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The effects of microstructural features and process parameters on the hottearing in direct chill cast.. Jamaly, M A M Nasim 2012

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The E ects of Microstructural Features and Process Parameters on the Hot Tearing in Direct Chill Cast Aluminum Alloys by M.A.M. Nasim Jamaly B.Sc, Materials & Metallurgical Engineering, Bangladesh University of Engineering and Technology, 2008 a thesis submitted in partial fulfillment of the requirements for the degree of Master of Applied Science in The College of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) September 2012 c M.A.M. Nasim Jamaly, 2012Abstract Hot tearing is an irreversible failure that occurs above the the solidus temperature of an alloy during casting, in the presence of a liquid phase. These cracks possess serious quality implications in industrial direct chill (DC) casting process. During solidi cation, thermal stresses are induced due to the heterogeneous temperature distribution, which causes variations in thermal strain and may result in cracks if these stresses are large enough. In order to investigate the occurrence of hot tears in DC casting, a DC casting  nite element process model for round billets was incorporated with (1) a new semi-solid constitutive law for aluminum alloy AA5182 that takes into account cooling rate, grain size and porosity, and (2) a model for cooling rate induced grain size variation. A hot tearing index was calculated from the semi-solid strain predictions from the model. This hot tearing index, along with semi-solid stress predictions from the model, was used to link hot tearing with microstructural features (i.e. grain size and coalescence temperature) as well as process parameters (e.g. casting speed). It was found that grain re nement plays an important role in the formation of hot cracks. In addition, lower assumed coalescence temperature and slow casting speeds were found to improve hot tearing resistance. In addition to simulation of DC casting, experimental studies on an as cast AA5182 ingot (DC cast) were made in terms of grain size, chemical composition and solidi cation kinetics. Samples for these experiments were collected from the steady state region of the ingot. The results of these experimental investigations show that, (1) grain size increases from surface to centre of the ingot, (2) there is considerable macrosegregation of the alloying elements along the cross section of the ingot, and (3) the solidi cation kinetics iivary as a function of both position and cooling rates. These experimental observations in uence the hot tearing susceptibility of the DC cast product. Thus, for the process model to be more accurate in predicting hot tears, inclusion of these factors, along with an improved model for grain size variation is suggested. iiiTable of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fabrication of Aluminum Components . . . . . . . . . . . . . . . . . . . 2 1.3 DC Casting of Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Defects in DC Cast Products . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Hot tearing in DC casting . . . . . . . . . . . . . . . . . . . . . . 9 2.3 DC Casting Process Models . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Semi-Solid Mechanical Behavior . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.1 Concept of Coalescence Temperature . . . . . . . . . . . . . . . . 16 2.4.2 Constitutive law: Semi-solid . . . . . . . . . . . . . . . . . . . . . 18 iv2.4.3 Constitutive law: Fully Solid . . . . . . . . . . . . . . . . . . . . . 22 2.5 Processing E ects on Hot tearing . . . . . . . . . . . . . . . . . . . . . . 23 2.5.1 Casting Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5.2 Pouring Temperature and Water Flow Rate . . . . . . . . . . . . 24 2.6 E ect of Cooling Rate on Microstructural Features . . . . . . . . . . . . 25 2.6.1 Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.6.2 Volume Fraction Solid (fs) . . . . . . . . . . . . . . . . . . . . . . 28 2.7 Hot Tearing Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.7.1 Mechanical Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7.2 Non Mechanical Criteria . . . . . . . . . . . . . . . . . . . . . . . 31 2.7.3 Combined (Mechanical and Non Mechanical) Criteria . . . . . . . 32 2.7.4 Application of Hot Tearing Criteria into DC casting Process Models 35 2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Scope and Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Development of Direct Chill Casting Process Model . . . . . . . . . . 38 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Finite Element Analysis Formulation . . . . . . . . . . . . . . . . . . . . 39 4.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.3 Addition of Layers . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3 Thermal Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4.1 Thermal Boundary Conditions . . . . . . . . . . . . . . . . . . . . 42 4.4.2 Boundary Conditions - Mechanical . . . . . . . . . . . . . . . . . 45 4.5 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.5.1 Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . 45 4.5.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . 47 v4.6 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.6.1 Microstructural Features . . . . . . . . . . . . . . . . . . . . . . . 53 4.6.2 Casting Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5 Hot Tearing Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2 Hot Tearing Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.3 Simulations for Di erent Processing Conditions . . . . . . . . . . . . . . 58 5.4 Results and Discussion from the Base Case . . . . . . . . . . . . . . . . . 59 5.4.1 Evolution of Temperature and Hoop-Stress . . . . . . . . . . . . . 59 5.4.2 Contour Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.4.3 Identifying the Startup and the Steady-State Regions . . . . . . . 61 5.4.4 Evolution of Hot Tearing Strain . . . . . . . . . . . . . . . . . . . 64 5.5 E ects of Microstructural Features and Processing Parameters . . . . . . 73 5.5.1 E ect on the Hoop-Stress . . . . . . . . . . . . . . . . . . . . . . 73 5.5.2 E ect on Hot Tearing Strain . . . . . . . . . . . . . . . . . . . . . 74 6 Microstructural Analysis of an AA5182 DC Cast Ingot - Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.2 Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.3 Grain Size Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.4 Chemical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.5 Solidi cation Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7 Microstructural Analysis of an AA5182 DC Cast Ingot - Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 vi7.2 Grain Size Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.3 Chemical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.4 Solidi cation Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.4.1 E ect of Location . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.4.2 E ect of Cooling Rate . . . . . . . . . . . . . . . . . . . . . . . . 100 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 8 Conclusion and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . 104 8.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 8.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 viiList of Tables Table 2.1 Summary of semi-solid constitutive laws found in the literature . . . . 19 Table 4.1 Summary of thermophysical properties used in the process-model . . . 46 Table 4.2 Parameters of the modi ed Ludwik equation . . . . . . . . . . . . . . 50 Table 5.1 List of simulated processing conditions . . . . . . . . . . . . . . . . . . 59 Table 6.1 Process parameters used for casting the AA5182 ingot piece, obtained from Rio Tinto Alcan . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Table 7.1 Average grain size (  d, measured by Je rie’s Method) of samples taken at various distances from the center of the ingot . . . . . . . . . . . . 90 Table 7.2 Average compositions of major alloying elements in AA5182 with re- spect to distance from the center . . . . . . . . . . . . . . . . . . . . . 93 Table 7.3 Comparison of averaged solidus, luquidus, and solidi cation reaction temperatures of as cast AA5182, experimental values correspond to a cooling rate of 10oC/min (L = Liquidus, S = Solidus, the standard deviation for each data point is shown in the parenthesis) . . . . . . . 99 Table 7.4 Comparison of solidus, liquidus, and solidi cation reaction tempera- tures of as cast AA5182 between literature and experimental values in terms of cooling rate. (CR = Cooling Rate, L = Liquidus, S = Solidus, Ref.1=B ackerud et al. (1990)) . . . . . . . . . . . . . . . . . . . . . . 101 viiiList of Figures Figure 1.1 DC casting process for production of (a) ingots; (b) billets (Grasso 2004) 4 Figure 1.2 Schematic representation of the DC casting process (Larouche et al. 1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Figure 2.1 Schematic representation of common defects that may arise in a DC cast ingot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Figure 2.2 Hot tearing crack at the centre of a DC cast AA6063 billet (star crack) (Thevoz et al. 2002) . . . . . . . . . . . . . . . . . . . . . . . . 10 Figure 2.3 Ductility in the semi-solid state for an Al-4.5%Cu alloy, after Magnin et al. (1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Figure 2.4 Schematic representationist of all 4 feeding mechanisms active within a casting,after Campbell (1991) . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.5 Temperature contour of a DC cast billet 1000 sec after start-up pre- dicted by an axi-symmetric DC casting process model (Drezet and Phillion 2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 4.1 Schematic presentation of the incremental addition of layers adopted in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Figure 4.2 Thermal boundary conditions applied in the process model. . . . . . 43 Figure 4.3 Solidi cation path of AA5182 used in the model (after Thompson et al. (2004)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 ixFigure 4.4 Variation of elastic modulus (E) as a function of temperature for Tcoal = 602oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Figure 4.5 Variation of thermal expansion coe cient ( ) as a function of temper- ature for Tcoal = 602oC . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Figure 4.6 Semi-solid stress/strain response used in the simulation at di erent fs, (a) for fs;coal = 0:90 (b) for fs;coal = 0:75. For both (a) and (b),  d = 150 m and _" = 10 3 (Equation 4.9-4.12) . . . . . . . . . . . . . . . . 49 Figure 4.7 Semi-solid stress/strain response according to Phillion et al. (2009) for di erent  d, at fs = 0:98 and _" = 10 3 . . . . . . . . . . . . . . . . . . 52 Figure 4.8 E ect of cooling rate on grain size (  d) in AA5182, after Easton et al. (2010). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Figure 5.1 Schematic presentation of the strain perpendicular to heat  ux in a DC casting billet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Figure 5.2 Location of X and Y in the casting domain. . . . . . . . . . . . . . . 66 Figure 5.3 Evolution of Temperature and  H at locations X and Y with time. For X (Y), t=0 sec. corresponds to t=78.33 (57.50) sec. after the start of casting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Figure 5.4 Contour plots from Case A showing (a) Grain size, and (b) Hot tearing strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Figure 5.5 (a) Temperature  eld of the billet, and (b) Contour plot of hoop stress ( H) at the end of the simulation (after 728 seconds) . . . . . . . . . 68 Figure 5.6 Temperature pro le at di erent locations along the centerline of the billet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Figure 5.7 Temperature pro le at di erent locations along the chill-surface of the billet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Figure 5.8 Variation of  H as a function of distance from the bottom block along the centerline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 xFigure 5.9 Variation of  H in the horizontal direction as a function of distance from the centerline at 12 mm distance from the bottom block . . . . 70 Figure 5.10 Variation of  H in the horizontal direction as a function of distance from the centerline at di erent distances from the bottom block, where x = distance from the bottom block . . . . . . . . . . . . . . . . . . . 71 Figure 5.11 Variation of hot tearing strain as a function of distance from the bottom block along the centerline of the billet . . . . . . . . . . . . . . . . . 71 Figure 5.12 Variation of hot tearing strain as a function of distance from the cen- terline along the horizontal direction, 8 mm away from the bottom block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Figure 5.13 Variation of hot tearing strain in the horizontal direction as a function of distance from the centerline at di erent distances from the bottom block, where x = distance from the bottom block . . . . . . . . . . . 72 Figure 5.14 Variation of  H as a function of distance from the centerline along the horizontal direction, 8 mm away from the bottom block for cases A, D, and E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Figure 5.15 Variation of  H as a function of distance from the bottom block along the centerline for cases A, D, and E . . . . . . . . . . . . . . . . . . 78 Figure 5.16 Variation of  H as a function of distance from the bottom block along the centerline for cases A, B, and C . . . . . . . . . . . . . . . . . . . 79 Figure 5.17 Variation of hot tearing strain as a function of distance from the cen- terline along the horizontal direction, 8 mm away from the bottom block for cases A, D, and E . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 5.18 Variation of hot tearing strain as a function of distance from the bottom block along the centerline for cases A, D, and E . . . . . . . . . . . . 80 Figure 5.19 Variation of hot tearing strain as a function of distance from the bottom block along the centerline in the startup region for cases A, D, and E 80 xiFigure 5.20 Variation of hot tearing strain as a function of distance from the cen- terline along the horizontal direction, 8 mm away from the bottom block for cases A, B, and C . . . . . . . . . . . . . . . . . . . . . . . 81 Figure 5.21 Variation of hot tearing strain as a function of distance from the bottom block along the centerline for cases A, B, and C . . . . . . . . . . . . 81 Figure 6.1 Locations in the ingot from where the samples were taken for charac- terization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Figure 6.2 Typical thermal cycle for running solidi cation tests in DSC . . . . . 86 Figure 7.1 Optical micrographs of samples taken from (a) center (b) 62.5 mm from the center (c) 125 mm from the center (d) 187.5 mm from the center (e) at surface, at 50 magni cation, viewed under cross-polarized light with sensitive tint attachment . . . . . . . . . . . . . . . . . . . . . . 89 Figure 7.2 Variation of grain size as a function of distance center in a steady state region, obtained from simulation results of case A . . . . . . . . . . . 91 Figure 7.3 Distribution of relative concentration of di erent alloying elements as a function of distance from the centre . . . . . . . . . . . . . . . . . . 94 Figure 7.4 Solidi cation curve of a sample of AA5182 from the DC cast ingot piece, cooling rate = 10oC/min . . . . . . . . . . . . . . . . . . . . . 96 Figure 7.5 DSC curves of samples samples of as cast AA5182 taken from di erent locations of the ingot, cooling rate = 10oC/min . . . . . . . . . . . . 97 Figure 7.6 DSC curves of samples samples of as cast AA5182 taken from di erent locations of the ingot in the range of 500 to 575oC, cooling rate = 10oC/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Figure 7.7 Solidi cation path of samples of as cast AA5182 taken from di erent locations of the ingot, cooling rate = 10oC/min . . . . . . . . . . . . 98 Figure 7.8 DSC curves of samples of as cast AA5182 taken from same location of the ingot tested at 2 cooling rates, 10 and 20oC/min. . . . . . . . . . 100 xiiFigure 7.9 Solidi cation path of samples of as cast AA5182 taken from same lo- cation of the ingot tested at 2 cooling rates, 10 and 20oC/min . . . . 101 xiiiAcknowledgments First of all, I want to thank all mighty Allah for giving me the strength and courage to ful ll this masters project. Next, I want to thank my supervisor and mentor, Dr. Andre Phillion for his guidance and support during this project. He has been very patient in familiarizing me with the casting simulation tools, especially because I did not have any prior simulation experience. Moreover, I always found a friend in him not only during the bliss, but also during the stressful periods of academic and personal life. We spent hours together discussing about research, religion and Canadian culture. I also would like to thank Dr. Jean-Marie Drezet (EPFL, Switzerland) for the fruitful discussions about the process model and the results through numerous emails as well as in person during the TMS conference of 2012 in Orlando, Florida. I am thankful to Muntasir Ul Alam (PhD student, UBCO) and his wife Sharmin for making my stay at Kelowna an enjoyable and enriching experience. I am also thankful to my colleague and friend Hamid (PhD student, UBCO) for being the best person to share an o ce with. I would like to acknowledge Natural Sciences and Engineering Research Council of Canada for the  nancial support for whole duration of this study. Last but not the least, I am thankful to my mother, Nazneen Khanam for being the endless means of support for me. Despite living seven thousand miles away, she has always been there for me when I needed the most. xivChapter 1 Introduction 1.1 Aluminum Alloys Aluminum is the most abundant metal found in the earth’s crust. Despite its apparent availability, it was not one of the early metals used by humankind, since it is always found as a compound with oxygen in nature, owing to its high chemical reactivity. In- dustrial re nement of aluminum began in the late 1800’s when Charles Hall in USA and Paul Heroult in France independently developed an electrolytic process for transforming alumina to elemental aluminum. This process, known as the Hall-Heroult Process, is still used today. The main cost when producing Al is the cost of electricity, as it consumes 500 Kilo-Watts per kg, enough to power 5 standard households for a day. As aluminum can be reprocessed e ectively several times without deteriorating its properties too much and the cost of producing recycled metal is only 5% as compared to virgin ore, it is only desirable to recycle aluminum. The additional pressures related to sustainable industrial practices also make recycling of Al quite desirable. Consequently, the amount of alu- minum recycled has more than doubled between the early 1990’s to 2005 (EAA 2005). Aluminum alloys demonstrate good physical properties such as electrical and ther- mal resistance. However, the most important properties of Al are its lightness (density of 2.7 g/cc, whereas steel has 8 g/cc) and high speci c strength. Its lower density, 1good corrosion resistance, along with moderate mechanical properties (such as the ten- sile strength and elastic modulus) have enhanced the use of aluminum and its alloys in many applications over the past few years. Currently, the use of aluminum alloys in the automotive, rail, marine and aerospace transportation industries occupy the majority of the total usage of aluminum around the world (about 36%) (EAA 2005). Aluminum alloys are especially appreciated in the transportation industries due to their low density, corrosion resistance, shock absorption capabilities, and strength. 1.2 Fabrication of Aluminum Components Based on their fabrication method, aluminium alloys are classi ed into two principal groups: cast alloys and wrought alloys. Cast alloys are used in processes where the liquid metal is directly solidi ed in a mold that is similar in geometry to the end use compo- nent. Cast aluminum alloys, such as A356 (Al - 7%Si) have properties such as a low melting point, high  uidity, and attractive as-cast solidi ed structures. The advantages of this process are: (1) it can produce  nished or nearly  nished products; (2) it is suit- able for complex geometries; (3) it is economical for both small and large number of parts. On the other hand, wrought alloys are those that are shaped for use by plastic defor- mation through rolling/forging/extrusion etc. Wrought alloys are suitable for components with simple geometry, such as blocks, sheets and wires. The relevant forming techniques requires the wrought alloys to be designed to have attractive mechanical properties, such as low yield strength in the as-cast state, high ductility, good fracture resistance, and excellent strain hardening. Wrought aluminium is also produced as AlcladTM material, in which a thin layer of corrosion resistant commercial purity aluminium is bonded to one or both surfaces of a high strength alloy during rolling and the material is further processed as a composite. Aluminum alloys of series 1xxx, 2xxx, ..., 7xxx are examples of wrought alloys. 21.3 DC Casting of Aluminum Alloys As was discussed in the previous section, components made from wrought aluminum alloys need to go through some sort of deformation processing to create their  nal shape. The primary input for these processes are aluminum alloy as-cast billets (cylindrical shape, typical dimensions of L = 10 m, D = 50 cm) and sheet ingots (rectangular cross section, typical cross-sectional dimensions of 2 m  1 m), i.e. castings with at least one plane of symmetry. Wrought aluminum alloy billets and ingots must possess a constant cross section, have good surface quality and be defect free in order to produce high quality products in downstream processes. Since the 1940’s, the standard technique for pro- ducing wrought aluminum alloys has been the semi-continuous Direct-Chill (DC) casting process (Emley 1976, Stefanescu 1988). In  gure 1.1, DC cast billets and ingot are shown. In the DC casting process, a mold consistent with the desired cross section shape is paired with a vertically movable starter block at the bottom. Sometimes, the mold is covered with a hot-top to alter the cooling conditions. A schematic of the typical DC casting process is shown in  gure 1.2. The process is as follows. First, the alloy is melted in a holding furnace and the molten metal is poured into the closed space created by the bottom block and the mold. Grain re ners are added to control the  nal microstructure. Second, the molten metal solidi es in contact with the mold and the bottom-block to form a solid shell. Third, once the solid shell has achieved su cient strength to support the liquid pool, the bottom block is moved downwards with a velocity generally referred to as the casting speed. Molten metal is continuously fed into the mold from the top. The casting speed may be constant over the whole process, or it may vary with time. Finally, once the casting has reached the desired length, the casting velocity is reduced to zero and the billet/ingot is allowed to fully solidify. It is then removed from the casting pit and the process is started again. 3Figure 1.1: DC casting process for production of (a) ingots; (b) billets (Grasso 2004) From a phenomenological stand point, the process can also be divided into three re- gions. In the \start-up phase", there exists a thermal  eld throughout the casting. In this stage, the thermal  elds are not yet stationary but vary both with position and with time. The \steady state" is achieved after the casting length has reached about 0.5 m, and is characterized by thermal  elds that are constant with respect to position. After this, the casting can be continued for several metres with good casting quality. In the \ - nal stage", the thermal  elds again become transient as the feeding is stopped and the bottom block is arrested. 4Figure 1.2: Schematic representation of the DC casting process (Larouche et al. 1998) Although the DC casting process has gone through numerous optimizations over the years (Emley 1976), it remains identical in principle to the original process  rst intro- duced in the 1940’s. One of the important features of the DC casting process is the di erential cooling conditions experienced by the cast surface as it descends into the casting pit (Sengupta et al. 2004). Firstly, the casting is in contact with the mold and heat is extracted at a high rate from the molten metal. The cooling of metal from direct contact with the mold is termed primary cooling. As the metal solidi es, it then shrinks due to thermal contraction and consequently loses contact with the mold. Concurrently with the formation of this \air gap", heat transfer is signi cantly reduced, which may lead to partial re-melting due to heat  ow from within the molten metal pool to the surface. 5Secondly, the casting is cooled via water sprays below the mold, termed secondary cool- ing. This cooling can be subdivided into several regimes, depending on the turbulence of the water jets and the temperature of the surface where the water impinges onto the casting (Caron and Wells 2006, Collier and Thome 1994, Larouche et al. 1998, Sengupta et al. 2004). Therefore, the convective heat transfer coe cient (h) at di erent regimes of primary and secondary cooling will vary considerably. Thirdly, the casting is cooled through the bottom block. As a result of thermal contraction, the contact between the bottom block and the end of the casting is lost close to the ingot lip. In this case, the e ciency of cooling depends on the size of the air gap formed at the bottom block/cast- ing surface. Note that an interesting phenomenon, known as water incursion, may occur if the secondary cooling spray water runs into this air gap (Sengupta et al. 2004). In the ingot case, the heat transfer in this air-gap is strongly a ected by the  ow of water from the rolling face side. As can be seen, there are complex heat transfer phenomena associated with the DC casting process. An understanding of these processes is crucial for improving casting quality. 1.4 Summary In this chapter, an overview of aluminum alloys, along with the Direct Chill casting technique used for fabricating wrought alloys, has been presented. Now, it is worthwhile to mention that the DC casting process is subjected to considerable defects. In fact, many of the high-strength aluminum alloys recently developed to compete against traditional materials are not currently viable due to the high costs associated with defect formation. The current masters project involves the study of the formation of a speci c defect, hot tearing, during DC casting through the use of a process model based on  nite elements. In the next chapter, relevant literature of this defect and measures taken to minimize it will be discussed in detail. 6Chapter 2 Literature Review 2.1 Introduction In this chapter, an overview of the defects that arise during DC casting is presented. In this discussion of defects, special attention is given to those that form during solidi ca- tion. An important phenomenon occurring during solidi cation is the transition from the semi-solid behaving like a liquid to one where the behaviour is like a solid and capable of transmitting long-range stresses. This transition, known as mechanical coalescence, is a large factor in uencing the extent to which defects occur. In order to predict and reduce defect formation, computer simulation of the DC casting process has increasingly been utilized over the past few decades. These computer simulations are termed process models. The past research and present trends of the development of these DC casting process models and associated topics available in the published literature is critically reviewed. Now, the mechanical behavior of the alloy during solidi cation is the most important matter to understand for study of defect formation during solidi cation. Mod- els developed by researchers for semi-solid mechanical behavior of aluminum alloys are thus discussed in detail, as are the relationships between processing variables and the occurrence between casting defects. Finally, the available defect formation criteria that exist to assess the susceptibility of a casting to the formation of defects are summarized. 7Figure 2.1: Schematic representation of common defects that may arise in a DC cast ingot 2.2 Defects in DC Cast Products There are numerous defects that may arise during the DC casting process. Some of the industrially relevant defects include: macro / micro segregation, loss of dimensional sta- bility, inclusions, porosity, and the formation of hot tears and cold cracks. Some of the typical defects that can arise in a DC cast ingot are shown schematically in  gure 2.1. Hot tearing is a failure that occurs above the the solidus temperature of the alloy, in the presence of a liquid phase. Conversely, cold cracking is a failure that occurs below the solidus temperature. The cooling of the billet in the DC casting process is achieved mainly by the cooling water jet and partially by the bottom block. These di erential cooling conditions at di erent locations of the billet results in dissimilar contraction and ultimately causes thermal stresses to arise within the billet (Grand eld and McGlade 1996, Yu 2002). Process parameters for DC casting, such as water  ow rate (Matsuda et al. 1996) and casting speed (Commet et al. 2003, Matsuda et al. 1996) can exacerbate 8the cold cracking problem by modifying the thermal stress levels in the billet. Other factors that can a ect the cold cracking susceptibility are geometry and size of the bil- let (Grand eld and McGlade 1996). Loss of dimension of the billet bottom (butt curl) and appearance of surface cracks are also considered to be due to the aforementioned thermal stress, particularly in the ‘start-up phase’ of the casting process. The stress lev- els in the start-up phase are a strong function of the shape of the bottom block (Benum et al. 2002). Droste et al. (2002) experimentally measured butt curl in DC casting and found that butt curl increases when the border area of the tail of the billet is cooled by water jet (secondary) cooling. Experimental quanti cation of butt curl in DC casting of alloy AA5182 by Sengupta et al. (2004; 2005a) revealed that increasing the water  ow rate increased distortions of the ingot-base and vice versa. The variation of chemical composition along the cross-section of the DC cast billet, or macrosegregation can be both positive (increasing solute content from surface to center) or negative. The incipience of grain cells close to the centerline of the billet is attributed to the centerline or negative macrosegregation (Eskin and Katgerman 2009). Low casting speeds enhance positive segregation in DC cast billet, independent of its size (Eskin and Katgerman 2009). Moreover, billets can be cast at higher speeds with positive segrega- tion, if a proper level of grain re nement is ensured (Eskin et al. 2008). The present study is related to the defect known hot tearing or solidi cation cracking. A brief overview of the hot tearing defect within the context of DC casting is presented below. 2.2.1 Hot tearing in DC casting Hot tearing is one of the key defects that may arise during DC cast aluminum alloys. During solidi cation, thermal stresses are induced due to the heterogeneous temperature 9Figure 2.2: Hot tearing crack at the centre of a DC cast AA6063 billet (star crack) (Thevoz et al. 2002) . distribution, which causes variations in thermal strain and may result in cracks if these stresses are large enough (Drezet and Rappaz 2001, Drezet et al. 1996a, M’Hamdi et al. 2002, Sengupta et al. 2004). Hot tearing occurs not only in DC casting but in other casting processes including shape casting and welding as well. Example of a hot tearing defect is shown in  gure 2.2. In these cases, the cracked section of the billet must be cut o before the casting can be used for subsequent deformation processing. Often, the formation of a hot tear leads to component rejection. So, if present in any extent, hot tearing will substantially reduce productivity. Campbell (1991) describes the salient features of hot tearing as follows: 1. Hot tears are found often in the hot spots of the casting or at locations where strains are concentrated. 2. Hot tears mainly propagate in an inter-granular fashion. 3. Hot tears visually appear to be ragged and branching cracks. 4. The onset and extent of hot tearing may vary even if the processing conditions are kept constant. Hot taering is closely linked to semi-solid ductility. Since the early 1950’s, researchers have been experimentally measuring semisolid ductility, with the  nding that there is 10Figure 2.3: Ductility in the semi-solid state for an Al-4.5%Cu alloy, after Magnin et al. (1996) a critical temperature range in the semi-solid region where the ductility of the alloy is extremely low. For example, Singer and Cottrel (1946) showed that Al-Si alloys exhibit a sharp decline in ductility at just above Tsol and a corresponding change in morphology of the fractograph. In the same year, Pellini studied the solidi cation of aluminum and steel plates and reported a steep decline in ductility just above Tsol. Later, Magnin et al. (1996) executed tensile tests for an Al-Cu alloy in the semi-solid state for a range of temperatures between solidus and the mechanical coherency point. It was observed that there is a brittle temperature range, between 540 and 580oC where the ductility of the alloy is virtually zero as shown in  gure 2.3. Similar observations were made by Zhi-ming et al. (2010), on a study focused on the as-deformed A250 aluminum alloy, but within the context of semi-solid processing. More recently, Twite et al. (2004) conducted tensile tests on AA6061 alloys in the semi- solid regime, and found that the tensile strength of the alloy dropped to zero between 560-570oC, depending on the source of the alloy. In the same year, Colley et al. (2004) conducted tensile tests on alloy AA5182 at high temperatures (500 - 580oC) to determine mechanical properties of the alloy in the semi-solid state. These tensile tests revealed that, in the semi-solid state, ductility of the alloy decreases sharply at around a volume 11fraction solid (fs) of 0.95. Moreover, the fs at which the alloy looses its ductility is strongly dependent on the applied strain rate, a conclusion drawn by both Colley et al. (2004) and Twite et al. (2004). Haaften et al. (2002) also conducted semi-solid regime tensile tests on alloy AA5182 and AA3004 in the as cast state. They also observed the strain rate sensitivity on the tensile strength, and found that strength dropped to a very small value above 550oC. From the works of Singer and Cottrel (1946), Pellini (1952), Magnin et al. (1996),Van Haaften et al. (2002), Colley et al. (2004), Twite et al. (2004), Zhi-ming et al. (2010), it is evident that in aluminum alloys, there is a range of temperature at the semi-solid state where the ductility/strength of an alloy in minimum. In DC casting, as previously discussed, thermal stresses are generated due to di erential cooling conditions experienced by di erent parts of the casting billet. If these stresses are high enough at the low ductility/strength range in the semi-solid state, cracks may appear. These cracks are termed hot cracks if they have  rst appeared in the semi-solid regime. 2.3 DC Casting Process Models DC cast products encounter numerous solidi cation defects. In order to increase pro- ductivity and reduce scrap, these defects must be properly understood. The study of solidi cation defects in DC casting is generally simulated with small scale experiments within the laboratory. But it is challenging to compare the results obtained from these simulations with the industrial scale, simply because factors causing solidi cation defects are sensitive to casting geometry and processing conditions. Another choice is to study solidi cation defects in-situ during production. But performing hot tearing experiments on an industrial scale by ‘playing’ with the process parameters is time consuming and expensive. The limitations concomitant with the experimental work has necessitated the devel- opment of DC casting process models. Using the  nite element (FE) method, researchers 12can estimate both the thermal  eld and stress-strains in the cast body throughout the casting process. Well described and experimentally validated models allow one to vary the process parameters within the model domain. The e ect of changes in casting pa- rameters can then be understood by observing the changes in the predicted stress, strain and temperature contours given by the model. The evolution of stresses and strains at di erent location of the casting can be used to develop an idea of when and where the defects (e.g. hot tearing) may occur. Many researchers have worked extensively on developing DC casting thermal and stress models for aluminum alloys. Most of these e orts have focused on only one as- pect of the DC casting process, either the thermal, e.g. (Sengupta et al. 2001; 2003) or thermo-mechanical analysis, e.g. (Drezet et al. 1996a). Also, the models have been mainly one-dimensional, e.g. M’Hamdi et al. (2002) or axi-symmetric (Weckman and Niessen 1982), although the process model developed by Sentupta was three-dimensional. In or- der to simplify the simulation, most researches focused on round-shaped and small billets. In one of the earliest works on process models, Weckman and Niessen (1982) used the thermocouple data of DC cast AA6063 ingots to develop a thermal model of DC cast- ing. They observed that the use of a set of previously determined e ective heat transfer coe cients in the model induces errors in predicted temperature pro le. They combined the existing nucleate boiling, forced convection and  lm boiling heat transfer concepts to propose a novel routine for de ning boundary conditions for surface regions of the ingot below the mold cooled by a water stream running down the surface. A thermomechanical DC casting process model for alloy A6063 was proposed by Fjaer and Mo (1990). In this work, residual stresses generated after the ingot has been cooled was calculated and these values were shown to agree quantitatively with the available data in the literature. Wiskel and Cockcroft (1996) used one-dimensional and two-dimensional thermal mod- 13els to investigate heat  ow within the casting. They showed that their simulations could generate cooling curves that conform well with the known cooling curves of the sys- tem, through a validation against experimentally-obtained data from an industrially cast AA5182 sheet ingot. In the 1990’s, Drezet and colleagues developed  nite element thermomechanical mod- els of DC casting to forecast dimensional instability of ingots (Drezet and Rappaz 1996a) and in uence of mold shape on ingot distortions (Drezet et al. 1996b). Experimental work to determine the alloy thermophysical properties and to  ne tune the boundary condi- tions for these models were carried out during this time (Drezet et al. 2000b). These models (Drezet and Rappaz 1996a, Drezet et al. 1996a;b) were validated by comparing the results from these models with experimental data (Drezet et al. 1995). Sengupta et al. (2004) proposed a comprehensive three dimensional FE thermal model containing phenomena including primary cooling at the mold, secondary cooling by wa- ter jet, and cooling by the bottom-block during the startup phase of the DC casting process. This work considered the air gap formation between the ingot and the bottom block due to thermal contraction at the base of the casting, and entrapment of water into these air gaps dripping from the surface of the ingot (termed water-incursion). The model was extensively validated by comparing the predicted temperature evolutions with thermocouple measurements made in the full scale industrial DC casting experiments. In a companion work (Sengupta et al. 2005a), the stress-strain simulation was validated by comparing the amount of base deformation known as \butt curl" with the same quantity in the model. Good agreement was found between the two results. Further work was done to develop industrially-relevant process models of DC casting by Grealy et al. (2001), who proposed methods for optimization of the metal distribution system, solidi cation, and heat transfer mechanism in large commercial ingots. This work 14demonstrated that such models have also found frequent use in industrial practice, in ad- dition to being an academic exercise. Williams et al. (2003) presented a three dimensional DC casting model for AA1201 alloy. Their model was a multi-physics model since melt  ow, stress and heat transfer were coupled for early stages of DC casting. On the other hand, the majority of the literature relating to DC casting process simulations relates to thermo-mechanical models, where the  uid  ow is ignored and the mush is considered as a solid body of lower strength. The major weakness of Grealy’s model was that it was not experimentally veri ed. They also used an idealized bottom block shape and thus the predicted butt curl appears to be underestimated, contrary to the work of Sengupta et al. (2004). In the model developed by Bagnoud and Plata (2000), the discrepancy in the results with regards to butt-curl (as compared to Sengupta et al. (2004)) is probably related to their assumption of ideal plasticity as the e ect of strain hardening is ignored. More recently, Drezet and Phillion (2010) developed an 2D axi-symmetric billet model to estimate residual stresses in billet. They used the POLDI neutron di raction (ND) facility at the Paul Scherrer Institute in Villigen, Switzerland, to estimate the residual stresses in an industrially cast AA6061 billet, and found a fairly good agreement between the predicted and the measured values. Similar experimental work was performed by Hao et al. (2010) to validate a DC casting process simulation of Mg alloy AZ31. The results indicate that the stress-strain predictions show the same trend as the residual strain mea- surements using neutron di raction techniques. From the above references, it has been found that the research community has been able to develop a series of DC casting simulations which are capable of predicting the evolution in thermal and displacement  elds during industrial processing. To some extent, these simulations have been successful in also predicting casting defects such as ingot distortions (Drezet and Rappaz 1996a, Drezet et al. 1996a;b), butt curl (Sengupta et al. 2004; 2005a), residual stresses (Drezet and Phillion 2010), hot tearing (Suyitno et al. 152005), etc. However, much work remains. One of the main challenges in the development of the DC casting process models that are capable of quantitatively predicting defects is a description of the mechanical behavior of aluminum alloys in the semi-solid state. 2.4 Semi-Solid Mechanical Behavior 2.4.1 Concept of Coalescence Temperature Before discussing the mechanical behavior of aluminum alloys in the semi-solid, it is logical to discuss a very important phenomenon that occurs during the solidi cation of aluminum alloys, namely mechanical coalescence. This mechanical coalescence happens at a temperature between the solidus and liquidus, and is strongly e ected by numerous casting parameters and the composition of the alloy. The mechanical response of semi- solids to applied loads is quite di erent at temperatures above and below this coalescence point. The concept of mechanical coalescence can be understood by studying the various stages of solidi cation in metallic alloys. Clyne and Davies (1981) proposed four stages of solidi cation of metallic alloys within the semi-solid based on the permeability of the solidifying network - mass feeding, interdendritic feeding, interdendritic separation and interdendritic bridging. These feeding mechanisms are shown in  gure 2.4, and further described below: 1. Mass Feeding In the mass feeding regime, the microstructure is essentially solid particles contained in liquid, moving freely under mechanical loading and contraction stresses. 2. Interdendritic Feeding In this regime, the free movement of the solid is restricted by grain size and shape. The solid loses its ability to move freely in response to mechanical load and the 16Figure 2.4: Schematic representationist of all 4 feeding mechanisms active within a casting,after Campbell (1991) remaining liquid is forced to  ow through the dendritic network to accommodate stress. 3. Interdendritic Separation At higher fraction solids, a continuous and interconnected liquid  lm exists that surrounds the dendrites. Stress is released by the formation of micro-pores and hot-cracks because the dendrites have not yet bridged to take the load and yet the low permeability of the structure prevents liquid  ow. The semi-solid is able to transmit stress, but cannot accomodate strain. 4. Interdendritic Bridging At this terminal stage of solidi cation, the cast structure attains considerable strength as dendrites bridge and the solid network can transmit long range stresses and strains. The transition between each of the four stages is generally assumed to be a function of factors including alloy composition, cooling rate, grain shape and grain density. When the solidi cation process transitions from interdendritic feeding to interdendritic bridging, the dendrite arms tangle with each other to form a continuous solid network. This point, or stage of solidi cation, is referred to as mechanical coalescence (Backuerud et al. 1990), with the temperature, time, and fraction of solid at this point given the corresponding names coalescence temperature, coalescence time, and coalescence fraction solid (Chai 17et al. 1995, Jiang et al. 1999). For the last few decades, the mechanical coalescence has been accepted as a critical characteristic in cast aluminum alloys (Veldman et al. 2001). This transition causes the solid network to attain structural integrity and prohibit mass feeding. As a result, the remaining liquid metal must  ow through the solid network of the dendrites to compensate for the solidi cation shrinkage (Jiang et al. 1999). The combination of applied stress and limited feeding at temperatures below mechanical co- alescence can result in a hot tear. At temperatures above mechanical coalescence, the liquid will simply  ow in response to the applied load. 2.4.2 Constitutive law: Semi-solid The constitutive behaviour of semi-solids is complex due to the signi cant transitions occurring within the permeability of the mushy zone during solidi cation process as shown in the experimental work presented in section 2.2.1. Modeling the semi-solid constitutive behaviour has always been a challenge to researchers because of the large range of viscosity between 0 < fs < 1, and the stochastic nature of the solidi cation process. As shown in table 2.1, a number of di erent constitutive laws have been developed for semi-solids. One successful approach, initiated by Drezet and Eggeler (1994), was to use a modi ed creep law to describe the semi-solid behavior of aluminum alloys. The justi cation behind using this type of creep law is that at high fraction solid the liquid exists as isolated pockets in- between the continuous solid network. Any mechanical failure is thus almost exclusively dependent on the solid network. Hence, at high fraction solids, the mechanical response of the alloy with increasing temperature would be somewhat like a completely solid body. Consequently, it was assumed that the load is entirely carried by the existing solid network as the liquid can not bear any load. With this in mind, Drezet and Eggeler (1994) proposed that the area of load carrying is proportional to fs as shown in equation 2.1, where _"min is the minimum creep rate,  0 is applied stress, Q is the activation energy for creep, A is a material-dependent constant, T is the temperature, and R is the universal gas constant. 18Table 2.1: Summary of semi-solid constitutive laws found in the literature Proposed by Alloy system Features Equation Ludwik Equation N/A Inclusion of strain harden- ing and high temp creep 2.4 Modi ed Ludwik Equation N/A Introduction of o set con- stants for ease of FE simu- lation 2.13 Haaften et al. (2002) N/A Plastic strain based 2.2, 2.3 Ludwig et al. (2005a) N/A Accounts for anisotropic be- havior of Semi-solid 2.4 Drezet and Eggeler (1994) N/A Creep based law 2.1 Lu et al. (2008a) Al - Cu Valid at lower fs 2.5, 2.6, 2.7 Phillion et al. (2009) Al - Mg - Mn Inclusion of microstructural features 2.8 - 2.12 _"min = A   0 fs(T )  exp   Q RT  (2.1) The constitutive relationship by Drezet and Eggeler was re ned, in the work of Haaften et al. (2002), by considering the critical term to be (1 fLGB), where fLGB is the fraction of grain boundary area covered by the liquid, instead of the fraction solid term fs. They argued that the low melting (eutectic) phases present at the grain boundaries are the dominant factor for semi-solid deformation. The proposed law is shown in equation 2.2 and 2.3. In these equations, A,  0, and nH are constants related to material properties and  ss is the steady state stress. _" = A  sinh   ss  0   nH exp   Q RT  (2.2) _" = A   1 fLGB  nH exp   Q RT  (2.3) A further re nement, to utilize an internal variable, C, to represent the state of cohesion of the mush, was proposed by Ludwig et al. (2005a) as shown in equation 2.4. The variable C was introduced to account for the fact that the semi-solid body is much weaker in tension as compared to compression. 19_"ps = _"0 (Cs0)n  A2 3  Psl + 3 2 A3Ss  h A2  Ps 2 + A3   s 2 in 1 2 (2.4) where, _"ps is the plastic strain rate tensor, _" is the reference strain rate, n and so describe the rheology of the fully solid state, A2 and A3 are solid fraction functions,  Ps is the e ective pressure (taken positive on compression),  s is the von-mises stress, 1 is the unit tensor and Ss is the solid phase deviatoric e ective stress tensor. More recently, Lu et al. (2008a) carried out a study on the semi-solid deformation behavior of an Al-4%Cu-Mg alloy at very low fraction liquid. They concluded that defor- mation in the semi-solid regime is in uenced strongly by deformation induced evolution of microstructure in this regime. Based on the experimental results, they established that the  ow stress ( ) is linked to process parameters and microstructural characteristics as described in equations 2.5-2.7.  = F1:F2 (2.5) F1 :  = " m _"n(a bt)(1  f1) k (2.6) F2 : f(d) = A0 + A1( d d0 ) + A1( d d0 ) 2 (2.7) where, F1 is a function related to the process parameters, F2 is a function dependent on the microstructural evolution during deformation of the semi-solid mush, d0 ( m) is the grain size at the commencement of semi-solid deformation, d ( m) is the average grain size at the temperature of deformation (calculated based on an arti cial neural network model provided in reference (Lu et al. 2008b)). Finally, A0, A1, A2 are functions of the Zenner-Holloman constant (Z), deformation rate and material constants. 20In the context of DC casting, an alternative methodology to model the semi-solid behavior has been to extend the constitutive law used in the fully solid regime up to the temperature corresponding to the fraction solid for mechanical coalescence (Drezet and Phillion 2010, Sengupta et al. 2005a) and then to assume a low elastic modulus and high yield stress rheology above this point. Although this methodology is relatively easy to implement within the context of process models and has the advantage of minimizing false strain accumulation in the partially liquid state, its main drawback is that there is no link to the microstructural features of the solidifying semi-solid. Recently, a new constitutive equation for semi-solid AA5182 has been proposed by Phillion et al. (2009) that takes advantage of the bene ts of the Ludwik equation (see section 2.4.3) within an a FE simulation, while also including microstructural features. For this work, a 2 dimensional  nite element model was developed which can pre- dict mechanical behavior of the semi-solid mush (Phillion et al. 2008). This FE model included the following key microstructural complications: liquid  lled grain boundaries, liquid trapped at the triple junctions of grains, variable grain size and porosity. This model is valid for the range 0:75 < fS < 0:95, since the authors believe that hot tearing phenomenon occurs at this range. To validate this model, semi-solid tensile tests were performed with samples of aluminum alloy AA5182 that were (1) hot isostatic pressing (HIP) cast and (2) in the as cast state. A novel technique in terms of strain and tempera- ture control were used for these semi-solid tensile tests. The HIP cast alloys contain zero porosity, while there was considerable porosity in the as cast alloy. By comparing the tensile test results of these 2 types, the e ects of porosity on semi-solid deformation and in turn on the occurrence of hot tearing was illustrated. The constitutive law proposed by Phillion et al. is illustrated below:  (fs; fp;  d) = Kp(fs s)("p + "0) n(T )(1 fp 1 fs ) (2.8) 21with,  s = (483:5 0:77T ) _" (0:205+0:00006T ) p (2.9) h =  d(1 fs) 1 3 (2.10) n =  6:35e 4h2 + 0:0202h (2.11) Kp = Kp(fp) (2.12) where Kp is a parameter related to the fraction porosity, fp,  s is the solid  ow stress (MPa) of type elastic-perfectly-plastic, and  d is the average grain size, h is the thickness of the liquid channels between grains, and n is a strain hardening parameter related to the grain size of the solid skeleton. The phenomenological expression for n has been determined based on a regression analysis of semi-solid tensile deformation experiments and microstructure simulations. 2.4.3 Constitutive law: Fully Solid In addition to the semi-solid, the mechanical properties of the fully solid are needed when simulating the DC casting process since the metal in the external shell will solidify and cool long before the center-line is solid. Also, the mechanical properties of a semi-solid at high fraction solid in ltrated with liquid are related to the mechanical properties of the fully solid phase at high temperatures close to the solidus. In this section, di erent models of high temperature mechanical behavior that have been used for \computer sim- ulations of DC casting" will be discussed. In one of the earliest works Moriceau (1975) used a elastic-plastic constitutive behavior in a continuous DC casting simulation. This type of constitutive law ignores the e ect of variable strain-rates. On the other hand, the pure creep based equations (e.g. Drezet et al. (1996a)) do not take into account the e ects of strain hardening at low temperatures. Other researchers have utilized a plastic strain based equation for alloys AA1050, AA3104, and AA5182 (Haaften et al. 2002), a power-law creep-based equation for alloy AA3103 (Farup and Mo 2000), and a combina- tion of the two (Mathew and Brody 1976). In a unique study, Mo and colleagues (Mo 22and Holm 1993) developed an internal state variable approach that included a term for microstructure evolution during cooling below the solidus temperature in order to capture di erent constitutive behaviour in di erent regions of the casting as a function of cooling rate. Now-a-days, the generally-accepted practice for simulating the fully solid constitutive behaviour of aluminum alloys is to include the e ects of strain hardening and strain rate sensitivity through the use of the so-called extended Ludwik equation (Fjaer and Mo 1990, Haaften et al. 2002, Magnin et al. 1996), as shown in equation 2.13. This formulation allows a single equation to be used for predicting the constitutive behaviour throughout the ‘fully solid’ temperature regime of DC casting.  (T; "; _") = K(T )("p + "P0) n(T )( _"p + _"P0) m(T ) (2.13) where  is the stress (MPa), K is a material constant related to the strength of the material, n is the strain hardening exponent, m is the strain-rate sensitivity exponent, "p is the plastic strain, and _"p is the plastic strain rate (s 1). The values of K, m and n are generally determined by curve  tting method from the experimental results and are unique to each alloy. The two o set constants "p0 and _"p0 are incorporated into the equation to circumvent convergence issues. 2.5 Processing E ects on Hot tearing 2.5.1 Casting Speed Of the parameters responsible for solidi cation defects in DC casting billets/ingots, cast- ing speed is considered most important (M’Hamdi et al. 2002, Nagaumi et al. 2000). The other parameters, e.g. pouring temperature of the molten metal and water  ow rate from the water-jet are industrially considered to be less important (Nagaumi et al. 2000). Zheng et al. (2011) showed that increasing casting speed increases the size of columnar grains 23at the center of the billet and also increases the amount of macrosegregation in a Mg- Nd-Zn-Zr alloy. So, it is expected that an increase in casting speed would have similar detrimental e ects on the condition for hot-tearing in DC cast products. This is actually seen generally in the casting industry and has been demonstrated through both simula- tion (Drezet and Rappaz 2001, Hao et al. 2010, M’Hamdi et al. 2002, Suyitno et al. 2005) and through experimental observations (Hao et al. 2010). Based on the RDG criterion presented in section 2.7, Drezet and Rappaz (2001) calculated the depression pressure within DC casting billets and found that higher casting speeds result in larger pressure drops and consequently a higher hot tearing tendency. According to the RDG criterion, this drop in pressure increases the hot tearing susceptibility. (Hao et al. 2010) also used the RDG criterion with a DC casting simulation of alloy AZ31 to reach the same con- clusion. Suyitno et al. (2005) implimented several hot tearing criteria (see section 2.7) to a DC casting simulation, and found that all the criteria indicated exacerbation of hot tearing scenario at higher casting speeds. 2.5.2 Pouring Temperature and Water Flow Rate Pouring temperature and water  ow rate have some e ect on hot tearing tendency in DC casting. Increasing pouring temperature increases hot tearing tendency and vice versa (Li 2010). The reason behind this could be two fold. First, the higher pouring temperature decreases the cooling rate, and thus results in larger grain sizes (Li 2010). This in turn, reduces the structure’s ability to withstand thermal stresses generated during DC casting, and increases the hot tearing tendency. The second reason could be the thickening of liquid  lms due to large grain size. Thicker liquid  lms between grains tend to increase the hot tearing tendency (Suyitno et al. 2002) Although, increasing water  ow rate increases the cooling at the surface of the billet, this has the disadvantage of increasing the di erential thermal contraction, i.e. the surface cools and thus contracts faster than the center. This increases the possibility of hot tearing in DC casting of aluminum alloys, particularly at the solidi cation front. (Sengupta et al. 2005b). 24Figure 2.5: Temperature contour of a DC cast billet 1000 sec after start-up pre- dicted by an axi-symmetric DC casting process model (Drezet and Phillion 2010) 2.6 E ect of Cooling Rate on Microstructural Features Because hot tearing occurs in the semi-solid regime, the mechanical properties at this region are critical. As we have seen in section 2.4.2, the microstructural features play an important role in the mechanical properties of the semi-solid aluminum alloys (Lu et al. 2008a, Phillion et al. 2009). During the DC casting process, there exists a variety in temperature at di erent locations of the billet. A typical temperature pro le is shown in  gure 2.5 which was predicted by a DC casting process model for AA6061 billets, 1000sec 25after start of the casting (Drezet and Phillion 2010). From  gure 2.5, it it obvious that the side walls and the base of the casting cools very fast while the center of the casting remains at high temperatures. As a result, the di erent parts of the billet cools at di erent rates. The cooling rate is known to strongly in uence the microstructural features and solidi cation path in aluminum alloys. In the following subsections, the e ect of cooling rate on various microstructural features and volume fraction solid in DC casting process are discussed. 2.6.1 Grain Size Grain size is an important microstructural feature, especially when hot tearing is con- sidered since the columnar grains are highly susceptible to hot tearing whereas equiaxed grains are known to reduce hot tearing tendency. Moreover, hot tearing is less likely to occur in highly grain re ned cast aluminum alloys (Campbell 1991, Easton et al. 2004, Grand eld et al. 2005, Granger 1998). Other researchers such as Lin et al. (2007), Camp- bell (1991) also observed this phenomenon to some extent in wrought aluminum alloys. Grain re nement is thought to improve hot tearing by reorganizing the eutectic distribu- tion and reducing the scale of the liquid channels. As grain re nement increases the grain boundary area, it will also increase the amount of eutectic at the grain boundaries. It is well established (Lin et al. 2007) that the presence of low melting eutectic material at the grain boundaries helps to compensate for the solidi cation shrinkage and thus failure to compensate for this shrinkage may result in hot tearing. However, in some alloys, such as AA5182, the act of grain re nement alone cannot prevent hot tearing since there is simply not enough eutectic material to reduce hot tearing susceptibility. In these cases, varia- tion in processing parameters is also needed (Grand eld et al. 2005, M’Hamdi et al. 2002). As is well known, there is an inverse relationship between cooling rate and grain size. Larger cooling rates lead to increased grain nucleation and smaller grains. For exam- ple, Dobrzanski et al. (2007) recently showed that an increase in the solidi cation rate 26decreased the grain size, secondary dendrite arm spacing (SDAS), and also the secondary precipitates. Since, as shown in  gure 2.5 there is a variation in cooling conditions within the billet, we can expect grains of assorted sizes to form the length of the casting. One method that can be utilized to relate grain size and cooling rate is based on the growth restriction factor as developed by Easton and StJohn (2001). This factor, Q, is a function of the alloying elements and grain re ners that are added to the alloy and can be used to predict grain size as shown in equation 4.13, where the average grain size,  d is expressed as an inverse relationship with Q and a and b are constants related to cooling rate, _T . The equations for a and b are given in equations 4.14 and 4.15.  d = a+ b Q (2.14) b = 281 + 381 _T 1 2 (2.15) a =  22:08 _T + 222:88 (2.16) From equations 4.13- 4.15, it can be concluded that increasing the cooling rate de- creases the grain size in two ways. First, by increasing the number of nucleation cites, and second, by introducing constitutional undercooling. To the author’s knowledge, the DC casting process models available in the literature have not considered the provision for variable grain size as a function of the di erential cooling conditions across the DC cast billet or ingot. The variation in cooling conditions is the key here, because now- a-days high amount of grain re ners are used during the industrial DC casting process. Consequently, the e ect of grain re nement should be similar in all parts of the casting, and thus any grain size variation is only due to cooling conditions. 272.6.2 Volume Fraction Solid (fs) DC casting models also require the relevant solidi cation path of the alloy being sim- ulated. Is it important to accurately describe the start and termination of solidi ca- tion process and how the fraction solid evolves in the semi-solid regime as a function of temperature, because these parameters are linked strongly with semi-solid mechanical properties (Braccini et al. 2000, Lu et al. 2008a, Phillion et al. 2009). Thus, for good semi-solid stress-strain predictions, an accurate description solidi cation path of the alloy need to included in the model. The solidi cation path or the evolution of fraction solid of the aluminum alloys dur- ing casting have been estimated by di erent researchers over the years. In the series of books (B ackerud and Tamminen 1986, B ackerud et al. 1990), the solidi cation charac- teristics of all the common foundry (B ackerud et al. 1990) and wrought (B ackerud and Tamminen 1986) aluminum alloys have been compiled. In this magnum-opus, the solid- i cation paths were determined based on thermal analysis of the alloys in a di erential thermal analyzer (DTA). The e ect of cooling rate on the temperature of commencement of the solidi cation reactions as well as grain size, liquidus and solidus temperatures have been presented in these books. The results show that these parameters vary strongly as a function of the cooling rate. Jeng and Chen (1996) obtained cooling curves of aluminum alloy A356.2 using a di erential thermal analyzer (DTA). A mathematical model was then used to postprocess these DTA cooling curves to obtain the solidi cation path of the alloy. Solidi cation path of a complex Al-Mn-Be alloy was determined by Markoli et al. (2010). They conducted a series of experiments using di erential scanning calorimeter (DSC), and thermogravimetric analysis (TGA) at temperatures between 500 and 1100oC. The samples were simultaneously imaged using scanning electron microscopy (SEM). They estimated the solidi cation path of the alloy at a  xed cooling rate conjoining the results from DSC, TGA and SEM. Solidi cation path of 3 ternary mono-eutectic aluminum alloys were studied by Mirkovic et al. (2008) on the basis of thermodynamical description of the 28solidi cation and precipitation reactions. Similar work was done by Chang et al. (2004) who experimentally examined the solidi cation path of multi-component aluminum alloys and found that the experimental results are in good agreement with the fraction solids predicted by the Scheil’s model coupled with phase-diagrams. Thompson et al. (2004), in their work on on alloys A356 and AA5182, determined the temperature of all the transformation reactions occurring during solidi cation, as well as the solidi cation path. Probably the most important contribution of this article is to demonstrate the variation of all transformation temperatures due to variation in cooling rate. The authors referenced above have estimated the solidi cation path of aluminum alloys as a function of temperature alone. Most of them have ignored the e ect of cooling rate on evolution of fraction solid (fs). But from the work of Thompson et al. (2004) and B ackerud and Tamminen (1986), B ackerud et al. (1990) and some other researchers, it is evident that the solidi cation path of an alloy is highly sensitive to the cooling conditions. 2.7 Hot Tearing Criteria Over the last 60 years, a considerable amount of research has been undertaken to relate hot tearing with casting parameters in order to  nd a hot tearing criterion. These hot tearing criteria can be divided into two broad classes: mechanical criteria (i.e. ones based on a failure of the material) and non-mechanical criteria (i.e. ones based on casting and/or solidi cation parameters). An additional class of hot tearing criteria, which combines both the mechanical and non-mechanical criteria has also been discussed. The mechanical criteria can be further subdivided into stain based, strain rate based and critical stress based criteria. Non mechanical criteria are based on brittle temperature range, processing conditions and phase diagrams. The various hot tearing criteria relevant to DC casting are discussed below. 292.7.1 Mechanical Criteria Pellini in 1952 (Pellini 1952), was the  rst to propose a hot tearing criterion, by postu- lating that that if the total strain accumulated is greater than some critical strain, hot tears would form. The more recent criterion by Yamanaka et al. (1992), also relies on the same principle, but limits the strain accumulation speci cally to the brittle temperature region (BTR). Won et al. (2000) further modi ed Pellini’s criterion by including strain rate term to the BTR, in addition to the total strain accumulation. Prokhorov (1962) proposed a criterion that included the parameters of shrinkage and ‘apparent’ strain rate in the semi-solid structure as a predictor for hot tearing. These parameters were compared with the fracture strain of the coherent semi-solid body to assess hot tearing susceptibility. The proposed relationship of strain rates by Prokhorov et al. is shown in equations 2.17, where _"min, _"free and _"app are strain rates for minimum fracture strain, linear free shrinkage and apparent strain, respectively. Moreover, _"min is the strain rate for reserve of hot tearing strain in the brittle temperature region (BTR). A hot tear is thus likely to occur when _"min  0 or when equation 2.17 is satis ed.  _"res  _"min  _"free  _"app (2.17) HCS = t0:99  tcr tcr  tcoh (2.18) Another strain based criterion was proposed by Magnin et al. (Magnin et al. 1996), through a calculation of the hot tearing susceptibility as the ratio of plastic hoop strain ("pl  ) measured at solidus to the measured fracture strain at high fraction solid ("fr). Therefore, HCS = "  "fr (2.19) where HCS is the susceptibility to hot tear formation and thus hot tearing is likely to form when HCS  1. Braccini et al. proposed a critical strain rate ( _"C), shown in 30equation 2.20 which can also be used as an indication of hot tearing susceptibility. _"C = h 1 e l i    a   2 3PC  PM K(T; fs)   1=m + e l 2 (  a)2 PC  L (2.20) where l is gauge length, e liquid  lm thickness,  is half of grain size, a is the length of the crack, PC is cavitation pressure, PM is the metallostatic pressure, K is a material parameter and a function of T and fs , m is strain rate sensitivity,  is the permeability of the mush and  L is the liquid viscosity. 2.7.2 Non Mechanical Criteria Feurer (1976) attributed hot tearing as in uenced by alloy composition and solidi cation conditions. Two terms were de ned: liquid volumetric  ow rate per unit volume (SPV) and solidi cation front (SRG). When SRG<SPV , hot tearing occurs, with (SRG-SPV) being deemed the driving force for hot tear formation. Clyne and Davies (1981) proposed their hot tearing criterion based on the 4 stage response of the solidifying casting to stress. According to their studies, hot tearing sensitivity is related to the ratio of time spent in the vulnerable region (tv) to the time period during stress relief (tR), as shown in equation 2.21. Here, ts corresponds to the time when volume fraction solid is fs. HCS = tv tR = t0:99  t0:9 t0:9  t0:4 (2.21) An improvement to original criteria by Clyne and Davis was proposed by Camp- bell (Campbell 1991) by introducing the solidi cation interval ( T ), the coe cient of thermal expansion ( CTE) and casting dimensions into the index. The proposed equa- tion is shown below: CSCb =  CTE Tdtv l2tr (2.22) where L is the overall length of the casting, d is the grain size, l is the length of the hot spot measured in the direction of the strain for a 1-dimensional case. 312.7.3 Combined (Mechanical and Non Mechanical) Criteria Hot teaming criteria based on both mechanical and non mechanical in uences include Rappaz-Drezet-Gremaud (RDG) criterion (Rappaz et al. 1999). According to RDG cri- terion, if the pressure in the mushy zone becomes larger than a critical pressure, hot tears form. According to the criterion, the depression pressure in the mushy zone is calculated using equation 2.23, where  psh and  pmec are the drop in pressure of the mush related to the solidi cation shrinkage and the  uid  ow due to deformation, respectively.  is the density, h is the distance below molten metal level, and g is the gravitational con- stant. When  p   pc, hot tears will form. It seems that critical pressure  pc is alloy dependent and is assumed to be 2 KPa (Rappaz et al. 1999).  p =  psh +  pmec   gh (2.23) To calculate the pressure drop contributions, a mass balance was performed on a small volume of the mush by relating the pressure drop and the velocity of the liquid required to maintain this pressure drop using Darcy’s law. This mass balance is shown in equation 2.24. flvl =  K  dP dx (2.24) where vl is liquid velocity,  is the liquid viscosity and K is the permeability of the mushy zone. The classical Carman - Kozeny relation was used by the authors for formulation of K, as shown in equation 2.25. K =  22 180 (1 fs)3 f 2s (2.25) where  2 is the secondary dendrite arm spacing. Two assumptions were made at this point for mass balance calculations, (1) liquid  ows only in the direction of heat  ow, and (2) deformation of solid occurs perpendicular to the heat  ow. The resulting mass 32balance is shown in equation 2.26. @ @t ( lfl +  sfs) + @ @x ( lflvl;x) + @ @y ( sfsvs;y) = 0 (2.26) where, vl;x and vs;y are liquid and solid velocities in their respective directions. The RDG criterion was able to relate transverse strain rate with solid deformation by the relation _"p = @vs;y @y . Finally, the hot cracking sensitivity (HCS) was proposed as per equation 2.27. HCS = 1 _"max (2.27) where _"max is the maximum allowable strain rate before hot tears form at a given criti- cal pressure. The challenge of incorporating the RDG criterion in a DC casting process model is the value of Pcritical, which seemed to have been arbitrarily chosen as 2 MPa for aluminum alloys. Furthermore, the role of total strain has been ignored in this criterion (as opposed to total strain criterion by Pellini). Lastly, the void formation has been assumed to be the staring point of hot tearing. Since it is well known that voids may also give rise to microporosity, this criterion fails to distinguish between porosity formation and the formation of hot tears. Braccini et al. (2000) modi ed the RDG criterion to calculate the pressure drop in the mushy zone by proposing that the permeability term should be calculated according to the percolation theory, instead of the traditional Karmen-Cozeny relationship, as shown in equation 2.28. K = 1 32 (1 fs) 3(f cs  fs)   1 2 (2.28) where f cs is the coalescence fraction solid,  1 is the the primary dendrite arm spacing, and  is the viscosity. A solution to the the arbitrary assumptions of the critical pressure was proposed as well. In this case, Pc was calculated based on the liquid-vapour interfacial energy ( lv) and the wetting-angle ( ), as shown in equation 2.29. 33Pc = 4cos  lv (1 fs) 1 (2.29) To resolve the ambiguity of whether voids will develop into microporosity or into hot tears, Suyitno et al. (2002) modi ed the RDG criterion. Similar to the RDG approach, a mass balance was done with a small volume element in the mushy zone, but instead of the Darcy’s law, liquid feeding term from Feurer’s criterion (Feurer 1976) was used. The Gri th crack propagation theory was then applied to estimate the relationship between the minimum stress for crack propagation and diameter of void, as shown in equation 2.30. dcrit = 4 e E   2m (2.30) where dcrit is the crack length,  e is the surface tension of the liquid metal, E is the modulus and  m is the minimum stress. If  m is larger than the casting stress state, any pore of diameter larger than dcrit would become a hot tear. In this context, less amount of work has been done to propose a hot tearing criterion based on microstructural features such as grain size, coalescence temperature, etc. The criterion proposed by Campbell (1991) included the grain size (d). From this criterion (equation 2.22), it is seen that the hot tearing susceptibility increases with increasing grain size and vice versa, provided that the other parameters of the criterion remain unchanged. Similarly, work by Lin et al. (2007) suggests that hot tearing susceptibil- ity increases with decreasing grain size. A hot tearing susceptibility (HTS) index as a polynomial function of grain size (d) is proposed, as shown in equation 2.31. In this equation, d is in  m. By plotting HTS against d, it can be shown that below d  200 m, HTS is relatively independent of d. The authors also noted that it is important to take coalescence temperature into account when comparing HTS for di erent alloys. HTS = 6 10 5d2  0:014d+ 3 (2.31) 342.7.4 Application of Hot Tearing Criteria into DC casting Process Models Drezet and Rappaz (2001) calculated the depression pressure within a DC casting process model and found that higher casting speeds result in larger pressure drops and conse- quently a higher hot tearing tendency according to the RDG criterion (Rappaz et al. 1999). The authors also calculated the cracking sensitivity index based on (Clyne and Davies 1981), and found the opposite trend, i.e. lower casting speeds produce higher sensitivity to hot tearing. Thus, that the application of the criterion by Clyne is not appropriate for DC casting process models. Suyitno et al. (2005) applied 8 hot tearing criteria(Feurer (1976), Clyne and Davies (1981), Katgerman et al., Prokhorov (1962), Novikov, Pellini (1952) and Rappaz et al. (1999)) criterion into a DC casting process model for Al-4.5%Cu alloy and investigated the e ects of casting speed on hot tearing phenomenon. Of the 8 criteria, only the RDG criterion was in a position to explicitly decide if the crack is going to form or not, the other 7 were just able to access relative sus- ceptibility of hot tearing at di erent locations of the billet and for di erent casting speeds. Additionally, predictions from the RDG criterion were most successful in matching with the common industrial practice. 2.8 Summary In this chapter, the DC casting process models developed so far have been discussed and their advantaged and limitations have been critically reviewed. The main challenge for the development of DC casting process models is how to describe the mechanical properties of the semi-solid mush. The semi-solid material models proposed by di erent researchers have been presented in this chapter. The models that include microstructural features of the mush seems to be the most comprehensive ones. To enable hot tearing study, the model must valid for the range of solid fractions(fs) where it is most likely to occur. Other challenges include the problem of strain accumulation within the liquid which will overestimate the predicted strains within the cast body at high fraction solid. 35Chapter 3 Scope and Objective For the past 60 years, hot tearing has been an active  eld of study amongst the re- searchers concerned with metal casting. Both experimental and theoretical research have led to signi cant advances in the understanding of this complex phenomenon. However, quantitative prediction of the occurrence and extent of this defect remains very di cult, due to the great complexity of the problem. Several physical phenomena such as heat  ow, liquid  ow and deformation are occurring simultaneously. In addition, hot tearing is typically a multi-scale problem in which solid grains of typically 100 m are grouped in mushy zones that are a few cm thick and experience constraints imposed by an industrial process at the meter scale. Moreover, mushy alloys have properties that are neither easy to measure, nor straightforward to model. With these issues in mind, the main objective of this research project is to investigate occurrence of hot tearing in direct chill cast Alu- minum alloy AA5182 with respect to microstructural features and process parameters. In order to successfully achieve this goal, the following subgoals have been identi ed: 1. Develop a DC casting process model that incorporates a robust constitutive law for semi-solid behaviour. In this project, a thermo-mechanical process model has been developed based on the previous work by J-M. Drezet (Drezet et al. 2000a) and Joydeep Sengupta (Sengupta et al. 2005a) and incorporationg new semi-solid constitutive model proposed by Phillion et al. (2009). This constitutive law is 36particularly useful to study hot tearing with respect to microstructural features because it takes into account the grain size of the semi-solid mush. 2. To analyze the relative susceptibility to hot tearing of castings with various mi- crostructural features and cast under various processing conditions. In order to achieve this, a quantitative index for hot tearing susceptibility has been proposed that takes into account the semi-solid stress strain predictions from the process model. 3. To characterize various aspects of the structural features and solidi cation be- haviour of AA5182 in the as cast state. This work has been accomplished via optical microscopy, scanning electron microscopy, and di erential scanning calorimetry. The organization of this thesis follows these goals. In chapter 4, the development of the  nite element process model is discussed. In this chapter, the casting geometry, boundary conditions, and material properties for the model have been described in detail. In chapter 5, the development of the quantitative index has been presented. The relative hot tearing susceptibility DC cast products with respect to the structure and processing conditions is presented and discussed in this chapter using this quantitative index. In chapter 6, the experimental methodology for observing microstructural features and solidi cation behavior of as cast AA5182 has been presented. In the following chapter, the results from the experiments run on a DC cast AA5182 ingot has been presented and compared with the theory and available literature. In chapter 8, new  ndings from this research project, along with its limitations and possible future research on this topic have been registered. 37Chapter 4 Development of Direct Chill Casting Process Model 4.1 Introduction To study the formation of hot tearing defects in Direct Chill casting of aluminum alloys, the evolution in the thermal as well the displacement  elds must be known. The displace- ment  eld provides information relating to the strain and stress tensor at the startup and steady state regimes of the casting. The corresponding thermal  eld is required to de- termine the solidi cation sequence. The alloy chosen for this study is an aluminum alloy AA5182 (Composition : Mn 0.35%-Mg 4.5%-Al balance). This alloy is primarily used for the production of beverage can lids, and is prone to hot tearing. The development of a direct chill casting process model requires the following :  Finite element analysis formulation  Thermophysical properties of the material  Constitutive properties  Initial and boundary conditions 38A general purpose  nite element software ABAQUS version 6.10 has been chosen for the current research project. ABAQUS is a well known commercial platform that is highly capable of solving transient and highly non-linear mechanical and heat transfer problems. The process model that was used in this work is based on a earlier model developed by Dr. J.-M. Drezet (Drezet and Phillion 2010, Drezet and Rappaz 2001, Drezet et al. 2000a). In this earlier work, both the thermal  elds and residual stress  elds were validated against thermocouple data from industrial DC casting trials and strain measurements obtained via neutron di raction. 4.2 Finite Element Analysis Formulation Finite element modeling of the DC casting process involves the solution of both the partial di erential equations for heat transfer and force-displacement in matrix form. The governing equation for the heat transfer analysis of the model is shown in equation 4.1. 5 [k(T )5 T ] + _Q =  Cp @T @t (4.1) where  is the density in kgm 3, Cp is the speci c heat in Jkg 1K 1, k is the thermal conductivity in Wm 1K 1, _Q is the latent heat of solidi cation in Wm 3, and T is the temperature in K. For the mechanical simulation, ABAQUS solves for the force and momentum equilibrium on the whole domain by linking force  elds and nodal displace- ments using the sti ness matrix. The strain tensor is then calculated from these nodal displacements. The stress-strain state at each elemental integration point can then be calculated using the strain-displacement relation. The elements of the elastic sti ness matrix, [Del] are related to the elastic modulus and Poisson’s ratio. Within the elastic limit, total stress and total strain maintain a linear relationship (i.e. Hook’s law) as shown in equation 4.2. ( ) = [Del]("el) (4.2) 39where ( ) and ("el) are the stress and elastic strain tensors, respectively. In the plastic regime of material behavior, the plastic sti ness matrix, [Dep] is used to relate between current increment of stress tensor (d ) and current increment of the plastic strain ten- sor (d"ep) as per equation 4.3. The constitutive law used to describe the stress-strain relationship of the material is described in a later section. (d ) = [Dep]("ep) (4.3) For studying hot tearing in a DC casting process model, a fully coupled thermal- mechanical analysis is required. The coupled thermal-displacement analysis solves the thermal and mechanical equations simultaneously, rather than sequentially. Potential sources of coupling include the formation of an air gap between both the solidifying metal and the mold and the solidifying metal and the bottom block. In a fully coupled thermal mechanical analysis, the thermal and mechanical equations are simultaneously solved as per equation 4.4. 2 6 4 Kuu Ku K u K  3 7 5 8 >< >:  u   9 >= >; = 8 >< >: Ru R 9 >= >; (4.4) where, [Kij] are the submatrices of the fully coupled Jacobian matrix,  u and   are corrections for displacement and temperature, respectively, and Ru and R are residual vectors for thermal and mechanical analysis, respectively. In ABAQUS, a backward dif- ference method is utilized for the transient solution and Newton’s method is implemented to solve the fully coupled system. 4.2.1 Geometry A round billet has been chosen for analysis, of dimensions 800 mm in height and 320 mm in diameter. The computational domain is reduced to an axi-symmetric geometry as a result of symmetry and thus the dimensions of the simulation are 160 mm and 800 mm in the radial and axial directions, respectively, as shown in  gure 4.2. 40Figure 4.1: Schematic presentation of the incremental addition of layers adopted in the model 4.2.2 Mesh The domain is made up of 200 layers, each of 4 mm height. Each layer consists of 32 elements, with dimensions 4 mm in height and 5 mm in width. The elements are of type CAX4T, which are four-node bilinear temperature and displacement elements. As a result, the FE mesh of the domain consists of a total of 6400 elements and 6633 nodes. 4.2.3 Addition of Layers A Lagrangian approach is adopted to simulate the DC casting process. In addition, the thermal boundary conditions are gradually moved upwards at a rate compatible with the billet withdrawal speed. To simulate the mold  lling and gradual increase of billet height, horizontal layers each containing 32 elements were added incrementally into the domain as shown in  gure 4.1. In the 1st time step, one horizontal layer is added, then another layer is added in the 2nd time step, and so on. This approach is used in order to simulate the overall heat input into the system as a function of time. The casting simulation is  nished when all 200 layers have been added in 200 time steps. The time steps are calculated based on the height of each element layer and the casting speed. 414.3 Thermal Initial Conditions In a transient heat transfer problem such as the DC casting process, an initial thermal condition must be known to solve the heat equation. The initial temperature of the domain was set to 650oC, which is the typical pouring temperature of AA5182 during DC casting. The ambient temperature was assumed to be 25oC. 4.4 Boundary Conditions Both mechanical and thermal boundary conditions are imposed onto the calculation do- main. 4.4.1 Thermal Boundary Conditions The thermal boundary conditions for the model were set to re ect di erent modes of cooling taking place in di erent regimes of the billet. Each surface of the axi-symmetric domain was subject to thermal boundary condition(s), as shown schematically in  g- ure 4.2. These boundary conditions are reviewed below:  Centerline ( 1)  Top Surface ( 2)  Open Side (Primary Cooling) ( 3)  Open Side (Secondary Cooling) ( 4)  Bottom Block Interface ( 5) Both the centerline ( 1) and top surface ( 2) were assumed to be adiabatic because of symmetry. The billet surfaces ( 3 and  4) were subjected to Cauchy type boundary conditions during primary (mold) cooling and secondary (water) cooling. The bottom surface of the billet, in contact with the bottom block, was also subjected to a Cauchy type boundary condition. 42Figure 4.2: Thermal boundary conditions applied in the process model. Cauchy Type Boundary Condition (at  3,  4 and  5) A Cauchy type boundary condition is used in order to make the resulting heat  ux a function of both the surface and surrounding temperatures. As the surface temperature (T ) approaches the surrounding value (T1), the heat  ux (q) reduces to zero as shown below in equation 4.5, where h is the heat transfer coe cient. q = h(T  T1) (4.5) During DC casting, heat transfer on the open side of the billet is complicated due to the fact that the billet  rst passes through the mold, then an air gap, and then cooled by 43water sprays. The high temperatures of the billet surface result in the need to use com- plex heat transfer coe cients during secondary cooling, i.e. boiling water heat transfer relationships. The resulting heat transfer coe cients are non-linear in nature. At  3 As the liquid metal comes in contact with the mold, it starts to solidify and shrink away from the mold. So, as the temperature of the casting surface decreases, contact between the mould and the billet also decreases, an air gap between the surface of the casting and mold is created and increased. To account for this change in contact pressure, the heat transfer coe cient is varied as a function of volume fraction solid of the solidifying metal, since fs / T . At  rst, when there is a good contact between mold and metal, h is high, i.e, hcontact=2000 W/m2K (Fjaer et al. 1999). At the point when solid shell exits the mold, there is a considerable air gap between mold and casting surface. Thus, a low h is assumed for the air gap cooling (hgap = 50W/m2K) (Fjaer et al. 1999). Since the air gap is not known \a priori", it is assumed that the air gap is a function of volume fraction solid as shown in equation 4.6. h 3 = hcontact(1 fs) + hgap  fs (4.6) At ( 4) The secondary cooling on the billet surface by the cooling water jet can be further divided into 2 zones. First, the impingement zone where the water jet  rst comes into contact with the surface and second, the free falling zone where the sprayed water runs down the surface. In these two zones, the main mode of heat transfer is the boiling water heat transfer. Empirical boiling water curves were used in this model to determine the heat transfer coe cient (HTC) at the surface (Drezet and Rappaz 2001, Drezet et al. 2000a). The model calculates HTC at the surface depending on the temperature of the surface, the water  ow rate and the ‘current’ vertical distance below the impingement point. The model only considers nucleate boiling regime of the boiling curve. At higher temperatures 44of the surface, a lower rate of heat transfer happens due to a phenomenon called the  lm boiling. However, this is not included in the model, for simplicity. At ( 5) Cooling between the billet and bottom block is simulated using a constant heat transfer coe cient of 1000 Wm 2K 1. Although more complex conditions can arise, this constant value is su cient to investigate hot tearing formation. 4.4.2 Boundary Conditions - Mechanical A mechanical boundary condition is required to prevent separation of the bottom block and the billet at the centerline, as well as horizontal motion of the centerline itself. These boundary conditions prevent rigid body motion in order to avoid convergence issues during the simulation. The application of this boundary condition is simply to pin the bottom node at the centerline along the r and z directions. 4.5 Material Properties The alloy chosen for the simulation in this work is the aluminum alloy AA5182. AA5182 is a non heat treatable aluminum wrought alloy with nominal compositions of Mn 0.35%- Mg 4.5%-Al balance. During solidi cation, AA5182 spends more time in the brittle temperature region than many other aluminum alloys because it has a large solidi cation window (Tsol = 523oC and Tliq = 637oC). Thus it is well-known to be prone to hot tearing. 4.5.1 Thermophysical Properties The thermophysical properties that must be included in a thermal-mechanical  nite el- ement simulation are density, latent heat, heat capacity and thermal conductivity. The temperature dependent thermophysical properties are listed in table 4.1 and are taken from Mondolfo (1976). For ease of analysis, the latent heat was varied linearly between solidus and liquidus temperatures. In addition, the density of the domain is kept con- 45Table 4.1: Summary of thermophysical properties used in the process-model Property Temperature Range Equation Conductivity T<Tcoal 119:2 + 0:623T (Wm 1K 1) Tcoal  T  Tliq 594 0:484T  0:00048T 2 T>Tliq 69 + 0:033T Speci c Heat T<Tcoal 897 + 0:452T (Jkg 1K 1) Tcoal  T  Tliq  994:8 + 8T  0:0074T 2 T>Tliq 1097 Density(kgm 3) N/A 2400 Latent Heat _QLH = 397.1kJkg 1 Figure 4.3: Solidi cation path of AA5182 used in the model (after Thompson et al. (2004)) . stant to conserve the volume since the inclusion of a temperature-dependent density would change the heat balance of the system. The solidi cation path for this alloy is taken from the work of Thompson et al. (2004) as shown in  gure 4.3. The change of solidi cation sequence with cooling rate is not accounted for in this study. Finally, as  uid  ow is ignored in this simulation, the thermal conductivity of the semi-solid metal is arti cially increased to account for the convection of heat in the liquid. In the liquid state, the thermal conductivity value was increased to four times its actual value to take into account this convective transport. 464.5.2 Mechanical Properties The model requires a number of mechanical properties including Poisson’s ratio, coef-  cient of thermal expansion ( ), Young’s modulus (E) for deformation in the elastic region, and a constitutive law for deformation in the plastic regime. The Poisson’s ratio is assumed to be a constant value of 0.3. The Young’s modulus is temperature- dependent Mondolfo (1976), and is given in  gure 4.4. As can be seen, the value of E varies from 71 GPa at room temperature to 10 GPa at Tsol, and is then reduced to 0.1 GPa at T = Tcoal. Finally, at T = Tcoal + 5K, E is again reduced to 0.01 GPa. Linear interpolation is used between the various points on the graph. This step-wise transition in the semi-solid is used in order to simulate the transition from a coherent semi-solid at temperatures below Tcoal to one that is dominated by viscous-like  ow at temperatures above Tcoal. The variation in the coe cient of thermal expansion, shown in  gure 4.5, requires fur- ther explanation. The Abaqus FE code requires the use of a temperature dependent total thermal expansion coe cient. This can be thought of as the average or equivalent thermal expansion coe cient over the range of interest as shown below:  (T ) =  0 T  T 0 Z T T 0  (T )dt (4.7) where  is the e ective thermal expansion,  ’, the temperature-dependent thermal CTE, and T 0 a reference point specifying the temperature where the material is assumed to have zero strain. In the simulation, it is assumed that the reference temperature corresponds to Tcoal. Constitutive Law for Deformation in the Plastic Regime In order to simulate the evolution in  and " during DC casting, a constitutive law is needed to relate deformation (") to the material response ( ). The constitutive law is divided into 3 segments as a function of temperature. These segments are described below: 47Figure 4.4: Variation of elastic modulus (E) as a function of temperature for Tcoal = 602oC Figure 4.5: Variation of thermal expansion coe cient ( ) as a function of temper- ature for Tcoal = 602oC 48Figure 4.6: Semi-solid stress/strain response used in the simulation at di erent fs, (a) for fs;coal = 0:90 (b) for fs;coal = 0:75. For both (a) and (b),  d = 150 m and _" = 10 3 (Equation 4.9-4.12) 49Table 4.2: Parameters of the modi ed Ludwik equation Parameter Temperature range(oC) Temperature dependent equation K (MPa) 25  T<331  0:3409T + 361:83 331  T  500  1:1015T + 613:59 n 25  T<206  0:0003T + 0:170 206  T<361  0:0007T + 0:252 361  T  500 0 m 25  T<183 0 183  T<361 0:001T  0:183 361  T  500 0:0003T + 0:069 Constitutive Law Below Solidus At temperatures below Ts, the modi ed Ludwik equation developed by Alankar and Wells (2010) was chosen to simulate the constitutive behavior of the alloy, as shown in equa- tion 4.8. This equation is well suited to describe the transition from time independent plasticity at low temperatures ( strain hardening) to time-dependent plasticity ( visco- plasticity) at high temperatures, since the rheological parameters K(T ); n(T ); and m(T ) are continuous functions of temperature. The values for these parameters are shown in table 4.2. Note that, the equation 4.8 is only valid only up to 500oC. Between temper- atures 500 and Tsol, the constitutive behaviour is assumed to be a linear interpolation between values obtained by equation 4.8 at 500oC and equation 4.9 at Tsol = 523oC (from the semi-solid deformation behaviour).  (T; "; _") = K(T )("p + "P0) n(T )( _"p + _"P0) m(T ) (4.8) Constitutive Law Between Solidus and Coalescence Temperature Within the temperature range Ts < T < Tcoal, the constitutive behavior is modeled according to the model proposed by Phillion et al. (2009) as shown below:  (fs; fp;  d) = fs s("p + "0) nss(T )Kp(1 fp 1 fs ) (4.9) 50with,  s = (483:5 0:77T ) _" (0:205+0:00006T ) p (4.10) h =  d(1 fs) 1 3 (4.11) nss =  6:35e  4h2 + 0:0202h (4.12) where Kp is a parameter related to the fraction porosity, fp,  s is the solid  ow stress (MPa) of type elastic-perfectly-plastic,  d is the grain size, h is the thickness of the liquid channels between grains, and nss is a strain hardening parameter related to the grain size of the solid skeleton. The phenomenological expression for nss has been determined based on regression analysis of semisolid tensile deformation experiments and microstructure simulations. This formulation enables a link between the semisolid microstructure and the resulting constitutive behavior. The resulting semisolid stress-strain relationships for AA5182 are presented graphically in  gure 4.6 (a) for various fractions of solid, and (b) for various grain sizes. As can be seen, the semisolid strength increases with increasing fs and yet decreases with increasing  d. The strain hardening that occurs is a phenomenon of semisolid deformation has been previously observed both experimentally (Ludwig et al. 2005b) and through simulation (Phillion et al. 2008). Constitutive Law Above the Coalescence Temperature Above the coalescencente temperature (Tcoal), a low constant yield strength is speci ed . This constant yield strength is the stress calculated by the equations 4.9- 4.12 for T = Tcoal. Examples of these can be seen graphically in  gure 4.6. 51Figure 4.7: Semi-solid stress/strain response according to Phillion et al. (2009) for di erent  d, at fs = 0:98 and _" = 10 3 . Figure 4.8: E ect of cooling rate on grain size (  d) in AA5182, after Easton et al. (2010). 524.6 Simulation Parameters 4.6.1 Microstructural Features Grain Size The constitutive law used for semi-solid deformation includes the e ects of microstructure and its evolution, i.e. average grain size (  d). The variation of the semi-solid stress/strain response as a function of  d is shown in  gure 4.7. The presence of variable cooling conditions as the cast surface results in di erent zones of the casting domain solidifying at di erent rates and hence di erent grain sizes. The main driving force behind gradient in grain size across the casting domain is taken to be the average cooling rate between temperatures Tcoal and Tliq. Other factors in uencing grain size are ignored. Thus, the local average grain size can be calculated using the methodology of Easton et al. (2010), which is based on the growth restriction factor, and equations 4.13, 4.14 and 4.15. The growth restriction factor (Q) for alloy AA5182 is calculated using the nominal composition of the alloy. The  tting parameters ‘a’ and ‘b’ are dependent on the cooling rate( _T ) and taken from Easton et al. (2010). The variation of average grain size with cooling rate for aluminum alloy AA5182 is shown in  gure 4.8.  d = a+ b Q (4.13) b = 281 + 381 _T 1 2 (4.14) a =  22:08 _T + 222:88 (4.15) Variation in Mechanical Coalescence Temperature The model predictions are also highly sensitive to the choice of coalescence temperature. This parameter directly a ects many of the mechanical properties including the thermal 53expansion coe cient as this will a ect the onset of thermal contraction, the elastic mod- ulus as this will a ect the onset of the sti ness, and the semi-solid constitutive law. In this model, two Tcoal are used, 580oC (0.90) and 602oC (0.75). The corresponding volume fraction solids (fs) are shown in the parentheses. Campbell (1991) reported that if there is any deformation induced to the semi solid due to thermal stress, etc. above Tcoal, cracks occurring due to strain will be healed by interdendritic  ow of liquid. Thus, temperatures above (Tcoal) should not be considered for hot tearing study. In the current model, when a Tcoal of 602oC is assumed, a low constant  y is used below the corresponding fs = 0.75 as shown in  gure 4.6 (a). The same approach is followed when using a Tcoal of 580oC, as shown in  gure 4.6 (b). 4.6.2 Casting Parameters Casting parameters play an important role in the formation of solidi cation defects such as hot tearing. These parameters include :  Pouring temperature  Cooling water  ow rate  Casting speed Among these casting parameters, only casting speed is taken as a variable in this study to observe its e ect on hot tear formation since this parameter is the only one to have been found industrially to be relevant for hot tearing. Two casting speeds are investigated: 66 mm/minute, and 40 mm/minute, i.e. values that are typical of fast and slow casting speeds. 4.7 Summary In this chapter, the details of the process model that has been used to simulate the DC casting process for round billets have been presented. The novelty of the simulation developed for the current masters project are the inclusion of a semi-solid constitutive 54law containing stress/strain dependence on grain size, and the prediction of this grain size based on cooling rate e ects. The details of these have also been provided in this chapter. Using this process model, simulations were run with the commercial FE package ABAQUS varying di erent parameters. The stress-strain and hot tearing predictions from this process model under di erent conditions will be presented in chapter 5. 55Chapter 5 Hot Tearing Predictions 5.1 Introduction We now have an axisymmetric DC casting process model for round billets coupled with a semi-solid constitutive model which includes microstructural features and cool- ing rate e ects. Using this process model, numerous simulations have been run varying the microstructural features and casting parameters using the  nite element software ABAQUS (version 6.10). The next task is to relate the stress-strain predictions from this thermo-mechanical process model to hot tearing. To access the relative hot tearing susceptibility as a function of location in the round billet and with respect to casting parameters and microstructural features, a quantitative hot tearing criterion must be applied to the simulation data. This index must be calculated according to the fac- tors known to in uence hot tearing. For the current work, a term named \hot tearing strain" is proposed as the index for hot tearing susceptibility and is described in the next section in detail. In the later sections of this chapter, the hot tearing defect in DC casting of round billets is discussed with the help of the simulation data and the hot tearing index. 565.2 Hot Tearing Criteria For the current project, a term called the \hot tearing strain" is taken as the hot tearing criterion. An overview of the hot tearing criteria available in the literature was summarized in chapter 2. The concept of this hot tearing strain is based on al- ready available strain-based hot tearing criteria in the literature, namely Pellini’s total strain criterion (Pellini 1952), Yamanaka’s criterion (Yamanaka et al. 1992), observations by M’Hamdi et al. (2002), and Prokhorov’s criterion (Prokhorov 1962). All of these re- searchers have concluded that if the strain accumulated in the semi-solid regime goes above a critical value, then hot tears will form. Hot tearing can then be assessed quan- titatively by comparing the strain accumulated in di erent regions of the casting with a critical value or qualitatively with the philosophy that the higher the hot tearing strain, higher the susceptibility for hot tearing. In this work, hot tearing strain is calculated as the strain accumulated in the brittle temperature region, between the mechanical coa- lescence f coals and the point at which continuous liquid  lms disappear from the mushy zone (fs = 0:98). In this range, the ductility is very low (Magnin et al. 1996) and thus the semi-solid material is most prone to hot tearing. During the last 2% of the solidi cation, dendrites have already bridged and thus the structure is able to withstand mechanical loading and resist hot tears. Furthermore, observation made by M’Hamdi et al. (2002) indicated that only the plastic strain is important for hot tearing. The hot tearing strain is computed as the sum of (1) component of the plastic strain tensor ("plij) normal to the thermal gradient and in the axi-symmetric plane, and (2) the out of plane plastic hoop strain ("plzz). The hot tearing strain is calculated as shown in equations 5.1 - 5.5 through a rotation to an angle corresponding to the direction of heat  ow. "plij = 2 6 4 "11 "12 "21 "22 3 7 5 (5.1) 57T = 2 6 4 cos( 2   ) sin(  2   )  sin( 2   ) cos(  2   ) 3 7 5 (5.2) A = T  "plij  T 0 (5.3) and, "HT = A11 + " pl zz (5.4) "HTBTR = "HT (@f coal s ) "HT (@fs = 0:98) (5.5) Where,  is the rotation angle between the X-axis and the direction of the thermal gradient, T is the transformation matrix, "HT is the hot tearing strain, and "HTBTR is the hot tearing strain accumulated in the brittle temperature region (BTR). Figure 5.1: Schematic presentation of the strain perpendicular to heat  ux in a DC casting billet. 5.3 Simulations for Di erent Processing Conditions The process model was simulated for two  xed grain sizes of 300 and 75  m, for two di erent mechanical coalescence temperatures of 580 and 602oC, and at two di erent 58Table 5.1: List of simulated processing conditions Case Casting Speed Tcoal  d mm/min oC  m A 66 602 Eq.4.13 B 66 580 Eq.4.13 C 40 602 Eq.4.13 D 66 602 75 E 66 602 300 casting speeds of 40 and 66 mm/min. With variable grain size (described in chapter 4), 3 additional simulations were run. These 3 simulations are termed cases A, B and C. The simulations run with  xed grain sizes are termed Cases D and E. In total, 5 processing conditions have been modeled to investigate the e ects of casting speed, coalescence temperature, and grain size, as outlined in table 5.1. In this table,  d is the grain size, and Tcoal is the mechanical coalescence temperature. From here on, case A will be termed as the ‘base case’. 5.4 Results and Discussion from the Base Case The results and discussion of this section will be based on the base case (Case A). 5.4.1 Evolution of Temperature and Hoop-Stress The FE simulation can be used to provide a detailed description of the evolution of stresses, strains, and temperature during the casting process. In this study, a refer- ence fs = 0:98 is selected to study this evolution of hoop stress. In  gure 5.3, the predicted evolution of hoop stress and temperature is provided as a function of time for two di erent locations within the casting domain for comparison purposes. The hoop stress is shown since it is considered to be the major driving for hot tear formation. Lo- cation X is 60 mm above the bottom block and at the centerline, while Location Y is at the same height but just below the cast surface as shown in  gure 5.2. As can be seen from  gure 5.3, point Y cools much faster as compared to X, owing to the presence of 59boiling water heat transfer boundary condition at the surface. Although the evolution of hoop stress at point X is approx. three times slower as compared to Y, the evolution follows the same trend, i.e. close to zero up to Tcoal, then through a compression followed by an increasingly tensile regime towards the end of solidi cation and in the solid state. 5.4.2 Contour Plots In  gure 5.4, two contour plots are provided to show the distribution of  d and "HTBTR during casting. The section shown is 400 mm in height and 160 mm in radius. As can be seen in  gure 5.4a,  d varies from 175 to 275  m, with the largest grains predicted to form just above the base of the casting. These predictions agree relatively well the results found experimentally by Suyitno (2005) for billets that have not been grain re ned. The contour plot of "HTBTR, shown in 5.4b indicates that only a small portion of the billet actually undergoes tensile strain in the brittle region, near the base of the billet and both along the centerline and at the surface. Thus, once the casting has successfully completed the start-up region, hot tearing is not an issue. The compressive strains seen further up are a result of the combination of thermal contractions upon cooling and the aggressive surface cooling. Figure 5.5a shows the temperature contour plot of the billet cross-section at the end of the simulation (728 seconds). The pool of liquid has a red appearance in  gure 5.5a. The hoop stress distribution is shown in the billet cross section is shown in  gure 5.5b, which was also taken at the end of the simulation. Hoop stress is very high at the surface and the center as shown by the  gure, ranging between :249 and +251 MPa. Moreover, there is only a slight variation in the distribution of the hoop stress except at the ends which is an indication that the casting has reached the steady state. The billet center is in tension but high compressive stresses have concentrated at the surface. This type of tension and compression stress regime arises due to the high cooling rates imposed during the process. This e ect is also known as the \skin-core" (Drezet and Rappaz 601996b). The cooling conditions applied at the surface cools the surface down very fast and creates an external shell. The interior is still hot, whereas the shell has cooled. This solidi ed shell counteracts the contraction of the hot core and results in the high tensile stresses at the centre (251 MPa). This e ect has also been reported to have appeared during the quenching of heat treatable alloys (Heymes et al. 1997) and considered to be one of the causes of crack formation during casting (Boender et al. 2004, Lalpoor et al. 2009). 5.4.3 Identifying the Startup and the Steady-State Regions In chapter 1, the DC casting process was divided into three regions from a phenomeno- logical point of view. The  rst stage is the startup phase, where the thermal  elds are not stationary, but can vary with position and time. At higher distances from the bottom block into the casting, there exists the steady state, where the thermal and other  elds are stationary, i.e. invariant with respect to time and location. From a hot tearing point of view, it is critical to identify the startup and the steady state regions of DC casting. The reason behind this is two-fold. First, hot tearing is seen industrially to occur in the startup phase of the casting process. Second, the set of casting parameters needed to avoid hot tearing for the startup and the steady state region are di erent. The DC casting simulation model developed for this project is well described both in terms of thermal and mechanical considerations. In order to distinguish between the startup and the steady state in this simulation, the temperature pro le of di erent lo- cations need to be examined. For the base case, temperature vs. time data at di erent distances along the centerline have been extracted from the simulation, as shown in  g- ure 5.6. Note that, for each location, the time t = 0 sec corresponds to the time when the corresponding layer has been added (activated) in the simulation. In this  gure, it is seen that the temperature pro le of the  rst 2 locations (0, 100 mm) are farthest apart from each other. This range denotes the startup stage of the casting process. As the 61distance from the bottom block increases, the temperature pro les start to come closer to each other. At and beyond 400 mm distance from the bottom block, the temperature pro les start to overlap each other. Thus, after the billet has been cast for about 400 mm height, it reaches a steady state at the centerline. Now, lets turn our attention towards what happens along the chill surface of billet in the simulation. The temperature pro les of di erent locations along the chill surface of the billet from the simulation are summarized in  gure 5.7. A very interesting di erence as compared to the temperature pro les for the centerline is revealed in this  gure. The temperature pro les at the points on the surface start merging at around 100 mm away from the bottom block. Thus, the steady state is achieved only within 100 mm away from the bottom-block. The thermally transient state lasts for only the  rst 100 mm for points on the surface. It seems that, faster cooling regimes (surface) tend to shift the steady state region to much lower heights. This variation of attainment of steady state has important implications with respect to the hot tear formation in the DC casting process. The steady state regime can also be identi ed from a mechanical point of view. The evolution of hoop stress ( H) in the vertical direction as a function of distance from the bottom-block is shown in  gure 5.8. The hoop stress values at di erent locations have been taken at the time when the point has reached a fraction solid of 0.98. Close to the bottom-block, the stress is negative (-10 MPa), and as the distance from the bottom- block increases, the hoop stress starts to increase towards the positive side. At around 80 mm distance from the bottom block, the hoop stress becomes zero. The stress keeps increasing and reaches a maximum value of +2.5 MPa at 100 mm distance. Beyond this point, the stress starts decreasing again, and shifts again to the negative regime after 160 mm. The stress decreases steadily, before reaching a negative plateau of about -13 MPa at and beyond 400 mm distance. The hoop stress  eld remains relatively constant after 62a distance of 400 mm from the bottom block. This distance (400 mm) was identi ed as the start of the steady state region from the thermal  elds shown in  gure 5.6. Thus, in addition to the thermal  eld, the (hoop) stress  eld also becomes stationary in the steady state. The hoop stress in the horizontal direction as a function of the distance from the centerline at 12 mm distance from the bottom block is shown in  gure 5.9. Similar to  gure 5.8, the hoop stress values are taken at the time when the fraction solid of the point is 0.98. At this height, the casting is still in the startup stage. In this startup stage, the hoop stress is compressive near the center of the billet. The hoop stress remains relatively constant at a value of about -9.5 MPa up to 90 mm distance from the center. Further away from the center, the stress gradually increases, and is highly tensile. The stress is highly tensile (+9 MPa) on the surface. This occurs because the surface solidi es rapidly to the cooling of the mould, which tends to ‘squeeze’ the material within. This squeezing action results in the compressive stresses close to the center. The variation in hoop stress along the horizontal direction at di erent distances from the bottom block are shown in  gure 5.10. In  gure 5.10a (100 mm away from the bottom block), the stress is highly tensile at the center up to about 80 mm from center, but shifts to compressive close to the surface. Similar observations are made at a distance 200 mm from the bottom-block ( gure 5.10b). If we compare the maximum tensile stresses achieved in  gures 5.10a and 5.10b, we see that the maximum tensile stresses achieved in both cases are similar. But location of maximum stress for these 2 cases are di erent. The maximum stress at x = 100 mm is observed at the center, but at x = 200 mm, it is seen at 40 mm from the center. Thus, the maximum tensile hoop stress moves away from the center as we go further up the billet. Moreover, at the center, the hoop stress decreases as the top of the billet is approached (compare with  gure 5.8). 635.4.4 Evolution of Hot Tearing Strain In this project, a ‘hot tearing strain’, as discussed in section 5.2, has been used as the criterion for hot tear evaluation in DC casting billet. Tensile (positive) hot tearing strain would mean susceptibility to hot tearing. But, compressive (negative) hot tearing strain would mean no susceptibility to hot tearing. In fact, compressive hot tearing strain should help to heal the hot tears by directing the  uid  ow into areas where feeding is inadequate. The variation of hot tearing strain as a function of distance from bottom block along the centerline of the billet is shown in  gure 5.11. As seen in the  gure on the top, the hot tearing strain is compressive close to and also further away from the bottom block. Only at 4 to 8 mm from the bottom block, the strain goes through a tensile region, which can be seen in the magni ed bottom (blue background)  gure. Thus, this region (4-8 mm distance) close to the bottom block at the centerline is most prone to hot tearing. The hot tearing susceptibility reduces considerably further away from the bottom block. Another salient feature of this curve is the noise associated with it, which is seems to have exacerbated after 100 mm distance from the bottom block. The main reason behind this noise is the incremental addition of layers. The addition of a layer causes the bulk sti ness of the structure to change, and thus acts to induce  uctuations in the value of the strain tensor. Another cause of this  uctuation could be addition of layers from another aspect. The layer being added has a  at surface, but the layer added in the previous time step has cooled and is no longer  at due to contraction. So, the addi- tion of the  at surfaced layer on the contracted surface could also contribute to this noise. Hot tearing strain in the horizontal direction 8 mm away from the bottom block is shown in  gure 5.12. The hot tearing strain is tensile at the center, but gradually de- creases to zero at around 10 mm from center. Further away from the center, hot tearing strain is compressive. But, between 100 - 160 mm from the center (close to and at the surface), the hot tearing strains have small tensile values. From these two observations of 64tensile strains, it can be concluded that the center of the billet close to the bottom block is highly susceptible to hot tear formation. Furthermore, to a lesser degree the surface close to the bottom block may also be susceptible to hot tearing. So far, we have looked at variation in hot tearing strain in the horizontal direction very close to the center. Now, lets look at hot tearing strain along horizontal lines higher up the billet. The horizonal evolution in hot tearing strain at di erent heights are shown in  gure 5.13. If we look at the strain further into the casting, at both x = 100 mm ( gure 5.13a) and at x = 200 mm ( gure 5.13b), the strain regime is exclusively compressive. So, at these heights, the casting is not susceptible to hot tearing at all. Similar trends are seen in both these  gures, i.e. the strain is highly compressive at the center and gradually changes to a less compressive value close to the surface of the billet. From these  gures, it can be concluded that only the region close to the centerline and bottom block of the billet are susceptible to hot tearing. At higher distances from the bottom block, the hot tearing tendency diminishes. The other important feature of the strain evolution at x =100 and 200 mm, are there is considerable noise in the evolution in hot tearing along the cross-section. As discussed earlier, this is most probably due to the changes in sti ness every time a layer is added. Moreover, along the horizontal direction, the noise level seems to be higher at larger heights of the casting. 65Figure 5.2: Location of X and Y in the casting domain. Figure 5.3: Evolution of Temperature and  H at locations X and Y with time. For X (Y), t=0 sec. corresponds to t=78.33 (57.50) sec. after the start of casting. 66(a) Grain Size (b) Hot Tearing Strain Figure 5.4: Contour plots from Case A showing (a) Grain size, and (b) Hot tearing strain 67(a) (b) Figure 5.5: (a) Temperature  eld of the billet, and (b) Contour plot of hoop stress ( H) at the end of the simulation (after 728 seconds) 68Figure 5.6: Temperature pro le at di erent locations along the centerline of the billet Figure 5.7: Temperature pro le at di erent locations along the chill-surface of the billet 69Figure 5.8: Variation of  H as a function of distance from the bottom block along the centerline Figure 5.9: Variation of  H in the horizontal direction as a function of distance from the centerline at 12 mm distance from the bottom block 70(a) x = 100 mm (b) x = 200 mm Figure 5.10: Variation of  H in the horizontal direction as a function of distance from the centerline at di erent distances from the bottom block, where x = distance from the bottom block Figure 5.11: Variation of hot tearing strain as a function of distance from the bottom block along the centerline of the billet 71Figure 5.12: Variation of hot tearing strain as a function of distance from the centerline along the horizontal direction, 8 mm away from the bottom block (a) x = 100 mm (b) x = 200 mm Figure 5.13: Variation of hot tearing strain in the horizontal direction as a function of distance from the centerline at di erent distances from the bottom block, where x = distance from the bottom block 725.5 E ects of Microstructural Features and Processing Parameters Up to this point, we have limited our discussion to the results obtained from the base case. In this section, we will be exploring the other cases (B - E). Based on the results from these simulations, the e ect of microstructural features on stress and strain predictions will be discussed in detail. 5.5.1 E ect on the Hoop-Stress E ect of Grain Size Figure 5.14 shows the variation of hoop stress along the horizontal direction at a height 8 mm from the bottom block and at fs = 0:98 for three simulations with both variable  d (Case A) and  xed  d [cases D (175  m) and E (300  m)]. As can be seen,  H is compressive close to the base of the billet and then gradually shifts to the tensile regime further away. The hoop stress is maximum both in the tensile (at surface) and compres- sive (at center) for the simulation with case A. Conversely, the lowest stress is seen for the simulation of case A (variable grain size). Note that the grain size range is 175 - 275  m for case A simulation (shown earlier through a contour plot). Finally, the stress levels for simulation of case D lies in between case A and E. The stresses generated in the casting body for these simulations vary with grain size, and there seems to be a direct relation between stress and grain size if we consider cases D and E only. But, the high stress generated for the case A needs more attention. The variable grain size is somehow changing the strength of the casting at fs = 0:98, and resulting in a relative higher stress. Figure 5.15 shows the variation in hoop stress at di erent heights of the billet along the centerline, taken at fs = 0:98 for the three simulations A, D, and E. The highest tensile stress is reached at close to the top of the casting. Though the highest compressive stress is observed for case A, but the highest tensile stress is observed for case E, the lowest grain size simulation. The lowest tensile hoop stress observed for case E. In terms 73of reaching the steady state from a mechanical point of view, both the  xed grain size simulations (D and E) reach the steady state much earlier (at around 300 mm) than the variable grain size simulation (at around 400 mm). E ects of Coalescence Temperature and Casting Speed Figure 5.16 is provided to demonstrate the e ects of coalescence temperature and casting speed on hoop strain variation in the vertical direction at fs = 0:98. In this  gure, where the vertical variation of hoop stress along the centerline is shown, we can see that the highest stresses are observed for the case B simulation (Low Tcoal of 580oC). The low Tcoal means that the coalescence temperature is much closer to the temperature at with the hoop stresses are taken (corresponding to fs = 0:98) compared to higher assumed Tcoal=602oC for the base case. So, the strength is much lower for the casting using case B parameters. The lowest stresses are seen for simulation with base case. But for case C (low speed), the stress never goes through a tensile zone. Moreover, the steady state is achieved for case C much earlier (around 150 mm) than case A and B. The early attainment of steady state is related to the casting speed by the depth of the sump. Weckman and Niessen (1982), Zheng et al. (2011) experimentally showed that the depth of the sump during DC casting of billets increases with the casting speed. An increase in depth of the sump thus delays the attainment of steady state. The early achievement steady state for the low casting speed indicates that it spends relatively less time in the transient startup state, which is believed to be the zone where the hot tears form. So, low speeds would have low hot tearing susceptibility, as compared to casting with high speed (base case). 5.5.2 E ect on Hot Tearing Strain E ects of Grain Size Figure 5.18 shows the variation of hot tearing strain for in the vertical direction along the centerline as a function of the distance from the bottom block for  xed (D and E) 74and variable (A) grain size simulations. As can be seen from the  gure, there is some variation of evolution of hot tearing strain due to variation in grain size. The maximum tensile strain arises at around 8 mm from the bottom block for all three simulations. Although it is not clear from the  gure because of the scales used in Y axis, the highest tensile strain occurs for case E (highest grain size). The hot tearing strain in the startup region (up to 25 mm height) is shown in  gure 5.19. The lowest strain is achieved for case E. Moreover, the maximum tensile strain for the  xed grain sizes are observed at 4 mm away from the bottom block, but the maximum strain achieved for the variable grain size simulation is at 8 mm away from the bottom block. Thus, the hot tearing susceptibility is observed for the highest grain size, but the minimum minimum hot tear- ing susceptibility is is observed for the variable grain size simulation with grain sizes in the range of 175 - 275  m. The lowest grain size simulation (case D) shows maximum tensile strains with values in between case A and E. It is expected that a structure with larger grain size would exhibit higher strains, because it possesses lower strength in the semi-solid range. Conversely, using the same logic, the structure with smallest grain size (case D) should show the lowest strain and consequently lowest hot tearing tendency, because it has the highest strength in the semi-solid. Moreover, if larger grains exist in the semi-solid, the grain boundary area is less than with smaller grains. Consequently, the interdendritic liquid channels become wider for larger grains, which exacerbates the hot tearing problem. Either of these two reasons will contribute to higher resistance to hot tearing for smaller grains. But clearly, it is not the case. This could be due to two reasons. First, it could be due to decrease in di erential thermal contractions imparted by the range of grain sizes spread across the billet cross section, which would lead to lower hot tearing susceptibility. Second, it could be due to a term called the ‘over grain re nement‘ e ect. This e ect postulates that although grain re nement increases the hot tearing resistance in general, but grain re nement below 100  m actually increases the hot tearing tendency in wrought aluminum alloys. 75Figure 5.17 shows the horizonal variation of hot tearing strain at various distance from centerline at 8 mm away from the bottom block for the cases A, D, and E. The maximum tensile strain is shown at the center for all three simulations. The highest hot tearing strain is shown by case E (d = 300 m) and lowest strain is shown is shown for case D (d = 75 m). The strain for case A lies in between those of cases D and E. So, along this line, the largest grain size structure is the most susceptible to hot tearing, while the lower grain size structure has the lowest susceptibility. On the other hand, along the horizontal line at 4 mm away from the bottom block, the hot tearing tendency is highest for the largest grain size structure, but the lowest hot tearing susceptibility is shown not by the lowest grain size structure (case D) but by the variable grain size structure. So, the claim made in the previous paragraph that the hot tearing tendency is not the lowest for the lowest grain size simulation holds true for this line at 4 mm from the surface, but not for the horizontal line at 8 mm from the surface. But, in any case, if we consider the highest strain value for the three cases, and not the position, the lowest tendency to hot tear is for the variable grain size structure (case A). E ect of Coalescence Point and Casting Speed Figure 5.20 and 5.21 show the e ect of variation in coalescence point and casting speed in the evolution in hot tearing strain. First,  gure 5.21 shows the hot tearing strain in the vertical direction along the centerline, and second, the hot tearing strain in the radial direction at 8 mm from the bottom block is shown in  gure 5.20. Beginning with a modi cation of the coalescence temperature from 602oC to 580oC (Case A to Case B), it can be seen that a reduction in coalescence temperature will increase the hot tearing strain. For the lower coalescence temperature, the semi-solid body is weaker at fs=0.98, because it is relatively closer to the coalescence temperature at this fs. Consequently higher strains are observed for simulation with case B. It can also be seen that only a negligible amount of hot tearing strain is accumulated 76when a slow casting speed of 40 mm/min (Case C) is used. In fact, the strain along the radial direction and along the centerline is always compressive for this simulation. For a slower casting speed, the material being cast is in contact with the mold and the spray water for a longer version of time. Thus, there is a small thermal gradient and hence a smaller di erential thermal contraction. So, the simulation with lower casting speed is much more resistant to hot tearing, as found previously by Hao et al. (2010) as well as by Drezet and Rappaz (2001). This result will hold as long as the secondary water cooling conditions remain in the nucleate boiling regime. However, a lower casting speed decreases the length of the nucleate boiling zone of secondary cooling (Weckman and Niessen 1982) and tends to shift the secondary cooling regime from nucleate to  lm boiling. If the cooling conditions are such that  lm boiling occurs on the surface of the casting, heat transfer is drastically reduced and severe hot tears can form (Sengupta et al. 2005a). An interesting discussion could be commenced on the change of grain re nement scenario by variation of casting speed and its implications on hot tearing. The higher casting speed should increase the cooling rate and thus, decrease the grain size. As the results from the simulations show that smaller grain size tends to increase hot tearing resistance, also validated by previous experimental work on this topic. But, the hot tearing resistance here is shown to be higher for lower casting speeds. Thus, it seems that the reduction in di erential thermal contraction overrides the e ects of grain re nement in terms of hot tearing susceptibility. To summarize, the comparison of Cases A, B, and C in Figures 5.20 and 5.21 indicates that larger strains will accumulate in the semisolid when the casting conditions are such that the metal has a lower coalescence temperature and/or the casting speed is elevated. 77Figure 5.14: Variation of  H as a function of distance from the centerline along the horizontal direction, 8 mm away from the bottom block for cases A, D, and E Figure 5.15: Variation of  H as a function of distance from the bottom block along the centerline for cases A, D, and E 78Figure 5.16: Variation of  H as a function of distance from the bottom block along the centerline for cases A, B, and C Figure 5.17: Variation of hot tearing strain as a function of distance from the centerline along the horizontal direction, 8 mm away from the bottom block for cases A, D, and E 79Figure 5.18: Variation of hot tearing strain as a function of distance from the bottom block along the centerline for cases A, D, and E Figure 5.19: Variation of hot tearing strain as a function of distance from the bottom block along the centerline in the startup region for cases A, D, and E 80Figure 5.20: Variation of hot tearing strain as a function of distance from the centerline along the horizontal direction, 8 mm away from the bottom block for cases A, B, and C Figure 5.21: Variation of hot tearing strain as a function of distance from the bottom block along the centerline for cases A, B, and C 81Chapter 6 Microstructural Analysis of an AA5182 DC Cast Ingot - Experimental Methods 6.1 Introduction The development of a DC casting process model, and its use in predicting semi-solid deformation and hot tearing were presented in chapters 4 and 5, respectively. The model predictions indicated that grain re nement and solidi cation characteristics of the alloy, among others have a strong in uence on hot tear formation. In order to conduct an experimental study of these factors, an experimental study was carried out to charac- terize the microstructure of an AA5182 DC cast ingot provided by Rio Tinto Alcan. In table 6.1, the casting parameters used for casting this ingot are summarized. The ingot had cross-sectional dimensions of l = 1650 mm, and w = 510 mm. The purpose of this chapter is to describe the methodology used for studying the solidi cation characteristics of the alloy, the resulting microstructure, and also the e ects of cooling on these characteristics. In addition, the methodology for measuring grain size including preparation of metallograpic samples is also reported. The results from these 82Table 6.1: Process parameters used for casting the AA5182 ingot piece, obtained from Rio Tinto Alcan Parameter Value Casting Speed 78 mm/min Water Flow Rate 975 L/min Casting Temperature 705oC Figure 6.1: Locations in the ingot from where the samples were taken for charac- terization experiments will be reported in the following chapter. 836.2 Sample Selection A number of samples of dimensions 10 mm 10 mm 10 mm were taken along the centre- line of the rolling face, as shown in  gure 6.1. For this analysis, a 125 mm section of the ingot was taken from the steady state region of the casting. Samples were then collected for grain size measurements, chemical analysis and for determination of the evolution in fraction solid with temperature. 6.3 Grain Size Measurements For grain size measurements, metallographic samples were taken as shown in  gure 6.1 from di erent positions along the centreline of the ingot’s rolling face. First, the sam- ples were mounted with a thermosetting resin. The mounted samples were then coarse ground, and then polished down to a 1  m  nish with colloidal silica in a automatic metallographic polisher. After cleaning in an ultrasonic cleaner, the samples were then electrochemically etched with Barker’s reagent to reveal the grain boundaries. The choice of the etching reagent is important for aluminum alloys because they are very reactive and thus one of the hardest groups of metals to etch properly. Many etching reagents were tried for this project, from hydro uoric acid (HF) to more caustic NaOH. These regents mostly revealed the general or dendritic structure of the alloy in question, but failed to reveal the grain boundaries. Barker’s regent was found to be most e ective in this regard. The etched samples were then viewed under polarized light with sensitive tint attachment in a ‘Zeiss Axio’ metallurgical microscope. The grain size was measured by Je rie’s procedure, a standard methodology described in the ASTM E112. In this method, a circle of appropriate size (usually 5000mm2 or with a diameter of 79.8 mm) is drawn on a metallograph image. Magni cation is selected so that the circle partially/fully inscribes at least 50 grains. The grain density (with no magni cation) is then given by equation 6.1. 84NA = f(Ninside + Nintercept 2 ) (6.1) where Ninside is the number of grains completely inscribed by the circle, Nintercept is the number of grains partially inscribed in the circle, and f is known as the Je ries’ multi- plier, which is a function of magni cation used. Finally, average grain size (  d) is estimated using a table provided in the ASTM E112 guide that relates grain size with NA. 6.4 Chemical Analysis Chemical analysis was carried out using an Oxford Instruments X-max 80 mm2 energy dispersive spectroscope (EDS) attached to a Tescan Mira 3 XMU scanning electron mi- croscope (SEM). Each of the samples shown in  gure 6.1 was analyzed using SEM-EDS. For each sample, an EDS signal was acquired on 10 to 12 rectangular subregions, each with a dimension of approximately 100 m 100 m. The compositions of each element from di erent locations within the same sample were then averaged to represent the bulk composition of that element within that sample. 6.5 Solidi cation Kinetics Characterization of the solidi cation kinetics within the DC cast AA5182 ingot was car- ried out by performing Di erential Scanning Calorimetry (DSC) measurements on a series of small specimens in a similar location to the specimens for grain size measurement and chemical analysis using a Netzsch STA 449 F3 apparatus. This DSC apparatus consists of two di erent furnaces - (a) SiC furnace operating between 25oC and 1500oC, and (b) Steel furnace operating between  150oC to 1000oC. Both furnaces were used as part of this study in order to achieve various heating and cooling rates, in combination with N2 gas and liquid N2. In this apparatus, small samples between 15 and 25 mg are heated and cooled at a controlled rate in a crucible. The thermocouple attached to the sample carrier 85Figure 6.2: Typical thermal cycle for running solidi cation tests in DSC records the change in temperature during heating and cooling as well as the change in temperature in a reference crucible in order to determine the amount of energy evolved of absorbed during the thermal cycling. This evolution of energy presents indications of phase changes and/or precipitation reactions and thus can provide knowledge of the solidi cation kinetics. The speci c testing procedure used for measuring the solidi cation kinetics of AA5182 was as follows. First, each sample was weighed and then placed into an alumina crucible within the sample carrier of the DSC. Second, the chamber was closed and then evacuated and purged with N2 gas. This process of evacuation and purging was repeated 3 times to remove as much O2 gas as possible. Third, the testing cycle was programmed into the software, requiring the operator to specify the evolution of temperature with time. The aluminum alloy in question, AA5182 has its solidus and liquidus between 500 and 700oC. Moreover, as the interest is in observing the solidi cation kinetics, only the cooling cycle is important and must be properly controlled properly. The samples were heated at a constant rate of 20oC/min to 700oC and the cooled to 400oC at di erent cooling rates. A typical thermal cycle applied to the equipment is shown in  gure 6.2. To ensure that 86the results were reproducible, at least 3 samples from each location were tested using this procedure. Moreover, samples from the same location were also tested at di erent cooling rates. 6.6 Summary Microstructural features, chemical composition and the evolution in fraction solid of an alloy strongly in uence the hot tearing phenomenon in casting. The experimental methodology for grain size measurements, chemical analysis and the determination of solidi cation kinetics of within an AA5182 have been described in this chapter. The experimental results for an as cast AA5182 ingot will be presented and analyzed critically in the following chapter. 87Chapter 7 Microstructural Analysis of an AA5182 DC Cast Ingot - Results and Discussion 7.1 Introduction In the previous chapter, the experimental methodology for analyzing the microstructural features of as-cast AA5182 (grain size, chemical composition, and solidi cation kinetics) was presented. In this chapter, the results from these experiments will be reported. The objective of this chapter is also to discuss and explain the results by comparing them with the theory and related work found in the literature. Finally, we relate the  ndings to the simulation results from chapter 5. 7.2 Grain Size Measurements 5 samples were analyzed, showing the variation in grain size from the centre of the ingot out towards the surface along the centerline of the rolling face. The quantitative measure- ments are shown in table 7.1, with the corresponding micrographs provided in  gure 7.1. As can be seen, the grains are equiaxed dendritic throughout the cross-section, but the grain size does vary considerably. The grains are largest at the centre but gradually 88Figure 7.1: Optical micrographs of samples taken from (a) center (b) 62.5 mm from the center (c) 125 mm from the center (d) 187.5 mm from the center (e) at surface, at 50 magni cation, viewed under cross-polarized light with sensitive tint attachment 89Table 7.1: Average grain size (  d, measured by Je rie’s Method) of samples taken at various distances from the center of the ingot Distance from the centre (mm)  d ( m) S.D.a 0.0 (centre) 514.30 30.84 62.5 394.16 27.09 125.0 257.24 28.98 187.5 257.03 35.14 250.0 (surface) 122.77 402.96 aStandard Deviation decrease in size as the surface is approached. The qualitative observation made from the micrographs are evident in the measurements, i.e. the average grain size (514.30  m) is more than 4 times larger than the value found at the surface (122  m). The decrease in grain size from center to surface can be attributed to the variable cooling conditions experienced throughout the cross section of the ingot. At the surface, the rate of heat removal is high due to the primary (mould) interfacial cooling and secondary cooling by cooling water jets. This e ect diminishes away from the surface, as the rate of heat removal is controlled rather by the rate of heat conduction through the casting body. This conduction rate is in turn controlled by the thermal conductivity ( ) through fully solid, fully liquid as well as through the semi-solid metal. The results presented in table 7.1 and in  gure 7.1 match well qualitatively with the microstructural studies made by various researchers on DC cast products (Erdegren et al. 2012, Nadella et al. 2008a, Suyitno 2005). Suyitno (2005), in his PhD work, observed microstructure of the DC cast billets and measured grain sizes for various compositions of Al-Cu alloys. Micrographs observed at the center of the billet in this work are similar to the ones shown in  gure 7.1. In addition, grain size was reported to increase with increasing distance from the surface and with a decrease in Cu concentration. Nadella et al. (2008a) experimentally measured the grain size of DC cast Al-Mg billets from center to surface. It was found that grain size is maximum at the center of the billet. 90Figure 7.2: Variation of grain size as a function of distance center in a steady state region, obtained from simulation results of case A Interestingly, grain size was found to be lowest in the sub surface region. Similar results were found by Nagaumi (2001) on a porosity and microstructure study of DC cast ingot of Al-4.4%Mg Alloy. Erdegren et al. (2012) arranged experiments in the laboratory to simulate the DC casting process in 6xxx series alloys. Measurements on the samples from these simulated experiments indicated that grain size increases monotonously from surface to center, which conforms well with our measurements. Now, let us compare the microstructural measurements with the simulation results. For comparison, the base case (table 5.1) is selected where variation of grain size as a function of the cooling rate is incorporated. The grain size predictions from this simula- tion are shown in  gure 7.2. In this  gure, horizontal variation of grain size at di erent distances from the centre of the billet is shown. The horizontal line along which the grain sizes were extracted was at the steady stage region at 400 mm height from the bottom block, to match the fact that the experimental samples also came from the steady state region. The  gure shows that the grain size generally decreases from the center to the surface. This is in agreement with the grain size measurements reported in this chap- 91ter. Discrepancies between the simulation and the experimental measurements are most prominent in terms of the location of the maximum and minimum grain sizes. In the simulation, the maximum and minimum grain sizes occur in the area adjacent to the center and in the subsurface region, respectively. Conversely, the measured grain sizes show the maxima and minima at the centre and the surface, respectively. For the grain size measurements, distance between two samples was 62.5 mm. On the other hand, the simulated grain size predictions show minimum grain size at about 50 mm inside the surface. The lack of resolution in the variation of grain size (between 250 and 187.5 mm distance from the center) could be the reason why the minimum grain size is not shown experimentally at the subsurface region. Interestingly, the simulation results agree well with the experimental results found by Nagaumi (2001) and Nadella et al. (2008a) in terms of the location of maximum and minimum grain size. In addition, there is a size di erence between the simulation billet (radius = 160 mm) and the ingot used for these experimental measurements (center to surface distance of 250 mm). The larger center to surface distance in the ingot should have important implications in terms of heat transfer from center to surface during the casting. As heat is only extracted from the surface during casting in the steady state region, a larger distance from the center to surface means heat has to travel a much longer path from center to dissipate into the surface. As the heat transfer is limited by the thermal conductivity of the alloy (same for both ingot and billet), the cooling rate at the centre of the ingot should be much lower for the ingot as compared to the billet during casting. The lower cooling rate at the centre may increase the grain size in this region. This is evident in the results, i.e. very large grains (514  m) are seen experimentally at the centre of the ingot as opposed to that predicted by the simulation of the billet (260  m). The smaller radius of the billet has resulted in a smaller grain size throughout the cross section compared to those of the ingot except at the surface. Furthermore, it seems that the range of grain size in the billet (400  m) is about ten times larger than that of the ingot (40  m). This variation in the range of grain size could be due to two reasons. First, it be attributed the the size 92Table 7.2: Average compositions of major alloying elements in AA5182 with respect to distance from the center Alloying Element (Weight %) Distance from the centre (mm) Mg Mn Cr 0 (centre) 3.445 0.368 0.191 62.5 3.998 0.399 0.178 125.0 4.009 0.396 0.181 187.5 4.113 0.385 0.178 250.0 (surface) 4.032 0.377 0.171 di erence between the ingot and the billet and the resulting change of the heat transfer phenomenon. Second, it could be due to the e ect of grain re nement. As the ingot has been heavily grain re ned during casting, the high cooling rates at the surface activate a huge number of heterogeneous nucleating cites created by the grain re ners and result in smaller grain size at the surface (122  m). The simulation of the billet does not account for any heterogeneous nucleation, and thus have a relatively large grain size at the surface (225  m), and a small di erence between the grain size at the centre and the surface. 7.3 Chemical Analysis A compositional analysis of each of the experimental samples was carried out via SEM - EDS. The major alloying elements of AA5182 are Mg and Mn. Additionally, small amount of Cr (around 0.20%) was reported in the chemical analysis. The summary of chemical analysis from the center to the surface is shown in table 7.2. The chemical analysis of samples taken from surface to center of the ingot revealed that there is signi cant macrosegregation. The macrosegregation of an alloying element in a particular location can be expressed as deviation from the nominal (average) com- position (Nadella et al. 2008b), as shown in equation 7.1. Deviation from the Nominal Composition = [X] [X]nominal [X]nominal (7.1) where [X] is the composition of element X and [X]nominal is the nominal composition of 93Figure 7.3: Distribution of relative concentration of di erent alloying elements as a function of distance from the centre element X in the ingot. Using the data in table 7.2, the graphs in  gure 7.3 are obtained, which show deviation from nominal composition of each alloying element at di erent distances from the centre. Values greater than zero of this deviation indicates ‘posi- tive’ macrosegregation. Conversely, values less than zero indicate ‘negative’ macrosegre- gation. As can be seen from  gure 7.3, Mg has considerable negative macrosegregation at the centre of the ingot typically found in DC cast billets and ingots (Erdegren et al. 2012, Eskin et al. 2004). The centerline segregation can be explained by a phenomenon called the  oating or showering crystals (Nadella et al. 2008b). Small particles of lower solute concentration detach from the  rst solidi ed shell and settle down at the centre causing this centreline macrosegregation . The particles settle since they have a higher density due to the lower Mg content and fall towards the base of the sump. In addition, there is also positive segregation of Mg close to the the chill surface. This phenomenon is most likely due to the presence of liquid richer in solute within the 94interdendritic channels close to the surface during solidi cation (Erdegren et al. 2012). Due to solidi cation shrinkage, liquid of higher concentration away from the surface is sucked back into these channels and this liquid solidi es with higher concentration of Mg. This results in a positive segregation of Mg at and close to the chill surface of the ingot. Mn shows negative segregation at the centerline, which could also be explained the theory of  oating crystals. Furthermore, positive segregation of Mn between the center and the surface is also reported similar to Mg. But, unlike Mg, Mn has negative seg- regation at the surface of the ingot, which is in contrary to the studies made by Eskin et al. (2004), Nadella et al. (2008b). One interesting work, which is on the contrary to our  ndings was done by Dons et al. (1999). In this work on DC cast Al-Si alloys showed that Mn somehow resists macrosegregation. Finally, the third element, Cr, shows a pos- itive segregation at the centre, no segregation at the middle and negative segregation at the surface of the ingot. Positive segregation of Cr could be due to the accumulation of intermetallic compounds containing Cr at the center of the ingot, and a consequent depletion of Cr rich particles from the surface. The process model for DC casting billet described in chapter 4 is a thermomechanical model, and does not take macrosegregation of the ingot into account. Thus, it is not possible to compare the macrosegregation results with the model predictions. 7.4 Solidi cation Kinetics Solidi cation tests with the samples of alloy AA5182 were carried out in a di erential scanning calorimeter (DSC). The output from DSC gives a curve of change in energy (amount of energy absorbed/ evolved) during heating/cooling as a function of temper- ature. These curves were analyzed in the software ‘NETZCH Proteus’, version 5 (com- panion to the NETZCH DTA unit). The region of interest of the solidi cation curves is between the solidus and liquidus temperatures. From a typical curve given by the DSC, 95Figure 7.4: Solidi cation curve of a sample of AA5182 from the DC cast ingot piece, cooling rate = 10oC/min the liquidus and the solidi cation reactions are easily identi able as sharp extremities in this curve. The alloy being investigated (AA5182) goes through the following reactions during solidi cation (B ackerud et al. 1990):  Start of solidi cation and formation of  -Al (Tliq)  R1 : Start of eutectic reaction : Liq !  -Al + Al6(FeMn)  R2 : Precipitation of Mg2Si : Liq ! Al + Mg2Si  R3 : Complex eutectic precipitation : Liq ! Al + Al3Fe + Mg2Si + Al8Mg5  End of solidi cation (Tsol) A typical solidi cation curve for an ingot sample obtained from DSC is shown in  gure 7.4. Note that the DTA signal is negative when there is an exothermic reaction (energy is released). Because the solidi cation phenomenon is an exothermic reaction, so the curve takes a downward path. The spikes in the curve are indicative of di erent solidi cation/precipitation reactions occurring at particular temperatures. Comparing 96Figure 7.5: DSC curves of samples samples of as cast AA5182 taken from di erent locations of the ingot, cooling rate = 10oC/min the sequence of reactions mentioned above with the extremities observed in this curve, the liquidus point, the eutectic point and the point of Mg2Si precipitation can be easily identi ed as shown in the  gure. But the solidus can not be identi ed easily. To estimate the solidus point, a third order polynomial baseline was drawn with the points well above the liquidus point and well below the solidus point from the curve. The intersection point of this baseline with this curve is a good estimate of the solidus point (B ackerud and Tamminen 1986), as shown in the  gure. 7.4.1 E ect of Location From the ingot described in chapter 6, 5 samples were taken between the centerline and the chill-surface for this study. DSC solidi cation tests were then run with these samples. Some of the results from these tests are summarized in  gure 7.5. It is clear from the  gure that the solidi cation behavior of the samples of the three positions : center, middle and the surface are di erent. There is a slight variation in liquidus, eutectic and precipitation reaction points due to variation in position. As the distance from the surface increases, all these points shift to lower temperatures, although there is virtually no di erence of 97Figure 7.6: DSC curves of samples samples of as cast AA5182 taken from di erent locations of the ingot in the range of 500 to 575oC, cooling rate = 10oC/min Figure 7.7: Solidi cation path of samples of as cast AA5182 taken from di erent locations of the ingot, cooling rate = 10oC/min 98Table 7.3: Comparison of averaged solidus, luquidus, and solidi cation reaction temperatures of as cast AA5182, experimental values correspond to a cooling rate of 10oC/min (L = Liquidus, S = Solidus, the standard deviation for each data point is shown in the parenthesis) Source L (oC) R1 (oC) R2 (oC) R3 (oC) S (oC) Exp. (Surface) 636.67(0.57) N/A 591.17 (0.76) 557.67 (1.53) 514.67 (1.52) Exp. (Middle) 636.33 (1.52) N/A 591.25 (1.5) 561.33 (1.4) 509.90 (2.09) Exp. (Centre) 634.87 (1.57) N/A 592.10 (2.32) 564.5 (1) 508.33 (1.42) Ref.1a 637 623 582 560 536 Ref.2b 632 621 586 557 470 Ref.3c 624 N/A 587 557 508 aArnberg et al. (1996),Cooling rate = 18 K/min bB ackerud et al. (1990), Cooling rate = 18 K/min cThompson et al. (2004), Cooling rate = 30 K/min the solidi cation curves for the ‘middle’ and the ‘center’ samples. The liquidus, solidus, the solidi cation reactions (R1, R2, R3) along with their range of variation within the same location are listed in table 7.3. This table also include the literature values of these points from di erent sources for the sake of comparison. As can be seen from the table, the points are reproducible, with the maximum standard deviation of 2.32. However, the R1 reaction could not be identi ed in the solidi cation curves obtained from DSC. The liqudus and the R2 point seem to be relatively invariant of the position. But R3 and solidus points vary with position. R3 temperature increases slightly from surface to center, and solidus point decreases considerably from as the distance from surface increases. The decrease in solidus temperature could be due to high negative macrosegregation of Mg and Mn in the center, and positive segregation of Mg at the surface. The change in solidus temperature with respect to position could have important in uence on the formation of hot tears in DC casting, since it is believed that hot tears form in the last stage of solidi cation at temperatures close to solidus. Moreover, there is a slight bump in the curve for the ‘middle’ sample at around 530oC, which is reproducible, and absent in samples from center/surface. This is not clear from  gure 7.5, so the DSC curves for a narrower range is shown in  gure 7.6, and the arrow in 99Figure 7.8: DSC curves of samples of as cast AA5182 taken from same location of the ingot tested at 2 cooling rates, 10 and 20oC/min. this  gure indicates the bump. This bump occurs at the last stage of solidi cation, and could have some in uence on hot tear formation. Another noticeable di erence among these curves is the area under the curve. This area under the curve is very important, since it is related to the evolution of fraction solid with temperature. Volume fraction solid vs temperature curves have been extracted from these solidi cation kinetics curves, as shown in  gure 7.7. There is a clear di erence in evolution of fraction solid at di erent distances from the center. The solidi cation path of the sample taken from center and the middle are almost identical, owning to similar solidi cation curves, while that of the sample at the surface is quite di erent. 7.4.2 E ect of Cooling Rate Samples taken from the same location of the ingot were subjected to di erent cooling rates. The solidi cation curves for di erent cooling rates of samples taken from the same location showed interesting variations. An example is shown in  gure 7.8. The liquidus, solidus, and reaction temperatures for these two cooling rates have been summarized in 100Figure 7.9: Solidi cation path of samples of as cast AA5182 taken from same lo- cation of the ingot tested at 2 cooling rates, 10 and 20oC/min Table 7.4: Comparison of solidus, liquidus, and solidi cation reaction temperatures of as cast AA5182 between literature and experimental values in terms of cool- ing rate. (CR = Cooling Rate, L = Liquidus, S = Solidus, Ref.1=B ackerud et al. (1990)) Source CR (K/min) L (oC) R2 (oC) R3 (oC) S (oC) Exp. 10 636.67 (0.57) 591.17 (0.76) 557.67 (1.53) 514.67 (1.52) Exp. 20 637.17 (1.05) 590.33 (1.53) 556 (0.5) 504.83 (1.04) Ref.1 18 632 586 557 470 Ref.1 54 632 584-581 556 470 table 7.4. This table also includes the temperature of each of these points found in the literature for 2 di erent cooling rates. First, the liquidus points occur almost at the same temperature for both cooling rates, but the reaction and solidus temperatures are shifted towards towards lower temperatures for a higher (20oC/min) cooling rate. This phenomenon can be explained by the well known theory that the phase diagram becomes depressed in terms of temperature at higher cooling rates, resulting in lowering of solidus, and other reaction temperatures. Comparing the the variation in solidus and liquidus temperatures from the experiments with the literature value (B ackerud et al. 1990), we 101can see that literature values of these temperatures are virtually invariant of cooling rate, while our experimental values show signi cant variations. This could be due to the fact that the literature values presented in the table deal with high cooling rates while the experiments conducted here deal with relatively low cooling rates. At these high values of cooling rates, the reaction temperatures may become insensitive to cooling rates, while at low temperature they may still be sensitive to cooling rate variation. Another main di erence between the DSC curves in  gure 7.8 is in the amount of energy released during solidi cation (i.e. area under the curve). Consequently, the solidi cation path for these two samples become very di erent, as shown in  gure 7.9. This will have important implications for hot tearing. 7.5 Summary The experimental results of grain size measurements, chemical analysis and solidi cation kinetics of as cast AA5182 have been reported. The grain size is found to increase substantially from surface to centre of the ingot. The grain size measurements are also compared with simulation results. There is qualitative agreement between trends in the variation between the predicted and measured grain size from centre to surface. The chemical analysis shows that there is substantial macrosegregation of Mg, Mn and Cr from centre to surface. Mg shows negative segregation at the centre and positive segregation at the surface. Mn shows negative segregation both at centre and surface, and positive segregation elsewhere. Cr shows segregation trends exactly opposite to Mg. Solidi cation kinetics experiments revealed that both location of the sample and cooling rate in uence the liquidus, solidus, reaction temperatures, as well as the evolution in fraction solid of as cast AA5182. Solidus temperature of as cast AA5182 decreases (1) with increasing cooling rates for samples from the same location; and (2) with the increase in distance from the surface of the ingot for samples from di erent location. The macrosegregation phenomenon seen here should in uence the semi-solid strength, because the strength of the solid network should vary with composition. This could alter the hot tearing behavior 102of an alloy as a function of position. Moreover, the di erence in solidi cation kinetics at di erent positions of the ingot in uences the evolution in fraction solid as a function of temperature. This means that the critical points such as the solidus, liquidus and the coalescence temperature vary as a function of cooling rate and position. These may also alter the mechanical behaviour of the mush, and consequently can revise the hot tearing susceptibility. 103Chapter 8 Conclusion and Perspectives 8.1 Conclusion Hot tearing is known to occur in mushy alloys under strain, when the network of solid grains is not fully percolated and feeding by the intergranular liquid is di cult. Even though the general context for the formation of this defect is known, quantitative theories are di cult to formulate and their predictive capability remains limited. The problem of hot tearing is very complex because numerous physical phenomena come into play and interact with each other. Moreover, the properties of the mushy alloys are di cult to measure and model accurately. In addition to this, the geometry of the casting and boundary conditions that it experiences may become quite complicated to describe. For all of these reasons, assessing the problem at hand is only possible provided e cient nu- merical modeling tools are available. Semi-continuous direct-chill (DC) casting of aluminium alloys su ers frequently from the hot tearing defect. This phenomenon takes place in the mushy state (i.e., at solid fractions, gs, lower than unity). In order to solve this problem, research moved towards the development of models for the prediction of the hot cracking sensitivity of any kind of alloy under given casting conditions. The current project involves the study of hot tearing during direct-chill (DC) casting of aluminum alloy AA5182 with respect to mi- 104crostructural features and casting parameters. Hot tears are believed to occur in the semi-solid at high fraction solids during solidi cation. So, for a thermomechanical pro- cess model of DC casting to have predictive capabilities in terms of hot tear formation, it is very important to incorporate a robust description of semi-solid behaviour of the alloy. In this work, a previously developed axisymmetric DC casting thermomechancial model for round billets was improved by incorporating a semi-solid constitutive law for AA5182 which includes the microstructural features of the semi-solid body. Now-a-days, the DC cast alloys are heavily grain re ned, and thus only the cooling rate has a bearing on determination of grain size within the casting. The process model for this project also includes the variation of grain size throughout the casting due to di erential cooling con- ditions experienced by the casting body. The underlying assumptions and simpli cations of the model are listed below:  The model only considers nucleate boiling heat transfer regime of secondary cooling by the spray water jet. It does not take into account the  lm boiling regime of the cooling, where the heat transfer coe cient drops drastically.  A  xed heat transfer rate at the billet-bottom block interface was assumed in the model.  Fluid  ow is ignored in this model. To account for the increased heat transfer by convection in the liquid, the e ective thermal conductivity is increased arti cially in the semi-solid and liquid state.  A low constant yield stress is assumed above coalescence temperature to avoid false strain accumulation in the slurry.  For the variable grain size case, the grain size is only a function of the average cooling rate between the liquidus and the coalescence temperature. Other factors of grain re nement are ignored.  An invariant solidi cation path is used for the model. 105 The e ects of macrosegregation are ignored. Using this DC casting process model, numerous simulations were run varying mi- crostructural features and process parameters. A relative hot tearing criterion called the ‘hot tearing strain’ was proposed, which was calculated using the stress-strain predic- tions from the model. For observing the e ect of grain size, coalescence temperature, and casting speed, 5 di erent scenarios (see table 5.1) were selected. The temperature, stress and strain  elds along with the hot tearing strain were prepared along both horizontal direction (at various billet heights) and vertical direction (along the centreline). Through the temperature  elds in the vertical direction along the centreline and the surface, steady state and start up regions were identi ed. Along the centreline, the steady state was achieved at 400 mm from the bottom block, while at the surface it was at around 100 mm of casting. The steady state was also demonstrated mechanically, through the observation of variation of hoop-stress at fs = 0.98 along the centreline. Note that, as with the temperature  eld, the hoop stress  eld also becomes invariant of location in the steady state region. The variation of hot tearing strain along the horizontal and vertical directions revealed that for round billets, hot tears are most likely to occur close to the centreline and and to the bottom block in the start up stage of the DC casting process. In addition, the area close to the surface and the bottom block is also found to be susceptible to hot tearing, but to a lesser extent compared to the area close to the centreline. Once the startup state is over, the hot tearing susceptibility diminishes into the steady state region. When the relative hot tearing susceptibility for various grain sizes, coalescence tem- peratures and casting speeds were compared, the following conclusions could be made: 1. Hot tearing susceptibility is shown to vary with grain size. The hot tearing suscepti- bility generally decreases with decreasing grain size, owing to the higher strength of the casting body in the semi-solid region for smaller grains. The lowest hot tearing susceptibility is shown for the variable grain size simulation (Case A). But, when 106the lowest grain size is approached (75  m), the hot tearing susceptibility actually increases. 2. The hot tearing susceptibility is very sensitive to casting speed. Decreasing casting speed decreases the hot tearing susceptibility, provided that the secondary cooling by water jet remains in the nucleate boiling regime. If the heat transfer mode shifts to the  lm boiling region, the heat transfer coe cient is drastically reduced and severe hot tears may form. 3. The choice of mechanical coalescence temperature is a critical factor when assessing hot tearing susceptibility. For a lower assumed coalescence temperature, the hot tearing susceptibility is drastically increased , and vice versa. Thus, for a good semi- solid stress-strain predictions, it is critical to choose the appropriate coalescence temperature. In addition to simulating the DC casting process, grain size measurements, chemical analysis, and DSC experiments were carried out on the samples collected from an as cast (DC cast) ingot of AA5182. The grain size measurements from the samples taken along the centerline of the rolling face indicated that the grain size decreases steadily from centre to surface, owing to the di erent cooling conditions experienced across the cross-section of the ingot. The chemical analysis of the samples revealed that there is considerable macrosegregation of Mg and Mn from center to surface of the ingot. The DSC solidi cation kinetics experiments on the smaples of as cast AA5182 demonstrated that the solidus, liquidus and the reaction temperatures vary both as a function of the cooling rate and distance from the centre of the ingot. By comparing the experimental results from the as cast AA5182 with the predictions and underlying assumptions of the simulation, the following conclusions could be made : 1. The measured grain size from as cast AA5182 and the predicted grain size from the simulation of round billets agree qualitatively. The larger size of the ingot (250 107mm) as compared to the billet (radius = 160 mm), induced larger grain sizes and and higher variation of grain size across the grain sizes. This comparison validates, at least qualitatively the assumption of variation of grain sizes based on the cooling rate in the semi-solid region. 2. There is a considerable amount of macrosegregation of alloying elements along the cross section of the casting. The model does not account for the this macrosegre- gation. The amount of alloying elements locally determine the semi-solid strength. Thus, if macrosegregation is present in the casting, the strength in the semi-solid region would vary as a function of position. This could alter the hot tearing sus- ceptibility of the cast structure. 3. The solidi cation kinetics tests of the samples reveals that there is considerable dif- ference in solidus, liquidus and solidi cation reaction temperatures within the ingot as a function of both the location and the cooling rate. Although the process model includes cooling rate induced variation of grain size, it assumes the solidi cation path (fs vs. Temp) to be invariant of the cooling rate and also composition (i.e. location). The evolution in fraction solid is one of the most important factors in determining the semi-solid mechanical behaviour and thus most of the constitutive laws include the fraction solid (fs) term. The temperatures at which solidus and liquidus occur are factors in determining the semi-solid mechanical behaviour, as it is a strong function of temperature. Therefore, any variation in the solidi cation path, and the liquidus and solidus temperatures will strongly in uence the strength of the semi-solid mush and thus have important implications on the hot tearing susceptibility. 8.2 Perspectives From the above discussion, it is clear that the process model is capable of capturing some aspects of solidi cation (such as grain size variation). The model is also able to predict 108hot tearing susceptibility in DC casting in terms of microstructural features and casting parameters with relative accuracy. Having said that, the model is rather simplistic is some aspects, ignoring factors that e ect the semi-solid mechanical behaviour such as macrosegregation and the variation in solidi cation kinetics. Another drawback of this model is that it does not account for the  lm boing regime of heat transfer during cooling by water jets. Thus, for this model to be more accurate, the following modi cations could be applied to the model: 1. A macrosegregation model could be included into the model to account for the variation in alloy properties with composition. 2. A more accurate model for variable grain size could be included. 3. A set of solidi cation paths for the alloy which include the e ects of grain size, chemical composition and cooling rate e ects could be incorporated. 109References Alankar, A. and Wells, M.A. 2010. 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