(ICME) of Aluminum Solidification and Casting DISSERTATION Presented

Integrated Computational Materials Engineering (ICME) of Aluminum Solidification and

Casting

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Colin Douglas Ridgeway

Graduate Program in Materials Science and Engineering

The Ohio State University

2020

Dissertation Committee:

Dr. Alan A. Luo, Advisor

Dr. Glenn Daehn

Dr. Steve Niezgoda

Dr. Roland Kawakami

Copyrighted by

Colin Douglas Ridgeway

2020

Abstract

Traditionally, the design and eventual casting of engineering components has been plagued by the assumption of homogeneous mechanical properties across the whole of the casting. Such an assumption is rarely the case and often leads to overdesign and excessive downstream waste. To combat this, the Integrated Computation Materials

Engineering (ICME) approach was implemented to provide an increased level of accuracy for the prediction of location specific properties in cast aluminum. Variable properties often result from variable cooling rates that occur in a structure resulting from cooling lines or chill blocks located within the mold package, variable alloying content and finally the defects present in the alloy. In the context of this research, variable cooling was studied using the concept of a maximum chill scenario where the heat transfer coefficient (HTC) was examined and found to develop over time. The resulting microstructure was included an extremely refined eutectic silicon within the interdendritic regions. Unique, time-dependent HTC maps were created for optimized maximum chill scenario casting conditions to provide unique cooling and solidification conditions across the whole of a casting. The effect of Magnesium on hypoeutectic Al-Si alloys Primary Dendrite Arm Spacing (PDAS) was examined next. Directional solidification experimentation was coupled with Cellular Automaton (CA) simulations to develop a model to predict the location specific PDAS within Al-Si-Mg alloys.

Additionally, location specific properties are known to result from defects within the

ii microstructure such oxide inclusions and porosity. These voided regions act as regions of increased stress and result in premature failure of engineered components. In this work the fluid flow, filling conditions and free surface of the molten aluminum was examined to create a new model that was accurately shown to predict the location specific defect content in a cast structure. Finally, the sum of this work was used to couple various

Computer-Aided Engineering (CAE) software tools to complete the ICME approach. By coupling various commercial software, exact location specific mechanical properties were shown to be accurately predicted using a method term the CA – FEA approach. The

CA – FEA approach is the first method for using physics based microstructure predictions to determine the location specific mechanical down to a cubic millimeter.

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Dedication

Dedicated to my loving family: my parents Doug and Mindy Ridgeway, and my future

wife, Rachael. You are my driving force.

Acknowledgments

I would first like to thank my graduate advisor, Dr. Alan A. Luo for accepting me into the

Light Metals and Manufacturing Research Laboratory at The Ohio State University. Dr.

Alan Luo provided me with a number of research and industrial opportunities to grow as a researcher and further my knowledge in the field of metallurgy. His expertise helped mold me into a better materials and metallurgical engineer, and for that I am thankful.

Along with Dr. Luo, I want to acknowledge the guidance of Dr. Glenn Daehn and Dr.

Stephen Niezgoda, both of which went above and beyond to aid me during my studies at

The Ohio State University.

I also want to thank and acknowledge my team in the Light Metals and Manufacturing

Research Laboratory. I want to thank Dr. Andrew Klarner, Dr. Scott Sutton, Dr. Zhi

Liang and Dr. Emre Cinkilic for setting the ground for our laboratory and teaching me how to be a graduate student. I want to thank Xuejun Huang for his friendship and aid as we completed every part of our collegiate careers together. Thank you to Dr. Cheng Gu for the opportunities to take a deep dive into solidification and teaching me how to publish papers. Last, I would like to thank Emre Cinkilic for his great friendship, I will always look back fondly of our time together.

Additionally I would like to acknowledge my research sponsors throughout my graduate research; specifically Duane Detwiler of Honda R&D Americas, and Keith Ripplinger of

Honda Engineering America. I greatly appreciate the immense amount of feedback, support and direction of the past five years. Duane, Keith, and Honda afforded me the

v resources and countless opportunities over the course of my PhD studies, and I want to thank them for everything they taught me along the way.

I would like to conclude by thanking everyone who has helped or aided me along the way during my nine years at The Ohio State University. From my freshman year in Bradley hall to my final years in Fontana, MacQuigg and Watts, I have made countless memories.

Thank you to Frank Ryan and Benson Jung who were with me every step of the way in undergrad. Thank you to Jake Phlipot who truly introduced me to metal casting for the first time. Thank you to my MSE family who introduced me to new cultures, new traditions, and supported me year after year. And finally, thank you to The Ohio State

University, Go Bucks!

Vita

2011...... Grandview Heights High School,

Grandview Heights, Ohio

2015...... B.S. Department of Materials Science and

Engineering, The Ohio State University

2018...... M.S. Department of Materials Science and

Engineering, The Ohio State University

2017 to 2019………………………………..Graduate Teaching Associate, Department of

Materials Science and Engineering, The

Ohio State University

2015 to 2020 ...... Graduate Research Associate, Light Metals

and Manufacturing Research Laboratory,

Department of Materials Science and

Engineering, The Ohio State University

Publications

1. C. Gu, C.D. Ridgeway, Y. Lu, E. Cinkilic, A.A. Luo. Predicting gas and shrinkage

porosity in solidification microstructure: a coupled three-dimensional cellular

automaton model. Journal of Material Science and Technology. Vol. 49, Pp. 91-105

(2020)

vii

2. C.D. Ridgeway, K. Ripplinger, D. Detwiler, A.A. Luo. Prediction of Entrained

Oxide Inclusions and Oxide Induced Defects during Directional flow in Aluminum

Casting. AFS Transactions. Vol. 128 (2020)

3. C.D. Ridgeway, C. Gu, A.A. Luo, Predicting primary dendrite arm spacing in Al-Si-

Mg alloys: effect of Mg alloying. Journal of Materials Science. Vol. 54, Issue 13. Pp.

9907-9920. (2019)

4. C. Gu, C.D. Ridgeway, A.A. Luo. Examination of dendritic Growth During

Solidification of Ternary Alloys via Novel Quantitative 3D Cellular Automaton

Model. Metallurgical and Materials Transactions B. Vol. 50, Issue 1. Pp. 123-135.

(2019)

5. C. Gu, Y. Lu, C.D. Ridgeway, E. Cinkilic, A.A. Luo. Three-dimensional cellular

automaton simulation of coupled hydrogen porosity and microstructure during

solidification of ternary alloys. Scientific Reports, 9, 13099. (2019)

6. E. Cinkilic, C.D. Ridgeway, X. Yan, A.A. Luo, A Formation Map of Iron-Containing

Intermetallic Phases in recycled Cast Aluminum Alloys. Metallurgical and Materials

Transactions A. Vol. 50, Issue 12. Pp. 5945-5956 (2019)

Fields of Study

Major Field: Materials Science and Engineering

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Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... vii

List of Tables ...... xvi

List of Figures ...... xvii

Chapter 1: Introduction ...... 1

1.1 Motivation of Research ...... 1

1.1.1 Vehicle Lightweighting ...... 4

1.1.2 Location Specific Properties ...... 6

1.1.3 Research Objective ...... 10

1.2 Dissertation outline ...... 11

Chapter 2: Background: Solidification and Casting ...... 13

2.1 Factors Affecting Solidification ...... 13

2.1.1 Casting Methodologies and Heat Transfer ...... 14

2.1.2 General Effects of Alloying ...... 19

2.1.3 Defects and Mechanical Properties ...... 26

Chapter 3: Heat Transfer Mapping ...... 35

3.1 Theory of Chills and Heat Transfer ...... 35

3.2 Enhanced Cooling Experiments ...... 39

3.2.1 Advanced Cooling Experimental Apparatus ...... 39

3.2.2 Enhanced Cooling Experimental Procedure ...... 42

3.2.3 Enhanced Cooling Variables ...... 42

3.3 Cooling Curves & Heat Transfer during Enhanced Cooling ...... 43

3.3.1 Pin Point Nozzle ...... 47

3.3.2 Fan Nozzle ...... 48

3.3.3 Stages of Heat Transfer during Enhanced Cooling ...... 49

3.4 Modeling Heat Transfer for Enhanced Cooling ...... 51

3.4.1 Building the Enhanced HTC Map ...... 52

3.4.2 Enhanced HTC Map Validation ...... 55

3.5 Maximum Obtainable HTC ...... 59

3.6 Prospectus of Heat Transfer Mapping ...... 59

Chapter 4: Effects of Mg Solute on Al-Si-Mg Alloys ...... 61

4.1 Traditional Roles of Mg alloying ...... 61

4.2 Existing Models for Dendritic Cell Size ...... 62

4.2.1 Empirical Relationships ...... 62

4.2.2 Growth Restriction Factor ...... 64

4.2.3 The Interdependence Theory ...... 65

4.3 Materials and Methods ...... 66

4.3.1 Three-Dimensional Cellular Automaton Simulation ...... 67

4.3.2 CA Implementation of Directional Solidification ...... 71

4.3.3 Directional Solidification ...... 72

4.4 Results and Discussion ...... 73

4.4.1 Three-Dimensional Simulation Results of Directional Solidification ...... 73

4.4.2 Solute Effects and Constitutional Undercooling ...... 76

4.4.3 Solute Effects and Dendrite Growth Velocity ...... 78

4.4.4 Experimental Directional Solidification Results ...... 81

4.5 Primary Dendrite Arm Spacing Model Formulation ...... 84

4.5.1 Solute effects on Dendrite Growth Velocity ...... 84

4.5.2 Solute Diffusion effects of PDAS ...... 84

4.5.3 Undercooling effect on PDAS ...... 85

4.5.4 Thermal Gradient effect on PDAS ...... 86

4.5.5 Competitive Growth effect on PDAS ...... 87

4.5.6 The PDAS Model ...... 87

4.5.7 Potential Outcomes of Increased Mg Content ...... 90

4.6 Mg Solute Effect Conclusions...... 92

Chapter 5: Oxide Entrainment and Oxide-Related Defects in Cast Aluminum ...... 94

5.1 Oxide Film Formation and Entrainment ...... 94

5.1.1 Oxide Formation in Molten Aluminum ...... 94

5.1.2 Entrainment Mechanisms ...... 96

5.2 Oxide Inclusion Detection and Prevention ...... 98

5.2.1 Entrained Oxide Detection ...... 98

5.2.2 Oxide Induced Defects ...... 99

5.2.3 Reality of Oxide Inclusion Defects ...... 100

5.3 Existing Oxide Inclusion Modeling Techniques ...... 101

5.4 Inclusion Induced Defects Model Methodology ...... 103

5.4.1 The Weber number and Gate Velocity ...... 104

5.4.2 Oxide Severity Term ...... 104

5.4.3 Effect of Shrinkage Porosity...... 105

5.4.4 Oxide Entrainment Number...... 106

5.5 Directional Flow Casting Design of Experiments ...... 107

5.5.1 Optimal vs Poor Filling Geometry Castings...... 107

5.5.2 Implementation of the OEN within ProCAST ...... 109

5.5.3 Casting of Cylindrical Molds ...... 109

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5.6 Simulation Results and Discussion ...... 110

5.6.1 Velocity Consideration during Mold Filling ...... 110

5.6.2 Oxide Severity Term ...... 112

5.6.3 Thermal Impact and Oxide Induced Defects ...... 114

5.6.4 OEN Prediction...... 115

5.7 Experimental Validation ...... 117

5.8 Effect of Gas Volume on the Oxide Entrainment Number ...... 120

5.8.1 Morphological Size of Porous Features...... 121

5.8.2 Development of the Entrapped Gas Volume Term ...... 122

5.9 OEN Validation for a Complex Geometry ...... 126

5.9.1 The Complex Casting ...... 126

5.9.2 Dividing the Node ...... 127

5.9.3 OEN Node Prediction ...... 127

5.9.4 CT Scans of Side A ...... 128

5.9.5 CT Scans of Side B ...... 130

5.9.6 OEN Correlation to Side A ...... 132

5.9.7 OEN Correlation to Side B ...... 135

5.9.8 OEN Oxide Volume Comparison ...... 136

5.9.9 Location Specific Mechanical Properties ...... 141

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5.9.10 Microstructure Evaluation of Location Specific Regions ...... 145

5.9.11 OEN – Complex Casting Conclusions ...... 146

5.10 Concluding Remarks on Oxide Inclusions and the OEN ...... 147

Chapter 6: CA – FEA: A Method for Predicting Location Specific Properties ...... 149

6.1 Homogeneous vs Heterogeneous Property Prediction ...... 149

6.2 Roadmap to Location Specific Property Prediction ...... 151

6.3 Microstructure Modeling Techniques ...... 152

6.3.1 Phase Field Microstructural Modeling ...... 152

6.3.2 Cellular Automaton Microstructural Modeling ...... 153

6.4 The Need for Connected CAE ...... 154

6.5 The CA – FEA Approach ...... 155

6.5.1 Boundary Conditions ...... 155

6.5.2 ProCAST to CA ...... 156

6.5.3 Cellular Automaton to FEA ...... 157

6.6 CA – FEA: Simulation of Wedge Casting ...... 158

6.6.1 ProCAST Examination of the Wedge Casting ...... 159

6.6.2 Cellular Automaton of the Wedge Casting ...... 162

6.6.3 Conforming Mesh Validation ...... 167

6.6.4 ABAQUS – Constitutive Model ...... 170

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6.6.5 Wedge – Simulated Location Specific Properties ...... 173

6.7 CA – FEA: Experimental Validation ...... 175

6.7.1 Wedge Casting Conditions ...... 175

6.7.2 Location Specific Micro-CT and Microstructure ...... 177

6.7.3 Location Specific Mechanical Properties ...... 181

6.8 Mechanical Property Degradation Modeling ...... 183

6.9 Outlook on Location Specific Property Prediction ...... 185

Chapter 7: Conclusions and Future Work ...... 186

7.1 Key Conclusions ...... 186

7.2 Future Work ...... 189

References ...... 191

List of Tables

Table 1: Heat transfer data for various casting methodologies...... 18

Table 2: The AA designation for cast aluminum alloys. [27] ...... 19

Table 3: Temperature dependent specific heat capacity for a 3xx series Al alloy and a

304L stainless steel...... 40

Table 4: Definition of variables used throughout Chapter 4...... 63

Table 5: Compositions of Al-7.6Si-xMg alloys used for directional solidification...... 67

Table 6: Experimentally measured PDAS compared to the present model...... 89

Table 7: Identification of the node tensile bars ...... 141

Table 8: Location Specific mechanical properties for node casting...... 143

Table 9: Simulated vs. Experimental solidification conditions...... 161

Table 10: Stress triaxiality parameters used for in the ABAQUS simulations...... 171

Table 11: Location specific ABAQUS inputs...... 173

Table 12: Location specific defect analysis of the wedge casting...... 179

Table 13: Secondary Dendrite Arm Spacing Comparison ...... 181

Table 14: Experimental location specific mechanical properties...... 183

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List of Figures

Figure 1: The Manufacturing ICME Framework...... 4

Figure 2: Design by zone methodology for a HPDC automotive component.[10] ...... 6

Figure 3: FEA of a steering wheel with (a) homogeneous property application and (b) heterogeneous property application compared to the (c)component failure.[3] ...... 7

Figure 4: Predictions of local fatigue life of a cylinder head.[2] ...... 8

Figure 5: Methodology for determining location specific properties in cast components.

...... 10

Figure 6: Traditional casting methodologies schematics: (a) Sand Casting [13], (b)

Permanent Mold Die Casting [14], (c) High Pressure Die Casting [15]...... 15

Figure 7: Aluminum A356 microstructure produced by (a) gravity die casting vs (b) sand casting.[19]...... 16

Figure 8: The Aluminum – Silicon binary phase diagram as calculated by ThermoCalc. 22

Figure 9: Eutectic silicon morphology in an 10wt% Al-Si alloy (a) unmodified (b) modified with the addition of 300 ppm strontium.[30] and A319 (c) unmodified (d) modified with 96ppm.[31] ...... 23

Figure 10: Fracture line initiation along Mg2Si precipitates in A356.[36] ...... 25

Figure 11: Aluminum-Copper phase diagram showing the intermediate precipitation of

Al-Cu precipitates.[38] ...... 26

Figure 12: Various forms and depictions of shrinkage. [40] ...... 28

xvii

Figure 13: Hydrogen solubility in pure aluminum.[41] ...... 30

Figure 14: Reduction in the (a) ductility[42] and (b) fatigue life [43] of cast Al-Si-Mg alloys due to various pore sizes...... 32

Figure 15: Bifilm formation mechanism due to a perturbed molten surface.[49] ...... 33

Figure 16: Bifilms trapped with the solidified aluminum material (a) Aluminum matrix

(B) Al Matrix – α interface (c) Primary Fe phase (β). [50] ...... 34

Figure 17: Experimental apparatus (a) Casting test block design. Thin cylinders represent thermocouple locations, while the 4 parallel horizontal cylinders represent cartridge heater locations. (b) Enhanced cooling experimental setup...... 41

Figure 18: Two-Dimensional representation of the front of the casting block. The naming convention and locations of the thermocouples are also shown...... 42

Figure 19: Water jet impingement and interaction area of the (a) pin point nozzle and the

(b) fan nozzle...... 43

Figure 20: Cooling curves for the pin point (PP) and fan nozzles at various locations on the enhanced cooling casting block for a 10 psi water jet 2 inches away from the casting block...... 45

Figure 21: Heat Transfer Coefficients for the various locations on the enhanced cooling casting block for a 10 psi water jet 2 inches away from the casting block...... 46

Figure 22: Three Phases of heat transfer during the solidification process for position

TC0...... 49

Figure 23: Thermal camera imaging displaying clear gradients in the (a) pin point and (b) fan nozzles on the casting block during the enhanced cooling chilling...... 53

xviii

Figure 24: Schematic of the instantaneous interfacial HTC variation across the vertical and horizontal axes of the enhanced cooling casting block...... 54

Figure 25: Instantaneous cooling provide of the casting block with a pin point nozzle. .. 55

Figure 26: Methodology used to develop and validate the Enhanced HTC Maps...... 56

Figure 27: Validation Step. Simulated vs experimentally measured cooling curves of the thermocouple locations in the casting block for the fan nozzle...... 58

Figure 28: Schematic of a discretized cellular automaton simulation domain...... 67

Figure 29: Cellular Automaton simulation of directionally solidified dendritic growth show the partitioning of Mg solute after 14 seconds of growth for (a) 0.5wt% Mg; (b)

1.0wt% Mg; (c) 1.75wt% Mg; and (d) 2.7wt% Mg...... 74

Figure 30: Cellular Automaton simulation of directionally solidified dendritic growth sectioned perpendicular to the growth direction showing the partitioning of Mg solute in

Al-7.6Si-xMg after 14 seconds of growth for (a) 0.5wt% Mg; (b) 1.0wt% Mg; (c)

1.75wt% Mg; and (d) 2.7wt% Mg ...... 75

Figure 31: Segregation of the Mg solute resulting in a reduction in lateral coarsening that occurs with an increased Mg solute content in Al-7.6-xMg alloys...... 76

Figure 32: Schematic representation of the decrease in constitutional undercooling that arises from an increase in Mg concentration. (a) Schematic of a phase diagram, (b)

Rejection of solute at the S/L interface at T*, and (c) Liquidus temperature away from the

S/L interface plotted with a constant thermal gradient...... 77

Figure 33: Tertiary to primary transition mechanism...... 80

xix

Figure 34: Refinement of directionally solidified dendritic microstructures viewed parallel to the growth direction with increasing values of Mg: (a) 0.5wt% Mg; (b)

1.02wt% Mg; (c) 1.78wt% Mg; and (d) 2.69wt% Mg...... 82

Figure 35: Refinement of directionally solidified dendritic microstructures viewed perpendicular to the growth direction with increasing values of Mg: (a) 0.5wt% Mg; (b)

1.02wt% Mg; (c) 1.78wt% Mg; and (d) 2.69wt% Mg...... 83

Figure 36: (a) The composition profile of the solute in the interdendritic region (b) The resulting liquidus temperate in the interdendritic region rising above the local liquidus temperature, creating a region where interdendritic nucleation can occur...... 85

Figure 37: Cooling Curve of Al-7.6Si-0.5Mg exhibiting no undercooling during directional solidification...... 86

Figure 38: PDAS Model flow chart describing the major solute effects of increased Mg solute in Al-Si-Mg alloys...... 88

Figure 39: (a) PDAS predictions of various models; and (b) Dendrite Growth velocity of various models compared to calcualted velocity for measured PDAS...... 89

Figure 40: Graphical summary of Chapter 4. The simulation and experimental work combine to show a decrease in the PDAS explained by the proposed PDAS equation. .. 93

Figure 41: Bifilms trapped with the solidified aluminum material (a) Aluminum matrix

(b) Al Matrix – α interface (c) Primary Fe phase (β).[50] ...... 95

Figure 42: Various oxide entrainment mechanisms where the black lines indicated oxidized surface. (a) Folding over waves entraining oxides, (b) An entrained bifilm, (c)

xx gas precipitation within a bifilm and initial stage of bifilm unfurling, (d) an internal pore with an oxidized surface, and (e) a bubble trail...... 97

Figure 43: Oxidation of particles during pouring using the SPH method. [101] ...... 102

Figure 44: Predicted final location of oxide particles in a casting using the OFEM method.[103] ...... 103

Figure 45: (a) Preferred filling mold designed for optimal filling. (b) Poor filling mold designed to create increased levels of entraining events...... 108

Figure 46: Fluid Velocity for the Poor filling Mold (a,c) compared to the velocity of the

Preferred Filling Mold (b,d) at various times. The color scale varies from 0m/s (purple) to

0.6m/s (red)...... 111

Figure 47: Oxide severity term for the (a) Poor Filling Mold and the (b) Preferred Filling

Mold. The scale bar spans from 0 (purple) to 3.0 (red) and applies to both (a) and (b) . 113

Figure 48: Individual terms that make up the thermal term for the OEN. (a) Thermal

Gradient [C/cm] (b) Cooling Rate [C/s] (c) Thermal Term [Cm/s]...... 114

Figure 49: The instantaneous Oxide Entrainment Number (OEN) for both the (a) Poor

Filling mold and (b) Preferred Filling Mold. The scale bar spans from 0 (purple) to 1000

(red) and applies to both (a) and (b)...... 116

Figure 50: The total volume of entrained oxide at each transverse slice along the vertical axis of the cylinders in the Poor Filling Mold and the Preferred Filling Mold...... 117

Figure 51: Micrographs of the transverse cross sections of the (A-D) Poor filling Mold and the (E-H) Preferred Filling Mold. The positions of the transverse sections are (A,E)

2cm, (B,F) 4cm, (C,G) 6cm, (D,H) 9cm...... 119

xxi

Figure 52: Experimentally measured defect volume for both mold types...... 120

Figure 53: Effect of cooling rate on morphological size of pores formed in aluminum alloys (a,d) 50C/s (b,e) 10C/s (c,f) 5C/s.[106] ...... 122

Figure 54: OEN validation steps including the (a) initial prediction of the OEN, (b) The

Entrapped Gas Volume term variation across the height of the cylinders, (c)

Experimentally measured defect volume compared to the Final OEN prediction...... 124

Figure 55: OEN comparison to the experimentally observed defect volume for the (a)

Poor Filling Mold (b) Preferred Filling Mold...... 125

Figure 56: Geometrically complex casting used for OEN validation...... 126

Figure 57: The division of the node into two halves with (a) representing Side A and (b) representing Side B...... 127

Figure 58: Initial OEN prediction for the node. (a)Instantaneous OEN prediction upon initial pouring and (b) final filling...... 128

Figure 59: CT scan of Node: Side A viewed from the front direction...... 129

Figure 60: CT scan of Node: Side A viewed from the (a) rear direction and (b) edge on direction...... 129

Figure 61: CT scan of Node: Side B viewed from the front direction...... 131

Figure 62:CT scan of Node: Side B, viewed from the (a) rear direction and (b) edge on direction...... 131

Figure 63: Location comparison of the defects located in Side A of the node (a) CT scan vs (b) Instantaneous oxide generation for OEN model...... 133

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Figure 64: OEN comparison to experimental CT for outer gate of Side A (a) sectioned region of Side A (b) CT slice of outer gate (c) Instantaneous OEN prediction of Side A

(d) OEN slice corresponding to outer gate in (b)...... 134

Figure 65: OEN comparison to experimental CT for outer gate of Side B (a)sectioned region of Side B (b) CT slice of outer gate (c) Instantaneous OEN prediction of Side B

(d) OEN slice corresponding to outer gate in (b)...... 136

Figure 66: (a-b)CT scans of Node compared to (c) OEN prediction of instantaneous oxide inclusion generation...... 137

Figure 67: Subdivided cross sections of (a) Side A and (b) Side B of the node. Each cross section is labeled with its designation of top, side and bottom...... 139

Figure 68: Location Specific OEN validation for (a) Side A and (b) Side B of the node.

...... 140

Figure 69: Locations chosen for tensile testing. (a) Location of tensile bar extraction on the cross section of Side A. (b) Location of tensile bar extraction on the cross section of

Side B. (c) The cast node showing the clean or low defect content regions from which tensile specimen were extracted...... 142

Figure 70: Location specific stress strain curves from (a) Side A and (b) side B...... 144

Figure 71: Fracture surface comparison of the (a) high defect (Position A1) and (c) low defect (Position A2) tensile bars. Corresponding EDS spectra show oxide content in (b) and a clean fracture surface in (d)...... 146

Figure 72: The connected CAE outline with key boundary conditions and outputs...... 156

Figure 73: Dimensions of the wedge casting from (a) front view and (b) side view. .... 159

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Figure 74: ProCAST simulation of solidification time for the wedge casting...... 160

Figure 75: Defect prediction via ProCAST (a) Dimensionless Niyama (b) Total shrinkage

Porosity...... 162

Figure 76: Cellular automaton microstructure simulation of grain structure (green) and porous defects (blue) for Positions A, B, and C in the wedge casting compared to experimentally observed defects (black) in the corresponding locations via microCT.

Position A: (a-c), Position B: (d-f) Position C: (g-i). [106] ...... 165

Figure 77: CA simulated microstructure of wedge casting at various locations (a,b,c) corresponding to Position A, Position B, Position C respectively. Post processing conforming mesh (d,e,f) corresponding to Position A, Position B, Position C respectively.

...... 168

Figure 78: ProCAST influenced CA simulation and High Fidelity Conforming Mesh. 169

Figure 79: Three branch fracture loci schematic. [127] ...... 172

Figure 80: Location specific tensile curves from the wedge casting: (a) CA – FEA

Simulation prediction, (b) Experimental tensile testing...... 174

Figure 81: Wedge casting (a) Permanent mold and (b) A356 Wedge Casting ...... 176

Figure 82: Experimental Cooling Curves for the wedge casting...... 177

Figure 83: MicroCT results for the wedge casting. Position A is represented by (a,d),

Position B is represented by (b,e), Position C is represented by (c,f)...... 178

Figure 84: Microstructure at (a) Positon A (b) Position B and (c) Position C of the wedge.

...... 180

Figure 85: Micro-tension specimen (a) dimensions and (b) cut samples...... 181

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Figure 86: Experimental vs. Simulated stress-strain curves for (a) Position A (b) Position

B and (c) Position C...... 182

Figure 87: Variation in defect content with changing cooling rates...... 184

Figure 88: Mechanical property prediction for varying defect volumes...... 185

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Chapter 1: Introduction

The art of transferring molten metal into a highly complex and functional structure has fueled mankind for the past 3000 years. From the introduction of the first simple decorative castings, the cast metals industry has exploded in development with the introduction of new alloys, new casting processes and increasingly intricate and complex castings. However, in the past 50 – 100 years the number of breakthroughs in casting technology has stagnated and many foundries rely on the same basic relationships and design principles that have been used since the dawn of casting. Thus, the cast metals industry has hit a tipping point. As the demands on cast structures become increasingly stringent, the foundries must adapt and begin to design and produce increasingly high quality castings at an unprecedented rate. This issue is addressed throughout the remainder of this work where the fundamentals of casting, solidification and design are explored to optimize and extend the capabilities of aluminum castings.

1.1 Motivation of Research

One of the largest obstacles the cast metals industry is currently facing is the traditional design process. When the traditional design process is applied to castings, the result is often over-designed, large and bulky castings which is attributed to excessive and

1 uniformly applied safety factors. Additionally the traditional design process does not account for any location specific property development during the casting process.

Instead, cooling rates are often correlated to a range of tensile properties in a series of lookup tables. However, cast components in service will likely see a variety of different stress states including tension, compression and shear. By not considering the microstructural development, the traditional design process will continue to produce over-designed castings that are not suitable for service. Thus, it is imperative that the cast metals industry undergoes a fundamental change in its approach to the design process to address the general lack of predictive capability that has stagnated the field of cast metals research.

To combat the lack of predicative capability for properties within castings, some foundries have begun using computational fluid dynamics (CFD) solvers to better understand how their castings fill and solidify. Unfortunately, missing from these solvers is the link that couples solidification and cooling rates to microstructural development.

Without the ability to accurately predict the microstructure, CFD solvers are unable to take advantage of the uniquely predicted solidification conditions. The result is that much of the cast metals research on solidification, microstructure and mechanical properties is often segmented or compartmentalized to solving a single problem with a single software. Such a segmentation results from the extreme computational expense in coupling multiple computational engines together. To spare the computational expense, many software suites specialize in a solving a single type of problem such as the fluid dynamics during casting or the mechanical response of a random microstructure.

The main consequence of segmented software is that a great deal of information is lost between each simulation step as required input parameters for solidification and mechanics simulations are often simply estimated. Consequently, a gap in the research of cast aluminum alloys has been created and provides an opportunity to build a connection between solidification, microstructure and mechanical properties.

To bridge the gap created by segmented software, the ICME framework or methodology was utilized. The ICME framework highlighted in Figure 1 and involves the combination of computational and experimental observations to rapidly build models to improve the design and production of cast components.[1–4] Within this work, the ICME framework is utilized to connect fluid dynamics, microstructural development and mechanics to achieve vehicle lightweighting, location specific property development and ultimately produce high quality structural aluminum castings.

Figure 1: The Manufacturing ICME Framework.

1.1.1 Vehicle Lightweighting

The goal or idea of lightweighting transportation vehicles for increased fuel economy and lower emissions is in no way novel or new. The CAFÉ standards called for an average of

54.5 miles per gallon as far back as 1975, yet no American automotive manufacturer has achieved the 45 year old mandate.[5] Many researchers believe the best way to reach the original CAFÉ goals is by lightweighting and often cite a 6-8% increase in fuel economy with a 10% reduction in weight which can be achieved by replacing high density components with aluminum and magnesium structural castings.[6–9]

To date, researchers have heavily relied on alloy development as the primary method for lightweighting of vehicles. This is a reasonable approach and has led to a number of new alloy inventions in the high strength low alloy steel (HSLA), aluminum and magnesium alloy systems. However, compared to ferrous components, aluminum and magnesium

4 alloy systems offer additional mass savings with 30-50% for aluminum and 40-60% for magnesium.[8] Though there is still room for improvement with additional alloy development, there has been a recent stagnation in the advancement of alloy development, specifically for aluminum alloys as newer generation HSLA are able to far exceed the mechanical properties of aluminum alloys at a fraction of the cost.

The alternative to alloy development has been to eliminate unnecessary mass in cast structures. To achieve a reduction in mass, castings must be optimally designed with location specific properties in mind instead of following the traditional design process which often includes excessive or uniformly applied safety factors that create over- designed, bulky structures. The primary method for estimating location specific properties has been accomplished by dividing a cast structure into different zones and tuning the properties of each zone to the required mechanical properties. The “by zone” design method can be seen in a Figure 2 and was the first methodology to optimizing a cast structure via location specific property analysis. When properly followed, the by zone design method can provide considerable mass savings for each casting by removing excess material in bosses or other non-critical regions. When this methodology is applied over the whole of a vehicle a considerable reduction in mass can be achieved.

Unfortunately, the by zone design method relies on the human element to subdivide a casting into specific zones which can be arbitrary in nature and is not robust enough for vast implementation within the cast industry. Thus, the cast metals industry is in dire need of fundamentally sound model or methodology that can aid in property prediction to allow location specific mass savings within castings.

Figure 2: Design by zone methodology for a HPDC automotive component.[10]

1.1.2 Location Specific Properties

As cast structures become more intricate and geometrically complex, there is a growing variation in properties across the structure. The main source of this variation can be attributed to the solidification conditions. Variable cooling rates at different cross sections, exposure to chilled regions, alloy segregation and defect formation will all force many unique microstructures and subsequent properties across a single component. To combat this disparity in properties, the prevailing theory has been to design entire components to possess the minimum properties needed for the application. This design method often leads to a highly over-designed component with excess waste as described in the Section 1.1.1. Further, by applying homogeneous properties across a material, it is likely that the minimum property applied may not be sufficient for the loads it will experience during use as seen in Figure 3. The steering wheel in Figure 3a shows that when homogeneous properties are applied to an entire component, there is little variation

6 in the stresses experienced during use and the cast structure appears suitable for use.

However, when heterogeneous properties are applied across a structure as in Figure 3b, it is clear that the spoke of the steering wheel will experience stress levels significant enough for failure which was shown to occur in Figure 3c. Therefore, it is imperative that all castings be designed with location specific properties in mind to not only save weight, but to properly inform design engineers of the load capacity of structural components.

(a) (b) (c) Figure 3: FEA of a steering wheel with (a) homogeneous property application and (b) heterogeneous property application compared to the (c)component failure.[3]

The concept of predicting location specific properties has been presented by several authors, however, many of the property predictions rely heavily on assumptions.[2, 3, 10]

A majority of these assumptions involve empirical relationships that are not always consistent across different casting methodologies. Additionally, empirical relationships often have little to no fundamental metallurgical science or reason behind these predictions. Instead a cooling rate is empirically registered to a microstructure, and the estimated microstructure is empirically fit to a range of properties. There are numerous assumptions applied when using this routine and often provide large sweeping 7 regions/areas of a casting with identical or homogeneous mechanical properties as seen in

Figure 4.

Figure 4: Predictions of local fatigue life of a cylinder head.[2]

The prediction of location specific properties for cast structures is vitally important for both optimization of the design as well as ensuring the safety of its use. The ideal design method for an optimally designed cast structure would involve examining the solidification conditions, calculating and predicting the resulting microstructure, and finally, correlating that true microstructure to mechanical properties. By following this methodology, the exact mechanical properties at the location specific level can be determined and can provide guidelines for safe, lightweight cast structures. The tools used to obtain these location specific mechanical properties are computational in nature and involve numerically solving complex and dynamic problems from a fundamental

8 physics based perspective.[2, 3] By examining the each stage of the casting process from filling to solidification to microstructural development and final mechanical properties from the numerical perspective, the level of accuracy of predicted properties can greatly increase as the simulations are back by fundamental science. In terms of casting science, the filling stage is currently leading this department as large scale computational fluid dynamics are routinely conducted on large scale industrial castings. However, there exists the need to begin to introduce high throughput microstructural and mechanics numerical simulations in unity with the CFD simulations to accurately predict local mechanical properties of cast components.

Following this methodology would result in the leanest systems or vehicles possible as each individual component would be optimized for its specific “strengths” with limited mass. The outline for the idealized method for location specific property prediction can be seen in Figure 5.

Figure 5: Methodology for determining location specific properties in cast components.

1.1.3 Research Objective

The knowledge of how to take a natural resource such as metal and convert it into a highly efficient structure has been vital to the human civilization. Many breakthroughs have been made over the last hundred years as humans have strived to create improved and efficient structures. Though mature in age, there are still significant advances yet to be discovered in the fields of fluid dynamics, solidification, microstructure prediction, defect formation and final property determination.

The goals of this work are to do exactly that stated above. The ultimate goal is to improve upon the fundamental science of solidification in metal casting and to provide guidelines for improved property prediction across the entirety of an aluminum cast structure.

1.2 Dissertation outline

The following work details a culmination of five years of cast metals research. The progression of the work is divided into chapters starting with the initial boundary conditions that drive solidification and progresses to the effects of alloying and defects on mechanical properties. The work concludes with a newly proposed property prediction methodology that combines the work from each of the previous chapters to provide insight on location specific properties of cast structures. A short description of each chapter can be seen below.

Chapter 2 provides the fundamentals background information for solidification as well as introduced the metal casting process. The chapter is subdivided into pertinent sections to aid the reader in the understanding of the later chapters.

Chapter 3 is a discussion on the heat transfer that occurs at the metal/mold interface during the metal casting process. Enhanced cooling rates are examined via a water spraying methodology and a location specific HTC mapping methodology is presented.

Chapter 4 details the effects of alloying on cast microstructures. Specifically magnesium is examined for its effect to refine the primary dendrite arm spacing in Al-7Si-Mg alloys.

A model to describe this phenomenon is also presented.

Chapter 5 describes the effects of casting defects with emphasis on oxide inclusions. A new model is proposed on the formation and final location of entrained defects in cast structures.

Chapter 6 combines the work done in Chapters 2-5 to provide a new model on how location specific properties can be determined and cast structures can be optimized during the design process.

Chapter 7 remarks on the final conclusions of the present research and offers insight on potential future experimentation.

Chapter 2: Background: Solidification and Casting

The idea of metal casting is one of the simplest and oldest scientific phenomena. A hollow cavity is created and consequently filled with molten metal. After the molten metal has solidified, the mold material is removed and the result is a cast structure. Cast structures can be as simple as a rectangular brick, or as geometrically complex as an engine block. Though simple in nature, small nuances in the casting process or design can have great consequences on the mechanical properties (yield strength, tensile strength, ductility, toughness, etc.) of the final structure. The mechanical properties can further vary throughout the structure depending on the location specific solidification conditions.

Numerous factors can affect the solidification conditions, however, they are most commonly altered by the type of casting or mold material, the alloy chemistry and the fluid dynamics of the casting process. Each of these factors has a unique effect on final location specific properties and will be explored throughout this work in the context of cast aluminum.

2.1 Factors Affecting Solidification

The solidification process consists of a phase transformation as a material transforms from liquid to solid. Regardless the type of material, solidification and the resulting

13 microstructure will be heavily dependent on the heat transfer at the solid/liquid interface, the diffusion and formation of microstructural constituents as well as the development of defects.

2.1.1 Casting Methodologies and Heat Transfer

The solidification process is controlled by how rapidly heat can be extracted from the molten material. For cast structures, the rate at which heat is extracted is controlled by the mold material and the effective heat transfer coefficient (HTC). Thus, it can be easily understood, that the casting methodology will have a great effect on the solidification process.

Sand casting is the oldest known casting methodology and is characterized by a mold made of sand or clay. Though archaic in practice, the sand casting method can be used to create intricately designed castings and can be seen schematically in Figure 6a. The sand casting process is often divided into two sub-categories: green sand, and chemically bound sand. Green sand is comprised of a dirt or clay mixture which is compressed over a pattern to create a cavity, whereas, chemically bound sand molds are comprised of fine silica or ceramic granules that are mixed with a series of chemicals that cause the sand grains to bond to one another and harden over top of a pattern. For both cases, the mold material (sand or clay) acts as a thermal insulator and possesses relatively low interfacial heat transfer coefficients ranging from 100-200W/m2K for green sand and 600-

900W/m2K. for chemically bound sand.[11, 12] The low HTC values are exacerbated due to the low strength of the sand, often requiring an increased thickness of the sand molds, further hindering the removal of heat. However, sand casting does have the benefit of

14 being inexpensive and renewable, though it is often associated with low cooling rates and solidification rates due to low heat transfer coefficients that result in coarse microstructures and poor mechanical properties.

Figure 6: Traditional casting methodologies schematics: (a) Sand Casting [13], (b) Permanent Mold Die Casting [14], (c) High Pressure Die Casting [15].

In order to increase the heat dissipation from cast structures, the sand mold can be replaced with metallic mold in a casting methodology termed permanent mold or die

15 casting. Metallic molds are often made of tool steel or copper. They offer the benefit of an enhanced HTC compared to sand molds providing a maximum interfacial heat transfer coefficient of ~6,000 W/m2K for tool steel molds and ~7,100 W/m2K for water chilled copper molds.[16–18] The increased HTC can be attributed to an increased thermal conductivity of the mold material which allows for a much greater rate of heat dissipation, and in turn, a faster solidification rate. The increase in heat transfer then reduces the time for the microstructure to grow and results in a greatly refined microstructure compared to sand casting as shown in Figure 7, and results in improved mechanical properties.

a b Figure 7: Aluminum A356 microstructure produced by (a) gravity die casting vs (b) sand casting.[19]

The only casting methodology with a higher HTC than permanent mold casting is pressure die casting. In both the low and high pressure die casting process, molten metal is forced into a metallic cavity and allows the formation of thin wall castings in the range

1.5-2mm. The thin walled castings lack the thermal mass of larger castings and allow for rapid heat dissipation and extremely large HTC ranging from 15,000 – 20,000

W/m2K.[18, 20] Heat transfer coefficients of this magnitude will cause near instantaneous solidification and large, complex structures can be cast in a matter of seconds.

Currently, sand casting, permanent mold casting, and pressure die casting are the most commonly used methodologies. In each cast the rate of heat transfer is controlled by the mold material and the previously unmentioned air gap. During solidification, the metallic materials will undergo a negative volume expansion, and will contract from the mold surface. This contraction will create a very small layer of air, called the air gap, between the mold wall and the casting surface. The air gap acts as a barrier to heat transfer and often causes a sharp decrease in the HTC magnitude following initial contact and solidification of the molten material. In the mid 2000’s John Grassi and Dr. John

Campbell proposed that if the mold could be removed upon solidification, then the air gap could be eliminated, and culminated in the ablation casting process.[21–24] During the ablation casting process, molten metal is poured into a chemically bound sand mold which is immediately sprayed with a series of water jets. The mold package is comprised of aggregate that is bound together using a water soluble binder, which will be washed away, or ablated, and expose the cast surface. The exposed casting surface will have fresh water continually flushed over the surface, effectively removing the air gap that is inherent to all other casting methodologies. With the elimination of the air gap, the ablation casting process will maintain a greater magnitude of HTC for a longer period of

17 time. During the ablation casting process the magnitude of heat transfer is initially low due to the insulating behavior of the sand mold, however, the HTC increases sharply once the water jets are able to impinge directly onto the cast surface and range from 3-

6000W/m2K. Though the HTC for ablation casting is not as great in magnitude as pressure die casting, the extended quench during solidification for ablation casting creates a unique microstructure that has been associated with excellent mechanical properties.[22, 25]

From the short survey presented, it is evident that the heat transfer rates can vary greatly across casting methodologies. Understanding heat transfer is the first step in understanding the solidification behavior of various casting methodologies and must be carefully examined to accurately describe solidification microstructures and eventual mechanical properties. The commonly quoted interfacial heat transfer coefficients for the various casting methodologies described in this section can be seen in Table 1.

Table 1: Heat transfer data for various casting methodologies.

Mold Thermal Interfacial HTC Casting Method Mold Material Conductivity (W/mK) (W/m2K) Sand Casting Sand/Clay 0.15 - 1.3 100 - 900 Permanent mold Tool Steel 23-50 2,000 - 6,000 Casting Copper 385 2,000 - 7,100 Pressure Die Tool Steel 23-50 15,000 - 20,000 Casting Ablation Casting Aggregate 0.5-1.3 3,000 - 6,000

2.1.2 General Effects of Alloying

In its elemental form, aluminum is a low density material with good ductility, corrosion resistance and electrical conductivity.[26] However, pure aluminum does not possess significant strength and is often alloyed with a combination of copper, magnesium, manganese, and silicon for increased strength and use in various applications. The resulting aluminum alloys are then categorized based on their principal alloying elements by the Aluminum Association (AA) and can be viewed in Table 2. The designations provided in Table 2 are used to easily identify general compositions of cast alloys and general properties of each of the alloys. It is worth noting that only the first digit provides compositional information while the second and third digits serve only as identifiers. The digits following the decimal points are referred to as the suffix and are used to signify the state the product is in with xxx.1 and xxx.2 referring to material to be melted and xxx.0 referring to material in the finished form.[27]

Table 2: The AA designation for cast aluminum alloys. [27]

Designation Description Principal Alloying Elements 1xx.x 99.0% Pure Al Al 2xx.x - Al + Cu Al + Si + Cu or 3xx.x - Al + Si + Mg or Al + Si + Mg + Cu 4xx.x Binary Al + Si 5xx.x - Al + Mg Often contain Cu, Mg, 7xx.x Cr, Mn, or combination Al + Zn 8xx.x - Al + Sn

Aluminum alloys possess excellent specific strength making them an attractive option for lightweighting of structural components, particularly in the automotive industry.[7] As the automotive industry looks to create lighter, more fuel efficient vehicles, aluminum alloys have been brought to the forefront of research for replacing traditionally heavier structural components.[6–8] The Society of Automotive Engineers defines structural mechanical components that “support vehicle weight and absorb road shock while maintaining shape…[as well as] absorb and manage collision energy.”[28] Consequently, alloys must possess a certain degree of strength and ductility to be used for the construction of a structural component. The aluminum alloy systems commonly used in structural components are the 3xx, 5xx, 7xx, and 8xx systems as designated by the

Aluminum Association.

The most commonly cast aluminum alloy system is the 3xx series and will be the focus for the remainder of this work. The main attraction of the 3xx series is the Al-Si eutectic formation which provides excellent fluidity over a large solidification range and allows formation of complex castings such as automotive transmissions, engine blocks and shock towers. The Al-Si eutectic is a divorced eutectic where the two phase mixture of aluminum and silicon has no solute exchange during solidification. Divorced eutectic systems are similar to a regular eutectic system, as the two phase mixture forms directly from the liquid phase, however, there is no cooperative growth and in the case of the Al-

Si eutectic, the composition of each constituent will be nearly pure. The reason for increased fluidity resulting from the Al-Si eutectic is two-fold. First, the solid solubility of Si in aluminum is quite low (1.57wt.%) and the eutectic composition is comparatively

20 large (12.6wt.%) as seen in the Al-Si phase diagram in Figure 8. The low solubility of Si within the Al matrix indicates that a majority of the elemental silicon will reside entirely in the eutectic as nearly pure silicon. As pure silicon solidified in the eutectic it will give off nearly five times the latent heat of fusion compared to primary aluminum. This excess in latent heat is sufficient to increase the temperature of the melt and allow the alloy to remain in the liquid state for a longer period of time and increase the overall fluidity of the alloy. The second reason for increased fluidity is due to the Al-Si eutectic solidification temperature. As seen in Figure 8, the Al-Si eutectic temperature is 557°C which is much lower than the liquidus line of any hypoeutectic composition, indicating that the eutectic will remain in the liquid state for a longer period of time and allows additional feeding and fluidity prior to solidification or freezing.

From the previous arguments it would seem likely that it would be favorable to maximize the amount of eutectic silicon in cast aluminum alloys. However when examining the microstructure, it can be seen that this is not the case. The microstructure of unmodified, as-cast eutectic silicon takes on an acicular or elongated flake like morphology as seen in

Figure 9a & 4c. The tips and edges of the flakes tend to have sharp corners and edges that serve as regions of concentrated stress that often lead to premature failure and reduced mechanical properties when mechanically loaded. Thus, a balance must be struck between maximizing the fluidity of the alloy so that it can be cast, and limiting acicular eutectic silicon that is associated with poor mechanical properties.

Figure 8: The Aluminum – Silicon binary phase diagram as calculated by ThermoCalc.

To combat the acicular or flake like morphology of eutectic silicon, strontium is often added to Al-Si alloys due to its modifying effects. When strontium is added to Al-Si alloys the eutectic silicon is modified and the morphology transitions from acicular flakes to a rounded, fibrous morphology as seen in Figure 9b & 4d.[29–33] The modification reduces the stress concentrations around the eutectic silicon which leads to an increased ductility and mechanical properties. The exact mechanism for this refinement is not fully understood, though there are two prevailing mechanisms. The first mechanism suggests that the strontium suppresses the eutectic growth temperature.[31] By suppressing the growth temperature, the eutectic phase is not able to grow into elongated flakes and instead growth is halted, forcing the eutectic phase into a fibrous morphology.

Figure 9: Eutectic silicon morphology in an 10wt% Al-Si alloy (a) unmodified (b) modified with the addition of 300 ppm strontium.[30] and A319 (c) unmodified (d) modified with 96ppm.[31]

Alternatively, it has been suggested that the strontium segregates into a rod like morphology between the Al-Si eutectic and interrupts the stacking sequence of Al-Si and prevents the coarsening of the eutectic silicon.[29]

Despite the mechanism, modification of eutectic silicon increases the balance of eutectic silicon that can be used in Al-Si alloys which often ranges from 5-9wt% Si.[27, 34] The most popular alloy in this range is undoubtedly A356 with a composition of Al-7Si-

0.3Mg.

The addition to magnesium to the 3xx series of aluminum alloys has historically been one of strengthening. Magnesium increases the strength of aluminum through solid solution strengthening as well as precipitation strengthening. Aluminum has a relatively high solid solubility of Mg which allows the for solid solution hardening. In addition to solid solution strengthening, Mg forms an intermetallic, Mg2Si with the silicon in the 3xx series alloys. The Mg2Si intermetallic greatly increases the strength and has been shown to increase proportionally to (Mg)1/2.[35] Unfortunately, if added in excess under slow cooling rates, Mg2Si will take on a needle like structure and result in greatly reduced ductility due to cracking along the intermetallic, as shown in Figure 10. Thus, the magnesium content in 3xx series often remains well below 1wt%.

Figure 10: Fracture line initiation along Mg2Si precipitates in A356.[36]

The final element yet to be discussed in the 3xx series is copper. Copper is known to increase the strength and toughness of the 3xx series, yet reduce the castability and corrosion resistance.[27, 37] Copper has a high solid solubility within the aluminum matrix and allows it to form act a strong solid solution strengthener and provides the opportunity for heat treatment and age hardening. The phase diagram for the Al-Cu system can be seen in Figure 11.

Figure 11: Aluminum-Copper phase diagram showing the intermediate precipitation of Al-Cu precipitates.[38]

Upon heat treatment, copper precipitates out coherent Guinier-Preston zones, or GP zones, and later semi coherent intermediate phases 휃′′ and 휃′ upon heat treatment that greatly increase the strength of the Al-Si alloys containing copper.

2.1.3 Defects and Mechanical Properties

Heat transfer and alloy chemistry as described above play important roles in determining the final microstructure and mechanical properties of cast components, however, metallurgical defects are a dominating factor in the mechanical properties of solidified

26 structures.[39] For the purpose of this work, metallurgical defects are defined as internal regions of the cast structure that negatively impact the mechanical properties. This is to clarify, traditional defects such as grain boundaries and dislocations will not be considered as these defects alone often improve the mechanical properties. Additionally, defects on the surface of the casting will not be considered as they can be easily prevented when best casting practices are followed.

The most common defect in cast structures is porosity, and can be generally defined as a voided three-dimensional space or hole within a casting that should be otherwise filled with solid material. Pores are considered defects as they weaken the overall structure by reducing the solid cross sectional area of the component, which in turn increases the local stress on the component. These regions are prone to premature failure and often lead to reduction in tensile strength and ductility.

Porosity within castings originates from two main causes, the volume contraction that occurs during solidification, and excess gas entrapped within the liquid. The first source of porosity described above is defined as shrinkage porosity. As a casting solidifies, the solid will occupy a smaller volume than the liquid, and results in contraction in the volume of the casting. This phenomenon is shown in Figure 12 where the solidified casting has pulled away from the edges of the mold and a cavity or pipe shrinkage has occurred near the pouring region. For Al-Si alloys the shrinkage volume ranges from 4.6

– 6.6% depending on the silicon composition.

Figure 12: Various forms and depictions of shrinkage. [40]

Shrinkage in aluminum alloys does not necessitate that defects will form, instead shrinkage defects in castings arise due to insufficient feeding pressure. In gravity sand or die casting, there is pressure supplied to the casting due to the sprue and the risers as described in Figure 6a & 1b. This pressure is called the metallostatic head pressure, or feeding pressure, and when sufficient pressure is provided, the internal solidification shrinkage can be eliminated. If insufficient pressure is applied, internal cavities will form as the molten material solidifies from the outside in. This often results in what is termed centerline shrinkage and is represented schematically in Figure 12. The pores resulting from shrinkage porosity can vary greatly in size and are characterized as either macro or micro shrinkage. Macro shrinkage pores are larger and often result from limited to no feeding, whereas, micro shrinkage pores are small and occur when some feeding exists 28 but is not sufficient enough to eliminate shrinkage. The typical size scale for macro and micro shrinkage pores are millimeters and micrometers respectively.

The second source of porosity in aluminum castings is due to air or gas entrapment beneath the surface of molten aluminum and is often called gas porosity. Gas porosity presents itself in aluminum alloys due to the large jump in solubility of hydrogen that occurs 660°C as shown in Figure 13. This spike in solubility is problematic as the pouring temperature of most aluminum alloys is near 700°C. Thus, prior to casting, the molten aluminum retained in a holding furnace or ladle will be exposed to significant amounts of hydrogen and other gases that are able to enter the melt. If no treatment is performed to the molten material before casting, the excess gaseous product will be quenched into the final casting and will precipitate out as porous voids. These voids are often spherical in nature with smooth surfaces and can vary in size from several microns to several millimeters.

Hydrogen porosity is much easier to combat than shrinkage porosity and can be effectively eliminated if proper processing is used. The main methods used to reduce or eliminate the hydrogen or gaseous porosity are rotary degassing, fluxing, filtering and when necessary, vacuum melting. Rotary degassing, fluxing and filtering the aluminum offer the cheapest methods to temporarily reduce the gas content in the melt, however, if a melt is left in a gaseous environment such as air, the hydrogen will re-enter the melt and require additional treatment. Vacuum melting on the other hand offers the best opportunity for long term, gas free molten material.

Figure 13: Hydrogen solubility in pure aluminum.[41]

From the above discussion on porosity, it is evident that despite the source of porosity, a pore or void in the casting is undesirable. Pores in cast aluminum structures have two main effects on mechanical properties, reducing both the ductility and fatigue life of the cast structure.[27, 42–44] The loss of ductility or elongation was touched on briefly above and can be visualized in Figure 14a. This large drop in elongation has been shown to be independent of the type of porosity or defect, and only depends on the overall loss of cross sectional area due to voided material.[42] Instead of relying on a single pore or void, total cross sectional area of voids can be idealized and superimposed into a single void. The singular void will then transfer the entire load to a small cross sectional area of solid material which also causes an increase in the local stress. The stress on the system will reach the critical value and begin yielding at lower value of elongation and

30 eventually fail after exhibiting minimal ductility. This mechanism can be described mathematically using the stress intensity factor, 퐾, in Equation 1 where 𝜎 is the applied stress, and 푎 is the pore radius.[27]

1 푎 퐾 = 2𝜎 ( )2 Equation 1 휋

Components designed for fatigue applications are intended to last thousands if not millions of cycles before failure. Though when a pore or void is introduced into the components, it will act as a crack and greatly reduce the life of the cycle. When determining the fatigue life of a component, individual pores cannot be combined, and instead the fatigue life is a function of the largest pore and how fast that pore grows.[27,

43, 44] This relationship can be described using the Paris equation for aluminum alloys as shown in Equation 2, where 푎 is the pore radius, 푁 is the number of cycles, and 퐶 is a material dependent constant.[27]

푑푎 = 퐶(푎)2 Equation 2 푑푁

Equation 2 shows that the pore radius or crack will grow fastest for the largest pore and will also result in a shortest fatigue life as suggested in Figure 14b. This trend is simple in nature, but has been recently verified by using X-Ray Computer Tomography (CT) and

31 finite element simulations to show increased stress levels immediately surrounding the largest pores.[44]

The significant drop in ductility and fatigue life associated with porosity highlight the importance of limiting and eliminating shrinkage and gas porosity in structural aluminum castings.

(a) (b) Figure 14: Reduction in the (a) ductility[42] and (b) fatigue life [43] of cast Al-Si-Mg alloys due to various pore sizes.

Aside from porosity, the next most common, and perhaps the most detrimental, defect in aluminum castings are entrained oxide inclusions. Oxide inclusion in aluminum castings are commonly called bifilms and exist as a thermodynamically solid, doubled over film in both liquid and solid aluminum.[45] Bifilms form whenever molten aluminum is exposed to an oxygenated environment such as air. The oxygen in the air instantaneously reacts

32 with surface of the molten aluminum and forms a thin film with the chemical formula of

Al2O3.[46] While on the surface, the flat oxide film acts as a protective barrier to the outside environment, however, if the film is perturbed, it will form a wave-like structure and upon crashing back into the surface of the melt, will entrained the folded-over bifilm defect as seen in Figure 15. During the folding over process to form the bifilm, a small pocket of air is entrapped between the two solid layers of the film and form a crack-like feature as shown in Figure 15c. Once entrained, bifilms are extremely difficult to remove from the melt due to the thermodynamic stability of the Al2O3 oxide within aluminum and are notorious for dramatically reducing the ductility of structures due to the crack like structure.[45, 47–49]

(a) (b) (c) Figure 15: Bifilm formation mechanism due to a perturbed molten surface.[49]

The crack like structure that forms along entrained oxide inclusions can be visualized in

Figure 16. It can also be seen in Figure 16 that the bifilm structure does preferentially nucleated any one phase or particle; instead it acts as a substrate for all solidification.

This can be highly detrimental to the ductility of a casting in the case where needle-like

β-phase precipitates form. The sharp crack morphology of the bifilm can be compounded with the sharp tips of the β phase to greatly increase the stress concentration and result in

33 premature failure. Even when the bifilm structure is not associated with the β phase, the large crack like structure of the bifilm can be millimeters in length as shown in Figure

16a, and will cause a reduction in ductility in a similar fashion as large pores.

(a) (b) (c) Figure 16: Bifilms trapped with the solidified aluminum material (a) Aluminum matrix (B) Al Matrix – α interface (c) Primary Fe phase (β). [50]

Chapter 3: Heat Transfer Mapping

Traditional casting methodologies often have fairly consistent heat transfer during the solidification process. However, with the introduction of chills, the local heat transfer can have a significant effect on the resulting microstructure and mechanical properties.

Chapter 3 begins with the examination of the interfacial heat transfer coefficient during the casting process, and explores the potential of using water to enhance the cooling effect immediately following solidification of a cast alloy. The variable, or location specific, heat transfer is then used to develop an HTC map to predict the local cooling of cast structure.

3.1 Theory of Chills and Heat Transfer

In traditional casting, the heat transfer is relatively constant throughout the solidification process as the mold material will continually draw heat from the casting at a constant rate. However, when a chill is introduced into the mold, the local heat transfer will change considerably and can dramatically change the interfacial heat transfer during solidification. Thus, accurately obtaining heat transfer data during casting processing is critical to process simulation and control of high performance castings, especially in the presence of a chill.

Chills are commonly placed in regions of a casting that require increased mechanical properties or have shrinkage issues during solidification. Chills are typically comprised of steel or copper and can contain water lines within them to enhance the cooling effect of the chill. In this work, the maximum effect of a chill is considered. Instead of using a standard metallic chill, a water jet will be sprayed directly onto the cast surface following solidification. This can be accomplished by removing the mold package from the casting either entirely or in a local region immediately once the molten material obtains a solid outer film. Once the mold package is no longer obstructing the casting from the water nozzles, the water jets can be allowed to spray the surface of the casting to examine the maximum capability, or upper limit of a chill.

Examining the scenario of maximum heat transfer creates a highly dynamic heat transfer situation involving mold removal, water impingement, air cooling, and requires conduction, convection as well as radiation to be considered. To date, there is not a mathematical model that can accurately simulate each of these phenomena simultaneously and accurately. For this reason, various heat transfer components are often grouped into an all-encompassing interfacial heat transfer coefficient (HTC), which describes how well and how fast heat can be removed from a body. In essence the HTC acts as the boundary conditions at the metal-mold or metal/chill interface for any heat transfer analysis/simulation.

The interfacial HTC is often a difficult value to measure. During the solidification process, the solidified metal shrinks away from the initial metal-mold interface, causing the interface to physically move. As the interface moves, an air gap is formed between

36 the metal and mold and the true metal-mold interface vanishes. To combat the moving interface thermocouples are often placed in either the mold or casting and the HTC is inversely calculated. The mathematics of inverse HTC calculations have been well documented and consist of solving Fick’s second Law in terms of heat transfer as shown in Equation 3.[51–53]

휕 휕푇 휕푇 (푘 ) = 𝜌푐 Equation 3 휕푥 휕푡 푝 휕푡

Where k is the thermal conductivity, T is temperature, t is time, ρ is the density of the

휕푇 casting, and 푐 is the temperature dependent heat capacity and the term (푘 ) represents 푝 휕푡 the HTC. This method is readily applicable to sand casting and gravity die casting, however when the mold experiences rapid changes, such as in high pressure die casting and or the maximum chill scenario, Equation 1 can be modified to Equation 4.[54]

푇̇ ℎ = 𝜌푐푝푉 Equation 4 퐴(푇푠−푇∞)

Where h is the HTC, V is the volume of the casting, A is the interaction area, 푇̇ is the instantaneous cooling rate, 푇푠 is the measured casting temperature and 푇∞ is the ambient temperature or cooling media temperature.

In determining the HTC for the maximum chill scenario, thermocouples must be placed within the casting as they cannot be placed within the mold that is removed. During

37 casting, the thermocouples provide cooling curves from which Equations 3 & 4 are used to calculate the HTC. Once the interfacial HTCs are obtained, a model can be created to predict the thermal history of a cast component in the presence of a chill. Traditionally, the measured or calculated HTC is uniformly applied over the entirety of a surface. This assumption is reasonable for casting methodologies where the mold material remains constant and the entirety of the cast surface would experience similar if not the same heat transfer boundary conditions. This method, however, is not applicable when the casting is solidifying in the presence of a chill.

When in the presence of a chill, the surrounding local region of the cast surface experiences a unique HTC based on the location of the chill and the efficiency of cooling lines within the chill. When examining the maximum effect of a chill, this becomes even more complicated as the HTC can vary greatly depending on whether or not the water jets impinge directly or indirectly on the surface, as well as variance in time of water impingement. Additionally a regenerative and continuous water supply, will prevent not only the formation of the air gap, but also eliminate the Leidenfrost Effect. If successful, the direct impingement of water on the casting can force directional solidification and prevent residual stress build up or any plastic strain that is often associated with quenching.[55]

The idea of a maximum chill attempts to explore the maximum capabilities of heat transfer during casting. To meet the maximum HTC, water must be used as the cooling media as its specific heat creates the most efficient form of heat dissipation. Though similar to quenching, this process still occurs prior to complete solidification and acts as a

38 hybrid between casting and quenching. This effectively creates a new and unique scenario for which the traditional assumptions of a uniform HTC is not compatible. Thus the maximum chill scenario requires a novel modeling approach to properly understand the heat transfer and eventual solidification and provides a window into the maximum cooling capabilities during casting.

3.2 Enhanced Cooling Experiments

To better understand the heat transfer process during the max chill scenario an enhanced cooling experiment was designed. The experimental apparatus was designed to replicate aluminum casting following the initial solidification of the surface skin of the casting.

3.2.1 Advanced Cooling Experimental Apparatus

When replicating the enhanced cooling experiments, a 304L stainless steel block with dimensions of 152.4x101.6x31.75mm was chosen to serve as the casting. A solid stainless steel material was chosen over molten aluminum so that numerous experiments and replicates could be quickly completed without the difficulty of removing the mold following solidification of aluminum. In choosing to represent the casting with 304L, it is known that there will be a general variance in the resulting cooling curves due to the specific heat difference as well as the heat of fusion that results from the phase transformation in 3xx series Al alloys. The difference in the specific heat capacity for aluminum and stainless steel can be seen in Table 3 and shows that the aluminum alloys require more energy to reduce the temperature of the casting. Additionally, Al-Si alloys will undergo the eutectic phase transition at 557°C which causes the release of latent heat

39 of fusion, whereas, the 304L has no phase change below 600°C. The combination of the difference in heat capacity and the release of heat of fusion indicates that the 304L casting block will cool at a faster rate than aluminum under the same conditions. Though these differences exist, the 304L casting block will still provide the same trend in in the cooling curves due to the both materials having a linear variation in the specific heat capacity. Likewise, the rapid quench like nature of the maximum chill is expected to provide sufficient undercooling that the isothermal nature of the Al-Si eutectic formation will be hidden or limited in the cooling curve, and makes the 304L a suitable option for examination using the enhanced cooling experiments.

Table 3: Temperature dependent specific heat capacity for a 3xx series Al alloy and a 304L stainless steel.

AlSi10Mg [56] 304L [57] Temperature Specific Heat Temperature Specific Heat (C) (J/kgK) (C) (J/kgK) 25 739 25 476 60 745 100 483 100 754 200 491 150 776 300 500 200 795 400 508 252 819 500 518 297 838 600 529 350 883 400 923

The casting block was heated for each experiment with a series of four 300W cartridge heaters inserted into the side of the block. To measure the temperature change, five ports were drilled in the rear of the casting block and thermocouples were inserted into each 40 port to a depth of 2.5mm behind the front wall. Additional thermocouples were added to the top and bottom of the casting block, and both were located 2.5mm behind the front wall. A schematic of the casting block can be seen in Figure 17a.

The thermocouples were numbered 0 through 6 with the naming scheme and placement shown in Figure 18. The center thermocouple, TC 0, was located in the center of the casting block. Each of the remaining thermocouples were placed 25mm from its nearest neighbor with thermocouples 1-4 located along the central horizontal axis and thermocouples 5 & 6 located along the central vertical axis. Thermocouples 1 & 2 were placed opposite of thermocouples 3 & 4 respectively, however the cooling curves for thermocouples 1 & 2 were not considered to limit redundancy due to symmetry.

(a) (b) Figure 17: Experimental apparatus (a) Casting test block design. Thin cylinders represent thermocouple locations, while the 4 parallel horizontal cylinders represent cartridge heater locations. (b) Enhanced cooling experimental setup.

3.2.2 Enhanced Cooling Experimental Procedure

For each Enhanced Cooling test the casting block was placed on a ceramic plate and heated with the four cartridge heaters until the block equilibrated at 580°C. The temperature was chosen to be between the liquidus and solidus to simulate an aluminum material that had just formed a solid skin at the metal/mold interface. Following the temperature equilibration, the cartridge heaters were then turned off, while a water jet was turned following a 4 second pause to ensure data collection. The water jet was placed in line with the center of casting block as shown in Figure 17b. All 7 thermocouples recorded the 7 cooling curves at an acquisition rate of 100 Hz until all thermocouples read temperatures below 400°C, after which the water jets were turned off and the test concluded. During the duration of the experiment, digital and thermal camera imagery was conducted using a FLIR A325sc camera.

Figure 18: Two-Dimensional representation of the front of the casting block. The naming convention and locations of the thermocouples are also shown.

3.2.3 Enhanced Cooling Variables

The general procedure listed above was followed for all enhanced cooling tests. While running the tests, several variables were altered to examine the max HTC achievable. The 42 variables examined included the water jet pressure, water jet temperature, the nozzle type, the nozzle distance from the casting block, and the number of nozzles.

Two types of nozzles were used during enhanced cooling experiments to examine the effects of the interaction area and local changes in the HTC of the casting block. The pin point nozzle (PP) expelled a direct stream of water with no lateral dispersion, while the fan nozzle and had a 60° lateral dispersion. The different nozzle types with spray patterns are shown in Figure 19. Each test was repeated a total of 5 times at pressures of 5, 7, 10,

12 and 15psi.

(a) (b) Figure 19: Water jet impingement and interaction area of the (a) pin point nozzle and the (b) fan nozzle.

3.3 Cooling Curves & Heat Transfer during Enhanced Cooling

Cooling curves from each of the thermocouple locations were obtained from the enhanced cooling experiments. Each thermocouple occupies a single point in the entire casting block, from which a corresponding heat transfer coefficient can be calculated

43 using Equation 4. An example of the cooling curves and the calculated HTCs variation over time can be seen in Figure 22 and Figure 22 respectively.

(a) (b)

(e) Figure 20: Cooling curves for the pin point (PP) and fan nozzles at various locations on the enhanced cooling casting block for a 10 psi water jet 2 inches away from the casting block.

(a) (b)

(e) Figure 21: Heat Transfer Coefficients for the various locations on the enhanced cooling casting block for a 10 psi water jet 2 inches away from the casting block.

3.3.1 Pin Point Nozzle

Figure 21 shows that the interfacial HTC does not vary significantly when the nozzle type is varied. Instead the larger differences can be seen in the total solidification time for the different thermocouple locations shown in Figure 20. By examining the cooling curves for the pin point nozzle it is seen that the first drop in temperature occurs at the center position or TC0 and is followed by a lateral dispersion towards TC3 and finally TC4.

This is intuitive as pin point nozzle is aligned over the center position of the casting block and the block will cool from the center of the chill outwards. This behavior aligns with the spray patterns shown in Figure 19a where the water jet was aligned directly over the center thermocouple. The HTC for the lateral positions also show that the maximum HTC occurs at TC0 and then decreases as the distance from the center nozzle increases. Such a drop in HTC magnitude is not unexpected as a smaller volume of water will impinge upon the surface as the distance from the nozzle increases.

The HTC along the vertical axis of the casting block shows a different trend. Positions

TC5 and TC6 possess a considerably greater HTC magnitude than all other thermocouple positions as shown in Figure 21. The increase in magnitude is attributed to three factors: the initial water jet displacement, the proximity to the edge of the casting block and gravity. When water jet first impinges upon the casting block surface, the water displaces into a circular pattern as shown in Figure 19. The force of the water jet causes a majority of the water to displace from the central region and spread uniformly in all directions until it boils off. Thus, a higher volume of water reaches the regions directly outside of the central region and allows for increased heat dissipation. Following this logic would

47 indicate that TC3 should also have a greater HTC magnitude compared to TC0. However, this is not the case and is described by the proximity to the edge of the casting block.

Position TC5 and TC6 are 25mm away from the top and bottom of the casting block respectively compared to TC3 which is 50mm away from both the top, bottom and nearest edge of the casting block. Therefore, TC3 possess a greater thermal mass and will effectively have a decreased rate of heat transfer compared to TC5 and TC6. The final point to consider for the vertical axis of the casting block is gravity. As the water jet impinges on the surface, not all of the water will boil off and gravity will pull the remaining water downward and will be able to further cool positions TC0 and TC6. The combination of continuous spraying and gravity cause TC6 to have the greatest heat transfer coefficient magnitude during the enhanced cooling experiment,

3.3.2 Fan Nozzle

The fan nozzle cooling curves and heat transfer coefficients show little difference in comparison to the pin point nozzle. The two discernable differences are the time of initial water jet impingement on position TC4 and the lower HTC magnitude for position TC5.

The shorter time required for initial water jet impingement for TC4 can be attributed to the lateral dispersion of the fan nozzle as shown in Figure 19b. The fan geometry allows water to reach the out edges of the casting block at an earlier time compared to the pin point nozzle and allows for slightly faster cooling. The fan geometry also prevents the same volume of water to reach position TC5 as does the pin point nozzle and results in lower HTC values for all times as shown in Figure 21e. Additionally the fan nozzle appears to have a slightly slower cooling rate for all locations aside from TC3 and TC4

48 which is likely due to the larger range over which the same volume of water is spread over the casting block.

3.3.3 Stages of Heat Transfer during Enhanced Cooling

Most of the HTC maps in Figure 21 display three unique stages of heat transfer and is further highlighted in Figure 22. Stage I occurs after the melt is delivered to the mold, where the heat transfer is dominated by conduction at the metal/mold interface. During

Stage I, the magnitude is quite low (<1000W/m2K for sand casting) compared to when the chill is turned on. The HTC in Stage I also remains constant due to the formation of the air gap which acts as an insulating layer. Near the middle of Stage I solidification of the casting at the metal/mold interface and continues until a sufficient skin is formed at the culmination of Stage I.

I II III

(a) (b) Figure 22: Three Phases of heat transfer during the solidification process for position TC0.

Stage II begins when the local chill is turned on and the water jet impinges directly on the skin of the casting. At this point the casting surface is still greater than 500°C meaning that the water will begin to undergo the three components of quenching: film boiling, boiling, and convective cooling.[58] For the duration of the three quenching stages the water jet shape will undergo a considerable changes.[59] During film boiling, the first component, there is an initial spike in HTC as the instantaneous cooling rate increases dramatically. Here the water jet has an explosive behavior after impinging with the casting surface. Water will deflect off of the casting block due to the combination of the film boiling and pressure of the water. The water jet/casting interface and interaction area is small and the heat transfer is dominated by convection from the water jet and radiation with the surrounding. Because the explosive/boiling nature of the casting/water jet, the water does not remain on the surface of the casting for a significant time, limiting the effects of conduction. This interaction causes an immediate increase in magnitude of the

HTC as shown in Figure 22. As the casting block temperature begins to decline, the water jet will have a more uniform flow over the casting block due to less boiling which leads into the second component of quenching. The more uniform flow causes the waterfront on the casting block to extend outward and rings form around the center of the water jet as shown in Figure 23. This explains why TC3 has a later increase in the magnitude of

HTC for the pin point nozzle shown in Figure 22. The rings will remain on the surface for a brief time until boiling occurs, meaning conduction through the block must also be considered in conjunction with convection and radiation.

Once the temperature of the casting block falls below ~350°C the volume of water from the water jet becomes too great for immediate boiling to occur. Instead the third component of quenching is reached where the casting block undergoes convective cooling. The water from the jet forms a thin film over the block which convectively removes the heat to reduce the temperature of the block. In Figure 22 this can be seen as a return to a baseline or constant HTC, near 1000W/m2K. These curves highlight the difference between the maximum chill scenario and a standard quench following heat treatment. In a standard quench, the HTC is relatively low and constant between 200°C-

500°C ranges then spikes between 100°C-200°C, however, during the maximum chill scenario and enhanced cooling experiments there is an initial spike in HTC after which a baseline value is reached.[58] This is likely due to the Leidenfrost effect that occurs during the immersion or dipping of a hot material into liquid. However during in the maximum chill scenario the water jet continually applies pressure to the surface of the casting and prevents the steam layer from building and forming an air gap that would cause a reduction in the HTC magnitude.

Though complex in nature, the heat transfer during the enhanced cooling experiments can be modeled by combining each of the individual components of heat transfer into a single, location specific, time-dependent heat transfer coefficient.

3.4 Modeling Heat Transfer for Enhanced Cooling

Though the complex interaction can be condensed down into a single effective HTC, the data obtained within the enhanced cooling experiments only provides information at

51 single distinct points within the casting. Unfortunately, due to the complex structures in

3D casting and dynamic conditions casting, the HTC calculated above cannot be applied uniformly as is done with other casting methods. Figure 21 shows that over a distance of

25mm in the horizontal direction, the HTC varied more than 2000 W/m2K for the pin point nozzle and resulted in a 150% increase in the solidification time. Thus, there is a need for the implementation of a new model in which a few data points can be used to apply boundary conditions to an entire surface and obtain accurate thermal histories.

3.4.1 Building the Enhanced HTC Map

In order to accomplish this task, the concept of an Enhanced HTC map model was developed. The concept involves a 2D map that can be projected onto a 3D surface, where each region of the map will be encoded with a specific HTC. As mentioned, the difficulty in this process is that the HTC is only known at a few discrete points from the enhanced cooling experiments. To understand how to design the map for each nozzle, thermal imaging was used to examine how the temperature and thermal gradients varied in the casting block during the enhanced cooling experiments due to the maximum chill.

Thermal image snapshots can be seen in Figure 23. The snapshots in Figure 23 show a clear temperature gradient that forms at the location of water impingement. The gradient was then interpolated as a normal distribution across the surface of the casting block in the known directions with the interpolation shown in Figure 24.

(a) (b) Figure 23: Thermal camera imaging displaying clear gradients in the (a) pin point and (b) fan nozzles on the casting block during the enhanced cooling chilling.

The data from the enhanced cooling experiments shows a strong correlation to gaussian distributions indicating the distributions are reasonable for HTC map implementation.

For the design of the geometric contours of the enhanced HTC map, the thermal camera images were utilized. The varying colors were defined as unique HTC regions where the

HTC would be constant throughout the indivudal region. The HTC were calcualted using the interpolated gaussian distributions in Figure 24 and then applied to that corresponding position on the block. This process was followed until the entire 2D surface of the casting was divided into a map with uniquely defined HTC regions and was termed an Enhanced

HTC Map. The Enhahnced HTC Map was modeled within the finite element analysis software ABAQUS and a Standard/Explicit model chosen. Within ABAQUS, the casting block was modeled with the same dimensions, and thermocouple locations. The casting block was given a global mesh size of 3mm and was modeled using DC3D10 elements

(A 10-node quadratic heat transfer tetrahedron). The specific heat capacity of the casting 53 block was defined as the corresponding values in Table 3 and the block was givena pre- defined homogeneous temperature of 580°C.

The ABAQUS simulation was divided into a two step simulation, with both defined as

Heat-Transfer (Transient) steps. The first step was 4 seconds long corresponding to the delay prior to the water jets being turned on and considered only radiative cooling and the emissivity value was set at 0.3. The second step corresponded to the water jet being turend on and considered radiation, convection and conduction. In the second step, the radiation value was reduced to 0.1 and the location specific HTC value was applied using a time dependent film coefficinet. Thorughout the simulation the time-step was constant and set at 0.25 seconds

Figure 24: Schematic of the instantaneous interfacial HTC variation across the vertical and horizontal axes of the enhanced cooling casting block.

The normal distribution example in Figure 24 was inserted into ABAQUS along with the above mentioned parameters and the resulting simulation thermal gradients can be seen in

Figure 25. The contour plot in Figure 25 matches the results shown in the thermal camera snapshot in Figure 23 and highlights the accuracy of the methodology used.

Figure 25: Instantaneous cooling provide of the casting block with a pin point nozzle.

3.4.2 Enhanced HTC Map Validation

In order to validate the enhanced HTC Maps developed, thermal camera imagery was also used at the back of the casting block, allowing two point validation. The methodology used is shown in Figure 26.

Figure 26: Methodology used to develop and validate the Enhanced HTC Maps.

Figure 26 details the two way validation. The first step in validation is obtaining the correct heat transfer coefficients. The HTC values are then applied to the front wall of the casting block while the validation is performed at the thermocouple locations 2.5 mm behind the front wall. The second validation is performed at the rear or back wall of the casting block. If the predicted cooling curves at each of these locations match the enhanced cooling experiments, it can be concluded that thermal history throughout the entirety of the block will be correct, and will confirm the heat transfer is valid within 3D space. The Enhanced HTC Map is then validated as time dependent boundary condition for simulation purposes and proper application of the map will allow the prediction of location specific interfacial thermal history during enhanced cooling experiment or maximum chill scenario.

The comparison of the experimental maximum chill scenario cooling curves and the

ABAQUS simulation using the Enhanced HTC Methodology described above is shown in Figure 27. Figure 27 shows the comparison of cooling curves at the thermocouple locations 2.5mm behind the front wall of the casting block, indicating the validity of the methodology used.

The simulation results show that the trend for all five thermocouple locations matches well with the experiments. The error in the time required for each of the thermocouple locations to reach a temperature 400°C and was found to vary between 1.46-2.98% indicating the accuracy of the model. The difference in the simulation can be attributed to a coarse discretization in the enhanced HTC Map. If finer discritizations are used, a greater level of accuracy can be obtained at the cost of computational time.

(a) (b)

(e) (f) Figure 27: Validation Step. Simulated vs experimentally measured cooling curves of the thermocouple locations in the casting block for the fan nozzle.

3.5 Maximum Obtainable HTC

Obtaining the maximum HTC in cast structures has been a common goal since the dawn of casting. In this work it is shown that even when a maximum chill is used, it is still not possible to obtain uniform heat transfer, though it can be rapidly accelerated. The pin point nozzle shows that the maximum HTC value is ~8000W/m2K at the central region of the chill and 16000W/m2K directly below the chill. The fan nozzle had a similar effect with a maximum HTC value is ~8000W/m2K at the central region of the chill and

13000W/m2K directly below the chill. The increased HTC values directly below the chill are the result of gravity and highlight the importance of orientation in considering the location specific heat transfer coefficients.

3.6 Prospectus of Heat Transfer Mapping

The validation of the enhanced HTC Map provides a new type of boundary condition that can now be implemented into casting software for accurate thermal history prediction.

Enhanced HTC Maps also offer an increased level of accuracy for future property prediction. As described in Chapters 1-2, location specific properties are derivative of location specific heat transfer which controls the location specific solidification. With the new methodology provided here, an unprecedented accuracy in property prediction is now available.

The concept of applying the HTC map to the surface of the casting begins the iterative process of empirically obtaining location specific heat transfer information. By fine tuning the time dependent HTC values within the ABAQUS thermal simulations, the

59 simulated locations specific cooling rates can be calibrated to any condition. In the experimental analysis above, it was shown that the enhanced HTC mapping technique is valid for a highly transient phenomenon of water chill. The situation of the water chill is the most dynamic heat transfer phenomenon within casting, indicating that the enhanced

HTC mapping should also work well for the implementation of standard copper or steel chills.

Additionally the Enhanced HTC mapping can be transferred to other casting methodologies in which include chills or cores to more accurately describe the interfacial heat transfer and location specific properties across a cast structures. The difficulty that lies ahead for this process is mapping of a two-dimensional Enhanced HTC Map to a geometrically complex cast surface. Three-dimensional curved surfaces and ledges offer unique challenges for interpreting how the heat transfer will vary for a cast component.

Nonetheless, the Enhanced HTC Map offers a new methodology for understanding the heat transfer during the casting process.

Chapter 4: Effects of Mg Solute on Al-Si-Mg Alloys

Chapter 4 switches the focus from heat transfer at the metal-mold interface to the effects of alloying on microstructure formation of Al-Si-Mg alloys. Excerpts of this chapter were taken from the author’s publication in the Journal of Materials Science: Predicting primary dendrite arm spacing in Al-Si-Mg alloys: effect of Mg alloying.

4.1 Traditional Roles of Mg alloying

Dendritic growth during solidification of Al–Si cast alloys is a critical phenomenon which has been extensively studied due to the importance of lightweight aluminum castings for the transportation and other industrial sectors.[35, 60–65] Recent efforts on integrated computational materials engineering (ICME) based design and manufacturing of castings have demonstrated the need of a robust and accurate dendritic growth model of Al–Si-based multicomponent alloys.[1]

In the production of lightweight aluminum alloys, magnesium is a critical alloying element, especially for commercially important Al–Si cast alloys. The known motivation for alloying aluminum–silicon alloys with magnesium has been twofold. First, Mg can supersaturate the solid solution leading to lattice distortions, providing solid solution strengthening. Second, Mg will react with Si to form Mg2Si precipitates that produce a

61 remarkable increase in strength, with the yield stress shown to increase proportional to

(Mg)1/2.[35, 37, 60]

The drawback of increased Mg content is that it also reduces ductility as Mg often partitions toward the p-phase (Al8-FeMg3Si6), a precursor to the often coarse, brittle intermetallic b-phase (Al5FeSi).[66] For this reason, Mg is rarely alloyed in excess of

1 wt% for cast Al alloys, and a balancing act is conducted in alloy design to optimize the trade-off between increase in strength and loss in ductility.

4.2 Existing Models for Dendritic Cell Size

4.2.1 Empirical Relationships

One of the often overlooked effects of Mg in Al–Si based alloys is the reduction in primary dendrite arm spacing (PDAS) and subsequent decrease in secondary dendrite arm spacing (SDAS). Spear and Gardner were the first to correlate the reduction in dendritic cell size in Al alloys with the addition of various elements. Unfortunately, a physical description as to why was not offered and instead, Spear and Gardener concluded that the degree of refinement reduces drastically as the solute alloying content is increased to 5wt%.[61] Though this conclusion provided insight to the effect of alloying, the Spear and Gardner observations were of the dendritic cell size and did not consider individual dendrites during dendritic solidification. McCartney and Hunt were next to examine the compositional effect and were able to show that the PDAS in the

Al-Mg-Si system followed the general trend expressed in Equation 5.[62]

−0.55 −0.28 0.32 휆 = 퐺 푣 퐶푆푖 Equation 5

Table 4: Definition of variables used throughout Chapter 4.

Nomenclature 푪풐 Nominal Composition 풎 Liquidus slope

ퟎ 푪풙 Composition of ‘x’ 𝝆 Number density of inoculant particles added to the melt 푳∗ 푪풙 Composition of element 푸 GRF ‘x’ at the S/L interface 푫 Diffusion Coefficient s Time required to reach final dendritic spacing 풅품풔 Grain size 흏푻 Slope of liquidus surface wrt solute 푳 element x 흏푪풙 풇 Fraction of particles that 푻ퟎ − 푻풍풐풄풂풍 Thermal undercooling successfully nucleate a grain ∆풇풔 Fraction solid ∆푻풏 Undercooling Required for nucleation 푮 Thermal Gradient ∆풕 Time Step for CA

휞 Gibbs-Thomson 흁풌 Dendritic growth Kinetic Coefficient Coefficient 풌 Partition coefficient 풗 Normal dendritic growth velocity

휿 Curvature of S/L interface ∆푥 Dendritic Growth Distance for CA

λ PDAS

The Hunt-Lu model was later developed by removing the compositional dependence of

Equation 1, and showed that by adjusting the exponential coefficients of G and v to -0.5 and -0.25 respectively, reasonably accurate results across multiple alloys systems.[63, 67]

Unfortunately, both the McCartney-Hunt and Hunt-Lu models are empirical in nature and neither provides an estimate with meaningful units nor a clear understanding of the

63 underlying mechanisms that result in a refined microstructure. Instead an empirical fit with arbitrary variables (G and v) was used to describe the phenomenon.

4.2.2 Growth Restriction Factor

In an effort to physically describe the role solute elements have in alloying, Greer et al. formalized the description of what is now called the growth restriction factor, GRF or

Q.[64]

푄 = 푚(푘 − 1)퐶0 Equation 6

By introducing the thermodynamic dependencies and the initial solute concentration, the

GRF provides an initial intuition. Mathematically, the GRF is the supercooling parameter multiplied by the partition coefficient, where the supercooling parameter is defined as the freezing range of the alloy and the partitioning coefficient is the ratio of eutectic concentration to the solubility limit of the alloy element.[68] Such a representation would mean that both the supercooling parameter and the GRF are related to how strong the partitioning or segregation is in the alloy system. If the alloy system is varied to one with a larger partitioning coefficient, the solute element has a greater affinity to segregate during the solidification process. Greater segregation results in a decrease in constitutional supercooling and an increase in the GRF. Numerous authors have examined the effect of the GRF on grain size, and have concluded that the reduction in grains size results from an increase in the GRF.[64, 68, 69] An increase in the GRF correlates to an increased number of nucleation events and is attributed to solute rejection

64 during solidification without examining the fundamental effect increased solute has on solidification.[65]

4.2.3 The Interdependence Theory

StJohn et al. is the modern champion of the GRF and has utilized it to describe his

Interdependence Theory described in Equation 7.[69–71] Though the GRF and

Interdependence Theory work to describe the grain size instead of primary or secondary dendrite arms, it is a step forward in describing the refinement mechanism associated with increased solute concentration. These theories state that as the solute content is increased, the melt is increasingly inoculated and prevents grain growth.[72] Much of the work involving the GRF focuses on the highly potent alloying particles such as TiB2 and the formation of a nucleation free zone, while often neglecting solute effects. Equation 7 can also be seen to be empirical in nature as many of the factors such as 𝜌: number density of inoculant particles, and 푓: fraction of particles that successfully nucleate a grain, must be estimated on a large number of experimental examinations. Furthermore, the remaining terms including the 퐷: diffusion coefficient, ∆푇푛: the undercooling required for nucleation, and 푣: normal dendritic growth velocity do not contain compositionall dependence information and the only true compositional dependence in

Equation 7 is located within the empirically determined GRF.

1 퐷∆푇 푑 = + 푛 Equation 7 푔푠 3√휌푓 푣푄

Each of the models described thus far has merits, but either lacks physical meaning

(McCartney & Hunt [73]), fails to provide meaningful units (Hunt-Lu [63]), describes the system on a larger length scale (StJohn et al. [68–71]), i.e. grain size, or simply omits the solute effects.

In order to develop a model that accurately describes the effect of solute content on

PDAS for microstructure modeling in casting design and process optimization, a series of directional solidification (DS) experiments and simulations were carried out. By using directional solidification, the nucleation and growth of primary dendrite arms can be studied without relying on averaging techniques used at the grain size level for bulk castings. Instead dendrites with a predetermined growth direction can be examined to determine the mechanisms at play with increasing solute concentration. Further, in this study a large range of factors are considered instead of the overly simplified correlations noted in the Hunt-Lu model.

4.3 Materials and Methods

The alloy chosen for microstructure evaluation during directional solidification was

Al-7.6Si-XMg, where the solute effects of Mg were examined. The range of Mg was chosen to mimic standard casting alloys as well as alloys with increased levels of Mg.

The compositions of the alloys used can be seen in Table 5.

Table 5: Compositions of Al-7.6Si-xMg alloys used for directional solidification.

Nominal Mg Al wt% Si wt% Mg wt% 0.5 91.94 7.56 0.50 1 91.25 7.73 1.02 1.75 90.81 7.41 1.78 2.7 89.41 7.90 2.69

4.3.1 Three-Dimensional Cellular Automaton Simulation

The Cellular automaton method (CA) is a simulation method in which simulation domain is discretized into a predetermined number of cells. Each cell is then given a state or condition which is then updated over time based on a set of governing equations. For solidification, the defined states are often the solid, solid/liquid interface and the liquid. A schematic of this discritization in two-dimensions can be seen in Figure 28. The schematic in Figure 28 shows the cells make up a checkerboard pattern in 2D which can be expanded to a three-dimensional domain by stacking each 2D pattern in the plane perpendicular to the page.

Figure 28: Schematic of a discretized cellular automaton simulation domain.

Recently, CA has been shown to accurately simulate microstructural evolution during solidification, maintain a high computational efficiency and is physically sound to incorporate the complexity of dendrite growth. For this reason, CA was used to examine the solute effects of Mg on the Al-7.6Si-xMg alloy.[74–77] The CA model used to develop the PDAS model in this study was developed by Gu et al. and has been shown to successfully model multicomponent dendritic solidification as well as the grain size of Al cast alloys.[77, 78] The basis of the Gu Model is outlined below beginning with the solute diffusion equation in Equation 8 and the total undercooling in Equation 9

휕퐶퐸 휕푓 푖 = ∇ ∙ ∑ 퐷 훻퐶퐸 + (퐶퐿∗ − 퐶푆∗) 푠 Equation 8 휕푡 푗=푆푖,푀푔 푖푗 푖 푖 푖 휕푡

The solute diffusion described in Equation 8 is applied to all cells in the simulation domain where all cells interact with their surrounding Von Neumann neighborhood; however, Equation 8 can only be solved at the dendrite tip if the fraction solid is known.

To obtain the fraction solid, the total undercooling is examined as shown in Equation 9.

The total undercooling represents the driving force for solidification where the constitutional undercooling term (left hand side of Equation 9) is expressed in terms of solute concentration.

휕푇 0 퐿∗ 휕푇 0 퐿∗ 푣 퐿 (퐶푆푖 − 퐶푆푖 ) + 퐿 (퐶푀푔 − 퐶푀푔) = 푇0 − 푇푙표푐푎푙 − 훤휅 − Equation 9 휕퐶푆푖 휕퐶푀푔 휇푘

Conveniently, the liquid concentrations in Equation 9 can be written in terms of the fraction solid by considering solute conservation at the S/L interface of the dendrite tip as shown in Equations 10 & 11.

퐿 퐿∗ 퐶푆푖 퐶푆푖 = Equation 10 1−(1−푘푆푖)∆푓푠

퐿 퐿∗ 퐶푀푔 퐶푀푔 = Equation 11 1−(1−푘푀푔)∆푓푠

By combining Equations 9-11 the fraction solid can then be solved for and yields

Equation 12.

1 ∆푓 = (−푏 ± √푏2 − 4푐), 0 ≤ ∆푓 ≤ 1 Equation 12 푠 2 푠

Where the variables b and c are defined as:

휕푇 0 휕푇 퐿 휕푇 0 휕푇 0 휕푇 퐿 휕푇 0 (1−푘푆푖)(∆푇푐− ∙퐶 + ∙퐶푀푔− ∙퐶푀푔)+(1−푘푀푔)(∆푇푐− ∙퐶푀푔+ ∙퐶 − ∙퐶 ) 휕퐶퐿 푆푖 휕퐶퐿 휕퐶퐿 휕퐶퐿 휕퐶퐿 푆푖 휕퐶퐿 푆푖 푏 = 푆푖 푀푔 푀푔 푀푔 푆푖 푆푖 휕푇 0 휕푇 0 (1−푘푆푖)(1−푘푀푔)( 퐿 ∙퐶푆푖+ 퐿 ∙퐶푀푔−∆푇푐) 휕퐶푆푖 휕퐶푀푔

휕푇 0 휕푇 0 휕푇 퐿 휕푇 퐿 −∆푇푐+ ∙퐶 + ∙퐶푀푔− ∙퐶 − ∙퐶푀푔 휕퐶퐿 푆푖 휕퐶퐿 휕퐶퐿 푆푖 휕퐶퐿 푐 = 푆푖 푀푔 푆푖 푀푔 휕푇 0 휕푇 0 (1−푘푆푖)(1−푘푀푔)( 퐿 ∙퐶푆푖+ 퐿 ∙퐶푀푔−∆푇푐) 휕퐶푆푖 휕퐶푀푔

푉푛 ∆푇푐 = 푇0 − 푇푙표푐푎푙 − 훤휅 − 휇푘

With the fraction solid term now isolated, the dendritic growth velocity can be obtained.

This is done by taking the fraction solid in each S/L interface cell and multiplying it by the known size of that cell per each time step, yielding Equation 13.

∆푥 푉 = ∆푓 Equation 13 푛 푠 ∆푡

The above derivation clarifies that the fraction solid, constitutional undercooling and dendritic growth velocity are entirely dependent upon the solute concentration. Thus, if the solute concentration is varied in an alloy, it will have a significant impact on the solidification process and resulting microstructure. The simulation method used in the Gu model relies on solving the diffusion equation in Equation 9 to calculate the alloy specific dendrite growth velocity shown in Equation 13. The growth velocity is then used to track the transformation process of individual cells across the simulation region, as cells transform from liquid cells to solid/liquid interface cells and from solid/liquid interface cells to solid cells.

As cells transform, it is known that the original crystallographic orientation of the dendrite will be lost during CA modeling and the resulting dendrites will always possess a crystallographic orientation parallel to the original coordinate system. Such a result is due to the Von Neumann neighborhood which only considers the 4 nearest neighbors in

2D and the 6 nearest neighbors in 3D. As the CA simulation calculations are performed, 70 the diagonals are not considered and the solidification transformations can only occur parallel or perpendicular to the original axis system.[79] CA has also been associated with mesh anisotropy, which has been shown to be reduced or eliminated through several methods [75, 80–82]. The anisotropy from the regular mesh, the capture rule, and the complete derivation of the velocity dependence on solute concentration can be found in the author’s previous works [77, 83].

4.3.2 CA Implementation of Directional Solidification

The CA model was run to simulate directional solidification of Al-Si-Mg ternary alloys with a homogeneous initial concentration field and a calculation domain of 200x200x20 uniform cubic cells and a mesh size of 5 μm. The domain size was chosen in order to match the size of micrographs obtained from DS experiments, while optimizing computational efficiency and limiting the influence of mesh size on convergence. The time step used in the CA simulation to accurately describe solute transport is shown in

Equation 14.

1 ∆푥2 1 ∆푡퐶 = 푚𝑖푛 ( 퐿 , ) Equation 14 5 |퐷 | ∆푓푠,푚푎푥 푖푗 푚푎푥

Symmetrical boundary conditions were chosen and applied to all surfaces within the calculation domain and a total of 50 evenly spaced seeds were placed in the calculation domain. The symmetric boundary conditions prevent solute flux across each of the boundaries and the gradient of all other variables at the boundary is zero. Symmetric boundary conditions were chosen to prevent the potential of solute buildup at the

71 boundary, which could deceptively alter the solute effects within the calculation domain.

The preferred crystallographic growth direction of the seeds was defined as perpendicular to the bottom plane of the domain. The initial temperature of the bottom of the domain was set to the liquidus temperature of the alloy while a temperature gradient of 28°C/cm and cooling rate of 1°C/s was applied. The temperature gradient was applied from the top to the bottom of the simulation domain to force directional solidification. The simulation was then run until a stable primary dendrite arm spacing was reached and the PDAS no longer varied with time, marking the end of the competitive growth process.

4.3.3 Directional Solidification

The effect of changing solute concentrations was isolated through a directional solidification experiment. In a DS experiment, the thermal gradient and pulling velocity remain constant, which in turn provides a constant constitutional undercooling and dendritic growth velocity throughout the length of the sample. Thus, by adjusting the composition of Mg in Al-Si alloys, the influence of the solute effects on the dendritic growth velocity and constitutional undercooling were able to be examined. Such a result is critical in determining the PDAS and SDAS in Al-Si-Mg alloys.

Directional solidification experiments were conducted using a Bridgman style furnace with three heating zones. Each zone center was located 9cm apart with the top and bottom heating zones totaling 15.25cm in length while the center heating zone was 5cm in length. Each zone was individually controlled and a constant thermal gradient was set at 27.8°C/cm. Alumina tubes with a 4.76mm inner diameter and 6.35mm outer diameter were filled with the desired alloy and were allowed to equilibrate within the Bridgman

72 furnace for 30 minutes. After equilibration, the furnace was pulled at a rate of 0.37mm/s providing a cooling rate of 1°C/s, close to that of industrial sand casting. Following directional solidification, the samples were removed and sectioned along the longitudinal and transverse axes at 4 cm from the uppermost portion of the solidified rod. Sectioned samples were polished and prepared for optical microscopy and were processed using

ImageJ software.

4.4 Results and Discussion

The following sections detail the results from the simulation and experimental work described in Section 3.3. The results are analyzed to help provide the foundation for a new model to describe the final PDAS in Al-Si alloys with varying levels of Mg.

4.4.1 Three-Dimensional Simulation Results of Directional Solidification

The resulting 3D CA microstructural simulations of directional solidification in the alloys researched can be seen in 29 & 30. Figure 29 shows the Mg concentration profile over a

2-D longitudinal cross-section of dendritic growth as the dendrite grow from bottom of the page towards the top. Figure 30 shows the Mg concentration profile across transverse cross section with the dendrite growing out of the page.

Figure 29: Cellular Automaton simulation of directionally solidified dendritic growth show the partitioning of Mg solute after 14 seconds of growth for (a) 0.5wt% Mg; (b) 1.0wt% Mg; (c) 1.75wt% Mg; and (d) 2.7wt% Mg.

Figure 29 & Figure 30 agree with the initial hypothesis and show a reduction in the

PDAS as the Mg solute concentration is increased. This behavior can be explained using

Equations 9 & 13, where both the constitutional undercooling and dendritic growth velocity are shown to be dependent on the solute concentration. This conclusion matches the results on binary and multicomponent dendritic solidification by Yao et al. [84] and

Rappaz et al.[85] Yao et al. was able to show that as the solute concentration is increased in aluminum alloys, the constitutional undercooling is decreased. Yao et al. attributed this phenomenon to solute enrichment in the liquid that occurs during solidification. Rappaz et al. then shows that the dendrite tip growth velocity is directly proportional to constitutional undercooling. Thus, it is evident that there is a direct relationship between the constitutional undercooling and dendritic growth velocity.

Figure 30: Cellular Automaton simulation of directionally solidified dendritic growth sectioned perpendicular to the growth direction showing the partitioning of Mg solute in Al-7.6Si-xMg after 14 seconds of growth for (a) 0.5wt% Mg; (b) 1.0wt% Mg; (c) 1.75wt% Mg; and (d) 2.7wt% Mg

4.4.2 Solute Effects and Constitutional Undercooling

Both CA microstructural predictions show clear solute partitioning following solidification. To better examine the partitioning a cross section was taken perpendicular to the growth direction and the Mg solute profiles were plotted in Figure 31.

Figure 31: Segregation of the Mg solute resulting in a reduction in lateral coarsening that occurs with an increased Mg solute content in Al-7.6-xMg alloys.

The partitioning of solute elements during solidification is not unique to the Al-Si-Mg system. However, the partitioning of solute can be used to describe the observed reduction in total undercooling and eventual drop in constitutional undercooling as discussed in section 3.4.1. To understand how the increased solute content effects

76 partitioning and constitutional undercooling, a solidification schematic is provided in

Figure 32.

Figure 32: Schematic representation of the decrease in constitutional undercooling that arises from an increase in Mg concentration. (a) Schematic of a phase diagram, (b) Rejection of solute at the S/L interface at T*, and (c) Liquidus temperature away from the S/L interface plotted with a constant thermal gradient.

Figure 32a shows two hypothetical alloys, Alloy 1 with a composition of C1 and Alloy 2 with a composition of C2. Alloy 2 has a greater solute content, C2, and a reduced solidification range compared to Alloy 1. If both of these alloys are allowed to solidify from the liquid state to a temperature T* as shown in Figure 32a, solute will redistribute as solidification occurs, resulting in the concentration profile shown in Figure 32b. The solute concentration of the first solid to form for each alloy are obtained by drawing a tie line at the liquidus temperature of the alloy and finding the point where it intersects the solvus line. This intersection point is shown in Figure 32a and shows that Alloy 2 will have a greater solute concentration in the solid compared to Alloy 1.

At the S/L interface shown in Figure 32b the solute concentration for both alloys will be identical as they are both solidified to the same temperature, T*, and both would have identical tie lines.. Ahead of the solidification front, in the liquid region, solute rejected from the solid phase begins to pile up immediately outside the S/L interface, causing a spike in the solute concentration which asymptotically levels off to the initial concentration of each alloy far from the interface. Figure 4b shows that alloy C2 will have a greater concentration of solute in both solid and liquid regions at all locations away from the solid/liquid interface and is what is shown in the solute profiles shown in Figure

31.

The local variation in solute content will result in a change in the liquidus temperature in the remaining liquid as described in Figure 4c. A higher concentration of solute will lead to a decrease in the actual local liquidus temperature of the remaining liquid and results in the liquidus of Alloy 2 to lie below Alloy 1. If a constant thermal gradient is applied, as in directional solidification, the alloy with a greater concentration of solute will have a decrease in both total and constitutional undercooling. This is represented by the area between the thermal gradient line and the liquidus line in Figure 4c. Thus, the relationship between solute concentration, constitutional undercooling, and dendritic growth velocity can be clarified. Increasing the solute concentration in an alloy will reduce both the constitutional undercooling and the dendritic growth velocity.

4.4.3 Solute Effects and Dendrite Growth Velocity

As the dendritic growth velocity slows, lateral coarsening of primary arms must also retard. A reduction in lateral coarsening increases the separation of primary arms and

78 allows for further nucleation within the interdendritic regions and an eventual reduction in PDAS, as suggested in Figure 30, Figure 31, & Figure 32. This is similar to the argument for the reduction of grain size proposed by Maxwell and Hellawell for inoculant particles.[72] Figure 30, Figure 31, & Figure 32 also show increased Mg rejection into the interdendritic liquid, which acts to promote the nucleation and formation of an increased number of primary arms. Increased nucleation prevents overall coarsening and results in an overall finer microstructure. Another potential mechanism for forming an increased number of primary dendrite arms is when a tertiary arm grows in a parallel direction to the primary arm as shown in Figure 33. If the lateral coarsening is sufficient and ample space is provided in a region of reduced constitutional undercooling, it is possible for a tertiary arm to become stable in the competitive dendritic growth process and grow as an additional primary arm. Once this transition occurs, the newly formed primary arm will be indistinguishable from a nucleated arm when viewed far from the origin of the event.

Figure 33: Tertiary to primary transition mechanism.

StJohn et al. [71] and Chen et al. [86] observed the drop in constitutional undercooling described in Figure 31 and Figure 32 as solute partitions, however, neither provides a mathematical formulation as to the underlying mechanisms. The phenomenon described here is fundamentally different. Instead of examining the rejection of solute during solidification as done by StJohn et al. [69, 71], this study focuses on the effect of an overall increase in Mg solute content in an alloy on the dendritic growth velocity and subsequent PDAS.

4.4.4 Experimental Directional Solidification Results

The resulting directional solidification micrographs shown in Figure 34 and Figure 35 confirm the predictions made using the Gu model shown in Figure 29 and Figure 30 where the PDAS is shown to decrease with an increase in Mg solute content. The PDAS results for each alloy system can be viewed in Similar to the CA simulations, Figure 34 and Figure 35 show a reduction in PDAS for both the plane parallel to the growth direction as well as the plane perpendicular to the growth direction. The resulting PDAS confirms the reduction in PDAS occurs three dimensionally during the solidification process.

The microstructure in Figure 34 displays columnar primary dendrites with secondary side branches and Figure 35 displays equiaxed dendrites growing out of the page. Figure 34 &

Figure 35 also show a thinning of the width of the primary arms as the Mg solute content is increased due to the reduction in the dendritic growth velocity.

The reduction in PDAS seen in Figure 34 and Figure 35 can be described with the aid of

Figure 31 and Figure 32. Figure 31 and Figure 32b show that the solute enrichment ahead of the S/L interface increases with the increase in Mg solute concentration and reduces the liquidus temperature. The reduction in the liquidus temperature prevents solidification from occurring outside of the S/L interface and is the cause for the reduction in lateral coarsening as this region will remain liquid and unable to allow dendritic growth.

Figure 34: Refinement of directionally solidified dendritic microstructures viewed parallel to the growth direction with increasing values of Mg: (a) 0.5wt% Mg; (b) 1.02wt% Mg; (c) 1.78wt% Mg; and (d) 2.69wt% Mg.

As two dendrites nucleate and grow as shown in Figure 36, a region of liquid will exist between them. This liquid region will have a high concentration of solute near each S/L interface and a lower solute concentration away from the interface and in the center of the interdendritic liquid as confirmed in Figure 31 and Figure 32b. The drop in solute concentration in this region increases the liquidus while the actual temperature of the melt remains constant as illustrated in Figure 36b.

Figure 35: Refinement of directionally solidified dendritic microstructures viewed perpendicular to the growth direction with increasing values of Mg: (a) 0.5wt% Mg; (b) 1.02wt% Mg; (c) 1.78wt% Mg; and (d) 2.69wt% Mg.

This phenomenon allows nucleation of a new primary dendrite arm or a tertiary to primary dendrite arm transition. Thus, increasing the Mg solute concentration will also increase the number of new nucleation sites between dendrites and leads to an increased number of primary dendrite arms, hence the reduction in PDAS.

4.5 Primary Dendrite Arm Spacing Model Formulation

4.5.1 Solute effects on Dendrite Growth Velocity

The results shown in Figure 34, Figure 35 and Table 6 follow the GRF trend noted in

Equation 7, however, there are other deviations from the previously discussed models.

StJohn et al. [69] states the diffusion coefficient is proportional and the velocity is inversely proportional to the microstructural length scale as described in Equation 7.

Conversely, Gu et al. concluded that with the addition of Mg to Al-Si-Mg alloys, there was a reduction in lateral coarsening which was attributed to a drop in the normal dendrite growth velocity.[77] Using the constitutional undercooling argument as described in Figure 32 and the results of Figure 34 & Figure 35, it is evident that the growth velocity must be inversely proportional to size of the microstructural features for a given cooling rate.

4.5.2 Solute Diffusion effects of PDAS

Additionally, if the solute diffusion coefficient increases from alloy to alloy, more solute is rejected into the interdendritic region at a greater rate. As more solute piles up at the

S/L interface at an earlier time step, the normal dendritic growth velocity will slow at earlier time step and lead to a reduction of lateral coarsening. The earlier reduction in coarsening forces the primary dendrite arms to become thinner and creates a larger interdendritic region which allows for the nucleation of additional primary arms as described in Figure 7. Thus, if the diffusion coefficient is increased from one alloy to another, the growth velocity will slow at an earlier time step allowing for a larger interdendritic region, increased nucleation and an overall reduction in the PDAS.

4.5.3 Undercooling effect on PDAS

Other fundamental solidification factors that must be considered are the undercooling required for nucleation, thermal gradient and the time to reach a stable dendritic spacing.

First, the undercooling required for nucleation is affected by the environment at which solidification occurs. When more heterogeneous nucleation sites are present, the undercooling required for nucleation is lowered, signifying a direct relationship between required undercooling and PDAS. In Al-7.6Si-xMg Alloys, Mg acts as a substitutional element for all compositions examined, meaning that the undercooling required for all situations was considered constant. Cooling curves of the DS experiments were extracted,

85 and it was evident that the undercooling present was not significant and is shown in

Figure 37, indicating little undercooling was required for nucleation. This matches the findings by StJohn et al. who reported ∆푇푛 values as low as 0.2-0.5°C for Al-Ti alloys.[69]

Figure 37: Cooling Curve of Al-7.6Si-0.5Mg exhibiting no undercooling during directional solidification.

4.5.4 Thermal Gradient effect on PDAS

The thermal gradient was shown to have an indirect relationship with PDAS which matches the Hunt model and can be explained by considering a solid liquid interface. As the solid front extends into liquid, the liquid experiences a thermal gradient imposed by the surrounding environment. If the imposed thermal gradient is large, the cooling rate is less gradual as the liquid is drawn into a region during DS, which quickly drops below the liquidus temperature. Large thermal gradients allow for faster cooling rates, which in turn, limit or prevent recalescence and refine the structure. 86

4.5.5 Competitive Growth effect on PDAS

The final parameter examined is the time required to reach a stable dendritic spacing. As the dendrites grow the PDAS will fluctuate due the competitive growth process, and the length of time required to reach a stable PDAS depends on the surrounding environment of the dendrite. If a large cooling rate is imposed, typically accompanied by a high thermal gradient, the dendrite will have little time at elevated temperatures to coarsen, leading to large interdendritic regions, increased nucleation and a smaller PDAS.

However, if a melt experiences a low cooling rate, the time for the primary dendrite arms to reach a stable spacing is increased, and there is more time for growth and coarsening of the primary arms, resulting in an increase in the PDAS. Such evidence indicates that the time required to reach a stable dendrite spacing must be directly proportional to the

PDAS.

4.5.6 The PDAS Model

The culmination of the above trends allowed the development of a new model to accurately describe the PDAS in Equation 15. Each of the terms were weighted evenly excluding the growth velocity and constitutional undercooling which were shown to have the greatest effect on reducing the lateral coarsening.

푘푣2∆푇2 휆 = 푛 ∗ 푠 Equation 15 퐺퐷푄

Equation 15 concisely summarizes the effect of various solidification factors on the final primary dendrite arm spacing in Al-Si-Mg alloys. The trend and effect of the major 87 modifying components of Equation 15 are highlighted in Figure 38 and the results to the experimentally observed PDAS are shown in Figure 39a.

Figure 38: PDAS Model flow chart describing the major solute effects of increased Mg solute in Al-Si-Mg alloys.

Figure 39a shows that the newly developed model provides a greater degree of accuracy for PDAS compared to other commonly used models. The StJohn (DSJ) model was developed for the prediction of grain size, however, it was compared to the PDAS to note trends. The values used for 푓 amd 𝜌 were 1% and 1.3 respectively, and were based on the

Interdependence Theory.[69] While the DSJ model shows a similar trend in the decrease of microstructural length scale with increasing solute content, it greatly over predicts the behavior at low Mg concentrations.

(a) (b) Figure 39: (a) PDAS predictions of various models; and (b) Dendrite Growth velocity of various models compared to calcualted velocity for measured PDAS.

Table 6: Experimentally measured PDAS compared to the present model.

0.5% Mg 1.0% Mg 1.75% Mg 2.7% Mg Longitudinal PDAS 511 368.9 265.6 240.2 (μm) Transverse PDAS (μm) 556 360 243 228.6 Average PDAS (μm) 533.5 364.4 254.2 234.4 Model PDAS (μm) 535.1 359.2 222.8 190.3 Exp. SDAS (μm) 52.0 31.8 30.4 28.9 89

On the other hand, the PDAS prediction by Hunt model has good agreement above

1.75wt% Mg, however, at lower levels of Mg, it considerably under predicts the PDAS.

The present model represented in Equation 15 shows a better degree of accuracy across all levels of solute content. While the other models describe the decrease in PDAS with an exponential decay, the current model follows a generalized logistic function which better captures the behavior for lower levels of Mg. The accuracy of the model described in Equation 15 indicates that Mg solute effects in Al-Si-Mg alloys play a major role in microstructural development. Further, the accuracy proves the mechanisms at play as described above. The increase of Mg will result in a local drop in constitutional undercooling and dendrite growth velocity, alloying for increased primary dendrite nucleation and a refined microstructure.

4.5.7 Potential Outcomes of Increased Mg Content

Refinement of the PDAS will inherently reduce the SDAS, shown in Table 2 and is often viewed as a strengthening mechanism resulting from increased barriers to dislocation movement [87]. Decreasing the PDAS, however, also increases the number of barriers for dislocations and it is quite likely that the combination of reducing both the PDAS and

SDAS simultaneously will add a previously unaccounted strengthening mechanism,

𝜎퐷퐴푆, to yield strength models commonly stated in Equation 16

𝜎푌푆 = 𝜎푖 + 𝜎퐺퐵 + 𝜎푒푢푡푒푐푡푖푐 + 𝜎푆푆 + 𝜎푃푃푇 + 𝝈푫푨푺 Equation 16

Figure 39b compares the dendrite growth velocity of this model to a recent publication using CA for multicomponent systems. The Chen model, contains no description of

PDAS while the drop in growth velocity is attributed to a slower diffusion in the liquid causing an increased solute concentration gradient at the S/L interface.[87] Although the trend is correct and explanation has merit, the Chen model shows a vast over prediction of the reduction in growth velocity and will likely result in a greatly refined microstructure compared to experiment.

Another potential benefit of the noted reduction in PDAS is refinement of intermetallics.

Caceres et al. stated a reduction in overall dendritic microstructure will reduce the size of intermetallics.[35] Consequently, an increase in Mg solute content will reduce the PDAS and will trap the intermetallics within the interdendritic region, forcing them to a finer length scale, effectively refining them. Such refinement has the potential to reduce the drop in ductility that arises due to coarse Fe containing intermetallics.[66, 88] Figure 36b also shows an increase of Mg content above 2.5% provides little to no additional refinement for PDAS experimental data and models displayed. Although the grain size can be reduced with additional Mg beyond 2.5%, it is not suggested due to the relatively low Hall-Petch coefficient of aluminum alloys and expense of additional alloying. Such an observation indicates that the max alloying content of Al-Si alloys should not exceed

2.5wt% for mechanical strengthening purposes or for the refinement of intermetallics.

4.6 Mg Solute Effect Conclusions

In summary, a 3D CA model was used to provide insights into a new mathematical formulation to describe the primary dendrite arm spacing due to alloying solute effects. It was shown that an increase in Mg solute within Al-7.6-xMg alloys greatly decreases the

PDAS by reducing the available undercooling and in turn reduces the dendritic growth velocity. The drop in growth velocity creates large interdendritic regions where the solute concentration reduced and allows for increased interdendritic nucleation equating to an overall refined microstructure. The phenomenon was described with a novel model and shows increased accuracy specifically in the lower Mg containing Al alloys compared to other commonly used models. The present model suggests that an increase in Mg content offers a previously neglected strengthening mechanism that is often not fully realized due to the lack of visible primary arms, and can offer a new level of incremental increase in strength while mitigating ductility loss. Such a revelation can allow elevated concentrations of Mg in aluminum alloys, up to 2.5wt%, for enhanced strength and an overall density drop for lightweight applications. This new growth model also provides a critical link between solidification microstructure as well as thermodynamic and kinetic factors of Al-Si-Mg cast alloys in ICME applications of lightweight castings and other solidification products. A graphical summary of the Chapter 4 is displayed in Figure 40.

Figure 40: Graphical summary of Chapter 4. The simulation and experimental work combine to show a decrease in the PDAS explained by the proposed PDAS equation.

Chapter 5: Oxide Entrainment and Oxide-Related Defects in Cast Aluminum

Chapter 5 discusses the formation of aluminum oxide inclusions and subsequent porous defects in cast structures. The chapter is divided into three major sections. In the first several sections the general formation of oxide inclusions is discussed and a model is built to predict the final location of the entrained defects. In the following sections the model is validated using first a series of simple geometric molds and then finally validated on a complex cast component for the automotive industry. Excerpts of this chapter were taken from the author’s publication in AFS Transactions: Prediction of

Entrained Oxide Inclusions and Oxide Induced Defects during Directional Flow in

Aluminum Castings.

5.1 Oxide Film Formation and Entrainment

5.1.1 Oxide Formation in Molten Aluminum

Entrained oxide inclusions are some of the most common and most detrimental defects that reside in castings with numerous studies citing a severe reduction in the tensile strength, fatigue strength and ductility.[47, 48, 50, 89, 90] The prevalence of oxide inclusions or bifilms in cast structures can be attributed to two factors: the rapid formation of oxides, and the stability of the oxides within the melt. Whenever the melt is

94 exposed to a gaseous environment such as air, the molten aluminum will instantaneously react with the air and form an oxide layer.[46, 91] Thiele has shown that in as little as 5 seconds at 700°C the aluminum oxide, or Al2O3, layer can be as thick as 24nm.[46] The newly formed oxide film often becomes entrained into the melt during ladle transfer, adding charge material, or during the pouring process. Alternatively, in alloys that contain greater than 2% Mg, MgO oxides films can form on the surface and are equally stable.[48] Once entrained, the oxides are extremely difficult to remove, as the they are thermodynamically stable and completely insoluble within the melt.[90] Once within the melt the bifilm acts as a substrate for solidification and presents itself in many forms as shown in Figure 16 and Figure 41.

(a) (b) Figure 41: Bifilms trapped with the solidified aluminum material (a) Aluminum matrix (b) Al Matrix – α interface (c) Primary Fe phase (β).[50]

Fluxing or degassing can be used to remove a majority of the oxides that form on the surface, however, during pouring, fresh oxides will instantaneously reform on the surface 95 of the melt pool as it is exposed to the atmosphere. These new oxides, often called ‘young oxides,’ due to the relatively small thickness, are then entrained as the molten material fills the mold. This process suggests that that entrained oxide inclusions are an unavoidable defect in aluminum castings.[92]

5.1.2 Entrainment Mechanisms

The thermodynamically stable oxide film on the surface of the molten aluminum does not harm the melt. Instead it acts as a protective layer to the molten aluminum below the oxide film. However, when the surface of the melt is disturbed, the oxide film will fold over itself and the solid film will be entrained below the surface. This mechanism and other common entrained defects are described in Figure 42. The structure of the entrained inclusions consists of two solid layers of film separated by a void of air or gas trapped between them. Due to the inability of the solids to re-bond, the inner surfaces of the bifilms remain permanently un-bonded and the void between them is permanently entrained.[93] The gaseous volume entrapped within the bifilm then becomes compressed into the thin tubular geometry most notably seen in Figure 42b Figure 42c. The geometry of the opening of the bifilm then offers an extremely small wetting angle and when combined with the back pressure of the compressed gas, the inner of the bifilm is often not back filled with molten aluminum upon filling. Conversely the outer portion of the bifilm is wetted to the molten aluminum below the surface and acts as a substrate for nucleation and solidification.

Figure 42: Various oxide entrainment mechanisms where the black lines indicated oxidized surface. (a) Folding over waves entraining oxides, (b) An entrained bifilm, (c) gas precipitation within a bifilm and initial stage of bifilm unfurling, (d) an internal pore with an oxidized surface, and (e) a bubble trail.

The oxide entrainment mechanisms are simple in nature, but are difficult to avoid. One of the most common ways for oxide films to become entrained below the surface is during movement or ladle transfer of the molten material. As the molten material is transferred for pouring, the surface is perturbed and small waves form as seen in Figure 42a. As the waves crash back into the surface, the surface film folds over itself and the double sided film structure of the bifilm is created, while the momentum of the wave pulls the bifilm beneath the surface, effectively entraining the structure. Bifilms can also be entrained by the addition of charge material to the melt. As additional material is added, the solid charge material will break the surface oxide film and drag the film below the surface.

During this process the solid film from the surface will tend to wrap itself around the

97 charge material and fold into a network like structure, increasing the surface area of the defect.

The last major mechanism in which oxides are entrained occurs during the pouring stage when the molten metal enters the mold. As the molten metal exits the crucible the previously non-oxidized material below the surface is exposed to the environment. The newly exposed material forms fresh young oxides which are then entrained due to turbulent flow as the molten material folds over itself inside the mold. Campbell has shown that turbulent flow occurs in aluminum alloys when the gate velocity exceeds

0.5m/s highlighting the need for proper molding design.[93]

5.2 Oxide Inclusion Detection and Prevention

5.2.1 Entrained Oxide Detection

Entrained oxide inclusions are often characterized by their size and are termed either

Young or Old Oxides. Old oxides range from 1-5mm in thickness and form when the molten surface is exposed to elevated temperatures for an extended period of time. Young oxides range from 10 - 500nm and form during the pouring process.[48] In general, old oxides can be completely removed from the melt prior to pouring and are no longer present in the final casting. Removal of old oxides is often done by drossing the surface prior pouring, pouring through a filter, and using fluxing agents. If old oxides do enter the cast structure, it is often difficult to detect them non-destructively. Extremely large oxides will occasionally appear on x-ray or micro computed tomography (micro-CT), however, online inclusion detection techniques such as LiMCA are rarely used in mass production

98 of aluminum castings.[94, 95] Thus, old oxides are often only identified after a component has failed and the fracture surface presents the entrained oxide.

Young oxides are much more prevalent in final cast structures and are much more difficult to detect. The current maximum resolution for micro-CT is ~400 nm making it nearly impossible to locate all entrained young oxides. Furthermore, the same issue as with old oxides occurs, micro-CT cannot be used for online oxide detection in mass production and oxides are often only detected in a destructive manner.

5.2.2 Oxide Induced Defects

Both young and old oxides also have large affinity to induce other forms of defects including gas porosity and shrinkage porosity. Campbell argues that the pressure required for gas pores to form either homogeneously or heterogeneously is so great that the practicality of such nucleation rarely occurs.[48, 90] Instead the non-wetted inner of the bifilm offers a perfect initiation site for the excess gas to reside with limited formation energy. Excess gas is able to permeate the solid and inflate or unfurl the bifilm as shown in Figure 42 (Area C). If sufficient gas is within the melt, the bifilm can be completely unfurled into a spherical morphology and give the appearance of a gaseous pore, though the surface area of the pore will be entirely oxidized. Similarly shrinkage porosity requires a critical drop in the metallostatic feeding pressure, and the easiest initiation site for shrinkage is in the presence of a bifilm. As the melt solidifies the dendrites will begin to pull away from one another. Thus, the presence of the crack-like structure of the bifilm offers a site for shrinkage initiation and each half of the bifilm is separated and creates an irregular shaped void. If this process were to occur without the presence of a bifilm, there

99 would be a significant amount of formation energy and pressure would be required as the solid would need to physically separate apart the surrounding solidified metallic material.

In the case that excess gas within the melt or casting is able to heterogeneously nucleate near the mold wall, it is still likely that this pore will contain some level of oxygen inside.

The oxygen trapped in the pore with will then instantaneously oxidize the surface area of the pore as described by Thiele and shown in Figure 42 (Area D). After oxidation, the gas pore will then float towards the top of the melt or casting due to its low density and in its wake leave a bubble train as shown in Figure 42E. The bubble trail left behind will also be made up of small defects with included surface areas.

5.2.3 Reality of Oxide Inclusion Defects

The culmination of the entrained oxides as well as each of these oxide induced defects can then lead to a greater volume of the defects within the casting. The greater volume of defects will then lead to a further degradation of mechanical properties as Caceres has shown in previous publications.[42]

For these reasons, a great deal of research has been conducted to create standards for mold design to prevent/minimize oxide entrainment.[90, 93, 96–98] Nonetheless, oxides are entrained in almost all castings and the final location of the entrained oxides and oxide induced defects within the casting is often unknown. Therefore, a new method for predicting oxide entrainment is needed for the design and manufacturing high-quality cast aluminum.

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5.3 Existing Oxide Inclusion Modeling Techniques

Several models have been developed to solve the issue of locating entrained oxides during pouring and mold-filling, most of which are based on the basic principles of entrainment established by Campbell.[93] These principles include the liquid gate velocity, Weber Number, Froude Number and the free surface of the fluid. Each of these principles or numbers have often been used as a criterion or as a “go-no-go” gauge to whether oxide entrainment occurs or not, with no prediction on entrainment quantity or locations.

The first breakthrough in determining the locations of oxide entrainment came from tracking the free surface of the liquid during pouring and mold-filling. Since, it is known that only the free surface can oxidize, the free surface can be followed through solidification, and the final location of the defects can be determined. Smoothed Particle

Hydrodynamics (SPH) was one of the first numerical methods to employ this theory for oxide defect prediction. SPH functions by discretizing the liquid into spherical particles that are able to simulate the pouring process. During pouring, only the particles that are on the free surface and exposed to the environment are oxidized and grow at a constant prescribed rate as shown in Figure 43. The oxide growth rate is based on a constant oxidation rate and is then followed through solidification.[99] Unfortunately, this method has a major drawback due to the resolution or size of the particles which ranges from 5-

12 mm.[100–102] This resolution is several orders of magnitude larger than the young oxides and this method will not capture the true size of the entrained oxides; likely over predicting the amount of oxide present.

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Figure 43: Oxidation of particles during pouring using the SPH method. [101]

A more rigorous model for determining the final locations of entrained oxides was developed by Reilly et al. and is called the Oxide Film Entrainment Model (OFEM).[103]

This approach uses a volume of fluid technique in combination with Boolean logic to determine when the fluid flow is turbulent enough for entrainment to occur. When entrainment does occur, particles are created and inserted into the fluid and are tracked through solidification. The created particles range from 25-31μm which is more realistic, though it will not capture or accurately depict all entrained oxides. The locational OFEM prediction is shown in Figure 44, however, the accuracy is still in question for the reasons mentioned above. Further hindering the OFEM methodology, the computation time is greatly increased with increasing resolution for full size castings, limiting the industrial usage of the OFEM.

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Figure 44: Predicted final location of oxide particles in a casting using the OFEM method.[103]

The current state of the modelling is quite successful at determining whether a casting will contain entrained defects; however, predicting the locations of the entrained oxide defects is extremely difficult. Moreover, no model exists that is able to accurately predict both the quantity and locations of entrained oxide defects while remaining computationally efficient for industrial scale castings.

5.4 Inclusion Induced Defects Model Methodology

In order to create a computationally efficient model that can be used to predict the location and severity of entrained defects and eventual oxide induced defects, the fundamentals set forth by Campbell and others in literature must be re-examined.

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5.4.1 The Weber number and Gate Velocity

The first parameter to examine is the Weber number, We, which is defined in Equation 17 where 𝜌 is the material density, 푣 is the liquid velocity, 푙 is the hydraulic radius of the wall thickness, 𝜎 is the liquid surface tension, 푔 is the acceleration due to gravity and h is the characteristic wave height. The We is a dimensionless number and is used to describe when a fluid transfers from laminar to turbulent flow. The We is dominated by the gate velocity and the wall thickness of the casting. An increase in velocity results in an increase in the amount or turbulence and a larger channel width provides more room for sloshing and increases the number of entraining events, thus a larger velocity and wall thickness result in greater turbulence.

휌푣2푙 푊푒 = Equation 17 휎

This dependence on velocity falls in line with Campbell’s assertion that there is a critical velocity above which entrainment will occur. However, unlike the critical velocity criterion, the We accounts for both the casting geometry and velocity and better describes the mold-filling conditions. The We is thus more insightful than the velocity criterion, but it only can be used to determine when entrainment will occur, not where the entrainment will occur.

5.4.2 Oxide Severity Term

To determine where the entrainment events occur, the free surface must be considered.

As described previously, oxidation of the melt only occurs on the free surface and if it 104 can be tracked, it can provide information on the location of the entrained defects. Thus, by combining the free surface with the We, the location at which entrainment events occur can be determined. However, as mentioned previously, oxides vary in size and thickness, with the thickness increasing with exposure time. Consequently, an oxide severity term was developed and is shown in Equation 18 where 퐹푠 is the free surface, and t is the amount of time the free surface has been exposed to the environment. Now, the location of the entraining event and the severity, or relative size, of the oxide entrained are known, but unfortunately the units of the combined term from Equation 17 and Equation 18 is [m2s] which does not provide a physical meaning and cannot be validated.

푂푥 = 퐹푠 ∗ 푡 Equation 18

5.4.3 Effect of Shrinkage Porosity

Aside from oxides, the most common defect in cast structures is the presence of shrinkage and gas porosity. Shrinkage porosity results from a lack of feeding of molten material that occurs during solidification. Limited feeding will result in insufficient pressure and small voids or pores will form. The most common criterion used for predicting these pores was developed by Niyama et al. and the critical pressure drop at which this occurs is shown in Equation 19 where the 푝 is the pressure, 푇̇ is the instantaneous cooling rate and G is the thermal gradient.[104]

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푇̇ Δ푝 ∝ Equation 19 퐺2

As the magnitude of the pressure drop increases from elevated cooling rates or low thermal gradients, pores will begin to form, often nucleating on pre-existing bifilms.[90,

105] Excess gas within the melt is also able to preferentially diffuse to these low energy voids. Once near the bifilm, the gas permeates the solid film and fills the void causing the bifilm to inflate and take on a spherical morphology. The entrapped air within the void then acts to further increase the thickness of the oxide, and the surface area of all pores within the structure will have some level of oxidation as shown in Figure 1D. Hence, it can be ascertained that shrinkage plays a role in the number and shape of the entrained bifilms.

5.4.4 Oxide Entrainment Number

To determine the correlation between porosity and bifilms the ratio in Equation 19 must be examined. Gu et al. has shown that the number of pores and morphology is dependent on the thermal surroundings of the melt. Specifically, Gu et al. was able to show that as the cooling and solidification rate increased, the total number of pores increases, but the average size of individual pores decreases.[106] When applying this to bifilms, it can be seen that elevated solidification rates will increase the overall volume of the entrained defects and can be considered in the determination of the total volume of inclusions in the casting. If the ratio in Equation 19 is altered to 푇̇ /퐺 , it is now equivalent to the solidification rate and it can be combined with Equations 17 & 18 to yield Equation 20 where Φ is defined as the Oxide Entrainment Number, OEN. 106

푊 푂 푇̇ 훷 = 푒 푥 Equation 20 퐺

The units of Equation 4 are equivalent to [m3] and correlate to the total volume of entrained oxides present. This is reasonable considering each term has a specific contribution to the determination of the total volume of entrained defects. The oxide severity term in Equation 2 tracks the free surface which is only entrained when the We indicates turbulent flow and provides the location of the entrainment. The final term is the solidification rate which correlates to the number of pores in the system. When these values are combined as in Equation 20, the total volume of entrained defects is calculated. Equation 20 provides a computationally efficient way to follow oxide entraining events and the location of entrained defects. This can be run with common commercial codes, such as ProCAST, MAGMA, or FLOW-3D.

5.5 Directional Flow Casting Design of Experiments

5.5.1 Optimal vs Poor Filling Geometry Castings

To validate the model developed in this study, two different castings were designed for simulation and experimental validation and are shown in Figure 45a & Figure 45b. Both castings contain cylindrical test coupons that are 100mm in length and 8mm in diameter.

The first design shown in Figure 45a was termed the preferred filling mold, and was designed to follow Campbell’s 10 rules of casting with bottom feeding, along with appropriate sprue and gating ratios. These design elements of the preferred filling mold will give it a quiescent, laminar flow with minimal chance for entraining events.

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Conversely, the design in Figure 45b possesses less than optimal filling conditions and was termed the “poor filling” mold. The poor filling mold has a non-tapered sprue, hard corners throughout the cavity which will induce splashing and folding of the melt front or free surface leading to increased entrainment. Further, the poor filling mold has a water- fall gate that will lead to large turbulence at the gate after which the fluid front will divide before re-converging which is often considered a worst case scenario for melt flow. In each casting design, the cylinders or test coupons will fill unidirectional (from the bottom up) allowing the effect of directional flow on Equation 20 to be understood. The two designs provide an opportunity to validate the model and Equation 20 for the best/worst case designs.

(a) (b) Figure 45: (a) Preferred filling mold designed for optimal filling. (b) Poor filling mold designed to create increased levels of entraining events.

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5.5.2 Implementation of the OEN within ProCAST

Equation 20 was implemented within the casting software ProCAST to follow the fluid dynamics during the casting process. ProCAST was setup using a 1mm tetrahedral mesh within the gate, and the cylinders of the preferred and poor filling molds, while a global

2mm mesh was used in the remaining portion of each model. The flow rate used for filling was 0.45kg/sec and the mold material was set as silica sand with a heat transfer coefficient of 500 W/m2K. Once the simulation completed, The OEN was inserted through the Metallurgical Tools function within ProCAST and the simulation is rerun.

The results of the OEN only produce location specific volume vs. time plots of oxide generation which were then transferred to MATLAB for further analysis. Within

MATLAB, the volume vs time plots are integrated over time at each location to obtain the total volume of oxide generation at each location. For the case of the cylinders, the

MATLAB integration and analysis was performed at 1 cm increments along the longitudinal axis.

5.5.3 Casting of Cylindrical Molds

Both the preferred mold and poor filling mold were cast with aluminum A356 using sand molds. Primary A356 ingots were melted in an induction furnace using graphite crucibles coated with boron nitride. Prior to casting, dross was skimmed from the surface of the melt and prepped for casting. The sand molds were made using a sodium silicate binder and were allowed 24 hours to dry prior to casting to eliminate any chance of gas vaporizing and entering the molten material in the mold cavity during casting.

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Once each of the designs was cast, the test coupons were sectioned along the longitudinal and transverse axis for metallographic examination. When sectioning along the transverse direction, samples were taken every 10mm and were mounted for polishing with the cross section face down. The first cross section was taken at the bottom of the cylinder and was termed the 0cm cross section. These cross sections were then cross compared with the data obtained from the ProCAST simulation of the OEN. After polishing, the samples were viewed under an optical microscope and ImageJ software was used for analyzing the resulting micrographs.

5.6 Simulation Results and Discussion

Both the preferred filling and poor filling molds were simulated using ProCAST and examined using the model established in Equation 20.

5.6.1 Velocity Consideration during Mold Filling

The fluid front velocity has already been described to be a key variable in determining if turbulent activity will occur and has been shown to have a strong influence on the Weber

Number and subsequent OEN. The fluid velocity serves as an initial assessment to determine if turbulent flow will occur during filling and can be seen for both molds in

Figure 46.

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(a) (b)

(c) (d) Figure 46: Fluid Velocity for the Poor filling Mold (a,c) compared to the velocity of the Preferred Filling Mold (b,d) at various times. The color scale varies from 0m/s (purple) to 0.6m/s (red).

In an ideally designed casting, the fluid front velocity will remain below 0.5m/s during filling to prevent entrainment events from occurring. Figure 46a & Figure 46b show that both molds have velocity exceeding the 0.5m/s criterion in the sprue and the runner region. This is expected as the aluminum falling just several inches will exceed the maximum velocity for entrainment as calculated by Campbell.[93] What is more important is the gate velocity or the velocity of the molten material entering the cast structure, which in the present case is the cylindrical rods. Once the fluid front reaches the gate, a slow quiescent flow is desired to prevent any chance for entrainment. Figure

46c & Figure 46d display the gate velocity of the fluid as it is entering the casting and 111 fills the cast structure. Figure 46c shows large velocities in the entirety of the cylinder coupons indicating entrainment of defects is likely, whereas Figure 46d shows a slow quiescent filling velocity in the cylinder sections with a laminar flow. This initial check confirms that the design intent of both molds is accurate and the fluid flow will be mostly turbulent for the Poor Filling Mold and laminar for the Preferred Filling Mold.

5.6.2 Oxide Severity Term

The second term considered in Equation 20 is the oxide severity. The oxide severity term is a cumulative function found within ProCAST and tracks the location of the free surface upon solidification. The final time cumulative step for the oxide severity term for both molds can be seen in Figure 47. As expected, Figure 47 shows little to no free surface in the sprue and most of the runner for both mold designs. This is because the free surface, by definition, remains at the fluid front and the material solidifying in the sprue and runners has had little to no exposure to the environment prior to entering the mold. Figure

47 also illustrates that the regions with a greater magnitude of the oxide severity term are located in the last-to-fill regions. In the poor filling mold this is the majority of the cylinder or test coupon which shows elevated levels throughout the cylinder with the highest magnitude region being located at the top of the cylinder. This would follow the conventional wisdom that the last-to-fill or last-to-solidify regions would contain the defected material, and is one of the reasons why risers are used in casting design to locate the defects in the unused part of the casting. The preferred filling mold shows a good example of locating the excess free surface in the nonessential regions of the casting including the runner and excess gate regions. There are some elevated levels at the top of

112 the cylinder coupons in Figure 47b, however, a majority of the cylinder coupons are clean, with limited free surface.

As previously described, the free surface is only harmful to the casting when it is entrained and when viewing Figure 46b &Figure 46d, the gate velocity is quite low and the free surface is unlikely to entrain in the preferred filling mold. This would indicate that the free surface shown in Figure 47b for the preferred filling mold is likely located at the surface not in the interior of the casting. The opposite is true for the poor filling mold where the velocity is elevated during filling and when combined with excess free surface, it is likely many oxide entraining events will occur and the free surface oxides have become trapped in the interior of the casting.

(a) (b) Figure 47: Oxide severity term for the (a) Poor Filling Mold and the (b) Preferred Filling Mold. The scale bar spans from 0 (purple) to 3.0 (red) and applies to both (a) and (b)

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5.6.3 Thermal Impact and Oxide Induced Defects

The final term to consider in the newly proposed model is the thermal term as it relates to the formation of pores in the casting. Theoretically, the Niyama criterion states that pores will form in regions of low thermal gradients and high cooling rates which lead to a large drop in the feeding pressure. The individual terms that make up the thermal term are shown in Figure 48. Figure 48a shows that in all cylinders, the thermal gradient is the lowest in the center of the cylinders and largest at the ends of the cylinder coupons. This is an intuitive result as the edges of the cylinders are able to dissipate heat faster as they have more surface area contacting the mold and results in an increased thermal gradient.

The next term to consider is the cooling rate which is shown in Figure 48b. Figure 48b shows that the cooling rate follows the thermal gradient with elevated cooling rates at the ends of the cylinders and lower magnitudes near the centers.

(a) (b) (c) Figure 48: Individual terms that make up the thermal term for the OEN. (a) Thermal Gradient [C/cm] (b) Cooling Rate [C/s] (c) Thermal Term [Cm/s].

Individually the thermal gradient and cooling rate do not provide an obvious indicator of the drop in pressure required for pore formation, and require the examination of the 114 thermal term shown in Figure 48c. The thermal term shows that the thermal gradient is more dominant than the cooling rate and the majority of the pores will exist in the centers of the cylinders of both mold designs when filled using directional flow. This occurs due to the relatively consistent cooling rate throughout the casting, and the greater variance in the thermal gradient across the length of the cylinders. This outcome does not follow conventional wisdom which would state most of the porosity would float to the top of the casting or would occur at the last to fill stages similar to the oxide severity term in Figure

47. Thus, the thermal term is able to provide a strong indicator as to the location of pore initiation which can be used to calculate the number of oxides present in the final casting.

5.6.4 OEN Prediction

Each of the terms above provides a good indicator of when and where defects might be located within a casting, however, as shown in Figure 46, Figure 47, and Figure 48 there is not a clear conclusion on where and how severe the entrained defect content will be.

This illustrates the need for the Oxide Entrainment Number to predict the volume and location of entrained defects. Without the OEN, individual entrainment terms can be misleading and can lead to poor design of patterns/molds. The results of the numerical simulation using Equation 20 can be seen in Figure 49.

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(a) (b) Figure 49: The instantaneous Oxide Entrainment Number (OEN) for both the (a) Poor Filling mold and (b) Preferred Filling Mold. The scale bar spans from 0 (purple) to 1000 (red) and applies to both (a) and (b).

The contour plot in Figure 49 displays the instantaneous volume generation of oxide content for both mold types. Figure 49 shows a larger generation in the poor filling mold compared to the preferred filling mold and has a strong resemblance to the velocity contour plots in Figure 46 highlighting the importance of velocity term. In order to convert these instantaneous values in Figure 49 to cumulative values, the instantaneous data was integrated over time to obtain the final OEN or volume of oxide and other induced defects at each element within the simulation. After obtaining the total volume generation, transverse slices, or cross sections, were taken every centimeter along the cylinder and the average OEN throughout the cross sections was calculated. The resulting values are shown in Figure 50 and depict how the total volume of entrained material changes over the length of the cylinder.

Figure 50 confirms that the total volume generation of the poor filling mold is greater than the preferred filling mold. However, the ends of the cylinders (0-1cm & 7-9.5cm)

116 show relatively low and similar volumes for both molds. These low volumes are likely due to larger thermal gradients at the ends of the bars, while the tip of the cylinder (7-

9.5cm) will have a relatively lower fluid velocity compared to the rest of the filling.

Figure 50: The total volume of entrained oxide at each transverse slice along the vertical axis of the cylinders in the Poor Filling Mold and the Preferred Filling Mold.

5.7 Experimental Validation

Upon completing the examination of the OEN, the same mold designs in Figure 45were prepared using sodium silicate bound sand and arranged for casting with aluminum

A356. Following casting, transverse cross sections were examined at every centimeter along the cylinder for both mold types to compare the oxide content and location to the

OEN prediction. Selections of the transverse cross sections are shown in Figure 51. The defects seen in Figure 51 are two-dimensional making it impossible to calculate the true volume of the oxides present without making assumptions. For this reason, a constant oxidation thickness of 500nm was assumed for all defects present in the cross section.

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This assumption was employed as it is often not possible to view oxide inclusions using standard microscopy methods. However, it is known that oxide inclusions are often the precursor to, or directly cause the initiation of porosity defects within the system. Thus, it is reasonable to conclude that each of the defects shown in Figure 51 will have a minimum oxidation film along the surface area of the defect similar to what is shown in

Figure 42.

The size of 500nm thickness was chosen as it is a common size of young oxides present in castings, and it is likely that a majority of the large, old oxides are eliminated during melt preparation. The thickness assumption allows the total volume of the included oxide volume in combination with the oxide induced defects to be calculated by multiplying the surface area of each defect by the thickness so it can be compared to the OEN.

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Figure 51: Micrographs of the transverse cross sections of the (A-D) Poor filling Mold and the (E-H) Preferred Filling Mold. The positions of the transverse sections are (A,E) 2cm, (B,F) 4cm, (C,G) 6cm, (D,H) 9cm.

Returning to Figure 51 it can be seen that in general there are lower quantities of defects in the cross sections taken near the ends (Figures A, D, E and H) compared to the centers

(Figures B, C, F and G). These results qualitatively match the predictions by the OEN shown in Figure 50. Additionally, Figure 51 shows that the model correctly predicts that there is not a large disparity in the number of defects for the two different types of molds.

Though these qualitative results are in good agreement, the quantitative volume of defects in the cylinders have some differences which can be seen when comparing the

OEN calculation of defect volume in Figure 50 to the experimentally measured defect volume in Figure 52. Figure 52 shows a low value of defects observed at the two ends of the bar (positions 0 and 9.5cm) with the centers of the bars having a relatively constant

119 defect volume in the centers of the bars. Figure 50, however, predicts a maximum defect volume between the 4-5cm locations of the bar.

Figure 52: Experimentally measured defect volume for both mold types.

5.8 Effect of Gas Volume on the Oxide Entrainment Number

The disparity between the OEN prediction and the experimentally measured defect content is the likely result of not considering the volume of gas within the aluminum melt. It is well understood that liquid aluminum has a high solubility of gaseous product that upon solidification is trapped within the casting will precipitate out as a porous feature. As previously described, these gases are able to permeate the solid oxide film and cause the bifilm to unfurl and inflate. The extent to which the process can occur is obviously determined by the amount of gas trapped within the casting. When more gas is present, more bifilms will be unfurled and cause an increase in the overall volume of

120 defects. Thus, the OEN requires an additional term to account for the volume of gas present in the casting.

5.8.1 Morphological Size of Porous Features

The quantity of gaseous product within a cast structure is often determined using an

Archimedes test. For aluminum melted in an a standard foundry environment the gaseous product is often found to range from 0.3-0.4ml/100g Al or 0.8% volume fraction.[106]

The morphology of the pores that precipitate within the microstructure has been shown to be dependent upon the cooling rate and solidification rate as shown in Figure 53. As the solidification rate increases, the number of pores is shown to increase while the average pore diameter of each pore decreases.[106] This phenomenon will cause the total surface area of the defects in the microstructures to increase. The increased surface area is then oxidized due to the gas within the pore, which in turn, increases the total volume of entrained oxide inclusions. When examining Figure 48, it can be seen that there is an increased solidification rate at the center of the cylindrical bars which explains the spike in defect volume in the shown in Figure 50 and Figure 51.

When using this logic, it must be stressed that the extent to which the bifilms can become unfurled or inflated is limited to the gas content within the melt. Even if more oxide inclusions exist, they are only inflated if sufficient gas is present to inflate them.

However, if more bifilms are present, it is likely that more pores will be present in the final casting as gaseous content within the melt will have a shorter distance to travel prior to porous initiation upon a bifilm.

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Figure 53: Effect of cooling rate on morphological size of pores formed in aluminum alloys (a,d) 50C/s (b,e) 10C/s (c,f) 5C/s.[106]

5.8.2 Development of the Entrapped Gas Volume Term

In the event that a gas pore is able to nucleate heterogeneously without the presence of a bifilm, it is likely that the pore will possess a lower density than that of the melt and the pore will float towards the top of the casting. Thus, when predicting the final location of included content, the volume of the gas trapped within the melt must be accounted for in a manner that accounts for oxide unfurling as well as heterogeneous pore floatation. In other words, the OEN should have an increased prediction of defect volume at the top portions of the cylinder while limiting the defect volume at the centers of the bars for a directionally filled casting. A function that best fits this description is a simple parabolic function as shown in Equation 21.

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푔 = 푣푥2 + 푏 Equation 21

Where g is the entrapped gas volume term or oxide induced defect term, v is the volume fraction of gas divided by 10, x is the vertical position of the directionally solidified cylinder and b is a fitting term. The process of applying the entrapped gas volume term is displayed in Figure 54. The entrapped gas volume term was centered at a vertical position of 4cm as this was the maximum defect volume observed in Figure 49 and it was only applied between vertical positons 3 thru 9.5cm. The entrapped gas volume term was not applied below 3cm as there is no increase in the defect volume at the bottom of the bar that will occur from the flotation of any heterogeneously nucleated pores. After applying the entrapped gas volume term to the OEN, it can be seen in Figure 54c that the OEN now provides an extremely accurate prediction of the volume of defects. It should be noted that the entrapped gas volume term applied here has only been validated on casting that are filled directionally with the two molds in Figure 45. If a complex casting with multi-directional flow were to be examined, it is likely that the entrapped gas volume term or oxide induced defect term would need to be altered, though the general principles of oxide entrainment and oxide induced defect formation remain the same. It is possible that the directional prediction can be used in the prediction of entrained oxides and oxide induced defects in complex geometries by examining the unique flow front after the melt has passed the gate region. For simple geometries, however, the entrapped gas volume

123 term provides accurate results for oxide entrainment and oxide induced defects while providing a valid explanation for its inclusion in the OEN.

(a) (b) (c) Figure 54: OEN validation steps including the (a) initial prediction of the OEN, (b) The Entrapped Gas Volume term variation across the height of the cylinders, (c) Experimentally measured defect volume compared to the Final OEN prediction.

After applying the entrapped gas volume term to the OEN to both the poor and preferred filling molds the OEN is shown to have good agreement to the experimental data for both cases as shown in Figure 55. Both mold types show that the cylinders have a relatively constant volume of defects through the majority of the cylinders excluding very bottom and top of the cylinders. This result is consistent with the OFEM predictions of Reilly et al. and the experimental results of Green et al.[103, 107]

The results in Figure 55 are also consistent with the mechanisms previously discussed.

Since the volume of gas for each casting is relatively constant, the amount of porous material or oxide induced defects should be similar. However, the poor filling mold will have a slightly increased volume of oxide induced defects due to the overall higher

124 number of bifilms which increases the potential or opportunity for pore initiation. This theory is confirmed in Figure 55.

(a) (b) Figure 55: OEN comparison to the experimentally observed defect volume for the (a) Poor Filling Mold (b) Preferred Filling Mold.

The two major differences between Reilly’s OFEM and the OEN presented in this study are the increase in computational efficiency of the OEN and the ability to predict the volume of the defects present in a cast structure. Figure 55 shows some general variance in the amount of oxide present, which is to be expected in this type of experiments and can also be seen in Figure 44. The complex dynamic situation of the filling process in casting will always have a level of variability, which Reilly et al. highlights in their development of OFEM. When using the OFEM Reilly et al. was not able to draw a correlation between location and severity of the oxide content nor were they able to couple it with other oxide induced defects such as unfurled bifilms or shrinkage porosity.

Thus, the OEN provides a strong predictor of the numeric volume and location of

125 entrained oxide inclusions as well as oxide induced defects present in the final cast structure.

5.9 OEN Validation for a Complex Geometry

Thus far, the OEN has only been shown to be valid for geometrically simple and directionally filled castings. Ultimately, the goal of this work is to push the limits of the

OEN and attempt to validate it on a geometrically complex component.

5.9.1 The Complex Casting

The cast structure chosen for validation is shown in Figure 56, hereafter referred to as the node. The structure was cast using aluminum A356 into a sodium silicate bound sand mold. The molten material was first poured into a pouring cup attached to the main mold which was then rotated 90° to perform tilt pouring. The molten metal entered the sand mold through the four gates located at the top of Figure 56.

Figure 56: Geometrically complex casting used for OEN validation.

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5.9.2 Dividing the Node

The size of the node is considerably large and was divided into two components for clarity in discussion. The division line was drawn vertically down the center of the node, with the two resulting halves shown in Figure 57. The two resulting halves were labeled as Side A and Side B respectively.

(a) (b) Figure 57: The division of the node into two halves with (a) representing Side A and (b) representing Side B.

5.9.3 OEN Node Prediction

The initial OEN prediction was run without the volumetric gas term as described in

Section 4.8 as it was not known how the defect content would vary throughout the cast structure. Even though the OEN is not optimized without the volumetric gas term, it still offers a reasonable prediction for the location specific oxide entrainment and the initial prediction for the node can be seen in Figure 58.

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(a) (b) Figure 58: Initial OEN prediction for the node. (a)Instantaneous OEN prediction upon initial pouring and (b) final filling.

A qualitative analysis of Figure 58 indicates that a majority of the oxides will be entrained upon initial filling and will reside near the gating system of the node. The gating system for the node is comprised of four large boss-like features with large cross sectional areas which greatly increase the gate velocity and allow for turbulence as the fluid front is unconstrained. Additionally, the OEN predicts that some included material may appear in the central region of the node near the end of filling. Though, intuition would suggest that the central region will likely not have any included material and the oxide will like reside on the free surface and not be entrained.

5.9.4 CT Scans of Side A

The validation of the OEN for the simple geometry was done using serial sectioning which is not practical for large geometrically complex components. Instead, a computed tomography (CT) scan was performed on Side A and Side B of the node. Both nodes were scanned and reconstructed with a voxel size of 76.32μm. The CT scans of Side A are shown in Figure 59 and Figure 60.

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Figure 59: CT scan of Node: Side A viewed from the front direction.

(a) (b) Figure 60: CT scan of Node: Side A viewed from the (a) rear direction and (b) edge on direction.

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The CT scans of Side A show that a majority of the defects originate near the two gates at the top of the casting. This is not surprising as it is the gate velocity that determines if the fluid front transitions from a laminar to turbulent flow causing the entrainment of bifilms.

Additionally, after passing through the gate, the molten material immediately hits the wall of the internal core which can cause instantaneous dissolution of the continuous fluid front and will lead to further entrainment of bifilms.

What was not expected was for a majority of the defects to be located in a single line wrapped around the outermost gate, as shown in Figure 60a. It is commonly believed that upon entrainment, oxide inclusions will be carried away by the flow of the molten fluid front until the casting solidifies. The CT scans on the other hand show there appears to be a correlation to the location of entrainment and the final location specific defect content.

The inner most gate of Side A shows a similar line of defects concentrated at the gate entrance. The variance between these two locations is not simply explained using basic fluid mechanics or general casting design and requires further exploration in terms of oxide entrainment modeling.

5.9.5 CT Scans of Side B

Side B of the Node was scanned in the same manner and can be seen in Figure 61 and

Figure 62. The CT scans of Side B shows similar results to Side A of the node with the majority of the defects originating near the gates. The outer gate of Side B also shows a high volume of defects concentrated near the gate entrance similar to Side A. The area surrounding the inner gate of Side B contains fewer defects than the outer gate similar to

130 what was observed for Side A. Thus indicating a similar mechanism must be occurring for Side A and side B.

Figure 61: CT scan of Node: Side B viewed from the front direction.

(a) (b) Figure 62:CT scan of Node: Side B, viewed from the (a) rear direction and (b) edge on direction.

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5.9.6 OEN Correlation to Side A

As previously described, the location and quantity of the defects noted in the CT scans were not obvious from analysis of general fluid front simulations and require further examination. Therefore, the OEN model was used to better understand the CT results for both Side A and Side B of the Node.

Initially, the OEN was run without the entrapped gas volume module that was described in Section 4.8, and the initial results are shown in Figure 63 - Figure 66. Qualitatively, the

OEN in Figure 63b shows the location of oxide induced defects predicted using the OEN and has a strong correlation with the CT scan. The OEN correctly predicts that only the outer gate of Side A will have a significant volume of defects which wraps around the whole of the casting. Additionally, the OEN correctly predicts that inner gate of side A will only contain defects in the immediate vicinity of the gate and the defects will not encompass the remainder of the casting. Ultimately, the results of the initial OEN on Side

A validate that the OEN is accurate not only at predicting oxides and oxide induced defects for simple geometries but complex geometries as well.

It was previously mentioned that the reason for the line of defects seen in Figure 60a was not originally understood. However, by using the OEN, this strange phenomenon can be examined. The line of defects in Figure 60a was sectioned out of Side A and is shown in

Figure 64b.

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(a)

(b) Figure 63: Location comparison of the defects located in Side A of the node (a) CT scan vs (b) Instantaneous oxide generation for OEN model.

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(a) (b)

(c) (d) Figure 64: OEN comparison to experimental CT for outer gate of Side A (a) sectioned region of Side A (b) CT slice of outer gate (c) Instantaneous OEN prediction of Side A (d) OEN slice corresponding to outer gate in (b).

When examining the line of defects with the instantaneous OEN in Figure 64d it is evident that the initial entrainment occurs during the molten material entering the mold.

The high gate velocity drives the entrainment process which falls off or decreases as the remainder of the casting is filled. Such a correlation would confirm the hypothesis that oxides are not carried by the flow of molten material and reside at or near the initial

134 location of entrainment and the instantaneous OEN can greatly aid in the prediction of oxide entrainment and oxide induced defects.

5.9.7 OEN Correlation to Side B

The same analysis performed on Side A was repeated for Side B. The OEN shows a strong correlation in the location of the entrained defects and with a majority of the defects residing near the gates as shown in Figure 65. Similar to Side A, Side B shows greater defect content located around the outermost gate which was confirmed in Figure

65c. However, the main difference between Side A and Side B is the random nature of the location of the defects. The large differences is likely due to the greater wall thickness in Side B compared to Side A, as shown in Figure 65b. A larger wall thickness will be unable to constrain the flow of molten material and instead will induce splashing and turbulent flow, thus, increasing the quantity of entrained material. As the molten fluid front becomes turbulent and splashes, the entrained material will take on random locations and will exhibit a random distribution within the large wall sections.

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(a) (b)

(c) (d) Figure 65: OEN comparison to experimental CT for outer gate of Side B (a)sectioned region of Side B (b) CT slice of outer gate (c) Instantaneous OEN prediction of Side B (d) OEN slice corresponding to outer gate in (b).

5.9.8 OEN Oxide Volume Comparison

The results of the initial OEN prediction in Figure 66 show a good agreement for the prediction of the location of entrained oxides and oxide induced defects. However, without including the volume content of gas, the OEN only provides a qualitative prediction of entrained defects. For this reason, the volume of gas within the melt was examined.

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(a) (b)

The gas content in the melt was determined by conducting Reduced Pressure Tests (RPT) on the melt prior to casting, followed by Archimedes density measurements. The density measurements showed an average gas volume fraction of 0.2%, which is equivalent to

0.0748ml/100g available to promote bifilm inflating and unfurling. Unfortunately, the volumetric gas term used for the simple geometries and displayed in Section 4.5 cannot be used as the complex geometry of the node does not fill in a directional manner. 137

Therefore, it was assumed that the local amount of bifilm unfurling must be equivalent to the volumetric fraction of gas in the melt. By following this assumption the local or location specific oxide entrainment and oxide induced defects can then be determined by multiplying the OEN by the volume of gas within the melt.

To examine the validity of the bifilm unfurling assumption, different regions of the node containing different defect contents must be examined. The regions containing elevated levels of defects were chosen were based off of the CT scans and it was chosen to examine the cross sections near the outer gate shown in Figure 64b and Figure 65b for

Side A and Side B respectively. Each cross section was divided into the top, side and bottom regions as shown in Figure 67, from which the location specific oxide volume was calculated. The experimentally measured oxide volume was determined by multiplying the surface area of the defects in each subsection noted in Figure 67 by a constant film thickness of 100nm resulting in the total volume of oxides at each location shown Figure 68. The film thickness was approximated by assuming a majority of the entrained oxides are young in nature (10 – 25nm in thickness) as best casting practices were followed.[50] The presence of older oxides (100nm – 1mm in thickness) is still possible and for this reason an average film thickness of 100nm was approximated.

The regions containing a limited quantity of defects were determined to be on the top of the node towards the front of the casting and are indicated in Figure 69 as A2 and B2 for

Side A and Side B respectively. These regions can be seen to be generally free of defects in Figure 60 and Figure 61, though the same procedure was followed to determine the entrained oxide volume and is shown in Figure 68.

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(a) (b) Figure 67: Subdivided cross sections of (a) Side A and (b) Side B of the node. Each cross section is labeled with its designation of top, side and bottom.

With the location specific volume of entrained oxides determined, the values were compared to the OEN location specific predictions. The OEN was examined at the same locations at which the experimental data was extracted with the only difference being the inclusion of the gaseous volume fraction. The gas volume fraction of 0.2% was applied uniformly across the node and the total volume generation was integrated over time to obtain the OEN prediction of the volume of entrained defects and is shown in Figure 68.

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(a) (b) Figure 68: Location Specific OEN validation for (a) Side A and (b) Side B of the node.

The OEN prediction in Figure 68 validates the ability of the OEN to accurately predict the location as well as the severity of entrained oxide inclusions within the cast node. For

Side A, the OEN correctly predicts a moderate volume of oxide induced defects for the top and side regions of the cross section, while a spike in volume occurs at the bottom of the cross section of Side A. Additionally the OEN accurately predicts an increased volume of entrained material for Side B compared to Side A. The increase in included material for Side B is attributed to the slightly larger wall thickness that allows for more material to flow for longer, effectively increasing film growth and the number of entraining events. For the regions that display limited defect content in the CT scans of the node, the OEN shows good agreement with minimal to no real oxide content in these defect free regions. The validation of the OEN volume predication demonstrates the utility of OEN as it is able to predict the location specific oxide content which can is critical in the development of high quality cast structures.

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5.9.9 Location Specific Mechanical Properties

To confirm the significance of the defects predicted by the OEN and observed via the CT scan, several locations were selected from which the mechanical properties were examined from two different node castings. The node locations chosen for tensile testing were the same as were used for validation of the bifilm volume and are shown in

Figure 69 and detailed in Table 7.

Each of the tensile specimens was sectioned into ASTM E8 Subsize specimens with a nominal thickness of 3.75mm thickness. Once the tensile bars were extracted, the specimens were heat treated at the T6 condition. The T6 treatment included a 3 hour solution anneal at 535°C followed by a quench in solution of 85% water and 15% ethylene glycol. The T6 treatment concluded with artificial aging at 150°C for 3 hours in an oil bath followed by air cooling. The tensile specimens were pulled using an MTS

Criterion Model 43 test frame with a strain rate of 0.0065mm/s. The strain was measured with an Electronic Instrument Research LE-01 laser extensometer.

Table 7: Identification of the node tensile bars

Location ID Description Side A A1 High Defect Content Side A A2 Limited Defects Side B B1 High Defect Content Side B B2 Limited Defect Content

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(a) (b)

(c) Figure 69: Locations chosen for tensile testing. (a) Location of tensile bar extraction on the cross section of Side A. (b) Location of tensile bar extraction on the cross section of Side B. (c) The cast node showing the clean or low defect content regions from which tensile specimen were extracted.

The tensile data from Side A and Side B of the node are shown in Figure 70 and Table 8.

Both Figure 70a and Figure 70b demonstrate the significance that entrained bifilms and oxide induced defects have on the mechanical properties and confirm that the OEN can now be successfully used to estimate a variation in location specific properties of cast components.

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Table 8: Location Specific mechanical properties for node casting.

Yield Strength (MPa) UTS (MPa) Elongation (%) A1 190.08 240.05 4.2% Side A A2 207.22 281.60 9.0%

B1 181.23 244.87 3.1% Side B B2 193.02 244.87 5.1%

The location specific stress strain curves show that the elongation is the most affected property by the presence of entrained oxides and oxide induced defects as it can be seen to drop from an average of 9% to 4.2% in Side A and from 5.1% to 3.1% for Side B. This dramatic drop of more than half the elongation in Side A and near half the elongation in

Side B can be explained by the mechanisms noted in Chapter 2.1.3. Here it was discussed how the increase in volume of defects will result in an increased stress state at a lower value of strain, subsequently leading to early failure. Additionally, entrained oxides and bifilms tend to have sharp points or features as shown in the fracture surface in Figure

71a, and can lead to a local increase in the stress state of the material and result in a reduction in ductility. Such a drop in ductility is expected and has also been observed in previous works. However, the variation in the severity of the defects present was intentionally varied over different castings to induce various levels of oxide entrainment instead of examining location specific entrainment information in a single casting.[50, 90,

108]

Along with the drop in ductility, a reduction in the ultimate tensile strength, UTS, was noted for both Samples A1 and B1 compared to Samples A2 and B2. The reduction in

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UTS is another result of the oxide entrainment. Due to the high local stress states, the regions of the casting containing increased volumes of entrained defects will prevent the sample form elongating and reaching the maximum or full strength as occurred for samples A1 and B1.

(a) (b) Figure 70: Location specific stress strain curves from (a) Side A and (b) side B.

Conversely, the yield strength was observed to have the smallest deviation for the tensile specimens containing a high defect content (A1, B1) and limited defect content (A2, B2).

The defect content is not expected to alter the general proof strength of the material as dislocation movement will not occur prior to the material yielding. The variance observed in the yield strength in Figure 70 can be attributed to slightly slower cooling rates for samples A1 and B1 due to the increased wall thickness near the gated sections. Slower cooling rates will result in a slightly coarser microstructure that correlates to a slightly different yield strength, but cannot account for the considerable drop in ductility.

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5.9.10 Microstructure Evaluation of Location Specific Regions

In order to confirm that the reduction in mechanical properties seen in Figure 70 were a result of oxide entrainment and not other general defects, the fracture surface was examined for various locations as shown in Figure 71. The fracture surface in Figure 71a was taken from location A1 as described in Figure 69b and clearly displays an oxide inclusion. The entrained oxide in Figure 71a has a large aspect ratio and a number of folded wrinkles which is consistent with old entrained oxide inclusions. The entrained oxide was confirmed using EDS mapping and is shown in Figure 71c. The EDS spectra for the inclusion indicated that the defect contained elevated levels of oxygen and was consistent with old oxide inclusions as described by Cao and Campbell.[50]

The fracture surface of Sample A2 was examined next and is shown in Figure 71b. The fracture surface for sample A2 is quite different than Sample A1 as it displays remnants of microvoid coalescence that hints at ductile fracture while generally lacking entrained defects as predicted by the OEN. To confirm the absence of entrained oxide inclusions,

EDS mapping was conducted on the fracture surface of Sample A2 as shown in

Figure 71d and was found to have little to no oxygen present. The absence of oxygen highlights the local cleanliness of the casting at A2 compared to the elevated levels of defects near region A1 and provides sufficient evidence for the variation in mechanical properties in these regions.

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(a) (b)

(c) (d) Figure 71: Fracture surface comparison of the (a) high defect (Position A1) and (c) low defect (Position A2) tensile bars. Corresponding EDS spectra show oxide content in (b) and a clean fracture surface in (d).

5.9.11 OEN – Complex Casting Conclusions

The general variation in properties seen from the different regions of the cast node highlights the necessity for location specific property prediction. From the discussion on mechanical properties above it can be seen that the properties can vary considerably throughout a cast structure. Generally, a variance in properties is attributed to a change in the local cooling rates, however, the cooling rate alone is not enough to fully describe the 146 phenomenological change in mechanical properties due to the presence of entrained oxide inclusions.

The OEN provides an accurate assessment of locations specific oxide entrainment as well as the quantity of oxide induced defects which have been shown to considerably alter the mechanical properties of a casting, most notably the ductility of a casting. By utilizing the

OEN during the casting design process, the entrainment of oxides and development of oxide induced defects can be limited in order to produce high fidelity, quality castings.

5.10 Concluding Remarks on Oxide Inclusions and the OEN

A new Oxide Entrainment Number (OEN) model has been developed to predict location- specific volumes of entrained defects as well as oxide induced defects in aluminum castings. The OEN is based on four key components, the Weber Number, the liquid free surface the local solidification rate and the total volume of gas in the melt. When these terms are combined, the OEN model provides an intuitive description of the oxide entrainment process and is able to accurately predict both the defect volume and location within the cast structure.

For directionally filled castings, the OEN model demonstrates that a majority of oxide induced defects are located within the center region of the cast cylinder coupons while the ends (top and bottom) possessed a smaller volume of defects during directional metal flow. This phenomenon was attributed to an increased velocity as well as a decreased thermal gradient in the centers of the cylinders. Using the entrapped gas volume term based on the volume of gas present within the melt, the OEN was also able to accurately

147 predict that the center portion of the cylinders would contain more gaseous pores than at the edges or ends of the cylinders, and was experimentally validated.

Additionally, the OEN was validated using a geometrically complex automotive component. It was found that many of the principles established for directionally filled castings also hold for geometrically complex castings. It was also shown that the OEN can be used to better estimate locations specific mechanical properties throughout the cast structure, and can be utilized during the design stage of casting to obtain optimal mechanical properties.

Overall, the OEN is a computationally efficient model that can be implemented into any commercial casting simulation software and shows promise for aiding casting/pattern designs for minimized oxide inclusions and oxide induced defects. If properly used in the design process, the OEN will successfully locate bifilms as well as oxide induced defects in unnecessary regions of the casting such as gates or risers and produce high integrity castings.

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Chapter 6: CA – FEA: A Method for Predicting Location Specific Properties

Each of the previous chapters of this work have handled various components to forecast the final microstructure in cast aluminum alloys and have provided insight into an undeniable fact: properties are not constant throughout a cast structure. No matter the root cause, the casting will have unique properties from location to location and the design process must be updated to reflect this new understanding. Instead of relying on traditional method for design, this chapter outlines a new design process that can account for the variation in mechanical properties while spanning multiple length scales. The new methodology of design offers an opportunity to attain a new level of precision in property prediction, as well as optimization of cast structures.

6.1 Homogeneous vs Heterogeneous Property Prediction

With the advent of Integrated Computational Materials Engineering (ICME) the rate of materials development and materials process development has dramatically increased.

The typical 10-20 year life cycle of alloy development has been rapidly accelerated and allowed for the introduction of numerous new alloys.[1] Simultaneously, the accuracy of the holistic materials property prediction has improved as new models have been developed.[3, 78, 106, 109, 110] Despite each of these advancements, the component

149 design process and methodology has not evolved at the same rate and instead, has remained relatively constant with entire components are designed with a single property in mind.

The traditional design process for structural castings begins with viewing the casting from the mechanics perspective. Often, the geometry of the structure is examined and altered to optimize the strength of the component. In terms of material selection, a single value for of strength, ductility, etc. is uniformly applied to the component and the design process concludes. The traditional design becomes problematic when the mechanical properties in the cast structure vary from location to location due to the development of unique microstructures or metallurgical defects such as gas porosity, shrinkage porosity, or entrained inclusions.[111–113] The presence of the metallurgical defects listed above often result in a reduction in the local mechanical properties as well as premature failure of the cast structure.

The common practice to combat the reduction or change in local mechanical properties is to apply a safety factor or increase the cross sectional thickness to allow components to handle greater loads. Unfortunately, neither method offers a rigorous solution for accounting for location specific mechanical properties. Instead, cast structures become bulky, overweight, and overdesigned as the section thicknesses are unnecessarily increased uniformly across the casting.

The deficiency in the traditional design process is becoming more and more apparent as cast products are increasingly required to possess lower weights and thinner walls while maintaining structural integrity.[30, 114–116] To meet this demand, the design process

150 must be revolutionized to account for heterogeneous properties are developed over the whole of a casting.

6.2 Roadmap to Location Specific Property Prediction

The first attempts at designing for location specific property prediction where performed using the by – zone design method.[10] The by – zone methodology involves discretizing a casting into a number of different regions and examining the filling and solidification conditions to empirically estimate the mechanical properties of a particular region of the casting. Unfortunately, the by – zone design method has several drawbacks, most notably, the discritization can vary from designer to designer and the empirical relationships developed often vary from one casting to another.

Recently, the Virtual Aluminum Casting method (VAC) was introduced by Allison et al. as a method to better predict location specific properties.[2] The VAC uses a combination of Computer Aided Engineering (CAE) tools including Computational Fluid Dynamics

(CFD) and Finite Element Analysis (FEA) to predict the local mechanical properties of a casting. Allison et al. was able to show the viability of the VAC methodology by predicting location specific fatigue strength of an automotive engine block. However, the

VAC appears to rely on empirical observations for local microstructure predictions and lacks evidence of experimental validation, causing concern for its robustness.

The difficulty of correctly predicting location specific mechanical properties lies in obtaining accurate location specific microstructures. However, even the most advanced thermodynamic and kinetic solvers in commercial software such as ProCAST (used in the

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VAC) rely on empirical relationships that are only able to predict the microstructural lengthscale such as the secondary dendrite arm spacing.[3] Though insightful, the SDAS only provides a general estimate of the tensile strength with no information on the ductility, toughness or other mechanical properties. Furthermore, commercial casting software suites such as Magma, ProCAST or Flow3D are quite poor at predicting the size and location of defects such as shrinkage, gas porosity and oxide inclusions. This is due to the large mesh size (3-5mm) used in the simulation of industrial castings, when the actual size of the porous defects is in the magnitude of 10s of microns. Such a large difference makes predicting the location specific mechanical properties difficult when only a single software is used and indicates that an improved methodology must be devised and employed to truly predict location specific properties.

6.3 Microstructure Modeling Techniques

The alternative to the microstructure estimation via empirical methods is to perform numerical simulation such as phase field (PF) or cellular automaton (CA). Both PF and

CA have been shown to provide a high level of accuracy in solidification and microstructural predictions down to the micron scale. [75, 77, 78, 85, 117–120]

6.3.1 Phase Field Microstructural Modeling

Phase field simulations are characterized by a general field or simulation domain called the phase field. Within the phase field, distributions, or phase-field variables are governed by a series of partial differential equations (PDE) that control general microstructural development during solidification. In PF modeling, there are no true

152 interfaces, instead the PDEs are continuous and are considered as a diffuse-interface due to the gradual change at the boundary. Because PF is defined by the diffuse interface, no boundary conditions are considered at the interface which allows for the prediction of extremely small and arbitrary microstructures. Recently phase field has been shown to successfully model the microstructure of a single micro pore as well as complex dendritic solidification.[119, 120] The drawback of PF is that it is computationally expensive due to the steep gradients that form along microstructural interfaces.[121] For this reason, the simulation domains of PF simulations are often quite small compared to other microstructural modeling techniques.

6.3.2 Cellular Automaton Microstructural Modeling

While PF considers solidification with a diffuse boundary, Cellular automaton examines solidification events using a sharp interface methodology. In CA the simulation domain is discretized into 2D or 3D grid-like structure that defines a series of cells. The cells are prescribed an initial condition or state which is then updated over time depending on a series of governing equations. Cellular automaton is often used for solidification simulations where the states of each cell are defined as solid, liquid, gas or an interface.

The solute diffusion, thermal conditions, and kinetics are all considered for each individual cell during the solidification process and are able provide a full description of the solidification phenomenon. The advantage of CA is that cell size can be set to any size, meaning that the simulation domain can be tuned to examine varying length-scales.

This greatly improves the computational efficiency and allows CA to accurately model microstructural features as small as a single dendrite or as large as the grain structure

153 across the wall thickness of a high pressure die cast component.[75, 78] However, it is often difficult to predict multiple phase precipitation following initial solidification when using CA.

6.4 The Need for Connected CAE

Regardless of the method chosen for microstructural simulation, the issue with phase field, cellular automaton and other microstructural simulations is that they are compartmentalized and in no way connected to the casting process simulation suites.

Moreover, due to the computational expense, it is not currently possible to run full microstructures simulations on industrial scale components. Instead, the microstructure simulations are often performed in isolation of the casting process simulations and design engineers are forced to rely on the poor microstructure estimations provided by

ProCAST, Magma, or other casting software.

Even if a microstructure is obtained via PF or CA, it is rarely coupled with finite element analysis software such as ABAQUS or LS Dyna. Instead, FEA simulations are often performed with a single set of materials properties for an entire component, and lack any capability of predicting accurate location specific properties.

This cycle continues throughout the design process as each software tool is used in isolation of the others. Casting software suites provide how a casting might fill and cooling conditions, PF and CA provide a unique microstructure, while ABAQUS or LS

Dyna provide mechanical properties. Each simulation tool uses its own specific set of

154 input variables, and empirical estimation that lower the overall accuracy of the final property prediction as the amount of true information is diluted through each step.

In order to limited the dilution from each CAE software, a process for connecting each

CAE tool must be devised. On their own, each CAE tool provides a specialized, but limited amount of information into the design process for manufacturing components. If the various CAE tools are combined in a scenario where the process simulation is connected to the microstructure simulation which is then connected to FEA software, location specific properties can be predicted with an unprecedented level of accuracy allowing for a new level of casting optimization.

6.5 The CA – FEA Approach

The approach of combining and connecting the various CA tools to obtain accurate location specific properties has been termed the CA – FEA approach and is outlined below. The specific commercial CAE tools discussed here are ProCAST and ABAQUS, though other CAE software could be used as well.

6.5.1 Boundary Conditions

When attempting to connect different forms of software, the key concern is the compatibility in boundary conditions. Without consistent boundary conditions, simulations are limited to estimated parameters, begin to lack fidelity and become empirical in nature. Fortunately, the outputs of the casting software suites are the exact input boundary conditions required for cellular automaton simulations and the outputs of

155 the microstructure can be directly input into the FEA solvers. The general process flow for connecting CAE using the CA – FEA approach is shown in Figure 72.

Figure 72: The connected CAE outline with key boundary conditions and outputs.

6.5.2 ProCAST to CA

The difficulty in connecting ProCAST to CA, lies in the size scale difference of the models. ProCAST simulations are often performed on large industrial components that can be a meter or more in length, while the max simulation domain for CA is rarely greater than a cubic millimeter for microstructural simulations. Performing a microstructure simulation of the entire cast structure using CA is also often unnecessary as the microstructure does not vary demonstrably from one millimeter to the next for 156 similar solidification conditions. Therefore, the regions in which CA simulations are performed must be directed or influenced by the output of the ProCAST simulations.

The key outputs of ProCAST simulations are the solidification conditions and general defect prediction. These outputs give insight into regions of the casting that may result in defects which can then be further investigated using CA microstructural simulations.

Thus, ProCAST acts as a filter and directs the user to regions in which microstructural simulations should be performed.

Once the locations for performing microstructural simulations are determined, the only true boundary conditions required to perform the CA simulation are the thermal parameters that induce solidification. All other variables such as diffusion coefficients, alloy chemistry, etc. are alloy dependent and can be directly input into the CA software.

With this knowledge, it was chosen to couple ProCAST with a self-written CA code which is derived in detail in the author’s previous publications.[77, 106, 117, 122]

6.5.3 Cellular Automaton to FEA

The vetted CA code is capable of outputting the location specific dendritic/grain structure, hydrogen/gas porosity formation, and shrinkage formation for a cubic millimeter of solidified material. The dendritic morphology and porous features are recreated at a resolution of 5μm per cell size and allow for a previously unattainable level of accuracy to be reached. Prior to transferring the simulated microstructure to ABAQUS, the entire microstructure is refined down to a 50nm or smaller mesh using a high fidelity conforming mesh.[123, 124] The highly refined mesh with exact microstructural features can then be directly imported into ABAQUS where the dendritic structure is assigned the

157 properties of the solid aluminum alloy and the pores are given zero mechanical strength.

The result is a cubic millimeter of material with a highly refined microstructural mesh that can be subjected to any number of loading conditions to predict the true location specific mechanical properties.

6.6 CA – FEA: Simulation of Wedge Casting

To validate the CA – FEA approach, a wedge shaped casting was chosen and is shown in

Figure 73. The geometry of the wedge casting forces a number of different cooling rates and solidification conditions to occur within a single casting which will undoubtedly lead to location specific mechanical properties. Three different locations were chosen along the vertical axis of the wedge to examine the development of location specific properties and were termed Position A, B, and C as shown in Figure 73.

To simulate the wedge within ProCAST, the mold material was set as plain carbon steel with a mold-casting HTC value of 3000 W/m2K. The pouring temperature was set as

710°C and pouring conditions were 0.35kg/s through a 20mm diameter inlet. The two open regions located at the top of the mold were prescribed standard air cooling conditions for heat transfer considerations. The mold was filled to 99% using a 1.5mm global mesh size using tetrahedral elements. The automatic time-step within ProCAST was applied throughout the filling and solidification of the wedge.

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(a) (b) Figure 73: Dimensions of the wedge casting from (a) front view and (b) side view.

6.6.1 ProCAST Examination of the Wedge Casting

The variation in solidification conditions for Positions A, B, and C were examined within

ProCAST and are shown in Figure 74 and Table 9. The simulation results show that the time required for solidification increases significantly as the cross section/wall thickness increases from Position A to Position C. At Position A, the molten material fully solidifies within 2.6 seconds, while the thicker cross section at Position C requires roughly 10 times longer to solidify as shown in Table 9. The increased time at elevated temperatures at Position B and C will lead coarsening of the microstructure, larger pores and will subsequently alter the local mechanical properties across the wedge.

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Figure 74: ProCAST simulation of solidification time for the wedge casting.

As previously discussed, microstructure simulations cannot be reasonably performed on an entire casting and the cellular automaton simulations must be directed by the

ProCAST simulations. The major defect that ProCAST is capable of estimating is macro and micro shrinkage porosity and the predictions are shown in Figure 75. Within

ProCAST, macro shrinkage porosity is correlated to local hotspots that remain between the liquidus and solidus temperatures for an extended period of time and are able to feed/fill in the surrounding porous regions. As the hot spot feeds other local regions of micro shrinkage, the hot spot, the hot spot loses material which is not able to be backfilled and result is an extended porous volume that often appears spherical in nature as in Figure 75b. Micro shrinkage porosity is defined in a slightly more rigorous way and is calculated based off of the Dimensionless Niyama criterion derived by Beckerman relating to the local drop in metallostatic feeding pressure that results in micro void formation as in Figure 75a.[125] No matter the type of porosity, porosity will certainly be 160 detrimental to the final mechanical properties and the full extent of porous defects must be further examined to accurately predict the local mechanical properties.

Table 9: Simulated vs. Experimental solidification conditions.

Solidification time (s) Cooling Rate (C/s) ProCAST Experimental ProCAST Experimental Position A 2.615 2.16 58.06 60.94 Position B 10.05 12.78 12.02 10.17 Position C 26.39 26.08 3.85 3.23

The ProCAST defect estimations in Figure 75 indicate several regions that require further investigation. The Dimensionless Niyama criterion in Figure 75a show that there is a small amount of micro voids forming at the very tip of the wedge near Position A and significant amount of porosity that will exist within the center of the wedge near

Position C. Micro void formation at the tip of the wedge occurs due to the near instantaneous solidification of molten material. The rapid rate of solidification prevents metallic feeding to the tip of the wedge and will lock in any porous features that do form.

As the distance from the wedge tip increases, the solidification time decreases and the

ProCAST simulation predicts a sound casting near Position B due to an increased level of metallic feeding. The feeding for Position B likely results from the top of the wedge, near

Position C and is depicted as a large void Figure 75.

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The defect location estimation in ProCAST provides the initial intuition into potential regions containing defects, however, the predictions must be used with caution as no true microstructural prediction was completed.

(a) (b) Figure 75: Defect prediction via ProCAST (a) Dimensionless Niyama (b) Total shrinkage Porosity.

6.6.2 Cellular Automaton of the Wedge Casting

ProCAST simulations were able to highlight the regions of potential defects within the wedge which can now be further investigated using CA microstructural simulations. The highlighted regions are shown in Figure 75, and are located near the tip and the base of the wedge, suggesting Positions A and C will possess significant porous defects while

Position B will be relatively defect free. This prediction was assessed using cellular automaton microstructure simulations at all three locations on the wedge using the input 162 boundary conditions for solidification from Table 9, while the complete boundary conditions are listed following the model formulation.

The major difference between the ProCAST microstructure estimation and the CA microstructure simulation is the ability of CA to simultaneously handle the solidification process, gas porosity formation and shrinkage porosity development while ProCAST relies on empirical relationships. During the solidification process, the CA model is able to consider dendritic nucleation and growth based on the total undercooling during solidification as well as solute segregation to predict the microstructural morphology.

Additionally, the CA model is also able to simultaneously account for the nucleation of gas porosity as well as shrinkage porosity. Gas porosity is based on the solubility of molecular hydrogen in aluminum alloys, where the hydrogen solubility in liquid aluminum far exceeds the solubility of the solid Al phase. Thus, upon solidification, the solid rejects the molecular hydrogen resulting in an increased hydrogen content that exceeds the solubility limit in the liquid phases and induces heterogeneous pore nucleation. The CA model handles the gas porosity following the stochastic porosity nucleation model as shown in Equation 22.[126]

푚푎푥 푁퐻 퐿 ; 퐶퐻 푁 (푆푚푎푥−푆푚푖푛) ( 퐿 >푆퐻 ) 푑푛퐻 퐻 퐻 푆퐻 = { 퐿 Equation 22 푑푉 퐶퐻 푁 ( 퐿 ≤푆퐻 ) 0; 푆퐻

푚푎푥 푚푎푥 푚푖푛 where 푁퐻 is the maximum pore nucleation density, 푆퐻 and 푆퐻 are the maximum

퐿 퐿 and minimum porosity nucleation saturation respectively, 퐶퐻 and 푆퐻 are the local 163 hydrogen concentration (mL/100g Al) and the local hydrogen saturation (mL/100g Al) in

푁 liquid respectively, and 푆퐻 is the critical saturation criterion for porosity nucleation.

Following the nucleation of the gas pore, the pore can grow by hydrogen absorption as well as a change in shrinkage pressure resulting from solidification shrinkage, where the total driving force is expressed in Equation 23.

∆푃 = 푃퐺 − (푃0 + 푃푚 + 푃휎) + 푃푠 Equation 23

Where 푃퐺 is the internal pressure of a gas pore, 푃0 is the standard atmospheric pressure,

푃푚 is the metallostatic pressure, 푃휎 = 2훾/푟푃 is the capillary pressure by liquid-gas surface tension, γ is the surface tension of the G/L interface, 푟푃 is the pore radius, and 푃푠 is the shrinkage pressure. Complete details on the formation and evolution of the gas and shrinkage porosity are in the author’s previous publications. [106, 122]

With the details of the CA model understood, microstructural simulations were performed on each of the three positions of the wedge. The CA simulation domain was set at 1x1x1mm3 with a cell size of 5μm while the initial hydrogen content was set at

0.3ml/100g Al and the shrinkage pressure was set at 0.5atm. Additional parameters

푚푎푥 11 −3 included the maximum pore nucleation density 푁퐻 = 1 × 10 푚 , that minimum

푚푖푛 푚푎푥 and maximum pore nucleation saturations 푆퐻 = 1.4 and 푆퐻 = 2.0 and the critical

푁 saturation criterion 푆퐻 = 1.2. The CA model microstructures can be seen in Figure 76.

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The CA microstructural simulations show that each location within the wedge contains a mixture of solid dendrites and porous defects. As the cooling rate decreases from Position

A to Position C, the number of defects increases while the size of the defects increase.

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This phenomenon can be explained by the time allowed for diffusion of the molecular hydrogen during solidification. At high cooling rates, (Position A) hydrogen is frozen into the structure and is then unable to diffuse to form larger pores at lower temperatures.

On the other hand, at Positions B and C, the longer solidification time causes pore growth due to an increased time for hydrogen diffusion as well as solidification shrinkage. The morphologies of the defects at each of the locations were compared to experimental

MicroCT scans of the same locations in the wedge and show a strong resemblance in size, quantity and morphology.

When comparing the defects predicted in ProCAST to the CA simulation, it is evident that the CA model possesses a superior ability to accurately reflect size and morphology of defects present within the casting. The ProCAST prediction only shows defects near

Positions A and C while the CA model is able to accurately represent the defects size and morphologies in all three Positions. Most notably is Position B where the CA model still depicts predicts the formation of porous features, where ProCAST does not. This is most likely because ProCAST does not have the ability to nucleate gas porosity rendering it unable to accurately determine where porous defects will reside within a casting.

The only discrepancies between the CA microstructural simulation and the microCT scan appears near Position A where the microCT scan shows the defects contain generally irregular shapes where the CA model predicts generally spherical morphologies. This is likely due to the pore nucleation criterion set by the CA model which forces pore nucleation to occur due to excess hydrogen within the solidifying melt.

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The solid, dendritic regions within the microstructural simulation also show a reasonable prediction of the size scale of the actual microstructure. The SDAS prediction from

Figure 76 can be seen in Table 13. The combination of the accuracy in the size and morphology of the defects at each location within the wedge and SDAS displays how insightful the CA microstructural prediction can be when properly combined with traditional casting software suites.

6.6.3 Conforming Mesh Validation

The location specific, CA microstructure simulations provide a highly accurate microstructure prediction, however, this microstructure must be prepared and transferred into a Finite Element Analysis (FEA) software to obtain the correlating location specific properties. Each cell within the CA simulation possesses an identity of solid, pore or solid/pore interface which can easily be encoded into a mesh usable within any FEA software. However, the mesh resolution is limited to 5μm which is equivalent to the CA model cell size. In order to refine the microstructural mesh the Conforming to Interface

Structured Adaptive Mesh Refinement (CISAMR) method was employed.[123, 124]

CISAMR is a non-iterative mesh generation algorithm that interpolates the microstructural features to produce an optimized arrangement of the true microstructure.

During the mesh refinement stage CISAMR is able to model the pore/solid interface to accurately represent the morphology of the pores in a high fidelity manner as shown in

Figure 77.

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Position A Position B Position C

(a) (b) (c)

(d) (e) (f) Figure 77: CA simulated microstructure of wedge casting at various locations (a,b,c) corresponding to Position A, Position B, Position C respectively. Post processing conforming mesh (d,e,f) corresponding to Position A, Position B, Position C respectively.

Figure 77 displays the utility of the high fidelity conforming mesh for each location within the wedges. By performing the series of ProCAST, CA, and CISAMR simulations, the microstructural lengthscale can accurately be taken from the millimeter lengthscale down to the nanometer level with little to no loss in microstructural features. The

ProCAST-CA-CISAMR process is highlighted in Figure 78.

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Figure 78: ProCAST influenced CA simulation and High Fidelity Conforming Mesh.

As discussed, the CA – FEA process begins with a ProCAST simulation of the cast structure. In the example of the wedge in Figure 78, a mesh size of 5mm was used for the

ProCAST simulation and displays massive defect regions near the base of the wedge. The coarse mesh and empirical relationships limits the information obtainable from ProCAST alone and was further examined using CA simulations. The CA microstructure simulation is able to refine the mesh down to a resolution of 5μm while using rigorous numerical methods to predict the size and morphology of the defects and microstructure at the location specific level. Finally the CA mesh is refined using CISAMR to produce a high fidelity mesh with a resolution down to 1nm around the individual defects. Such a level of accuracy has not been previously realized and emphasizes the strengths of using the

CA – FEA methodology.

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6.6.4 ABAQUS – Constitutive Model

Once the mesh was generated using CISAMR, it was directly imported into ABAQUS, a commercial FEA solver. ABAQUS allows the location specific properties under any condition to be examined for each of the microstructures examined, though it was chosen to examine Positions A, B and C in uniaxial tension.

The ABAQUS model l used was the standard/explicit database. Each 1x1x1mm cube from the wedge casting was modeled using C3D4 elements (a 4-node linear tetrahedron) where element deletion was selected as on and the max degradation of each element was set at 0.9999. The materials properties for each cube were: Youngs modulus = 70 GPa,

Poisson ratio = 0.3 while the elastic regime and plastic hardening were both considered to be isotropic.

The fracture criterion for each of the microstructures was based on the stress triaxiality argument for aluminum A356. Previous research conducted on the stress triaxiality for

A356 permanent mold castings is shown in Table 10, where an η value of 0 corresponds to pure shear and an η value of 0.33 corresponds to pure tensions. Within ABAQUS the

Stress triaxiality and effective failure strain data was from Table 10 was included using the Ductile Damage criterion where the sub-option of Damage Evolution was also included and the displacement at failure was set at 0.08.

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Table 10: Stress triaxiality parameters used for in the ABAQUS simulations.

Stress Triaxiality Effective Failure Strain (m/m) Average (η) Mae [127] Lee [128] Experimental -0.33 0.70 0.70 0 - 0.04 0.36 0.23 0.30 0.33 0.13 0.10 0.17 0.13 0.7 0.07 0.06 0.065 0.94 0.02 0.04 0.03

When the effective fracture strain is plotted against the stress triaxiality the three branch fracture locus can be determined is based on the Bao-Wierzbicki model which is summarized in Equation 24.[129]

1 휀̅ = 휀̅ + (휀̅ − 휀̅ )(3휂 − 1), 0 ≤ 휂 ≤ Equation 24 푓 푓,푡 푓,푡 푓,푠 3

Where 휀푓̅ is the effective plastic strain to fracture, 휀푓̅ ,푡 is the effective fracture strain under uniaxial tension, 휀푓̅ ,푠 is the fracture strain under pure shear. The Bao-Wierzbicki model in

Equation 24 is only applicable when the stress triaxilaity is between pure shear and pure tension, as highlighted by gray region in Figure 79, which makes it suitable for use in the uniaxial tension modeling of the three positions in the wedge. In addition to the effective failure strain obtained from literature, experimental tension stress strain curves were used to help train the ductile damage model at a stress triaxiality equal to 0.33 and was added to Table 10. 171

Figure 79: Three branch fracture loci schematic. [127]

The stress triaxiality dependent effective failure strain will undoubtedly be unique to each alloy as shown by both Mae and Lee, but it is also dependent on the location specific solidification conditions which effectively create micro-alloyed structures. In order to match the location specific tensile properties fully each position of the wedge was considered as an individual alloy and the unique stress triaxiality dependent effective failure strain was modified within ABAQUS and is shown in Table 11. The fracture strain chosen for the ABAQUS modeling were based on later experimental examination of each wedge location and highlights the difficulty in obtaining accurate models as constitutive modeling often requires a large amount of calibration to accurately describe the mechanical response of the alloy.

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Table 11: Location specific ABAQUS inputs.

Effective Fracture Strain (mm/mm) η Positon A Position B Position C -0.33 0.8 0.5 0.5 0.0 0.35 0.3 0.25 0.33 0.30 0.24 0.16 0.59 0.25 0.23 0.11 0.68 0.22 0.22 0.10 0.70 0.21 0.21 0.085 0.94 0.20 0.20 0.078

6.6.5 Wedge – Simulated Location Specific Properties

After defining the materials properties within ABAQUS, the specimens were loaded with a pulling velocity equal to 0.25mm/s on both the top and bottom surfaces of the cube. The time-step for each simulation was set at 0.0025 seconds and the resulting tensile curves can be seen in Figure 80a. The Positions A, B and C from the wedge all displayed unique mechanical properties which were attributed to a variation in microstructure as well as defect size and morphology. As the defect size increased from Position A to Position C, the largest change was the reduction in elongation. The larger pores at Position C cause a reduction in the cross sectional area which results in an early stress concentration and early failure. The smaller, refined, pores near Position A were shown to have a limited effect on the elongation, and show that material will exhibit excellent ductility, exceeding

15%.

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(a) (b) Figure 80: Location specific tensile curves from the wedge casting: (a) CA – FEA Simulation prediction, (b) Experimental tensile testing.

Additionally it was noted that there was a slight variation in the yield stress for each of the locations in the wedge. The change in yield strength can be attributed to the variation in cooling rate which will change the secondary dendrite arm spacing as well as the coarseness of the eutectic silicon phase. As the cooling rate increases and the microstructure becomes more refined, the lack of coarse particles in Particles in Position

A allow the tensile samples to also reach elevated magnitudes of ultimate tensile strength and eventually elongation.

The location specific mechanical properties highlighted Figure 80 demonstrate how critical location specific property prediction is in the development of quality castings.

Castings must be designed to account for a variation in the mechanical properties across the entirety of a casting and the CA – FEA process allows this to be done at a previously unobtainable accuracy. By using the fundamentals of solidification the CA – FEA methodology allows to obtain verifiably accurate microstructures at a previously 174 unobtainable resolution. This microstructure can then be inserted into an FEA model to understand how the microstructure will respond under any number of loading conditions.

The coupling of fundamentally sound solidification phenome and mechanics allows for highly accurate location specific properties that are not unachievable using traditional empirical engineering relationships.

6.7 CA – FEA: Experimental Validation

6.7.1 Wedge Casting Conditions

Following the completion of the CA – FEA simulation, the CA – FEA approach was experimentally validated using the same wedge casting geometry as in Figure 73. Each wedge was cast with primary aluminum A356 into a permanent mold comprised of plain carbon steel which can be seen in Figure 81. The A356 ingots were melted in clay- graphite crucibles, using an electric resistance furnace at 710°C, while a cover flux was used to limit the introduction of hydrogen gas. Prior to pouring, the melt surface was drossed and a 100 gram sample of molten A356 was taken to conduct a reduced pressure test where the average hydrogen content was found to be 0.3ml/100g aluminum.

The ports seen in the die in Figure 81a were used to insert thermocouples to extract the cooling curves from each location in the wedge casting. Positions A, B and C correlate to

TC1, TC2 and TC3 respectively in Figure 81b and the cooling curves and cooling rates can be seen in Figure 82 and Table 9. A total of five wedge samples were cast where one casting was used to obtain the cooling curves, one was used for microstructure and defect

175 evaluation and the three remaining castings were used to evaluate the mechanical properties at each location.

(a) (b) Figure 81: Wedge casting (a) Permanent mold and (b) A356 Wedge Casting

The cooling curves in Figure 82 display an obvious trend where the cooling rate was increases from the thick cross section at Position C to the thin cross section at Position A.

The cooling rate for each location was taken as the instantaneous derivative of the cooling curve at the experimental liquidus temperature which can be observed at the initial plateau that occurs between 605 - 613°C as shown in Figure 82. Experimental cooling rates were shown to have a reasonable agreement with ProCAST simulation in

Table 9 indicating cooling curves do not need to be measured for each location within a casting as the ProCAST prediction is sufficient for the input into the CA simulations.

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Figure 82: Experimental Cooling Curves for the wedge casting.

6.7.2 Location Specific Micro-CT and Microstructure

Once the wedges were cast, a cylindrical sample was extracted from the horizontal cross section at the very center of the wedge noted at Position A, B and C for performing X-ray

Micro Computed Tomography (microCT). The cylindrical specimens were each 6.35 in diameter and were extracted using a wire EDM. MicroCT was performed on each sample individually using a HeliScanTM MicroCT and were scanned at 90kV, 80μA and a resolution of 6.318μm per voxel. The exposure time was set to 0.11s and a 2mm aluminum plate was placed over the detector to act as a filter. The microstructural data was reconstructed and then analyzed using the ScanIP module in Simpleware. MicroCT was able to capture the pore/defect morphology which can be seen in Figure 83, as well as the defect volume, and surface area.

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Position A Position B Position C

(a) (b) (c)

(d) (e) (f) Figure 83: MicroCT results for the wedge casting. Position A is represented by (a,d), Position B is represented by (b,e), Position C is represented by (c,f).

MicroCT results show that as the cooling rate increased from Position C to Position A, the pore size/volume decreased while the number of pores increased. This trend was quantified in Table 12 and confirms the predictions observed qualitatively in the CA simulations in Figure 76. The change in defect size and morphology was previously described by the lack of hydrogen diffusion at elevated cooling rates. When a local region of the casting remains at elevated temperatures for extended periods of time as in Position

C, the hydrogen molecules are able to diffuse to form a fewer number of pores, that will be larger in volume. While at Position A, the high cooling rates prevent hydrogen

178 diffusion and the excess hydrogen in the solid solution is rejected into the already saturated liquid which initiates the formation of form numerous, smaller volume pores.

Table 12: Location specific defect analysis of the wedge casting.

Porosity Porosity Number of Cooling Rate volume volume disconnected (C/s) (풎풎ퟑ) fraction regions

Position C 0.567 0.597% 44 3.23

Position B 0.250 0.263% 59 10.17

Position A 0.0331 0.035% 67 60.94

The experimentally measured defect size and morphology were compared to the CA predictions shown in Figure 76. Because the MicroCT scans examined a larger volume that was reproducible using CA microstructural simulations, a representative region from each microCT scan was taken for comparison. The CA defect prediction matches the trends noted above with an overall smaller volume of porous defects observed and predicted for Position A compared to Position C. Additionally, the morphology appears to match well at the moderate and lower cooling rates. As the stable pores absorb additional hydrogen, the pore becomes more globular and irregular compared to

Position A. As previously mentioned, the CA model has a limited ability to accurately predict the morphology at Position A due to the pore nucleation criterion. However, the general size, spacing and morphology match well for all three positions of the wedge and 179 clearly indicate the source for the predicted reduction in location specific mechanical properties.

In addition to the microCT scans and measurements, standard metallographic evaluation was performed for each of the locations within the wedge and the microstructure are shown in Figure 84.

(a) (b) (c) Figure 84: Microstructure at (a) Positon A (b) Position B and (c) Position C of the wedge.

As the cooling rate increases from Position C to Position A, the SDAS and eutectic silicon become more refined and the porous regions become smaller and more numerous, matching the CA prediction and microCT scans. No coarse secondary particles or intermetallics were observed in any of the microstructures and suggest and mechanical property change is likely a result of the reduction of the SDAS, shown in Table 13, and the presence of the porous defects.

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Table 13: Secondary Dendrite Arm Spacing Comparison

CA Predicted SDAS (μm) Experimental SDAS (μm) Position C 33.33 32.85 Position B 20.07 21.12 Position A 14.28 13.85

6.7.3 Location Specific Mechanical Properties

The remaining three castings were used for examining the variation in mechanical properties across the wedge. Because location specific properties must be examined at the local level, the standard ASTM E8 tensile specimen cannot be used. Instead, a new micro-tension specimen was designed to obtain truly location specific properties. The tensile specimen is a scaled down version of the ASTM E8 Subsize tensile specimen and has a gauge length of 10mm with a cross section of 6mm2 and is shown in Figure 85.

(a) (b) Figure 85: Micro-tension specimen (a) dimensions and (b) cut samples.

Each of the tensile specimens was extracted from the wedge using a wire EDM with the dog-bone specimen oriented entirely in the horizontal plane so that the entire tensile

181 specimen possessed identical solidification conditions. The specimens were also cut so that the gauge section of the dog bone was located at the exact center of the wedge.

The tensile specimens were pulled using an MTS Criterion Model 43 test frame with a strain rate of 0.002mm/s. The strain was measured with an Electronic Instrument

Research LE-01 laser extensometer. The location specific stress-strain curves were then compared to the predicted stress-strain curves in Figure 86 for each location.

The location specific stress strain curves show the same trend predicted using the

CA – FEA approach. As the cooling rate increased from Position C to Position A, the elongation was the most affected property decreasing from 17.05% at Position A to

7.45% at Position C, while the yield strength was not significantly affected. The complete compilation of the experimental tensile data is shown in Table 14. Similar to the simulation, the experimental results also displayed a jump in the UTS for Position A compared to Position C. This jump in strength was due to the limited number of porous defects which allowed the material to experience its optimal strength.

(a) (b) (c) Figure 86: Experimental vs. Simulated stress-strain curves for (a) Position A (b) Position B and (c) Position C.

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The tensile testing results completed the CA – FEA validation and demonstrate the powerful tool that is the CA – FEA approach. For the first time, true location specific properties can be predicted as the CAE tools are combined to provide a highly accurate filling, microstructure, and property prediction.

Table 14: Experimental location specific mechanical properties.

Yield Strength Position UTS (MPa) Elongation (%) (MPa) Positon A 109.2 +/- 5.8 235.4 +/- 4.43 17.05% +/- 0.85% (High Cooling Rate) Position B 105.3 +/- 3.57 212.6 +/- 1.27 11.44% +/- 0.67% (Moderate Cooling Rate) Position C 104.8 +/- 2.28 196.7 +/- 2.28 7.45% +/- 0.97% (Low Cooling Rate)

6.8 Mechanical Property Degradation Modeling

In an ideal case, the complete CA – FEA approach would not require the complete examination and validation of properties for all locations within a casting. For this reason, an empirical estimate of properties can be used based on the high fidelity modeling used in the CA – FEA approach.

The two key variables that have the largest effect on the location specific properties are the cooling rate and volume of defects and the corresponding relationship can be seen in

Figure 87. The trend repeated throughout this chapter has been a decrease in the volume of porous defects with an increase in the cooling rate and the trend is shown to have a power law behavior. The advantage of using this formulation is that the mechanical

183 properties can be examined for different volumes of defects without repeating the

CA – FEA approach for constant cooling rates but varying initial hydrogen content within the melt.

Figure 87: Variation in defect content with changing cooling rates.

With the defect volume calculated, the local mechanical properties were plotted for each volume and were also shown to have an exponential decay in Figure 88. The curves in

Figure 88 follow a similar trend noted by Caceres, however, the volume of defects in this work originated during the solidification process, whereas, Caceres manually drilled defects in the samples tested.[42] Additionally, the property prediction curves in Figure

88 shed light onto the maximum properties obtainable for a perfect casting with no defects in the As-Cast condition. With this new information at hand, design engineers are now armed with a glimpse into the location specific properties without requiring the complete CA – FEA approach to be completed on each and every casting.

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(a) (b) (c) Figure 88: Mechanical property prediction for varying defect volumes.

6.9 Outlook on Location Specific Property Prediction

The CA – FEA approach offers a completely new method for predicting location specific mechanical properties at an unprecedented level of accuracy. It was shown that it is possible to seamlessly combine traditional CFD software such as ProCAST to cellular automaton microstructural modeling which can then be subsequently transferred into

FEA for property prediction. The CA – FEA approach offers a method for linking multiple length-scales with a limited amount of information loss between each transition.

By combining each of these CAE tools, the design process can be optimized to provide a fully comprehensive approach to the design engineer and aid in the production of high quality castings.

The ultimate goal of the CA – FEA approach is to extend and validate the model on complex, industrial castings to aid in the design and production of high quality cast components. Thus far, the CA – FEA has only been validated on the wedge casting, though has been shown to be incredibly accurate down to the nanometer level and shows promise to revolutionizing the design process for the casting industry. 185

Chapter 7: Conclusions and Future Work

The work summarized in the previous 6 chapters completes the ICME journey to obtain accurate location specific properties of cast components. As can be seen throughout this work, the key variable tied to each level of location specific mechanical property prediction has been solidification. Without properly understanding the fundamentals of the solidification process, it is not possible to accurately predict microstructural development, defect development or the eventual mechanical properties of a cast component. If the fundamentals of solidification are ignored for general empirical relationships, the field of casting and structural property development will be limited to minute levels of advancement for the foreseeable future. The lack of advancement will result in continued over-design, bulky structures that are poorly optimized for use within industry. In the context of the work presented here, the fundamentals of casting design, dendritic solidification, defect development and mechanics were explored to ultimately design optimized structures with location specific properties for cast aluminum alloys.

7.1 Key Conclusions

Throughout the discussion above it can be seen that there are two key stages of the casting process that greatly impact the development and variation in mechanical response

186 of cast structures: the filling stage and the solidification stage. Beginning with the filling stage in Chapter 5, it was shown that the design of casting can greatly affect the filling which ultimately leads to the entrainment of oxide inclusions and oxide-related defects.

The mere presence of oxide-related defects was shown to cut the ductility of local mechanical properties in half and demonstrated the need for predicting the location and severity of these defects. The introduction of the Oxide Entrainment Number was shown to greatly improve the predictive capability of the oxide inclusions and oxide-related defects as well as offering the potential to predict locations susceptible a severe drop in the ductility of cast structures. The OEN was also shown to provide a large improvement in the computational efficiency as it can calculate the location and severity of the oxide- related defects for large industrial components. Alternatively, all other oxide entrainment models can only roughly correlate the location specific entrainment for small, geometrically simple castings.

Following the filling stage, the onset of solidification begins, with the highlight of solidification on the mechanical response is most notably seen in the culmination of

Chapter 6, CA – FEA Modeling. Within the CA – FEA methodology, the key aspects from each of the previous chapters was explored to develop a CAE model that was shown to fully realize the location specific nature of property development with a cast structure.

The CA – FEA methodology begins with idea of location specific solidification conditions. It was observed that the geometric constraints of the wedge casting resulted in the development of unique dendritic microstructures as well as defect formation. Using the CA microstructural simulation and phenomenological understanding of dendritic

187 nucleation and growth explored in Chapter 4, the unique microstructural formation at each location in the casting were able to be determined. When the microstructural simulations were combined with porous oxide-related defects such as those discussed in

Chapter 5, the newly developed CA code was shown to accurately portray microstructural and defect development within a cast structure. The resulting variation in microstructure and defect development was shown to have profound effect on the local mechanical response within the single casting. By increasing the cooling rate, the rapid solidification resulted in refined microstructures with many small defects that often took on a spherical morphology and led to greatly improved ductility, yield strength and ultimate tensile strength. Slow cooling rates led to coarse microstructures, large, acicular or random morphology that led to increased stress concentrations and reduced elongation, yield strength and tensile strength. Though the trends are not surprising, the CA – FEA

Methodology offers the first computational model to predict the actual mechanical response of a cast structure while simulating the entire casting process from molten aluminum to final product.

Prior to the introduction of the CA – FEA methodology, the only way to estimate the mechanical response of cast structures was by using empirical relationships that correlated a general cooling rate to the likely mechanical property. Though this methodology is rooted in logic and can provide general trends in property prediction, empirical relationships can often miss the development of critical flaws or defects within the cast structure such as oxide entrained defects or hydrogen entrapment that can lead to catastrophic failure if not properly predicted or accounted for. The CA – FEA

188 methodology offers a solution to this lack of property prediction and allows for the introduction of a new design methodology where components can be designed to provide the strength of a casting only where it is needed to produce highly optimized cast structures.

Ultimately the CA – FEA methodology arms the casting design engineer with a new tool that can greatly cut the cost of design process. By utilizing the CA – FEA methodology to obtain accurate final mechanical properties, the costly validation step completed for each individual design can be eliminated allowing for improved, optimized, efficient design.

7.2 Future Work

When exploring the CA – FEA methodology, an obvious improvement would be to include the concept of location specific HTC maps as boundary conditions to the solidification process similar to the chill effect explored in Chapter 3. By implementing unique heat transfer throughout the casting, the fidelity cooling and solidification conditions can be greatly improved. The increased level of accuracy in solidification conditions will then enhance the accuracy of the microstructural CA simulations and ultimately allow for the increased accuracy of local mechanical response. The current difficulty in implementing the local HTC map is the computation problem of mapping a

2D map onto a complex 3D surface of the casting. If this can be accomplished, it would offer a great enhancement to the CA – FEA methodology.

A further improvement for the CA – FEA methodology would be to include further validation of location specific mechanical properties on a complex geometry casting.

189

Similar to how the OEN was validated using the directionally filled and node casting, the

CA – FEA methodology, must be proven to remain accurate for castings that do not force drastic variation in the cooling rates as was shown in the wedge casting. Future work should also be done to include precipitation modeling and microstructural variation in the as-cast microstructure so that the CA – FEA modeling can be used for heat-treated cast structures. Accomplishing this will allow the CA – FEA methodology to be applicable for all gravity cast situations.

The next obvious opportunity for the OEN is to extend its ability to predict local mechanical properties for pressure die cast structures. Microstructurally, the dendritic structure is no longer as discernable and the dendritic cell size or grain size must be examined. Additionally, the pressure die casting must account for new defects including air entrapment. The formation of these complex microstructures is currently under development and would serve to provide a fully coupled methodology for predicting the local mechanical response for all aluminum castings.

190

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