joint microstructure.  Process models can fall into three categories: analytical,  numerical and a combination o f analytical and numerical.  Analytical models present  elegant although inflexible solutions for the bonding process but can provide useful information with fast calculations. Numerical models sacrifice speed for flexibility and the ability to accurately predict the behavior o f real systems but are more complicated and slow. In combination models, numerical solutions are used but contain analytical solutions for portions o f the calculations providing intermediate speed and accuracy. In this chapter, the various models i n the literature are explored.  5.1 Analytical Models for TLP Bonding Conventional models describe T L P bonding as discrete stages which are modeled separately from each other as: heating, dissolution, widening, isothermal solidification  64  and homogenization. In general, the models o f T L P bonding depend on the diffusion o f the M P D within the joint assembly. mathematical  Accordingly, models are created by drawing on  solutions to F i c k ' s laws o f diffusion and depend on the  following  assumptions [71, 72]:  •  The materials compose a binary chemical system.  •  A state o f local equilibrium exists at the moving interface.  •  The moving interface is planar.  •  The diffusion coefficients, molar volume and activity coefficient o f the solute are independent o f composition.  •  The molar volumes in different phases are equal.  •  There is negligible liquid flow due to convection & stirring i n the liquid phase.  •  There is no effect o f latent heat.  •  The substrate is completely wetted by the molten filler material.  •  Buildup o f solute in the base material is negligible.  •  Perfect mixing o f solute i n the liquid phase.  •  The stages occur sequentially  5.1.1 Heat Up Niemann and Garrett proposed this solution to account for the diffusion that occurs during the heat up o f the component from room temperature to the brazing temperature [57]. This was proposed because o f the observed loss o f the electroplated copper layer during heat up from room temperature when joining B - A l composite materials using the eutectic bonding technique.  This problem was found to be significant when a thin C u  interlayer was used to produce a liquid in the A l substrate because the interlayer could be consumed during the heat up stage before a liquid was formed.  In Niemann and  Garrett's solution to this problem:  (6)  65  where x is the thickness o f the copper interlayer lost through diffusion, D is the diffusion 3  coefficient o f copper in aluminum, t is time, Cf  L  C°°  ,s  is the solubility o f copper in aluminum,  is the initial copper concentration i n the aluminum substrate, p  L  copper and p  s  is the density o f  is the density o f the alloy. However, this was formulated using constant  diffusion coefficients and solubilities, both o f which are a function o f temperature and cannot remain constant during the heating [5].  To account for this, MacDonald and  Eager suggested that an effective diffusion coefficient be calculated as proposed by Shewmon [29].  Shewmon showed that the contributing diffusive flux occurred above  80% o f the bonding temperature.  Assuming the Arrhenius form o f the diffusion  coefficient, the solution takes the form o f a slowly converging series function:  exp\  Q_ RT  Q\ In (R\  RT  +-  2-2! RT  1 3-3/  (  RT  +.  (?) 10.871  where f is the heating rate. It should be noted that this model does not take into account the change in solubility that would also occur during heating.  5.1.2 Liquid Dissolution The dissolution o f the liquid interlayer can be divided into two stages. Stage 1 occurs from the melting temperature o f the interlayer to the brazing temperature o f the joint. This requires the assumption o f local equilibrium at the solid/liquid interface which changes with temperature as the temperature is ramped to the brazing temperature. Stage 2 occurs at the brazing temperature when the interlayer is undergoing  isothermal  dissolution. A t the end o f this stage, the liquid width reaches a maximum. While there are have been no analytical solutions developed to model stage 1 dissolution, a considerable amount o f work has been performed on stage 2 dissolution. M a c D o n a l d and  66  Eager [29] reported that dissolution occurs first at the interlayer-base material interface forming a liquid and expands in both directions to consume the interlayer and partially dissolve the base material (Figure 32). A t the end o f stage 2 dissolution, the interlayer is  Substrate  Liquid  Interlaye  fully liquid.  Liquid  Substrate  Figure 32 - Schematic of the interlayer dissolution mechanism.  L i u outlines a dissolution model that accounts for the dissolution front proceeding into the interlayer as well as into the base material. This model utilizes F i c k ' s 2  n d  law subject  to the following assumptions [29]:  •  Uni-dimensional diffusion  •  The liquid is static with no convection effect  •  Constant diffusion coefficients  •  Local equilibrium exists at the solid-liquid interface  •  The base material is a semi-infinite domain  •  The solid/liquid interfacial area remains constant  The liquid/base material and liquid/interlayer interfaces are assigned growth constants K  a  and K  p  dimensionless  respectively. A s the motion o f both o f these interfaces are  linked, the growth constants need to be solved simultaneously by solving the two explicit functions derived for each interface:  67  ' —i—K'exp^-l? )-!?-^ _  (8)  2  LS,a  c  c  K ^[erf(K )-erf(K )]-exp(-K ) a  /3  a  =0  a2  (9)  The time for dissolution o f the braze interlayer o f initial thickness 2h at a given temperature can be calculated from the following equation which is a function o f the diffusion o f the M P D in the liquid phase, D : 1  (2h)' ( 1 0 )  The width of the liquid interlayer at the completion o f stage 2 dissolution is:  W =2h + 2K A D t a  r  (11)  T  L  d  These equations were re-derived in the present work and can be found i n Appendix A .  5.1.3  Widening  Widening is the continued dissolution o f the base material from the time after the interlayer is fully liquid until the liquid composition is reduced to the liquidus composition as defined by the equilibrium phase diagram.  The widening problem was  solved similarly by Ramirez & L i u by considering one interface rather than two [72]. Assuming that the diffusion o f boron i n the liquid is the limiting mechanism, the time o f widening and homogenization can then be calculated with the following equation:  '-TiFF  (12)  68  where K is a dimensionless parameter that can be calculated from the following equation [72, 73]:  K=  r is •c. c  SL  4n  \exp(-K ) 2  I erfc(K)  IE D'  r  C  SL  s~iLS  C°°'  SN  (13)  s~iSL  The interface displacement, Z is calculated from the following equation:  K  2  (14)  ,  The theoretical maximum width o f the liquid, concentration, C° , ,L  W, m  is a function o f the  initial  o f the M P D in the interlayer o f thickness, h, and the equilibrium  liquidus composition, C , LS  at the processing temperature [72]:  00,1  W=2h  (15) PL  C  However, this equation does not consider the solute concentration in the base material and assumes that there is a negligible amount present. These equations were re-derived in the present work and can be found in Appendix B .  The use o f an error function solution is considered a poor assumption for this stage because it is only applicable for a semi-infinite couple which is not satisfied i n the thin liquid region [5]. It is also suggested that base material dissolution depends on a nonparabolic relationship and thus no single rate constant should be able to characterize the  69  motion [74]. Zhou et al. noted that numerical techniques have been more successful for modeling this stage o f the bonding process than analytical solutions [5].  5.1.4 Isothermal Solidification During this stage, M P D diffuses from the liquid resulting in the solidification o f the joint. A s this stage is the most time consuming, a number o f models have been devised to determine the processing time required for the completion o f this stage. T w o o f the more popular analytical models were devised by Ramirez et al. [72] and Gale et al. [47].  In the model presented by Ramirez et al., the diffusion controlled moving-interface problem is solved similarly to the previous dissolution and widening stages. The solute distribution i n the liquid is considered uniform and therefore solute diffusion in the liquid can be ignored. In addition, the solid portion can be considered semi-infinite allowing for the use o f error function solutions. The solution for the dimensionless growth constant can be solved from [72, 73]:  K=  1  -C; )exp(-K )  fcf  ^  s  {cr-Cf ) L  2  (16)  erfc(K)  where Cf and C'r are the equilibrium solidus and liquidus concentrations as defined by L  s  the equilibrium tie lines at the bonding temperature. present i n the substrate material.  C*  s  is the M P D concentration  Solving the equation numerically, we can thus  determine the time o f solidification from the following equation which is a function o f the diffusion o f the M P D i n the solid phase, D : 5  (17)  \6K D 2  S  70  These equations were re-derived in the present work and can be found in Appendix C .  Gale et al. successfully applied an alternative model [47] to the isothermal solidification stage. In their model o f this stage, the assembly was treated as the diffusion o f solute from a finite interlayer into a semi-infinite solid substrate. B y utilizing Crank's solution o f F i c k ' s second law o f diffusion [75], the concentration o f a solute at a distance JC from the center o f the joint at a time t is calculated from the following equation:  C(x,t) = C" +\(C ' s  X L  -C°°' ) erf s  h-x  -erf  h+x  (18)  The completion o f isothermal solidification can be determined by calculating the time when the composition o f the center o f the joint, C(0,t ), equals the solidus composition, s  C. sl  Substituting x = 0 and C(0,ts) = C  SL  C -C ' SL  =(C  X S  M i  -C  c o S  into the above equation we get:  (19)  ) erf  5.1.5 Homogenization The homogenization o f cast alloys has been well studied separate from the T L P bonding process for which there are many suitable models.  In general, F i c k ' s law is used to  determine the diffusion o f solute away from the centerline where the concentration would be a maximum.  C=  C ' +(C°-C°' )erf x s  s  (20)  Dt s  71  where C° is the initial peak concentration o f solute in the joint where C = C  SL  at the  beginning o f homogenization for a joint immediately following the completion o f isothermal solidification.  5.2 Predictions from the Analytical Models A s mentioned in the previous chapter, o f the various stages o f the T L P bonding process, the isothermal solidification time and the maximum dissolution width hold the most practical importance. The error associated with ignoring the dissolution time is estimated to be approximately 30 seconds [47] which is insignificant when the time required for T L P bonding is measured in the order o f hours. above  were used to determine  dissolution widths.  In this chapter, the models presented  the predicted isothermal solidification times  and  However, as the modeling predictions are sensitive to the data  sources available, a critical assessment o f the modeling parameters is essential. For the modeling o f the T L P bonding process in C M 247 L C , data on the thermodynamic equilibrium o f the nickel-boron chemical system and diffusivity o f boron ( M P D ) i n the superalloy substrate is required.  5.2.1 Thermodynamic Data of the Ni-B System For the present work, equilibrium constants for the solubility o f boron i n nickel were obtained from several sources.  Equilibrium constants were calculated by using the  thermodynamic calculator Thermo-Calc*.  Two sets o f equilibrium constants were  provided by using the Kaufman Binary A l l o y s Database and the Rolls-Royce pic (London, U . K . ) / Thermotech (Guilford, U . K . ) N i - D A T A Superalloys Database.  The  Kaufman Binary A l l o y Database was produced by Larry Kaufman o f M a n Labs Inc. (Boston, U S A ) . The database was derived from data originally published i n a series o f articles i n the Calphad journal which cover binary systems o f Fe, C r , N i , B , C , C o , M o , N b , T i , W , M n , A l , S i and C u [76].  The Rolls-Royce pic / Thermotech N i - D A T A  database was obtained by measurement o f thermodynamic properties directly from nickel-base superalloys and contains information on the N i - A l - C o - C r - H f - M o - N b - T a - T i -  J  Thermo-Calc is a registered trademark of the Royal Institute, Stockholm, Sweden.  72  W - Z r - B - C system [77]. The A S M binary N i - B phase diagram was also used to obtain a third set o f equilibrium constants [46, 47].  Binary phase diagram tie-lines can be referenced  to determine  the  equilibrium  compositions established during isothermal solidification. However, the phase diagrams from these sources differ from each other. The eutectic temperature, solidus and liquidus lines all vary from one source to another. Furthermore, some phases are missing from the thermodynamic databases.  Figure 33 shows the N i - B phase diagram generated by  Thermo-Calc using the N i - D A T A superalloy thermodynamic database in comparison to the A S M phase diagram. Since these diagrams vary, the equilibrium compositions w i l l differ from each other as shown in Table 6.  15001400co 1300CO  1200-  LU  LIQUID+FCC_A1  ° l 1100LU tr 1000-  fe LT LU CL  sLU 1—  900800-  DIAMCTte_+M2B_TETR FCC_A1 +M2B_TETR  700600500-  0  1 ~~2 3 4^ 5 6 7 WEIGHT_PERCENT B  8  9~ 10 WEIGHT_PERCENT B  (A)  (B)  c  jrature  1300 H  3.^, 7.3  a E  900  10.7 CD  z  CT  70010 Weight Percent Boron  (Q Figure 33 - Nickel-Boron phase diagrams generated using Thermo-Calc and (A) N i - D A T A Superalloys Database [77] (B) Kaufman Binary Alloy Database [76] (C) Nickel-Boron phase diagram [46].  73  Table 6 - Equilibrium compositions obtained from the N i - D A T A Superalloy Database, Kaufman Binary Alloy Database and A S M Phase Diagram in atomic fraction. Ni-DATA Superalloys Database Solidus Liquidus  Temperature  Kaufman Binary Alloy Database Solidus Liquidus  ASM Phase Diagram Solidus  Liquidus  1070°C  0.003  0.168  0.0028  0.1546  0.003  0.181  l^'C  0.003  0.153  0.0021  0.1391  0.003  0.165  1170°C  0.003  0.138  0.0017  0.1254  0.003  0.152  5.2.2 Diffusion Coefficient of Boron in Nickel In general, when non-composition dependent diffusion coefficients are considered, the diffusivity can be calculated from the Arrhenius expression:  D = D exp 0  (21)  RT  Where Q is the activation energy for the diffusion jump i n J/mol, R is the universal gas constant and T is the temperature.  Thus the  diffusion coefficient  is temperature  dependent.  Data on the diffusivity o f boron i n nickel is scarce i n the literature.  Only a handful o f  studies have been conducted i n recent years partly because o f the difficulty i n detecting boron atoms (Table 7).  Table 7 - Diffusion coefficients for boron in nickel at 1 1 7 0 ° C . Do  Source  Q  &  m /s 2  J/mol  m /s 2.170E-10  2  Wang [78]  6.60E-07  9.62E+04  Nakao [34]  1.44E-01  2.26E+05  9.510E-11  Ramirez [72]  3.27E-04  1.66E+05  3.179E-10  Liping *  2.30E-07  7.95E+04  3.050E-10  1.10E-06  9.99E+04  2.664E-10  Chu  T  * As cited by Ramirez & Liu [72] t As cited by Campbell & Boettinger [56]  74  Wang [78] and C h u measured the diffusivity o f boron in nickel by performing particle §  tracking autoradiography experiments. results  by measuring  Ramirez [72] and Nakao [34] observed similar  the rate o f isothermal  solidification during T L P bonding  experiments with nickel-boron binary alloys.  Nakao showed that the apparent diffusion coefficients o f boron i n superalloys can also be calculated by measuring the residual liquid widths o f incomplete isothermal solidified joints created from conventional braze filler materials and superalloys [34].  When  plotted on a graph o f the residual liquid width vs. the square root o f time, the slope o f each isotherm, m, is related to the activation energy o f diffusion, Q, by the analytical solution o f isothermal solidification:  4C /(V p ) SL  ln(m) = ln  where ( ?  y2  s  '  and C  l / 2 l n { D o )  ~2^  ( 2 2 )  are the equilibrium concentration ratios o f the melting point  depressant and Vi and V are the molar volumes o f the liquid and solid phases s  respectively. In real multi-component systems it is not possible to determine equilibrium concentrations o f (f  L  or C . Instead, the first two terms are combined into a constant A. LS  Thus the activation energy o f diffusion is related to the isothermal solidification rate at a given temperature by a linear relation.  ln(m) = A—— 2RT  < > 23  In the present work, the residual eutectic liquid width was measured at the end o f each holding time by examining polished and etched transverse cross-sections of joints with an SEM.  !  The experimentally measured average eutectic width was plotted against the  As cited by Campbell & Boettinger [56]  75  square root o f time as shown i n Figure 34. Figure 35 shows the linear relation between In (m) and 1/T for the above data.  +  E  o  40  •  1070°C 1125°C 1170X  80 Time1«( 1/2) S  Figure 34 - Residual liquid measurement of samples processed at 1 0 7 0 ° C , 1 1 2 5 ° C and 1170°C.  76  0.00068  0.0007  0.00072  0.00074  0.00076  1/T(K- ) 1  Figure 35 - The linear relationship between In (m) and 1/T used to measure the apparent diffusion coefficient from T L P bonding experiments in C M 247 L C specimens.  The apparent activation energy o f diffusion for boron in C M 247 L C was found to be 219 kJ/mol. The activation energy for C M 247 L C is similar to values found in the literature for boron diffusion i n other superalloy measured by Nakao et al. [79].  The apparent  diffusivities had activation energies in the range 199-219 kJ/mol for polycrystalline superalloys and 266 kJ/mol for single crystal C M S X - 2 . Ojo performed similar work on the diffusivity o f boron i n I N 738 L C with close correlation to values measured by Nakao et al. for polycrystalline superalloys.  Ojo cited a frequency factor, D = 0.14 m Is, calculated by Nakao et al. [63]. However, 0  Ojo found that a frequency factor o f D - 0.014 m /s was more appropriate. 2  0  This value  was determined by first back calculating the diffusion coefficient o f boron in the substrate at each temperature by using the isothermal solidification model outlined by  77  Gale et al. [47] in equation (19). The extrapolated time to completion o f the isothermal solidification as measured from the plots o f residual liquid width vs. the square root o f time was used for this purpose.  These diffusion coefficients and their respective  activation energies were then used to determine a common value for D [63]. Using this 0  technique, it was found that a D value o f 0.0163 m /s was appropriate for the present 2  0  system.  The diffusion coefficient calculated in the present work resulted i n a value  similar to those o f other polycrystalline superalloys reported in the literature (Table 8). It should be noted that C M S X - 2 has a diffusion coefficient about two orders o f magnitude lower as compared with the other materials listed i n the table. This is due to the absence of grain boundaries in C M S X - 2 which is a single crystal superalloy.  Table 8 - Apparent diffusion coefficients for boron in nickel-base superalloys at 1 1 7 0 ° C .  m /s  Q J/mol  Present Work  CM 247 LC  0.0163  2.19E+05  1.93E-10  Ojo [63]  IN-738 LC  0.0144  2.18E+05  1.85E-10  Nakao [79]  IN-713  0.144  2.11E+05  3.32E-09  Nakao [79]  IN-600  0.144  2.09E+05  3.92E-09  Nakao [79]  MAR M-247  0.144  1.99E+05  9.03E-09  Nakao [79]  MM 007  0.144  2.19E+05  1.70E-09  Nakao [79]  CMSX-2  0.144  2.66E+05  3.39E-11  Source  Alloy  Do 2  D m /s s  2  5.2.3 Analytical Model Predictions In comparison to other stages, the isothermal solidification stage is the most significant when determining the processing time as this occurs over several hours whereas other stages take a matter o f seconds (with the exception o f the post-bond heat treatment). The heat up stage is generally disregarded because it refers to the loss o f the M P D in the interlayer through diffusion o f solutes during slow heating o f the assembly and can be overcome with faster heating rates. However, the dissolution stage is important due to its effects on the final liquid width. A large final liquid width is unwanted as it results i n longer isothermal solidification times. Using the analytical dissolution model described earlier, it can be shown that accompanying an increase in temperature is an increase i n  78  maximum joint width due to the lower solubility o f boron at higher temperatures i n the nickel-boron system (Figure 36).  Furthermore, larger interlayer thicknesses also  contribute to an increase in the liquid width due to the larger volume o f solute contained in the interlayer. To illustrate these points, the final width o f joints processed at different temperatures and initial gap widths were calculated for a filler material and substrate o f constant composition and shown in Figure 36.  o  11  i  i  ii i i  1300  i  ,  i  1350  1400  1450 1500 1550 Temperature, K  . , , 1600  I i 1650  1700  Figure 36 - Increase in liquid width with varying isothermal holding temperature and initial gap widths.  The dimensionless rate constant, K, responsible for the rate o f solidification is a function o f the saturation o f the substrate.  The saturation o f the substrate is the amount o f M P D  that is nominally present in the substrate against the amount o f M P D that is soluble in the solid phase.  A larger solubility o f the M P D i n the substrate results i n a shorter  solidification time. The saturation in the substrate is defined as:  Substrate Saturation =  (24)  79  The nominal concentration o f M P D i n the  interlayer is also o f importance  as  supersaturation o f the liquid results in widening o f the gap. Supersaturation o f the liquid occurs when the concentration o f M P D in the liquid is above the liquidus composition. While this is unavoidable because one needs a sufficient concentration o f M P D to depress the melting point o f the filler material below the processing  temperature,  excessive amounts o f M P D can lead to unnecessary widening and in-turn prolong the required processing time. The degree o f liquid supersaturation can be determined by:  Liquid Supersaturation  =  (25)  Thus, higher solubilities o f the  M P D in the  substrate and lower initial  solute  concentrations in the substrate and filler material promote a faster rate o f isothermal solidification. This is seen in Figure 37 by the shorter bonding time for cases with lower substrate saturations.  Increasing liquid supersaturations w i l l result i n longer bonding  times due to the increase in substrate dissolution.and increased widening o f the gap.  rye 0  1  1  1  1  1  i  i  0.1  0.2  0.3  0.4  0.5  0.6  0.7  i 0.8  Substrate Saturation, (C ' )/(C ) W S  SL  Figure 3 7 - Effect of saturation of M P D in the substrate and supersaturation in the liquid filler metal on solidification time.  80  In addition, for a given composition, the supersaturation o f the liquid w i l l decrease with temperature due to the decrease in the liquidus composition at elevated temperatures. This results in a higher solidification rate constant at elevated temperatures which aids the higher diffusion rate to produce a higher solidification rate (Figure 38). 0.02  0.006 1300  1350  1400  1450  1500  1550  1600  1650  Temperature, K Figure 38 - Change in the dimensionless solidification rate constant with temperature.  The advantage o f increasing the temperature to increase solidification rate can be nullified by the dissolution o f the base material. A t higher temperatures the maximum liquid width increases due to the equilibrium conditions, which results in only marginally faster processing times. A l s o , the increased economic cost o f heating assemblies to the higher temperature along with the possibility o f damaging the microstructure o f the base material discourages very high processing temperatures. Figure 39 shows the variation o f the total processing time due to the increase in temperature.  81  1250  1300  1350  1400  1450  1500  1550  1600  1650  Temperature, K Figure 39 - Required processing time with initial gap sizes at varying temperatures.  Simulations o f the bonds created in the experimental regime o f this work were performed using the isothermal solidification models outlined by Ramirez et al. and Gale et al. A gap size o f 40 microns was assumed for all bonds. The boron concentration o f the filler and substrate materials were assumed to be 18.1 at% and 0.078 at% boron respectively which correspond to the concentrations o f the M B F - 8 0 filler material and C M 247 L C superalloy. The equilibrium compositions were taken from each o f the three data sources listed i n Table 6.  The predictions made i n the present work based on the binary N i - B system were compared with the results obtained experimentally in the present work on T L P bonding o f C M 247 L C . Table 9 presents a comparison o f two sets o f data.  The width was  calculated according to equation (15) with the assumption o f a constant density i n both the liquid and the solid phases and no loss o f solute to the base metal.  82  Table 9 - Predicted dissolution width using the analytical model vs. average experimentally observed widths (microns). Ni-DATA  Analytical Kaufman  ASM  Experimental (+/-2.5)  1070°C  42.86  46.57  40.09  47.5  1125°C  47.06  51.76  43.77  62.5  1170X  52.17  57.42  47.32  67.5  Temperature  Predictions from the Kaufman database were the closest to the experimental data. However, i n all cases this equation underestimated  the diffusion  width observed  experimentally. The deviation may be a consequence o f the multi-component alloy used in the experimental investigation.  In multi-component systems, the difference i n  diffusion rates o f the alloying elements causes the local equilibrium to constantly change during bonding as noted by Sinclair [80]. The equation used i n the above calculation cannot take this effect into account.  Furthermore, the assumption o f constant density  between the liquid and solid phases is not realistic and is possibly another source o f error.  The dimensionless solidification constants, K, for the various sources o f data used i n this work is shown below i n Table 10.  These values were then used to determine the  isothermal solidification time using the model presented by Ramierz & L i u .  Isothermal  solidification time was also calculated using the model presented by Gale. Using the experimentally measured diffusion coefficient for the diffusion o f boron i n the nickelbase superalloy C M 247 L C and the predicted dissolution width, the predicted solidification  times  were  calculated and  compared  to values  extrapolated  from  experimentally observed data in Table 11.  Table 10 - Dimensionless solidification rate constants, K , calculated using the analytical model outlined by Ramirez et al. for equilibrium compositions defined by various sources at  1070°C, 1125°C and 1170°C. Temperature  Ni-DATA Superalloys Database  Kaufman Binary Alloy Database  ASM Phase Diagram  1070°C  0.7657E-2  0.7572E-2  0.7093E-2  1125X  0.8430E-2  0.5470E-2  0.7800E-2  1170°C  0.9376E-2  0.4216E-2  0.8487E-2  83  Table 11 - The predicted solidification time using analytical models proposed by Ramirez et al. and Gale et al. vs. experimentally observed times (hours). Ni-DATA  Ramirez Model Kaufman  ASM  Ni-DATA  Gale Model Kaufman  ASM  Experimentally Extrapolated  1070X  11.12  13.4  11.16  4.70  5.68  4.71  5.66  1125X  5.12  14.68  5.12  2.17  6.14  2.17  2.23  1170X  2.82  16.88  2.84  1.21  7.01  1.21  1.27  Temperature  Using equilibrium composition data from the N i - D A T A database and the N i - B A S M binary phase diagram, the predicted isothermal solidification times predicted by the model proposed by Gale et al. were closer values to experimentally observed times than in the model by Ramirez et al. Predictions using the model by Gale et al. resulted i n times only slightly underestimated from experimentally observed times.  The model  proposed by Ramirez et al. predicted times that overestimated the processing times.  The Kaufman Binary Database predicted poor results i n both models.  The predicted  solidification times were found to increase with temperature using these equilibrium constants.  This is due to increased substrate saturation because o f the decrease i n the  solidus composition with increasing temperature. increase  A s shown above in Figure 37, an  in substrate saturation results in a longer isothermal solidification time.  Interestingly, the equilibrium values from the N i - D A T A and A S M data sources produced values very close to each other in both models.  This is despite the difference in  calculated initial width which was used as the starting point o f isothermal solidification.  5.3 Numerical Models for TLP Bonding A major disadvantage o f analytical modeling is that it cannot be used to model the process as a whole.  The process is divided into stages corresponding to the different  stages and each is modeled individually. Consequently, solute fields that have formed in previous stages are ignored which is a source o f error. A l s o , many solutions rely on a parabolic growth law and error function solutions which are only  approximate.  Numerical solutions have the advantage that they can be applied to complex geometries including 2 or 3 dimensional shapes and allows the modeling o f dissolution, isothermal  84  solidification and homogenization i n one continuous model [74].  There were several  models created to model the motion o f the solid/liquid interface in transient liquid phase bonding. Binary component models mainly differ in the approach used to discretize the joint assembly and in numerical techniques used to solve the resulting systems o f equations.  Nakagawa [81] and Cain [82] made the assumption that the interface was located at one of the discretization points.  B y incrementing the position o f the interface to adjacent  points, the time required to remove the deviation from equilibrium was calculated using F i c k ' s law. In this way, the motion o f the solid liquid interface was modeled i n a stepwise manner.  However, as the interface was fixed on a discretized node, the resulting  calculated solute flux would inherit errors from the inaccurate interface position. More recent models by Zhou & North [71] and Shinmura [83] attempt to use a conservation o f mass across the solid/liquid interface coupled to F i c k ' s second law to determine the motion o f the interface. In this type o f model, the interface motion is tracked and is free to exist in-between discretization points. This type o f model is referred to as the moving boundary model ( M B M ) . These techniques are similar to the method used by Matan [73] and A k b a y [84] which used similar techniques to model the growth o f 2 nickel-base superalloys and steel respectively.  n d  phases in  These models however differ i n the  numerical techniques used. Shinmura used explicit finite difference methods while Zhou used an implicit finite difference method to reduce the number o f computation iterations for this problem. A n implicit finite difference model was also created by Illingworth using variable space discretization which provided faster computation times and had excellent agreement with other M B M s [85].  In the explicit scheme, the values at the previous time step are used explicitly to calculate future values. This has the unfortunate disadvantage o f only being stable for small time steps and step sizes which can lead to protracted computation time but has the advantage of being easy to solve. The implicit scheme is more computationally intensive than the explicit scheme requiring the need to solve simultaneous linear equations at each time  85  step. However, the method is unconditionally stable for time steps and step sizes and can potentially reduce computation time [86].  Variations o f the basic M B M model have been created in attempts to improve the understanding o f the T L P bonding process.  For example, Natsume created a M B M  model which takes into account large changes i n volume i n the bond region during the T L P bonding o f A l - C u joints [87].  The model also took into account the effects o f  variations in bonding loads through the modification o f the surface tension terms. Another variation was created by Natsume to test the effect o f deviations from the local equilibrium assumption at the solid/liquid interface during fast heating rates [88].  While the majority o f numerical modeling has focused on binary alloy systems there is an effort to model real systems by extending the computational modeling to ternary systems by Sinclair [89], Campbell & Boettinger [56] and Ohsasa [55]. Sinclair modeled the T L P bonding o f a ternary two-phase system using an explicit finite difference model and utilized the concept o f shifting tie lines due to changes i n local equilibrium during the bonding. Campbell & Boettinger and Ohsasa used commercial thermodynamic software (Thermo-Calc) to determine the equilibrium tie lines at the solid liquid interface.  The  advantage o f using such software is its potential for extension to higher order systems due to its flexibility for determining phase composition in multi-component systems.  5.3.1 Moving Boundary Models A M B M is based on a finite difference discretization o f the standard solution to F i c k ' s 1 law.  st  These models assume constant diffusion coefficients and determine the driving  force o f diffusion on the composition gradient between discretized nodes. What follows is an explicit discretization o f the T L P bonding problem.  In the model used in the present work, a 1-dimensional model symmetric about the center o f the joint was created to model the T L P bonding process.  The joint assembly is  assumed to be heated infinitely fast to the processing temperature thus avoiding the  86  effects o f the heat-up phase.  The dissolution o f the interlayer is also ignored and is  assumed to be fully liquid at the processing temperature with a M P D concentration equivalent to the initial concentration o f the filler material used. The joint is discretized into a number o f sub-systems,  o f width A z and interfaces, 4 with negligible width.  The joint is symmetric about h = I\.  Treatment o f phase boundary movement is  accomplished with the introduction o f an inter-phase node containing the solid/liquid interface.  Within this discretized assembly, there exists a single two-phase system  containing the solid/liquid interface located at S* = X.  A state o f local equilibrium is  assumed to exist at this interface. The bond assembly can be seen schematically below in Figure 40.  L/S 6  s  Si  3  s  4  It  l  k+l  s  5  Az Figure 40 - Schematic diagram of interface node. The liquid/solid interface is shown by the dashed line and is located in sub-system S =X= S . k  2  The molar volume is assumed to remain constant. The mass redistribution during a time step, A / , can be calculated from the flux inputs and outputs according to F i c k ' s 2  A, S  l+  c  t  =  ,S c  k  _VjI  t  _jh->y  n d  law:  (26)  At/Az  where C, is the concentration i f the solute species / i n units o f mols/m . The flux o f 3  solute atoms between each sub-system, j'", is calculated by F i c k ' s 1 law: s t  87  (27)  Where D refers to the diffusion coefficient o f the M P D i n the matrix present in that subT  system.  A liquid phase fraction vector f  L  is used to represent the extent o f solidification i n the  inter-phase node. Solidification is carried out such that it only occurs in the inter-phase node until complete transformation o f that node is achieved. Once completed, the interphase system moves to the adjacent node until the entire assembly is solid. In this way, phase boundary motion is achieved discontinuously and the exact position o f the interface can be determined by interpolation. The phase fraction is calculated by assuming that the compositions o f the solid and liquid components o f the inter-phase node are equal to their equilibrium compositions as defined by the binary phase diagram.  Given the mean  composition o f the two-phase interface sub-system we can then determine the liquid phase fraction o f the interface sub-system by the lever rule.  f  ~  £LS  (28)  QSL  _  where: C = Concentration o f the solute atom i n the interface sub-system C  SL  = Solidus concentration o f the solute atom  C " = Liquidus concentration o f the solute atom  The fluxes on either side o f the moving interface node are calculated using their relevant equilibrium compositions as determined by the isothermal processing temperature.  J ! * = - D  L  C  (29)  C a  Az  88  (30)  where: D = Diffusion coefficient o f the solute species in the liquid phase L  D - Diffusion coefficient o f the solute species in the solid phase s  Using this method, the solidification o f the transient liquid is modeled discontinuously meaning at the end o f solidification o f one liquid sub-system, the following one must reestablish equilibrium before solidification continues.  5.3.2 Predictions from the Moving Boundary Model The explicit M B M model was validated against models and experimental data by Zhou & North [74] and Illingworth [85] (Pigure 41). In this simulation, the joining o f plates o f pure nickel was simulated using a N i - 1 9 at% P braze filler. Illingworth showed that the implicit model employed by Zhou & North did not conserve solute and exceeded the theoretical maximum width possible in the joint.  The experimental data provided by  Zhou & North also exceeded the theoretical maximum value, as determined by equation (15). It has been speculated by Illingworth that this error is the result o f the questionable validity o f the use o f a constant molar volume assumption in the theoretical maximum width calculation used, or alternatively, the experimental results may have been affected by unaccounted liquid flow [85].  The moving boundary model used in the present work has excellent correlation with Illingworth's data produced by using an implicit numerical model.  The predicted  maximum width was similar to Illingworth's prediction and did not exceed the theoretical maximum width because the conservation o f mass was also implemented in the M B M model created in the present work. The explicit scheme used in the M B M however is at a disadvantage  i n terms o f computation speed when compared to implicit models.  Illingworth's implicit model is reported to finish simulations such as the one shown i n  89  Figure 41 i n an order o f minutes whereas the explicit model, which is limited by time step and step size instability, takes several hours for completion.  However, this  comparison shows the capability o f this type o f model to provide reasonable predictions for the processing time o f a T L P bonding process.  Time (s)  Figure 41 - Validation of the moving boundary model against other M B M (Zhou & North and Illingworth) and experimental data from Zhou & North [74,85].  Simulations were performed o f the bonding o f joints at 1070°C, 1125°C and 1170°C with an initial half-liquid width o f 20 um.  The compositions o f the substrate and filler  material were taken to be Ni-0.078 at% B and a Ni-18.1 at% B respectively. Equilibrium compositions are applied from the various databases as discussed earlier and the diffusion of boron in C M 247 L C is assumed from the experimentally measured value.  The  diffusion coefficient o f boron in the liquid was taken to be l x l O "  The  8  m /s [72]. 2  resulting eutectic width is plotted against the square root o f time and is shown i n Figure 42 and the predicted  dissolution widths and times to completion o f isothermal  solidification are shown i n Table 12 and Table 13.  90  Solidification Curves 1170"C 1125°C 1070°C  2.5  Ni-DATA  "6  1.5  g  \  20  40  \  60  80  100  120  140  160  180  VTime, Vs Solidification Curves 1170°C 1125°C 1070°C  Kaufman  20  40  60  80 100 VTime, Vs  120  140  160  180  Solidification Curves  x 10  - 1170°C 1125°C 1070°C  2.5  ASM  -  •5  1.5  g  0  20  40  60  80 100 VTime, Vs  120  140  160  180  Figure 42 - Moving Boundary Model simulations of T L P bonds at 1 0 7 0 ° C , 1 1 2 5 ° C and 1 1 7 0 ° C with Ni-0.078 at% B substrates and Ni-18.1 at% B filler material.  91  Table 12 - Predicted dissolution width using the moving boundary model vs. experimentally observed widths (microns). Ni-DATA  MBM Model Kaufman  ASM  Experimental (+/- 2.5)  1070X  43.0  46.8  40  47.5  1125°C  47.2  52.0  43.8  62.5  1170°C  52.2  57.6  47.6  67.5  Temperature  Table 13 - Predicted solidification times using the moving boundary model vs. experimentally observed times (hours).  1070X  6.92  MBM Model Kaufman 7.94  6.92  5.66  1125X  3.18  6.52  3.18  2.23  1170X  1.76  5.52  1.76  1.27  Temperature  Ni-DATA  ASM  Experimentally Extrapolated  The model gives poor correlation with the predictions from the analytical solution for the dissolution widths.  Like the analytical solution, the effect o f the change in density  between the liquid and solid phase is not taken into account i n the present M B M model and may be a source o f errors. Another source o f error between the predicted values and the experimental data may arise from the binary component data used in the modeling when the experiments were performed on a complex superalloy and ternary component braze filler.  The predictions o f bonding times are overestimated when compared to experimentally observed times. However, these results are better estimations compared to the Analytical solution proposed by Ramirez et al. The solidification times predicted by this M B M model for equilibrium data from the N i - D A T A and A S M Phase diagrams are very close despite predicting different dissolution widths.  The trends observed in the predictions  from this model suggest that the model is behaving in accordance with accepted models; however, the data on the nickel boron system requires further development.  A large  limitation o f this model is that it w i l l inherently be unable to predict the solidification i n multi-component systems.  92  5.3.3 Phenomenological Model The data available for higher order (above ternary) systems are scarce. Because o f this, real systems cannot be represented by phase diagrams and only rough estimates o f the behavior o f a system can be modeled using binary component equilibrium data. Grushko and Weiss attempted to investigate the microstructure evolution o f a braze joint i n I N 718 using a complicated quasi-quaternary phase diagram on the N i - C r - N b - S i system [90]. A possible solution to this problem is the use o f computational thermodynamics through the C A L c u l a t i o n o f P H A s e Diagrams ( C A L P H A D ) method which allows the calculation o f chemical equilibrium in multi-component systems [77].  The C A L P H A D method is based on the minimization o f the free energy o f a system and can be related to any alloy system and any number o f components provided sufficient thermodynamic data are available. Extrapolation to higher order systems can also be calculated but may result in poor correlation to real systems. In the C A L P H A D method there are many models that describe the Gibbs energy o f a phase.  For the commonly  used sub-regular solution model, the molar Gibbs energy o f a phase can be expressed as [91]:  ex  where  (31)  g is the reference energy, g'* is the energy o f ideal mixing and g is the excess ref  ex  jx  energy term representing interactions between different components i n the system. Each of these terms can be calculated from the following equations:  .re)  g  ,0  (32) (33)  g  ex  j- k)  x  x  +  jk(xj-x ) '+...)  L2  2  k  93  (34)  where: g° = Reference energy o f element i Xt = M o l e fraction o f constituent i L  jk  - Interaction parameter between components j and k  The complexity o f this thermodynamic description increases with the use o f sub-lattices to differentiate substitutional and interstitial elements [92].  This calculation can be  performed by using a thermodynamic calculator such as Thermo-Calc [93].  The goal o f the coupled phenomenological model is to use experimentally measured thermodynamic and mobility databases to produce an accurate model with no adjustable parameters [94]. The diffusion o f solute atoms can be modeled using a thermodynamic database by relating the diffusive flux to the Onsager force-flux equation. In this model, a thermodynamic description o f the chemical system is coupled with a phenomenological description o f the mobility o f the solute atoms.  W i t h such a model, it is possible to  model complex multi-component systems provided that accurate thermodynamic and kinetic data are available. The diffusive flux at each interface boundary is given by the Onsager force-flux relationship assuming a lattice-fixed frame reference[95]:  (35)  J;> 7=1  The flux equation is composed o f a phenomenological parameter, L *, representing the 1  mobility o f the solute atoms and a thermodynamically derived chemical potential gradient,  V / / j * , which represents the driving force for chemical equilibrium.  At  equilibrium, a system with constant temperature, pressure and composition, the chemical potential gradient is zero for all components and the Gibbs energy is at a minimum. Thus the driving force for diffusion is the chemical potential between two spatial points. The chemical potentials for a system o f n components are related to the molar Gibbs energy by the Euler equation (equation 36). In this way the chemical potentials o f a system can  94  be calculated for the phenomenological model. In this work this task is performed by using the commercial thermodynamic calculator: Thermo-Calc.  S  = ZM*/  (36)  i=\  The chemical potential gradient at interface k for component j is calculated at the interface by the chemical potentials evaluated from the chemical potentials o f the adjacent sub-systems:  M  '  -  where  ^  ///  (37)  ^  is the  chemical potential o f component j  i n sub-system  S. k  The  phenomenological parameter, L'*, at each interface is evaluated by an average o f the phenomenological parameters evaluated at the adjacent sub-systems, Lj/.  >j=CM =fM  L  J  j  ( 3 g )  The mobility term, Mj, is calculated from an experimentally measured mobility database. The mobility term represents the ability o f a solute atom to move and is dependant on composition, temperature and pressure.  Andersson and Agren determined in a simple  disordered substitutional phase, such as the nickel-rich y phase i n a nickel-base superalloy, the off-diagonal terms o f the diffusion mobility matrix are zero [95]. For the lattice-fixed frame o f reference, the diagonal terms o f the mobility matrix are calculated by  [96]:  95  AG; V  RT  (39)  J  where: M . = Mobility o f species i in a given phase M  Q  = Product o f atomic jump distance squared and jump frequency  A G * = Activation energy o f diffusion o f species /  M and A G * are both dependant on composition, temperature and pressure, however, it is 0  commonly accepted to assume that M  0  has a value o f 1 m / s and to represent the  combined dependence solely on A G * which is expressed in terms o f a Redlich-Kister polynomial [96]:  AG,*=2>,G/ + p  J>P  (40)  k  where Gf and Gf represent interaction parameters between the different atomic species and are linear functions o f temperature and pressure.  The motion o f the solid/liquid interface is tracked in the same way as in the M B M model. The phenomenological parameter  in the inter-phase  sub-system is calculated by  evaluating the phenomenological parameters at the equilibrium concentrations on either side o f the interface as defined by the local equilibrium assumption (L , L ). s  L  (j  tj  The  chemical potentials on either side o f the solid liquid interface are calculated similarly.  5.3.4 Predictions from the Phenomenological Model Simulations were performed using the above phenomenological model at  1070°C,  1125°C and 1170°C with an initial gap half-width o f 20 um. The simulation assumes the compositions o f the substrate and filler are Ni-0.078 at% B and Ni-18.1 at% B  96  respectively.  The N i - D A T A Superalloys Database was used for the thermodynamic  description o f the nickel-boron binary system. The kinetic description o f this system was taken from the work o f Campbell and Boettinger who determined that the diffusional activation energy for boron i n a solid F C C nickel phase could be represented by the following relations in units o f J/mol [56]:  Mobility of Boron FCCQ*M:B  _  -94,500-110 *T  FCCQ*Ni:Va  _  -94,500-110 *T  Mobility ofNickel FCCQ*NUB  _  -287,000 - 69.8 * T  FCCn'Ni-.Va  _  -287,000 - 69.8 * T  The superscript notation in each o f the terms represents the species that contribute to the interaction energy.  Va refers to the vacancies which are present in the sub-lattice model.  However, it was noted by Campbell & Boettinger that these values required adjustment and provided poor predictions. To obtain agreement with experimental results the boron mobility was reduced by a factor o f 3. In the same work it was assumed that the mobility o f species i n the liquid phase could be assumed to be 1 x 10" m /s. 9  2  The motion o f the interface calculated by the coupled phenomenological model and compared to data measured experimentally in this work is shown i n Figure 43 and the predicted dissolution widths and isothermal solidification times calculated by the coupled phenomenological model are shown below in Table 14 and Table 15.  97  Figure 43 - Phenomenological model simulation of TLP bonding at 1070°C, 1125°C and 1170°C with Ni-0.078 at% B substrates and Ni-18.1 at% B filler material.  98  Table 14 - Predicted dissolution width using the coupled phenomenological model vs. experimentally observed widths (microns). Temperature  Phenomenological Model  Experimental (+/- 2.5)  1070°C  43.0  47.5  1125°C  47.2  62.5  1170°C  52.2  67.5  Table 15 - Predicted solidification time using the coupled phenomenological model vs. experimentally observed times (hours). Temperature  Phenomenological Model  Experimentally Extrapolated  1070X  2.46  5.66  1125X  1.76  2.23  1170°C  1.37  1.27  The predicted dissolution widths are underestimated  i n this model.  The predicted  maximum width is found to be equal to those predicted in the analytical models and the M B M model. A s this model treats the dissolution o f the base material similarly to the M B M model and shares the same equilibrium data values, it is not surprising that the values would be the same. The phenomenological model provides reasonable estimates of the solidification time at the highest temperature o f 1170°C but is underestimated for lower temperatures. O f the two lower temperatures, the lowest temperature has the most error. The modification o f the boron mobility was applied i n the work o f Campbell and Boettinger to account for the difference between experimentally observed data and the simulations performed at 1315°C.  A s this modification o f the mobility term is not a  temperature dependant, it is understandable that the predictions at the higher temperatures would be underestimated.  The phenomenological model used i n this work is a binary model and does not take into account the interactions o f the other elements in the thermodynamic description o f the system or the mobility. Both o f which have interaction parameters which depend on the concentrations o f the other solute species.  Furthermore, as noted by Campbell &  Boettinger, the mobility description o f boron in nickel is poorly defined i n the literature  99  and requires refining. questionable.  The current work contains a modified boron mobility which is  In this case, the phenomenological model was not capable o f accurately  modeling the T L P bonding process due to lack o f reliable data.  Another drawback o f the current phenomenological model is that it is significantly slower than the regular M B M model due to the complicated calculations required. A n expansion o f the model to multiple components would further protract the calculation time.  A  revised numerical scheme should be considered and an implicit method should be utilized as this would allow the model to operate under a larger time step and allow a coarser discretization mesh which would significantly reduce the number o f iterations (and computation time) that would be required for the model to reach completion.  100  Chapter 6  Conclusions  6.1 Summary In this work, the Transient Liquid Phase ( T L P ) bonding technique was investigated for the joining o f the nickel-base superalloy C M 247 L C .  The following conclusions were  made from this work:  •  The liquid widths in all bonds were found to reduce linearly with the square root o f time during isothermal solidification. The rate o f solidification was observed to be greater on samples bonded at higher temperatures. However, it was found that the completion o f isothermal solidification was not sufficient for good mechanical properties in the joints. Tensile tests showed brittle joints in samples created at all processing conditions including those that completed isothermal solidification.  S E M analysis o f the fracture surfaces showed evidence o f boron  containing precipitates. Post-bond heat treatment would likely improve the joint properties by dissolving the precipitates in the base metal and allow the diffusion o f alloying additions not present in the joint to diffuse from the base material and homogenize the bond.  101  In incompletely isothermal solidified joints, a binary eutectic consisting o f nickel solid solution and nickel borides as well as a ternary eutectic consisting o f a mixture o f nickel solid solution, chromium borides and nickel borides was found in the residual liquid.  This centerline phase was much harder than the base  material with average micro-hardness values o f 850 HV0.0025 compared to the base material with a nominal hardness o f 450 HV0.0025. The existence o f these phases is detrimental to the properties o f the joints because o f their brittle properties and their continuous morphology along the joint interface.  Bordering either side o f the centerline eutectic was a proeutectic solid solution nickel-rich phase. This was formed by the isothermal solidification process. The isothermally solidified microstructure was softer than the base material with an average hardness o f 400 HV0.0025. E D S scans across this interface showed it to be deficient i n many o f the alloying elements necessary for the formation o f the y' phase necessary for a good joint. Homogenization did occur during bonding with evidence o f cuboidal precipitates existing in the isothermal solidification region in samples processed at higher temperatures and longer duration. This is likely due to the diffusion o f said alloying elements into this region which is promoted by the higher temperature and longer processing time.  In all samples, the base material contained precipitation from the diffusion o f boron from the filler material into the substrate. B l o c k y and acicular precipitates were observed in the regions adjacent to the joint/substrate interface.  Blocky  precipitates further away from the center o f the joint were observed to be aligned in the direction o f acicular precipitates.  E D S analysis showed the precipitates  were similar in composition despite the difference i n morphology.  The  precipitates were slightly nickel depleted and tungsten rich compared to the surrounding material and contained detectable levels o f boron indicating these precipitates may be nickel-borides. The precipitates i n the base metal increased the hardness adjacent to joint interface exhibiting average hardness values o f 600  102  HV0.0025 compared to the base metal with an average o f 100 HV0.0025.  The  precipitation o f these phases could also be a cause o f poor joint properties.  The apparent diffusion coefficient o f boron in C M 247 L C was experimentally measured by observing the rate o f isothermal solidification.  The apparent  activation energy is found to be 219 K J / m o l with a pre-exponential factor D = 0  0.0163 m /s. These values are similar to values in the literature for the diffusion 2  o f boron i n other polycrystalline superalloys.  Modeling o f dissolution stage using analytical and numerical models were found to be inadequate for predicting the experimentally observed dissolution width o f the T L P bonding o f C M 247 L C with the commercial N i - C r - B - C filler alloy. The assumption o f constant density between the solid and liquid phases is likely a source o f error i n this calculation.  The data in the literature on the N i - B system is lacking with scarce data available on both thermodynamics and kinetics.  Isothermal solidification times were  calculated using analytical and numerical models. The analytical model proposed by Gale et al. predicted better isothermal solidification times than the model by Ramirez et al. The numerical model developed under the M B M scheme predicted satisfactory isothermal solidification times but were overestimated i n all cases. The phenomenological model produced satisfactory results for 1170°C but underestimated Inaccurate  the  isothermal solidification  times  for lower temperatures.  predictions were produced with thermodynamic data  from  the  Kaufman Binary A l l o y Database while better predictions were possible with the N i - D A T A database and A S M phase diagram. The current mobility data available for boron is inadequate for a phenomenological model to be applied.  103  6.2 Recommendations for Future Work •  This study was performed with only one gap size and filler material composition. A s the gap size w i l l vary especially in repair and overhaul applications, data on the microstructures produced with joints o f varying sizes is vital. Furthermore, it is unknown i f the composition o f the filler material used is optimal. Commercial braze fillers are available with a higher level o f alloying and can possibly improve joint properties and/or reduce processing time.  •  The refractory element rich precipitates that were observed in the base material require further analysis. Currently the understanding o f the mechanism o f their formation is lacking.  T E M work should be performed to properly characterize  and understand these precipitates.  •  The tensile properties o f the bonded joints were poor. A n addition o f a post-bond heat treatment would most  likely improve the properties  because o f the  dissolution o f precipitates in the bond microstructure and the homogenization o f strengthening alloying additions. Further work is needed to optimize post-bond heat treatment.  •  The phenomenological model created i n this work is based on the binary N i - B system. The model can be further expanded to multi-component systems which represent the real superalloy systems.  A n expansion o f this model to a  multicomponent model could potentially improve its accuracy w i t h respect to experimentally observed data since the phenomenological model allows for no fitting parameters. The quality o f the predictions made by a phenomenological model is based entirely on the available data.  •  Predictions o f isothermal solidification time using the phenomenological model produced poor results compared to the other models (numerical and analytical) and experimentally observed data. Further, the boron mobility in the literature is modified by a factor which is not appropriate. This indicates that the data used in  104  the phenomenological model is not refined to the point where it can reliably predict isothermal solidification  in the  current  alloying system.  Further  development o f the kinetic and thermodynamic descriptions o f boron and its interactions with alloying elements in the  superalloys system is required.  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It is assumed that the process is controlled by Fick's 2  n d  law:  dC, f, d Cf —- = D 7 dt dy 2  L  L  2  where D  L  (i);  -  u  is the diffusion coefficient in o f the solute atom in the liquid phase, C\ is the  solute concentration and y is the distance. If we further assume:  •  The diffusion coefficients are constant and not composition dependant  •  Local equilibrium exists at the solid/liquid interfaces  •  Semi-infinite domains  then F i c k ' s 2  n d  law has a standard solution given by an error function expression:  C =A + B-erf  y  (2)  t  where A and B are constants. W e can now define the displacement, y, at a given time, t, for each phase, a and P:  y =K yJ4D t a  a  (3)  L  112  (4) where K' is the non-dimensional growth rate constant for phase i. Taking the derivative o f these expressions with respect to time we get the expressions for interface velocity:  dt  dt  dt  dt  yffrt  (5)  V t  (6)  Taking the derivative o f the standard solution with respect to K we get the concentration gradient:  Bexp(-K f  dC*-  a  L  (7)  dy  Btxp(-K f  dC p  p  L  (8)  4nb t L  A mass balance at each o f these interfaces provides the velocity o f each o f the interfaces:  dy dt  dy_^ dt  D  L  dC  L  s~ia,LS C?°-C dy  (9)  ao  -D  dC'  Cf-Cf^  dy  y=Y°  (10) y=Y"  Substituting the above derivatives into the mass balances and considering only the diffusion o f solute atoms in two semi-infinite planes located between y-0&y  113  =  y& a  • y = y & y = co with the following boundary conditions we get two explicit expressions fi  o f the dimensionless growth constants:  • K is dependant on t  • C = C° at y = 0 • C=C  aJS  aty = y  a  . C = C -'- atj; = / p  • C =C  M  s  at.y =  oo  g , ^ ^ e x p ( ^  2  - ^ ) - ^  =  0  K ^[erf(K' )-erf(K )]-cxp(-K ) a  3  a  =0  a2  (12)  W e can solve for the dimensionless growth constants by simultaneously solving these two equations. The time for dissolution o f the braze interlayer o f initial thickness 2h at a given temperature can be calculated from the following equation:  () \6K b' 2h  t  (13)  pi  The width o f the liquid interlayer at the completion o f dissolution is:  W =2h + 2K [D t~ a  L  (14)41  T  y  114  Appendix B - Analytical Solution for the Widening and Homogenization Stage After the establishment o f a fully liquid interlayer, further dissolution o f the parent metal takes place as solute diffuses from the liquid into the solid substrate.  This process  proceeds until the liquid is fully homogenized and has a concentration equal to the liquidus. Similar to the previous stage, the concentrations in the solid (S) and liquid (L) regions w i l l vary according to F i c k ' s 2  n d  Law:  dCf _ n d Cf 2  dt  0)  dz  2  dC^ _ ~ dt  d C\ 2  L  (2)  dz  2  Again, we assume:  •  The diffusion coefficients are constant and not composition dependant  •  L o c a l equilibrium exists at the solid/liquid interface  •  Semi-infinite domain  The standard solution for F i c k ' s 2  f  C =A + B-erf  n d  law is again:  z  (3)  :  V  W e can now define  Where:  115  K = Dimensionless growth constant X = Boltzmann's change o f variable z = c% at the solid/liquid interface  Considering only the diffusion o f solute atoms in a semi-infinite single phase located between z = £ & z = oo with the following boundary conditions:  • E, is dependant on t  • C = C at z = | 4  • C = C°° at z =  oo  erfc(A) erfc(K)  q=cr+(cf-c;)  (4)  Taking the derivative o f the standard solution with respect to X we get the following equations:  (  (c° -cr) {~ jy L  ~dz~  exp  b ^ L  2  A2  s  dCf _  (Cf  (5)  D  s  yjxb t  erfc  -C: )exp(-X ) L  ylnDJ-t  2  (6)  erfc(K)  A mass balance can be examined by equating the fluxes across the solid/liquid interface:  D  l  dC, dz  i  -„  dC.  (7)  Substituting equations (5) & (6) into equation (7) we get:  116  exp 1  nt  s~iLS  D  s  (8)  s~iSL  erfc  D  s  Differentiating z with respect to t:  KD dr'-  dt  1  D  (9)  Wt  Substituting equation (9) into (8) and evaluating the resulting equation at K = A  2  Cf  f  K=  -C; )exp(-K ) L  2  erfc(K)  4K  D  D_  Cp-C,  \D  L  s~iLS  (10)  s-iSL  erfc  Solving the equation numerically, we can thus determine the dimensionless growth constant. Assuming that the boron diffusivity i n the liquid is the controlling mechanism, the time o f dissolution can then be calculated with the following equation:  2  (11)  TV  \6K D A  Where the interface displacement, (Z) is:  f  Z=\  W -2h m  (12)  117  The theoretical maximum width o f the  liquid,  W  m  region is a function o f the  concentration ( C " ' ) o f melting point depressant in the interlayer o f thickness, h, and the 1  equilibrium liquidus composition (C ) LS  W =2h m  PL  at the processing temperature [72]:  (13)  •LS  C  Appendix C - Analytical Solution of the Isothermal Solidification Stage During the isothermal solidification stage solute from the liquid phase continues to be redistributed to the substrate.  In the liquid phase, the concentration o f solute can be  considered to be uniform due to the completion o f homogenization i n the previous stage and therefore solute diffusion in the liquid is ignored. process can again be described by F i c k ' s 2  dCf dt  fi,  n d  The isothermal solidification  law:  d Cf dz 2  0)  2  Again, we assume: •  Constant diffusion coefficients  •  L o c a l equilibrium at the solid/liquid interface  •  Semi-infinite domain  Thus allowing the standard solution to F i c k ' s 2  n d  law can be written as an error function  expression: C =A t  + B-erf  (  z  (2)  118  We can now define  Where: K = Dimensionless growth constant X = Boltzmann's change o f variable z = £ at the solid/liquid interface  Considering only the diffusion o f solute atoms i n a semi-infinite single phase located between z = £ & z = oo with the following boundary conditions:  • £ is dependant on t • C =  at z = £  • C = C " a t z = oo  (3)  Taking the derivative o f the standard solution with respect to X we get the following equation:  acf_  &  (Cf-C;)exp(-A ) 2  4nD t s  (4)  erfc(K)  A mass balance can be examined by equating the fluxes across the solid/liquid interface:  (5)  Substituting equation (4) into (5), we get:  119  (6)  erfc(K)  at' -* 1  Differentiating z with respect to t:  KD  D  s  (7)  Substituting equation (7) into (6) and evaluating the resulting equation at K = A  sL_ ^s\ (-K ) 2  c  K=  c  s-iLS  exp  /-.Si  (8)  *fc{K) er,  Solving the equation numerically, we can thus determine the dimensionless growth constant. The time o f solidification can then be calculated with the following equation:  t=-  (9)  2 r\S \6K D Z  120  

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