MICROSTRUCTURE-PROPERTY MODELS FOR HEAT ... - cIRcle

MICROSTRUCTURE-PROPERTY MODELS FOR HEAT TREATMENT OF A356 ALUMINUM ALLOY

by LEO JOHN COLLEY

M.A.Sc. The University of British Columbia, 2003 B.Eng. University of Wales, Swansea, 2000

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

in

The Faculty of Graduate Studies (MATERIALS ENGINEERING)

THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)

March 2011 © Leo John Colley, 2011

ABSTRACT The evolution of microstructure and mechanical properties during heat treatment of an industrially-cast A356 aluminum alloy was studied in an extensive experimental investigation. The temperature ranges of interest were; solution treatment at 500-560°C, natural ageing at room temperature, and artificial ageing at 150-200°C. The changes in dendritic composition and eutectic morphology due to solution treatment were quantified by microprobe and image analysis for a wide range of processing conditions. Subsequently, a microstructure model for solution treatment was constructed using sub-models for; i) the dissolution of Mg2Si particles, ii) the fragmentation of eutectic fibres, and iii) the coarsening of the fragmented eutectic. For the ageing investigations, characterisation of mechanical properties was done by hardness and tensile testing, and the kinetics of precipitation was determined by an isothermal calorimetry technique. A model to predict the evolution of yield strength during artificial ageing was developed based on established physical theories. A yield strength model for natural ageing was also proposed using data from isothermal calorimetry tests performed close to room temperature. Two model Al-Si-Mg alloys were investigated in order to extend both ageing models to include the effects of; i) alloy chemistry, ii) incomplete solution treatment and iii) natural ageing prior to artificial ageing.

The validity of the models was verified using independent experimental

measurements and literature data, and they were subsequently used as a tool to identify potential optimisation strategies for industrial heat treatment processes. The linkages between the models revealed details of processing challenges arising from the interdependence of the heat treatment stages, such as reduced strengthening during ageing due to incomplete solution treatment, and delayed strengthening during artificial ageing as a result of prior natural ageing.

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TABLE OF CONTENTS

ABSTRACT ....................................................................................................................................ii TABLE OF CONTENTS .............................................................................................................. iii LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ........................................................................................................................ ix LIST OF SYMBOLS ..................................................................................................................... xv ACKNOWLEDGEMENTS.......................................................................................................... xix CHAPTER 1 INTRODUCTION ..................................................................................................... 1 CHAPTER 2 LITERATURE REVIEW .......................................................................................... 3 2.1 Introduction ........................................................................................................................... 3 2.2 Overview of Al-Si-Mg Casting Alloys ................................................................................. 3 2.3 Heat Treatment of Al-Si-Mg Casting Alloys ........................................................................ 5 2.3.1 Solution Treatment .......................................................................................................... 5 2.3.2 Quenching ....................................................................................................................... 7 2.3.3 Ageing Processes ............................................................................................................ 7 2.4 Microstructure Evolution during Heat Treatment ................................................................. 9 2.4.1 Dissolution of Soluble Second Phase Particles ............................................................... 9 2.4.2 Homogenization of Solute Elements ............................................................................. 10 2.4.3 Morphological Change of Insoluble Second Phases ..................................................... 11 2.4.3.1 Fragmentation ..................................................................................................... 12 2.4.3.2 Coarsening .......................................................................................................... 14 2.4.4 Precipitation .................................................................................................................. 14 2.5 Strengthening Mechanisms in Aluminum Alloys ............................................................... 17 2.5.1 Precipitation Strengthening Mechanisms ...................................................................... 17 2.5.1.1 Obstacle Strength ................................................................................................ 19 iii

2.5.1.2 Contribution of Precipitate Hardening towards the Yield Strength.................... 20 2.5.1.3 Obstacle Spacing ................................................................................................ 21 2.5.1.4 Superposition of Effects ..................................................................................... 22 2.5.2 Strengthening due to Second Phase Particles................................................................ 22 2.6 Precipitation Kinetics .......................................................................................................... 24 2.6.1 Effect of Natural Ageing on Precipitation Kinetics ...................................................... 25 2.7 Microstructure-Property Models for Ageing Processes ...................................................... 27 2.8 Summary ............................................................................................................................. 29 CHAPTER 3 SCOPE AND OBJECTIVES .................................................................................. 31 CHAPER 4 EXPERIMENTAL METHODOLOGY ..................................................................... 33 4.1 Introduction ......................................................................................................................... 33 4.2 Materials .............................................................................................................................. 33 4.3 Sample Preparation ............................................................................................................. 38 4.4 Heat Treatment Experiments............................................................................................... 38 4.4.1 Solution Treatment ........................................................................................................ 39 4.4.2 Artificial Ageing ........................................................................................................... 40 4.5 Material Characterization .................................................................................................... 41 4.5.1 Sample Preparation ....................................................................................................... 41 4.5.2 Microscopy.................................................................................................................... 41 4.5.3 Electron Probe Microanalysis (EPMA) ....................................................................... 44 4.5.4 Tensile and Hardness Testing ....................................................................................... 45 4.5.5 Isothermal Calorimetry ................................................................................................. 46 CHAPTER 5 EXPERIMENTAL RESULTS ................................................................................ 49 5.1 A356 Alloy Behaviour during Solution Treatment ............................................................. 49 5.1.1 Qualitative Description of Microstructure Changes ..................................................... 49 5.1.2 Quantitative Description of Microstructure Changes ................................................... 52 iv

5.1.3 Electron Probe Microanalysis ....................................................................................... 56 5.1.4 Mechanical Properties of Solution Treated Material .................................................... 58 5.2 A356 Alloy Behaviour during Ageing ................................................................................ 59 5.2.1 Natural Ageing Behaviour ............................................................................................ 59 5.2.2 Immediate Artificial Ageing ......................................................................................... 62 5.2.3 Artificial Ageing after Natural Ageing ......................................................................... 66 5.3 Heat Treatment Behaviour of Model Alloys ....................................................................... 70 5.3.1 Behaviour of Al-11.1Si-0.22Mg ................................................................................... 70 5.3.1.1 Solution Treatment Behaviour ............................................................................ 71 5.3.1.2 Natural Ageing Behaviour .................................................................................. 72 5.3.1.3 Artificial Ageing Behaviour ............................................................................... 72 5.3.2 Behaviour of Al-1.3Si-0.3Mg ....................................................................................... 76 5.3.2.1 Natural Ageing Behaviour .................................................................................. 76 5.3.2.2 Immediate Artificial Ageing ............................................................................... 77 5.3.2.3 Artificial Ageing Following Natural Ageing ...................................................... 78 5.4 Discussion of Experimental Results.................................................................................... 80 5.4.1 Metallurgical Behaviour of A356 during Solution Treatment ...................................... 80 5.4.1.1 Dissolution of Mg-rich Phases............................................................................ 80 5.4.1.2 Eutectic Silicon Fragmentation and Coarsening ................................................ 81 5.4.1.3 The Relationship between Solution Treatment and Yield Strength ................... 83 5.4.2 Comparison of Ageing Behaviour of A356 and Model Alloys .................................... 84 5.5 Concluding Remarks ........................................................................................................... 90 CHAPTER 6 MICROSTRUCTURE-PROPERTY MODELLING .............................................. 91 6.1 Overall Approach ................................................................................................................ 91 6.2 Solution Treatment .............................................................................................................. 93 6.2.1 Dissolution of Mg2Si .................................................................................................... 94 v

6.2.2 Morphological Change of Eutectic Silicon ................................................................... 99 6.2.2.1 Fragmentation of Silicon Particles ..................................................................... 99 6.2.2.2 Coarsening of Spheroidal Silicon Particles ...................................................... 104 6.2.3 Solution Treatment Model Results and Summary ...................................................... 106 6.3 Artificial Ageing ............................................................................................................... 107 6.3.1 Modelling of Precipitation Strengthening ................................................................... 109 6.3.1.1 Obstacle Strength .............................................................................................. 110 6.3.1.2 Obstacle Spacing .............................................................................................. 111 6.3.1.3 Estimation of Precipitate Volume Fraction ...................................................... 112 6.3.1.4 Calculating σppt ................................................................................................. 115 6.3.2 Calibration of the Model ............................................................................................. 116 6.3.3 Model Results.............................................................................................................. 117 6.4 Natural Ageing .................................................................................................................. 120 6.5 Artificial Ageing after Natural Ageing ............................................................................. 124 6.5.1 Estimation of fr ............................................................................................................ 124 6.5.2 Evolution of Yield Strength ........................................................................................ 128 6.5.3 Model Calibration ....................................................................................................... 129 6.5.4 Model Predictions and Validation ............................................................................... 130 6.6 Modelling of Al-Si-Mg Alloys.......................................................................................... 133 6.6.1 Development of Extended Model ............................................................................... 133 6.6.1.1 Effect of Silicon Content .................................................................................. 133 6.6.1.2 Effect of Mg Content ........................................................................................ 135 6.6.1.3 Effect of Incomplete Solution Treatment ......................................................... 136 6.6.2 Assessment of Extended Model .................................................................................. 138 6.6.2.1 Effect of Alloy Content .................................................................................... 138 6.6.2.2 Effect of Incomplete Solution Treatment ......................................................... 140 vi

6.6.2.3 Assessment using Literature Data for Al-Si-Mg Casting Alloys ..................... 142 6.6.3 Summary ..................................................................................................................... 147 6.7 Application of the Model for Optimization of Industrial Processes ................................. 148 6.7.1 Optimization of Solution Treatment Process .............................................................. 148 6.7.1.1 Effect of Soak Temperature .............................................................................. 148 6.7.1.2 Effect of Heating Rate ...................................................................................... 150 6.7.1.3 Effect of Charge Temperature .......................................................................... 153 6.7.1.4 Effect of Simultaneous Changes to Solution Treatment Parameters ................ 154 6.7.2 Optimization of Artificial Ageing ............................................................................... 157 6.7.2.1 Effect of Natural Ageing .................................................................................. 157 6.7.3 Summary ..................................................................................................................... 159 CHAPTER 7 CONCLUSIONS AND FUTURE WORK............................................................ 161 7.1 Conclusions ....................................................................................................................... 161 7.2 Future Work ...................................................................................................................... 164 REFERENCES ............................................................................................................................ 167 APPENDIX A CORRELATION BETWEEN YIELD STRENGTH AND VICKERS HARDNESS ................................................................................................................................ 175

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LIST OF TABLES Table 4.1: Chemical composition (wt%) of the A356 aluminum alloy used in this study ......... 33 Table 4.2: Chemical compositions (wt%) of the Al-Si-Mg model alloys used in this study ...... 34 Table 4.3: Predicted Microstructure Characteristics of the A356 Alloy and Model Alloys in the Solution Treated Condition ........................................................................................ 36 Table 5.1: FactSage-predicted equilibrium values for phase and solute content in the three alloys at solution treatment temperatures investigated in the present work ............... 85 Table 5.2: Summary of the yield strength contributions from solid solution strengthening, solute clusters, precipitates and eutectic particles for the three alloys studied in the as-quenched, naturally aged and peak aged conditions ............................................. 89 Table 6.1: List of microstructure variables and internal state variables for the metallurgical processes occurring during solution treatment ........................................................... 94 Table 6.2: Physical constants and values used in the dissolution model .................................... 96 Table 6.3: List of adjustable parameters in the fragmentation model and their values ............. 101 Table 6.4: List of adjustable parameters in the coarsening model and their values .................. 105 Table 6.5: Calculated Avrami coefficients for the JMAK equation used to describe the evolution of relative volume fraction of precipitates during immediate artificial ageing of the A356 alloy .......................................................................................... 114 Table 6.6: List of calibration parameters for the A356 alloy artificial ageing model ............... 116 Table 6.7: List of calibration parameters for the A356 alloy natural ageing model ................. 122 Table 6.8: Calibration parameters for the artificial ageing model for 24hr naturally aged A356 ... .................................................................................................................................. 130 Table 6.9: FactSage thermodynamic calculation results for eutectic silicon content assuming equilibrium conditions at the typical solution treatment temperature of 540°C ...... 134 Table 6.10: Model predictions for completion of each microstructure process during solution treatment with various heating profiles (illustrated in Figure 6.32)......................... 152 Table 6.11: Solution treatment parameters used for the model investigation into the effect of simultaneous parameter changes on the total processing time................................. 155 Table 6.12: Model predictions for completion of solution treatment with various heating profiles (details of heating profiles are in Table 6.11) .......................................................... 156 viii

LIST OF FIGURES Figure 2.1: The Al-rich section of the Al-Si phase diagram [after Massalski et al (1998)] .......... 4 Figure 2.2: Microstructure of Al/Si eutectic phase in an as-cast A356 aluminum alloy; (a) Unmodified alloy, (b) Modified with an addition of 156ppm strontium [Nafisi et al (2006)] ........................................................................................................................ 4 Figure 2.3: Morphological evolution of eutectic silicon in A356 (Al-7Si-0.4Mg) aluminum alloy during solution treatment at 540ºC; (a) as-cast, (b) 2 hr, (c) 8 hr. [Apelian et al (1990)] ........................................................................................................................ 6 Figure 2.4: Schematic illustrating a rod-shaped eutectic particle that fragments into a series of spherical particles [after Ogris et al (2002)] ............................................................. 13 Figure 2.5: Model results for silicon spheroidisation model presented by Ogris et al (2002) .... 13 Figure 2.6: Schematic view of three stages of the dislocation cutting mechanism ..................... 17 Figure 2.7: Schematic view of three stages of the Orowan looping mechanism ........................ 18 Figure 2.8: Schematic representation of a glide dislocation moving though an array of point obstacles [after Ardell (1985)] .................................................................................. 19 Figure 2.9: Variation of hardness in A356 alloy artificially aged at 180ºC without natural ageing and after 24 hours of natural ageing [after Shivkumar et al (1989)]............. 26 Figure 4.1: Example of an automotive wheel indicating the wheel rim area used for the present . .................................................................................................................................. 34 Figure 4.2: The end-chill casting apparatus and as-cast ingot at Rio Tinto Alcan ..................... 35 Figure 4.3: As-cast microstructures of: a) Al-1.3Si-0.32Mg and b) Al-11Si-0.22Mg alloys ..... 37 Figure 4.4: An example of the measured sample temperature-time profile during solution treatment in the salt bath ........................................................................................... 39 Figure 4.5: Schematic representations of the heat treatment processes studied: a) natural ageing at room temperature, b) immediate artificial ageing between 150ºC-200ºC, c) a period of natural ageing followed by artificial ageing between 150ºC-200ºC ......... 40 Figure 4.6: The equivalent circle diameter (ECD) is the diameter of a circle with area equal to that of the projection of the particle at a plane (i.e. Areaparticle = Areacircle) ....... 43 Figure 4.7: The aspect ratio (AR) is the ratio between the major axis length and the minor axis length. Major and Minor are the primary and secondary axis of the best fitting ellipse ........................................................................................................................ 43 ix

Figure 4.8: The circularity is a function of the perimeter P and the area A that has values between 0 and 1, where a value of 1 indicates a perfect circle ................................. 44 Figure 5.1: Optical micrographs of A356 alloy after solution treatment at 540°C (x500) a) as cast, b) 2 minutes, c) 30 minutes, d) 240 minutes .................................................... 50 Figure 5.2: Deep etched micrographs of A356 alloy after solution treatment at 540°C (x4000) a) As-cast, b) 2 minutes, c) 15 minutes, d) 30 minutes, e) 240 minutes ................... 51 Figure 5.3: BSE maps showing distribution of Si and Mg in A356 in the: a) as-cast condition, b) solution treated condition (following 240 minutes at 540°C) ............................. 52 Figure 5.4: The distribution of eutectic particle shape characteristics following solution treatment at 540°C: a) equivalent circle diameter, b) aspect ratio, c) particle roundness .................................................................................................................. 53 Figure 5.5: Change in average eutectic particle characteristics during solution treatment at 540°C: a) equivalent circle diameter, b) aspect ratio, c) particle roundness ............ 55 Figure 5.6: The distribution of a) magnesium and b) silicon across secondary dendrite arms in the A356 alloy in the as-cast condition and during solution treatment at 540°C ..... 57 Figure 5.7: Mechanical property behaviour for A356 in the as-cast and as-quenched condition following solution treatment at 540°C...................................................................... 58 Figure 5.8: The mechanical property behaviour of the A356 alloy in the as-quenched (AQ) condition, and after natural ageing at room temperature for 2 hours, 24 hours and 2400 hours ................................................................................................................ 60 Figure 5.9: Exothermic heat flow traces for natural ageing of A356 at 25°C, 40°C and 60°C .. 61 Figure 5.10: The evolution of heat during natural ageing of A356 at 25°C, 40°C and 60°C ....... 62 Figure 5.11: The mechanical property behaviour of the A356 alloy in the as-quenched (AQ) condition, and after artificial ageing at 180ºC for various times .............................. 63 Figure 5.12: Ageing curves based on Vickers hardness data for artificial ageing of the A356 alloy in the temperature range 150°C-200°C ........................................................... 64 Figure 5.13: Thermograms for the artificially aged A356 alloy at 150°C, 180°C and 200°C ...... 65 Figure 5.14: The evolution of the relative fraction of heat during artificial ageing of A356 at: a) 150°C, b) 180°C, c) 200°C ....................................................................................... 66 Figure 5.15: The evolution of yield strength during artificial ageing at a) 150°C and b) 180°C following various natural ageing histories ................................................................ 67

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Figure 5.16: Thermograms for isothermal calorimetry of A356 artificially aged at 165°C, 180°C and 200°C following 24 hour natural ageing at room temperature .......................... 68 Figure 5.17: Thermograms of exothermic heat flow measured in A356 alloy during artificial ageing at 180°C following various natural ageing histories ..................................... 69 Figure 5.18: The distribution of magnesium across secondary dendrite arms in the as cast and solution treated Al-11Si-0.22Mg alloy ..................................................................... 71 Figure 5.19: The evolution of yield strength during natural ageing of Al-11Si-0.22Mg alloy..... 72 Figure 5.20: The evolution of yield strength during artificial ageing of Al-11Si-0.22Mg alloy in the temperature range 150°C-200°C......................................................................... 73 Figure 5.21: The evolution of yield strength during artificial ageing of the Al-11Si-0.22Mg alloy at 180°C following a) no natural ageing, b) 24 hours natural ageing at room temperature ............................................................................................................... 74 Figure 5.22: The exothermic heat flow curves for Al-11Si-0.22Mg at 180°C during immediate artificial ageing and artificial ageing after 24 hours natural ageing ......................... 75 Figure 5.23: Exothermic heat flow curves for the Al-11Si-0.22Mg alloy during artificial ageing at 165°C, 180°C and 200°C following 24 hours natural ageing............................... 75 Figure 5.24: The evolution of yield strength during natural ageing of Al-1.3Si-0.32Mg alloy.... 76 Figure 5.25: The evolution of yield strength during ageing of homogenized Al-1.3Si-0.32Mg .. 77 Figure 5.26: The evolution of yield strength during artificial ageing of the Al-1.3Si-0.3Mg alloy at 180°C following a) no natural ageing, b) 24 hours natural ageing at room temperature ............................................................................................................... 78 Figure 5.27: The exothermic heat flow curves for the Al-1.3Si-0.3Mg alloy artificially aged at 180°C following: i) no natural ageing and ii) 24 hours natural ageing .................... 79 Figure 5.28: Thermograms for isothermal calorimetry of Al-1.3Si-0.3Mg alloy artificially aged at 165°C, 180°C and 200°C after 24 hour natural ageing at room temperature ....... 79 Figure 5.29: The average magnesium content in A356 and Al-11Si-0.22Mg alloy during solution treatment at 540°C, calculated from the microprobe data ........................................ 81 Figure 5.30: Results of a sensitivity analysis to determine an appropriate particle roundness limit as a criterion for fragmented eutectic silicon particles in the A356 alloy ................ 82 Figure 5.31: The evolution of yield strength during solution treatment at 540°C, and the time periods over which each of the various metallurgical processes occurring are dominant ................................................................................................................... 83

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Figure 5.32: The evolution of yield strength in the underaged condition during immediate artificial ageing of the three alloys studied at 180°C................................................ 85 Figure 5.33: The evolution of yield strength during the first 24 hours natural ageing at room temperature for the three alloys studied.................................................................... 89 Figure 6.1: Schematic diagram showing the solute concentration around a dissolving particle .... .................................................................................................................................. 95 Figure 6.2: Schematic diagram of the solute and eutectic content around the dissolving particle . .................................................................................................................................. 96 Figure 6.3: Dissolution model predictions of the relative volume fraction of an Mg2Si particle for solution treatment involving a heating at 40°C/s to soak temperatures of 500°C, 540°C & 560°C. The symbols and lines represent measured data and model predictions respectively ............................................................................................ 98 Figure 6.4: Experimental data vs. model predicted values at: a) 500°C, b) 540°C and c) 560°C .. .................................................................................................................................. 99 Figure 6.5: The Arrhenius relationship between the JMAK constant k and temperature ......... 101 Figure 6.6: Model predictions and experimental data for fragmentation of the eutectic silicon phase during solution treatment at 500°C, 540°C and 560°C. The symbols and lines represent the measured data and model predictions respectively ........................... 102 Figure 6.7: Schematic representation of the fragmentation process showing the geometries of a rod containing a perturbation and a sphere that is of equal volume to the perturbed rod ........................................................................................................................... 103 Figure 6.8: Coarsening model predictions (lines) compared with experimental data (symbols) for solution treatment temperatures at 500°C, 540°C and 560°C .......................... 105 Figure 6.9: Process model predictions (lines) and experimental results (symbols) for solution treatment at 540°C .................................................................................................. 106 Figure 6.10: ln ln (1/(1-fr)) vs. ln t for the range of volume fraction between 0.05 and 0.95..... 113 Figure 6.11: A comparison of the experimental data (solid lines) and model predictions (dashed lines) for the evolution of the relative volume fraction of precipitates in the A356 alloy during immediate artificial ageing ................................................................. 114 Figure 6.12: The JMAK coefficient k has an Arrhenius relationship with temperature ............. 115 Figure 6.13: Comparison of model predictions and experimental data for the evolution of yield strength during immediate artificial ageing of the A356 alloy at: a) 150°C, b) 180°C & c) 200°C. A heat ramp of 5°C/s from 20°C to the soak temperature is included at the start of the model .............................................................................................. 118 xii

Figure 6.14: Comparison of model predictions and experimental data for the evolution of yield strength during immediate artificial ageing of the A356 alloy at a) 190°C, b) 220°C. A heat ramp of 5°C/s from 20°C to the soak temperature is included at the start of the model. ............................................................................................................... 119 Figure 6.15: A comparison of the experimental data (thick lines) and model predictions (dashed lines) for the evolution of relative volume fraction of precipitates during natural ageing...................................................................................................................... 122 Figure 6.16: Comparison of model predictions and experimental data for the evolution of yield strength during natural ageing of the A356 alloy at 20°C ...................................... 123 Figure 6.17: Deconvoluted dissolution and precipitation at 180°C after 24 hours natural ageing ... ................................................................................................................................ 125 Figure 6.18: Arrhenius plot for k and B ...................................................................................... 128 Figure 6.19: Comparison of model predictions and experimental data for the evolution of yield strength during artificial ageing of the naturally aged A356 alloy at a) 150°C, b) 180°C, c) 200°C ...................................................................................................... 131 Figure 6.20: Comparison of model predictions and experimental data for the evolution of yield strength during artificial ageing of the naturally aged A356 alloy at 190°C .......... 132 Figure 6.21: Comparison of σeut values obtained from tensile test measurements with predicted values from Equation 6.16 ...................................................................................... 134 Figure 6.22: The effect of magnesium content, CMg, on strengthening due to precipitates (cppt) and solute clusters (ccluster) in the peak aged and naturally aged conditions in Al-SiMg alloys ................................................................................................................ 135 Figure 6.23: Model predictions for strengthening during immediate artificial ageing at 180°C for the A356 alloy and the two model alloys investigated ........................................... 139 Figure 6.24: Model predictions for strengthening during artificial ageing at 180°C following 24 hours natural ageing for the A356 and Al-11Si-0.22Mg alloys ............................. 139 Figure 6.25: Model predictions for strengthening of A356 alloy during immediate artificial ageing at 180°C following short solution treatments of 2 minutes and 5 minutes at 540°C, compared with full solution treatment of 30 minutes at 540°C ................. 141 Figure 6.26: Model predictions for Al-11Si-0.22Mg during immediate artificial ageing at 150°C, 180°C and 200°C following 30 minutes solution treatment at 540°C (fdis = 0.76) ...... ................................................................................................................................ 142

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Figure 6.27: Model predictions for Al-7Si-Mg alloys with varying Mg content during artificial ageing at: a) 160°C and b) 180°C, compared with literature data from Moller et al (2008)...................................................................................................................... 144 Figure 6.28: Model predictions for Al-7Si-Mg alloys with varying Mg content during natural ageing at 20°C compared with literature data from Moller et al (2008) ................ 145

Figure 6.29: Model predictions for Al-7Si-Mg alloys with varying Mg content during artificial ageing at: a) 160°C and b) 180°C after natural ageing, compared to data from Moller et al (2008) .................................................................................................. 146 Figure 6.30: Effect of soak temperature on the time required for microstructure changes during solution treatment. (Fixed process parameters: Dendrite Arm Spacing = 30µm, Initial silicon rod diameter = 0.5µm, Charge Temperature = 20°C, Solution treatment heating rate = 40°C/sec) ......................................................................... 149 Figure 6.31: Effect of heating temperature on microstructure changes during solution treatment. (Fixed process parameters: Dendrite Arm Spacing = 30µm, Initial silicon rod thickness = 0.5µm, Soak Temperature = 540°C, Charge Temperature = 20°C) .... 151 Figure 6.32: Modelled heating profiles, including the base case and two-step strategies .......... 152 Figure 6.33: Comparison of model predictions for solution treatment using a range of heating rates in the cases of cold charging (20°C) and hot charging (200°C) the as-cast component............................................................................................................... 153 Figure 6.34: Schematic illustrating heating profiles used to obtain model predictions, including the base case (0.2°C/sec to 540°C), and two-step strategies detailed in Table 6.11 .... ................................................................................................................................ 154 Figure 6.35: Comparison of model predictions for the time to peak strength during immediate artificial ageing and after a 24 hour natural age at room temperature. Model predictions are given by solid lines and experimental data by symbols ................. 158 Figure A.1: Correlations and best fit equations between yield strength and Vickers hardness for the A356, Al-1.3Si-0.32Mg and Al-11Si-0.22Mg alloys used in this study .......... 176 Figure A.2: Correlations and best fit equation between yield strength and Vickers hardness for the Al-7Si-xMg alloys (where x= 0.28, 0.34 & 0.45) studied by Moller et al (2008).. ................................................................................................................................ 176

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LIST OF SYMBOLS

Appt

area under the heat flow curve for immediately artificially aged material

Adis

total heat absorbed due to the dissolution of natural ageing zones during subsequent artificial ageing

ANA

area under the heat flow curve for previously naturally aged material

B

temperature dependent parameter used in defining the dissolution kinetics of solute clusters

B0

pre-exponential constant used in defining the temperature dependence of the dissolution kinetics parameter

b

magnitude of the Burgers vector

Ci

solute concentration at the matrix-precipitate interface (wt%)

Cp

solute concentration in the precipitate (wt%)

Ct

solute concentration in the matrix at ageing time, t (wt%)

C0

solute concentration in the matrix (wt%)

CMg

magnesium concentation in the matrix (wt%)

CMg,ac

solute magnesium concentration in the as-cast condition (wt%)

CMg,st

solute magnesium concentration in the solution treated condition (wt%)

CSi

silicon concentration in the matrix (wt%)

c

a proportionality constant

ceutectic

constant factor for contribution to the yield strength from eutectic phase

cppt

constant factor for contribution to the yield strength from precipitation

cclusters

constant factor for contribution to the yield strength from solute clusters

D

diffusion coefficient of the solute in the matrix (m2/s) xv

D0

proportionality constant for the diffusivity equation

F

obstacle strength, maximum obstacle-dislocation interaction force

Fpeak

average obstacle strength at the peak aged condition

f

volume fraction of precipitates

feutectic

volume fraction of eutectic phase

ffrag

volume fraction of fragmented eutectic silicon particles

fpeak

volume fraction of precipitates in the peak aged condition

fr

relative volume fraction of precipitates

f0

initial volume fraction of precipitates

fr,0

relative volume fraction of solute clusters at the beginning of artificial ageing

k

a constant (specific details for each use are described in the text)

k0frag

proportionality constant for fragmentation

k0c

proportionality constant for coarsening

k0ppt

proportionality constant for precipitation

k0cluster

proportionality constant for solute clustering

L

effective obstacle spacing on the slip plane (m)

M

Taylor factor

mppt

constant factor relating the magnesium content to the magnitude of the precipitation contribution to the yield strength (MPa wt%-1/2)

mcluster

constant factor relating the magnesium content to the magnitude of the solute cluster contribution to the yield strength (Nm-5/2wt%-1)

NA

number of precipitates per unit area of the slip plane

n

a numerical exponent for the JMAK relationship xvi

Q

an activation energy for a process (specific processes described in text)

Qfrag

apparent activation energy for the fragmentation of as-cast eutectic silicon rods (kJ/mol)

QMg

activation energy for diffusion of magnesium in aluminum (kJ/mol)

QSi

activation energy for diffusion of silicon in aluminum (kJ/mol)

Qppt

apparent activation energy for precipitation (kJ/mol)

Qcluster

apparent activation energy for clustering of solute (kJ/mol)

Qdis

apparent activation energy for dissolution of solute clusters (kJ/mol)

Qd

activation energy for diffusion of solutes in the matrix (kJ/mol)

Qs

enthalpy of solution for solute clusters (kJ/mol)

R

universal gas constant (J/mol-K)

r

radius of a spherical particle, or radius of the circular cross-sectional area of a precipitate on a slip plane (m)

rcell

radius of a spherical matrix cell containing a single particle (m)

rrod

radius of an as-cast eutectic silicon rod (m)

r0

initial radius of a spherical particle (m)

rpeak

average radius at the peak aged condition (m)

S1, S2, etc

internal state variable

T

temperature (K)

t

time

tpeak

time to peak-aged condition

Vfrag

volume of fragmented eutectic silicon particles (m3)

Vtotal

total volume of eutectic silicon particles (m3)

α

a dimensionless constant xvii

η

a parameter related to Ci, Cp, and C0

λ

characteristic wavelength for fragmentation of eutectic silicon rods (m)

σys

yield strength (MPa)

σaq

as-quenched yield strength (MPa)

σα-Al

contribution from α-Al phase to the yield strength (MPa)

σclusters

contribution from solute clustering to the yield strength (MPa)

σeutectic

contribution from eutectic phase to the yield strength (MPa)

σint

intrinsic yield strength (i.e. frictional stress of the α-Al lattice (MPa)

σppt

contribution from precipitation strengthening to the yield strength (MPa)

σ'ppt

contribution from a mixture of precipitates and solute clusters to the yield strength (MPa)

σss

contribution from solid solution strengthening to the yield strength (MPa)

σ0ss

contribution from solid solution strengthening to the yield strength for the as-quenched material (MPa)

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ACKNOWLEDGEMENTS This thesis was made possible with the help of many colleagues, and I would like to take this opportunity to give special thanks to the following;

I would like to express my gratitude to my supervisors Dr. Mary Wells and Dr. Warren Poole, for their insight, and continuous support, guidance and encouragement throughout my studies.

Many thanks to Chris Hermesmann at Canadian Autoparts Toyota (CAPTIN) and Fred Major at Rio Tinto Alcan for supplying the materials that were used for this work. Financial support from AUTO21 and the Rio Tinto Alcan Research Fellowship is also gratefully acknowledged.

I would like to thank Mati Raudsepp, Edith Czech, Mary Fletcher and Gary Lockhart for their help with the experimental work, Ross McLeod, Carl Ng and David Torok for their assistance with sample preparation, and Michelle Tierney, Mary Jansepar and Fiona Webster for all manner of administrative help. Many thanks also to Michael Lin, Michael Mendenhall and Andrew Carne, who gave their time and effort as part of the Undergraduate Summer Research Assistant (USRA) program.

Special thanks to Jason Mitchell, Babak Raeisinia, Sujay Sarkar, Angela Kubiak, Qiang Du, Payman Babaghourbani, Jayant Jain, Hamid Azizi-Alizamini, Reza Rouminia and all other friends at UBC for stimulating discussions covering a wide range of topics.

Finally, I am forever indebted to my wife Lindsey, my son Nathan, and my parents Ingrid and John for their constant love, sacrifice, patience and support. Thank you for everything. xix

CHAPTER 1 - Introduction

For many years, one of the largest potential markets for aluminum alloys has been the transportation sector, primarily due to their increasing use in automotive applications as a way of light-weighting cars. The major driving forces for this increase have been the implementation of graduated government standards for vehicle fuel efficiency and recyclability, as well as the effects of higher fuel costs to the consumer. As a consequence, automotive manufacturers have a strong incentive to reduce fuel consumption while maintaining product performance and cost levels. One of the most cost effective ways of addressing these challenges has been to substitute lightweight materials such as aluminum alloys in existing automotive designs.

Cast components account for over 80% of aluminum alloy use in vehicles [Kaufman and Rooy (2005)]. These castings have replaced their steel counterparts on a part-by-part basis over a number of years, and include relatively large items such as engine blocks, transmission cases and wheels. Often, these aluminum cast components are given a heat treatment after casting to improve their mechanical properties. An important aspect of the research efforts aiming to meet the demand for highly reliable cast automotive components is that an improved understanding of alloy behaviour during multi-stage heat treatment can allow the optimisation of the process from the standpoint of the material, resulting in lower variability in the properties of the heat treated component.

In addition there is a need to understand the heat treatment process from a

metallurgical standpoint so that efficient heat treatments can be developed.

Although the benefit of heat treatment is undisputed, there exist several challenges for heat treatment operators, including market expectations of higher performance and reliability, lower production costs and energy use, as well as concern over environmental impacts. Standard heat 1

treatment practises were established many years ago, and require re-examination as they remain unchanged despite product and process improvements occurring in the interim. Developments in casting process technologies have led to changes in the scale of the as-cast microstructure, while current furnace designs produce higher heating rates and lower thermal variation within the charged components during heat treatment. Consequently, there is scope for the optimisation of heat treatment processes by reducing the times and temperatures of each stage. The main objective of this work is to develop a model framework that predicts the evolution of microstructure and mechanical properties during heat treatment and can be used as a tool to optimise industrial heat treatment operations and enable the production of components with consistently uniform microstructures and properties that are tailored to their specific application.

2

CHAPTER 2 - Literature Review

2.1

Introduction

The following sections provide a review of the heat treatment of Al-Si-Mg casting alloys, the theory of relevant metallurgical processes such as the precipitation and dissolution of soluble second phase particles, and the morphological change of insoluble particles, ending with a discussion of process models developed to predict the evolution of microstructure and mechanical properties during heat treatment.

2.2

Overview of Al-Si-Mg Casting Alloys

Hypoeuctectic Al-Si-Mg alloys are common non-ferrous foundry alloys due to their excellent castability, fluidity and corrosion resistance. The as-cast microstructure consists of primary dendrites of α-Al containing magnesium and silicon in solution, surrounded by an Al/Si eutectic phase arising from the eutectic transformation shown in the Al-Si binary phase diagram presented in Figure 2.1. The size and morphology of the eutectic silicon depends on the casting conditions, as well as the presence of chemical modifiers such as strontium, sodium or antimony. Without modification the eutectic silicon forms as coarse platelets, shown in Figure 2.2a, whereas a fine ‘fibrous’ or ‘coral-like’ structure occurs in modified alloys, Figure 2.2b. Other phases found in as-cast Al-Si-Mg alloys include Mg2Si particles, which are taken into solid solution and precipitated during heat treatment, and minor Fe-rich phases including α-Al5SiFe, β-Al8Si2Fe and π-Al8Mg3Si6Fe that arise from the presence of melt impurities.

3

700 660°C

Temperature (°C)

650

Liquid

600 577°C 12.2 550

Eutectic Point α-Al

500 α-Al +Si 450

400 0 Al

5

10 15 Silicon Content (at%)

20 Si

Figure 2.1: The Al-rich section of the Al-Si binary phase diagram [after Massalski et al. (1998)].

Al/S i Eutec tic α-Al

a)

50µm

b)

50µm

Figure 2.2: Microstructure of Al/Si eutectic phase in an as-cast A356 aluminum alloy; (a) Unmodified alloy, (b) Modified with an addition of 156ppm strontium [Nafisi et al (2006)]†.

†

Reprinted from Materials Science and Engineering: A, 415, 1-2, S. Nafisi, R. Ghomashchi, Effect of modification during conventional and semi-solid metal processing of A356 Al-Si alloy, pp. 273-285, Copyright (2006), with permission from Elsevier. 4

2.3

Heat Treatment of Al-Si-Mg Casting Alloys

Controlled heat treatment of aluminum alloys can significantly influence properties such as strength, ductility, toughness, and corrosion resistance, as well as the formation of residual stresses and the thermal and dimensional stability of the component. The main heat treatment process applied to cast Al-Si-Mg alloys is precipitation hardening, which is carried out to improve the mechanical strength of the casting and consists of three stages; solution treatment, quenching and ageing.

The ASTM standard procedure for T6 heat treatment of castings

produced using the alloy studied in this work, A356 (Al-7Si-0.3Mg), involves [ASTM (2002)];

1) Solution treatment at 540°C for 4-12 hours, 2) Immediate water quench, 3) Natural age at RT for 8 hours, followed by artificial age at 155°C for 6-12 hours.

Each stage of this process is reviewed in the following section.

2.3.1

Solution treatment

Solution treatment requires long soak times at high temperature in order to produce a homogeneous solid solution with maximum solute concentration.

The soak temperature is

determined by alloy composition and solid solubility limit, and is typically close to the eutectic temperature. Industrial Al-Si-Mg alloys are solution treated at a maximum temperature of 550°C to avoid localised melting. Underheating can result in incomplete dissolution of particles, low solute concentrations, and inhomogeneous solute distributions in the matrix; all of which cause a reduction in the strengthening potential of the alloy.

5

The dissolution of non-equilibrium particles and homogenization of solute can take up to 24 hours depending on the soak temperature, the scale of the as-cast microstructure, the casting dimensions and furnace temperature. However, studies by Closset et al (1986) and Shivkumar et al (1989) to examine the solution treatment behaviour of A356 alloys found that dissolution of Mg2Si particles and homogenization of solute were complete after 30 minutes at 550°C, and other researchers report faster rates during solution treatment of permanent mould castings [Zhang et al. (2002)]. Typically, small amounts of magnesium and silicon are also present in the as-cast alloy as components of Fe-rich phases that are slow to dissolve, such as π-Al8Si6Mg3Fe; Gustafsson et al. (1986) found these particles dissolve after 4 hours at 520°C.

Another important metallurgical process during solution treatment is the change in shape of insoluble second phase particles. In the case of Al-Si-Mg alloys this involves a change in the eutectic silicon phase from the as-cast structure to spheroidal globules. The spheroidization process is illustrated in Figure 2.3, which shows (a) the as-cast eutectic silicon network, (b) its fragmentation, and (c) coarsening of fragmented particles during solution treatment.

Al 20mm 20µ µm

Si Particles Al-Si Eutectic

a)

?mm 20mm 20µµ 20µ

b)

?m µ 20mm 20 m 20µ µ

c)

20mm 20µ µm

Figure 2.3: Morphological evolution of eutectic silicon in A356 aluminum alloy during solution treatment at 540°C; (a) as-cast, (b) 2 hours, (c) 8 hours, [Apelian et al. (1990)]. ©1990 American Foundry Society, Schaumburg, Illinois, USA. Used with permission. 6

The use of fluidized beds for rapid heat transfer during solution treatment of Al-Si-Mg casting alloys has been studied in recent years. Chaudhury et al [2006] found that the increased heating rate due to the fluidized bed resulted in faster spheroidisation times than conventional furnaces. This has been attributed to brittle fracture of eutectic silicon particles due to strains induced by the thermal expansion mismatch between the silicon and aluminum phases during heat up..

2.3.2

Quenching

Following solution treatment the alloy must be rapidly cooled to produce a highly supersaturated solid solution containing large numbers of “quenched-in” vacancies. The greatest benefit from the standpoint of alloy properties is achieved with the fastest quench as it ensures the maximum supersaturated solute concentration, but concerns regarding the development of residual stresses mean that industrial processes typically use a hot water quench. Zhang and Zheng (1996) quenched specimens of an A356 alloy in various media, and compared their mechanical properties during artificial ageing, and found a significant decrease in yield strength and ultimate tensile strength when the quench rate is slower than 110°C/sec (i.e. in water above 60°C).

2.3.3

Ageing processes

Ageing involves the controlled precipitation of a fine dispersion of second phase particles from a supersaturated solid solution.

This can be achieved by exposing the alloy to a suitable

combination of temperature and time. Typically, precipitation reactions involve the formation of intermediate phases prior to the equilibrium phase, each of which influences the overall strength.

Natural ageing refers to the decomposition of a supersaturated solid solution over time at room temperature following quenching. Depending on the alloy, natural ageing occurs over a few

7

hours to several years, and results in an increase in strength from the as-quenched condition due to the formation of solute clusters or GP zones. This condition is referred to as the T4 temper.

The decomposition of a supersaturated solid solution at an elevated temperature is commonly known as artificial ageing. In this process, the solute elements form second phase precipitates that greatly increase the strength of the alloy. Typical artificial ageing temperatures are in the range 150°C to 250°C, and artificial ageing times can be as long as 12 hours. Industrial artificial ageing strategies are designed to produce the optimum size, distribution, type and morphology of strengthening precipitate, and may involve one or more stages at different temperatures, a period of natural ageing prior to artificial ageing, or an intermediate ageing treatment at lower temperature (usually 60-120°C) known as “preageing” prior to artificial ageing. The peak-aged condition (i.e. T6 temper) typically involves precipitate sizes in the range of 10nm, although many castings are “overaged” and contain larger precipitates to ensure dimensional stability during service at the expense of some strength (i.e. T5 and T7 temper).

In Al-Si-Mg casting alloys, natural ageing prior to artificial ageing is generally considered detrimental because the clustering of solute atoms during natural ageing reduces the driving force for precipitation and increases the time needed to reach the peak aged condition during artificial ageing. Despite this, a period of natural ageing is included in the ASTM standard, mainly because it is difficult to avoid at least a short delay between quenching and artificial ageing during industrial processing.

This concludes a brief review of the heat treatment of Al-Si-Mg alloys. The following sections contain reviews of the metallurgical processes occurring during solution treatment and ageing.

8

2.4

Microstructure Evolution During Heat Treatment

Several metallurgical processes operate during heat treatment to alter the microstructure of the material. Phenomena occurring during solution treatment are: i) the dissolution of soluble second phase particles, ii) the homogenization of solute and iii) the morphological change of insoluble second phase particles. Quenching involves rapid cooling to form a supersaturated solid solution although some precipitation is expected to occur at slower cooling rates. The supersaturated solution decomposes during artificial ageing as the precipitation of a fine dispersion of second phase particles takes place. Each process is discussed separately in the following sections.

2.4.1

Dissolution of soluble second phase particles

A number of theoretical approaches have been applied to describe the diffusion-controlled dissolution of a second phase particle in an infinite matrix [Whelan (1969), Aaron et al. (1970)]. While these analyses consider a single particle in an infinite matrix, the presence of other particles cause overlapping of the diffusion fields and this has been taken into account by using a finite diffusion field approach [Tanzilli and Heckel (1968), Nolfi et al. (1969), Aaron and Kotler (1971)]. This approach is commonly known as the “cell concept” [Nolfi et al. (1969)], and assumes the particles are equidistant and of uniform size. Reasonable descriptions of dissolution processes have resulted from the application of the cell concept to a number of alloy systems containing non-equilibrium particles [Aaron and Kotler (1971), Myhr and Grong (1991)].

In recent years numerical models have been developed to describe the dissolution kinetics of second phase particles [Tundal and Ryum (1992a, b), Vermolen et al. (1996), Vermolen et al. (1998a, b), Chen et al. (1999)]. Rometsch et al. (1999) presented a model simulating dissolution 9

of the Mg2Si phase and homogenization of magnesium in Al-Si-Mg alloys during solution treatment, and predicted complete dissolution and homogenization after 15 minutes, consistent with the experimental findings for the A356 alloy [Zhang et al. (2002)]. Subsequently, a numerical model based on a mass balance was developed to predict co-dissolution of Mg2Si and π-Al8Si6Mg3Fe in A356 [Rometsch et al. (2001)].

They predicted that Mg2Si dissolves

completely within 4 minutes at 540°C, whereas most π-Al8Si6Mg3Fe particles dissolve within 30 minutes and complete dissolution occurs within 12 hours.

2.4.2

Homogenization of solute elements

The homogenization of segregated solid solutions has been thoroughly reviewed previously [Martin (1980)]. It is known that the dendrite arm spacing of the as-cast alloy, the level of solute segregation within the dendrite, and the diffusion coefficient of the solute element in the matrix control homogenization kinetics. Purdy and Kirkaldy (1971) have shown that the decay of a segregation profile can be represented by a cosine function with a time-dependent relaxation parameter, τ, as follows;

 2π x   −t  C ( x ) = C0 + Ca cos   exp    d  τ 

(2.1)

4d 2 π 2D

(2.2)

where;

τ=

In Equations 2.1 and 2.2, C0 is the bulk composition of the alloy, Ca is the amplitude of the segregation profile (both in wt%), d is the width of the dendrite arm and D is the temperature-

10

dependent diffusion coefficient for the solute element in the matrix (in m2/s). A study by Ward (1965) showed that the value of τ controls the kinetics of homogenization, and that homogenization times close to 3τ are usually sufficient to remove solute concentration gradients.

2.4.3

Morphological change of insoluble second phases

In Al-Si-Mg casting alloys, the eutectic silicon phase evolves during solution treatment from the as-cast morphology to spheroidal particles. Many authors [Parker et al. (1982), Rhines and Aballe (1986), Meyers (1986)] have analyzed this spheroidization process using the eutectic particle size, spacing and aspect ratio, and found that modified eutectic particles spheroidize faster than unmodified particles [Shivkumar et al. (1989), Apelian et al. (1990), Paray and Gruzleski (1994)] due to the refined structure’s larger interfacial area and driving force for morphological change. In recent years the availability of 3-dimensional analytical methods led to renewed interest in this area. Lasagni et al. (2007) combined focussed ion beam milling and energy dispersive spectroscopy (FIB-EDX) to obtain element maps for a sequentially milled strontium-modified Al-7Si alloy and reconstruct the three-dimensional silicon network. Lower particle sphericities were reported using the 3-D reconstructions than equivalent 2-D element maps.

The spheroidization and coarsening of eutectic silicon particles is driven by the reduction of the surface energy associated with the Al/Si interface [Martin and Doherty (1980)].

At high

temperature, the size and frequency of surface perturbations at the Al/Si interface increase, causing the breakdown of the eutectic into a series of near-spherical particles that subsequently coarsen to further reduce the interfacial area. The processes of eutectic fragmentation and particle coarsening are discussed separately in the following two sections. 11

2.4.3.1

Fragmentation

The shape instability problem was first addressed by Lord Rayleigh (1879) who considered the fragmentation of a continuous water jet into individual droplets. This approach has been used to describe instabilities in several metallic systems that contain rods embedded in a matrix [Marich (1971), Nakagawa and Weatherly (1972), Walter and Cline (1973)]. In a later work, Stuwe and Kolednik (1988) developed an analytical model for the transformation of potassium cylinders into spheres within a tungsten matrix, and more relevantly Ogris et al. (2002) applied this approach to the disintegration of a eutectic silicon rod into spheres in a hypoeutectic Al-Si-Mg alloy, as shown in Figure 2.4. The difference in surface area between a perfect cylinder and a cylinder with a perturbation having been expressed mathematically by Stuwe and Kolednik, Ogris considered the increase in surface energy when a single atomic layer diffuses from the neck to the bulge to increase the perturbation. Subsequently they calculated the evolution of the perturbation assuming a constant driving force for the diffusion of silicon, and found the fluctuation wavelength that results in the maximum growth rate. They estimated the time taken for a cylinder with a known initial radius to fragment, and the dependency of fragmentation time on initial silicon branch radius is shown in Figure 2.5. The results of the work by Ogris indicate that the fragmentation time for eutectic silicon rods during solution treatment is highly dependent on the initial radius of the rod, and the solution treatment temperature.

12

Fluctuation Wavelength

Cylinder Radius

Solution Treatment Time

Sphere Radius

Figure 2.4: Schematic illustrating a rod-shaped eutectic particle that fragments into a series of spherical particles [after Ogris et al. (2002)].

0.3

Radius of Silicon Rod (µm)

0.25

0.2

0.15 400ºC

0.1

450ºC 0.05

500ºC 540ºC

0 0

3

6

9

12

15

18

21

24

Fragmentation Time (min)

Figure 2.5: Model results for silicon spheroidization model presented by Ogris et al. (2002).

Kovacevic (2008) used a phase field modelling approach to predict the spheroidization of a eutectic silicon plate 5µm long and 0.2µm thick in an Al-Si alloy. The driving force for spheroidization is taken to be the minimization of surface energy at the Al/Si interface, assuming isotropic conditions. The model forces the plate to spheroidise as a single particle and does not 13

allow for it’s fragmentation into several smaller spheroids, as would be expected when considering the large aspect ratio of the initial plate. Furthermore, the initial size of the silicon plate is small when compared to typical as-cast silicon particles in unmodified alloys, although the model results were in reasonable agreement with experimental observations at solution treatment temperatures when an interfacial energy of 1J/m2 is assumed.

2.4.3.2

Coarsening

The rate of coarsening of eutectic silicon particles in Al-Si-Mg alloys modified by additions of strontium can be described by a power law shown in Equation 2.3 [Parker et al. (1982), Rhines and Aballe (1986)] following the theory of diffusion-controlled growth proposed by Lifschitz and Slyozov (1961) and Wagner (1961), and known commonly as the LSW model.

r 3 − r03 = kt

(2.3)

In unmodified alloys, the coarsening of eutectic silicon was also found to behave according to the LSW model of diffusion-controlled growth after an initial delay during which time the fragmentation of the silicon plates occurs [Meyers (1985), Shivkumar (1989)].

2.4.4

Precipitation

Precipitation hardening in aluminum alloys was discovered in the early years of the twentieth century when Wilm (1911) reported increasing strength with time at room temperature in Al-Cu alloys after quenching from high temperature. Subsequently, Merica et al. (1920) suggested this behaviour is due to precipitation of a second phase not observed by optical microscopy. Attempts to uncover the mechanism of precipitation strengthening followed. Mott and Nabarro

14

(1940) introduced the concept of a dislocation-precipitate interaction, and Orowan (1948) presented the first quantitative model for precipitation hardening.

Direct evidence of

dislocation-particle interactions became available with the introduction of transmission electron microscopy techniques [Kelly and Nicholson (1963)], and in recent years the development of novel microscopic and analytical techniques, such as high-resolution transmission electron microscopy [Andresen et al. (1998)] and 3-dimensional atom probe analysis [Edwards et al. (1998), Murayama et al. (1999)] have contributed towards an increased understanding of precipitation reactions and their associated strengthening mechanisms. Several reviews of precipitate hardening have been published [Brown and Ham (1971), Gerold (1979), Ardell (1985), Lloyd (1985), Nembach (1997), Martin (1998), Hornbogen (2001), Polmear (2004)], and an overview of precipitation in Al-Mg-Si alloys follows in this section, with the strengthening mechanisms and kinetics of precipitation discussed later.

Precipitation occurs as a result of a diffusional transformation in which thermally activated atomic movements control the nucleation, growth and coarsening of second phase particles forming within a supersaturated solid solution.

The precipitation reaction is expressed as

follows;

α’
α + β

where α’ is the initial supersaturated solid solution, β is a stable or metastable precipitate, and α is a more stable solid solution with an equilibrium composition [Porter and Easterling (1992)]. As the precipitate has a different composition to the matrix, long-range diffusion of solute is required, and the precipitation rate is temperature-dependent.

15

Typically, a series of metastable phases precipitate during ageing prior to the equilibrium phase. Despite having a lower driving force for their precipitation, these transition phases have a lower activation energy barrier for nucleation and therefore the free energy of the system can be reduced more quickly through their formation in preference to the direct formation of the equilibrium phase.

Geisler and Hill (1948) and Guinier and Lambot (1948) observed needle-

shaped ‘GP zones’ in artificially aged specimens of dilute Al-Mg-Si alloys as a precursor to the plate-like form of the equilibrium Mg2Si phase. Although, there is still discussion regarding the exact details of the early stages of precipitation, it is now agreed that the precipitation sequence in Al-Mg-Si alloys is as follows [Dutta (1991), Edwards et al. (1998)]:

Supersaturated Solid Solution
Clusters of Mg and Clusters of Si
Co-clusters of Mg and Si
GP Zone I / Small Precipitates (equiaxed)
GP Zone II / Metastable β’’ (Mg5Si6 needles)
Metastable β’ (Mg2Si rods)
Equilibrium β (Mg2Si platelets)

The compositions of the early clusters and small precipitates remain relatively unknown, whereas the β″ precipitate, which is associated with the peak strength, is needle shaped and aligned along 100 along 100

Al

Al

[Pashley et al. (1966), and (1967)]. The β′ phase is rod shaped and aligned

with a hexagonal crystal structure (a=7.05Å and c=4.05Å). The equilibrium

Mg2Si platelets lie in {100}Al planes with the face-centred cubic anti-fluorite structure (a=6.39Å) [Thomas (1961)].

Precipitation reactions result in significant strengthening in Al-Mg-Si alloys, and many other alloys can also be heat treated to improve properties via precipitation of second phase particles. This subject has been investigated in detail, and our fundamental knowledge of the strengthening mechanisms and kinetics of precipitation will be discussed in the following sections. 16

2.5

Strengthening Mechanisms in Aluminum Alloys

In this section, the strengthening mechanisms arising from the presence of precipitates as well as larger second phase particles are discussed, as these are both relevant to Al-Si-Mg casting alloys that contain strengthening precipitates and eutectic particles.

2.5.1

Precipitation Strengthening Mechanisms

The strengthening effect of precipitation is related to the interaction of glide dislocations with the precipitated particles, which act as obstacles to dislocation movement, and is dependent on several factors, including the particle characteristics (i.e. size, shape and volume fraction), their distribution within the matrix, and the nature of the particle-matrix interface.

Several

strengthening mechanisms have been proposed to arise from dislocation-precipitate interactions. While a dislocation will move past the precipitate by the most energetically favourable method available, in general there are only two types of interaction; particle cutting in the case where the particle is shearable, and dislocation-looping around unshearable particles.

In the early stages of ageing, the precipitates are small and coherent or semi-coherent with the matrix and thus are shearable by dislocations, as illustrated in Figure 2.6.

a)

b)

c)

Figure 2.6: Schematic view of three stages of the dislocation cutting mechanism. 17

The following strengthening mechanisms are considered to arise in the presence of coherent/semi-coherent particles and the dislocation cutting mechanism [Brown and Ham (1971), Gerold (1979), Ardell (1985), Lloyd (1985)]; •

Coherency Strengthening - Coherent/semi-coherent particles increase the free energy of the system due to the elastic misfit between the particle and matrix.

•

Modulus Strengthening - If the particle has a higher elastic modulus than the matrix, a larger stress is required for the dislocation to continue moving forward.

•

Chemical Strengthening - There is an increase in interfacial energy when the particle is cut by the dislocation.

•

Atomic Order Strengthening - If an ordered particle is cut by a dislocation, the free energy increases due to creation of an anti-phase boundary.

•

Stacking Fault Strengthening - This arises from differences between the stacking fault energy of the matrix and precipitate.

As ageing continues the precipitate grows and becomes incoherent with respect to the matrix. In this case, the dislocation bows between precipitates and forms loops in order to move forward, as shown in Figure 2.7. Strengthening arises from bowing of the dislocation which is opposed by its line tension, as well as the formation of dislocation loops (Orowan loops) around precipitates.

a)

b)

c)

Figure 2.7: Schematic view of three stages of the Orowan looping mechanism. 18

2.5.1.1

Obstacle Strength

In general, it is useful to define precipitates and other obstacles as a ‘strong’ or a ‘weak’ obstacle depending on how far the dislocation must bow out before the obstacle is overcome. Considering a dislocation interacting with an array of obstacles within the matrix, as shown in Figure 2.8, the critical dislocation bowing angle at which the obstacle is overcome, ψc, is smaller when the obstacles are stronger.

F Γ

ψ

θc

c

2

Γ

2

θc 2 Dislocation Line

L

Rc

Direction of Dislocation Motion

Obstacle

Figure 2.8: Schematic representation of a glide dislocation moving though an array of point obstacles [after Ardell (1985)].

The maximum interaction force, F, between an obstacle and dislocation can be described using Figure 2.7 as:

ψ  F = 2Γ cos  c   2 

(2.4)

where Γ is the dislocation line tension.

19

2.5.1.2

Contribution of precipitate hardening towards the yield strength

The critical stress, τc, required to bow the dislocation to the critical angle, ψc, at which the dislocation overcomes the obstacle is given by [Gerold (1979), Martin (1998), Lloyd (1985)];

τc =

Γ bRc

(2.5)

where b is the magnitude of the burgers vector and Rc is the radius of curvature of the dislocation. Rc is also related to the effective obstacle spacing, L:

θ  2 Rc sin  c  = L 2

(2.6)

where θc/2 = π/2 – ψc/2. Using Equation 2.4 and 2.6 to replace for Γ and Rc respectively in Equation 2.5 gives:

τc =

F bL

(2.7)

Converting from shear stresses, τc, to normal stresses [Courtney (1990)], the contribution of precipitation strengthening, σppt, to the yield strength can thus be expressed as:

σ ppt =

MF bL

(2.8)

where M is the Taylor Factor. 20

2.5.1.3

Obstacle spacing

In the case of a dispersion of weak obstacles, the dislocation line is almost straight and the effective obstacle spacing, Ls, along the dislocation is larger than the mean obstacle spacing, L. The Friedel spacing [Martin (1998)] can be used to show that the stress required to overcome a weak obstacle is given by:

Gb   ψ c   cos τc = Ls   2  

3/ 2

(2.9)

In the case of strong obstacles, a large amount of dislocation bowing occurs and the effective obstacle spacing approaches the mean obstacle spacing. The critical stress required to overcome a strong obstacle with ψc