Predicting and Validating Multiple Defects in Metal Casting Processes Using an Integrated Computational Materials Engineering Approach

Home , Casting defect

Dissertation

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

Yan Lu

Graduate Program in Materials Science and Engineering

The Ohio State University

2019

Dissertation Committee:

Professor Alan A. Luo, Advisor

Professor Glenn S. Daehn

Professor Wei Zhang

Yan Lu

2019

Abstract

Metal casting is a manufacturing process of solidifying molten metal in a mold to make a product with a desired shape. Based on its own unique fabrication benefits, it is one of the most widely used manufacturing processes to economically produce parts with complex geometries in modern industry, especially for transportation and heavy equipment industries where mass production is needed. However, various types of defects typically exist in the as-cast components during the casting processes, which may make it difficult for post-processing and limit the service life and further application of products. It becomes imperative to analyze the processes in actual manufacturing conditions to predict and prevent those casting defects. Since it can be quite time consuming and costly to assess the processes experimentally, a computer-aided approach is highly desirable for product development and process optimization.

In recent decades, computer-aided engineering (CAE) techniques have been rapidly developed to simulate different casting processes, which have great benefits to tackle casting defects in a more practical and efficient way. This work focuses on using

ProCAST®, a finite element analysis (FEA) software, together with other necessary simulation and modeling techniques, including Computer-Aided Design (CAD),

Calculation of Phase Diagrams (CALPHAD) and Cellular Automaton (CA), to study relevant defects in actual metal casting foundries. Specifically, three different cases have been mainly investigated, including

(i) veining defect caused by thermal cracking in resin-bonded silica sand

molds/inserts for sand casting process;

(ii) thermal fatigue cracking in H13 steel dies/inserts for high pressure die

casting process; and

(iii) Hydrogen-induced gas porosity in A356 castings for gravity casting process

with permanent molds.

For each case, CAD model was designed and FEA model was constructed with validated materials database based on CALPHAD simulation, experiment tests and/or literature references. Coupled calculations of heat transfer, fluid flow for mold filling, and/or stresses and strains were run to obtain thermal and structural data for subsequent defects analyses and predictions. More importantly, key experiments at laboratory scale were designed and performed to reproduce those defects. Test results were employed to correlate and validate the predictions from simulation. The highlight of this dissertation is that an improved model and/or prediction criterion is proposed for each defect case and is dedicated to engineering applications, including

(i) a statistics-based cracking criterion of resin-bonded silica sand molds or

inserts in casting processes;

(ii) a temperature-based fatigue life prediction criterion for thermally-induced

cracking in H13 steel dies for die casting; and

(iii) a coupled CA-FE model for location-specific prediction of gas porosity in

A356 gravity castings with permanent molds.

This research is aiming at demonstrating that the integration of different CAE techniques and key experimental validations can help tackle the defects in various casting processes in a time-efficient and cost-effective manner. The results and the approach may be of great benefits to casting engineers for defect assessments and design optimizations in different casting processes.

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Dedicated to my beloved parents,

For their unconditional love, unwavering support and endless encouragement.

Acknowledgements

I must first express my deepest appreciation to my advisor, Prof. Alan A. Luo, for his continuous support and overarching guidance during the past five years. My graduate study and research were fully funded by industrial projects owing to his remarkable experience in industry. I would also like to thank him for encouraging me to explore into different research projects and for helping me grow as an independent researcher.

I would like to thank Prof. Wei Zhang and Prof. Glenn S. Daehn for serving as my committee members starting from my candidacy exam to my dissertation overview and to my dissertation defense. I also acknowledge Prof. Anthony F. Luscher for being the faculty representative in my dissertation defense. I am truly grateful for their valuable comments and constructive suggestions to make this work more complete.

I would also like to acknowledge Mr. Keith Ripplinger from Honda of America

Manufacturing, Inc. and Mr. Duane Detwiler from Honda R&D Americas, Inc. for their kind help and collaboration. Their friendly inputs and discussions in the regular project update meetings help improve this work.

I must also extend my sincere thanks to each and every colleague in the group for their great amount of support. I had the great pleasure of working with and learning from them, including Dr. Weihua Sun, Dr. Renhai Shi, Dr. Jiashi Miao, Andrew Klarner, Scott

Sutton, Zhi Liang, Emre Cinkilic, Xuejun Huang, Colin Ridgeway, Janet Meier and

Thomas Avey. Specifically, thanks to Dr. Huimin Wang for helping get started on my research here. Many thanks to Mr. Geoffrey Taber, a truly skilled artisan, for helping me build a key test unit in my research. Also many thanks to Dr. Cheng Gu for sharing his expertise in Cellular Automaton to help with my research.

I would also like to acknowledge SIMCenter at OSU for providing supercomputer resources to run the simulation and for offering access to quite a few softwares for my research purpose. I also acknowledge the technical assistance from Ross Baldwin, Steve

Bright, John (Pete) Gosser and Kenneth Kushner for their expertise and help in some parts of my experiments.

Last but not least, I am deeply indebted to my parents for their unconditional love.

They have always supported me and encouraged me to be brave and confident, no matter the path in life I choose. I also feel so lucky to meet my beloved girlfriend here at OSU, who has shared my joys and pains throughout my PhD life. For her constant support and dedication as always by my side, I thank her.

Vita

2010…………………………………………...Shanghai High School

2014…………………………………………...B.E. Materials Science and Engineering,

Shanghai Jiao Tong University

2014 to present...... Graduate Research Associate, Department

of Materials Science and Engineering, The

Ohio State University

Publications

1. Y. Lu, K. Ripplinger, X. Huang, Y. Mao, D. Detwiler, A.A. Luo, “A New Fatigue

Life Model for Thermally-Induced Cracking in H13 Steel Dies for Die Casting”,

Journal of Materials Processing Technology, September 2019, vol. 271, 444-454.

2. G. Cheng, Y. Lu, E. Cinkilic, J. Miao, A.D. Klarner, X. Yan, A.A. Luo, “Predicting

Grain Structure in High Pressure Die Casting of Aluminum Alloys: A Coupled

Cellular Automaton and Process Model”, Computational Materials Science, April

2019, vol. 161, 64-75.

3. E. Cinkilic, A.D. Klarner, Y. Lu, J. Brevick, A.A. Luo, M. Zolnowski, X. Yan, K.

Sadayappan, G. Birsan, “High Integrity Structural Aluminum Castings Produced with

Vacuum High Pressure Die Casting”, Die Casting Engineer, November 2018, 24-28.

4. Y. Lu, A.A. Luo, K. Ripplinger, D. Detwiler, “Simulation and Experimental

Evaluation of H13 Steel Thermal Fatigue Life in Die Casting”, North American Die

Casting Association Transactions, October 2018, T18-011.

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5. A.D. Klarner, E. Cinkilic, Y. Lu, J. Brevick, A.A. Luo, J. Shah, M. Zolnowski, X.

Yan, “A New Fluidity Die for Castability Evaluation of High Pressure Die Cast

Alloys”, North American Die Casting Association Transactions, September 2017,

T17-101.

6. Y. Lu, H. Wang, K. Ripplinger, A.A. Luo, “Process Simulation and Experimental

Validation of Resin-Bonded Silica Sand Mold Casting”, American Foundry Society

Transactions, 2017, vol. 125, 215-220.

7. H. Wang, Y. Lu, K. Ripplinger, D. Detwiler, A.A. Luo, “A Statistics-Based Cracking

Criterion of Resin-Bonded Silica Sand for Casting Process Simulation”,

Metallurgical and Materials Transactions B, February 2017, 48(1), 260-267.

Fields of Study

Major Field: Materials Science and Engineering

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Table of Contents

Abstract ...... ii

Acknowledgements ...... v

Vita ...... vii

List of Tables...... xiii

List of Figures ...... xiv

Chapter 1: Introduction ...... 1

1.1 Metal Casting ...... 1

1.2 Why Modeling? ...... 2

1.3 Casting Simulation Software ...... 3

1.4 Scope of Research ...... 5

1.5 Outline of Dissertation ...... 6

Chapter 2: Thermal Cracking in a Resin-Bonded Silica Sand Mold...... 7

2.1 Motivation and Problem Description ...... 7

2.1.1 Background and Motivation ...... 7

2.1.2 Literature Review of the Problem ...... 8

2.1.3 Abstract for the Research ...... 9

2.2 Mechanical Properties of Test Sand ...... 10

2.2.1 Three-Point Bending Test ...... 11

2.2.2 Tensile Test ...... 14

2.2.3 Hardness Test ...... 15

2.3 Fracture Probability Map ...... 17

2.3.1 Weibull Statistics for Three-point Bending Test ...... 17

2.3.2 Cracking Probability Map Based on Three-point Bending Results ...... 21

2.4 Sand Cup Mold Model ...... 23

2.4.1 Sand Cup Mold Design ...... 23

2.4.2 Construction of Model Database ...... 24

2.5 Sand Casting Experiment Validation ...... 26

2.5.1 Temperature Profile Comparison ...... 27

2.5.2 Cracking Position Comparison ...... 29

2.5.3 Finalized Fracture Probability Map ...... 32

2.5.4 Scope and Limitations of the Map ...... 34

2.6 Conclusions and Highlights ...... 36

Chapter 3: Thermal Fatigue Cracking in an H13 Steel Die ...... 38

3.1 Motivation and Problem Description ...... 38

3.1.1 Background and Motivation ...... 38

3.1.2 Literature Review of the Problem ...... 38

3.1.3 Abstract for the Research ...... 42

3.2 Experimental Procedures ...... 43

3.2.1 Samples and Materials ...... 43

3.2.2 Thermal Fatigue Test Unit ...... 45

3.3 Simulation Model ...... 49

3.3.1 Materials Database...... 49

3.3.2 Simulation Setup...... 51

3.3.3 Geometry Optimization ...... 52

3.4 Experimental Results ...... 56

3.4.1 Temperature Contours ...... 56

3.4.2 Cracking Failures ...... 63

3.4.3 Hardness Profiles ...... 66

3.5 Thermal Fatigue Life Prediction Criterion ...... 68

3.5.1 Derivation of the Criterion ...... 68

3.5.2 Fitting the Criterion ...... 72

3.5.3 Scope and Limitations of the Criterion ...... 75

3.6 Conclusions and Highlights ...... 78

Chapter 4: Hydrogen Gas Porosity in an A356 Casting ...... 80

4.1 Motivation and Problem Description ...... 80

4.1.1 Background and Motivation ...... 80

4.1.2 Literature Review of the Problem ...... 81

4.1.3 Abstract for the Research ...... 83

4.2 Experimental Procedures ...... 84

4.2.1 Samples and Materials ...... 85

4.2.2 Wedge Casting Experiment ...... 86

4.2.3 Hydrogen Content Measurements ...... 87

4.2.4 Metallography Analyses ...... 87

4.2.5 Micro-Computed Tomography Analyses...... 88

4.3 Process Simulation and Microstructure Modeling ...... 90

4.3.1 Finite Element Analysis for Process Simulation ...... 90

4.3.2 Cellular Automaton for Microstructure Modeling ...... 91

4.4 Results and Discussion ...... 94

4.4.1 Initial Hydrogen Content ...... 94

4.4.2 Temperature Profiles...... 96

4.4.3 Microporosity Characterization – Qualitative Analysis ...... 99

4.4.4 Microporosity Characterization – Quantitative Analysis ...... 104

4.5 Scope and Limitations of the Coupled Model ...... 107

4.6 Conclusions and Highlights ...... 109

Chapter 5: Summary and Future Work ...... 111

5.1 Summary ...... 111

5.2 Recommendations for Future Work ...... 114

References ...... 116

Appendix A: MATLAB Code ...... 127

Appendix B: Programmable Logic Controller Code ...... 130

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List of Tables

Table 1. Commonly-used commercial casting simulation softwares...... 5

Table 2. Three-point bending test results and data wrangling...... 19

Table 3. Summary of casting experiments for the three sand cup molds...... 30

Table 4. Effective volume calculations for each type of sand cup mold...... 33

Table 5. Temperature-dependent effective volume and maximum stress using intact sand cup mold as an example...... 35

Table 6. Chemical composition of tested H13 samples in wt.%...... 44

Table 7. Cycle time details for the two different geometry samples...... 48

Table 8. Cases of different geometries for MDI sample...... 53

Table 9. Temperatures from experimental test and FEA simulation for SP sample...... 60

Table 10. Surface temperatures between experimental test and FEA simulation for MDI sample with different heating methods...... 61

Table 11. Summary of thermal fatigue test for SP samples...... 65

Table 12. Summary of thermal fatigue test for MDI sample...... 74

Table 13. Chemical compositions of tested A356 wedge casting...... 85

Table 14. Instantaneous and average cooling rates for three locations...... 97

Table 15. Quantification of the microporosity number, volume and fraction at different cooling rates...... 104

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List of Figures

Figure 1. Multiphysics for metal casting processes [5]...... 2

Figure 2. Flowchart for main modules in casting process simulation...... 4

Figure 3. Typical veining defects on castings as highlighted in red dashed circles...... 7

Figure 4. Heated shell curing accessory for making dog-bone tensile samples and rectangular three-point bending samples...... 11

Figure 5. Schematic of three-point bending test setup and sample dimensions...... 12

Figure 6. Typical force vs. deflection curve of a three-point bending sample...... 13

Figure 7. Gaussian probability distribution of three-point bending fracture stress...... 14

Figure 8. Uniaxial tensile test for a dog-bone sample and the sample dimension...... 15

Figure 9. Surface hardness scratch on a three-point bending sample after test...... 16

Figure 10. Least squares fitting for Weibull modulus calculation...... 20

Figure 11. Estimated coefficient information for the linear regression model...... 21

Figure 12. Fracture probability map by three-point bending test...... 22

Figure 13. (a) Schematic cross-section of intact sand cup mold, and actual cured sand cup molds for (b) intact cup mold, (c) flat-notch cup mold and (d) V-notch cup mold...... 24

Figure 14. Linear hardening isotropic elasto-plastic model [18]...... 25

Figure 15. (a) Side view and (b) top view of the thermocouple setup in the experiment, and (c) corresponding center node selection in FEA model...... 27

Figure 16. Comparison of A356 temperature profiles between FEA simulation and thermocouple measurement for intact sand cup mold...... 28

Figure 17. Comparison of sand temperature profiles between FEA simulation and thermocouple measurement for intact sand cup mold...... 29

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Figure 18. Snapshots of V-notch cup mold at (a) t = 3s (Pouring finished), (b) t = 8 s (5 s after pouring), (c) t = 33 s (30 s after pouring) and (d) t = 53 s (50 s after pouring)...... 30

Figure 19. Simulation and experimental results of three different geometry cup molds: (a)

1st principal stress from FEA casting simulation; (b) and (c) Cup molds before and after pouring, respectively...... 31

Figure 20. Fracture probability map with all points, including three-point bending tests, tensile tests, original intact cup mold, flat-notch cup mold and V-notch cup mold...... 34

Figure 21. Classic water jacket insert and typical thermal fatigue crack on it [52]...... 39

Figure 22. Schematic drawing of the SP sample for thermal fatigue test...... 44

Figure 23. MDI sample for (a) and (b) schematic drawing with major dimensions, and (c) machined test sample with a clamping rod...... 45

Figure 24. Schematic drawing of thermal fatigue test setup in this work...... 46

Figure 25. Different perspectives of finalized dipping test unit...... 47

Figure 26. Hardware and wirings in the control panel...... 47

Figure 27. Material properties of SP and MDI samples for thermal simulation...... 50

Figure 28. Temperature-dependent properties of MDI samples for stress simulation...... 51

Figure 29. Boundary conditions for SP sample with applied alternating temperatures and heat transfer coefficients...... 52

Figure 30. Geometry features of MDI samples from top view for (a) Case 1; (b) Case 2;

Figure 31. Temperature contours (top row) and the 1st principal stress contours (bottom row) during coolant cooling stage for (a) Case 1; (b) Case 3 and (c) Case 6...... 55

Figure 32. FEA calculations of temperature and the 1st principal stress evolutions of notch

xv tip AB (Case 6) for MDI sample...... 56

Figure 33. Thermal camera measurements of SP sample after it is taken out from kiln.

Kiln temperatures are at 750 °C, 850 °C and 950 °C from left to right, respectively...... 57

Figure 34. FEA results of SP sample temperature contours after it is taken out from kiln.

Kiln temperatures are 750 °C, 850 °C and 950 °C from left to right are, respectively. .... 58

Figure 35. Comparison of SP sample temperature contour after sample is water cooled between FEA simulation (left) and thermal camera measurement (right)...... 59

Figure 36. Correlation between thermal camera measurements and FEA simulation of

MDI sample for maximum temperature (left two) and minimum temperature (right two) using kiln chamber heating method...... 61

Figure 37. Typical sticky Al captured (a) in thermal camera and (b) on MDI sample. .... 62

Figure 38. Thermal cracking observation for SP sample of (a) original notch, (b) notch after 4570 cycles for 750 °C kiln heating, (c) notch after 1590 cycles for 850 °C kiln heating, and (d) notch after 870 cycles for 950 °C kiln heating...... 64

Figure 39. Notch tip of MDI sample with dye penetrant inspections...... 66

Figure 40. Micro-hardness changes with respect to distances from the surface of a water jacket insert before and after about 15000 cycles in service...... 67

Figure 41. Experimental 푁푓 vs. ∆푇 data and model fitting for SP sample...... 72

Figure 42. Relationship between pore size and fatigue life of cast 319 Al alloy [92]...... 80

Figure 43. Definition and classification of shrinkage and porosity defects [95]...... 81

Figure 44. Schematic of wedge cast with locations of thermocouples in red dots...... 85

Figure 45. Permanent mold of wedge casting (left) and actual wedge cast sample with locations of thermocouples labelled (right)...... 86

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Figure 46. Schematic diagram of reduced pressure tester...... 87

Figure 47. Cylindrical samples cut from wedge cast (left) and hot-mounted in Bakelite powder (right)...... 88

Figure 48. Schematic of microCT scan setup for (a) side view and (b) top view...... 89

Figure 49. Schematic of Cellular Automaton cells in 2-D [124]...... 91

Figure 50. Calculation flowchart for grain growth with porosity evolution...... 93

Figure 51. Cooling curves measured by thermocouples at three locations...... 96

Figure 52. Cooling curve comparisons between FEA and experiments...... 98

Figure 53. Comparisons of optical microstructures and CA simulated results at different cooling rates of (a) & (b) 64.75 K/s, (c) & (d) 10.67 K/s, and (e) & (f) 2.52 K/s...... 100

Figure 54. Longitudinal and cross-sectional 2-D microCT images...... 101

Figure 55. 3-D reconstructed microporosity for different cooling rates at (a) 2.52 K/s, (b)

10.67 K/s, and (c) 64.75 K/s...... 102

Figure 56. Comparisons of the porosity morphology between microCT results and CA simulated results at different cooling rates. Specifically, microCT results are in (a), (d), and (g); simulated porosity morphology in (b), (e), and (h); and simulated dendrite morphology in (c), (f), and (i). The cooling rates are: 64.75 K/s for (a)-(c); 10.67 K/s for

(d)-(f); and 2.52 K/s for (g)-(i). (Grains are shown in green; porosity is shown in black in

(a), (d), and (g), and in blue in (b), (e), and (h))...... 103

Figure 57. Distributions of individual porosity volume (left) and its equivalent radius

(right) at different cooling rates...... 105

Figure 58. Sphericity distribution of microporosity at different cooling rates...... 106

Figure 59. Schematic illustrating how defect formation incorporates phenomena which

xvii span six orders of magnitude of both the spatial and temporal scales [134]...... 107

Figure 60. Schematic diagram of coupled process simulation and microstructure modeling for multi-scale grains and porosity during solidification [135]...... 108

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Chapter 1: Introduction

1.1 Metal Casting

Metal casting is an ancient technology with a glamorous history of more than

5,000 years, which can be dated back to the origination of human civilizations [1]. Its technological advances have generated a huge impact on the development and advancement of human cultures [2]. Nowadays, it has become one of foundations in manufacturing industry and is the main wealth producer within the world economy.

According to the 2018 American Foundry Society survey [3], United States ranks third globally in castings production, trailing only China and India. As measured by tonnage per plant, United States ranks second in productivity, trailing only Germany. Meanwhile, when rated on a value-added basis, metal casting is one of the ten largest U.S. industries and the state of Ohio is leading the nation by number of foundries.

Generally speaking, metal casting is the process of forming metallic objects by melting metal, pouring it into the shaped cavity of a mold and allowing it to solidify [4].

It is a truly interdisciplinary field with multiple simultaneous physical phenomena. As shown in Figure 1, it can be clearly seen that for casting process, everything happens at the same time and is fully coupled, which is one of the biggest benefits and its biggest downfall as well [5]. In this way, changing one process parameter will impact many relevant casting features that will define the ultimate product quality. Therefore, metal casting is probably the most complex process among current known manufacturing techniques. In addition, when considering different casting conditions, modern advances in casting technology have led to a broad array of specialized casting methods, including sand casting, plaster mold casting, lost-wax casting, high/low pressure die casting,

1 investment casting, squeeze casting and other processes. Despite that each method can provide its own unique fabrication benefits, there is no “perfect” castings and imperfections always exist during the process. Some defects are ubiquitously seen in various casting processes, while others are unique to a specific process.

Figure 1. Multiphysics for metal casting processes [5].

Over the decades, many efforts have been done to optimize process conditions to eliminate defects as best as one can. A well-known example is the book by Prof. John

Campbell discussing about ten rules for making reliable castings [6]. However, process engineers typically use trial-and-error methods based on empirical relationships between processing parameters and product quality. As today’s casting industry demands lower cost, shorter lead time and better quality assurance, casting process simulation has gained acceptance as a universal tool in foundry, especially in the past two decades.

1.2 Why Modeling?

During the past few decades, there have been a general trend that discovery and

2 development of new materials have gradually migrated from meticulous experimental exploration using “trial-and-error” and “design of experiments” methods to material design approaches based on thermodynamics and kinetics for engineering application [7].

Process modeling enables engineers to make virtual castings using computer-aided techniques to evaluate the products by modifying a set of processing parameters easily.

Over the years, continual joint efforts have been made by universities, government laboratories and industries for substantial progress in process simulation area, particularly in removing roadblocks to the further advancement of the technology and by creative examples [8–15].

However, it is still quite challenging to develop a comprehensive model to represent all physics. Sine each defect has its own unique characteristics which have a dominant effect on the quality of resultant product, developing a model that captures those characteristics with reasonable assumptions is often not only technically sufficient, but also cost effective [16]. It is up to designers and engineers to decide whether a descriptive or predictive model should be developed and what kind of conditions need to be simulated to predict and control each specific defect in the available software package.

Therefore, it has been the subject of intensive investigations to provide proper simulation models and criteria to tackle various defects in casting processes for making products with better quality and lower cost.

1.3 Casting Simulation Software

In general, almost all process simulation softwares consist of three main modules, i.e. preprocessor, solver and postprocessor, which apply to casting simulation as well.

Figure 2 presents the three main modules and the flowchart of important procedures in each module. To be more specific, casting process simulation analyses include:

1. Pre-processing: a CAD model is first developed and its geometry is divided

into smaller basic elements and connected at discrete nodes through the

process of meshing. Then the materials properties are assigned based on the

database constructed using CALPHAD, experiments and/or literature

references. In addition, every node is assigned with some initial and boundary

conditions, such as loads, constrains, heat transfer coefficient (HTC), etc.

2. Solving: the problem is solved temporally and spatially using numerical

methods. Based in the solvers executed, different field variables will be

computed, such as temperature field, fluid flow, stress and strain,

microstructures, and so on. Some software may have its own built-in modules

for defect predictions as well.

3. Post-processing: the final results get visualized using graphical display.

Meanwhile, depending on the software interface, subroutines can be defined

using user-defined criterion functions and/or results can be exported for

subsequent simulations, such as Cellular Automaton.

Figure 2. Flowchart for main modules in casting process simulation.

Furthermore, Table 1 summarizes the current commonly-used commercial casting simulation softwares in research institutes and manufacturing foundries around the world.

Based on different discretization methods to solve different physical phenomena, the three most common methods are Finite Element Method (FEM), Finite Difference

Method (FDM) and Finite (Control) Volume Method (FVM) [17]. Since the author mainly uses ProCAST for his research, let’s take ProCAST as an example. It is a FEM- based software that involves the modeling of thermal heat transfer (including radiation), fluid flow (including mold filling), and stresses fully coupled with the thermal solution

(thermomechanics) [18]. In addition, modeling and simulation of microstructure, heat treatment, grain structure and porosity are integrated in the software as well.

Table 1. Commonly-used commercial casting simulation softwares. Software Name Numerical Method Vendor Country Flow-3D Cast FDM / FEM Flow Science Inc. USA EKKcapcast FEM EKK Inc. USA ProCAST FEM ESI Group France MAGMAsoft FDM Magma GmbH Germany ADSTEFAN FDM Hitachi Japan AnyCasting FDM AnyCasting Co. Ltd. South Korea © InteCAST FDM Huazhu CAE China

1.4 Scope of Research

Previous sections have introduced metal casting processes and brief information about casting process simulation as well as current software packages. This research work concentrates on utilizing casting process simulation and some other necessary computer-aided engineering techniques to tackle defects in different casting processes.

Although the author has been involved in the research for several defects project, this dissertation only focuses on demonstrating three types of defects by taking three case studies. These cases studies have been encountered in practical industrial applications,

5 and this research work has attempted to solve them.

In general, for each case study, the problem background and motivation will be first described. Then the fundamental model development will be presented with a focus on developing an accurate and efficient model with considerations of corresponding casting process conditions. By reproducing each defect at laboratory scale, the model is then evaluated and validated with experimental data. Specific criterions and/or general guidelines are proposed, based on analyses of the simulation and experimental data. The ultimate objective is to predict and control each defect for engineering applications.

1.5 Outline of Dissertation

The dissertation is structured in the following way.

Chapter 2 presents the results of research performed on veining defect caused by thermal cracking in resin-bonded silica sand molds/inserts for sand casting process.

Chapter 3 presents the results of research conducted on fatigue cracking in H13 steel dies/inserts for high pressure die casting process.

Chapter 4 presents the results of research carried out on Hydrogen-induced gas porosity in A356 castings for gravity casting process with permanent molds.

Chapter 5 summarizes the work of the dissertation, and presents ideas for further research related to the three types of defects in casting processes.

Chapter 2: Thermal Cracking in a Resin-Bonded Silica Sand Mold

2.1 Motivation and Problem Description

2.1.1 Background and Motivation

Sand casting is the most commonly used casting process, which accounts for about 90% of all casting production. Sand can be used for making molds and cores, and components with intricate cavities can be cast by inserting sand cores. Among all the aggregates used to produce sand molds/cores, silica sand is the most popular in producing highly dimensionally accurate castings at a cost more favorable than other materials, such as zircon, chromite, and mullite ceramic [19]. In molding operations, resin binders and hardeners are generally added into silica sand. Sand with these mixtures is called resin- bonded sand, and it typically consists of 93-99% silica and 1-3% binders [20].

Veining is a casting defect occurred during filling and solidification due to the crack in sand molds/cores. As schematically shown in Figure 3 (image courtesy of Honda of America Manufacturing, Inc.), such defects are tiny burrs or fins on as-cast products that are too difficult to detect and remove in post machining. Therefore, a robust cracking criterion, relating sand properties and stress/thermal conditions, is needed in predicting and/or controlling veining defects to optimize casting design.

Figure 3. Typical veining defects on castings as highlighted in red dashed circles.

2.1.2 Literature Review of the Problem

In order to control the veining defect, many studies have been done focusing on the improvement of sand properties by adding sand additives to reduce the thermal expansion. Campbell proposed that veining defects were originated from the thermal expansion of sand [21]. Thiel et al. did some studies to modify the binder compositions to improve the sand anti-veining property [9, 12]. Baker and Werling enumerated a couple of expansion control methods for sand cores [23]. Liu et al. investigated the factors that affect performance of no-bake resin bonded sand and optimized the furan resin, curing agent and boric acid content for magnesium alloy casting [24]. Bargaoui et al. compared foundry sand cores and bonding resin behaviors between room temperature and 723.15 K

(450 °C) [25]. However, aside from the investigation and improvement of sand thermal expansion, the geometry design, mechanical support and thermal history of the sand molds/cores should also be considered to better understand veining defect.

In addition, there has only been a limited work on predicting the veining defect.

One that is worthy of most noting is that Dong et al. have carried out experiments to establish a cracking criterion for resin-coated silica sand and managed to combine the criterion with casting simulation results to predict cracking [26]. They employed Weibull statistics in failure probability prediction, where Weibull statistics was proposed by

Weibull in 1939 for brittle material strength distribution [27]. However, there are several issues in this study that need further discussion. First of all, they used tensile test results of sand samples to generate the cracking probability map. Previous studies have shown that tensile test is not appropriate for brittle materials to generate the map [28]. In tensile test, the stress concentration near the jaws of the testing machine causes failure to occur

8 at the jaw locations, not in the gauge section of the specimen. Due to the failure near the jaws for some of the sand samples in their study, a larger effective volume than the gauge section was used for cracking probability map calculation and they assumed both the transition section and the gauge section were under the same tensile stress. However, the cross section of the transition region has much more area and lower tensile stress than the gauge section. The determination of effective volume has a significant effect on the accuracy of cracking probability map. A larger effective volume moves the curve plots in the cracking probability map upward. Secondly, only 10 tests were carried out in their study. From a statistical point of view, it is significantly lower than the minimum requirement (30 tests) to have good confidence in Weibull modulus calculation [29].

Thirdly, substituting the equation 2 variables in their paper with their measured and calculated data, the calculation of constant 푐 is in error, which will further affect their plots and predictions accuracy. Based on the above discussion, a more accurate cracking probability map for sand molds/core is needed. Despite these deficiencies, their work has been innovative in employing statistics to predict the “brittle” behavior of sand as a probability event, which provided a good starting point for further advancement in this research.

2.1.3 Abstract for the Research

In this research, resin-bonded silica sand with 98.7% silica and 1.3% phenolic resin binder was studied. Mechanical tests, including three-point bending test, tensile test and hardness test, were first performed to obtain the basic characteristics of the sand.

Experimental data from mechanical tests, together with some key data from literatures,

9 were used to build a material model for sand molds/cores for casting process simulation.

Furthermore, Weibull statistics was employed to generate a cracking probability map for the sand based on the three-point bending test results of sand samples. The safe and unsafe regions were distinguished on the map using both three-point bending test and tensile test results. With the constructed sand material model, casting simulation for three different geometries of sand cups was performed, and the cracking probability map was applied for the cup mold cracking prediction in A356 alloy gravity sand casting. Finally, corresponding laboratory experiments were carried out to validate the simulation results and the accuracy of the map. The good correlation suggests potential applications of cracking probability maps and process simulations in the design of sand molds/cores to prevent and control sand cracking during casting.

2.2 Mechanical Properties of Test Sand

Mechanical tests, including three-point bending test, uniaxial tensile test and hardness test were performed. Rectangular three-point bending samples and dog-bone tensile samples were made and cured using a Heated Shell Curing Accessory unit from

Dietert Foundry (Detroit, Michigan, USA) as shown in Figure 4. The pattern for dog- bone samples came along with the curing accessory, while the pattern for rectangular three-point bending sample was made in-house. The same curing condition with 523.15

K (250 °C) for 40 seconds was used to make all test samples. Since resin-bonded silica sand behaves more like a brittle material, its fracture stress varies in a much wider range as compared to that of ductile one. Thus, 36 three-point bending samples were tested so that the results would be more representative and statistically reliable. In addition, 7

10 uniaxial tensile tests were completed as a supplement for mechanical properties. The reason that more bending tests were planned than tensile is due to the fact that normally tension test is not preferred for brittle materials. The stress concentration near the jaws of the testing machine causes failure at the jaws, rather than in the gage section [30]. Thus, more specimens were tested in bending than in tension.

Figure 4. Heated shell curing accessory for making dog-bone tensile samples and rectangular three-point bending samples.

2.2.1 Three-Point Bending Test

Three-point bending test is commonly used to understand foundry sand properties.

For example, Stauder et al. employed the test to investigate mechanical and functional properties of foundry sand with four different organic bind systems [31]. Additionally, studies have shown that the results from three-point and four-point bending tests have no statistically significant differences between elastic modulus values. However, flexural strengths are statistically higher in three-point bending than four-point bending, and the volume under stress is smaller in three-point bending than the one under four-point bending [32]. Since for sand its strength is typically below 10 MPa, to ensure that the data is not too small in absolute value to be differentiated, three-point bending test was

11 chosen for analyses. The test was completed at room temperature with standard MTS testing system using a load cell of 44.48 N (10 lbf ) with a noise of ±0.2 N and a loading speed of 0.27 mm/s. Each sample was made with a dimension of 114.3 × 19.05 × 6.35 mm. Figure 5 presents the schematics of test setup and sample dimensions. The test setup and sample dimensions were designed based on ASTM C1341-13 standards. The ratio of thickness to support span was chosen to be 1:16, and thus the support span of each three- point bending sample was 101.6 mm.

Figure 5. Schematic of three-point bending test setup and sample dimensions.

Both the sample deflection 퐷 and loading force 퐹 were obtained from the MTS testing system. The deflection 퐷 here represents the distance that a bending sample is displaced under a loading force 퐹. Using these data, fracture stress and elastic modulus for three-point bending test were calculated as [33]

3퐹퐿 휎 = Eq.1 푓 2푏푑2

퐿3 퐹 퐸 = ( ) Eq.2 4푏푑3 퐷 where 퐹 is loading force, 퐿 is support span, 푏 is the width of bending sample and 푑 is the thickness of the sample.

For the bending samples, the material behaved in a predominantly elastic manner and fractured in a brittle mode as expected. However, one-third of the tested specimens exhibited a linear hardening behavior right before failure occurred. A representative curve of force vs. deflection for this bilinear behavior is shown in Figure 6. The red line was fit to both the elastic portion and linear hardening stage. The presence of inelastic behavior of resin-bonded silica sand is rarely reported, but a similar phenomenon was also found by Thole and Beckermann in three-point bending tests of phenolic-urethane no-bake (PUNB) bonded sand that plastic deformation was observed before the specimen fractured [34]. While the elastic part is expected to be the same under different loading conditions, the inelastic behavior may mainly be particular to three-point bending tests.

Figure 6. Typical force vs. deflection curve of a three-point bending sample.

Furthermore, from Eq.1 and Eq.2, the average fracture stress of total 36 tested samples was calculated to be 3.233 MPa with a standard deviation of 0.585 MPa. The average elastic modulus was 2300 MPa. Sample mass was also measured and density was calculated as 1628 kg/m3. To further highlight the fracture stress distribution, Gaussian probability distribution function was introduced as

1 (푥 − 휇)2 푓(푥; 휇, 휎) = 푒푥푝 (− ) Eq.3 휎√2휋 2휎2 where 휇 is average fracture stress, 휎 is standard deviation and 푥 is the random variable.

Based on Eq. 3, the distribution curve is plotted in Figure 7, where there are 31 samples fall in 휇 ± 휎 region, 3 samples in 휇 ± 2휎 and 1 in 휇 ± 3휎. There is only one sample that is out of 휇 ± 3휎 region, indicating a good consistency in bending tests.

Figure 7. Gaussian probability distribution of three-point bending fracture stress.

2.2.2 Tensile Test

Uniaxial tensile test was completed at room temperature as well using the MTS testing system with a load cell of 2224 N (500 lbf ) with a noise of ±0.3 N and a loading speed of 0.02 mm/s. The dog-bone tensile test sample was prepared based on AFS 3307-

11-S standards with thickness of 6.35 mm. Figure 8 shows the MTS uniaxial tensile test for a dog-bone sample and the sample dimension details with unit in inches.

Figure 8. Uniaxial tensile test for a dog-bone sample and the sample dimension.

For the 7 tensile test samples, the average ultimate tensile stress (UTS) was 1.450

MPa with a standard deviation of 0.258 MPa. It is evident that the average fracture stress from three-point bending is about two times the average UTS from uniaxial tensile tests.

A primary reason may be that there is no axial load in bending test as that is in tensile one.

Instead, the beam type bending samples give rise to large shear deformations during tests.

In three-point bending test, the top half part of the sample is in compression while the bottom half in tension, which is unlike the uniform stress in the cross section area of tensile specimens. In this way, extra loading force, and thus higher fracture stress is required for three-point bending tests.

2.2.3 Hardness Test

The main objective for hardness test is to employ it as a semi-quantitative method to confirm the consistency of curing conditions. Hardness test was performed using an

Electronic Scratch Hardness Tester from Simpson Technologies (Aurora, Illinois, USA).

After rotating three revolutions of a four-point cutter to penetrate the test sample surface, the depth of penetration into the sample determines the hardness. Figure 9 presents a

15 scratch on a three-point bending sample after test. Typical hardness values of the cured sand samples were located in 60-70, with 20 being 1 mm penetration depth. Attention should be paid that the sand surface hardness value in this study may not be comparable to other systems, and it is mainly utilized to provide a more dependable judgement of curing degree rather than looking at the curing color with naked eyes.

Figure 9. Surface hardness scratch on a three-point bending sample after test.

It needs to be further emphasized that sand cores/molds often appear uniform to the naked eyes, but density gradients have been existed as inevitable in all molds/cores formed using foundry sand [35]. Such gradient refers to the non-uniform distribution of sand and it has been universal in sand products. Successful use of the sands requires proper placement and compaction to ensure adequate performance. In foundry, a couple of measures have been employed to check the uniformity, such as combining optical profilometry for surface roughness quantifications and acoustic simulation for density variations [35], evaluating density gradient formation during the compaction by X-ray computed tomography [36], and following standard procedures of Maximum and

Minimum Index Density (ASTM D-4253 and ASTM D-4254) or other procedures [37].

In this study, for laboratory test, surface hardness test was employed as a simple and low cost way to ensure that uniformity was within acceptable range.

2.3 Fracture Probability Map

Weibull statistics was proposed by Weibull in 1939 to evaluate the strength distribution of brittle materials [27]. It is based on the weakest link in the material, where the material fails if its weakest volume fails. The theory presumes that flaws are likely to be evenly distributed in the sample and that the probability of having the weakest link depends on the material volume under stress, which is called “effective volume”. Thus, the failure probability of the material is not only related to the applied stress, but also to the effective volume. Weibull statistics has been widely applied to ceramics [38], glass

[39], dental materials [40], and polyethylene films [41]. In this study, based on three- point bending test results, Weibull statistics is employed to construct a cracking probability map for the sand.

2.3.1 Weibull Statistics for Three-point Bending Test

In Weibull statistics, failure probability under applied stress 휎 is expressed as

휎 푚 푃푓 = 1 − 푒푥푝 [− ∫ ( ) 푑푉] Eq.4 푉 휎0 where 푃푓 is the failure probability, 푚 is Weibull modulus that relates to stress distribution or data scatter and is material property related, and 휎0 is nominal strength as a symbolic parameter without specific physical meaning. Mathematically, effective volume 푉퐸 is

휎 푚 푉퐸 = ∫ ( ) 푑푉 Eq.5 푉 휎푚푎푥 where 휎푚푎푥 is the maximum fracture stress in test samples. Equivalently, Eq.4 can be expressed with the term of effective volume 푉퐸 as

푚 휎푚푎푥 푃푓 = 1 − 푒푥푝 [− ( ) 푉퐸 ] Eq.6 휎0 which is a general form of Weibull statistics for failure probability calculation, and both

푚 and 휎0 can be derived from a least-square fit of experimental data [42].

Specifically, in three-point bending test, the effective volume can be calculated from the integral form of Eq.5 as

푉 푉 = Eq.7 퐸 2(푚 + 1)2 where 푉 is volume of the tested three-point bending sample. Plug Eq.7 into Eq.6 yields

푚 휎푚푎푥 푉 푃푓 = 1 − 푒푥푝 [− ( ) 2] Eq.8 휎0 2(푚 + 1)

Move around and take natural logarithm transformation on both sides will further yield

푉 푙푛 (−푙푛(1−푃 )) = 푚푙푛(휎 ) + 푙푛 ( ) − 푚푙푛(휎 ) Eq.9 푓 푚푎푥 2(푚 + 1)2 0

In this way, the failure probability equation for three-point bending sample is transformed to a linear regression model, where Weibull modulus 푚 represents the slope of the linear relationship and 휎0 can be calculated from the fitted intercept.

Concretely, for three-point bending tests, 휎푚푎푥 is deemed as the fracture stress calculated in Eq.1 for each sample. Meanwhile, failure probability 푃푓 of each three-point bending sample can be calculated using median rank method as

푗 − 0.3 푃 = Eq.10 푓 푛 + 0.4 where 푗 is the rank in ascending order of three-point bending fracture stress data and 푛 is the number of tested samples. As mentioned in previous Gaussian probability distribution results, there are 35 samples within ±3휎 region, which are considered as statistically

18 significant and 푛 = 35 in this case. By assorting 휎푚푎푥 values of the 35 samples in an ascending order, the corresponding failure probability can be calculated as in Table 2.

Table 2. Three-point bending test results and data wrangling.

Rank 푗 Force / N 휎푚푎푥 / MPa 푙푛(휎푚푎푥) 푃푓 푙푛 (−푙푛(1−푃푓)) 1 13.747 2.727 1.003 0.020 -3.913 2 13.891 2.756 1.014 0.048 -3.012 3 14.211 2.819 1.036 0.076 -2.534 4 14.318 2.841 1.044 0.105 -2.204 5 14.356 2.848 1.047 0.133 -1.949 6 14.411 2.859 1.050 0.161 -1.740 7 14.630 2.903 1.066 0.189 -1.562 8 14.670 2.910 1.068 0.218 -1.405 9 14.904 2.957 1.084 0.246 -1.266 10 14.990 2.974 1.090 0.274 -1.139 11 15.163 3.008 1.101 0.302 -1.022 12 15.297 3.035 1.110 0.331 -0.913 13 15.377 3.051 1.115 0.359 -0.811 14 15.406 3.057 1.117 0.387 -0.715 15 15.511 3.077 1.124 0.415 -0.623 16 15.769 3.129 1.141 0.444 -0.534 17 15.852 3.145 1.146 0.472 -0.449 18 15.979 3.170 1.154 0.500 -0.367 19 16.034 3.181 1.157 0.528 -0.286 20 16.167 3.208 1.166 0.556 -0.207 21 16.586 3.291 1.191 0.585 -0.129 22 16.894 3.352 1.210 0.613 -0.052 23 16.903 3.354 1.210 0.641 0.025 24 16.906 3.354 1.210 0.669 0.102 25 17.655 3.503 1.254 0.698 0.179 26 17.692 3.510 1.256 0.726 0.258 27 17.815 3.535 1.263 0.754 0.339 28 17.876 3.547 1.266 0.782 0.422 29 18.201 3.611 1.284 0.811 0.510 30 18.257 3.622 1.287 0.839 0.602

31 18.304 3.632 1.290 0.867 0.703 32 20.728 4.113 1.414 0.895 0.815 33 20.902 4.147 1.422 0.924 0.945 34 21.743 4.314 1.462 0.952 1.111 35 23.827 4.727 1.553 0.980 1.367

Based on the data in Table 2, and by using least squares fitting, Eq.9 can be fitted as shown in Figure 10. From the fitted linear regression curve, Weibull modulus 푚 can be calculated as 8.0928 for slope, and 휎0 is computed from the fitted intercept as 0.466

MPa. These data will be further used in constructing the cracking probability map later.

Figure 10. Least squares fitting for Weibull modulus calculation.

In addition, from the estimated coefficient information as shown in Figure 11, it can be seen that the model is statistically significant with a p-value of 9.14e-13, and R- squared value suggests that the model explains approximately 79.1% of the variability in the response variable of the double logarithm of Weibull probability, 푙푛(−ln(1−Pf)).

Figure 11. Estimated coefficient information for the linear regression model.

2.3.2 Cracking Probability Map Based on Three-point Bending Results

In Weibull statistics, for a given failure probability 푃푓, failure stress 휎퐹 is defined as the mean fracture stress 휎̅ divides a safety factor 푆푃 as

휎̅ 휎퐹 = Eq.11 푆푃 where 푆푃 is a safety coefficient calculated as

1 훤 (1 + ) 푆 = 푚 푝 1 Eq.12 1 푚 (푙푛 ( )) 1 − 푃푓 where 훤(푥) is the Gamma function, and 푚 is Weibull modulus calculated as 8.0928 in previous section. Meanwhile, the mean fracture stress 휎̅ in Eq.11 is computed as

휎 1 휎̅ = 0 훤 (1 + ) 1 푚 Eq.13 (푉퐸 )푚 where 휎0 is the nominal strength that has been calculated as 0.466 MPa in previous section. By substituting Eq.12 and Eq.13 into Eq.11, the final relationship between failure stress 휎퐹 and effective volume 푉퐸 is established as

1 휎 1 푚 0 Eq.14 휎퐹 = 1 (푙푛 ( )) 1 − 푃푓 (푉퐸)푚

Based on the dimension of three-point bending sample and Eq.7, the effective

3 volume of three-point bending sample can be computed as 83.6 mm . Given 푃푓 as 0.1%,

1%, 5%, 50% and 99%, the cracking probability map, relating failure stress and effective volume, can be plotted in Figure 12 and the 35 three-point bending results are included on the map as well.

Figure 12. Fracture probability map by three-point bending test.

Meanwhile, tensile test results are also added to the cracking probability map.

Here the effective volume of tensile test samples is considered to be the gauge section, which is 12.6 cm3 in volume. It can be easily observed that all points are above 5% line.

Therefore, 5% line can be set as the safety line for the tested resin-bonded silica sand, and the region below 5% line is deemed to be safe. For example, if the sand molds/cores are above 5% line on the map, without doing practical test for the molds/cores, it is clear that

22 the design and/or casting process parameters need to be changed to minimize either the failure stress or the effective volume to lower the point into the safe region of the map.

2.4 Sand Cup Mold Model

To validate the cracking probability map, sand cup molds with three different types of geometries, named as intact cup mold, flat-notch cup mold and V-notch cup mold, were designed for process simulation and experimental validation. In addition, temperature-dependent thermomechanical database of the tested resin-bonded silica sand was established to run the casting simulation.

2.4.1 Sand Cup Mold Design

Figure 13(a) shows the schematic cross-section of an intact sand cup. It has a uniform thickness of 5.7 mm, depth of 70.0 mm, 100 mm in height with 30 mm in base, top inner diameter of 38.0 mm and a 1.5° draft for easy release from the stainless steel mold after the sand is cured. Meanwhile, Figure 13(b)-(d) present the snapshots of the actual sand cup molds for the three different geometries. In general, the minimum wall thickness is the only difference among the three cup molds, where it is 2.4 mm for the flat-notch mold and 1.2 mm for the V-notch mold, while the original intact mold has a uniform wall thickness of 5.7 mm. Through the only change of geometry, the main idea is to create different stress conditions for each cup mold during heating and cooling of a casting process. Additionally, both the flat notch and V notch shapes are acting as stress risers with different levels, and such changes will cause stress variations in the casting process. All cup-shaped sand molds were made in a stainless steel mold by compacting

23 the sand first with a CT-200 compaction table from Tinker Omega Manufacturing LLC

(Columbus, Ohio, USA) and followed by curing at 523.15 K (250 °C) for 45 minutes in a muffle furnace from MTI Corporation (Richmond, California, USA). Silicon aerosol was also sprayed on the stainless steel mold as a mold release agent for easy release after the sand cup mold was made.

Figure 13. (a) Schematic cross-section of intact sand cup mold, and actual cured sand cup molds for (b) intact cup mold, (c) flat-notch cup mold and (d) V-notch cup mold.

2.4.2 Construction of Model Database

Finite element analysis (FEA) model for the cup mold was done using ProCAST at Simulation Innovation and Modeling Center (SIMCenter), The Ohio State University.

CAD file was generated in Solidworks first and then imported to ProCAST. The stress- strain behavior of original cup mold, flat-notch cup mold and V-notch cup mold during aluminum casting process was simulated, respectively. To obtain accurate stress results of the sand, linear hardening isotropic elasto-plastic model in ProCAST was chosen as in

Figure 14 [18]. The model agreed well with bilinear behavior of the previous force vs. deflection curve in three-point bending tests in Figure 6.

Figure 14. Linear hardening isotropic elasto-plastic model [18].

Mathematically, the linear hardening isotropic elasto-plastic model is expressed as

푝푙 휎 = 휎푦 + 퐻휀 Eq.15

푝푙 where 휎푦 is yield stress, 휀 is plastic strain and 퐻 is plastic modulus.

The thermo-physical and thermo-mechanical properties of the cup mold were calibrated based on both experimental measurements and literature data. Specifically, the room temperature density and Young’s modulus from three-point bending tests were employed to calibrate the material database card in ProCAST. High temperature Young’s modulus, yield stress and plastic modulus were extrapolated based on room temperature value and the high temperature values measured by Thole and Beckermann [34]. Thermal expansion at 973.15 K (700 °C) was measured by HA International LLC (Westmont,

Illinois, USA) as 1% for calibration. Temperature-dependent thermal expansion coefficient was extrapolated based on the high temperature measurement by Thiel [19].

Both Young’s modulus and thermal expansion coefficient are significant input parameters in the stress-strain behavior prediction with FEA simulation.

Attention needs to be paid for constructing the temperature-dependent properties of the sand for stress simulation. Take Young’s modulus as an example, in Thole and

Beckermann’s paper [34], it is argued that the variation of the sand Young’s modulus vs.

25 temperature is a strong function of heating rates and times. Such measurements are much closer to the conditions in actual casting processes. Therefore, extrapolation of Young’s modulus was done based on their experimental results to consider the effects of heating rates and times to ensure more accurate stress simulation for the sand cup molds.

For the database of aluminum alloy A356, default properties of A356 in ProCAST were used in the simulation. Element mesh size for intact cup mold was a uniform 1 mm with 387,176 for total 3D element. For flat-notch cup mold, minimum mesh size was at the thinned region with 0.9 mm and total 3D element was 393,549 for the sand mold. For

V-notch cup mold, minimum mesh size was 0.7 mm for the notch and total 3D element was 432,037 for the sand mold. Four-node linear tetrahedral element was employed for filling and solidification simulation. A constant heat transfer coefficient of 1000 W/m2·K between sand and A356 is employed in all three cases. For stress computation, a fixed boundary condition with zero XYZ displacement is applied at the bottom of sand cup mold. Simulation calculations were compared with experimental results.

2.5 Sand Casting Experiment Validation

Casting experiments were carried out by pouring molten A356 at 1003.15 K

(730 °C) into the cup-shaped molds with a filling time of about 3 seconds. Prior to pouring, each cup mold was put into a furnace preheated to 673.15 K (400 °C) and held for 40 s to mimic the thermal exposure encountered in actual casting processes. The casting process was recorded digital with camera.

During the intact cup mold casting, temperature profiles were measured using K type thermocouple wires with a 0.2 mm diameter from Ninomiya (Part No. 0.2 x1P K-H,

Kawasaki-shi, Kanagawa Prefecture, Japan) and collected using a data acquisition system

NI 9219 from National Instrument (Austin, Texas, USA). One thermocouple was positioned at the cup center to measure the A356 cooling curve during casting, and the other was inserted about 3 mm away from the outside surface of the mold to measure the temperature in sand. Both thermocouples were 35 mm below the top and they lied in 180° with each other. Figure 15(a)-(b) present the experimental setup of measuring temperature profiles from side and top views, respectively. Figure 15(c) shows the center node selection in FEA model of corresponding measured A356. Temperature profiles from simulation and experiment can be compared in this way.

Figure 15. (a) Side view and (b) top view of the thermocouple setup in the experiment, and (c) corresponding center node selection in FEA model.

2.5.1 Temperature Profile Comparison

Temperature profiles of A356 from simulation and experiment are plotted in

Figure 16. Both solidus temperature [TS = 821.15 K (548 °C)] and liquidus temperature

[TL = 886.15 K (613 °C)] lines are indicated on the plot. From the cooling curve, the average cooling rate between TL and TS can be computed as 0.157 K/s, and the cooling rate at the initial 25 s of the curve is about 4 K/s. The simulation result agrees well with the experimental data in the first 300 s. After 300 s, discrepancy between experimental

27 measurement and simulation calculation is presented in the slope and temperature values.

Such discrepancy may be due to that the heat transfer coefficient around solidus temperature Ts as the boundary condition setting in FEA model is not accurate enough.

The author has tried with a couple of different heat transfer coefficients, but it turned out the simulated temperature profiles in this case is not sensitive to heat transfer coefficients.

This is also confirmed by Bazhenov et al. that the variation in heat-transfer coefficients barely affects the average of their error function when simulating A356 casting into no- bake sand molds [43], where the specific reason behind this is still unclear. Nevertheless, such discrepancy does not affect the prediction since veining defects occur when the alloy is still mostly in liquid state. For the high temperature range, the plot indicates a good agreement between experiment and simulation, and thus for accurate predictions.

Figure 16. Comparison of A356 temperature profiles between FEA simulation and thermocouple measurement for intact sand cup mold.

Meanwhile, temperature profiles of the sand in original intact cup mold are drawn in Figure 17. The simulation curve shows a good agreement with experimental measurement during the initial temperature rise region. There is little discrepancy at 100

~ 350 s between the simulation and experiment, but the general trend is similar during this period. After 350 s, as in the case of Figure 16, more discrepancy is seen in the slope and temperature values. As previously discussed, the reason for such discrepancy at long- term time period is not fully clear, but it is less critical after the solidification. Instead, simulation prediction at high temperatures and initial stages of solidification and casting processes is of primary focus.

Overall, for both graphs, the experimental measurements and simulation results of

A356 and sand in the original intact sand cup mold demonstrate good agreement at high temperatures in the beginning, which indicates that the improved input data and the selected material model for the sand are accurate and reliable.

Figure 17. Comparison of sand temperature profiles between FEA simulation and thermocouple measurement for intact sand cup mold.

2.5.2 Cracking Position Comparison

The three cup molds are all cured at same conditions through the same process, and casting experiments are done at roughly the same parameters, which are summarized in Table 3. It is observed that there is no failure in either intact or flat-notch cup mold,

29 and the only crack occurred on the V-notch cup mold.

Table 3. Summary of casting experiments for the three sand cup molds. Sand cup Mold Minimum Thickness / mm A356 Mass / g Result Intact 5.7 178.80 No crack Flat-notch 2.4 177.60 No crack V-notch 1.2 174.40 Crack at notch tip

Figure 18 shows the snapshots of V-notch cup mold at different stages. It can be observed that after the mold is filled at 3 s, crack initiates at the V-notch tip at t = 8 s (5s after pouring). The black color indicates burning effect, which starts at the V-notch from the bottom to the top. When it is 30 s after pouring, the crack at notch tip can be easily seen. At t = 53 s (50 s after pouring), the whole wall of sand cup mold is all burned in dark black color except for the base with a larger thickness. In summary, it can be concluded that the sand degrades at high temperature and the concentrated stress causes final cracking at the notch tip of V-notch cup mold.

(a) (b)

Figure 18. Snapshots of V-notch cup mold at (a) t = 3s (Pouring finished), (b) t = 8 s (5 s after pouring), (c) t = 33 s (30 s after pouring) and (d) t = 53 s (50 s after pouring).

Furthermore, process simulation and laboratory casting experimental results were compared for three different geometries of sand cup molds. Figure 19(a) presents the simulation results of maximum 1st principal stress during the process with a scale bar labeled in a unit of MPa. Figure 19(b) and (c) show snapshots of cup molds before and after pouring, respectively. The 1st principal stress is normal to the plane in which the shear stress is zero, and is commonly used in FEA to check the maximum tensile stress induced in the component due to the loading conditions.

Figure 19. Simulation and experimental results of three different geometry cup molds: (a) 1st principal stress from FEA casting simulation; (b) and (c) Cup molds before and after pouring, respectively.

From the simulated 1st principal stress contour, it can be observed that tension stress is on the outer surface of cup molds and compression on the inner. The maximum

1st principal stress is increased from 1.332 MPa of original intact cup mold, to 2.372 MPa of flat-notch cup mold and to 4.205 MPa of V-notch cup mold, respectively. The stress concentration of V-notch mold is on the tip of the notch as highlighted and labeled.

Therefore, cracking is supposed to initiate at this location if it would occur. This also confirms that it is tensile stress that tears the mold apart to cause cracking. Experimental results in Figure 19(c) validated the simulation results. There was no cracking occurred on intact cup mold or flat-notch one. From the color difference between flat notch and intact cup, the mold was increasingly damaged with thinner wall thickness. As for the V- notch cup mold, cracking finally initiated from the tip of notch at 5 s after pouring and propagated vertically along the notch. Therefore, with the only change in wall thickness, stress was gradually concentrated from intact mold to flat-notch mold to V-notch mold, which eventually resulted in cracking. In this case, such phenomena could be well captured and predicted through process simulation.

2.5.3 Finalized Fracture Probability Map

The application of fracture probability map can be integrated in ProCAST. In

FEA model, the general form of effective volume calculation in Eq.5 can be transformed to calculate the numerical value of effective volume as

푚 푚 푚 푉 휎1 휎2 휎푛 푉퐸 = [( ) + ( ) + ⋯ ( ) ] Eq.16 푛 휎푚푎푥 휎푚푎푥 휎푚푎푥 where 푉 is the initial 3D volume of the part that can be read from either Solidworks or

ProCAST, 푛 is the total node number in mesh of the part (available in ProCAST), 푚 is

st the Weibull modulus (8.0928 in this study), 휎1, 휎2, 휎3 … 휎푛 are the 1 principal stress at

st each node (calculated from ProCAST), and 휎푚푎푥 is the maximum 1 principal stress during filling and solidification on the part, i.e., 푚푎푥{휎1, 휎2, 휎3 … 휎푛} . Here 휎푚푎푥 can be viewed as the fracture stress 휎퐹. In the FEA model, the effective volume calculation function was added through user defined function in the result panel of ProCAST. In this way, both the maximum 1st principal stress and effective volume can be retrieved from

ProCAST. By sorting out the necessary information in effective volume calculation, the results for each type of sand cup mold are summarized in Table 4.

Table 4. Effective volume calculations for each type of sand cup mold.

3 3 Sand cup Mold Node Number 휎푚푎푥 / MPa 푉 / cm 푉퐸 / cm Intact 77,687 1.332 100.82 2.545 Flat-notch 78,401 2.372 97.98 0.094 V-notch 86,258 4.205 100.25 0.015

Due to the stress concentration effect, the effective volume of V-notch mold is the

st smallest one among the three. Based on the maximum 1 principal stress 휎푚푎푥 and effective volume 푉퐸 results, the location of each cup mold can be determined on the fracture probability map. Figure 20 presents the fracture probability map with all data points, including three-point bending, tensile tests, and the three cup molds with different geometries. It can be seen that the cracking probability of the original intact cup mold, flat-notch cup mold and V-notch cup mold is about 1%, 5% and 50%, respectively. The intact cup mold is in the “safe” region, the flat-notch mold is on the boundary and the V- notch cup is high above the safety line. Therefore, based on the predictions of fracture probability map, original intact cup mold will not crack, and flat-notch cup mold may or may not crack, while the V-notch cup mold will most likely have cracks. Such results

33 have been validated with experimental tests as discussed in previous sections.

Figure 20. Fracture probability map with all points, including three-point bending tests, tensile tests, original intact cup mold, flat-notch cup mold and V-notch cup mold.

In summary, it is demonstrated that based on the proposed fracture probability

st map, and combined with the maximum 1 principal stress 휎푚푎푥 and effective volume 푉퐸 results from FEA model, the susceptibility to cracking of resin-bonded silica sand molds or inserts can be predicted in an efficient way. Moreover, for the implementation of

Figure 20, MATALB code is detailed in Appendix A: MATLAB Code.

2.5.4 Scope and Limitations of the Map

Further Attention needs to be paid when the proposed fracture probability map is employed for predictions. The first concern is that the proposed probability map in this study is constructed based on three-point bending tests at room temperature condition.

The map is then employed for veining defect predictions at elevated temperature. A natural question is the scope of utilizing the map constructed at room temperature for

34 predictions at high temperatures. The author would agree that temperature variable is not explicitly included in equations of Weibull statistics. However, the highlight in Weibull statistics is the concept of effective volume, which is based on the weakest links in the material where the material fails if its weakest volume fails. It is both the effective volume and the fracture stress that determines the location and shape of the probability map. Since both the fracture stress and effective volume are temperature dependent, the author would argue that temperature effect is implicitly considered in Weibull statistics.

To support this argument, the intact sand cup mold was taken as an example to run

ProCAST simulation at different pouring temperatures. Table 5 presents the results of effective volume and maximum 1st principal stress. It can be seen that the higher pouring temperature is, the larger thermally induced stress is and the smaller effective volume becomes. This also makes sense by checking Eq.5 and Eq.9, where mathematically effective volume is related to Weibull modulus and fracture stress. If fracture stress changes at different temperatures, so does the effective volume. Thus, for the same tested sand in this study, the fracture probability map is all about fracture stress and effective volume, and it does not matter whether the fracture stress and effective volume is obtained from room temperature or elevated temperature. On the other hand, it is worth exploring whether the map would remain the same when the three-point bending test is performed at high temperature, though.

Table 5. Temperature-dependent effective volume and maximum stress using intact sand cup mold as an example.

Pouring temperature / °C 750 700 650 st Max 1 principal stress 휎푚푎푥 / MPa 2.508 2.212 1.865 3 -3 -2 -2 Effective volume 푉퐸 / cm 5.426 × 10 2.227 × 10 4.858 × 10

The other limitation is the effect of materials. The investigated resin-bonded silica sand has a 1.3% phenolic resin binder. If the binder content is largely different, or the sand curing condition is changed, it is likely that both the fracture stress and effective volume will change again. From the conservative point of view, it is suggested that the fracture probability map be reconstructed following the same methodology described in previous sections. The exact association between fracture stress and sand chemistry is still not clear, although it probably varies case by case.

For the above two points, limited research has been done so far. Thus, there still exists potential research opportunities to further clarify the ambiguity and push the limit of the knowledge as for future work.

2.6 Conclusions and Highlights

In this chapter, a commercial resin-bonded silica sand mixture with 98.7% SiO2 and 1.3% phenolic resin binder was studied, and its cracking criterion was proposed by considering both the maximum tensile stress and the effective volume based on Weibull statistics. The detailed conclusions are listed below.

 Mechanical tests (three-point bending, tensile and hardness) and literature data

were employed to for cross calibration to develop an accurate sand database

for the subsequent casting process simulation.

 Using Weibull statistics, a fracture probability map was generated based on

three-point bending test results of sand samples. The tensile test results

confirmed its accuracy in predicting the cracking.

 Simulation of sand cup molds with three different geometries were done using

ProCAST and validated by actual A356 casting experiments. Good agreement

of temperature profiles between simulation and experiments were obtained,

especially at the high temperature range.

 By integrating the fracture probability map and ProCAST simulation, cracking

susceptibility of V-notch sand cup mold was successfully predicted and

validated with experimental results.

Overall, the successful prediction suggests potential applications of the integrated fracture probability map and FEA simulation in the design of sand molds/cores to prevent veining defects of sand cracking during casting processes.

Chapter 3: Thermal Fatigue Cracking in an H13 Steel Die

3.1 Motivation and Problem Description

3.1.1 Background and Motivation

Die casting is a high-volume manufacturing process for making geometrically intricate, near net-shaped products with close tolerances and excellent surface finishes in a cost-effective manner [44]. In a typical aluminum alloy high pressure die casting

(HPDC) process, molten aluminum (670 – 710 °C) is injected under high pressure of the order 50 – 80 MPa into the cavity of H13 steel dies at velocities of 30 – 100 m/s [45].

Due to the severe conditions in the process (high temperature, high pressure and chemical attack by molten metal), die casting dies/inserts are prone to surface damage [46]. Most common failure modes in dies/inserts are thermal fatigue cracking [44], die soldering

[47], corrosion dissolution [48], erosion and wear [49]. Those tooling failures are significant loss due to their high cost of maintenance and replacement. In particular,

Starling and Branco emphasized that thermal fatigue cracking was the principal failure mode in hot-work tooling and it specifically accounted for 70% of failures in die casting tools [50]. Therefore, predicting and increasing thermal fatigue life of hot-work dies has become a major concern to die casting industry.

3.1.2 Literature Review of the Problem

Materials that are used in high temperature applications are generally exposed to rapid temperature fluctuations which cause thermal stresses and risks for damage [51]. A typical example is H13 steel water jacket insert used in aluminum alloy high pressure die casting processes for making water passages of car engine blocks. Figure 21 presents a classic water jacket insert for four cylinders and a typical thermal fatigue crack on it [52].

Figure 21. Classic water jacket insert and typical thermal fatigue crack on it [52].

In general cases, the fatigue failure produced by fluctuating thermal stresses is defined as thermal fatigue failure. Thermal stresses are produced when the expansion or contraction of a component caused by a temperature change is restrained. The constraint may be internal or external [53]. External constraints produce forces that act on a component that is alternately heated and cooled. Internal constraints may result from temperature gradients across the section (simply because heat is not able to flow quickly enough in response to the external changes), structural anisotropy and different coefficients of expansion in adjacent phases or grains [54]. Meanwhile, thermal fatigue resulting from the action of internal constraints is also known as thermal cycling damage.

In die casting, thermal fatigue of a steel die/insert is caused by alternating heating and cooling cycles in die casting operations. The cyclic heating and cooling conditions produce large thermal gradients in the die, and thus put the tooling in compression during heating and tension during cooling. Such alternating tension-compression states will lead to cyclic deformation on the die, where elastic and plastic strains are produced depending on thermal loading conditions. As the number of cycles increases, the cyclic strains will eventually initiate cracks on the die, which is considered as thermal fatigue failure. In the meantime, such failure is not only considered in aluminum die casting processes, but also prevalent in many other fields, such as brass die casting dies [55], W-W brazed joints in

39 welding [56], ball grid array packages in electronic engineering [57], gas turbine casings in aerospace [58], and high-speed railway brake discs in transportation [59].

Traditionally, in die casting industry, dies are designed and run to have higher thermal fatigue resistance for prolonged life. A couple of common measures includes

[60]: i) coatings can be applied to establish a low thermal gradient between the surface and the underlying layer to decrease the stress in the dies; ii) water cooling lines are added in the dies to lower the surface temperature to preserve the hardness and hence the strength; and iii) microstructures can be tuned with the presence of strong carbide-former elements like chromium, molybdenum and vanadium to reduce the softening by preserving a fine distribution of carbides.

To simulate the thermal fatigue conditions experienced in die casting processes, a dipping test apparatus was first built at Case Western Reserve University in late 1960s

[61]. The main concept of the test was to achieve as similar thermal fatigue loadings as in

HPDC processes through repeated immersion of steel die samples in a bath of molten aluminum followed by lube spray cooling. Over the years, such testing concept has been widely used to study thermal fatigue characteristic of tool steels. For example, Klobčar et al. compared thermal fatigue resistance between H11 and H13 steels [62], Abdulhadi et al. conducted microstructural analyses of H13 steel after its thermal fatigue test [63], and

Kang et al. evaluated H13 steel thermal fatigue resistance for die life [64]. In particular,

Li et al. investigated the effect of initial hardness on the thermal fatigue behavior of H13 steel by both experiments and simulation [65], and Srivastava et al. employed finite element modeling for thermal and structural analyses of test samples to study the thermal fatigue test [66]. Furthermore, such test unit was also employed to evaluate other die

40 materials such as Inconel alloy 718 by Antony and Smythe [67]. However, one major drawback of such dipping test is the difficulty to distinguish interwoven mechanisms that lead to sample final failures. Due to the existence of molten aluminum, there used to be interfacial reactions and erosions in addition to thermal loadings in the test. Thus, it is a challenge to evaluate thermal fatigue resistance through dipping test since it is difficult to quantify how soldering and erosion would affect the fatigue crack failure in the presence of aluminum melt.

To only focus on the effect of thermal loadings, Li et al. conducted some thermal fatigue tests of H13 and H21 steels using a similar thermal fatigue test unit, but through furnace heating instead of immersion in aluminum melt crucible [68]. They proposed a temperature-based equation for thermal fatigue crack initiation (TFCI) life based on classical Manson-Coffin expression. However, the work needs some major improvements.

Firstly, they controlled the temperature fluctuations through different residence periods for samples in the furnace. This would cause cycle time inconsistent between different test conditions, and affect the accuracy of the final life prediction curves. Secondly, the exponent value in the TFCI life prediction came directly from Manson-Coffin expression as -0.5, whereas a more accurate value could be used to improve the prediction. Thirdly, it would be more convincible if there were some validations from either experimental measurements or simulations to verify temperature difference during the tests, and thus improve final accuracy. Furthermore, just like the simple sample shape in their work and many other previous literatures, specimens used in laboratory tests generally have regular geometries, such as cylindrical (rods, tubes or rings) and flat plates. Those shapes are too simple to be geometrically similar to the working pieces in actual die casting, which is

41 always a concern in applying the lab-scale model to practical die casting dies/inserts with complex geometry. Despite these drawbacks, their work has provided a good starting point for further advancement in this research.

3.1.3 Abstract for the Research

In this study, the fatigue life of thermally-induced cracking of H13 tool steel was investigated. Thermal fatigue cracking was reproduced through cyclic heating and cooling based on the conventional dipping test concept. Finite element models were built to understand the thermal loadings and the results were correlated with experimental measurements. A temperature-based prediction criterion, derived from the modified universal slopes equation, was proposed to describe thermal fatigue crack life. A simple plate specimen was designed and tested at different temperature conditions by residing in the kiln to establish the criterion. Furthermore, application of the model was extended to a miniature die insert, where the sample geometry was designed to resemble the critical features of an actual water jacket insert in an automotive engine block. Meanwhile, the test conditions of the complex geometry sample were chosen to be close to actual die casting process. Specifically, the sample heating was achieved through with and without the presence of molten alloy, i.e., (i) the conventional immersion in A380 melt; and (ii) residing in a kiln chamber. The same methodology can be applied to other similar hot- work tool materials, and the model can help die casting engineers for die life assessment and improvement in a simple and practical way.

3.2 Experimental Procedures

Experimental tests were performed to establish the correlation between temperature difference and thermal fatigue life. The commonly used die material H13 tool steel was used for tests. Sample geometry was purposed designed to improve test efficiency. As part of this investigation, two different sample geometries have been proposed and tested: (1) a simple plate (SP) sample, and (2) a miniature die insert (MDI) sample. In addition, a thermal fatigue test apparatus was built for this study. Sample surface temperature evolutions during testing were captured with an infrared camera.

Temperature data were used to correlate with thermal loadings from finite element model.

3.2.1 Samples and Materials

The SP sample, as shown schematically in Figure 22, is made of standard H13 tool steel, and its chemical composition is listed in Table 6, with an initial hardness of

Rockwell B95 without heat treatment. The sample is designed to be a rectangular plate with V-shape notches added at both long and short edges. The rectangular plate has a dimension of 152.4 × 25.4 × 6.35 mm (L × W × H). Such geometry is defined to obtain an effective thermal gradient during test, and thus will increase test efficiency. V-shape notch is cut using a copper wire Electrical Discharge Machine (EDM) to generate stress concentration on the sample. Notch details follow ASTM E23-16b standards with 45° as notch angle and 0.25 mm in notch radius. It needs to be mentioned that thickness has a significant effect on thermal fatigue test, which is primarily due to geometrical factors as pointed out by Bhuyan and Vosikovsky [69]. However, since it is not the focus of this study, it is not deliberately consider here. Meanwhile, currently typical wall thickness for

43 a die/insert tooling feature is about several millimeters, and the same scale in thickness has been chosen in sample design.

Table 6. Chemical composition of tested H13 samples in wt.%. Composition C Si Mn Cr Mo V N SP sample 0.44 1.09 0.39 5.30 1.37 0.78 / MDI sample 0.22 0.18 0.93 5.69 2.43 0.48 0.50

Figure 22. Schematic drawing of the SP sample for thermal fatigue test.

Meanwhile, a more complex geometry was proposed and machined as shown in

Figure 23. It is made of modified H13 steel with nitriding surface coating and heat treatment, which includes annealing, quenching and tempering, followed by a nitriding process and a final cryogenic treatment. The final surface chemical composition is listed in Table 6, with an initial hardness of Rockwell C45. The MDI sample was specifically designed to resemble the critical features of an actual H13 water jacket insert used in high pressure die casting process for making aluminum engine blocks. The geometry features two symmetrical cylindrical rings with 39.0 mm in diameter for each one. The distance between the centers of two rings is 36.0 mm, and the inner surface has a 2° draft. A uniform 3.0 mm thickness is designed on the top edge and the largest thickness is 9.0 mm at the middle connection region. A 60° notch is added at the thickness transition area. The

44 width of the sample is 42.0 mm and length is 78.0 mm. During tests, the specimen was vertically held with a 40.0 mm clamping rod attached to it. Such geometry was optimized through multiple simulation iterations to come up with the most concentrated stress conditions at notch tip to improve test efficiency, which will be further explained in later sections.

Figure 23. MDI sample for (a) and (b) schematic drawing with major dimensions, and (c) machined test sample with a clamping rod.

3.2.2 Thermal Fatigue Test Unit

There have been several test units reported to evaluate thermal fatigue property of hot work mold materials so far. The major difference among those units is the method to achieve thermal gradients during tests, especially the ways of heating test samples, such as traditional aluminum melt heating by Benedyk et al. [61], furnace air heating by Li et al. [68], high frequency induction coil heating by Sjöstrom and Bergström [70] and Chen et al. [71], surface heating using a pulsed diode laser beam by Caliskanoglu et al. [72] and heating by exposure to X-ray beam by Ravindranath et al. [73]. This study employs both the kiln air heating by residing in the kiln chamber and the conventional Al melt immersion method. Schematic drawing of our test unit is presented in Figure 24. The unit is defined and built to (i) focus on thermal fatigue crack failure that is induced by thermal loadings; (ii) control thermal loadings between heating and cooling similar to actual die

45 casting; and (iii) run experiments in a more cost-effective manner. During experiments, temperature evolutions on sample surfaces were measured using a FLIR® A325sc thermal imaging camera. The infrared camera was calibrated before the test and the data collected during experiments were later used to correlate with finite element modeling.

Figure 24. Schematic drawing of thermal fatigue test setup in this work.

The author would like to further emphasize the challenge in building the test unit.

A similar test unit was built in Department of Integrated Systems Engineering, The Ohio

State University as detailed in a thesis [74]. Based on this reference, a skilled technician helped the author build the desired dipping unit from scratch in six months before the unit could be run in a stable condition. Figure 25 presents the different views of the final unit, which has been covered with mild steel sheets for safety. It can be noticed that the control panel is attached to wall as shown in the right photo of Figure 25. The detailed hardware and wirings are presented in Figure 26.

Figure 25. Different perspectives of finalized dipping test unit.

Figure 26. Hardware and wirings in the control panel.

During the test, heating of the SP sample was achieved by residing in kiln chamber for 60 s where the kiln temperature was maintained at 750 °C, 850 °C and

950 °C, respectively. For MDI sample with furnace air heating method, furnace was set at

850 °C and test sample was kept in the chamber for 45 s. For MDI sample immersed in

Al melt, the sample was thoroughly dipped into A380 melt for 28.1 s, where 5806.0 g

(12.8 lbs.) of A380 was melted in a crucible and kept at 670 °C as similar to actual melt temperature in die casting. There was an opening hole with 101.6 mm (4 in.) in diameter on the kiln lid so that samples could be lowered into the kiln chamber. For SP sample,

47 after heating it was translated into a 22.71 liters (6 gallons) water coolant tank for 4 s quench cooling, and followed by another 4 s of compressed air blow. For MDI sample, both water cooling and air spray last for 3 s, respectively. In both cases, water was circulating in the tank so that the water temperature was kept at 20 °C. Air blow was set at 517 kPa (75 psi) to have enough pressure to blow off remaining water droplets on the sample. Automatic movement was set by a programmable logic controller Direct Logic

06 D0-06DD2, with detailed automation code listed in Appendix B: Programmable Logic

Controller Code. Both samples were attached to a gear motor for self-rotation, so that both the inner and outer surfaces could be sprayed. During the test, fatigue loading of the specimen was achieved by cyclic movements from kiln chamber, through atmosphere air at 25 °C into water tank cooling and followed by compressed air blow. Table 7 details the information of test cycles for the two different geometry samples with heating methods labeled. Total cycle time is 108 s for SP sample, while 93.5 s for MDI sample. Both of them are similar to the casting cycle time in real die casting production.

Table 7. Cycle time details for the two different geometry samples. Water Water Time / s In kiln Air starts Air ends Total starts ends SP (Furnace) 60 78.5 82.5 88 92 108 MDI (Al melt) 28.1 54.9 57.9 59.9 62.9 93.5 MDI (Furnace) 45 64.5 67.5 69.5 72.5 93.5

Before a sample was inspected and evaluated for fatigue cracking failure, it was cleaned in ultrasonic bath at 40 kHz with 24% NaOH solution at 50 °C for 1 hour. Based on the measurements made on sections of failed die casting dies, it is summarized by

Parishram that a noticeable crack had an average of 0.5 mm in length [75]. Therefore, from the viewpoint of die casting application, the cycle number at which a 0.5 mm crack

48 is observed on the sample is considered as final thermal fatigue life.

3.3 Simulation Model

The design geometry was first generated as a CAD file in Solidworks and then imported to ProCAST. The main objective of FEA simulation is to examine thermal loadings of the samples under different testing conditions. The model employed four- node linear tetrahedral elements for thermal analysis. For SP sample, meshing was refined near the notch tip with a minimum element size of 0.2 mm and total element number of the sample was 204,749. For MDI sample, meshing was refined near the notch tip and 3 mm top edge with a minimum element size of 0.5 mm, and total element number of the sample was 1,225,927.

3.3.1 Materials Database

The H13 steel composition in Table 6 was employed as input for calculating material properties to construct the simulation database. ProCAST has an embedded module for material property calculations, where a database for Fe-based system from

CompuTherm® is included and Scheil condition can be selected for modeling temperature-dependent thermodynamic properties for the two compositions. Furthermore, the calculated properties have been calibrated with previous experimental measurements of H13 as summarized by Benedyk [76] to ensure the accuracy of those properties. For temperature field calculations, two of the most important properties are thermal conductivity and enthalpy, and those two temperature-dependent properties in this study are plotted in Figure 27.

Figure 27. Material properties of SP and MDI samples for thermal simulation.

In addition, structural simulation has been done for MDI sample for a qualitative analysis. The reason is that it is generally impractical to validate the simulated stress or strain results with experimental measurements in die casting. Thus, structural analyses are only included to provide a qualitative trend to optimize the geometry of MDI sample.

Figure 28 presents the temperature-dependent thermal expansion secant, Young’s modulus, yield stress and plastic modulus of MDI sample for its stress simulation. For temperature-dependent thermal expansion secant of MDI sample, reference temperature is 30.16 °C. In aluminum die casting, the maximum temperature of H13 steel seldom exceeds Al melt temperature. Therefore, the above temperature-dependent material properties are only up to 800 °C to cover the temperature range that is of interest in this study. For this particular temperature range, H13 steel remains solid and Poisson’s ratio is set at 0.28 as a constant. In addition, a linear hardening isotropic elasto-plastic model is used to construct the stress database as Eq.15. It should be pointed that the stress database is not only related to the material, but also the state and preparation of the material, since different heat treatment and machining processes will have different effects on the final

50 properties. Nevertheless, using the current temperature-dependent properties, a predicative model could be developed to qualitatively observe the trend of stress evolutions for geometry optimization of MDI sample.

Figure 28. Temperature-dependent properties of MDI samples for stress simulation.

3.3.2 Simulation Setup

In FEA model, a series of 15 cycles of temperature simulation were run first for both SP and MDI samples to reach a quasi-steady-state condition. Then for MDI sample in the 16th cycle, stress simulation was coupled with thermal results to provide structural data. Such strategy is commonly used in FEA simulation to balance between computation cost and calculation accuracy.

For thermal boundary conditions, surface heating and cooling was introduced based on the cycle details in Table 7 by alternating surrounding temperatures and heat

51 transfer coefficients (HTC). Figure 29 describes the boundary condition of SP sample for one cycle when the kiln chamber is set at 750 °C. The same idea applies to MDI sample as well, except for the difference in cycle time details. All HTC data are employed from previous literature [66], where the HTC between Al and steel is 4016.64 W/m2·K during melt immersion, air and steel is 23.85 W/m2·K for air convection, and water and steel is

4184 W/m2·K for quench cooling. A higher HTC value of 60 W/m2∙K is defined at air blow stage to account for the effect of compressed air cooling. For stress computation of

MDI sample, a fixed boundary condition with zero XYZ displacement is applied at the end of rod to represent clamping on the specimen in tests.

Figure 29. Boundary conditions for SP sample with applied alternating temperatures and heat transfer coefficients.

3.3.3 Geometry Optimization

To investigate the geometrical effect of MDI sample designs, six different cases were simulated for dipping in Al melt as listed in Table 8. Each case was iterated from the simulation of previous design, and Case 1 was the original design.

Table 8. Cases of different geometries for MDI sample. Case number Thickness ratio Notch Angle Center distance / mm 1 1 : 1 No / 43.5 2 1 : 2 No / 43.5 3 1 : 3 No / 43.5 4 1 : 3 No / 36.0 5 1 : 3 Yes 90° 36.0 6 1 : 3 Yes 60° 36.0

Figure 30. Geometry features of MDI samples from top view for (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4 and (e) notch angle details in Case 5.

As illustrated in Figure 30, from Case 1 to 3, the only change in geometry was the thickness ratio between ring wall and connection wall, which can be seen from the top view perspective. Case 1 had a uniform 3 mm wall thickness, while Case 3 had 3 mm thickness for two cylindrical ring walls and a maximum of 9 mm in thickness for middle connection region as 1:3. Case 4 kept all features of Case 3 except that the distance between centers of two rings was reduced from 43.5 mm to 36.0 mm. Furthermore, Case

5 remained the same as Case 4 except that a 90° notch was added at the thickness transition position on the top edge. Finally, Case 6 had the only change in notch angle from 90° to 60°, which was the sample shown in Figure 23.

Figure 31 presents the temperature and the 1st principal stress contours at coolant

53 quenching stage for sample geometry of Case 1, Case 3 and Case 6, respectively. Both temperature and stress distributions indicate a symmetrical pattern for the two rings. For temperature results, all top edges cool fastest due to the minimum thickness there. For

Cases 3 and 6, their middle connection walls have a maximum thickness of 9 mm as a ratio of 1:3. Thus, more heat is trapped there, and higher temperature is observed as compared to Case 1. The corresponding 1st principal stress contours for each case are given in the bottom row of Figure 31. Since Case 1 is symmetrical and uniform in geometry, the stress is relatively low. When it comes to Case 3 where thickness ratio is increased from 1:1 to 1:3, stress concentration can be found at the middle connection wall, especially the top and bottom rims in red color. This is mainly due to that extra thickness in the connection wall would create more bending moment during thermal expansion and contraction. For Case 6, the reduction in distance between two circles centers leads to an even higher curvature at the connection wall than Case 3, which results in the most concentrated stress among all cases. Meanwhile, the 60° notch acts as a stress concentrator as shown in the contour. It is added at the thickness transition position that is close to the middle connection wall while still has a relative small thickness. Although the result of 90° notch is not presented here, it is less effective than 60° in providing minimum failure load for damage as discussed in the previous experimental work by

Strandberg [77] and computational work by Carpinteri et al. [78].

(a) (b) (c)

Figure 31. Temperature contours (top row) and the 1st principal stress contours (bottom row) during coolant cooling stage for (a) Case 1; (b) Case 3 and (c) Case 6.

For further analysis, Case 6 is taken as an example and the notch tip is the primary region we are interested in. Figure 32 presents the simulation results of the 1st principal stress and temperature evolutions of notch tip AB in one cycle. In the model, there are seven nodes for the notch tip, including points A and B. Both the temperature and 1st principal stress data of those seven nodes are averaged to represent the result of notch tip. It can be seen that the temperature reaches maximum at 28.1 s and then decreases gradually due to air cooling. During this period, notch tip is under compressive state. At coolant quenching stage, temperature drops dramatically and stress immediately converts to tensile stress to reach its maximum. Notch tip remains in tension state until the end of cycle. This proves that the cyclic heating and cooling conditions produce large thermal gradients on the sample, and thus put the sample in compression during heating and tension during cooling. Such alternating tension-compression states will eventually lead to thermal fatigue cracking.

Figure 32. FEA calculations of temperature and the 1st principal stress evolutions of notch tip AB (Case 6) for MDI sample.

3.4 Experimental Results

MDI sample geometry was optimized based on the iterative simulation. Then both the SP and MDI samples were tested in laboratory scale to reproduce the thermal fatigue cracking. When the test was running in a stable condition, temperature contours of the sample were measured using infrared thermal camera. Then the result was then compared with FEA simulation. Cycle numbers to failure were recorded and cracking morphology of both samples were characterized as well.

3.4.1 Temperature Contours

During each test cycle of SP sample, maximum temperature is reached at the end of kiln heating. Figure 33 shows temperature contours of SP sample after it is taken out from kiln chamber for 750 °C, 850 °C and 950 °C heating temperatures, respectively. The same level of temperature scale (300 ~ 625 °C) has been defined for the color bar so that maximum temperature for different test conditions can be easily observed. It can be seen

56 that the edges have higher temperatures than middle surfaces for all samples. Among the three notches, the bottom one has a slightly higher temperature than the two on side edges.

Despite of the large aspect ratio for more effective heat transfer at bottom edge and corners, this may also because that the sample is vertically held during heating. In this way, the bottom part is the first to come into kiln chamber and the last to leave, and thus having a little longer time for heating, which leads to the final higher temperature.

Figure 33. Thermal camera measurements of SP sample after it is taken out from kiln. Kiln temperatures are at 750 °C, 850 °C and 950 °C from left to right, respectively.

Furthermore, Figure 34 presents FEA results of SP sample temperature contours when the sample finishes heating, and the temperature results are from the tenth cycle in simulation to match a quasi-steady-state heat transfer condition of the sample in actual test. To compare the simulation results with experimental measurements in Figure 33, the same level of temperature scale (300 ~ 625 °C) has been defined for the color bar. It can be observed from overall patterns of temperature contours that there is a good correlation

57 between experiments and simulation. Specifically, as kiln heating increases from 750 °C to 950 °C, the maximum temperature in one cycle increases as well. Meanwhile, among all three notches, the maximum temperature is located around the vicinity of the bottom notch boundary, as there is more effective heat transfer phenomenon for bottom notch area. Such pattern is also confirmed in the experimental measurements in Figure 33. It should be mentioned that there are minor differences in absolute temperature values between experimental measurements and simulation calculations. However, the overall temperature contours agree well and it is believed that any small discrepancies fall within reasonable error range.

Figure 34. FEA results of SP sample temperature contours after it is taken out from kiln. Kiln temperatures are 750 °C, 850 °C and 950 °C from left to right are, respectively.

The effect of water cooling in one cycle is presented in Figure 33. The same scale of temperature (20 ~ 50 °C) is set on the color bar for both experiment and simulation

58 results. Similar to the kiln heating results, the bottom and side edge regions have lower temperatures than the middle area due to more effective heat transfer on surfaces.

However, the temperature in the upper part of test plate is higher than that of the lower part. This is due to the extra cooling time in the lower part when the sample is vertically held during water cooling. The lower is the first to get in contact with water and the last to leave, and thus having a little longer time for cooling which leads to lower final temperatures. Overall, such pattern is well captured and indicates a good correlation between simulation and experiments, especially for edges of the test plate where notches are located as the key areas of interest.

Figure 35. Comparison of SP sample temperature contour after sample is water cooled between FEA simulation (left) and thermal camera measurement (right).

For SP sample, Table 9 summarizes the experimental tests and FEA simulation of maximum temperature 푇푚푎푥 and minimum temperature 푇푚𝑖푛 for different kiln chamber

59 temperatures. Since the bottom notch has the highest maximum temperature than the other two side notches after kiln heating as well as the lowest minimum temperature after water cooling, Table 9 employed bottom notch thermal results to represent the sample. It can be seen that the minimum temperature is more consistent for different testing temperatures due to efficient cooling of circulating water. The minimum temperatures between simulation and experiment are also in good agreement. However, there is about

15 ~ 20 °C difference for maximum temperatures between simulation and experiments.

This can be explained by the time delay when sample is taken out of the kiln chamber during test. The actual maximum temperature is supposed to be reached in the kiln chamber. But in reality, there is some unavoidable heat loss from surrounding air when the sample just comes out of kiln chamber. On the other hand, such time delay was not accounted in FEA model. Thus, its measured maximum temperature is lower than what it is predicted in simulation within a reasonable range.

Table 9. Temperatures from experimental test and FEA simulation for SP sample. Thermal camera measurements FEA simulation Kiln chamber / °C 푇푚푎푥 / °C 푇푚𝑖푛 / °C 푇푚푎푥 / °C 푇푚𝑖푛 / °C 750 405.3 24.2 423.2 24.5 850 507.8 25.7 525.5 25.0 950 604.3 27.6 619.3 25.3

Similarly, for the optimized MDI sample, surface temperatures from experiments and simulation are summarized in Table 10, which includes maximum temperature 푇푚푎푥, minimum temperature 푇푚𝑖푛 and temperature difference ∆푇 in one cycle. For the heating method of Al melt immersion, the 푇푚𝑖푛 is about 180 °C from FEA simulation while it is significantly higher in actual test as roughly 400 °C. During Al melt immersion test, there existed die soldering interfacial reactions and sticky Al layers formed on the sample. Due

60 to the existence of sticky Al, effective cooling of test sample was inhibited during each cycle. Thus, a desired temperature difference in each cycle was not achieved, which had critical impact on thermal fatigue cracking.

Table 10. Surface temperatures between experimental test and FEA simulation for MDI sample with different heating methods. Immersion in A380 melt Residing in kiln chamber

푇푚푎푥 / °C 푇푚𝑖푛 / °C ∆푇 / °C 푇푚푎푥 / °C 푇푚𝑖푛 / °C ∆푇 / °C FEA simulation ~ 630 ~ 180 ~ 450 ~ 500 ~ 50 ~ 450 Thermal camera ~ 650 ~ 400 ~ 250 ~ 490 ~ 40 ~ 450

On the other hand, there was no such interference of die soldering if the sample was heated in kiln chamber. As shown in Figure 36, there is a good agreement of both maximum and minimum temperatures between experimental measurement and FEA calculation. Since the bottom of sample was the first to come into chamber and the last to leave, maximum temperature reached ~ 490 °C on the bottom. The minimum temperature after water quenching and air blow was ~ 40 °C. Therefore, temperature difference ∆T was ~ 450 °C in each cycle. Meanwhile, the notch tip had a maximum temperature of ~

440 °C, and ∆T at that location was ~ 400 °C.

Figure 36. Correlation between thermal camera measurements and FEA simulation of MDI sample for maximum temperature (left two) and minimum temperature (right two) using kiln chamber heating method.

The author would like to further emphasize the drawbacks due to the existence of sticky Al in achieving a desired cyclic temperature range for MDI sample. During the dipping test, multiple measures have been taken to mitigate potential interfacial die soldering reactions, including (i) Al – 10 wt.% Fe master alloy was added to increase Fe content from 1.03 wt.% to 1.33 wt.% in the melt; (ii) test sample was preheated to 150 °C;

(iii) oxides on A380 melt surface in the crucible was skimmed off now and then; and (iv) boron nitride coating was applied on sample surface. Despite the measures mentioned here, there were still sticky Al layers formed on the sample surface. Figure 37(a) presents a typical thermal camera snapshot of MDI sample when it comes out of the kiln, where the sticky Al is in cyan color for temperature contours. Figure 37(b) shows the sticky Al on actual MDI sample, which mainly stays on the rim and fills the gap of two circles.

There are also some white stains, indicating remaining boron nitride on the surface.

(a) (b)

Figure 37. Typical sticky Al captured (a) in thermal camera and (b) on MDI sample.

Due to the existence of sticky Al, the effective cooling through coolant spray and air blow on test piece was inhibited. Instead, when the sticky Al came out of the kiln as semi-solid, it solidified to a lower temperature during coolant spray and air blow. When

62 the cycle continued, the solidified Al layer was melted again in the crucible and thus decreasing melt temperature in each cycle, reducing test efficiency greatly. On the other side, in FEA simulation, such sticky phenomenon was not able to be considered since the imposed boundary conditions only included alternating surrounding temperatures and heat transfer coefficients. Thus, there exists an obvious discrepancy for ∆푇 of immersion test between experiment and simulation as recorded in Table 10. In the meantime, in actual die casting, molten Al is forced to flow into the die cavity instead of staying still in the crucible. The effect of fluid dynamics and mold erosion caused by fluid impact was not able to be fully approximated in the lab-scale thermal fatigue test setup.

Nevertheless, this does not mean that there is no point in doing Al dipping or immersion test. Instead, the interfacial reaction between steel die/insert and molten Al is a crucial problem and it is coupled with thermal fatigue issue in die casting processes.

Therefore, Al dipping test has been extensively used to study the issues of die soldering, thermal fatigue, and other phenomena. Such test still features the advantage of low cost and maintains the most similar conditions in an actual die casting process. In this study of thermal fatigue, the key concept for the test setup is to obtain a similar cyclic temperature gradient for thermal fatigue life prediction. By running the samples through kiln chamber air heating, the interference of sticky Al layers can be eliminated and a more desired cyclic temperature difference can be obtained.

3.4.2 Cracking Failures

For SP samples, cracks were observed on both sides of the notch across the sample thickness and all three notch tips initiated cracks. Based on conservative concerns,

63 the larger cracks at the bottom notch were considered as the cracking failure for the entire sample. Figure 38 illustrates the original notch and thermal cracking for different testing temperatures observed using an optical microscope observation at 50 x magnifications. It can also be clearly seen that thermal fatigue cracking initiates from the vicinity of the notch tip. Meanwhile, there is typically more than one crack in failure, which may due to the imperfection of the sample formed during testing and sample preparation.

Based on the failure observation in Figure 38, a noticeable cracking failure of the sample with at least 0.5 mm crack length is found at 4570 cycles for 750 °C kiln heating,

1590 cycles for 850 °C kiln heating and 870 cycles for 950 °C kiln heating. Furthermore,

64 temperature difference of the sample in one cycle can be calculated based on thermal camera measurements. In this way, sample temperature difference ∆푇 and cycle life 푁푓 can be summarized in Table 11. It should be mentioned that the measured thermal results are inherited from Table 9, where the bottom notch temperatures are employed to represent the sample for parameters calibration of the criterion. It can be observed that the sample temperature difference is in a linear relationship with kiln temperatures. In spite of the little deviation, ∆푇 would increase about 100 °C for every 100 °C raised temperature in kiln chamber.

Table 11. Summary of thermal fatigue test for SP samples.

Kiln / °C Sample 푇푚푎푥 / °C Sample 푇푚𝑖푛 / °C Sample ∆푇 / °C Cycle life 푁푓 750 405.3 24.2 ~ 380 4570 850 507.8 25.7 ~ 480 1590 950 604.3 27.6 ~ 580 870

For MDI sample, after 3120 cycles of Al melt immersion test combined with

13360 cycles of kiln chamber heating test, a crack was initiated at notch tip of the test sample. The cyclic temperature difference in the notch tip region is roughly 250 °C for Al melt dipping test and 400 °C for kiln chamber heating test. Figure 39 presents the dye penetrant inspection to validate the cracking initiation at notch tip without any destruction to sample. Due to the small length scale of the crack, it is difficult to show in a regular digital camera, especially at a high resolution. In addition, unlike the flat rectangular geometry of SP sample, the notch tip of MDI sample is located in a concave region, which makes it difficult to use optical microscope to focus on the crack for observation.

On the other hand, if the tip region is cut, the sample will be ruined and there will be induced stress during cutting, which will potentially impose an impact on the original actual result. Therefore, to better validate the cracking initiation at notch tip without any

65 destructions to sample, dye penetration was used. After developer was sprayed, penetrant bled out from defects onto the surface to form a visible indication, which can be observed as the red color at notch tip as highlighted in dashed circle.

Figure 39. Notch tip of MDI sample with dye penetrant inspections.

3.4.3 Hardness Profiles

To further investigate the property change caused by thermal fatigue process, an actual water jacket insert with the same hardness of nitriding surface was tested by an industrial partner for about 15000 cycles at a cyclic temperature range of 400 °C before the part was about to fail. Cross-sectional micro-hardness profiles before and after the tests were recorded and plotted in Figure 40. Both profiles were measured using a

Buehler Micromet II hardness tester under a load of 25 g and a dwell time of 20 s. Due to the existence of nitriding surface, it can be observed that hardness is very high near the surface in both profiles and decreases across the nitriding layer to the core base metal.

Nitriding depth can be estimated from both profiles to be approximately 60 μm. Diffusion of nitriding layer is not obvious since both profiles have about the same depth. In addition, in nitriding layer region, micro-hardness value of original insert before test is about 40

HV higher than that of tested one. Similarly, in the core base metal region, there is about

20 HV in difference. Both suggest softening for the whole part after about 15000 cycles of service. Similar phenomenon has been observed and studied in previous literature [79].

It is concluded that the essence of thermal fatigue issue is a tempering process of tool steels, where the excess hardness is reduced while toughness is increased. From the point of microstructural change, as pointed out by Telasang et al, such soften phenomenon is that H13 tool steel after quenching and tempering condition consists of the tempered martensite with high dislocation density and the chromium-rich, molybdenum-rich, and vanadium-rich carbides. After many heating and cooling cycles, accompanied by the annihilation of dislocation, the chromium-rich and molybdenum-rich carbides will transform to M23C6 and M6C types carbides, respectively, which leads to the decrease in hardness [80]. Aside from surface hardness, Abdulhadi et al. also analyzed the effect of as-machined surface roughness on thermal fatigue properties of H13 tool steels [81].

500 After 15000 cycles 450 Original insert

400

350

300

Hardness / Hardness HV 250

200

150 0 50 100 150 200 250 300 350 400 Distance / μm

Figure 40. Micro-hardness changes with respect to distances from the surface of a water jacket insert before and after about 15000 cycles in service.

3.5 Thermal Fatigue Life Prediction Criterion

Thermal fatigue failure has been a major issue in casting industry for almost half a century. The cycle life of thermal fatigue failure in dies typically varies from several thousands to tens of thousands of cycles. Such life span falls in Low Cycle Fatigue (LCF) domain where fatigue life is generally lower than 104 cycles or around. This type of fatigue is often more accurately described by strain cycles rather than stress loadings. So far there have been a few empirical models developed for the fatigue life prediction.

Based on the advantages and limitations in previous models, a temperature-based fatigue life prediction criterion is derived and proposed.

3.5.1 Derivation of the Criterion

One of the most well-known expressions in predicting LCF life is the Coffin-

Manson equation, which was proposed by Coffin [82] and Manson [83] independently.

The equation postulates that materials experience a significant of inelastic deformation for LCF conditions, and has been widely used to describe LCF life as

∆휀 푐 푝 = 휀′(2푁 ) Eq.17 2 푓 푓

′ where ∆휀푝 is plastic strain range, 푁푓 is the number of cycles to failure, 휀푓 is an empirical constant known as the fatigue ductility coefficient and 푐 is also an empirical constant known as the fatigue ductility exponent varying between -0.5 and -0.7 for metals.

Later, Manson proposed the original universal slopes equation for predicting fatigue life using only static tensile data [84]. The relationship between cycle life 푁푓 and plastic strain range ∆휀푝 is expressed as

0.6 −0.6 ∆휀푝 = 퐷 (푁푓) Eq.18 where 퐷 is ductility. The exponent value in Eq.18 is universalized as -0.6 for all materials.

Furthermore, Muralidharan and Manson proposed the modified universal slopes method based on least squares fitting of 47 materials at room temperature range, where the parameters and coefficients of plastic strain range term were further optimized as [85]

−0.53 −0.56 ∆휀 = 0.0266퐷0.155 [휎푢] (푁 ) Eq.19 푝 퐸 푓 where 휎푢 is ultimate tensile strength and 퐸 is Young’s modulus. The 휎푢/퐸 term is newly introduced into the coefficient to indicate that LCF life is also influenced by material tensile strength. In a study conducted by Park and Song, they evaluated and compared six different methods for estimation of fatigue life [86]. The modified universal slopes method was concluded to provide the best correlation, and has been commonly used to evaluate fatigue test data for a wide range of materials.

However, there are a couple of issues that limit the application of Eq.19 to die casting. Firstly, its empirical constants are based on fitting data of uniaxial static tensile tests, while the actual thermally-induced stress from expansion and contraction in die casting is multi-axial stress state. Secondly, it is optimized based on room temperature test data, while actual die casting process has a wide range of temperature fluctuations.

Finally, even with accurate temperature-dependent properties of 휎푢, 퐸 and 퐷, there is another big challenge to calculate robust stress and strain values from FEA simulation to yield an accurate fatigue life 푁푓, especially for large complex geometries in industry. A simple demonstration is that if ∆휀푝 in Eq.19 doubles and all other coefficients remain the same, 푁푓 will decrease as 3.5 times as its original fatigue life, indicating that cycle life 푁푓 is very sensitive to plastic strain range ∆휀푝.

Therefore, to take into account of temperature fluctuations and make the equation applicable to die casting industry, a simplified temperature-based equation for thermal fatigue life prediction is proposed. Based on the above three equations, the relationship between the cycle life 푁푓 and plastic strain range ∆휀푝 can be generalized in the form of

푐 −0.56 ∆휀푝 = 퐶푝푁푓 = 퐶푝푁푓 Eq.20 where 퐶푝 is a material property-related constant that includes 휎푢, 퐸 and 퐷 as compared to the equation of modified universal slopes method. Fatigue ductility exponent 푐 is viewed as -0.56 based on modified universal slopes method. Despite that 푐 will vary a little with temperature, it has been shown that the modified universal slopes method can give reasonably good predictions for cryogenic fatigue properties as validated in the previous study by Muralidharan and Manson [85]. Therefore, for convenience, a constant value of

푐 as -0.56 is inherited from Eq.19, and is regarded as an average value of 푐 for most of the materials across different temperature ranges.

In the meantime, it is well known that for most solid bulk materials, temperature fluctuations lead to thermal stress upon expansion and contraction between different parts and produce thermal strains. By definition, thermal expansion is proportional to temperature change, and the thermal strain ∆휀푡ℎ associated with it can be expressed as

∆휀푡ℎ = 훼∆푇 = 훼(푇푓𝑖푛푎푙 − 푇𝑖푛𝑖푡𝑖푎푙) Eq.21 where 훼 is thermal expansion coefficient and ∆T is temperature change between final state Tfinal and initial state Tinitial. For thermal fatigue problems, it is mainly the cyclic thermal stress that causes accumulated local plastic strains and leads to final fatigue failure. As temperature fluctuates, thermally induced stress will act as additional loading to affect the material’s mechanical behaviors. If the thermal stress overpasses the elastic

70 limit, there will be plastic strain. In this proposed model, it is assumed that the larger cyclic temperature difference, the larger thermally induced stress. Similar to the concepts of elastic and plastic strains, cyclic temperature change can also be split into two stages.

For small temperature changes, the induced thermal stress is relatively small and only causes elastic strain. For large cyclic temperature changes, however, the thermal stress is large enough to activate plastic deformation. In this case, the thermal strain ∆εth can be

e p divided into thermal elastic strain ∆εth and thermal plastic strain ∆εth, depending on the temperature range, to denote the plastic deformation caused by thermal stress that is originated by temperature change. Since plastic strain is more dominant in LCF life, the thermal plastic strain can then be expressed as

푝 푒 ∆휀푡ℎ = ∆휀푡ℎ − ∆휀푡ℎ = 훼∆푇 − 훼∆푇푐 Eq.22 where ∆푇푐 is defined as a critical temperature change that only causes thermal elastic strain and starts to cause thermal plastic strain. In this way, the plastic strain ∆εp in Eq.20

푝 is expressed in terms of temperature change. By substituting thermal plastic strain ∆휀푡ℎ for thermal fatigue life expression in Eq.20, there is

−0.56 퐶푝푁푓 = 훼∆푇 − 훼∆푇푐 Eq.23 where a relationship between cycle life 푁푓 and temperature difference ∆푇 is established.

Rearranging the above the equation by writing 푁푓 in terms of ∆푇 will further yield

−1.786 −1.786 푁푓 = [훼/퐶푝] (∆푇 − ∆푇푐) Eq.24

−1.786 where [훼/퐶푝] is a coefficient related to material properties and can be replaced by a coefficient 푘 as

−1.786 푁푓 = 푘(∆푇 − ∆푇푐) Eq.25

71 where k is a material property-related constant and ∆Tc is the critical temperature change to induce thermal plastic strain. In this way, a general form that relates cycle life Nf to temperature difference ∆T is established. Applications and limitations of the model will be further discussed in the later sections.

3.5.2 Fitting the Criterion

Using the experimental data, model parameters in Eq.25 can be calibrated. For SP sample, the proposed fatigue life criterion can be fitted by the number of cycles to cracking failure vs temperature difference in one cycle from Table 11. Figure 41 shows

푁푓 vs. ∆푇 for all three different test conditions in experiments, and the data were then used to fit the model, as also shown in the plot. The R-Square value is 0.9996, indicating a good fitting of the model. Therefore, Eq.26 gives the final fitted thermal fatigue life prediction based on SP sample tests.

7 −1.786 푁푓 = 2.589 × 10 × (∆푇 − 253.6) Eq.26

Figure 41. Experimental 푁푓 vs. ∆푇 data and model fitting for SP sample.

Mathematically, Eq.26 has a vertical asymptote at 253.6 °C, which means that when sample temperature difference is no larger than this value, the tested H13 steel will not produce thermal fatigue damage. With the established criterion for this test material, engineers can run further FEA simulation to obtain cyclic temperature fluctuations at different casting conditions for quick and reliable assessments of thermal fatigue life. It can also be seen that by controlling temperature difference to a lower value, thermal fatigue damage can be reduced to extend die life. An intuitive percept is that the magnitude of thermal stress is positively correlated with cyclic temperature difference of the die (∆푇 = 푇푚푎푥 − 푇푚𝑖푛). Therefore, it would be common practice to preheat the die to raise 푇푚𝑖푛, or add more cooling line and apply coatings to the die to lower 푇푚푎푥. In this way, ∆푇 will be minimized and die life will be extended.

For MDI sample, in addition to the combined Al melt immersion test and kiln chamber heating test, a linear cumulative fatigue damage concept was employed to establish the equations to solve coefficients 푘 and ∆푇푐 in Eq.25. It is one of the most widely used cumulative damage models for fatigue failures developed by Miner [87]. The concept assumes that the total damage caused by a number of stress cycles is equal to the summation of damages caused by each individual stress level. Mathematically, it can be expressed as

푘 푛푖 ∑𝑖=1 = 푇 Eq.27 푁푖 where ni and Ni are accumulated cycles and total life cycles under ith loading level, respectively. 푇 denotes the damage, and failure occurs when 푇 equals 1.

For MDI sample, there are 3120 cycles in Al melt dipping and 13360 cycles in furnace heating. Using the linear damage accumulation rule and combining with previous

15000 cycles performed by an industrial partner, a set of equations can be written as

−1.786 15000 = 푘(400 − ∆푇푐) { 3120 13360 Eq.28 −1.786 + −1.786 = 1 푘(250−∆푇푐) 푘(400−∆푇푐)

By calculating the two unknown variables, final temperature-based life prediction criterion for MDI sample can be expressed as

8 −1.786 푁푓 = 9.78 × 10 × (∆푇 + 96.04) Eq.29

Using Eq.29, the corresponding cycle life of a given test method can be computed.

Table 12 summarizes the damage accumulation for the two different test methods for

MDI sample. In this case, the predicted cycle life for Al melt dipping test is 28540 cycles, where 3120 cycles account for 10.9% of the total damage. The remaining 89.1% is produced by furnace heating where 13360 out of 15002 cycles have been tested. As mentioned in previous SP sample, the predicted thermal fatigue life will be extended as cyclic temperature difference decreases.

Table 12. Summary of thermal fatigue test for MDI sample. Methods Notch tip ∆푇 / °C Tested cycles Predicted life Damage percent Al melt dipping ~ 250 3120 28540 10.9% Furnace heating ~ 400 13360 15002 89.1%

Meanwhile, mathematically Eq.29 has a vertical asymptote at -96.04 °C that represents the thermal fatigue limit. Theoretically this asymptote limit would be a non- negative value, but plugging 0 °C into the equation will yield a fatigue life of 281630 cycles, which is reasonable to be viewed as a large number of thermal fatigue limit. A plausible explanation for the asymptote discrepancy is due to the LCF domain. As cyclic temperature fluctuation ∆푇 approaches the asymptote, cycle life 푁푓 will be much larger than tens of thousands of cycles, which is no longer in the domain of LCF. In this case,

74 both the elastic strain and plastic strain will need to be considered. However, when ∆푇 is away from the asymptote, LCF remains the dominant type of failure. As claimed by

Persson et al., the thermal cracking nucleation is associated to accumulation of the local plastic strain in the surface, which is typical of LCF [88]. Thus, the new temperature- based fatigue life model present in this work, as tested by both a SP sample and a MDI sample, would be a good approximation model to predict thermal fatigue cracking in H13 steel dies, especially when die life is in LCF regime lower than 104 cycles or close.

Although only two equations would be required to solve the two unknown parameters in Eq.25, it needs to be emphasized that, from a statistical point of view, the more data that are collected, the better in fitting and calibrating those parameters.

However, since the cycle time in this study is relatively long and only one sample can be tested at each time, it takes quite a lot efforts to complete even a couple of samples and examine the failures. Nevertheless, the main objective of experimental tests in this study is to demonstrate the calibration of parameters and validate the predictive thermal fatigue model in the power law form. From that perspective, the experimental results in this work have served the purpose.

3.5.3 Scope and Limitations of the Criterion

The dominating failure mode in die-casting tooling is thermal fatigue cracking.

During thermal cycling of die casting processes, compressive and tensile stresses are alternatively generated, which gradually cause plastic strain on surface materials and leading to LCF failure. For thermal fatigue life predictions, many of the previous studies employed the well-known Coffin-Manson empirical equation with explicitly material

75 property-related parameters, such as stress, strain, ductility and Young’s modulus in

Eq.19 or its similar derivations. The biggest advantage of such model is that a direct relationship between stress/strain states and fatigue life can be established. Theoretically, with a reliable stress/strain calculation in FEA model, an accurate cycle life can be predicted. However, for die casting with very high cooling rates, it is quite challenging to construct accurate temperature-dependent mechanical databases (especially for those considering the effect of cooling rates). Meanwhile, it is also difficult to calculate reliable stress/strain values in FEA model for products with complex geometries in industry.

Therefore, almost all the previously mentioned studies just used a very simple geometry for stress simulation, and ran simple tests for demonstrations.

From the perspective of engineering applications, it is usually more cost-effective and time-efficient to measure temperature results and compare with FEA predictions than to validate stress results. In this study, even though reasonable stress evolutions of MDI sample notch tip can be calculated as shown in Figure 32 for a qualitative trend, it is still quite challenging to measure stress and strains from experiments for a quantitative validation, especially for irregular industrial components. Thus, the temperature-based criterion will have the advantage of performing a more feasible and reliable validation with temperature results in foundry. On the other side, instead of using the explicitly multiple material property-related parameters in Eq.19, hardness has been proposed as an empirical indicator for thermal softening to determine the critical point for thermal fatigue failure such as by Caliskanoglu et al. [72]. It has been revealed that cracking can be suppressed by the higher tool hardness levels by Persson et al. [88]. However, it is known that softening is the result of steel tempering for thermal fatigue problems, where

76 the root cause is the presence of temperature gradients in thermal cycling. It is the cyclic temperature fluctuations that lead to thermal fatigue loadings, which causes surface softening and final crack formation. Therefore, in this work, the model focuses on cyclic temperature difference and explicitly expresses it as a key parameter for thermal fatigue life predictions.

Meanwhile, due to the different surface hardness and geometric effect, it turns out that the calibrated SP sample criterion cannot be directly used for the MDI sample validation, and there exist two different calibrated criteria for the SP and MDI samples, respectively. This is because that Eq.25 does not explicitly include either the geometric effect or surface hardness as a parameter. Even at a similar cyclic temperature range, the cycle life to failure varies between different materials and geometries, which has been a common limitation in predictive models. On the one hand, the more parameters to be included in the expression, the more accurate it will be to capture the most physics phenomena. On the other hand, the complexity in those models makes it difficult for parameter calibrations and inconvenient for engineering applications. In this proposed model, the cyclic temperature fluctuation ∆T is considered the most important factor in thermal fatigue failures in die casting processes. Based on previous models, a predictive power law form is proposed with ∆T being explicitly expressed in the equation. The model is first calibrated by the SP sample. The MDI sample serves as a further validation of the methodology and calibration of the power law form expressed in Eq.25.

Further attention also needs to be paid when applying the criterion due to the assumptions made to the proposed thermal fatigue life model, including (i) crack initiates from the notch tip where stress is mostly concentrated, whereas actual die casting

77 generally have other mechanical loadings and unexpected stress concentration locations; and (ii) temperature difference ∆푇 in one cycle is assumed to be constant during the stable test, whereas actual die casting may have ramp time and temperature difference variations are too large to be neglected. Since the model does not explicitly consider the geometric effect, its application is limited to case by case when the geometry is changed.

However, for die casting industry, it is difficult to change geometries due to design restrictions and property requirements of the casting. Instead, it is more often to change casting process parameters to make a desired product. In this way, this model will be convenient once the model constants have been calibrated for a given geometry. Using the calibrated model, casting engineers can virtually try with different casting conditions in FEA simulation to get the cyclic temperatures for quick and reliable assessments of thermal fatigue life.

In summary, the methodology can be applied to other similar hot-work tool materials, and the model revealed that temperature fluctuation in die casting is a key contributor to thermal fatigue life. With the simplicity of the model expression, it can also help die casting engineers predict thermal fatigue failures in a cost-effective and time- efficient manner.

3.6 Conclusions and Highlights

In this chapter, thermally-induced cracking of H13 hot-work tool steel, a common failure in die casting industry, was investigated and a temperature-based approach was proposed to predict thermal fatigue life. The detailed conclusions are listed below.

 A thermal fatigue life model, based on temperature differences and thermal

fatigue crack cycles, has been developed based on a modified universal slopes

equation. It is found that high temperature difference leads to shorter thermal

fatigue life. Thus, die life can be prolonged by reducing temperature

difference in a casting cycle.

 Through cyclic tests for samples in heating and cooling conditions, thermal

fatigue cracking can be reproduced at laboratory scale. Two types of H13 steel

samples with different surface hardness were tested. Sample geometries were

optimized through iterative simulation to increase test efficiency.

 Thermal loadings of can be simulated using FEA model with ProCAST. For

heating in kiln chamber without existence of sticky Aluminum layers on the

sample, good agreement of temperature contours between FEA simulation and

experiments was obtained for both samples.

 In addition to the simple sample as a rectangular plate, the proposed thermal

fatigue life model was further calibrated to a more complex sample with

geometrically similar to a water jacket insert in an automotive engine block.

Overall, the good correlation between simulation results and experimental tests as well as the simplicity of the criterion suggest a promising application to evaluate fatigue life of die casting dies in a convenience way.

Chapter 4: Hydrogen Gas Porosity in an A356 Casting

4.1 Motivation and Problem Description

4.1.1 Background and Motivation

Aluminum casting alloys are important industrial raw materials and have been widely used in transportation, aerospace and many other fields. In spite of their excellent casting characteristics, reasonable mechanical properties and options for heat treatment, porosity or shrinkage voids are usually undesirable and exists ubiquitously in the casting products. It is claimed by Sigworth and Wang that about one half to three quarters of scrap castings are lost due to porosity and shrinkage [89].

Porosity is known to reduce mechanical properties of castings, especially ductility and fatigue resistance [90]. The absence of porosity has a large effect on the fatigue life in cast aluminum alloys. Studies in 356-type Al alloys have shown that the elimination of porosity can increase average fatigue life by a factor of up to 10 [91]. Similarly, Figure

41 presents that in cast 319 Aluminum alloys, increasing pore size leads to the decreasing fatigue life due to the effect of porosity on crack initiation [92].

Figure 42. Relationship between pore size and fatigue life of cast 319 Al alloy [92].

From a scientific point of view, the problem of porosity formation is complex and interesting. It has been studied for over 60 years, but so far there appears to have been no clear agreement as to which mechanisms control the formation of porosity and shrinkage, and foundry engineers keep sticking to empirical rules to design the molds [93]. Thus, it remains a major concern and need for casting industry to predict, control and hopefully eliminate porosity.

4.1.2 Literature Review of the Problem

There are two major types of porosity observed in aluminum castings [94]: (1) shrinkage porosity due to solidification shrinkage and inadequate feeding during casting, and (2) gas porosity due to air entrapment and insoluble gases, which is mainly hydrogen.

Figure 42 illustrates the definition and classification of shrinkage and porosity defects

[95]. In aluminum-based alloys, hydrogen is the only diatomic gas that the solubility is considerably greater in liquid aluminum than in solid aluminum to lead to porosity formation [6]. Thus, this work focuses on the gas porosity developed by the presence of hydrogen dissolved in molten aluminum, which falls into the category of microporosity with a length scale of tens to hundreds of micrometers.

Figure 43. Definition and classification of shrinkage and porosity defects [95].

Many experiments have been done to understand the hydrogen microporosity in casting processes, such as in situ observation of hydrogen pores in Al-Si castings [96], different pre-treatments to control hydrogen levels [97] and calculations of effective hydrogen diffusion coefficient [98]. However, experiments are limited in providing more insights and details about the formation of hydrogen pores during solidification process.

In the last few decades, modeling and simulation techniques have been greatly developed, which features the two most important milestones including the concept of Integrated

Computational Materials Engineering (ICME) proposed in 2008 [99], and the program of

Materials Genome Initiative (MGI) was launched in June 2011 [100]. The key idea is to save time and cost using ICME approach as compared to the conventional experimental procedures based on trial-and-error, and it has been a research protocol that combines theoretical analysis, materials design, and materials processing across different length scales to capture the process-structures-properties-performance of a material.

Regarding the modeling techniques to simulate and understand the microstructure during solidification, several studies have been done since the 1980’s with a focus on the grain nucleation and growth, including analytical micro-macro models of solidification

[101–104], criteria models based on empirical functions such as Niyama criterion [105] and some other criteria based upon statistical analysis of experimental observations [106,

107], numerical solutions of general Stokes flow (Darcy’s law [108]) coupled with conservation and continuity equations to evaluate local pressure drop [109–111], and stochastic grain structure models such as Cellular Automaton coupled with Finite

Element (CA-FE model) [112, 113]. Later new algorithms and parallelization strategies have been implemented in order to predict grain structure formation for much larger

82 castings within reasonable computation times [114].

When it comes to the numerical simulation of microporosity formation, models have been pioneered by Piwonka and Flemings [115] and later improved by Kubo and

Pehlke [116] and Lee and his group [94]. However, there are still a couple challenges that need to be addressed. Firstly, as reviewed in previous literatures by Sabau [117] and

Rappaz [118], modeling of solidification microstructures needs to first solve the mass- and momentum conservation equations in the mushy zone with appropriate boundary conditions. Secondly, for microporosity modeling, it will further need to consider the formation of the new phase, i.e. the pores. Things get more complicated since nucleation and growth of pores involves segregation and diffusion of gaseous and/or volatile solute elements into the liquid, which is essentially the coupled nucleation and growth of both dendrites and pores. Thirdly, most of the previous models focus on predicting the final porosity in binary casting alloys (such as Al-Si or Al-Cu alloys), and modeling of the porosity size and porosity distribution with graphical morphology outputs are limited.

Therefore, it is necessary and critical to predict porosity coupled with dendrite growth of multi-component alloys in an ICME framework to obtain location-specific microstructure models for location-specific mechanical property predictions [7]. In this way, combining the microstructural modeling of hydrogen microporosity formation with corresponding process simulation model, an essential link across two different length scales can be established in ICME approach for the casting industry.

4.1.3 Abstract for the Research

In this research, hydrogen microporosity in A356 gravity castings was studied. To

83 investigate the effect of cooling rates on the microporosity, a V-shaped wedge casting was used to generate different cooling rates across various regions. Hydrogen content in the melt was first measured prior to the casting process. A Finite element (FE) model was built to simulate the process and temperature fields were correlated with thermocouple measurements. Thermal histories of the casting were then extracted and used in the subsequent mesoscale Cellular Automaton (CA) modeling, where grain growth and porosity evolution with multi-grains growth was both considered and simulated. Based on the microstructure modeling, 3-dimensional microporosity morphology was visualized qualitatively and the porosity size and distribution was computed quantitatively. X-ray micro-Computed Tomography (microCT) reconstructions and metallography analyses were performed on cylindrical samples from different locations in the wedge cast. The results were employed to validate both 2-dimensional (2-D) and 3-dimensional (3-D) predictions of location-specific microporosity in terms of size, fraction, distribution and morphology. The good correlation suggests potential applications of coupled CA-FE model in serving a critical link in ICEM approach for the casting industry.

4.2 Experimental Procedures

Laboratory experiments were carried out to reproduce the hydrogen gas porosity in a commonly used casting alloy A356. Wedge samples were made using gravity casting process in a permanent steel mold. Prior to pouring, hydrogen content was measured by making small samples in reduced pressure test. During the casting process, cooling rates were measured using thermocouples, and temperature data were used to correlate with thermal fields from finite element model. Cylindrical samples were cut from the wedge

84 cast for metallography analyses in 2-D and microCT analyses in 3-D to examine the microporosity defects. The experimental observations were then used to correlate with microstructure predictions in CA model.

4.2.1 Samples and Materials

The casting experiment was implemented on a commonly used aluminum cast alloy A356, with its chemical composition listed in Table 13. To investigate the effect of cooling rates on the microporosity, a V-shaped wedge casting was used to generate different cooling rates from the bottom tip to the top region. Figure 44 presents the schematic geometry of proposed wedge cast in this study from two different perspectives.

The labelled red dots represent locations of thermocouples in experiments.

Table 13. Chemical compositions of tested A356 wedge casting. Composition Si Mg Ti Fe Sr V Al A356, wt.% 6.78 0.33 0.13 0.11 0.02 0.015 Bal.

Figure 44. Schematic of wedge cast with locations of thermocouples in red dots.

4.2.2 Wedge Casting Experiment

During the experiment, the alloy ingots were melted in a graphite crucible in a kiln and the melt temperature of 700 ˚C was maintained throughout the casting process.

The inside surface of graphite crucible was coated with boron nitride to form a non-wet layer to aluminum melt and minimize chemical reactions. The oxide layer on the top of aluminum melt in the crucible was removed right before the casting. Three K-type thermocouple wires with a 0.2 mm diameter (Part No. 0.2 x1P K-H from Ninomiya) were put in various locations as shown in the red points of Figure 44, and the corresponding temperature profiles were measured during the casting process. Thermocouple wires were shielded in Alumina tubes, while the thermocouple junctions were exposed directly to the melt for faster response time and improved accuracy. During the casting process, temperature profiles were collected using a data acquisition system (NI 9219 from

National Instruments) with the acquisition rate at 50 Hz. Figure 45 present the two half inner surfaces of steel permanent mold for wedge casting and actual wedge cast sample with locations of three thermocouples labelled.

Figure 45. Permanent mold of wedge casting (left) and actual wedge cast sample with locations of thermocouples labelled (right).

4.2.3 Hydrogen Content Measurements

The Straube-Pfeiffer vacuum solidification test, or equivalently the reduced pressure test (RPT), has been widely used to check gas contents of molten aluminum alloys. It correlates the sample density with its hydrogen contents, which is a simple and cheap test in contrast to the existing high-cost equipment. In this study, RPT was carried out using a reduced pressure tester from Palmer Manufacturing & Supply, Inc. as schematically shown in Figure 46, and three sets of tests were performed to take the average of density measurements. For each test, approximately 100 g of A356 alloy was first melted in a muffle furnace at 700 ˚C. Then the sample melt was poured into a metal cup about the size of an egg cup and solidified at a pressure of 100 mmHg for 20 minutes.

The average density was calculated based on Archimedes Principle after the dry weight and wet weight of each sample was measured. Finally, the measured density can be correlated with hydrogen content.

Figure 46. Schematic diagram of reduced pressure tester.

4.2.4 Metallography Analyses

To clearly observe the morphology of dendrites and microporosity, conventional metallography characterization were analyzed using 2-D optical microstructures. As

87 shown in Figure 47, cylindrical samples with a diameter of 6.35 mm (0.25 in) at the measured cooling rates locations were cut using a copper wire Electrical Discharge

Machine (EDM) and cold-mounted in Bakelite powder to prepare metallography specimens. Then they were ground and polished in standard metallographic procedures.

Specifically, grinding was first employed to remove the Alumina thermocouple sheath.

The rest grinding was completed with progressively fine SiC metallographic abrasive paper, from 180-grit down to 1200-grit paper, using water to wash away abraded material.

Polishing was accomplished with progressively fine diamond abrasive in an alcohol suspension, from 3 μm down to 1 μm grit abrasive. The obtained optical metallography results were then compared with the 2-D simulated results in CA.

Figure 47. Cylindrical samples cut from wedge cast (left) and hot-mounted in Bakelite powder (right).

4.2.5 Micro-Computed Tomography Analyses

3D microCT analyses provide a metric to measure location-specific microporosity in terms of size, fraction, distribution and morphology. Such metric can help foundry engineers to easily assess improvements in the casting quality due to parameter change

88 and product optimization. In this study, the same cylindrical samples with a diameter of

6.35 mm (0.25 in) were excised from the three different locations in the wedge cast to provide a range of cooling rates. Samples were scanned at 90 kV, 80 μA and a resolution of 6.318 μm per voxel using HeliScanTM microCT at Center for Electron Microscopy and

Analysis (CEMAS). An exposure time of 0.11 s and a 2 mm-thick Aluminum plate as a filter on detector were employed. As shown schematically in Figure 48, during the scan, the sample was positioned between a fixed X-ray source and detector. The sample was moving up while it was self-rotating, creating a helix trajectory for the scan. A scanning mode of 2 × 2 pixel binning and 2880 projections per revolution was chosen during the scan. For each scan, a large amount of reconstruction data was generated, including the morphology, volume, surface area and location of each pore. The reconstructed results were further analyzed and visualized using the image processing module, ScanIP, in

Simpleware software. For the comparison between different samples, a consistent domain was defined as a cylinder with 6.35 mm (0.25 in) in diameter and 3 mm in height. The domain was selected to be as close as to the thermocouple positions to represent the pore results at different measured cooling rates.

Figure 48. Schematic of microCT scan setup for (a) side view and (b) top view.

4.3 Process Simulation and Microstructure Modeling

A Finite element (FE) model was developed in ProCAST first to simulate gravity casting process to provide temperature conditions for subsequent Cellular Automaton

(CA) microstructure modeling at mesoscale. Different thermal conditions from FE results were used to simulate grain nucleation and growth coupled with hydrogen porosity nucleation and growth during solidification. The location-specific details of porosity morphology, size, distribution and fraction were obtained by CA modeling. Simulated results were validated by experimental measurements in later sections.

4.3.1 Finite Element Analysis for Process Simulation

For FE model, CAD file was first generated in Solidworks and then imported to

ProCAST. The model employed four-node linear tetrahedral elements for filling and solidification simulation. Meshing was refined near the bottom tip of wedge cast with a minimum element size of 0.7 mm, and total element number of the sample was 1,593,067.

The temperature-dependent thermal physical (thermal conductivity, density, enthalpy and fraction solid) and thermal mechanical (Young’s modulus, Poisson’s ratio and thermal expansion coefficient) properties of A356 alloy were calculated based on the chemical compositions in Table 13, which is a built-in capability in the software package that a database for Al-based system from CompuTherm® was included and Scheil condition could be selected. The calculated properties were then calibrated with literature data

[119]. In the simulation, a constant heat transfer coefficient of 4016.64 W/m2·K was selected between melt and permanent mold based on the experimental result in literature

[66]. Air cooling was defined as the boundary condition on the exterior surfaces of the mold and casting. Pour temperature was set at 700 ˚C and pouring time was set at 3 s to

90 be the same conditions in actual casting experiment. In this model, thermal and filling simulation was run for one cycle since stress was not considered.

4.3.2 Cellular Automaton for Microstructure Modeling

Cellular Automaton (CA) is a mathematical model developed by Von Neumann

[120] in 1948 to simulate complex systems or processes. It is an algorithm that describes the discrete spatial and temporal evolution of complex systems by applying local (or sometimes long-range) deterministic or probabilistic transformation rules to the cells of a regular (or non-regular) lattice [121]. Such method was introduced into materials field by

Hesselbarth and Göbel [122], and later popularized by Rappaz and his group [123] in the

1990s. For CA model in this research, it was coded in Fortran and was mainly built upon

Dr. Gu’s PhD dissertation [124]. As exemplified in Figure 49 for a 2-D demonstration, the simulation domain is discretized into square cells and each cell represents the phase state or interface type at the current time step. The state of each cell evolves as time goes.

Figure 49. Schematic of Cellular Automaton cells in 2-D [124].

In this research, a 3-D CA model was developed to simulate the formation and evolution of both hydrogen porosity and grains during the solidification process. Since the three majoring elements in Table 13 was Al, Si and Mg, the rest alloying elements were neglected in the simulation. Al-7wt.% Si-0.3wt. %Mg ternary alloy was used in the

CA model as a reasonable approximation. Other assumptions used in the model include:

(1) the effect of fluid flow is not considered; (2) solidification shrinkage is neglected; and

(3) the eutectic solidification is not considered.

The calculation domain consisted of 200 × 200 × 200 mesh with a uniform cell size of 5 μm. Symmetrical boundary conditions were used on all the six surfaces of the simulation zone. Temperature was assumed to be homogeneous in the entire computation domain. The cooling rates were set to be the instantaneous cooling rates from previous

FEA calculations that were validated with the cooling curves observed in the experiments.

The initial hydrogen concentration in the Al melt was set as the same measured from the experiments. As solidification proceeds, solid grains begin to nucleate and grow. During such process, solutes (Si and Mg) are rejected from the solid, and accumulate at the S/L interface due to the phase equilibrium. Since hydrogen is much less soluble in solid Al than in liquid Al, the excess hydrogen will be rejected from the solid into the remaining liquid phase. With the increase of hydrogen concentration in the liquid, hydrogen pores will form in the gas state when the atomic hydrogen reaches the solubility limit in the liquid. Based on the local hydrogen concentration levels and the diffusion rate, pores are able to grow or shrink. As the temperature decreases in the casting, thermodynamically stable grains and hydrogen pores will grow. Figure 49 outlines the flowchart of full calculation procedures for grain growth with porosity evolution.

Figure 50. Calculation flowchart for grain growth with porosity evolution.

It can be seen from the flowchart that there are two main parts in each iteration step. Grain nucleation and growth were first considered, and then porosity formation and growth were established. In this way, porosity evolution is coupled with dendrite growth in the CA model for location-specific microstructures.

4.4 Results and Discussion

Wedge die casting experiments were done in laboratory to validate simulation results. Initial hydrogen content was measured, and temperature profiles were collected and compared with FEA calculation. The microporosity information from wedge die casting experiments was obtained by X-ray microCT measurements. Qualitative results, including porosity distribution and morphology in 2-D and 3-D, were visualized and compared with CA predictions. Meanwhile, quantitative analyses, including porosity size, fraction and sphericity, were calculated to study the effect of cooling rates on porosity formation and evolution.

4.4.1 Initial Hydrogen Content

Obtaining a reliably accurate estimate of the melt hydrogen level prior to casting has led to the development of several techniques, among which the reduced pressure test

(RPT), basically a comparative and qualitative test that appears to be the one widely used in foundries due to its simplicity and easy adaptation to the foundry floor [125]. Attempts have been made to quantify the tests, which is initially proposed by Rosenthal and Lipson

[126] by assuming all of the porosity is due to hydrogen. The hydrogen content [H] (in ml/100 g Al) can be expressed as

1 1 [퐻] = 퐾 ( − ) Eq.30 퐷푟푝 퐷푡ℎ where Drp is density of the reduced pressure sample, Dth is theoretical density, and K is gas law constant which can be further expressed as

푃 273 퐾 = 2 × × 100 Eq.31 760 푇2 where 푃2 and 푇2 are reduced pressure (unit: mm Hg) and alloy solidus temperature (unit:

3 K). In the test case, the average measured density of sample is 퐷푟푝 = 2.26 g/cm , and

RPT pressure is 푃2 = 100 mm Hg. Meanwhile, for this commonly used A356 alloy, its

3 theoretical density is 퐷푡ℎ = 2.68 g/cm , and its solidus temperature is 푇2 = 830 K (557 °C).

By plugging these numbers into Eq.30 and Eq.31, hydrogen content can be calculated as

[H] = 0.3001 ml / 100 g Al. In the CA microstructure modeling, this value is employed as an initial condition.

Attention needs to be paid that the above calculation of hydrogen content is based on relative density and pressure, which is more like an empirical estimation. It does not measure all the dissolved hydrogen gas content in the melt directly. In practice, at least three tests should be done to take an average to ensure the repeatability. In addition, RPT is insensitive to the very low hydrogen contents obtained/required in ingots prepared from properly filtered and degassed melts for fabrication purposes, which is another main drawback [127]. It is also found that the RPT results are influenced by the inclusions present in the melt, where inclusions are known to act as nucleating agents that facilitate bubble formation during solidification of the sample under reduced pressure [128]. By removal of such inclusions, bubble formation will be affected without changing the absolute hydrogen content, which leads to misinterpretation of the results if the observed

95 densities of the reduced pressure samples are related to gas contents of their respective melts. Nevertheless, due to its simplicity and low cost, RPT is employed as a practical and efficient way of estimating hydrogen content in the present lab-scale work as a first approximation.

4.4.2 Temperature Profiles

Figure 51 presents the three temperature profiles measured by thermocouples at the three different locations of wedge casting in Figure 45. For this particular A356 alloy, the solidus and liquidus temperature is 557 °C and 616 °C, respectively. Due to the turbulent fluid flow, the initial temperature drop stage shows a pattern of chaotic fluctuations. Nevertheless, the general trend is clear that the bottom location has fastest drop in the temperature with the highest cooling rate, the middle location is the next and the top location has the lowest cooling rate.

660 Bottom (TC3) 640 Middle (TC2)

620

C Top (TC1) ° 600

580

560

Temperature / Temperature 540

520

500 0 10 20 30 40 Time / s

Figure 51. Cooling curves measured by thermocouples at three locations.

Numerically, the cooling rates can be calculated from the experimental measured

96 cooling curves as summarized in Table 14. The instantaneous cooling rate is computed as expressed in Eq. 32

푑푇푙𝑖푞 퐶푅𝑖푛푠 = Eq.32 푑푡푙𝑖푞 where 푇 is the temperature at liquidus and 푡 is the time at which the materials is at liquidus temperatures. Equivalently, Eq.32 calculates the slope or the first derivative at liquidus temperature. Meanwhile, the average cooling rate is the temperature difference between solidus and liquidus divide by the time difference between solidus and liquidus temperatures. Mathematically it is described as

푇푙𝑖푞 − 푇푠표푙 퐶푅푎푣푒 = | | Eq.33 푡푙𝑖푞 − 푡푠표푙 where 푇 is the temperature at liquidus and solidus, and 푡 is the time at which the material is at liquidus and solidus temperatures. It can be seen that for the measurement of the same location, its instantaneous cooling rate is typically larger than its average cooling rate, especially when the initial temperature drop is dramatic. In CA model of this work, instantaneous cooling rate is more critical and is used as initial conditions for simulating microstructures.

Table 14. Instantaneous and average cooling rates for three locations. Location Bottom Middle Top Instantaneous (K/s) 64.75 10.67 2.52 Average (K/s) 15.64 4.69 2.77

Furthermore, the cooling curve comparison between FEA and experiments at each measured location is plotted in Figure 52. The same temperature range of 500 ~ 660 °C is retained as that of Figure 51. It can be seen that all the simulation curves present a good agreement with experimental measurements during the initial temperature drop region,

97 especially when temperature is at above 610 °C. There is some discrepancy between the simulation and experiment when temperature is at 570 ~ 610 °C, but the general trend is similar during this period. Specifically, for the bottom location, the overall trend agrees well when temperature is above 570 °C. After 570 °C, more discrepancy is observed in the slope and values between FEA and experiments in all three locations. The reason for such discrepancy is not fully clear, but it is less critical. As discussed previously, the instantaneous cooling rate at liquidus temperature is more critical and will be used in subsequent CA model, while the temperature after solidification is not of primary focus.

At high temperature range, the plot indicates a good agreement between experiment and simulation, and thus for accurate predictions of instantaneous cooling rates.

Figure 52. Cooling curve comparisons between FEA and experiments.

4.4.3 Microporosity Characterization – Qualitative Analysis

In order to clearly observe the morphology of dendrites and microporosity, 2-D optical microstructure with different cooling rates was characterized and compared with the 2-D simulated CA results as shown in Figure 53. Optical micrographs were taken at the same 100x magnification for the three locations of thermocouple measurements. In the optical microstructure, both dendrites and porosity can be clearly observed. With the decreasing in cooling rate, it can be easily observed that the dendrites become coarse and pores grow larger. It can also be seen that overall the simulation dendrite morphologies in

CA model match well with the observed optical results as shown in the white triangle of

Figure 53(c) and (d). However, the pores do not appear as round morphologies and it seems to follow the shape of dendrites. Meanwhile, the pore sizes do not present a clear increasing trend with the decreasing of cooling rates. This is attributed to the 2-D cross- section can only show a slice of complete 3-D information [129]. Nevertheless, it shows that CA is a feasible method to model microstructures with reasonable results. The 2-D simulated microstructures present a good agreement with the optical metallography, both the dendrite morphology and porosity morphology.

Figure 53. Comparisons of optical microstructures and CA simulated results at different cooling rates of (a) & (b) 64.75 K/s, (c) & (d) 10.67 K/s, and (e) & (f) 2.52 K/s.

To further accurately characterize microporosity features, microCT scan was employed and Figure 54 presents the longitudinal and cross-sectional 2-D images from microCT scan. Due to the difference in density, there exist differential absorptions of X-

100 ray photons between different materials, which lead to the contrast on the final image.

Denser materials typically have larger attenuation coefficient. For example, thermocouple has higher density than A356, while voids have the lowest density. In this way, it can be observed that the voids are represented as black on radiograph while thermocouple has the brightest while color on Figure 54. During microCT scan, hundreds of the similar 2-D images are generated. Those acquired 2-D images are then reconstructed into 3-D volumetric data, which is typically performed based on variations of a filtered back- projection algorithm [130].

Figure 54. Longitudinal and cross-sectional 2-D microCT images.

The reconstruction data were then imported into ScanIP module in Simpleware for image processing, where the porosity features were extracted and masked in 3-D as presented in Figure 55. There is an obvious qualitative trend that with the increase in instantaneous cooling rates, the finalized porosity becomes smaller and more numerous in numbers. It is known that the increase in cooling rate causes the increase of supercooling degree, which can lead to larger driving force for increased nucleation of grains, faster grain growth rate and eventually a finer grain size. The increased number of solidified

101 grains then impedes the diffusion of hydrogen in the remaining liquid and the growth of the nucleated pores. So the pores end up with irregular shapes that follow the dendrites morphology. Such hindered growth also leads to an increased number of individual pores formed as the melt has less time for hydrogen to diffuse and pores to grow, resulting in smaller size and increased number of porosity. Meanwhile, the less time for hydrogen to diffuse at higher cooling rates, the more hydrogen will be present in the remaining liquid.

In this way, there is smaller volume of hydrogen porosity at higher cooling rates than that at lower cooling rates.

Figure 55. 3-D reconstructed microporosity for different cooling rates at (a) 2.52 K/s, (b) 10.67 K/s, and (c) 64.75 K/s.

Furthermore, CA modeling was performed for comparison with wedge die casting experimental microCT scan for the same 1 mm × 1 mm × 1 mm domain. The results of 3-

D distribution and morphology of microporosity at various cooling rates are presented in

Figure 56 as superimposed with dendrite grains. It can be seen that porosities are mainly constrained between the dendrites. The growth of microporosity appears to be blocked by the dendrite morphology, and vice versa. With the decrease of cooling rate, there is a qualitative trend that porosity ends up in a larger size and the total number of individual pore decreases, which is similar to what we have previously been discussed. Since the hydrogen pores surrounded by dendrites are not able to escape from the remaining liquid,

102 they form microporosity in the final casting. In summary, it shows that CA modeling can be used to visualize the porosity morphology by simultaneously simulating both porosity and dendrites, and the simulated results agree well with the experimental measurements.

103

4.4.4 Microporosity Characterization – Quantitative Analysis

Aside from the qualitative results of microporosity distribution and morphological observation in 2-D and 3-D as previously discussed, quantitative analyses of porosity size, volume fraction and sphericity can be obtained as well. For example, the total porosity volume 푉푝 is given by

푁

푉푝 = ∑ 푣푝,𝑖 Eq.34 𝑖=1 where 푁 is the total number of pores in the scan and 푣푝,𝑖 is the volume of each individual pore with 푖 = 1, 2, 3, ... 푁. The volume averaged porosity (%) in the scan is therefore

푉푝 퐹푝 = × 100% Eq.35 푉0 where 푉0 is the total volume of the scan domain. Here the scanned cylindrical sample has a diameter of 6.35 mm (0.25 in) and 3 mm in height. Thus, 푉0 is the cylindrical volume as

95.01 mm3. Table 15 presents the quantification of discrete porosity number, porosity volume and its fraction for the three different cooling rates. Once again, the results confirm the qualitative trend that with the increase in cooling rates, there is an increase in the total number of individual porosity while the pores volume is decreasing.

Table 15. Quantification of the microporosity number, volume and fraction at different cooling rates.

Instantaneous Number of discrete Total porosity Porosity volume cooling rate (K/s) microporosity volume (mm3) fraction 2.52 44 0.567 0.597% 10.67 59 0.250 0.263% 64.75 67 0.033 0.035%

The microporosity volume data in Table 15 represents the total volume. To have a better idea of the individual microporosity, the distributions of each porosity volume and

104 its equivalent radius at different cooling rates are displayed in Figure 57. The box plot is a standardized way of displaying the distribution of data based on the five-number summary of minimum, first quartile, median, third quartile, and maximum. For the median in Figure 57, it is displayed in red line and is the most representative for trend comparisons. For example, the longest sample has the slowest cooling rate and median of its porosity volume is the highest, since pores have more time to grow larger at lower cooling rate. On the other hand, the shortest sample is at the bottom of wedge cast and has the fastest cooling rate, so the median of its porosity volume is the lowest. Similarly, the equivalent pore radius is defined as the radius of a sphere that has an equal volume to the microporosity [131]. Mathematically, it is given by

3 3푣 푟 = √ 푝,𝑖 Eq.36 푝,𝑖 4휋

Despite for the large data spread in longest sample in both plots, the same trend can be easily observed from the median line locations that with the decrease of cooling rate, the microporosity ends up in a larger size of equivalent pore radius.

Figure 57. Distributions of individual porosity volume (left) and its equivalent radius (right) at different cooling rates.

105

Furthermore, the differentiation between shrinkage microporosity and hydrogen microporosity can be confirmed by examination of the pore shape factor, or as known as sphericity, to quantify the pore morphological differences [132]. The pore shape factor is the ratio of the sum of the measured surface area over the sum of the surface area of the spherical pore of an equivalent volume, and it is unity for a spherical porosity [133].

Mathematically, it can be expressed as

(36휋푉2)1/3 휀 = Eq.37 푆 where 푉 is the porosity volume and 푆 is the porosity surface area. Figure 58 presents the sphericity distribution versus equivalent pore radius at different cooling rates. The fitted power law curves are included as well. It shows that for the measured three different cooling rates, sphericity is mainly concentrated between 0.2 and 0.6, and it decreases with the increase in equivalent pore radius. However, it remains a big challenge to fully differentiate the shrinkage-driven and gas-driven porosity, where the two concomitant mechanisms occur concurrently during solidification but are characteristically different.

0.6 Top Middle 0.5 Bottom Power (Top) Power (Middle) 0.4 Power (Bottom)

0.3 Sphericity y = 0.6771x-0.177 0.2 y = 0.8836x-0.252 y = 1.4353x-0.452 0.1 0 50 100 150 200 250 Equivalent pore radius (μm) Figure 58. Sphericity distribution of microporosity at different cooling rates.

106

4.5 Scope and Limitations of the Coupled Model

Phase transition phenomena in metallic alloys involve complex physical processes occurring over a wide range of temporal, spatial and energy scales [134]. Multi-scale modelling has become a powerful methodology to understand these intertwined complex systems. Taken cast Al alloy as an example, Figure 59 summarizes the different temporal and spatial scales of the many phenomena occurring during casting process where the final properties in cast Al alloy components are dependent upon.

Figure 59. Schematic illustrating how defect formation incorporates phenomena which span six orders of magnitude of both the spatial and temporal scales [134].

Specifically, for solidification process of metal casting in this work, Figure 60 illustrates the schematic diagram of coupled process simulation and microstructure modeling for multi-scale grains and porosity [135]. As previously demonstrated, the process simulation using FEA model at macroscale yielded temperature fields, where instantaneous cooling rates for the area of interest were calculated for subsequent CA model at mesoscale. For the microstructure modeling, nucleation and growth of both grains and pores, especially the impingement of the growing pores upon the developing dendrites were considered to predict the porosity shape. Such multi-scale modelling provides an essential link in ICME approach for location-specific predictions.

107

Figure 60. Schematic diagram of coupled process simulation and microstructure modeling for multi-scale grains and porosity during solidification [135].

However, it needs to be mentioned that the current coupling between macro FEA model and micro CA model only requires the instantaneous cooling rates at liquidus temperature. Since the length scale of characterizing heat flow is usually orders of magnitude larger than that of describing microstructures, a FE mesh much coarser than the CA grid is always used. To couple the two different length scale models, the other commonly used method is by interpolating the temperature field results among the grid in macro mesh, where the temperature at each grid in the micro mesh is the interpolation of its neighboring grid in macro mesh [136]. In this way, the thermal history of macro simulation is fully included to construct micro temperature fields.

In addition, in the micro CA model, shrinkage porosity was not included. It is known that porosity is formed and trapped in the mushy zone of solidifying alloys as a result of two concomitant mechanisms [137]: (i) solidification shrinkage induces a suction of the viscous liquid towards the fully solid region, thus creating a liquid pressure drop in the mushy zone; and (ii) molten alloys usually contain traces of gaseous elements that are less soluble in the solid phase, solidification induces an enrichment of gas in the interdendritic liquid. It is often, if not always, difficult to differentiate to differentiate the two mechanisms to conclude whether shrinkage porosity or hydrogen porosity is more

108 dominant when looking at the final porosity morphology. Lee and Hunt experimentally observed porosity formation in Al-Cu alloys using an X-ray temperature gradient stage, and they found the pressure drop caused by shrinkage to be negligibly small [138]. In this work, the simulated CA porosity results without considering shrinkage effect showed a good correlation with experimental observations of porosity morphology and distribution.

Nevertheless, it is worthy of exploring to simulate the porosity in the micro CA model by including the effect of pressure drop due to shrinkage.

Finally, there still exist deficiencies and limitations in the underlying hypotheses of CA-FE model. In particular, the growth algorithm cannot predict correctly the actual kinetics of dendrite tips [118]. Furthermore, a significant problem encountered in the CA formulation has been the presence of artificial anisotropy in growth kinetics introduced by a Cartesian CA grid [139]. This is known as grid dependent anisotropy, or simply put, the grain growth process is very sensitive to the mesh shape and size [140]. For the modeling of dendrite growth with cubic crystal structure materials, meshes of rectangular elements have been widely used. So far this disadvantage has been mainly addressed using pseudo-front tracking techniques [141], which requires a much finer mesh and a much more refined algorithm for the estimation of interfacial curvature. This makes CA models computationally expensive, especially for 3-D calculations. From the perspective of potential research opportunities, it remains as a challenge for future work.

4.6 Conclusions and Highlights

In this chapter, hydrogen microporosity in A356 gravity castings was studied by considering the effect of cooling rates. Process simulation in FEA model at macroscale

109 was coupled with CA model at mesoscale for microstructure modeling. The detailed conclusions are listed below.

 A V-shaped wedge casting was used to reproduce the microporosity and to

generate different cooling rates across various regions. Hydrogen content in

the melt was measured to be 0.3001 ml / 100 g Al.

 FEA model was built to simulate the gravity casting process and the simulated

thermal results showed a good correlation with thermocouple measurements.

Instantaneous cooling rates at liquidus temperature were calculated and used

in the subsequent mesoscale CA model.

 CA model can be used to simulate nucleation and growth of both grains and

pores of a ternary alloy, where 3-D porosity morphology and distribution was

computed and visualized.

 X-ray microCT reconstructions and metallography analyses were employed to

validate both 2-D and 3-D predictions of location-specific microporosity,

where simulated CA results agreed well with experimental observations.

Overall, the good agreement suggests a promising application of the coupled CA-

FE model as an indispensable part in connecting location-specific process conditions and location-specific microstructure models for ICME of casting products.

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Chapter 5: Summary and Future Work

5.1 Summary

Defects matter in castings. On the one hand, the undesired defects deteriorate the mechanical properties of castings, leading to conservative design rules such as larger safety factors. On the other hand, casting defects are similar to flaws in humans as there is no perfect person in the world. Instead, it is the flaws and imperfections that make each person unique and different. That is what makes this world imperfect but beautiful.

There are many types of defects in casting processes that may result from many different causes. Sometimes the defects can be tolerated, but most of the time measures need to be taken to eliminate those defects. One of the biggest challenges in casting process is that everything happens almost simultaneously. Therefore, casting defects are often very difficult to be completely isolated and they are more or less coupled. Some of the remedies to certain defects may be the cause for other types of defects. Due to the intertwined complex mechanisms, it is quite difficult to establish a clear relationship between a specific defect and its corresponding causes.

Thanks to the vast development of computer-aided engineering over the past few decades, the distinct multi-physics phenomena in casting processes can be virtually visualized for further analyses, such as fluid flow, heat transfer and distortion. Nowadays, foundries have kept expanding the simulation techniques in optimizing manufacturing designs and reducing production cycles and costs, especially by integrating defect models into casting software.

This dissertation has been focusing on three different types of defects in casting processes, including

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i) casting shape defects (fins or burrs due to melt penetration);

ii) mold material defects (cut, rat tail or crack on the mold) and

iii) gas porosity defects (trapped gas due to less solubility in solid metal).

Each of the three different types of defects has been reported in literatures more than half a century ago, and probably they existed from the first day of casting history.

However, not until the past two decades did researchers and engineers start to employ the new tool, computer-aided engineering techniques, to come up with “new solutions” to try to solve these “old problems”.

Specifically, in this dissertation, three representative cases were investigated to demonstrate the utilizations of computer-aided engineering techniques to tackle those different types of defects in casting processes.

The first case is about veining defects on castings caused by thermal cracking in commercial resin-bonded silica sand where it is a mixture with 98.7% SiO2 and 1.3% phenolic resin binder. The mechanical properties of the sand were tested and a material database for the sand was established to run process simulation model. Based on Weibull statistics, a cracking probability map was constructed by considering both the maximum tensile stress and the effective volume. Lab-scale casting experiments for three different sand cup molds were conducted to validate the accuracy of the map. The successful validation suggests potential applications of the integrated fracture probability map and process simulation model in the design of sand molds/cores to prevent veining defects of sand cracking during casting processes.

The second case is related to thermally-induced cracking of H13 hot-work tool steel in die casting dies. A thermal fatigue test unit was built in laboratory and samples

112 were tested in repetitive heating and cooling conditions to reproduce the thermal fatigue cracking. An improved thermal fatigue life model, based on temperature differences and thermal fatigue crack cycles, has been developed based on a modified universal slopes equation. The model was calibrated for both a rectangular plate sample with simple shape and a more complex sample with geometrically similar to a water jacket insert in an automotive engine block. In furnace heating test, simulated temperature fields exhibited good correlation with experimental measurements. The simplicity of the criterion suggests a promising application to evaluate fatigue life of die casting dies in a cost- effective and time-efficient way.

The third case is focusing on Hydrogen-induced gas porosity in A356 castings. A

V-shaped wedge casting was used to generate different cooling rates across various regions. Instantaneous cooling rates at the liquidus temperature of A356 were measured and compared with results from process simulation. Together with the initial Hydrogen content, those cooling rates were imported in subsequent microstructure model, where nucleation and growth of both grains and pores were considered. X-ray microCT reconstructions and metallography images validated both 2-D and 3-D results of location- specific microporosity from microstructure modeling in terms of overall distribution and morphology. The good agreement suggests a promising application of the coupled process-microstructure model in ICME approach for casting industry.

In summary, it can be observed that the general methodology in the three cases is the same, which is a combination of simulation and experiments to provide new scientific insights to solve old engineering problems. Iterative simulation was employed to greatly accelerate and optimize the design of experiments. A few key experiments were then

113 performed to validate simulation predictions. This type of complement serves to better understand the engineering problems by gaining more scientific insights. The ultimate goal is to solve those long-standing problems in engineering with the introduction of the new tools and methods.

5.2 Recommendations for Future Work

In spite of some progresses demonstrated in this work, continuous improvements can be done, such as more tests and validations in experiments, further optimization in the models and new proposals for the criterions. In each of the three cases, the scope and limitations of each model was discussed in Section 2.5.4 Scope and Limitations of the Map,

Section 3.5.3 Scope and Limitations of the Criterion and Section 4.5 Scope and Limitations of the Coupled Model. Those limitations indicate potential research opportunities to further push the limit of the knowledge as for future work.

Specifically, for resin-bonded silica sand case, more work can be done to confirm whether the proposed probability map would remain roughly the same when three-point bending tests are performed at high temperature as compared to the current ones at room temperature. In addition, the effect of sand chemical composition on the probability map can be further investigated. The same methodology can be repeated to construct the maps for different binder weight percentages, or even different bind types.

Then, for the proposed thermal fatigue life prediction criterion, it turns out that the calibrated criterion for one case cannot be directly used for a different geometry. As a compromise of neglecting the stress and/or strain terms in previous conventional criteria, the proposed model does not explicitly include either the geometric effect or surface

114 hardness as a parameter. In addition, the effects of heating and cooling rates in casting cycles are of key interest. For example, Gleeble system can be used to produce controlled heating and cooling rates to understand how different heating and cooling rates affect the thermal cracking failures. Due to the high speed heating rate of direct resistance heating system in Gleeble test, there is a concern that the thermal gradient on the sample may not be large enough to generate thermal stress. An alternative solution is to focus only on the thermal strain induced by cyclic heating and cooling, which can still be approximated to the similar conditions in a thermal fatigue issue.

Finally, for the coupled process-microstructure model in Hydrogen-induced porosity, only instantaneous cooling rates at the liquidus temperature of A356 were used.

To further improve the model, more work can be done to fully include the thermal history of macro simulation to construct micro temperature fields. Additionally, more physical phenomena need to be included in microstructure modeling, such as solidification shrinkage and its induced porosity, and the effect of fluid flow. In this way, the coupled process-microstructure model can be extended to study more complicated but realistic casting processes.

115

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Appendix A: MATLAB Code

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% Calucation of Sigma_F and Effective volume for a given measurement of stress function FractureProbabilityMap(RawStress, Volume) PercentValue = 0.01*[0.1 1 5 50 99]; EffectiveVolumeRange = 0.01:0.01:100; datalength = length(RawStress); OrderRawStress = zeros(2,datalength); OrderRawStress(1,:) = 1:1:datalength; OrderRawStress(2,:) = sort(RawStress); % Calucation of fracture probability, eq. in this dissertation P = (OrderRawStress(1,:) - 0.3) ./ (datalength + 0.4); y_m = log(-log(1-P)); x_m = log(OrderRawStress(2,:)); % least-square fitting for calculation of Weibull Modulus m Coeff = polyfit(x_m, y_m, 1); m = Coeff(1); Stress_ave = mean(OrderRawStress(2,:)); % calculate effective volume for three-point bending sample Veffective = Volume / (2*(m+1)^2); % calculate sigma_zero (eq.6 in this dissertation) Sig_0 = Stress_ave * (Veffective)^(1/m) / gamma(1+1/m); % construct map for different probability based on three-point bending test PercentNum = length(PercentValue); for i = 1:1:PercentNum Sig_F(i, :) = Sig_0./(EffectiveVolumeRange).^(1/m).*(log(1/(1-PercentValue(i))))^(1/m); % Eq.4 in this dissertation end % plot the map for visualization figure(1); semilogx(EffectiveVolumeRange, Sig_F(1,:), '--r'); hold on; semilogx(EffectiveVolumeRange, Sig_F(2,:), '--b');

128 semilogx(EffectiveVolumeRange, Sig_F(3,:), '-r'); semilogx(EffectiveVolumeRange, Sig_F(4,:), '--m'); semilogx(EffectiveVolumeRange, Sig_F(5,:), '-.k'); xlabel('$V_{E} \ / \ cm^3$','Interpreter','Latex') ylabel('$\sigma_{F} \ / \ MPa$','Interpreter','Latex') title ('Fracture probability map by three-point bending') % append three-point bending fracture probability points on the map a = [0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836 0.0836]; b = [2.727 2.756 2.819 2.841 2.848 2.859 2.903 2.910 2.957 2.974 3.008 3.035 3.051 3.057 3.077 3.129 3.145 3.170 3.181 3.208 3.291 3.352 3.354 3.354 3.503 3.510 3.535 3.547 3.611 3.622 3.632 4.113 4.147 4.314 4.727]; plot(a, b, 'k.', 'markersize', 12) % append tensile test fracture probability points on the map c = [12.6 12.6 12.6 12.6 12.6 12.6]; d = [1.342 1.380 1.576 1.626 1.632 1.652]; plot(c, d, 'b.', 'markersize', 12) % append sand cup calibration experiments fracture probability points on the map plot (0.01481, 4.205, 'ro', 'markersize', 7) plot (0.0936, 2.372, 'mo', 'markersize', 7) plot (2.545, 1.332, 'ko', 'markersize', 7) legend ('0.1%', '1%', '5%', '50%', '99%', 'Three-point bending test', 'Tensile test', 'V-notch cup mold', 'Flat-notch cup mold', 'Original cup mold') % when call the function, use command FractureProbabilityMap([2.727 2.756 2.819 2.841 2.848 2.859 2.903 2.910 2.957 2.974 3.008 3.035 3.051 3.057 3.077 3.129 3.145 3.170 3.181 3.208 3.291 3.352 3.354 3.354 3.503 3.510 3.535 3.547 3.611 3.622 3.632 4.113 4.147 4.314 4.727], 13.826)

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Appendix B: Programmable Logic Controller Code

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PLC code was compiled using DirectSOFT 5. As an example, the ladder program with annotations for Aluminum dipping test with a cycle time of 93.5 s is shown below, where there are 31 rungs with 177 words in total. For furnace heating test, PLC code is similar but with minor modifications.

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