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Strain evolution during hot tearing in aluminium alloys Mitchell, Jason Brian 2009

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STRAIN EVOLUTION DURING HOT TEARING IN ALUMINIUM ALLOYS  by  JASON BRIAN MITCHELL B.Eng.(Hon.), Sheffield Hallam University, UK, 1998 M.A.Sc., The University of British Columbia, Canada, 2002  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies (Materials Engineering)  The University of British Columbia (Vancouver)  November 2009  ©Jason Brian Mitchell, 2009  Abstract  Hot tearing refers to cracks that frequently occur within the mushy zone during cooling from the liquid to solid state during shape and ingot casting. Both ferrous and non-ferrous alloys may be affected, and there is some evidence to suggest those with long freezing ranges are more susceptible. Due to the nature of this defect the economic impact is often significant and can result in an immediate productivity loss. It is therefore important for industry to be able to better predict the susceptibility of various alloys to hot tearing.  Various theories have been proposed and several different types of experimental methods have been developed to interpret the properties of alloys in the semi-solid state. However, many of these techniques do not produce good quantitative data (i.e. strain) that can be used to calibrate a thermal-mechanical computer simulation of casting. Existing experimental methods often measure strain indirectly by means of a load train frozen into the end of the casting. However, local strain at the hot tear initiation site would be more valuable for computer model calibration. Clearly, the use of traditional measurement techniques, such as strain gauges, is not a viable option and therefore an alternative was investigated.  In this work the use of digital image correlation to determine the evolution of strain and strain at the onset of localisation resulting in a hot tear has been evaluated. Data has been determined for aluminium alloys AA6111, AA3104, CA32118, Al-0.5% wt pct Cu under slow cooling conditions and AA3003 under directional solidification using a water cooled copper chill.  A new hot tearing experiment has been developed which localises strain to promote hot tearing to occur in only one region of the casting and is cooled by directional solidification. Images of this region were captured during solidification via a glass window embedded in the mould of the experiment. These images were correlated with  ii  each other to determine strain accumulated during hot tearing using 3rd party commercial digital image correlation software.  iii  Table of Contents Abstract.............................................................................................................................. ii Table of Contents ............................................................................................................. iv List of Tables ................................................................................................................... vii List of Figures................................................................................................................. viii Acknowledgments .......................................................................................................... xiii Chapter 1 – Introduction.................................................................................................. 1 1.1  An overview of the hot tearing problem ............................................................. 1  Chapter 2 – Literature review ......................................................................................... 4 2.1  Hot tearing theory and associated criteria of susceptibility ................................ 4  2.2  Experimental methods for determining susceptibility of alloys to hot tearing . 14  2.2.1  Ring casting .......................................................................................... 14  2.2.2  “Dogbone” or constrained solidification tests ...................................... 15  2.2.3  “Cold finger” testing ............................................................................. 22  2.2.4  Tensile testing ....................................................................................... 24  2.2.5  Tensile testing to determine properties in the semi-solid state ............. 25  Chapter 3 – Scope & Objectives .................................................................................... 30 3.1  Industrial scope ................................................................................................. 30  3.2  Thesis objectives ............................................................................................... 30  Chapter 4 – Observation of Hot Tearing During Solidification ................................. 32 4.1  Introduction....................................................................................................... 32  Chapter 5 – Results of Hot Tearing Observation During Solidification.................... 39 5.1  Introduction....................................................................................................... 39  5.2  Experimental results and discussion ................................................................. 39  5.3  Chapter summary .............................................................................................. 53  Chapter 6 – Development of a New Hot Tearing Experiment.................................... 55 6.1  Introduction....................................................................................................... 55  6.2  Directionally solidified ring casting.................................................................. 56  6.3  Restrained casting development ....................................................................... 60  6.3.1  Stage 1 – Restrained casting with stress raiser ..................................... 60  6.3.2 Stage 2 – Improving the effectiveness of the hot spot and bottom pouring to eliminate shrinkage pipe .......................................................................... 67  iv  6.3.3  Stage 3 – Implementation of glass viewing window ............................ 75  6.3.4  Modifications to the casting pouring inlet ............................................ 77  6.4  Experimental procedure .................................................................................... 81  6.4.1  Mould preparation................................................................................. 81  6.4.2  Alloy preparation .................................................................................. 81  6.4.3  Digital image correlation system set-up and calibration....................... 81  6.4.4  Thermocouples...................................................................................... 84  6.4.5  Mould preheat ....................................................................................... 85  6.4.6  Melt pouring and argon purge............................................................... 86  Chapter 7 – UBC Experimental Results & Discussion................................................ 87 7.1  Introduction....................................................................................................... 87  7.2  Alloy composition analysis............................................................................... 87  7.3  Thermo-Calc™ fraction solid predictions.......................................................... 88  7.4  Image and field of view .................................................................................... 89  7.5  Thermocouple results........................................................................................ 93  7.6  Thermal model development ............................................................................ 94  7.6.1  Thermal model ...................................................................................... 96  7.6.2  Model inputs ......................................................................................... 97  7.6.3  Thermal model boundary conditions .................................................... 99  7.6.4  Correction of uneven cooling.............................................................. 101  7.6.5  Thermal model predictions ................................................................. 101  7.6.6  Results................................................................................................. 104  7.7  Digital image correlation using the LaVison™ system .................................. 106  7.7.1  Correlation results for test A1............................................................. 108  7.7.2  Field size comparison ......................................................................... 111  7.7.3  Strain field mapping............................................................................ 112  7.7.4  Virtual strain gauge results ................................................................. 116  7.7.5  Local strain at the hot tear location..................................................... 119  7.7.6  Localisation of strain across the tear using previous approach........... 122  7.7.7  Strain rate comparison ........................................................................ 125  7.7.8  Alternative approach to single-site localisation at the tear ................. 125  7.7.9  Local strain at the hot tear and fraction solid development ................ 131  7.8  Summary ......................................................................................................... 134 v  Chapter 8 – Conclusions............................................................................................... 135 8.1  Future work ..................................................................................................... 137  References ...................................................................................................................... 139 Appendix A – UBC Experimental Set-up Images...................................................... 142 Appendix B – Subroutine for Chill/Casting Heat Transfer ...................................... 144 Appendix C – Digital Image Correlation.................................................................... 146  vi  List of Tables  Table 4-1: Test alloy compositions wt%, with the remainder attributed to Aluminium. . 34 Table 5-1: Summary of background strains before localisation and maximum strains at which tear opens. .............................................................................................................. 50 Table 7-1: Alloying elements present in A3003. .............................................................. 87 Table 7-2: Thermo-physical properties of AA3003 [42, 43] ................................................ 98 Table 7-3: Local strain at the hot tear at a time when it becomes visible...................... 122 Table 7-4: Summary of strains at the onset of localisation............................................. 125 Table 7-5: Fraction solid and localisation strain for test A1........................................... 132  vii  List of Figures  Figure 1-1: Filled hot tear in Al-10Cu alloy (Spittle and Cushway 1983 [4]) taken from Campbell [5]......................................................................................................................... 1 Figure 2-1: As fraction solid increases the liquid inflow becomes restricted until isolated pockets of liquid exist [19].................................................................................................... 5 Figure 2-2: Schematic showing equiaxed dendritic solidification with various hot tearing phenomena (adapted from Refs. [15] and [21]). ..................................................................... 8 Figure 2-3: Schematic of formation of a hot tear in between columnar dendrites as a result of localisedstrain transmitted by coherent dendrites below. Graph of pressure of interdendritic liquid shown. [19] ......................................................................................... 12 Figure 2-4: Ring Moulding Technique [24], figure adapted from [9]. Top figure shows the mould, the bottom shows the casting. ............................................................................... 15 Figure 2-5: Schematic of water cooled dogbone moulding test rig. Adapted from [25]. ... 16 Figure 2-6: Vertical section through closed dogbone mould, Spittle and Cushway, 1981. Adapted from [4]. ............................................................................................................... 18 Figure 2-7: Constrained solidification test, adapted from Instone et al [28]. ..................... 19 Figure 2-8: Bottom half of hot tearing mould, casting dimensions in mm. (adapated from Paray et al) [3]. ................................................................................................................... 20 Figure 2-9: Hot tearing rig, from Olivier et. al. 2008 [30].................................................. 22 Figure 2-10: "Cold Finger" hot cracking test, adapted from Warrington & McCartney, 1991[8]. .............................................................................................................................. 23 Figure 2-11: Langlais and Gruzleski [2] solidification unit before and after 90° rotation. 25 Figure 4-1: Modification of Rig for Observation of Hot Tearing Initiation [29]................ 33 Figure 4-2: Rig for Observation of Hot Tearing Initiation showing locations of thermocouples during the UBC/UQ collaboration. .......................................................... 34 Figure 4-3: Rig for Observation of Hot Tearing Initiation showing locations of thermocouples during the UBC/UQ collaboration ........................................................... 36 Figure 4-4: Rig for Observation of Hot Tearing Initiation showing the camera location during the UBC/UQ collaboration. ................................................................................... 36 Figure 4-5: Polished aluminium mirror showing reflection of glass window and casting 37 Figure 5-1: Sample image showing a visible hot tear, taken during solidification of Al0.5% Cu alloy. Dashed lines refer to area in which contours were taken on Figure 5-2. . 40 Figure 5-2: Image correlation strain contours for Al-0.5% Cu alloy. Notice the coalescence of strain fields on the images for 0.399 s and 0.665 s. Images shown relate to dashed area in Figure 5-1. ................................................................................................. 40  viii  Figure 5-3: (a) Specimen surface photograph and (b) image correlation strain contour and for Al-0.5%Cu alloy................................................................................................... 42 Figure 5-4: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macro-etched specimen surface for AA6111a. ................................................................. 43 Figure 5-5: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macro-etched specimen surface for AA6111b.................................................................. 43 Figure 5-6: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macro-etched specimen surface for AA3104.................................................................... 44 Figure 5-7: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macro-etched specimen surface for AA3128.................................................................... 44 Figure 5-8: Strain vs. Distance across the hot tear for Al-0.5%Cu, showing the fluctuation in strain and subsequent localisation of strain over time (from reference image). ........... 46 Figure 5-9: Strain vs. Distance across the hot tear for AA6111b, showing the fluctuation in strain and subsequent localisation of strain over time (from reference image). ........... 47 Figure 5-10: Strain vs. Distance across the hot tear for AA6111a. .................................. 48 Figure 5-11: Strain vs. Distance across the hot tear for AA3104. .................................... 49 Figure 5-12: Strain vs. Distance across the hot tear for CA3128. .................................... 49 Figure 5-13: Evolution of temperature with time for all alloys, showing similar cooling rates for all alloys.............................................................................................................. 52 Figure 5-14: Evolution of strain with time for all alloys (including linear approximation of strain rate). .................................................................................................................... 52 Figure 6-1: External schematic of experimental set-up for large ring casting................. 58 Figure 6-2: Schematic cross-section of experimental set-up for large ring casting.......... 58 Figure 6-3: Example castings from large ring casting experiments. Large hot tears are not suitable for image correlation experiments due to A) Asymmetric strain build up around the core which causes tear to split paths at the upper and lower sections of the casting. B) Variable surface finish around the area of the hot tear. C) Hot tear would often deviate from the hot spot. .............................................................................................................. 59 Figure 6-4: S.E.M micrograph of hot tear surface from preliminary ring casting experiment......................................................................................................................... 60 Figure 6-5: First stage of restrained bar casting, showing various parts of the mould. ... 62 Figure 6-6: Restrained bar casting showing a schematic of the steel stress raiser. ......... 62 Figure 6-7: Example 1 of restrained bar casting carried out with an N-17 stress raiser.. 64 Figure 6-8: Example 2 of restrained bar casting carried out with an N-17 stress raiser.. 65 Figure 6-9: Example of restrained bar casting carried out with a stainless steel stress raiser.................................................................................................................................. 66  ix  Figure 6-10: Schematic of modified casting, showing the positioning of the ceramic insulation........................................................................................................................... 67 Figure 6-11: Example of restrained bar casting carried out with a ceramic paper strip to promote a hot spot in the centre of the casting. ................................................................ 70 Figure 6-12: Example of restrained bar casting carried out with a ceramic paper strip to promote a hot spot in the centre of the casting. ................................................................ 71 Figure 6-13: Example of restrained bar casting carried out with bottom filling. ............ 72 Figure 6-14: Example of restrained bar casting carried out with bottom filling and a ceramic paper strip to promote a hot spot in the centre of the casting.............................. 73 Figure 6-15: Example of restrained bar casting carried out with bottom filling but without ceramic fibre insulation at the hot spot................................................................ 74 Figure 6-16: Schematic of final experimental set-up, N.B. the steel front panel has been reversed to better indicate how the glass is fitted into the panel. ..................................... 75 Figure 6-17: Press fit of borosilicate glass into the front panel of the mould using ceramic fibre paper to provide a seal. The surface shown is in contact with the casting. .............. 76 Figure 6-18: Photographs of successful bar test A1 showing A) pouring modification to direct metal flow away from the centre of the casting and away from the glass window, B) unwanted surface texture from filling directed away from centre of casting and C) the surface impression caused by the glass window in front of the hot tear........................... 78 Figure 6-19: Photograph of the centre of casting A1, indicating the shrinkage pipe caused by feeding problems (A) and also the impression left by the glass (B) on the front of the casting. The height and positioning of the correlation image is also shown in the “front” picture. .............................................................................................................................. 80 Figure 6-20: Image capture of the LaVision Calibration card. The user defines three points and the software detects the remaining points and reports a statistical error......... 83 Figure 6-21: Schematic of test set-up showing the various data acquisition equipment. . 83 Figure 6-22: Schematic of thermocouple locations in the back face of the casting.......... 84 Figure 6-23: Map of thermocouple locations in the back face of the casting................... 85 Figure 7-1: Predicted fraction solid curve of AA3003 of given composition. ................. 88 Figure 7-2: Sample images captured during the solidification of test A1. Image A) shows the mould full of liquid metal before the pull away front moves into view. Image B) shows the pull away front 10 seconds later. The chill is located at the top of these images. ........................................................................................................................................... 90 Figure 7-3: Further images of test A1 showing further development of the tear. A) Shows a flatting out of the solidification front and extension of the tear. B) Shows the solidification front passing out of the field of view. ......................................................... 91 Figure 7-4: (a) Distance of solidification front from chill versus time, (b) front velocity versus distance from chill for test A1 ............................................................................... 92 Figure 7-5: Temperature vs. Time data for test A1 – AA3003......................................... 94 x  Figure 7-6: Evolution of temperature for test A1 for the first three thermocouples; TC0, TC1, TC2. ......................................................................................................................... 95 Figure 7-7: Model mesh of casting and chill. ................................................................... 97 Figure 7-8: Shows the partitioning of the model to account for the simulation of the ceramic fibre insulation..................................................................................................... 98 Figure 7-9: Heat transfer across mould/casting and glass/casting interfaces to account for gap formation during solidification (same boundary condition used for both interfaces). ......................................................................................................................................... 100 Figure 7-10: Heat transfer across chill/casting interface to account for gap formation during solidification. ....................................................................................................... 100 Figure 7-11: Thermal model predictions vs. experimental data for centre nodes in the casting. ............................................................................................................................ 102 Figure 7-12: Thermal model predictions versus experimental data shifted by 4s. ......... 102 Figure 7-13: Thermal model predictions for face nodes at the positions where the point strain measurements were acquired. ............................................................................... 104 Figure 7-14: Predicted fraction solid data for face nodes at the positions where the point strain measurements were acquired. ............................................................................... 105 Figure 7-15: Vector grid output after A, one frame and B, final correlation frame for test A1.................................................................................................................................... 107 Figure 7-16: The first image frame of test A1 – showing the thermocouple positions. As the camera was mounted upside down during the test, the top of the image lies closest to the chill............................................................................................................................ 109 Figure 7-17: The last image in test A1 – where the tear has opened throughout the field of view. Thermocouple positions have been marked as well as the locations of virtual 7mm strain gauges.................................................................................................................... 110 Figure 7-18: Schematic of displacement line movement during bulk contraction of the alloy. Case (A) movement due to bulk contraction is tracked by the software; case (B) tear opening displacement may be exaggerated if the displacement line is sheared during solidification. .................................................................................................................. 111 Figure 7-19: Comparison of two window sizes for a 4mm virtual strain gauge, 16mm from the chill................................................................................................................... 112 Figure 7-20: Development of tear, strain and pull away front during test A1. Note: Arrow indicates extent of progress of pull-away front in window............................................. 114 Figure 7-21: Further development of tear, strain and pull away front during test A1. Note: Arrow indicates extent of progress of pull-away front in window. ................................ 115 Figure 7-22: Final development of tear, strain and pull away front during test A1. ...... 116 Figure 7-23: Normalised and rotated plot of test A1 – showing the position of thermocouples, locations of 7 mm strain correlations and the window position............ 117 Figure 7-24: Strain vs. time for 2, 4 and 7mm virtual strain gauge lengths, test A1...... 118 xi  Figure 7-25: Infinitesimal 1D Strain............................................................................... 119 Figure 7-26: Development of local strain at the hot tear at increasing distances from the chill. Also demarcated is the time at which the tear is visible to the eye. ...................... 121 Figure 7-27: Strain vs. Distance across the tear at various distances from the chill....... 124 Figure 7-28: Evolution of strain with time. .................................................................... 126 Figure 7-29: Strain accumulation at, and in the region of the hot tear localisation site at various distances from the chill ...................................................................................... 128 Figure 7-30: Single-site localisation strain at various distances from the chill .............. 129 Figure 7-31: Plot of predicted thermal gradient and velocity at the solidus temperature (640ºC) versus distance from the chill for the locations at which strain was measured on the surface of the casting................................................................................................. 129 Figure 7-32: Local strain at the hot tear versus fraction solid based on thermal model. 133 Figure 8-1: Complete casting setup showing water cooling. .......................................... 142 Figure 8-2: Interior of mould showing thermocouple locations relative to the chill surface, casting restraining bolts and ceramic fibre insulation required to create the hot-spot in the centre of the casting. ....................................................................................................... 142 Figure 8-3: Interior of the mould showing the steel insert modification which was necessary to divert incoming liquid metal away from the glass during pouring. ........... 143 Figure 8-4: Rear of the mould showing thermocouple connector placement. ................ 143 Figure 8-5: Tracking of point on a deforming surface over time, from t to t″................ 146 Figure 8-6: Tracking the movement of pixels as a group, usually called a window or subset. The associated displacement is shown as d. ....................................................... 147 Figure 8-7: Example of greyscale interpretation in digital image correlation. White pixels are registered as 100 and black as 0, to form a matrix of natural integers...................... 148 Figure 8-8: New greyscale values are recorded after deformation, these are stored in memory. .......................................................................................................................... 148 Figure 8-9: Schematic of greyscale values before and after motion with a 5x5 subset neighbourhood defined. A correlation algorithm is required to determine the new position of the subset. ................................................................................................................... 149  xii  Acknowledgments  First and foremost I would like to thank my supervisor Dr. Steven Cockcroft for his guidance during the course of this project. Without his inexhaustible academic, moral and financial support I would certainly not have been able to complete this work or undertake the amazing experience of carrying out research abroad in Australia.  I wish to thank Dr. Daan Maijer for his help in editing this thesis and his support in all things related to computer modelling of my work, his knowledge has been invaluable. Throughout the years I have constructed several different types of experiment which have all been built by the expertise of Mr. Ross McLeod, Mr. Carl Ng and Mr. David Torok, I thank them for their sterling efforts.  I am grateful to Rio-Tinto Alcan for the materials supplied to this research programme; and Auto 21, a national research initiative supported by the Government of Canada through the Networks of Centres of Excellence for their funding of this work.  I would like to thank the Nadeau and Wilson families for their support through the John S. Nadeau Memorial Scholarship.  Without the help of my office mates and colleagues at UBC I would never have made it this far. In particular I would like to thank; Lloyd Bridge, Leo Colley, Massimo Di Ciano, Jun Lu and Riley Shuster, for their friendship, support and help with my experiments.  Finally, I would like to thank my family. Although I am far away from them their support and faith in me has been a constant source of inspiration.  xiii  Chapter 1 – Introduction  1.1 An overview of the hot tearing problem  Hot tearing refers to cracks that frequently occur during cooling from the liquid to solid state during shape and ingot casting. Both ferrous and non-ferrous alloys may be affected, and there is some evidence to suggest those with long freezing ranges are more susceptible  [1, 2]  . It is believed that hot tearing occurs due to thermal stresses which  develop during thermal contraction of the casting, with restrained sections being more vulnerable  [3]  . For example, complex casting geometries are vulnerable because of  variations in cross-section and because temperature gradients may exist that prevent solidification to occur at a uniform rate in all locations in the casting  [4]  . Hot tears are  easily identifiable as they take the form of ragged, intergranular cracks that often occur at a hot spot or thin section within the casting [5] (see Figure 1-1). Due to the nature of this defect the economic impact is often significant and can result in an immediate productivity loss [2, 6]. It is therefore important for industry to be able to better predict the susceptibility of various alloys to hot tearing.  Figure 1-1: Filled hot tear in Al-10Cu alloy (Spittle and Cushway 1983 [4]) taken from Campbell [5].  1  Studies have shown that pure metals and alloys of eutectic composition exhibit zero or negligible susceptibility to hot tearing [4] and therefore early work concluded that hot tearing was linked to freezing range of the alloys. It is now understood that the freezing range is important but the structures developed during solidification are also significant [7]. Hot tearing is not uniquely related to composition but is affected by a range of interrelated factors including: composition, superheat, hot-spot size, grain structure and size, solid/liquid interface morphology, casting geometry and mould type  [3]  . The  difficultly therein is to gauge the susceptibility of various alloys to hot tearing as theoretical analysis is extremely complex with many parameters interacting with one another. Since the 1940's a great deal of research work has been carried out to investigate the problem of hot tearing. Various theories have been proposed and several different types of experimental methods have been developed to interpret the properties of alloys in the semisolid state. In general the majority of the experimental methods for determining hot tearing susceptibility aim to induce the defect by means of constraining the casting (thus producing stresses that act on the semisolid material) and then quantifying the severity of the resultant crack or tear. What these experiments do not provide is quantitative data, such as localisation strain at the tear site that can be either compared to or used for the calibration of thermo-mechanical models. This document thus describes the work undertaken to prepare a new hot tearing test for aluminium alloys which allows quantitative measurements of hot tears in a test casting that are reproducible under carefully controlled conditions. This thesis is organised as follows. A two-part literature review is given in chapter 2 which describes the experimental work that has been carried out on hot tearing and also theories associated with hot tear formation. This is followed with a brief overview of the industrial scope and objectives in chapter 3. Chapter 4 describes experimental work carried out in collaboration with The University of Queensland, Australia using their hot  2  tearing experimental rig. Chapter 5 examines the results of the collaboration including results of digital image correlation on alloys AA6111, AA3104, AA31218 and a noncommercial Al-0.5% wt pct Cu. Based on the results from the collaboration a new hot tearing experiment was designed and a detailed account of its development is given in Chapter 6. Specifically the transition from a ring type casting to a constrained bar design and the associated problems encountered. In Chapter 7 the results of the final experimental design are presented and discussed. The process and suitability of digital image correlation is addressed and strain data for global strain across the developing tear, using a virtual strain gauge, and local strain measurements at the tear itself are presented. In addition a thermal simulation of the cooling behaviour of the casting was also carried out in an effort to investigate the development of fraction solid with strain at the hot tear; results of this model are also detailed.  3  Chapter 2 – Literature review  The formation of macroscopic cracks within semi-solid alloy castings has been the subject of metallurgical research since the 1940's. These cracks may be referred to as hot cracking, hot tearing, solidification cracking etc. and are a major cause of defects in aluminium alloys [8]. Published works in the field of hot tearing have usually presented an experimental method to assess the probability or susceptibility of particular alloys to hot tearing, together with a theory that attempts to explain or rationalise the observations. Other works have taken previous theories and experiments and modified them to include additional phenomena that the researchers have felt important to better assess the hot tearing susceptibility of a particular alloy. Many of the experimental methods seem particularly suited to specific casting technology (e.g. Direct Chill casting). A good review paper has been published by Eskin  [9]  that encompasses many of the hot tearing  criteria, theories and experimental methods that have been used to asses hot tearing susceptibility and also to investigate semi solid alloy behaviour. The reader is referred to this paper and also Sigworth [1] for a detailed review of hot tearing. As the aim of this work was to develop a new experimental method for assessing the susceptibility of alloys to hot tearing, this literature review is divided into two sections; (i) current theories of hot tearing and (ii) experimental methods for determining the susceptibility of alloys to hot tearing.  2.1 Hot tearing theory and associated criteria of susceptibility In the interest of brevity only the most widely referenced hot tearing theories/mechanisms will be discussed. To better understand what drives the formation of hot tears it is useful to first consider how an alloy solidifies.  4  Whereas pure metals solidify at one single temperature, alloys undertake a more gradual transformation from liquid to solid, often over a wide temperature range. Within this temperature or solidification range, liquid and solid will be present in varying proportions. On cooling from a temperature where the metal is all liquid, the solid phase will start to nucleate in the form of grains. These grains may be globular or dendritic depending on the alloy content and may be equiaxed or columnar depending on the solidification conditions. As the fraction solid increases the grains will gradually begin to interact with each other: first, chemically as the diffusion fields impinge; and second, physically as the grains begin to impinge with one another. The point at which they physically interact with each other is referred to as the geometric coherency point. On further cooling the grains will grow and the alloy will gain 'rigidity' forming a continuous network in the solid phase (known as the rigidity point or mechanical coherency point). Only when the alloy has gained rigidity does it begin to be able to support load and accumulate strain in the traditional sense.  With regards to dendrite coherency it has been noted by Warrington and McCartney  [8]  that fined grain microstructures develop mechanical coherency later than  coarse grained microstructures and thus exhibit a greater 'hot tearing strength'. This is because the small grains are able to move much move freely and accommodate strain more readily than courser grains [10, 11].  Figure 2-1: As fraction solid increases the liquid inflow becomes restricted until isolated pockets of liquid exist [19].  5  It is generally accepted that hot tears form in the “mushy zone” or two-phase region. It is also generally accepted that they form when the solid fraction is quite high and in the range of 0.85 to 0.95 [5, 12]. At this point, the mushy zone may be mechanically coherent and able to bear load but still retain a continuous liquid film between the grains [12, 13]  . Mass feeding (liquid movement on the scale of multiple grains) is limited at these  solid fractions and thus the displacement of grains away from each other by the application of a load cannot be accommodated by the inflow of liquid  [11]  (Figure 2-1).  Consequently, the pressure within inter-granular liquid drops beyond that normally associated with solidification (normally there is mass feeding occurring in association with the need to conserve volume during solidification and a dynamic pressure drop in the liquid is needed to drive the flow). As the pressure drops associated with deformation, pores or damage can form and grow. On continued application of load, these cavities may grow further and coalesce to form tears. It is thought that alloys with large freezing ranges are especially vulnerable to hot tearing as the alloys spend a much longer period within a so-called “vulnerable state” in which thin liquid films exist between dendrites [14]. When discussing liquid films it is important to consider the wetting of grain boundaries as this will have an effect on the hot tearing susceptibility. The degree of wetting is determined by the surface tension between liquid and solid phases. If the surface tension is relatively low then the liquid may be able to coat the surface of the grain boundary easily. This will reduce the dendrite coherency which in turn weakens the mush tending to promote hot tearing [15]. However, if the surface tension is such that the liquid remains as droplets at the grain junctions, the network may hold its strength and hot tears are avoided. Figure 2-2 is a schematic illustrating the different length scales (slurry, mush and solid) during solidification of an equiaxed alloy and some of the phenomena discussed above. The diagram shows melt flow at the top, with gradually increase fraction solid towards the bottom. When the solid fraction is low, fluid flow is unrestricted and small nucleated grains are free to move. As solidification continues the melt becomes a slurry  6  where feeding is still relatively good and will penetrate deep into the developing structure healing potential tears. Further down the diagram the dendrites have grown much larger and start to touch. Liquid films may wet the grain boundaries promoting hot tearing and flow on the scale of multiple grains becomes difficult. Near the end of solidification at fractions solid above ~0.97 only isolated pockets of liquid remain.  In addition to liquid films, one may also consider the nature of stresses imposed during the transition of liquid metal to a solid state. Consider that the liquid to solid transition will be accompanied by a volume contraction of 5-6 %. If adequate liquid is present then solidification may be considered as a constant volume process and the process of solidification does not itself generate stress. The development of loads in castings arise from a number of sources including differential thermal contraction of the solid due to temperature gradients, interaction of the casting with the mould (such as occurs in a constrained casting) and from externally applied loads. Once solid, strain will be generated by thermal contraction loads (2-3 %). A problem will arise if either of these contractions are impeded or constrained and cannot be accommodated by movement of grains, liquid or by plastic deformation. If this is the case then internal stresses will build and areas of the casting with weaker mechanical properties (or semi-solid material in a hot spot) will be vulnerable to hot tears [16]  .  7  Melt flow compensates solidification shrinkage and thermal contraction  Free flow, no tearing  Feeding  Slurry Healed tears Wetting  Liquid film rupture  Mush Coherency  Plastic deformation of grain bridges Liquid metal embrittlement High temperature creep  Solid Macroscopic stress  Eutectic  Figure 2-2: Schematic showing equiaxed dendritic solidification with various hot tearing phenomena (adapted from Refs. [15] and [21]).  The current understanding of the mechanisms of hot tearing, including liquid film theory, began in the 1950's. Until then confusion in the literature led one to believe that hot tearing was a phenomenon that only occurs at temperatures below the solidus and was related to composition Tearing”  [13]  [1]  . In 1952 Pellini published his paper “Strain Theory of Hot  and introduced a new theory regarding intercrystalline liquid films. Pellini  was extremely critical of the experimental practices previously used, in particular the use of thermocouples, as it is believed that their presence may act to initiate hot tears. The theory gives a general explanation of the mechanism of hot tearing in terms of strain developed in the liquid film regions. It is the liquid film that creates the condition that permits hot tearing, but it is the 'mechanical factors' such as strain accumulation that creates the hot tear. If segregates exist then the liquid film stage can be increased from a few seconds to a few minutes depending on the alloy and cooling rate. Amongst the array of experiments carried out by Pellini, of note was the x-ray analysis of aluminium and  8  steel plates during solidification that revealed hot tearing to occur between 5–15 °C above the solidus. Pellini's experiments determined that semi-solid materials have limited ductility. Consequently, solidifying castings can only withstand a certain critical strain, which is affected by the alloys coefficient of thermal expansion, its freezing range and the casting geometry  [1]  . The main points of this strain accumulation theory are: (i) cracking will  always occur in a hot spot, (ii) hot tearing is strain-rate controlled and occurs if the strain in the hot spot exceeds a critical value, (iii) the strain accumulated in the hot spot is dependent on strain rate and the time in which the alloys spends in the intergranular film stage [9, 13]. The mid-nineteen seventies saw the introduction of hindered feeding theories. In particular, Fuerer  [17]  considered the possibility that hindered feeding of the solid phase  by the liquid phase could be the main cause of hot tearing in alloys. This lack of feeding was compared with the rate of stress build-up due to solidification contraction over the freezing range. Hot tears will initiate if liquid feeding is unable to compensate for solidification shrinkage, for example, the opening of an intergranular region. Fuerer's work was found to compare favourably with experimental data from a variety of sources [7]  , even though it does not consider interdendritic opening due to thermal contraction in  the solid or uniaxial tensile deformation. In 1981 Clyne and Davies [7] expanded on Pellini's strain theory of hot tearing, to include the time spent in the mushy state and produced a criteria to determine hot tearing susceptibility. Instead of merely implying that alloys with larger freezing ranges are more susceptible to hot tearing because of the amount of time spent in the vulnerable liquid film stage, their work looked at the time interval over which the structure exhibits certain characteristics. Although very successful, their criterion is not based on fundamental physics, but gives “crack susceptibility coefficient” curves that indicate the tendency for hot tearing to occur for a given alloy composition.  9  Based on the feeding and permeability the solidification processes that occur in the vicinity of the hot spot during solidification can be divided into four stages [5, 7 and 9]:  1. Strain accommodation by solid movement (mass feeding) – Rearrangement of growing solid dendrites under the influence of the contraction stress. Although the grain structure and size will have an influence both liquid and solid move freely.  2. Strain accommodation by liquid movement (interdendritic flow) – Liquid flow assists hot tear healing by continuous interdendritic feeding, allowing a relaxation between neighbouring dendrites. It is possible that due to solidification shrinkage deeper in the mush a pressure gradient may develop across the mushy zone; however pores are unlikely because the mush still has a high permeability.  3. Interdendritic separation – Although the liquid film is still present it becomes fragmented. The permeability is decreasing as solid fraction is increasing and liquid flow is restricted. Thermal contraction results in the formation of pores.  4. Interdendritic bridging – At the late stage of solidification only isolated pockets of liquid exist (fs > 0.95), the interdendritic film is no longer continuous as adjacent dendrites become coherent. If a continued application of tensile stress is applied the pores may become interlinked and a hot tear develops. However hot tears that occur in DC casting are not always fully continuous. The use of X-ray tomography (XMT) to investigate the growth and mechanisms of damage accumulation during hot tearing was carried out by Phillion et al in 2006  [18]  .  AA5182 tensile specimens were reheated to 582ºC (fraction solid=0.98) and loaded to varying degrees of strain. Due to a parabolic temperature gradient in the specimen a hot spot is formed in the centre of the tensile gauge length. The work illustrated how the presence of as-cast porosity coalesces on application of strain in addition to nucleation of new voids in the semi-solid casting. A quantitative evolution of hot tears can be obtained by plotting the distribution of internal hot tear voids normalised by the volume captured  10  in each tomograph as a function of equivalent void radius. Based on the results of this study it was postulated that the critical strain to avoid hot tearing is the strain at which significant coalescence of the larger voids begins. The authors report that this critical range would be between 0.02 and 0.06 strain. This appears to be a fairly wide range and needs to be investigated at smaller strain increments. The development of a hot tearing criterion based on deformation of the mush and liquid feeding has been researched by Rappaz, Drezet and Gremaud  [19]  . This can be  considered an extension of Feurer's work with the inclusion of tensile deformation of the solid material. The RDG criterion (which has also been applied to DC casting of aluminium alloys  [20]  ) is based on a mass balance performed over the liquid and solid  phases. It allows calculation of the maximum strain rate that the roots of the dendrites can undergo without initiation of hot tears. The pressure drop in the interdendritic liquid from the solidification front to deep in the mush is a function of the permeability and the strain rate. If the pressure in the liquid drops lower than a cavitation pressure then a pore is initiated. Figure 2-3 shows the formation of a hot tear in between columnar dendrites as a result of localised strain transmitted by coherent dendrites  [19]  . This criterion determines  pore nucleation, and does not describe hot tear propagation. It has also not been correlated with actual cracking observed in practice. It has predicted cracks in billets where no cracks have been found under given casting conditions [15].  More recently, Lahaie and Bouchard have published a model that describes the deformation of a semisolid body in the latter stages on solidification when macroscopic flow becomes restricted  [10]  . The model calculates the deformation stresses related to  viscous flow and deformation stresses related to liquid dilation. For a constant tensile strain rate, the model calculates the stress resisting deformation as a function of total strain. This stress is compared with a critical stress for hot tearing which is based on the stress required to separate two plates that are held together by capillary forces.  11  Figure 2-3: Schematic of formation of a hot tear in between columnar dendrites as a result of localisedstrain transmitted by coherent dendrites below. Graph of pressure of interdendritic liquid shown. [19]  In summary, hot tearing criteria can be divided into three categories, mechanical, non-mechanical and a combination of both. Mechanical criteria are those which place emphasis on the strength of the casting in the latter stages of solidification. When the fraction solid is high, the local strain and strain rate may be such that the mushy material cannot compensate and so a tear is formed. Non-mechanical criteria generally place an emphasis on liquid feeding and pressure drop through a porous network to predict whether or not the conditions are right for a hot tear to form. They may take into account the dendrite arm spacing, cooling rate and the temperature at which the dendrites become coherent. The last category combines both mechanical and non-mechanical mechanisms including the local strain rate and pressure drop into the mush, such as the RDG criterion. In 2007 Eskin and Katgerman  [15]  published another review paper detailing the  current state of hot tearing models and criteria and their implementation into thermomechanical models of DC casting. The paper highlighted the sensitivity and inconsistencies of the most widely published and accepted hot tearing criteria when compared to actual casting practice. In particular it examines the sensitivity of these criteria to increases in casting speed, ramping of casting speed during start-up, the  12  amount of hot tearing in the centre of the casting and correlation with actual cracking observed in practice. Of the nine criteria selected for comparison only the criteria of Suyitno  [22]  was capable of reacting to all tested parameters listed above. However, this  criterion is extremely reliant to the careful selection of Young’s modulus of the mush, permeability of the mush and liquid–solid surface tension. Data for these parameters is extremely scarce and must be determined experimentally. Techniques for measurement of these parameters are not widely accepted as being reliable. Clearly, additional work is needed to predict hot tearing more reliably and quantitatively. Eskin goes on to suggest that to advance the state of hot tearing research a new criterion needs to be developed which takes into account all of the possible mechanisms for hot tear initiation and propagation at different stages of solidification and should be based on fracture mechanics. This does appear to be the next logical step and Eskin does make a well-informed argument for this direction. However this approach also requires new a experimental design to investigate hot tear nucleation and propagation and to produce quantitative data (e.g. strain accumulation up to nucleation) and as is suggested would require different casting models for ingots, billets and other castings due to the vastly different conditions of stress that these castings are subjected to. In addition these models also need to include parameters to take into account compositional and structural differences at a microstructural level. Over the past few years there are has been a concerted effort on the modelling side of hot tearing research and emphasis on producing data to calibrate the models. In the casting industry productivity is very important. If the rejection rate due to defects is high it will affect the profitability of the casting facility. Therefore it is important to balance low rejection rates and increased production rates to optimise profitability. Also by providing a range of alloys the manufacturer can increase their sales or market share  [6]  . However, increasing alloy content, casting speeds or billet diameter  has been shown to increase the susceptibility to hot tearing. It is therefore necessary to quantify and predict an alloys susceptibility to hot tearing so that the optimum casting process can be achieved quickly thus avoiding prolonged periods of low productivity.  13  2.2 Experimental methods for determining susceptibility of alloys to hot tearing As one would expect a number of methods for determining the susceptibility of alloys to hot tearing have been investigated over the past half century. The majority of these methods aim to induce hot tearing and quantify the amount of tearing (e.g. total crack length) for different alloys. What follows is a review of the most referenced experimental methods from the literature.  2.2.1 Ring casting Some of the earliest hot tearing work to be documented was carried out during the 1940's by Singer and Cottrell  [23]  . They used a ring casting technique to gauge the  susceptibility of Al-Si alloys to hot tearing. This technique is a very simple qualitative technique that encourages the alloys to crack, however it is difficult to control the rate of solidification [9]. The setup consists of an open cast iron mould in the shape of a ring with a slightly tapered core. The casting is quite small with a external diameter of 58.42mm (2.3in) in., internal diameter of 38.1mm (1.5in). and approximately 19.05mm (0.75in) high (see Figure 2-4).  The melt is poured into the ring at approximately 100°C above the liquidus (N.B. work by Singer and Jennings [24] suggested that the pouring temperature can influence the results), and the casting solidifies on the core. The core resists the solidification shrinkage and thermal contraction causing tensile stresses to build in the casting. If these stresses exceed the strength of the solidifying body then a crack will occur. The test produced radial cracks across the section of the ring that were measured when the casting cooled to room temperature.  14  Figure 2-4: Ring Moulding Technique bottom shows the casting.  [24]  , figure adapted from  [9]  . Top figure shows the mould, the  The hot cracking susceptibility is related to the total crack length (the sum of individual crack lengths). If the height of the melt is not controlled the experimental results may be affected by metallostatic head  [9]  . By increasing the ring size the test may  be modified to accommodate alloys that exhibit low solidification shrinkage. Although this test quantifies crack length (which includes all crack off-shoots) it does not measure crack opening, which can be used to measure accumulation of strain during cracking. In addition, determining the location of cracks within the casting can be a problem. To control the rate of solidification when using the ring test, it is necessary to control the cooling of the inner ring. This can be achieved by chilling the inner ring and controlling the water flow rate accordingly, encouraging solidification to start at the core. Crack length measurements are taken in the same way as for the original ring casting method to determine the hot cracking susceptibility.  2.2.2 “Dogbone” or constrained solidification tests This method uses a dog-bone format casting - see for example Clyne and Davies [25]  . A temperature gradient from the centre to both ends is created by preheating the  centre of the mould. The temperature gradient causes the ends of the casting to solidify first into the 'shoulders' of the mould. This provides restraint which causes axial 15  loading/stresses and induces a hot tear to occur in the centre of the casting (Figure 2-5). As the ends of the casting solidify first, a load cell may be frozen into one end to record the amount the load.  The hot cracking sensitivity used by Clyne and Davies is defined as the final cross-sectional area due to cracking (measured by a complicated electrical resistance method) divided by the initial cross sectional area.  200 mm  Plan  50 mm  Copper conducting rods  Cooling tubes  Mould cavity Centre line section  50 mm  Ejector pins  Figure 2-5: Schematic of water cooled dogbone moulding test rig. Adapted from [25].  A variation on this method is to cast several bars of different lengths (or diameters of bar of the same length) at the same time. In this way it possible to create a situation where varying amounts of stress can be produced in a single test. The susceptibility to hot tearing can then be expressed as a minimum critical length in which hot tearing occurs [26]  . Although this is relatively qualitative method of characterising hot tearing it was still  reportedly used in the literature as late as 2007 by Lin et al [27] albeit with a modification to evaluate the severity of tears. The work is quite comprehensive with a range of  16  wrought aluminium alloys tested, all with varying degrees of grain refinement. Four constrained rods of varying lengths were cast simultaneously and then rated for type of crack, severity and location within the whole casting (the shorter rods were given higher ratings as they were less likely to hot tear, and if they did it would reflect that the alloy is more sensitive to hot tearing). Severity was classed from hairline crack to full separation. Each alloy was assigned a hot tearing susceptibility rating based on the summation of the individual hot tearing rating for the four bars. The ratings of the four bars were plotted on a footprint graph from which it was a simple case of taking the area of that chart as the susceptibly. As a purely qualitative way to assess the hot tearing susceptibility this approach does work. It is possible to rank these alloys for susceptibility very quickly and the metallography carried out in this work is useful for investigating the mechanisms of hot tearing. However, this type of hot tearing study does not provide the necessary quantitative data for researchers that are currently developing and modelling hot tearing criteria to predict initiation, propagation and location of hot tears within castings. In practice, it is very difficult to measure the stress and strain at the location of the hot tear in these types of tests. In the case of the stress, the load measured using a load cell located at one end of the constrained casting includes loads associated with frictional forces between the mould and the casting. In the case of strain, the accumulation of strain is inhomogeneous along the length of the bar and it is not possible to attach a conventional strain gauge in proximity to where the crack forms. Spittle and Cushway [4] designed a closed mould dogbone test (Figure 2-6) with a feeder to provide the hot spot access to liquid metal during testing. In their opinion, previous open top mould results from other researchers may be “masked” by the lack of feed metal available to the hot spot and therefore the hot spot was less able to compensate for liquid contraction during solidification. However, in complex castings an adequate feeding source may not be available and therefore these tests may not necessarily be more valid than previous work.  17  Graphite Mould  Insulating sleeve  Water cooled copper chill  Steel insert  Mould cavity  95mm  195mm  Figure 2-6: Vertical section through closed dogbone mould, Spittle and Cushway, 1981. Adapted from [4].  In the Spittle and Cushway [4] design, the mould is chilled at both ends causing a hot spot in the centre of the graphite mould which is directly below a feeder. Restraint is provided during solidification by shoulders at each end next to the chills. Depending on the amount of superheat the solidification was unidirectional with the growth of columnar grains normal to the chill faces. The hot tearing susceptibility in this case is expressed as the effective fractional area of cracking. Spittle and Cushway reported that increasing superheat enhances the susceptibility to tearing because it increased the grain size resulting in fewer, but larger inter-granular liquid channels on which strain acts. They also determined that if an alloy has a higher volume of eutectic, interdendritic feeding will be increased and healing of tears will become more prevalent. Instone et al  [28, 6]  developed a constrained solidification test that uses a modified  tensile testing machine with a special mould that controls both thermal and mechanical parameters during alloy solidification. The test was aimed at providing a test rig that would physically model the solidification conditions in Direct Chill (DC) casting, and one that could be instrumented to gain insight into load development and strain accommodation (Figure 2-7). The configuration has an ‘H’ form, with the liquid metal poured into the feeder located in the centre of two moulds. One mould is rigged with thermocouples and the other contains rods connecting the casting to a load cell.  18  Mould  Displacement transducer mount Load cell  tensile bar Tensile machine  Thermocouples  Figure 2-7: Constrained solidification test, adapted from Instone et al [28].  The design allows temperature data to be recorded (assuming symmetry exists between the two sides) without thermocouples interfering with the solidifying material in the tensile bar section, as oxide skins, air bubbles and thermocouples are all thought to be capable of initiating cracks [28]. Temperature data is important as it can be used to determine the evolution in fraction solid along the bar. As the casting is constrained at the ends, strain accumulation will occur in the middle of the bar in the hot spot where the load bearing capacity of the material is lowest. The rate of strain accumulation in the hot spot is controlled by a tensile testing machine. The experiments yielded cracks that were characteristic of hot tears, as well as cooling and load data. Interestingly, further work using this test rig showed that strength development in alloy AA194 (commercially pure aluminium) did not occur until 0.9 fraction solid, however, for the extended freezing range alloy AA7075 (~2.75 wt.% Mg, 1.95 wt.% Cu, 5.5 wt.% Zn) the strength developed at 0.7 solid fraction  [6]  . Presumably,  the extended freezing range alloy develops an interconnected dendritic network (structural coherency) at a lower fraction solid. In 2005 further development of this test rig was carried out by Davidson et al [29]. The mould was modified to incorporate a window above the hot spot region to allow  19  observation of hot tear formation for correlation with the load and temperature measured during solidification. The results, using Al-0.5wt% Cu alloy, showed that load tended to develop at approximately 0.9 fraction solid with a hot tear forming a short time later between 0.93 and 0.96 fraction solid. They also noted that hot tearing initiated at a very low load. Again, it is not clear what frictional effects are acting on the casting during solidification and how this may affect the accuracy of the measured load. Frictional effects may be further exacerbated by the insulation that lines sections of the mould itself.  Ø 50  Hot Spot Freezes into fins  200  Mould cavity 65  400  Figure 2-8: Bottom half of hot tearing mould, casting dimensions in mm. (adapated from Paray et al) [3] .  Another tensile test that involves constrained solidification was designed by Paray et al [3]. The closed cast iron mould has two halves, with a semi-circular casting cavity on the bottom (see Figure 2-8). Features of the mould include a pouring basin at one end and 25 mm fins that act to restrain the casting during solidification to produce tensile stresses. To localise strain in the centre of the mould an insulating coating was applied to create a hot spot, forcing this area to solidify last. The mould was pre-heated to 275 °C, after which the melt is poured into the basin. The casting is removed after 7 minutes and the hot tear examined. It was difficult to control 'experimental parameters' and the results showed considerable variability in results. To quantify the degree of hot tearing a hot tearing index was created using crack length, crack width and depth of the crack into the casting – e.g. crack severity. The tests were used to determine what effect the addition of strontium has on the susceptibility of alloy 319 (6.25 wt.% Si, 3.62 wt.% Cu). It was reported that strontium can reduce the  20  tendency of alloy 319 to hot tear although the optimum level seems dependent on the level of hydrogen in the melt. The addition of strontium may reduce the appearance of shrinkage cavities which may in turn lead to hot tears; in effect the strontium redistributes macro-shrinkage as fine internal porosity. The level of hydrogen in the melt was also investigated with fewer hot tears occurring when the hydrogen level is higher. One plausible explanation for this behaviour is that the associated increase in hydrogen based porosity could have resulted in a reduction in the volumetric contraction of solidification and a reduction in the contraction of the sample. In 2008 an experiment design was published by Olivier et al [30] to investigate hot tearing in steels. This constrained bar casting (Figure 2-9) has a larger section in the centre of the casting coupled with heaters in the same area to create a hot spot. Water cooled chills were located on both ends of the casting to ensure solidification proceeds inwards toward the centre. Anchors were solidified into the casting to provide mechanical loading of the mushy zone. A mould insert made of steel or insulating ceramic was also used opposite the feeding position to increase the effectiveness of the hot spot, although tearing was only initiated with a ceramic insulator. Some of their tests initiated hot tears in the centre of the casting as expected, however if the solidification was such that additional hot spots developed at the in-gate three hot tears would develop, two either side of the in-gate and one opposite it. This highlights the difficulty of designing hot tearing experimental geometries.  From the other diagrams in the publication it would appear that the mould surface around the in-gate was being heated by the filling riser increasing the likelihood of hot spots adjacent to the inlet.  21  Feeder  ½ Mould  Solid  Liquid  Anchor Water cooled chills  Mould insert  200 mm  Figure 2-9: Hot tearing rig, from Olivier et. al. 2008 [30].  2.2.3 “Cold finger” testing  The late eighties saw the introduction of a new hot cracking test by Warrington and McCartney [8]. The test has been dubbed the “cold finger” test as it requires a tapered water cooled copper chill to be 'dipped' into a pre-heated steel crucible filled with liquid aluminium (Figure 2-10). The aluminium is pre-melted using an induction furnace to within 10K of the test temperature then poured into the steel crucible for testing. The steel crucible was set within a furnace to stabilise the melt temperature, after which the chill cone is lowered to commence freezing.  The water cooled chill forces directional solidification perpendicular to the chill surface. Warrington and McCartney report that the surface finish of the chill is related to the reproducibility of the tests and therefore the chill was cleaned and polished before each test. This is presumably to remove any material from previous tests that would cause additional friction and/or alter heat transfer.  22  Water outlet  Water inlet  Copper chill  Thermocouple  Furnace  Molten Metal Steel crucible  Figure 2-10: "Cold Finger" hot cracking test, adapted from Warrington & McCartney, 1991[8].  An 8 mm width strip of colloidal graphite was painted in a line down the chill to produce a hot spot in the casting. This is to force the hot tear to occur in a certain region of the chill. Data was collected using thermocouples both in and away from the hot spot, from which cooling curves were produced. It is not clear if the thermocouples that were located in the hot spot had an effect on the nucleation of hot tearing. The resulting cracks that were formed are confined to the hot spot region, and show large open tears running along a portion of the solid shell. The length of these cracks was proposed to be a measure of the hot cracking susceptibility. Further analysis of these intergranular cracks showed structures that varied with composition, in both equiaxed and columnar morphologies. It was determined that cracks were likely initiated within the hot spot next to the chill surface during a temperature interval when the alloy was semi-solid and held some strength but low ductility. Hot tearing does not occur unless a hot spot is present, and the sequence of expected solidification events is as follows:  23  1. Solidification in the hot-spot occurs some time after the rest of the ingot has started to freeze. 2. Strain is localised in the hot-spot but initially accommodated by liquid flow between dendrites and grain boundaries. 3. When the temperature drops sufficiently and mass feeding ends then further accumulation of the strain results in the accumulation of damage. 4. If during cooling, sufficient strain is built up which exceeds a critical value an intergranular crack will nucleate. 5. In some cases, there will be the possibility of liquid flow from the higher temperature region of the hot spot to heal the crack. It is interesting to note that their studies also include the influence of grain structure on hot-cracking. Their research showed that with only a small amount of grain refiner the crack lengths recorded were reduced, however with larger amounts of grain refiner 0.05% Ti) cracking susceptibility increased. It is thought that fine-grained equiaxed-dendritic structures can accommodate strain by liquid flow and grain movement and therefore the low ductility temperature interval will be decreased and hot tearing resistance will increase.  2.2.4 Tensile testing  To study hot tearing, Langlais and Gruzleski  [2]  constructed a solidification unit  aimed at reproducing the conditions present in DC ingot casting. The unit consists of a refractory container and a metal chill plate with anchors that are positioned to allow application and measurement of load (which can be converted to tensile stress). The unit has thermocouples inserted in the base to record temperature in various parts of the casting. During testing the container is preheated and then filled with superheated molten metal. The chill plate is positioned on top and the unit is rotated 90° (Figure 2-11), allowing the liquid metal to come into contact with the chill and the anchors. At a prescribed temperature the anchors are then displaced outward away from each other  24  resulting in a tensile stress that is perpendicular to the face of the chill (or the direction of principal heat extraction). The hot tearing susceptibility is given by the inverse of the maximum tensile stress in the shell zone section (SZS).  Chill plate  Anchors Metal head  Liquid metal (Al)  Chill plate  Liquid metal (Al)  Refractory Container  Shell zone  Figure 2-11: Langlais and Gruzleski [2] solidification unit before and after 90° rotation.  2.2.5 Tensile testing to determine properties in the semi-solid state  Many hot tearing susceptibility tests do not produce the required quantitative data (temperature, tensile stress, strain and strain rate) that is needed when developing a computer simulation of the thermal-mechanical behaviour of a solidifying casting. Both solid and semi-solid regime mechanical property data is crucial if accurate stress-strain predictions are to be produced [31]. Behaviour in the solid state has been well documented, however high temperature constitutive behaviour for partially solidified alloys in the region of the solidus has been lacking until recently. This is because tensile behaviour is extremely difficult to record as semi-solid samples exhibit low strength and ductility in the presence of liquid at the grain boundaries.  Recently tensile testing of aluminium alloy AA5182 in the semi-solid state has been achieved at several strain rates (from 10-4 to 1.0 s-1) above and below the solidus (500 °C to 580 °C) by Alhassan-Abu  [31]  and Colley  [32]  . Their work examines how the  25  strength and ductility change with the variation in liquid fraction at high fraction solid. Colley's work used cylindrical machined specimens from DC cast ingots. The specimens were machined normal to the casting direction so that specimen cracking takes place in the same orientation as hot tearing occurs in DC casting. The samples were placed in a custom designed test rig in an Instron mechanical tensile testing machine and rapidly heated using electro-resistance heating via a Gleeble Thermo-mechanical Simulator. A 4.5 kN load cell was used to capture the low loads associated with the partially solidified metal. Strain measurement was achieved by a non contact method using a high-resolution digital video camera with zoom lens. The instantaneous diameter of the specimen was measured using the captured images which were then converted to strain (taking into account the thermal expansion at the testing temperature). Work has also been carried out in a similar manner by James et al [33], Van Haaften et al [34] and Dahle et al [35].  Several experiments have been designed to characterise the tensile stress and elongation (strain) in solidifying shells. The general approach was to simulate the formation of the solid shell in DC casting. A common feature in this approach is to pour the molten metal into a dog-bone mould and then to immediately chill the metal on the top surface of the casting. A shell is formed within 10 seconds, at which point the chill is removed and an extensometer is attached to the surface, after which tensile testing begins and elongation is recorded. Magnin et al.  [36]  used the technique to investigate the ductility and rheology of  Al-Cu alloys from room temperature to the dendritic coherency point. When the chill is removed there is a reheating effect by the liquid metal under the shell and as the desired test temperature is reached tensile testing begins. An elastoviscoplastic law was then used to describe the rheological behaviour between room temperature and the coherency point. Dickhaus et al.[37] also used the same apparatus to determine stress and elongation in AlMgSi (AA6063) alloys. The work describes the used of an inductive extensometer which is placed on the free surface of the specimen after the chill is removed allowing elongation to be measured directly on the shell and not based on hydraulic cylinder movement. In this work the strain rate is measured from shell elongation and duration of  26  tensile testing. Tensile strength results were used in a mechanical behaviour model based on a system of parallel plates which are wetted and separated by a liquid film. The results investigate the mechanical properties of solidifying shells showing the sensitivity to stresses during the transformation from liquid to solid, in particular the effect of extension rate. The work found that low extension rates tend to be combined with lower tensile strength and higher elongation at fracture. In 2006 Larouche et al.  [38]  used the experimental apparatus of Laglais et al  [2]  to  investigate the tensile behaviour of semisolid Al-4.5 pct Cu alloy near solidus. This work was also concerned with the shell zone with a strain gauge being attached after a chill was removed. After the strain gauge was attached tensile testing began. The findings of the work showed that load versus strain curves of the shell region showed a near linear increase of the load with strain up to the point where the authors presume that hot tears initiate. Furthermore a constitutive model was developed based on solid fraction and liquid channel thickness distribution (between grains). They inferred that as the strain increases, the grain boundaries within the developing solid become subjected to friction sliding and may pose a higher resistance than a fully lubricated sliding condition. Hence this may result in a gradual increase of stress with strain.  In all three shell zone experiments the macro elongation has been measured on the surface of a thin solidified shell layer, which is suitable for the calculation of macrostrains. While this information is valuable for macro-scale stress models it is not suitable for the investigation of strain development on a smaller scale and for the investigation of damage initiation, accumulation and coalescence on the scale of the as-cast microstructure. Martin[39] et al. conducted experiments with eutectic Sn-Pb alloys using an adaptation of the ring tests by applying an axial deformation (internal pressure) with a “highly deformable balloon” filled with silicon oil. During the experiment, the axial stress exerted on the balloon can be calculated by a simple relationship which states that the pressure in the balloon equals the axial stress exerted on the balloon surrounded by the semi-solid ring minus the axial stress on the balloon if the balloon was deformed alone in the same  27  strain conditions. The authors then go on to show how axial strain rate can be calculated in a similar manner.  In summary, a review of the literature has highlighted important work concerning the development of hot tearing susceptibility tests. From the literature we can recognise some key issues in the design of a new hot tearing test.  All of the tests detail the need for supplying mechanical constraint during solidification, which will help to initiate hot tearing and separation of the metal. This is the basis of many of the older testing methods such as ring casting and backbone testing. These tests are very simple; however they have significant shortcomings that lie in the way that key data can be obtained. For example, the test results do not address the issue of crack severity. In some of the tests they report hot tearing susceptibility based on cumulative crack length or on whether a hot tear was produced. In particular backbone tests, where different lengths of rod are cast simultaneously, the results are reported as the minimum critical length from which hot tearing occurs and is therefore it is difficult to apply the results to other cases in which crack formation may be a problem. In essence, these tests do not produce any valuable quantitative data such as for example stress at failure and strain at failure [16]. Some researchers have realised the need for such data and have tried to design an experimental set-up with these ideas in mind. For example the constrained solidification test designed by Instone et. al.  [6]  , uses a load cell to record load accumulation during  solidification of a directionally solidified bar. This method seems to give a good indication of load however it is uncertain what effects friction may have on the measured loads as these tests usually lay horizontally on a flat surface and there is friction between the mould and the casting. Another finding from a review of the literature is the importance of producing a local hot spot. Many of the newer tests state the need for a hot spot as means of encouraging strain to accumulate within a certain area of the casting. This would seem a good idea if the measurement of strain in the hot spot can be achieved, and keeping the  28  material hotter for longer would allow strain elsewhere in the casting to be concentrated at the point of interest. Temperature data should be recorded as the thermal history is valuable for linking the accumulation of load or strain with fraction solid. In addition, the design of the test should consider the location of thermocouples carefully as poor placement may have an unwanted influence on hot tearing. In addition, good directional solidification should be obtained to avoid the occurrence of significant shrinkage void formation in the area under examination. As noted in the literature review above, many studies have been conducted to investigate hot tearing. The simplicity of these methods varies, and their application is dependent of the casting process they are based upon. Based upon the literature a new hot tearing vehicle has been produced.  29  Chapter 3 – Scope & Objectives  3.1 Industrial scope Hot tearing is potentially very costly to the aluminium industry especially in circumstances where the defect occurs during ingot or billet casting. In such cases; time, energy and raw materials have been wasted on producing a product which cannot be further processed due to the defect. It therefore follows that it is important for industry to be able to better predict the susceptibility of new and existing alloys to hot tearing.  As detailed in the literature review, simple testing methods are available, however these experiments have tended to “quantify” the susceptibility of tearing in terms of crack length or severity of cracks to produce hot tearing indexes to rank various alloy systems. There is a need to develop a new test that can quantitatively rank alloys for hot tearing susceptibility.  In addition, good quantitative data (i.e. local strain development at the hot tear) may also be used by the research community to help calibrate thermal-mechanical computer simulations of casting processes and hot tearing models that are in development to investigate mechanisms of the phenomenon.  3.2 Thesis objectives From the review of literature, industrial scope and through consideration of what work may be useful to the research community the following objectives are sought after in this work:  1. Development of a new and novel hot tearing test experiment: - the goal is to design an experiment that is capable of initiating reproducible hot tears in  30  commercial alloy castings. The test rig should employ a method for strain analysis during tearing.  2. Where possible determine a quantitative approach to ranking commercial alloys for their susceptibility to hot tearing.  3. Produce quantitative data that may be used to help calibrate a thermo-mechanical model of solidification defects. This type of data is not present in the current literature and would be a significant contribution to the field.  31  Chapter 4 – Observation of Hot Tearing During Solidification  4.1 Introduction In 2000 Instone et. al  [6]  introduced a new hot tearing test apparatus. It consisted  of a modified tensile testing machine attached to an H-shaped mould that provided constraint during solidification and generated information concerning strength development and strain accommodation in the mushy zone. The apparatus was also designed to physically model the solidification conditions in the DC casting process. In DC casting hot tears usually form in the mushy zone at the base of the liquid sump, and can be physically modelled by casting a bar which is constrained at both ends and has a feeder junction in the centre of the bar. Because the feeder junction keeps the metal hot in the centre of the bar it is analogous to the sump in centre of the DC cast billet. Solidification occurs from both ends of the bar and moves inward to the centre. In the case of the Instone set-up two bars are cast simultaneously and both are fed from a centre pouring reservoir. One bar was used to track load development, the other contained thermocouples at various points to obtain temperature data during casting, in this way the thermocouples do not interfere with load measurements. Figure 4-1 shows a plan view of the hot-tearing rig used in this work, which is located at The University of Queensland. The rig was modified by Davidson et al  [29]  to  allow observation of the hot spot region during solidification. The experimental set-up allows for two bar sections to be cast simultaneously, which are fed via a central runner and riser. One of the bar sections is typically fully restrained. The other side is instrumented with thermocouples and has one end fixed to a load cell to allow both temperature and load data to be acquired.  32  Figure 4-1: Modification of Rig for Observation of Hot Tearing Initiation [29].  A hot spot is created in the centre of both bars by means of ceramic fibre insulation (1 mm thick) and also by virtue of proximity to the runner. A lid lined with 3mm thick fibre insulation is then placed on top of the mould. The lid has been modified to include a window made of commercial borosilicate glass that has been placed directly above the hot-spot region to observe the surface of the casting in the location where the hot tears form. A type-K thermocouple was also inserted through the lid and positioned in the centre of the hot spot region directly below the window, in front of the in-gate (Figure 4-2). Prior to casting, the whole mould is covered in ceramic fibre insulation and is preheated to 200ºC for 2 hours to remove moisture and prevent cold spots. In the current work the load cell was disconnected. This proved necessary to consistently produce a hot tear under the glass window as the load-train compliance allowed some relaxation. Several commercial alloys were tested (AA6111, CA31218, AA3104) in addition to a Al – 0.5 wt% Cu alloy that has previously been found to be susceptible to hot tearing [34]. The compositions of these alloys can be found in Table 4-1. Each alloy was poured at 100ºC above its liquidus prior to pouring into the mould.  33  Figure 4-2: Rig for Observation of Hot Tearing Initiation showing locations of thermocouples during the UBC/UQ collaboration.  Table 4-1: Test alloy compositions wt%, with the remainder attributed to Aluminium.  Alloy  Mg  Si  Cu  Fe  Mn  Ti  Cr  Zn Ni AA6111 0.5-1.0 0.7-1.1 0.5-0.9 <0.4 0.15-0.45 AA3104 0.8-1.3 0.6 0.05-0.25 0.8 0.8-1.4 0.1 Al-Cu 0.5 CA31218 0.22 0.12 0.86 0.25 0.87 0.085 0.0025 0.025  34  A Sony DFW-SX900 digital camera was used to acquire images, 1280 x 960 pixels in size, of the surface of the sample during casting and cooling. Figure 4-3 details the position of the camera in relation to the glass window and Figure 4-4 is a photograph of the camera and mould setup during the tests.  In order to accommodate macro shrinkage away from the glass and to ensure adequate depth of field is available during testing, focusing is carried out on the mould system containing a previously cast solid specimen before mould heating. The camera is focused on the solid sample through the glass and the position of the camera tripod is marked on the floor with scotch tape, although the tripod and camera are not moved after focusing. After focusing the mould is disassembled and the focusing block removed. Figure 4-5 is a photograph of the window reflection in the polished aluminium mirror. Because the load frame is positioned directly above the mould it is not possible to locate the camera and lens directly above the glass window, therefore a polished aluminium mirror angled at 45° to the window was used to allow the camera to be positioned at the side of the mould. However, problems from distortions due to thermal instability in the air were encountered even though a long-focal length lens was used to keep the camera a suitable distance from the hot mould. These distortions were minimised by using a small fan to blow a steady stream of cool air through the image path.  35  Figure 4-3: Rig for Observation of Hot Tearing Initiation showing locations of thermocouples during the UBC/UQ collaboration  Figure 4-4: Rig for Observation of Hot Tearing Initiation showing the camera location during the UBC/UQ collaboration.  36  Figure 4-5: Polished aluminium mirror showing reflection of glass window and casting  The actual field of view captured was approximately 7 mm x 5 mm on the sample surface. Sequential images were captured at a rate of 7.5 frames per second including during mould filling. Images were stored without compression, to ensure no artefacts were added. Image capture was synchronized to the temperature data by identifying the image at which the metal first entered the field of view, which was taken as the zero time reference. As a thermocouple was located directly under the window, the first large temperature increase was taken to be zero time. After cooling to room temperature, radiographs of the thermocouple position were taken together with macro images of the hot tears. These post-solidification radiographs revealed significant variability in thermocouple placement and therefore it was difficult to extract precise quantitative temperature data of the hot tear initiation site. The samples were also sectioned and etched to delineate the as-cast structure. Following capture, selected images were correlated (compared) with one another to determine displacement evolution (and subsequently strain evolution) on the surface of the casting. The technique used is called optical digital image correlation, and was carried out using the commercial software package VIC-2D[40]. The technique is ideal for situations such as this where traditional measurement equipment (i.e. strain gauges)  37  cannot be attached to the surface of the specimen. The technique works by comparing a reference image with subsequently deformed images. The method tracks subtle changes in the grey scale pattern in small areas on the surface of the sample (see Appendix C). The suppliers of VIC2D claim a displacement resolution of ~1/50 pixel is achievable under good conditions; however in the current set-up (which has a small field of view) the resolution is approximately 0.2 µm, at best, in displacement or 0.001 in strain based on the image width (which is 1280 pixels or 7mm) and on software set-up. Software set-up parameters determine an approximate equivalent gauge length. The window (subset) size in pixels multiplied by the step size (the distance in pixels between windows) divided by the resolution in pixels/mm will result in the gauge length for the analysis. In this set-up the gauge length was calculated gauge to be 400 µm, however because the software filter is heavily centre weighted the gauge length is 200 µm. The image correlation analysis is carried out from the time the partially solidified metal finishes contracting away from the glass until the hot tear is just visible on the surface of the casting. In this manner the in-plane displacement accumulated from the onset of thermal contraction (approximate end of mass feeding) until the hot tear occurs can be estimated (note: with the present equipment, only in-plane displacements can be tracked and not shear displacements on the surface). It proved impossible to track the development of strain earlier into the solidification process as the surface lacked sufficient features to allow digital image correlation.  38  Chapter 5 – Results of Hot Tearing Observation During Solidification  5.1 Introduction In this chapter the results of the collaboration with the University of Queensland will be discussed. The suitability of digital image correlation for measuring strain on the surface of a solidifying casting will be proven and strain evolution data for the various commercial alloy systems will be presented.  5.2 Experimental results and discussion As discussed previously, the liquid metal initially lies in close contact with the borosilicate glass window, without wetting it. After a short time (approximately 60 to 90s) the surface morphology of the casting changes becoming irregular and the surface can be seen to pull away from the glass. The pull away represents the onset of local macro thermal contraction and may be argued to occur approximately consistent with the end of mass feeding. The hot tears were found to form a short time (few seconds) after pull away of the cast surface. A sample image captured after cooling to room temperature of the Al-0.5 wt% Cu alloy bar surface is shown in Figure 5-1. The hot tear, seen on the left hand side of the image, is dark in colouration compared to the as-cast structure and is oriented roughly vertical or normal to the load developed due to thermal contraction of the bar. Following cooling, the hot tears are typically fairly open and are readily visible, however, there is still significant bridging across the crack and it is necessary to load the sample to get it to fracture into two pieces. Figure 5-2 shows a series of selected strain distribution contours determined from the Al-0.5wt% Cu alloy sample using the technique described above. The section of the surface used for image correlation is demarked in Figure 5-1 by the dashed lines. The time indices appearing in the images are the times from the onset of thermal contraction (as described above) and are not the times from the onset of image acquisition. 39  2 mm  Figure 5-1: Sample image showing a visible hot tear, taken during solidification of Al-0.5% Cu alloy. Dashed lines refer to area in which contours were taken on Figure 5-2.  Figure 5-2: Image correlation strain contours for Al-0.5% Cu alloy. Notice the coalescence of strain fields on the images for 0.399 s and 0.665 s. Images shown relate to dashed area in Figure 5-1.  40  Referring to Figure 5-2, the first snap shot of strain on the as-cast surface is taken at 0.133s after surface pull away from the window. It is evident that even at 0.133s the distribution of strain on the surface is somewhat irregular. By 0.266s unevenness in the distribution of strain is more pronounced and there is evidence of some localisation of strain in isolated pockets of material. Continuing further in time, by 0.399s there has been both growth of some of the areas of strain concentration and coalescence of others to form a nearly continuous band of high strain that extends from the lower right-hand-side of the image to the upper left-hand-side. The snap shot taken at 0.665s, indicates there is additional coalescence (as labelled), further localisation of strain within the band of high strain and, what would appear to be, some break-up of the band of high strain in the upper left-hand region. By 1.197s there is additional coalescence (rejoining in the upper lefthand region), localisation within the band and broadening, resulting in a band of high strain that is well defined and continuous. Note: there is also some additional localisation of strain in areas adjacent to the main band. The final image, showing the contour of strain at 2.403s, represents the time at which the hot tear is first detected visually on the surface of the casting (note the branches of high strain extending outward from the main band). There is no distinguishable variation in displacement from the optical images of the cast surface prior to detection of the crack. Based on the sequence of strain contours observed in Figure 5-2, the process seems to be consistent with localisation of strain, discrete growth of areas of localised strain and growth by a process of coalescence. The results described above for the Al-0.5 wt% Cu are typical of those observed in the other alloys. In terms of the correlation of strain with the defect observed in the as-cast Al-0.5 wt%Cu sample, the band of high strain corresponds well with the location of the main hot tear shown in Figure 5-1. Likewise the location of the branches of high strain extending outward from the main band also appear to agree with the branching observed from the main hot tear. Overall, the contour images produced using this technique appear to yield strain distributions that are qualitatively consistent with the cracking observed in the Al0.5 wt% Cu sample.  41  The strain contour results for Al-0.5 wt%Cu and the commercial alloys, AA6111, AA3104, and CA31218 are shown in Figures 5-3 to 5-7, respectively. Each figure contains an image of the surface of the casting and the corresponding strain contour map. Figures 5-3 to 5-7, also contain an image of the as-cast surface following polishing and application of a macro-etch to delineate the as-cast structure (note: to clearly see the crack, the images of the casting surface are shown at least 5 seconds after the tear has opened; also the sample used to examine the as-cast structure has been taken from the second bar produced in the test at an approximately equivalent position, so as to avoid destruction of surface used for image correlation). The results for the commercial alloys also show a good correlation between the distribution of strain on the surface of the casting and the location of the hot tear. Note: there are regions of high strain appearing on the surface that do not ultimately form an open hot tear (following cooling to room temperature). All of the commercial alloy ascast structures were equiaxed and varied in grain size from a low of ~150 µm for AA6111 to a high of <1 mm for AA3104. The Al-Cu alloy grain size was approximately 10mm and was extremely large. The hot tears appeared to be intergranular in all of the cases examined.  a) b)  Strain  Figure 5-3: (a) Specimen surface photograph and (b) image correlation strain contour and for Al0.5%Cu alloy.  42  a) b)  Strain  c)  Figure 5-4: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macroetched specimen surface for AA6111a.  a) b)  Strain c)  Figure 5-5: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macroetched specimen surface for AA6111b.  43  a) b)  Strain c)  Figure 5-6: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macroetched specimen surface for AA3104.  a) b)  Strain c)  Figure 5-7: (a) Specimen surface photograph, (b) image correlation strain contour and (c) macroetched specimen surface for AA3128.  44  In order to gain a more quantitative insight into the development of strain on the surface of the as-cast samples, strain profiles have been plotted along lines perpendicular to the hot tear at various times relative to the first pull away of the liquid metal from the window. These plots have been generated in terms of strain vs. distance (over 4 mm) across the tear for all of the alloys tested. Figures 5-8 and 5-9 show the strain profiles for two of the alloys, Al-Cu and AA6111b, respectively in which the data for each time has been plotted separately for clarity. The data for the other alloys has been plotted on combined graphs and are shown in Figures 5-10 to 5-12. The profiles obtained 0.133s after pull away indicate that the strain is nominally zero for all of the alloys tested, but shows some random variation with position. It is interesting to note that there are some positions showing negative values of strain. The positive strains may be associated with areas of tension however, because the displacements (and associated strains) are measured relative to a datum taken to be the image captured when the metal pulls away from the surface, it is not possible to conclusively say whether or not the negative values represent compressive stress. They may simply represent areas of reduced tensile strain that have developed as a result of the grains within the semi-solid moving to accommodate the macro-displacement.  45  Figure 5-8: Strain vs. Distance across the hot tear for Al-0.5%Cu, showing the fluctuation in strain and subsequent localisation of strain over time (from reference image).  46  Figure 5-9: Strain vs. Distance across the hot tear for AA6111b, showing the fluctuation in strain and subsequent localisation of strain over time (from reference image).  47  As can be seen from the profiles presented in Figures 5-8 to 5-12, strain is accommodated in localised areas and is not uniformly distributed over the surface of the sample. In some of the samples the distribution of strain is clearly much more random in amplitude and location. For example, in the case of AA6111b, 5-9, the distribution of strain is highly variable along the length of the sample line, whereas in Al-0.5 wt%Cu (5-8) and CA3128 (5-12), the distribution of strain is much less variable. In the case of the Al-0.5 wt%Cu alloy the grain size is ~10 mm and thus the strain profile has evolved between two grains. A common feature of all of the profiles is that the strain becomes localised in one or two areas and that at longer times (further application of load) all of the strain is accommodated in the region that ultimately corresponds to where the hot tear forms. The maximum strain observed in the profiles typically falls in the range of 0.015– 0.019, which corresponds to when the crack first appears. It is important to point out that this should not be correlated with alloy sensitivity to hot tearing as it represents a magnitude of strain where the crack is first visible and hence should be very similar for all of the alloys examined.  0.022  Time (s) after Reference 0.133  0.017  1.067 2.002 0.012  Strain  2.937 4.405  0.007  0.002  -0.003 0.00  0.50  1.00  1.50  2.00  2.50  3.00  3.50  4.00  Distance (mm) Figure 5-10: Strain vs. Distance across the hot tear for AA6111a.  48  0.022  Time (s) after Reference 0.133  0.017 0.533 0.934 0.012  Strain  1.335 1.602  0.007  0.002  -0.003 0.00  0.50  1.00  1.50  2.00  2.50  3.00  3.50  4.00  Distance (mm) Figure 5-11: Strain vs. Distance across the hot tear for AA3104.  0.022  Time (s) after Reference 0.133  0.017 0.267 0.534 0.012  Strain  0.801 1.068  0.007  0.002  -0.003 0.00  0.50  1.00  1.50  2.00  2.50  3.00  3.50  4.00  Distance (mm) Figure 5-12: Strain vs. Distance across the hot tear for CA3128.  49  Table 5-1: Summary of background strains before localisation and maximum strains at which tear opens.  Alloy AA6111a AA6111b Al-0.5%Cu CA31218 AA3104  Average peak strain before localisation > 0.0077 > 0.0069 > 0.0021 > 0.0047 > 0.0123  Average macro strain before localisation 0.0020 0.0016 0.0011 0.0010 0.0036  Strain at which tear opens 0.0167 0.0170 0.0155 0.0151 0.0186  A potentially more meaningful indicator of alloy sensitivity to hot tearing would be the strain at which single-site localisation of damage first occurs. Application of this approach to the present set of tests would indicate that CA31218 and Al-0.5%Cu are the most prone to cracking, as localisation of strain occurs at relatively little strain (the two peaks in the Al-0.5%Cu are both associated with the hot tear observed on the surface). In the case of the alloys that exhibit a more variable distribution of strain, with significant strain build-up in a number of areas prior to single-site localisation (alloys AA6111 and AA3104), it is not possible to rank them as there is insufficient resolution in the data. A summary of the average peak strains prior to localisation, the average macro strains (across the whole profile) just prior to localisation and the maximum strain at which the tear was first visible can be found in Table 5-1. However, it should be borne in mind that hot tearing is highly dependent on the alloy grain size, and that this ranking is based on the grain size of the alloys cast. The results for the two tests run on AA6111 are similar and hence the technique appears to yield results that are reproducible. In the context of a macro model, the average macro strain at the onset of localisation could be used. Whereas, in a micro-scale model it may be more appropriate to use the average peak strain. From the data presented it appears that the “wavelengths” of the strain peaks are greater than the grain size, suggesting that the strain measurement is not capturing strain on a local enough scale. For the commercial alloys tested, the grain sizes range from 150 µm to 1mm, so a spatial resolution of 0.2 micron should be adequate to capture strain behaviour on the scale of the grains in all of our samples. However, because the “wavelengths” of the peaks are  50  greater than the grain size this suggests that not all grain boundaries show a strain localisation. In fact localisation seems to occur roughly every 10 grains in the case of 6111A. It is assumed that during solidification strain localisation will differ from grain to grain; for example larger grains may be subjected to a higher concentration of strain than smaller ones due to a reduction in their ability to move – e.g. smaller grains may rearrange themselves to relax the strain. Comparison of the results of this study with those of Colley  [32]  on AA5182 and  from other tests conducted on AA6111, AA3104 and CA31218, using the same approach and equipment (to be published) shows relatively good agreement. In the test conducted on as-cast material reheated into the semi-solid state the strain-to-failure was found to lie in the range of 0.006 to 0.019 when loaded at strain rates ranging from 0.002 to 0.003s-1. These results compare favourably with the strains for single-site localisation of damage between 0.015 and 0.019 found in this work. Finally, the data from the image correlation technique has been examined by plotting the evolution of strain with time and temperature with time in each of the alloys examined. The results are presented in Figures 5-13 and 5-14, respectively. In Figure 5-13, the slope of the various lines represents the cooling rate determined from a thermocouple embedded in the bar close to the location of the hot tear. In the cases examined the cooling rates are all similar however with the current data it is not possible to relate the thermocouple data to the temperature or fraction solid at the location of the hot tear as there was considerable variability in the location of the thermocouples relative to where the hot tear formed. For example, the differences in the temperatures recorded for tests 6111a and b reflect differences in the location of the thermocouple – i.e. in 6111b the thermocouple was closer to the runner and therefore hotter. X-rays of tests AA3104, Al-0.5%Cu, CA31218 also showed that the thermocouple had been forced into the ingate towards the riser, hence these results should be taken as being preliminary. Turning to 5-14, which shows the evolution of strain with time, it is apparent that the strain evolves at different rates for the alloys examined.  51  640 6111a 6111b Al-Cu 3104 3128  630  Temperature (oC)  620 610 600 590 580 570 560 0  1  2  3  4  5  Time (s) Figure 5-13: Evolution of temperature with time for all alloys, showing similar cooling rates for all alloys.  0.018 0.016 0.014  Strain  0.012 0.010 0.008 6111a (0.0037) 6111b (0.0051) Al-Cu (0.0063) 3104 (0.0096) 3128 (0.0133)  0.006 0.004 0.002 0.000 0  1  2  3  4  5  Time (s) Figure 5-14: Evolution of strain with time for all alloys (including linear approximation of strain rate).  52  The sample with the highest apparent strain rate was alloy CA31218 and the sample with the lowest was alloy AA6111.  The thermocouple data indicates that the cooling rates for all alloys were similar, and therefore, the difference in strain rate might be attributed to differences in the thermal contraction behaviour of the alloys. The difference in strain rate may also be a factor in determining alloy sensitivity to hot tearing. Comparing the strain rate data to the strain localisation data there is a similar trend in that the alloys with the highest strain rate, AA3128 and AA3104 are most prone to cracking, with AA6111 being the least sensitive to hot tearing.  5.3 Chapter summary The collaboration work with The University of Queensland to observe tear formation in commercial alloys was extremely constructive and yielded some interesting results. A digital image correlation technique was used to determine strain evolution for several alloys (four commercial) during hot tearing experiments. The results can be summarised as follows: 1. The optical image correlation technique proved capable of predicting areas of high strain concentration consistent with the location of the hot tear on the surface of the casting. 2. Depending on the alloy, the distribution of strain on the surface of the casting in the early stages of deformation can vary from being relatively evenly distributed to being highly variable and random. Single-site localisation of strain was found to occur at relatively low strains in the alloys that exhibited an initially relatively uniform distribution of strain. Whereas single-site localisation of strain was found to occur at relatively high strains in the alloys that exhibited a highly variable distribution of strain.  53  3. The process of hot tear formation in the alloys examined seems to be consistent with localisation of strain, discrete growth of areas of localised strain and growth by a process of coalescence. 4. The minimum strain at which strain localisation occurs was found to be >0.0069 in AA6111, >0.0123 for AA3104, >0.0047 for CA31218 and >0.0021 for Al0.5%Cu based on displacements measured from the point at which mass feeding ends and thermal contraction begins.  5. The thermocouple data indicates that the cooling rates for all alloys were similar and therefore difference in strain rate might be attributed to differences in the thermal contraction behaviour of the alloys. The difference in strain rate may also be a factor in determining alloy sensitivity to hot tearing.  54  Chapter 6 – Development of a New Hot Tearing Experiment  6.1 Introduction The collaboration work with The University of Queensland was successful and demonstrated that digital image correlation could be used to investigate strain development leading up to hot tear formation. However, this work was conducted using an apparatus that resulted in complex solidification conditions (non-directional) in the location where the hot tear formed making characterisation of the thermal gradient and solidification rate difficult. Moreover, the thermal history data was not collected due to problems with the thermocouple positioning on pouring. Without temperature data it is impossible to determine fraction solid values during solidification and to make any connection to strain accumulation during hot tearing. This type of quantitative data is not present in the current literature and would be a significant contribution to the field. Due to the design of the previous testing apparatus there is also a question of what role friction on the bottom of the mould may play during solidification. For example, a tear may be initiated in the semi-solid shell of the casting by friction at the mould wall where strainrate can be high  [21]  . It was therefore decided to design a new hot tearing experiment at  UBC.  The apparatus has undergone several design iterations which are summarised before presenting the final version in detail. The final design consists of a 17.5 cm × 17.5cm × 2cm mould cavity. At the bottom, the mould is comprised of a water cooled copper chill to facilitate directional solidification. The cavity is fed through the top with the in-gate located in the middle of the top surface. The mould sides and top are constructed of mild steel. The sides of the mould each contain 7 restraining bolts to provide constraint against horizontal contraction. This chapter gives a brief overview of the design evolution of our current apparatus.  55  6.2 Directionally solidified ring casting  Early development of the new hot tearing apparatus concentrated on a directionally solidified ring casting variant for hoop strain generation and a vertically oriented crack.  The ring casting test provides constrained solidification via a centre core and has been in use since the 1940's. It has proved to be a quick and relatively simple test to assess the susceptibility of an alloy to hot tearing. The technique generally results in one or more vertically oriented or axial cracks around the cast ring, with the susceptibility to hot tearing reported in terms of cumulative total crack length. One of the main criticisms often levelled at ring casting is that the rate of solidification is difficult to control; hence it cannot be compared to some casting techniques which have a relatively high solidification rate. Nevertheless with some modifications it was hoped that this problem could be attended to.  The experimental set-up is shown Figures 6-1 and 6-2. It is essentially a modification of ring casting that allows for directional solidification and a continuous variation in the gradient and cooling rate with increasing distance from the chill. Other improvements include localisation of strain in a hot spot on the casting. The purpose of strain localisation is to force hot tear initiation to occur at one location only on the casting and is achieved by the introduction of insulation. The design was rationalised based on the assumption that the decreasing temperature gradient, and the associated increasing mushy zone length, would lead to an increasing tendency to produce hot tears with increasing distance from the chill. The set-up consisted of four parts, a chill plate, core, pouring crucible and mould (Figures 6-1 and 6-2). The copper chill was fitted with quick release fittings allowing the water cooling system to be connected just before pouring. The mould, pouring crucible and core were all made of stainless steel to avoid excessive oxidation. All parts were bolted together and a ceramic fibre paper layer was inserted between the crucible and  56  mould. Before casting, the complete apparatus was pre-heated in a furnace to between 200–400ºC in a nitrogen gas atmosphere. Nitrogen was required to prevent oxidation of the copper chill when heated in air which forms as a thick black scale that covers the surface inhibiting heat transfer from casting to chill and which also represents a significant health hazard. A strip ceramic fibre paper was applied onto the surface of the core with high temperature cement to decrease the cooling rate under the pouring inlet, thus increasing the likelihood of a hot spot in the casting. The strip was 25mm wide and ran the length of core down to the chill. Hot tears were not initiated in preliminary tests conducted without the ceramic fibre strip. The inside face of the steel crucible was coated with boron nitride hard coat to prevent heat transfer and also to allow easy removal of the solid head material after testing. Each casting was approximately 170mm in height and 10mm thick. The diameter of the top and bottom of the casting was 80mm and 140mm respectively. This set-up was able to produce large hot tears in most castings. Figure 6-3 shows two AA3104 aluminium alloy castings produced using this setup. The mould preheat was 400°C and the test pouring temperature of the metal was approximately 770°C in each case. These castings both show defects common to this casting geometry. It was expected that in these castings a hot tear would initiate at a height on the casting where the mushy zone experienced restricted feeding to occur.  This initiation height may be expected to vary for different alloy compositions. In the case of these castings the tears appear to have extended the full length of the casting; however at the base they appear to be smaller and there is also evidence of branching indicated a possibility of more than one initiation site. These castings also exhibited a variable surface quality around the area of the hot tear (see locations A, B and C) and some variability in the location of the tear. This latter characteristic was deemed to be potentially problematic for image correlation.  Due to the problems described above it was decided to abandon this format and to pursue an alternate geometry. 57  Stainless steel pouring crucible  Stainless steel mould  Water Cooling Water cooled Copper Chill Figure 6-1: External schematic of experimental set-up for large ring casting  Stainless steel pouring crucible  Riser  Stainless steel mould  Stainless steel core  Water cooled Copper Chill Figure 6-2: Schematic cross-section of experimental set-up for large ring casting.  58  B  C  A  Figure 6-3: Example castings from large ring casting experiments. Large hot tears are not suitable for image correlation experiments due to A) Asymmetric strain build up around the core which causes tear to split paths at the upper and lower sections of the casting. B) Variable surface finish around the area of the hot tear. C) Hot tear would often deviate from the hot spot.  These ring casting experiments were also used to determine the nature of cracks produced under constrained solidification, to assess whether the defects may be classed as hot tears. In order to be consistent with the literature the cracks produced in the successful tests should have occurred above the solidus and thus be intergranular in nature if they were to be designated as hot tears. S.E.M. micrographs of the crack fracture surfaces revealed clearly visible dendrites as well as some dendrite arm fracture (Figure 6-4). It is possible that these dendrite arms were coherent with others and were bridging the crack until failure. In general, the micrographs indicated dendrites which are mainly intact implying that the crack was intergranular and occurred above the solidus in the interdendritic liquid film.  59  Figure 6-4: S.E.M micrograph of hot tear surface from preliminary ring casting experiment.  6.3 Restrained casting development 6.3.1 Stage 1 – Restrained casting with stress raiser  Figure 6-5 shows the first stage of development of the restrained casting test apparatus that was ultimately used in this work. The mould consists of five mild steel parts, a water cooled copper chill and a ceramic fibre pouring crucible which feeds the mould from the top. All of the parts fit together to form a sealed mould which does not allow leakage of liquid metal during the test. The side panels of the mould each have 7 evenly spaced holes to seat 2 inch (50.8mm) bolts that extend into the casting and act to restrain the casting in the horizontal direction (parallel to the chill) as it solidifies. This is a similar method of applying constraint to a bar style casting similar to that of the University of Queensland hot tearing rig (the reader is referred back to Chapter 3). The solid copper chill has a water channel bored through the centre; the water lines are connected using quick-connect fittings.  60  Ceramic fibre paper was also fixed onto the underside of the top of the mould with high temperature cement and was in direct contact with the casting, limiting a chilling effect from the steel. The top of the mould also has a small riser hole located on one end to allow air to escape on pouring; this also serves to indicate when the mould is full. Finally ceramic fibre paper was also used on the various surfaces of the copper chill which are in contact with the steel mould parts to retard chilling of the back, front and sides. Approximately 2.5kg of alloy was melted in a box furnace with 100ºC superheat; the mould setup was heated to 200ºC in a separate box furnace. Initially no insulation was used at the centre of the casting. It was anticipated that the heat conduction through the pouring hole might be sufficient to give rise to a hot spot in the centre; however this was not the case and no hot tears were initiated. Figure 6-6 is a schematic of the same set-up with the addition of a stress raiser located under the filling position.  The stress raiser approach was investigated because; 1) it raises the local stress in the centre of the casting due to the small cross section and 2) it reduces the amount of constraint required to initiate a hot tear. The use of a stress raiser also generally gives a better surface finish in the final casting when compared to ceramic paper or a boron nitride coating. Several tests were conducted with an N-17 stress raiser. N-17 is a graphite fibre reinforced, high purity, calcium silicate board which is used in the nonferrous casting industry for pipes, trough liners etc. The material exhibits good strength, low thermal shock and shrinkage.  Figure 6-7 shows a relatively successful first test of the geometry with an N-17 stress raiser that was attached to the back face of the mould with high temperature ceramic paste. The alloy used for this casting is AA3003, an Al-Mn alloy. The test conditions consisted of a 200°C mould preheat with an 800°C pour temperature. The front view shows a fairly straight hot tear running vertically below the filling point.  61  Ceramic Fibre Crucible  Side profile of top panel  Riser hole Restraining Bolts Steel front and back panel Steel Side Panels Water cooled copper chill  Figure 6-5: First stage of restrained bar casting, showing various parts of the mould.  Ceramic Fibre Crucible  Riser hole Restraining Bolts  Steel Stress Raiser  Steel front and back panel Steel Side Panels  Water cooled copper chill  Figure 6-6: Restrained bar casting showing a schematic of the steel stress raiser.  62  On the reverse side the cavity where the stress raiser was located is clearly visible. The surface of casting that had been in contact with the N-17 contains a lot of porosity in the vicinity of the hot tear, indicating that perhaps the thin cross section was poorly fed during solidification. It is likely that this porosity has played a considerable role in initiation and propagation of the hot tear in this casting. Figure 6-8 shows the second test of the geometry with an N-17 stress raiser. The test conditions were the same as the first test (200°C mould preheat, 800°C pour temperature). Once again the test produced a fairly large hot tear on the front of the casting; however the tear has initiated at the side of the stress raiser away from the filling position and would most certainly have been out of the field of view for image capture.  The back of the casting reveals very small tears in the area of the stress raiser and a porous surface on the left hand side face of the stress raiser which corresponds to the hot tear on the front face.  In an attempt to reduce the amount of porosity in the vicinity of the stress raiser the N-17 material was replaced with stainless steel. The front flat surface of the stress raiser was coating with boron nitride hardcoat to reduce heat flow into the mould under the filling point. Figure 6-9 shows photographs of an AA3003 casting in which the mould was preheated to 200°C and the pouring temperature was 800°C. Two thin hot tears were initiated in this test. The first 100mm tear on the right hand side of the casting centreline extends from 60mm above the chill to 10mm from the top of the casting. The second also starts 60mm above the chill on the left hand side of the filling position and extends upwards 60mm in length as indicated by the lines marked on the photograph in Figure 6-9. Other tests conducted with the stainless steel riser gave rise to similar results and confirmed that constraint generated in this configuration is clearly large enough to initiate hot tears if this is coupled with a hot spot in the area where a hot tear is being encouraged.  63  FRONT  BACK Figure 6-7: Example 1 of restrained bar casting carried out with an N-17 stress raiser.  64  FRONT  BACK Figure 6-8: Example 2 of restrained bar casting carried out with an N-17 stress raiser.  65  FRONT  BACK Figure 6-9: Example of restrained bar casting carried out with a stainless steel stress raiser.  66  6.3.2 Stage 2 – Improving the effectiveness of the hot spot and bottom pouring to eliminate shrinkage pipe  The hot tears initiated in the previous castings were encouraging. Clearly the amount of constraint on the casting induced by the bolts embedded in the casting was sufficient; however more control over the location of the tear was required, otherwise the capture of images for use with image correlation would remain difficult and unpredictable. To address this situation focus was shifted to optimisation of the hot spot and a 25.4mm (1 inch) wide strip of ceramic fibre paper insulation was fixed to the back panel of the mould with high temperature cement. The cement was cured in a furnace at 106°C (the maximum curing temperature) for 24 hours to remove all moisture from the cement and binders from the ceramic paper. Figure 6-10 is a schematic of the modified apparatus showing the positioning of the ceramic insulation. Figures 6-11 and 6-12 show the results of tests using ceramic paper insulation to induce an artificial hotspot in the casting.  Both tests were performed with a mould preheat of 200°C, a pouring  temperature of 800°C and were cast from remelted commercial AA3003.  Ceramic Fibre Crucible  Ceramic Fibre Paper insulation  Riser hole Restraining Bolts  Steel front and back panel Steel Side Panels Water cooled copper chill  Figure 6-10: Schematic of modified casting, showing the positioning of the ceramic insulation.  67  A large, straight hot tear can be seen in the front of the casting in 6-11; it is centred on the artificial hot spot and runs from 25mm above the chill upwards to the top of the casting. This implies that the ceramic insulation was sufficient to maintain a higher temperature in the centre of the casting and consequently better localise the strain. On the reverse side of the casting the tear can be seen to have penetrated the thickness of the casting, however the casting surface reveals a great deal of porosity. At the top of the casting a large cavity has formed under the filling point, suggesting that liquid metal flow into mould was cut off and feeding was restricted toward the end of solidification. 6-12 shows a casting carried out with ceramic fibre to insulate and promote a hot spot in the casting. Once again, a large hot tear was initiated and runs nearly the full height of the casting. The reverse side once again shows porosity around the hot hear and has a large cavity under the filling position.  In an effort to remove the amount of piping that occurred in the centre of these castings, the mould design was changed to facilitate bottom filling (Figure 6-13). Two tests were carried out, one with insulation on the inside of the mould and one without (Figures 6-14 and 6-15). The casting parameters were the same as for the previous castings with a 200ºC mould pre-heat and 800 ºC pour. In the casting without the insulation continuous tears were formed on both the front and back of the casting. The casting suffered from poor feeding at the top of the casting which resulted in a large horizontal cavity that extended down 15mm into the casting. Surface shrinkage in the casting thickness direction was also present directly in front of the filling inlet. The hot tear initiated directly above the filling inlet.  In the second casting with ceramic insulation a straight hot tear can be seen on the front of the casting in proximity to hot spot; however this tear is accompanied by several smaller vertical tears that run parallel to it and another that has initiated near the top of the casting. On the back of the casting a large pipe cavity has formed which penetrates deep into the centre of the casting towards the top. The formation of these pipes can be  68  attributed to cooling path of the casting and will be addressed later in the modelling results section. Ultimately, the bottom filling method was rejected due to the poor feeding which lead to the pipe formation coupled with inadequate control of the hot tear position. It is likely that the filling runner solidifies soon after pouring is complete as the inlet is close to the chill plate. However, even if this were not the case, filling the casting so close to the chill may interfere with the directional nature of solidification.  69  FRONT  BACK Figure 6-11: Example of restrained bar casting carried out with a ceramic paper strip to promote a hot spot in the centre of the casting.  70  FRONT  BACK Figure 6-12: Example of restrained bar casting carried out with a ceramic paper strip to promote a hot spot in the centre of the casting.  71  NB: Ceramic Fibre Crucible (NOT SHOWN)  Runner  Riser hole Ceramic Fibre Paper  Restraining Bolts  Bottom pour  Steel Side Panels Water cooled copper chill  Steel front and back panel  Figure 6-13: Example of restrained bar casting carried out with bottom filling.  72  FRONT  BACK Figure 6-14: Example of restrained bar casting carried out with bottom filling and a ceramic paper strip to promote a hot spot in the centre of the casting.  73  FRONT  BACK Figure 6-15: Example of restrained bar casting carried out with bottom filling but without ceramic fibre insulation at the hot spot.  74  6.3.3 Stage 3 – Implementation of glass viewing window  Figure 6-16 shows the third stage of development of the test apparatus. In this version the front panel of the mould has a 34mm (1.3inch) × 147mm (6.2 inch) × 6.3mm (0.25 inch) slot machined into the face. This slot was designed to accommodate a press fit borosilicate glass window to allow images of the solidifying metal to be recorded by the image correlation camera system.  Riser hole  Steel Pouring Assembly  Ceramic Insulation  Restraining Bolts  Steel Front Panel  Water cooled copper chill  Borosilicate glass window  Figure 6-16: Schematic of final experimental set-up, N.B. the steel front panel has been reversed to better indicate how the glass is fitted into the panel.  75  As the liquid metal enters the mould cavity the glass window is pressed against a ridge running around inside of the hole forming a leak resistant tight fit. Thin strips of ceramic fibre insulation are also fitted between the glass and the hot mould for further safety and to minimise friction on the glass (Figure 6-17). A strip of ceramic fibre insulation, 25.4mm (1 inch) wide, is pasted onto the inside back face of the mould with high temperature cement and is positioned directly opposite the window. The strip runs the total height of the mould from chill to pouring hole. This strip is used to insulate the middle section of the casting with the aim of slowing the cooling in this area allowing strain to accumulate in the centre of the casting in front of the window. As before 7 × 50.8mm (2 inch) bolts are solidified into the casting and act to restrain the casting in the horizontal direction as it solidifies.  Borosilicate Glass Window  Ceramic Fibre  Figure 6-17: Press fit of borosilicate glass into the front panel of the mould using ceramic fibre paper to provide a seal. The surface shown is in contact with the casting.  76  6.3.4 Modifications to the casting pouring inlet The casting procedure was identical to that described in the previous section with one modification to the pouring inlet. Detailed photographs of the casting set-up have been provided in Appendix A.  In the tests at University of Queensland no wetting of the glass window occurred due to the location of the glass above the casting. During the work carried out at UBC many tests incorporating the borosilicate window suffered from metal/glass chemical reactions during pouring, leaving a reflective coating similar to a mirror on the inside of the glass prohibiting the recording of images for correlation. To curb this reaction, a stainless steel insert was designed to deflect incoming metal away from the glass. The insert is located directly under the metal inlet and was coated with boron nitride to inhibit heat transfer during pouring. The underside of the insert was lined with ceramic fibre paper. Figure 6-18 is a photograph of successful casting A1. The pouring modification is marked (A). An additional benefit of the modification is that the lapped or folded surface texture (B) is moved away from the centre of the casting. This surface texture is caused by chilling on the sides of the mould as the metal is poured and can interfere with the collection of clear images of the as-cast surface.  Based on previous tests, heat flow from the inlet material (metal head) has little effect on the temperature in the hot spot when ceramic insulation is used to influence the temperature in the centre of the casting. Therefore redirecting the inflow of metal has no detrimental effect on the ability of the set-up to initiate a hot tear.  Without the insert this surface texture, which often includes folding of the semisolid metal, frequently obscures the hot tear as it is forming. The impression of the glass window on the surface of the casting has been indicated (C). The thermocouple positions may be observed on the back side in a staggered pattern near the bottom (chill end) of the casting.  77  A  B  C  FRONT  BACK Figure 6-18: Photographs of successful bar test A1 showing A) pouring modification to direct metal flow away from the centre of the casting and away from the glass window, B) unwanted surface texture from filling directed away from centre of casting and C) the surface impression caused by the glass window in front of the hot tear.  78  A shrinkage pipe at the rear of the casting is also visible; however, the distance from the chill at which the pipe starts is above that of the camera frame on the front of the casting. This being the case it can be assumed that the area viewed by the correlation camera has received an acceptable amount of liquid metal feeding. The formation of the pipe is due to insufficient feeding, coupled with the fact that this area is the last to solidify.  The photographs in Figure 6-19 are close-ups of the hot tears in casting A1. The poor surface quality in the shrinkage pipe (A) and the impression left by the glass window (B) are shown as well as the locations of the thermocouples. The mineral oil applied to the glass was sufficient to inhibit a reaction during initial contact of the liquid and in particular, the region in which the images were taken for strain correlation the glass suffered little or no damage. The height of the image recorded by the LaVision software has also been marked on the photograph. As previously mentioned the start of the shrinkage pipe lies above the image field of view.  79  Figure 6-19: Photograph of the centre of casting A1, indicating the shrinkage pipe caused by feeding problems (A) and also the impression left by the glass (B) on the front of the casting. The height and positioning of the correlation image is also shown in the “front” picture.  80  6.4 Experimental procedure 6.4.1 Mould preparation Before testing, any parts of the mould that have ceramic fibre insulation pasted onto them are fired in an electric box furnace at 110°C for 24 hours to allow full curing of the high temperature paste and also to remove any moisture/binders within the ceramic fibre. After firing, pouring and vent holes are cut into the fibre insulation that is attached to the top of the mould. Holes for thermocouples are made through the insulation covering the back panel of the mould.  6.4.2 Alloy preparation 2.5 kg of metal alloy is placed in a ceramic crucible that has been treated with boron nitride hardcoat and heated from room temperature to the required pouring temperature. Heating from room temperature ensures that all moisture is removed safely from the as-cast ingot pieces, eliminating the risk of explosion due to any water that may be inadvertently present. The pouring temperature is generally 60-100°C above the liquidus temperature for the alloy used. It was determined that the Borosilicate glass was sensitive to attack by liquid aluminium alloys containing Magnesium above 700°C, which results in a magnesium oxide coating on the surface of the glass. The oxide appears as a silver/black coating that obscures the casting surface. Therefore it was necessary to reduce the preheat of the alloys accordingly to avoid this reaction. A light silicon oil was also applied to the glass directly before preheat in an attempt to further discourage the reaction. Melting can take up to 4 hours, during which time the Digital Image Correlation system is set-up.  6.4.3 Digital image correlation system set-up and calibration This work uses a LaVision  [41]  digital image correlation system to acquire images  and to process them to correlate displacements and subsequent strains within the area of the hot tear. The software used with the LaVision system is their commercial DaVis 81  Intelligent Imaging program with the Strainmaster package. The system is operated in 2D mode which requires a single camera and tracks displacement in the x and y directions. Relative to the set-up, x is horizontal and perpendicular to long axis of the tear and y is vertical and parallel to long axis of the tear. No topographical data is collected. The camera used is a LaVision Imager QE equipped with a Nikon AF Micro-NIKKOR 60mm f/2.8D lens which allows for a minimum focusing distance of 0.229m (9 in.). The Imager QE is a High dynamic CCD camera with a progressive scan sensor and an internal cooling system. The resolution of the images is 1376 x 1040 pixels. The camera has a very low readout noise allowing high image quality. The system records images at approximately 8 frames per second (fps). Data is acquired starting immediately after pouring and ends once the hot tear can be seen. This usually amounts to approximately 30 seconds of data. To calibrate the system the camera must first be focused with adequate depth of field to take into account the contraction of the metal away from the glass upon cooling. Focusing is carried out on the mould system containing a previously cast solid specimen (trimmed to allow it to be slotted into the mould). The camera is focused on the solid sample through the glass, using an aperture setting of f8 as the lens has been proven to give a soft focus at wider apertures. The position of the camera tripod is marked on the floor with scotch tape, although the tripod and camera are not moved after focusing. The chill resides in a holder in front of the camera during casting and the position of the chill is marked on the holder for ease of placement after the mould is removed from the preheat furnace prior to testing. After focusing the mould is disassembled and the focusing block removed. The image correlation system also requires a calibration in space. This is necessary to allow the software to adjust the displacements measured for camera misalignment, thus adjusting for perspective in the captured image. For a 2-D correlation set-up using one camera the LaVision package requires an image to be captured of a focusing block or printed card as in Figure 6-20. The mould is reassembled with the focusing card attached firmly to the inside of the glass window. The set-up is repositioned in the chill holder in front of the camera. The software package is set to calibration mode  82  and an image is captured of the focusing card. The user must enter the frequency and width of the crosshair marks into the software and also manually selects 3 points (as indicated on Figure 6-20) before the software automatically locates the remaining dots on the image. Once this is complete a root mean squared error is reported to allow the user to determine the accuracy of the fit which has been determined. For a 3-D setup using two cameras it is necessary to place the calibration card at various orientations to allow the software to locate the angle at which each camera is pointed towards the specimen. For the 2-D setup one calibration image is sufficient.  Detected points  User Defined Points Figure 6-20: Image capture of the LaVision Calibration card. The user defines three points and the software detects the remaining points and reports a statistical error.  Data Acquisition for Thermocouple Measurement  LaVision Correlation System  Liquid metal reservoir Halogen Lamp Light Source USB Data Acquisition Card  CCD Camera  Lens  Water cooled copper chill  “E” type Thermocouples  Figure 6-21: Schematic of test set-up showing the various data acquisition equipment.  83  6.4.4 Thermocouples Once the image correlation system calibration is complete and the focusing card is removed, the thermocouples are attached. Figure 6-21 describes the entire experimental set-up as a schematic, showing the image correlation system and thermocouple data acquisition  setup.  OMEGA  E-type  (“Chromel”–Ni-Cr,”Constantan”–Cu-Ni)  thermocouples were used which have an accuracy of ±1.7°C over a temperature range of 0°C to 900°C. The thermocouple wire comes coated with ceramic and encased in stainless steel sheath. The sheathing is stripped back a few millimetres and the wires were welded together and checked to be in good working order with a thermocouple reader. During casting the thermocouples are connected to a computer data acquisition system (Measurement Computing, China) which is connected to a PC laptop via a universal serial bus (USB) port. 8 channels of temperature data are recorded at the locations shown in Figure 6-22.  Thermocouple 0 (TC0) is located 12mm from the chill face, with the remaining 7 thermocouples (TC1−TC7) staggered every 5mm vertically up the casting to a maximum height of 35mm. The thermocouples were staggered to minimise the effect of the thermocouples influencing the propagation path of the hot tear. The actual position of the thermocouples before each casting can be gathered from the first image of the correlation capture prior to filling as shown in Figure 6-23.  6 4 2 0  7 5 3 1  Figure 6-22: Schematic of thermocouple locations in the back face of the casting.  84  Figure 6-23: Map of thermocouple locations in the back face of the casting.  6.4.5 Mould preheat After the thermocouples have been attached a light silicon oil is applied to the glass inner surface and the mould is rebuilt. During melting the complete mould with glass and thermocouples inserted is preheated in a separate box furnace to 200°C to remove moisture before casting. The preheat furnace is top opening and is constantly purged with nitrogen during heat up to avoid oxidation of the copper chill plate. This allows for quick removal and deployment of the mould into the stand before casting. On casting, the temperature of the mould has generally dropped to approximately 150°C. When the metal alloy has reached pouring temperature the image correlation system is started and the furnace and the nitrogen stream are both turned off. The mould is removed from the furnace using fireproof gloves and is placed in front of the camera in the chill plate holder. The water cooling is attached to both sides of the chill and the thermocouple wires are connected to the computer data acquisition system and temperature data recording begins.  85  6.4.6 Melt pouring and argon purge Once the mould is ready the liquid metal is carefully removed from the melting furnace and the surface is skimmed to remove oxidation products. The temperature is recorded with a handheld thermocouple reader (K-type). During this time a second person purges the mould with Argon to help reduce the oxidation reaction between the glass and the liquid metal. The assistant then stands back. The metal is poured into the mould top crucible. After pouring the top of the crucible is covered with stiff ceramic fibre board and the cooling water is turned on within 10 seconds. The incoming water temperature is generally quite constant at around 14−16 °C and the flow is set to 10 litres/min via an adjustable flow meter at the inlet.  86  Chapter 7 – UBC Experimental Results & Discussion  7.1 Introduction In this chapter the results and analysis of the most successful restrained bar casting test (designated test A1) will be presented. The suitability of image correlation to measure displacements and subsequent strain development during hot tearing in aluminium alloys will be presented. The gathered strain data will be compared to thermocouple data to investigate the evolution of strain with fraction solid during directional solidification.  7.2 Alloy composition analysis As this work is also aimed at understanding strain accumulation in conjunction with the evolution in the fraction solid, a sample of the alloy used for this test was sent to RioTinto Alcan for analysis. The chemical composition (shown in Table 7-1) was subsequently used in the thermodynamic and phase diagram software Thermo-CalcTM to estimate the evolution in fraction solid with temperature and will be discussed later in the chapter.  Table 7-1: Alloying elements present in A3003.  Alloying Element – weight % (remainder Al)  AA3003  Si  Fe  Cu  Mn  Mg  Ni  Zn  Ti  Ga  V  0.09  0.66  0.08  1.04  0.03  0.01  0.01  0.01  0.01  0.02  87  7.3 Thermo-Calc™ fraction solid predictions As fraction solid vs temperature data for AA3003 is not readily available in the literature, the commercial software Thermo-Calc™ was used to carry out thermodynamic and phase diagram calculations for the fraction solid development. The Thermo-Calc analysis was completed using the Scheil formulation, which assumes that solute does not diffuse back into the solid and is rejected completely into the liquid. The simulation was run assuming the following phases will be present during solidification: Al3Fe, FCC alpha and Al6Mn. The predicted fraction solid curve for AA3003 supplied can be seen in Figure 7-1. The fraction solid versus temperature curve describes a reasonably short solidification interval of 17ºC with as little as 5ºC (652ºC) of cooling until the fraction solid has risen to 0.92, it is around this value that hot tearing is believed to occur.  658 656  Temperature (oC)  654 652 650 648 646 644 642 640 0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0  Fraction Solid  Figure 7-1: Predicted fraction solid curve of AA3003 of given composition.  88  7.4 Image and field of view In this directionally solidified casting, pull away from the glass appears as a band or front which travels steadily upwards away from the chill. Lagging behind this front by ~3-5mm is the opening of the hot tear in an unzipping motion. In the previous study, using the apparatus at The University of Queensland, pull away from the glass due to bulk contraction was observed to occur evenly over the entire field of view. After which displacement/strain measurement by means of digital image correlation commenced.  Figure 7-2A shows the mould full of liquid before the solidification front has passed into view. Because the imaging camera needed to be positioned close to the foundry floor the camera had to be affixed upside down onto a tripod, thus the chill is located at the top in these images. For the purpose of discussion and to avoid confusion, the orientation as appears in the images will be used. Figure 7-2B shows the same test almost 10 seconds later. The pull away front can be clearly delineated advancing at an angle, which suggests there is a horizontal variation in the cooling rates. Also noticeable is the early formation of the tear which initiated at a location between the chill and top of the field of view. The top of the field of view corresponds approximately to the bottom of the glass window and is located ~10mm from the chill face.  Figure 7-3A and Figure 7-3B are further images of test A1 captured at 5s and 7s after Figure 7-2B. They show continuing advancement of the solidification front and hot tear. Figure 7-3A indicates that the pull away front has flattened out. In Figure 7-3B the solidification front has completely passed out of view.  By tracking the position of the front as a function of distance from the chill over time it is possible to determine the velocity of the solidification front itself. Figure 7-4a shows the distance of the solidification front from the chill versus time and Figure 7-4b show the related velocity of the front as a function of distance from the chill.  89  CHILL  A Tear  CHILL  Pull away front  B  Figure 7-2: Sample images captured during the solidification of test A1. Image A) shows the mould full of liquid metal before the pull away front moves into view. Image B) shows the pull away front 10 seconds later. The chill is located at the top of these images.  90  CHILL  Pull away front  A CHILL  B  Figure 7-3: Further images of test A1 showing further development of the tear. A) Shows a flatting out of the solidification front and extension of the tear. B) Shows the solidification front passing out of the field of view.  91  22  Distance from chill (mm)  21 20 19 18 17 16 15 14 13 8  9  10  11  12  13  14  15  16  17  18  19  20  Time (s)  (a) 0.0010 0.0009  Front velocity (m/s)  0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.0000 14  15  16  17  18  19  20  21  Distance from the chill (mm)  (b) Figure 7-4: (a) Distance of solidification front from chill versus time, (b) front velocity versus distance from chill for test A1  92  7.5 Thermocouple results As previously discussed, eight thermocouples were embedded in the casting at various distances from the chill and within the field of view of the camera. A plot of the temperature versus time data for test A1 is shown in Figure 7-5.  On careful inspection of the cooling data it becomes apparent that there are four pairs of thermocouple responses, which is contrary to what would be expected for thermocouples that are set at uniformly increasing distances from the chill in the case where there is 1-D heat transfer (note: the increments range from 4 to 6mm, with the majority at 5mm). As there are two columns of thermocouples displaced horizontally ~10mm from one another, the pairing effect is likely related to a horizontal variation in the heat transfer which is consistent with the pull away front angle as discussed earlier. There are at least three possible reasons for this effect. Firstly, as the water entering the chill is slightly cooler than that leaving the chill there may be a slight increase in cooling on the inlet side. Secondly, bulk contraction during cooling will tend to promote gap formation between the chill and the casting. It is likely that the casting will contract upwards towards the first set of horizontal restraining bolts. However, on the side of the casting which shows an increased cooling there is evidence that some liquid metal leaked down between the chill and mould side panel. This would have restricted vertical bulk contraction of the casting and would have increased cooling in that area. Finally, it is possible that a slight misalignment of the mould on the chill will cause the same effect. The chill and mould are separated by ceramic fibre paper to insulate the chill effect on the mould walls. This generally forms a tight fit however a small vertical misalignment may have been present.  93  700 TC0 - 12mm TC1 - 17mm TC2 - 21mm TC3 - 27mm TC4 - 32mm TC5 - 37mm TC6 - 42mm TC7 - 47mm  675  Temperature (oC)  650 625 600 575 550 525 500 0  20  40  60  80  Time (s) Figure 7-5: Temperature vs. Time data for test A1 – AA3003.  7.6 Thermal model development As previously described one of the major shortcomings of the University of Queensland work was the lack of temperature data, negating the possibility of a comparison between strain evolution and fraction solid evolution. To overcome this shortcoming the casting was designed to facilitate directional solidification with thermocouples in close proximity to where the crack would occur. Due to a combination of factors – e.g. the thermocouple data was acquired at the centre of the thickness, whereas the strain data was acquired at the surface, and that the thermocouple data was obtained at discrete locations, whereas the strain data was acquired at different locations – it was necessary to develop a 3-D transient thermal model of the casting to fill in the gaps in the temperature data.  94  Temperature data was recorded at a rate of 1Hz from a time before the metal was poured into the mould. The first thermocouple was placed just below the glass window, 12 mm from the chill, with the remaining seven positioned in a staggered fashion every ~5 mm upwards at a width of 10 mm apart.  Figure 7-6 shows the heating and cooling data plotted as temperature vs. time for the first three thermocouples from the chill in test A1; TC0, TC1 and TC2 which were located 12, 17 and 21mm from the chill respectively. All of the strain measurements were taken between TC0 and TC2 in this test. Figure 7-6 also shows the rapid heating that occurs in the three thermocouples during pouring when they first come into contact with the liquid metal. In this alloy, 640ºC is taken to be the solidus temperature and 657ºC the liquidus temperature.  658 TC0 (12mm) TC1 (17mm) TC2 (21mm)  656  Temperature (oC)  654 652 650 648 646 644 642 640 0  5  10  15  20  25  30  Time (s) Figure 7-6: Evolution of temperature for test A1 for the first three thermocouples; TC0, TC1, TC2.  95  Note that it appears that the rapid cooling from the chill resulted in TC0 not being exposed to material at the liquidus such that it only reached a maximum temperature of 656ºC. In the case of the other two thermocouples, it is interesting to note that they only reached the liquidus indicating a significant loss of heat during metal transfer from the furnace and during pouring.  7.6.1 Thermal model A 3D thermal model was created using the ABAQUS 6.7-5 finite element package. A mesh was created of the casting and the chill only, neglecting the mild steel mould. The effect of the mould on the casting was modelled using free convection type boundary conditions on the casting surfaces. The model also neglects mould filling and assumes that the mould is full at the start of the simulation. Figure 7-7 shows the domain mesh created for the model.  The mesh in the y-direction (the height of the casting) is relatively fine (1 mm) allowing temperatures to be predicted at the same distances from the chill as the strain locations obtained from the correlation analysis. The mesh resolution in the width direction (z) is 5.83mm over a 35mm section at the centre of the domain and 11.75mm away from the centre. It is comparatively lowered due to the fact that only a small thermal gradient in the width direction is expected in the regions of interest. The resolution in the through thickness (x) direction is more critical and so a higher resolution (2.5mm) is required to resolve the temperature. The chill has been modelled with a course mesh and allows for the presence of a gap (gap conductance) between the base of the casting and the chill.  The front, back and bottom surfaces of the casting mesh have been partitioned to facilitate the placement of boundary conditions that simulate the effect of the glass fibre insulation.  In this way the heat transfer across the fibre/casting and mould/casting  interfaces can be varied independently with temperature as described below. The partitioning is shown in Figure 7-8. 96  7.6.2 Model inputs Model inputs for the thermo physical properties were based on data gathered for AA5182  [42]  (an aluminium magnesium alloy), pure Aluminium as well as limited data  available for AA3003. The data includes solidus and liquidus temperatures; thermal conductivity, specific heat, density and latent heat at different temperatures. The density has been assumed to be constant at 2710 kg/m3. The input data has been summarised in Table 7-2. The release of latent heat is temperature dependent and is based on the estimated fraction solid development from the Thermo-Calc predictions.  Figure 7-7: Model mesh of casting and chill.  97  Insulation partition Water channel Figure 7-8: Shows the partitioning of the model to account for the simulation of the ceramic fibre insulation.  Table 7-2: Thermo-physical properties of AA3003 [42, 43]  Property  Temperature  Equation (T in ºC)  Solidus (ºC) Liquidus (ºC) Conductivity (W m-1 K-1)  640 657 25 ≤T ≤660 T < 536 536≤T ≤637 T > 637 640 ≤T ≤657  n/a n/a 0.0787T + 138.03 897+0.452T -994-8T-0.00074T2 1097 2710 397100  Specific Heat (J kg-1 K-1) Density (kg m-3) Latent Heat (J kg-1)  98  7.6.3 Thermal model boundary conditions The initial temperatures of the casting (657ºC) and chill (147ºC) were fixed, uniform and reflected the experimental conditions. All external surface boundary conditions were of a convection type as shown in Eq. 7-1. q = h(Tsurface − Tambient )  7-1  where q (W/m2) is the convective heat flux, h (W/m2 • °C) is the convective heat transfer coefficient, and Tsurface and Tambient (K) are the surface and ambient temperatures. The heat transfer coefficient given for external surfaces in contact with air (mainly on the chill) was 50 W/m2/°C  [44]  . As the chill is water cooled the heat transfer to the water was  accounted for by using a constant surface film heat transfer coefficient of 6400 W/m2/°C [43]  . The insulation on the rear of the casting which acts to create the hot spot was given a  constant film heat transfer co-efficient of 0 W/m2/°C or zero heat flux. The initial temperature of the mould and glass window just prior casting was 147°C.  The sides of the casting in contact with the mould were given a convection type boundary condition that varied with temperature (Figure 7-9) to account for gap formation which would occur during bulk contraction of the casting. The heat transfer between the glass and casting has also been attended to in a similar manner to the mould/casting interface. Note: that the model domain did not include the mould or glass.  Interfacial heat transfer between the casting and chill also has to include any effects of gap formation during solidification and shrinkage of the casting. Initially the liquid is in good contact with the surface of the copper chill, but as time progresses solidification will occur and the casting will contract away from the chill. This is especially important in this set-up where the casting has bolts which are frozen into the sides. Solidification contraction will in effect lift the casting slightly off the chill after the solidification front passes the first set of bolts.  99  Heat transfer co-efficient (W/m2.°C)  900 Mould heat transfer  800 700 600 500 400 300 200 100 0 500  525  550  575  600  625  650  675  Temperature (oC) Figure 7-9: Heat transfer across mould/casting and glass/casting interfaces to account for gap formation during solidification (same boundary condition used for both interfaces). 27500  Heat transfer co-efficient (W/m2.°C)  25000  Right side chill/casting Left side chill/casting  22500 20000 17500 15000 12500 10000 7500 5000 2500 0 0  100  200  300  400  500  600  700  Temperature (oC) Figure 7-10: Heat transfer across chill/casting interface to account for gap formation during solidification.  100  To account for this, the effective heat transfer coefficient is decreased as the temperature of the surface of the casting in contact with the chill decreases.  7.6.4 Correction of uneven cooling To account for the uneven cooling between the chill and the base of the casting, as described earlier, it was necessary to write a FORTRAN subroutine within ABAQUS to allow for the interfacial heat transfer to vary with both position (spatially) and temperature. The subroutine (which has been included as Appendix B) merely instructs ABAQUS to use one of two sets of gap conductance data based on nodal position on the chill. This data has been plotted in Figure 7-10.  7.6.5 Thermal model predictions The comparison between the results of the thermal model and the experimental data is shown in Figure 7-11. The plot shows that the model over predicts the amount time taken for the cooling front to reach the various thermocouple positions – e.g. the cooling front is predicted to reach TC0 at 11 s whereas at 12 mm from the chill TC0 starts to cool at 7 s. A similar offset in cooling is experienced at the other thermocouple locations 17 and 21mm from the chill. As the rate that the cooling front propagates through the casting is a function of the material thermal diffusivity, and assuming the input data used in the model is basically correct, it is believed that the offset is due to a delay in the time associated with the thermocouple data acquisition.  To address this problem the thermocouple data has been shifted in time by 4 s. This alignment can be justified as the time taken to pour the liquid metal into the mould is also approximately 4 s. A comparison between the TC data and the model predictions following the addition of 4 seconds to the thermocouple data is shown in Figure 7-12, and shows a very good fit.  101  658 656  Temperature (oC)  654 652 650 648 646  TC0 (12mm) TC1 (17mm) TC2 (21mm) 12mm Model 17mm Model 21mm Model  644 642 640 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s) Figure 7-11: Thermal model predictions vs. experimental data for centre nodes in the casting.  658 656  652  o  Temperature ( C)  654  650 648 TC0 (12mm) TC1 (17mm) TC2 (21mm) 12mm Model 17mm Model 21mm Model  646 644 642 640 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s) Figure 7-12: Thermal model predictions versus experimental data shifted by 4s.  102  As previously indicated, the cooling data that is actually required from the model is for nodes at the surface of the casting and at the locations where the displacement data was acquired. Figure 7-13 is a plot containing the variation in temperature with time predicted by the model at the surface of the casting at a series of distances from the chill. These positions are consistent with where the displacement measurements were made during digital image correlation.  To reiterate, as there is a temperature gradient between the centre of the casting and the surface it is necessary to use the model to estimate the temperature on the surface. The problem with this approach is that the temperature evolution predicted by the model at the surface is a function of the boundary condition imposed within the model at the casting/glass interface, and there is no rigorous method within the current experimental setup to verify that the boundary condition and associated surface temperature evolution is correct.  To attempt to address this problem the pull away front seen moving downward in the images has been used to tune the model boundary condition at the casting/glass interface. The approach used was to adjust the casting/mould boundary condition until the time at which the front passed each thermocouple corresponded to a temperature relating to a solid fraction of between 0.8 and 0.9, which is believed to correspond to the end of mass feeding and beginning of volumetric contraction.  To avoid the obvious shortcomings of this approach the problem was constrained by also requiring that the temperature predicted by the model at the centre of the casting, corresponding to the location of the thermocouples, agreed with the thermocouple data.  103  658 656  Temperature (oC)  654 652 650 648  14mm 15mm 16mm 17mm 18mm 19mm 20mm 21mm  646 644 642 640 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s) Figure 7-13: Thermal model predictions for face nodes at the positions where the point strain measurements were acquired.  7.6.6 Results Figure 7-14 shows the predicted fraction solid data for surface nodes at the positions where the point strain measurements were acquired. These predictions are based on the thermal model output and the estimation of solid fraction evolution with time from the Thermo-Calc software. Also demarked on the plots is the time at which the pull away front passes the position plotted.  Each plot shows that pull away from the glass occurs at approximately 0.8–0.9 fraction solid as described above. As the front progresses the fraction solid at which pull away occurs rises slightly further away from the chill.  104  1.0  658  656  0.9  656  Temp. 14mm Fraction Solid Front pull away  650 0.5 648 0.4 646  0.3  644  0.6 650 0.5 648 0.4 646  642  0.1  642  640  0.0  640  8  10  12  14  16  18  20  22  24  26  28  30  0.1 0.0 0  2  4  6  8  10  12  Time (s) 1.0  658  656  0.9  656  Temp. 16mm Fraction Solid Front pull away  0.8  650 0.5 648 0.4 646  0.3  644  20  22  24  26  28  0.7  0.3 0.2 0.1 0.0 0  2  4  6  8  10  12  Time (s)  Temp. 18mm Fraction Solid Front pull away  1.0  658  0.9  656  0.8  650 0.5 648 0.4 646  0.3  644  30  22  24  26  28  0.8 0.7  0.4 646  640  20  0.9  0.5  0.0 18  1.0 Temp. 19mm Fraction Solid Front pull away  0.3  30  0.2 0.1 0.0 0  2  4  6  8  10  12  Time (s)  14  16  18  20  22  24  26  28  30  Time (s)  658  1.0  658  1.0  656  0.9  656  0.9  0.8  650 0.5 648 0.4 646  0.3 Temp. 20mm Fraction Solid Front pull away  644 642  0.2  640 0  2  4  6  8  10  12  14  16  Time (s)  18  20  22  24  26  28  30  0.7  652  o  o  0.6  Fraction Solid  0.7  652  0.8  654  Temperature ( C)  654  Temperature ( C)  28  648  640 16  26  0.6  642  14  24  650  0.1  12  22  652  642  10  20  644  0.2  8  18  o  Fraction Solid  0.6  Temperature ( C)  652  6  16  654  0.7  o  Temperature ( C)  654  4  14  Time (s)  656  2  0.8  0.4  30  658  0  0.9  Temp. 17mm Fraction Solid Front pull away  646  640  18  1.0  0.5  0.0 16  30  648  640 14  28  0.6  642  12  26  650  0.1  10  24  652  642  8  22  644  0.2  6  20  o  Fraction Solid  0.6  Temperature ( C)  652  4  18  654  0.7  o  Temperature ( C)  654  2  16  Time (s)  658  0  14  Fraction Solid  6  0.2  Fraction Solid  4  0.3  0.6 650 0.5 648 0.4 646  0.3 Temp. 21mm Fraction Solid Front pull away  644  0.1  642  0.0  640  Fraction Solid  2  0.7  652  644  0.2  0  0.8  o  Fraction Solid  0.6  Temperature ( C)  652  0.9  Temp. 15mm Fraction Solid Front pull away  654  0.7  o  Temperature ( C)  654  0.8  1.0  Fraction Solid  658  0.2 0.1 0.0  0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s)  Figure 7-14: Predicted fraction solid data for face nodes at the positions where the point strain measurements were acquired.  105  7.7 Digital image correlation using the LaVison™ system In this section results of the image correlation analysis will be presented and the suitability of image correlation will be discussed. As previously described the LaVision commercial system was used to acquire images and correlate displacement during initiation of hot tears. It should be noted that the system does not correlate displacements on-the-fly; the image data is captured during the test and post-processed afterwards. Correlation processing is reasonably CPU intensive and can take up to 4 hours to complete.  As previously discussed digital image correlation is a method of comparing two images and matching either patterns, or in this case, grey scale values (pixel intensity) from one image to another. Each image is divided up into much smaller regions called “windows” or “subsets” which are interrogated to determine the relative movement of each window from one image to another [45] by maximising a correlation co-efficient. In this work the first image captured, known as the reference image, was compared to each subsequent image in sequence. A multi-pass approach was adopted for window size, using three passes in total. The first pass used a window size of 64×64 pixels with 50% overlap of windows. The remaining two passes used a window size of 32×32 pixels, also at 50% overlap. The software then calculates displacement vectors and subsequent strains which are extracted and reported. For the purposes of this study only the εxx direction has been extracted, where the x-direction is horizontal relative to the images captured or perpendicular to the crack.  An example of the vector grid output for test A1 is given in Figure 7-15. The vector grid marked (A) was captured one frame or 0.125s into the correlation and shows the near original 32x32 mesh. The grid marked (B) was captured at the end of the correlation and illustrates the extent of the deformation caused by a combination of the hot tear during solidification and cooling and any bulk motion. Note that the grid marked (B) are missing grid points within the mesh, these are caused when either the software cannot maximise the correlation co-efficient or when the displacement vectors become  106  too large or unreasonable compared to the surrounding vectors. Therefore, extracting data from these areas is unreliable.  The reference image for test A1 was selected as the frame just before the solidification/pull away front passes into view at the top of the image (Figure 7-15) and the mould is full. In the present example, the crack appeared from above the window and initiated at a location between the chill and window. The displacements and subsequent strains that have been measured are therefore the strains associated with propagation of the tear rather than initiation as in the previous collaboration with The University of Queensland.  CHILL  A  A  Tear location  B  B  Figure 7-15: Vector grid output after A, one frame and B, final correlation frame for test A1.  107  This first reference image was captured 3.348s after the liquid metal enters the mould and has touched the first thermocouple. The final image was selected as the frame in which the tear has opened and is only just visible at the bottom of the camera field of view, some 240 frames later. The size of each image captured is 1376×1040 pixels, with a resolution of approximately 46.58 pixels/mm (21µm/pixel). As the image capture rate (exposure time) is dependent of the light level, a bright halogen lamp was used to light the surface of the casting allowing a relatively fast exposure to be used. The images were captured at ~8 frames per second.  7.7.1 Correlation results for test A1 Test A1 was carried out with a metal pre-heat temperature of 720°C and a mould preheat of 200°C. The alloy used was AA3003 also designated as CA31209. The glass window was coated with silicon oil to inhibit the reaction between the borosilicate glass and liquid metal.  The image in Figure 7-16 shows the camera view immediately before the metal enters the frame. The axes shown (in mm) are the software’s interpretation of dimensions in the field of view; these are based on the calibration (see experimental setup). Also immediately obvious in the photograph are the locations of the thermocouples making it easy to pin-point their exact positions before the test. This is useful for comparison with the thermal model and will be discussed later.  The image correlation software is quite versatile and is able to determine displacement and subsequent strains in several different ways. This work utilised two methods for estimating the strain based on the displacements. The first involves placing a virtual strain gauge across the area of interest, much like measuring displacement in a traditional tensile test. The second method records strain at a single point to investigate strain development on a small scale.  108  Figure 7-16: The first image frame of test A1 – showing the thermocouple positions. As the camera was mounted upside down during the test, the top of the image lies closest to the chill.  An example of the first method is shown in Figure 7-17 which is an image captured of the final correlation frame of test A1. Overlaid on the image are the thermocouple locations and positions of several 7mm ‘virtual strain gauges’ which are located at various distances (14−21mm) from the chill. In the course of the analysis data was also collected at the same vertical locations using strain gauge lengths of 2 and 4mm. Unfortunately, the correlation software was not able to process greyscale values above TC2, this may be due to lighting or a trapped air bubbled on the surface of the casting. Displacements were measured at 1mm intervals from near the top of the window, with the midpoint of the virtual gauges lying on the centre of the forming tear. To achieve this, the images were rocked back and forth in animation to locate the exact location that the tear opened. An investigation was carried out to determine if the software was susceptible to error if the displacement line was not centred, however this was found not to be an issue.  109  TC0  TC1  TC2 TC3  TC4  Figure 7-17: The last image in test A1 – where the tear has opened throughout the field of view. Thermocouple positions have been marked as well as the locations of virtual 7mm strain gauges.  As the tests were carried out very close to the chill, running animations of the test showed a reasonable amount of displacement in the y-direction which can be attributed to bulk contraction. The software is capable of accounting for bulk motion by tracking the locations of the ends of the displacement lines, as described in the schematic in Figure 7-18a. However, it is possible that if shearing of the tear occurs at lower solid fractions then exaggerated tear opening strains may result, as shown schematically in Figure 7-18b.  110  Solidification Contraction  A  A  Solidification Contraction  B  A′  B  A′  B′ B′  Software can account for movement  This effect may give rise to exaggerated measured hot tearing strains  (A)  (B)  Figure 7-18: Schematic of displacement line movement during bulk contraction of the alloy. Case (A) movement due to bulk contraction is tracked by the software; case (B) tear opening displacement may be exaggerated if the displacement line is sheared during solidification.  7.7.2 Field size comparison The error in displacement calculation is dependent on pixel window or field size. In general, the error increases with decreasing window size. For the system used at UBC, which utilised a window size of 128×128 pixels, the associated error can be as high as 0.1% strain and decreasing the window size to 64×64 pixel increases the error up to 0.3% strain. However, the field size also depends to a great extent on the grey scale pattern that is being tracked, if the pattern is very small then much smaller window sizes may be used. The system manufacturers recommend that the ideal window size be based on the estimated maximum displacement to be measured in pixels multiplied by a factor of 4 in order to minimise error. Figure 7-19 shows a comparison of the strain associated with two different window sizes (64x64 pixels and 32x32 pixels) for a 4mm virtual strain gauge located across the opening tear, 16mm from the chill face. The strain results for the “64x64 pixel” curve were calculated by running a correlation with two passes and a constant window size of 64x64 pixels. The strain results for the “32x32 pixel” curve were generated starting at 64x64 pixels with a second pass at 32x32 pixels. The plots show that there is not a substantial difference in reported strain.  111  0.12 64x64 pixel field 32x32 pixel field  0.10  Strain  0.08  0.06  0.04  0.02  0.00 0  5  10  15  20  25  30  35  Time (s) Figure 7-19: Comparison of two window sizes for a 4mm virtual strain gauge, 16mm from the chill.  7.7.3 Strain field mapping As in the case of the University of Queensland data, a 2-D contour of the strain development around the tear with time can be extracted from the data. This is a somewhat qualitative interpretation of the data; however it provides an adequate description of discrete areas of strain localisation ahead of the tear opening. Figures 7-20 to 7-22 are correlation images and their associated strain maps from test A1 in sequence from A-G.  Figure 7-20A is the first frame of the correlation, at this point the mould is full of liquid metal and the solidification/pull away front has not yet moved into the image frame and consequently no strain has been measured. The dashed box on the correlation image marks the area over which the correlation was carried out; areas outside this mask are disregarded during the correlation, this is done to minimise computation time. Also imprinted on the images is the total time from the start of the correlation. The camera is  112  started before the liquid metal is removed from the furnace and therefore the first image is timed at approximately 83s. Turning to Figure 7-20B which is a snapshot of strain 4.7s later, the pull away front has moved into view on the correlation image and its length indicated by the white arrow on the left hand side. The hot tear is not yet visible but the associated strain map shows localisation of strain at the top of the window.  1.65 seconds later, in Figure 7-20C, coalescence of the two discrete areas of strain has occurred and the tear is just starting to form at the top centre of the casting image. Elsewhere on the strain map there are other areas of tension and compression that build and subside throughout the test without localising into permanent damage.  Figure 7-21 reveals further progression of the solidification front and tear formation. The strain map in Figure 7-21D reveals that although only a small tear 2mm long has formed at the top of the associated image, strain has already started to accumulate at least 3-4mm ahead and is keeping pace with the pull away front as it moves down the image. Once again discrete areas of strain have localised at the tear location and by Figure 7-21E have coalesced. By Figure 7-21F the pull away front has passed by the bottom of the image window and the strain map shows a clear and definite path that the hot tear will follow even though it currently lags some 5mm behind. It is also interesting to note that the width of the strain field far ahead of the tear is approximately 2mm; however in the final image in 7-22G, the total width of the strain field is on the order of 1mm confirming the process of distributed damage prior to single site localisation found in the previous University of Queensland study.  113  CHILL A  CHILL B  CHILL C  Figure 7-20: Development of tear, strain and pull away front during test A1. Note: Arrow indicates extent of progress of pull-away front in window.  114  CHILL D  CHILL E  CHILL F  Figure 7-21: Further development of tear, strain and pull away front during test A1. Note: Arrow indicates extent of progress of pull-away front in window.  115  CHILL G  Figure 7-22: Final development of tear, strain and pull away front during test A1.  7.7.4 Virtual strain gauge results In the previous work, which used the commercial software Vic-2D, the option of a virtual strain gauge was not available and therefore it is interesting to be able to investigate the suitability of this technique. For clarity, the plot in Figure 7-23 shows tear path, thermocouple position, virtual strain gauge position and window position as a function of distance from the chill and distance across the borosilicate glass window.  The strain versus time plots in Figure 7-24 show the development of global strain over gauge lengths of 2, 4 and 7mm with time for various distances from the chill. Each of the plots generally shows two regions of strain accumulation behaviour. At first, all three gauge lengths produce similar levels of strain. After a period of time, which increases with increasing distance from the chill, the curves begin to diverge with the 2 mm gauge length exhibiting the highest rate of increase followed by the 4 and 7mm gauge length based analyses. The point, or time, of divergence is thought to represent the onset of localised damage. This is consistent with the fact that once the accumulation of strain has been localised a small gauge length would result in a larger calculated strain (smaller denominator) as is observed.  116  28  Hot tear path  TC3  Distance from the chill (mm)  26  24  TC2  22  20  18  TC1 16  14  Bottom of window  TC0  12  10 0  5  10  15  20  25  Distance across window (mm)  Figure 7-23: Normalised and rotated plot of test A1 – showing the position of thermocouples, locations of 7 mm strain correlations and the window position.  117  0.24  0.24  14mm from Chill  0.22 0.20 0.18  0.18  0.16  0.16  0.14  0.14  0.12 0.10  0.12 0.10  0.08  0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02 0  2  4  6  8  2mm Gauge 4mm Gauge 7mm Gauge  0.20  Strain  Strain  15mm from Chill  0.22 2mm Gauge 4mm Gauge 7mm Gauge  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s) 0.24  Time (s) 0.24  16mm from Chill  0.22 2mm Gauge 4mm Gauge 7mm Gauge  0.20 0.18  0.18  0.16  0.16  0.14  0.14  0.12 0.10  0.12 0.10  0.08  0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02 0  2  4  6  8  2mm Gauge 4mm Gauge 7mm Gauge  0.20  Strain  Strain  17mm from Chill  0.22  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s) 0.24  Time (s) 0.24  18mm from Chill  0.22 0.20 0.18  0.18  0.16  0.16  0.14  0.14  0.12 0.10  0.12 0.10  0.08  0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02 0  2  4  6  8  2mm Gauge 4mm Gauge 7mm Gauge  0.20  Strain  Strain  19mm from Chill  0.22 2mm Gauge 4mm Gauge 7mm Gauge  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s) 0.24  Time (s) 0.24  20mm from Chill  0.22 0.20 0.18  0.18  0.16  0.16  0.14  0.14  0.12 0.10  0.12 0.10  0.08  0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02 0  2  4  6  8  2mm Gauge 4mm Gauge  0.20  Strain  Strain  21mm from Chill  0.22 2mm Gauge 4mm Gauge 7mm Gauge  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  Figure 7-24: Strain vs. time for 2, 4 and 7mm virtual strain gauge lengths, test A1.  118  7.7.5 Local strain at the hot tear location All of the evidence thus far points to hot tear formation as being due to a process of damage nucleation, coalescence and growth on a relatively small scale within the evolving solidification structure. Therefore the global strain measured using the strain gauge technique is only representative of the strain up to the point of localisation in an analogous manner to the calculation of strain based on gauge length in a conventional tensile test prior to the formation of a neck. It follows that the strain accumulated at the scale of the damage occurring within the microstructure will be much higher than the strain reported by the virtual strain gauge.  Within the LaVision software package it is possible to accurately select a point on the image set, track the movement of that point and calculate the accumulation of strain on a local scale. Using this approach, the point of crack initiation has been selected, the accumulation of displacement of this point has been acquired and the value of the local strain has been determined.  L P  0 x  X dx u  0 x’  P’  X  dx’ L’  Figure 7-25: Infinitesimal 1D Strain  119  Referring to Figure 7-25, the local strain at an arbitrary point, P, on a bar which has a position vector x and an infinitesimal neighbour dx has been illustrated. If during our test, point P moves to point P’, which has a position vector x’, then the step dx is stretched out to dx’. The strain at point P can be defined as;  ε=  dx'−dx dx  7-2  Since the displacement is; u = x'− x  7-3  It follows that the strain is;  ε=  dx'− dx du = dx dx  7-4  The plots in Figure 7-26 show the development of local strain at the hot tear at increasing distances from the chill. The time at which the tear is visible to the eye at that specific height above the chill has also been demarcated. As previously mentioned, the hot tear opens in a zip like fashion from the chill upwards through the casting. To acquire the approximate time at which the tear front opens the image set is rocked back and forth in sequence until the exact frame is identified. In addition, the contrast of the images is also gradually decreased in steps, providing a distinct increase in detail at each step. Using this method it is possible to systematically narrow down the number of frames to within 4 frames or approximately 0.5 seconds in time.  Table 7-3 lists the local strains at which the tear appears to open at increasing distances from the chill. It is immediately obvious that the strains reported here are some 4-7 times larger than the previous study conducted at the University of Queensland. The predominant reason for this difference is the difference in spatial resolution in the images acquired in the two different tests.  120  0.6  0.6 14mm from chill  15mm from chill  0.5  0.5  0.4  Tear Visible  0.3  Strain  Strain  0.4  0.2  0.3  0.2  0.1  0.1  0.0  0.0  -0.1  Tear Visible  -0.1 0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  Time (s)  0.6  0.6 17mm from chill  16mm from chill  0.5  0.5  0.4  Tear Visible  0.3  Strain  Strain  0.4  0.2  0.3  0.2  0.1  0.1  0.0  0.0  -0.1  Tear Visible  -0.1 0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  Time (s)  0.6  0.6 19mm from chill  18mm from chill  0.5  0.5  0.4  Tear Visible  0.3  Strain  Strain  0.4  0.2  0.2  0.1  0.1  0.0  0.0  -0.1  Tear Visible  0.3  -0.1 0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  Time (s)  0.6  0.6 21mm from chill  20mm from chill  0.5  0.5  0.4  Tear Visible  0.3  Strain  Strain  0.4  0.2  0.2  0.1  0.1  0.0  0.0  -0.1  Tear Visible  0.3  -0.1 0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  0  2  4  6  8  10 12 14 16 18 20 22 24 26 28 30 32 34 36  Time (s)  Figure 7-26: Development of local strain at the hot tear at increasing distances from the chill. Also demarcated is the time at which the tear is visible to the eye.  121  Table 7-3: Local strain at the hot tear at a time when it becomes visible.  Distance from Chill 14mm 15mm 16mm 17mm 18mm 19mm 20mm 21mm  Strain 0.104 0.137 0.179 0.141 0.161 0.144 0.081 0.087  In the University of Queensland test the field of view was 7mm x 5mm and the magnification was ~490 times, whereas in the UBC setup the field of view was 29.7mm x 22.28m and the magnification was ~280 times. As the detection of crack opening is done visually it will be highly sensitive to the image magnification and spatial resolution. As the magnification is lower in the UBC setup the crack opening will be detected at a higher strain than the experiments carried out at UQ. It follows that the higher strain recorded in tests with directional solidification will be larger and that there should be no correlation with distance from the chill.  7.7.6 Localisation of strain across the tear using previous approach Similar to the previous work, it is possible to plot strain versus distance across the hot tear to obtain an indication of how the strain in the vicinity of the tear develops. However, rather than plotting a single 2-D profile for the alloy, multiple plots from the same test but with increasing distances from the chill have been collated.  The previous plots in Figure 7-26 of strain at the location of the hot tear give a good indication of how the strain develops over time in test A1. What they do not show is the approximate strain at which the localisation occurs. To determine this information, strain contours across the width of the tear and beyond become valuable. In the previous University of Queensland based work, strain contours were plotted for several different  122  alloys and the average peak strain and macro (across the entire profile) strains before localisation were determined.  Figure 7-27 contains a series of strain profile plots for test A1 at various distances from the chill. Each plot shows six curves which have been selected from a series of more than 200. The last curve in each plot is the time at which the tear was seen to open with the bold curve being the time at which single site localisation occurs. The remaining curves represent the strain at intermediate times.  Table 7-4 is a summary of the average peak strains prior to localisation and the average macro strains (across the entire profile) just prior to localisation. The average peak strains before localisation are very similar to each other with the exception of 16 and 19mm distances from the chill which localised at lower strains. As with the previous University of Queensland derived data the strain initially occurs at several sites before single site localisation occurs. The results of this study reconfirm that the strain does not accumulate at every grain boundary as the wavelength of the early strain accumulation is approximately 7 times larger than the grain size which has been measured at 100-150µm. Because the spatial resolution should be adequate to capture strain behaviour on the scale of grains it may be inferred that the strain accumulation prior to localisation has a spatial frequency approximately 7x larger than the grain size. This result is consistent with recent work by Phillion [46].This finding is also consistent with the previous University of Queensland work.  The shaded area on the strain contour at 21mm from the chill has not been included in the determination of peak and macro localisation strains. Referring back to Figure 7-15B (final vector grid) it can bee seen that at coordinates x=6.5mm, y=10mm (21mm from the chill) the correlation has failed and displacement data has been discarded for this area. The strain accumulation in the shaded area is very close to this failed location. In addition, the strain builds very suddenly to its peak; it does not build gradually as is the case in the adjacent area to the left and in the other plots. It was therefore decided that this is a correlation error and was disregarded for consistency.  123  0.20  0.20 0.125s 0.867s 1.735s 2.975s 3.843s 4.835s  14mm from chill  0.18 0.16  Tear  0.14  Tear  0.16 0.14 0.12  0.10  Strain  Strain  0.12  0.08  0.10 0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02  -0.04  -0.04 0  1  2  3  4  5  6  7  8  9  10  0  1  2  Distance across tear (mm) 3.348s 5.083s 6.323s 6.943s 7.563s 12.563s  0.16 0.14 0.12  5  6  7  8  17mm from chill  0.18  9  10  0.125s 1.735s 3.595s 6.943s 8.555s 13.639s  0.16 0.14 0.12  Tear  0.10  Strain  Strain  4  0.20  16mm from chill  0.18  0.08  Tear  0.10 0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02  -0.04  -0.04 0  1  2  3  4  5  6  7  8  9  10  0  1  2  Distance across tear (mm)  3  4  5  6  7  8  9  10  Distance across tear (mm)  0.20  0.20 0.125s 3.595s 6.075s 7.935s 9.795s 11.903s  18mm from chill  0.18 0.16 0.14 0.12  0.16 0.14 0.12  Tear  0.10  0.125s 2.975s 6.075s 7.935s 10.415s 13.143s  19mm from chill  0.18  Strain  Strain  3  Distance across tear (mm)  0.20  0.08  Tear  0.10 0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02  -0.04  -0.04 0  1  2  3  4  5  6  7  8  9  10  0  1  2  Distance across tear (mm)  3  4  5  6  7  8  9  10  Distance across tear (mm)  0.20  0.20 0.125s 3.595s 8.555s 11.035s 12.895s 14.631s  20mm from chill  0.18 0.16 0.14  Tear  0.12  0.125s 6.075s 11.035s 14.135s 15.375s 15.499s  21mm from chill  0.18 0.16 0.14  Tear  0.12  0.10  Strain  Strain  0.125s 1.735s 2.975s 5.703s 6.695s 7.687s  15mm from chill  0.18  0.08  0.10 0.08  0.06  0.06  0.04  0.04  0.02  0.02  0.00  0.00  -0.02  -0.02  -0.04  -0.04 0  1  2  3  4  5  6  7  Distance across tear (mm)  8  9  10  0  1  2  3  4  5  6  7  8  9  10  Distance across tear (mm)  Figure 7-27: Strain vs. Distance across the tear at various distances from the chill.  124  Table 7-4: Summary of strains at the onset of localisation.  Distance from chill 14mm 15mm 16mm 17mm 18mm 19mm 20mm 21mm  Average Peak Strain before localisation 0.069 0.082 0.023 0.054 0.070 0.039 0.047 0.062  Average macro strain before localisation 0.010 0.018 0.010 0.011 0.016 0.011 0.011 0.009  7.7.7 Strain rate comparison From the 2-D profile data presented above it is very easy to obtain an indication the rate of strain evolution. By plotting the evolution of strain versus time at the tear site for each of the six time steps in each plot it is possible to determine how the strain rate varies with increasing distance from the chill. This data is shown in Figure 7-28. As expected there is a variation in the strain rate (slope) with time at each discrete location and a variation with increasing distance from the chill. As solidification progresses further away from the chill the strain rate is seen to drop which is caused by a decreased cooling effect by the chill further up the casting.  7.7.8 Alternative approach to single-site localisation at the tear A different approach to determine the strain at damage localisation has been used to analyse the data derived from the directional solidification experiments. Unlike in the University of Queensland data, where site localisation was estimated visually, plots of the evolution of strain at adjacent locations to the site of the crack have been made to determine when the surrounding areas cease strain accumulation. The higher temporal resolution obtained in the UBC data allows for a much more accurate determination of the exact strain at which localisation occurs using this method.  125  0.20 14mm from chill 15mm 16mm 17mm 18mm 19mm 20mm 21mm  Strain  0.15  0.10  0.05  0.00  2  4  6  8  10  12  14  16  18  20  Time (s) Figure 7-28: Evolution of strain with time.  The plots of strain vs. distance across the tear in Figure 7-27 describe the accumulation of strain in the vicinity of the final tear up to the time at which the open crack is visible to the eye. The strain builds in random locations over time until the point at which single-site localisation of strain occurs. It follows that by plotting the strain evolution of the sites which do not develop into a tear against the strain evolution at the tear it is possible to determine the exact strain at single-site localisation.  The strain versus time plots in Figure 7-29 show how strain evolves at the tear location in comparison with the adjacent areas that also experience some strain localisation prior to single-site saturation of strain. All plots have been zeroed in time from when the correlation starts.  The plots generally show one of two trends. In the first instance, strain may build relatively evenly at several locations up to a point where single-site localisation of strain occurs and the hot tear localises at one point, an example of this case is shown in the data for 14, 16, 18 and 19mm from the chill. Alternatively, the strain may initially build much 126  faster away from the position where the tear is to form but stops accumulating strain just prior to strain accumulation at the tear itself. This case is shown in the data for 15, 17, 20 and 21mm from the chill. It is believed that this simply reflects the stochastic nature of damage accumulation in semi-solid material and that it is occurring below the surface as well as at the surface.  As can be seen in the plots in Figure 7-29 there is clearly a point at which the strain at the surrounding areas ceases to evolve and that subsequently all of the strain accumulates at the site of the tear. The plot in Figure 7-30 shows the single-site localisation strains versus distance from the chill. Apart from at the 16 mm location, the data shows a trend to decreasing strain to single site saturation, with increasing distance from the chill. This is believed to be due to the decreasing thermal gradient. As the gradient decreases, the length of the mushy zone increases resulting in a reduction in liquid feeding. Consequently, there is a reduction in pressure and an increase of shrinkage induced porosity believed to be a key factor in reducing semi-solid ductility. As previously described, the strains at which the tear opens in the UBC work cannot be directly compared with the work carried out with the University of Queensland due to differences in magnification between the two set-ups. However, it is relevant to compare the localisation strains of both sets of work.  Comparing the average peak strains before localisation from the work at the University of Queensland with the single-site localisation strains in the directional solidification tests it is apparent that strains measured in this work are much larger. For example, the strain at 21mm from the chill in test A1 is almost 25 times larger than the average peak strain before localisation in the Al-0.4wt%Cu (most susceptible alloy tested) and 4 times larger than the average peak strain in AA3104 (least susceptible). It is believed that this difference is due to differences in the local solidification conditions present in the two tests.  127  14mm from chill  0.6  0.5  5.79mm 7.83mm  0.5  0.4  Strain  0.4  Strain  15mm from chill  0.6  3.05mm 5.82mm  0.3  0.3  0.2  0.2  0.1  0.1  0.0  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  0  2  4  6  8  10  12  Time (s)  16mm from chill  0.6  2.44mm 5.43mm 6.48mm 7.86mm  0.5  0.3  0.6  17mm from chill  0.5  2.06mm 5.15mm 6.48mm  18  20  22  24  26  28  30  18  20  22  24  26  28  30  18  20  22  24  26  28  30  18  20  22  24  26  28  30  0.3  0.2  0.2  0.1  0.1  0.0  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  0  2  4  6  8  10  12  Time (s)  16  19mm from chill  0.6  3.39mm 5.06mm  0.5  14  Time (s)  18mm from chill  0.6  2.06mm 3.73mm 5.36mm 6.55mm  0.5  0.4  Strain  0.4  Strain  16  0.4  Strain  Strain  0.4  0.3  0.3  0.2  0.2  0.1  0.1  0.0  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  0  2  4  6  8  10  12  Time (s)  16  21mm from chill  0.6  4.06mm 5.33mm 6.44mm  0.5  14  Time (s)  20mm from chill  0.6  3.43mm 4.80mm  0.5  0.4  Strain  0.4  Strain  14  Time (s)  0.3  0.3  0.2  0.2  0.1  0.1  0.0  0.0 0  2  4  6  8  10  12  14  16  Time (s)  18  20  22  24  26  28  30  0  2  4  6  8  10  12  14  16  Time (s)  Figure 7-29: Strain accumulation at, and in the region of the hot tear localisation site at various distances from the chill  128  0.10  Localisation Strain  0.09  0.08  0.07  0.06  0.05  0.04 13  14  15  16  17  18  19  20  21  22  Distance from the chill (mm) Figure 7-30: Single-site localisation strain at various distances from the chill  0.00100  3100  0.00095  2900  2800 0.00090 2700  2600  Velocity (m/s)  Thermal Gradient (oC/m)  3000  0.00085 Gradient Velocity  2500  2400  0.00080 13  14  15  16  17  18  19  20  21  22  Distance from the chill (mm) Figure 7-31: Plot of predicted thermal gradient and velocity at the solidus temperature (640ºC) versus distance from the chill for the locations at which strain was measured on the surface of the casting.  129  Based on the data presented in Figure 7-30, it is clear that a reduction in gradient will in general result in a reduction in the strain to single site saturation. This argument can be supported by plotting the predicted thermal gradient and velocity at the solidus temperature as a function of distance from the chill as shown in Figure 7-31. The plot shows a steadily decreasing thermal gradient and roughly constant velocity over the length analysed. This would indicate an increase in the mushy zone length and account for the decreasing single-site localisation strain.  The UBC test rig was specifically designed to produce a hot tear under directional solidification conditions where there is generally good liquid feeding. In contrast the University of Queensland test rig produced a hot tear in an area that would have experienced little of no directional solidification and generally poorer feeding.  There is evidence within the literature to support the link between gradient or feeding and hot tearing sensitivity. Work carried out by Sengupta et al.  [42]  investigated  stress and strain fields during the start-up phase of DC casting using a fully couple 3D thermal and stress model to model two extreme casting conditions. By reducing the initial bottom block filling time and decreasing the water cooling flow rate they created a “hot” casting condition, as well as a non-typical fast cooling or “cold” condition. In the cold casting the ingot experiences large stresses and deformations (the latter being referred to as butt curl) yet this condition is not conducive to the formation of hot tears. The conclusion is that large strains can be tolerated by the structure that forms as a result of high thermal gradients and good directional solidification. In contrast, the hot casting case produces little or no ingot deformation (butt curl) yet these conditions are conducive to hot tear formation. One may infer from this that the structure produced with a lower thermal gradient/low solidification rate is relatively less able to tolerate strains.  A number of studies have shown a strong correlation between the volume fraction porosity (thought to exacerbate hot tearing) and cooling rate  [47]  and show a substantial  increase in the volume fraction porosity with decreasing cooling rate. There has been no attempt to characterise the volume fraction porosity in these tests; however these results  130  are consistent with a higher volume fraction of solidification related porosity present in the University of Queensland than in the UBC-based tests.  In addition to the differences in cooling, it should be noted that since segregates and impurities are often more soluble in the higher temperature liquid ahead of the solidification front, directional solidification may act to force these impurities and bifilms towards the last parts of the casting to solidify [5]. This would increase the strength and strain to failure of the casting.  7.7.9 Local strain at the hot tear and fraction solid development One of the important objectives of this work was to investigate the accumulation of strain at the hot tear in relation to fraction solid development. It is believed that this type of data, coupled with the macro and micro localisation strains is extremely valuable to the solidification modelling community.  As previously described, the thermal model was used to determine the temperature at the surface of the casting, which was then related to fraction solid development using predicted data from Thermo-Calc. The plots shown in Figure 7-32, describe the development of strain and fraction solid with time for various distances from the chill. Also marked on each chart is the time at which the pull away front passes the distance from the chill for which the plot pertains. In addition the strain/time at which the single-site localisation occurs has been marked with a line “L” and the time/strain at which the tear becomes visible is marked on each plot with a line “O”.  The image correlation strain measurements are zeroed with the thermocouple data by determining the corresponding time at which the liquid metal is observed to touch the thermocouple closest to the chill (TC0). In this test the image correlation was started just before the front pull away moved into the window field of view, 3.348 s after the metal was seen to touch TC0. Referring back to results of the thermal model (Figure 7-12) the reader will be reminded that in order to align the model results with the thermocouple  131  data, the thermocouple data was shifted forward in time by 4 s to compensate for mould filling. It follows that as the timestamp on the image correlation strain data is zeroed with the thermocouple data it is therefore necessary to shift the strain data forward in time by 4 s.  As discussed above, all of the plots in Figure 7-32 show the pull away front corresponding to a fraction solid of between 0.89 and 0.94. Additionally, there is a general trend whereby strain accumulation at the hot tear commences as the pull away front passes at the related distance from the chill. The time at which localisation occurs is always after pull away, however there is no definite pattern to when localisation will occur. The fraction solid at localisation and the localisation strains for test A1 are summarised in Table 7-5. The fraction solid at which localisation occurs appears to correlate with distance from the chill. The variation observed likely reflects the stochastic nature of damage accumulation.  Table 7-5: Fraction solid and localisation strain for test A1.  Distance from chill (mm) Fraction solid at localisation Strain  14  15  16  17  18  19  20  21  0.94  0.95  0.89  0.94  0.93  0.92  0.98  0.98  0.0909 0.0797 0.0490 0.0757 0.0671 0.0554 0.0568 0.0530  132  1.0  L  0.8  0.5  0.6 0.3  0.5 0.4  0.2  0.8 0.7  O  0.4  0.6  Strain  O  0.3  0.5 0.4  0.2  0.3 0.1  0.3 0.1  0.2 Strain 14mm Fraction Solid Front pull away  0.0  0.1  0.2 Strain 15mm Fraction Solid Front pull away  0.0  0.0 4  6  8  10  12  14  16  18  20  22  24  26  28  0.0  30  0  2  4  6  8  10  12  Time (s)  14  16  18  20  22  24  26  28  30  Time (s) 1.0  0.6  L  0.8  0.8  0.7 0.6 0.5  0.3  0.4 0.2  0.7  O  0.4  0.6  Strain  O  0.4  0.9  L  0.5  Fraction Solid  0.5  Strain  1.0 0.6  0.9  0.5  0.3  0.4 0.2  0.3 0.1  0.3 0.1  0.2 Strain 16mm Fraction Solid Front pull away  0.0  0.1  0.2 Strain 17mm Fraction Solid Front pull away  0.0  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s) 1.0  0.6  L  0.8  O  0.9  L  0.5  0.8  O  0.7  0.5  0.3  0.4 0.2  0.4  0.7 0.6  Strain  0.6  Fraction Solid  0.4  Strain  1.0 0.6  0.9  0.5  0.3  0.4 0.2  0.3 0.1  0.3 0.1  0.2 Strain 18mm Fraction Solid Front pull away  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  0.1  0.2 Strain 19mm Fraction Solid Front pull away  0.0  0.0  30  0  2  4  6  8  10  12  Time (s)  14  16  18  20  22  24  26  28  L  0.8  O  0.5  0.6 0.3  0.5 0.4  0.2 Strain 20mm Fraction Solid Front pull away  0.1  0.0  0.7 0.6  0.3  0.5 0.4  0.2  0.3 0.2  0.8  O  0.4  Strain  0.4  0.9  L  0.7  Fraction Solid  0.5  Strain  1.0 0.6  0.9  0.3  Strain 21mm Fraction Solid Front pull away  0.1  0.2 0.1  0.0  0.0 2  4  6  8  10  12  14  16  Time (s)  0.0  Time (s)  0.6  0  0.1  30  1.0  0.1  0.1 0.0  30  Time (s)  0.5  Fraction Solid  2  Fraction Solid  0  0.1  18  20  22  24  26  28  30  Fraction Solid  0.4  0.9  L  0.7  Fraction Solid  0.5  Strain  1.0 0.6  0.9  Fraction Solid  0.6  0.0 0  2  4  6  8  10  12  14  16  18  20  22  24  26  28  30  Time (s)  Figure 7-32: Local strain at the hot tear versus fraction solid based on thermal model.  133  7.8 Summary The main focus of this work was to design an experimental set-up capable of initiating reproducible hot tears during the casting of aluminium alloys, to design a procedure and methodology for the measurement of displacement and the estimation of strain during hot tearing and to also simultaneously obtain temperature data allowing the estimated strains to be determined as a function of fraction solid. These goals have been achieved and it is now possible to apply this method for other commercial alloys.  134  Chapter 8 – Conclusions An innovative approach has been developed for qualifying strains on the surface of a casting leading to hot tearing. The method is based around an optical image correlation technique which has been shown to be capable of measuring areas of high strain concentration consistent with the location of the hot tear on the surface of the casting. The process of hot tear formation in the alloys examined seems to be consistent with the distributed accumulation of strain, localised accumulation of strain and growth by a process of coalescence. Digital image correlation is also suitable for measuring the macro strain across the hot tear and the micro localisation strain across the hot tear prior to single-site localisation. This is valuable information for the calibration of both micro and macro computer simulations. In the context of a macro model, the average macro strain at the onset of localisation could be used. Whereas, in a micro-scale model it may be more appropriate to use the average peak strain. In addition, the method has been used to track the local strain development up to the position at which the hot tear opens and the strain rate at which this occurs.  In addition, the approach was initially applied to an existing experimental set-up in collaboration with The University of Queensland, Australia. In application to the University of Queensland derived data it has been shown that digital image correlation is suitable for measuring the micro and macro localisation strains across the hot tear prior to single-site localisation. In this part of the study it was found that depending on the alloy, the distribution of strain on the surface of the casting in the early stages of deformation can vary from being relatively evenly distributed to being highly variable and random. Single-site localisation of strain was found to occur at relatively low strains in the alloys that exhibited an initially relatively uniform distribution of strain, whereas single-site localisation of strain was found to occur at relatively high strains in the alloys that exhibited a highly variable distribution of strain.  135  For the alloys tested the minimum strain at which strain localisation occurs was found to be >0.0123 for AA3104, >0.0069 for AA6111, >0.0047 for CA31218, and >0.0021 for Al-0.5 wt pct Cu based on displacements measured from the point at which mass feeding ends and thermal contraction begins.  Whereas in previous studies the susceptibility of alloys has often been ranked by comparing mostly qualitative data, such as crack length or crack geometry, it is now possible using this technique to rank alloys based on the strain a which single-site localisation of damage occurs. In this case Al-0.5%Cu is more prone to cracking because localisation occurs at relatively little strain. In addition it was found that semi-solid AA3104 can sustain twice the amount of macroscopic strain prior to localisation when compared to AA6111 and nearly four times as compared to CA31218. In fact this corresponds to the industrial experience related to the castability of these alloys. However, the ranking of susceptibility in these commercial alloys is highly dependent on the alloy grain size, changes to the alloy microstructure from re-melting (loss of grain refiners), the difference in solidification conditions from the industrial scale casting to the laboratory scale.  In the second part of this work a new and innovative hot tearing test based on improvements to the constrained bar casting technique has been designed. This experimental set-up is suitable for creating the conditions necessary to promote hot tearing in a range of alloys. The test includes a means for providing directional solidification in the casting and imparts constraint to produce localisation of strain to promote hot tearing to occur in only one region of the casting. The test is relatively simple and fast.  A series of thermocouples embedded in the hot spot of the test castings recorded cooling during hot tearing. This data was used to calibrate a thermal simulation to determine temperature at the surface of the casting at locations where strain was measured during digital image correlation. Subsequently, these temperature predictions  136  were used in conjunction with the commercial software Thermo-Calc™ to compare the accumulation of strain during hot tearing to the development of fraction solid in the casting. It was shown for AA3003 under directional solidification that the point at which single-site localisation of strain occurs coincides with a fraction solid of approximately 0.9 (which is in agreement with the literature).  A thermal model was developed of the new test rig which was calibrated using experimental thermocouple results. The model was used to predict temperature on the surface of the casting at the positions at which strain was measured using digital image correlation. This allowed the correlation of fraction solid evolution with strain development during hot tearing.  Finally, the usefulness of the new testing rig is twofold. In an industrial application the new hot tearing rig it has the capability of making a qualitative ranking of commercial alloys under the effects of directional solidification. This is especially relevant to industrial processes such as DC Casting. On the other hand, the strain versus fraction solid data is extremely useful to the modelling community as it provides data for micro and macro strain data which has been correlated with temperature and subsequently fraction solid evolution. Given a particular fraction solid or temperature the modeller will be informed of what strains they should expect for the conditions under evaluation in their model.  8.1 Future work This thesis has demonstrated the use of optical digital image correlation to measure the strain development on the surface of aluminium alloys. Further work can be carried out to optimise the experiment.  Firstly, although data has been collected using the borosilicate window in the mould there is still an issue with chemical attack at high temperatures. The application of light silicon oil helped to inhibit this process however this is likely to remain a problem 137  with the capacity to lead to wasted castings if the silicon oil fails. A suggestion might be to attempt the test with a quartz window.  Only one lens was available during testing and was supplied by the manufacturers of the image correlation system. However, the cameras have the capability of using any Nikon lens. Further study may include an investigation with different focal length lenses allowing closer focusing on the surface of the solidifying casting to determine whether accuracy can be improved.  In addition to the improvements in the glass window an improvement is necessary to the feeding system of the mould. Currently feeding is being cut off at the ingate. Widening of the ingate may help, although it is suggested that the ingate is fitted with heaters to keep the gate from solidifying too early or possibly lining it with ceramic refractory. Increased head material may be used however large amounts of liquid metal present a greater safety hazard. Improvements to the window and feeding would allow strains to be measured over a larger range of gradient and solidification rate.  Most importantly, there is a need to expand the number of alloys tested in the current setup. It is thought that the test rig will be able to initiate tears in many alloy systems. AA5182, AA6111 and AA3104 have also been tested and produced hot tears unfortunately due to problems with the chemical attack at the glass suitable images were not available for image correlation.  138  References 1. Sigworth, G.K., 1996. AFS Transactions, 96-155, pp. 1053-1062. 2. Langlais, J., Gruzleski, J.E., 2000. Materials Science Forums, 331-337, pp. 167172. 3. Paray, F., Kulunk, B., Gruzleski, J.E., 2000. International Journal of Cast Metals Research, 13, pp.147-159. 4. Spittle, J. A. and Cushway, A. A., 1983, Metals Technology, 10, pp. 6-13. 5. Campbell, J., Castings, 1991. Butterworth-Heinemann Ltd., ISBN:0750616962. 6. Instone, S., StJohn, D., Grandfield, J., 2000. International Journal of Cast Metals Research, 12, pp. 441-156. 7. Clyne, B. A., Davies, G. J., 1981. Institute of British Foundrymen, 74, pp. 66-73. 8. Warrington, D., McCartney, D.G., 1989. Cast Metals, vol. 2, 3, pp. 134-143. 9. Eskin, D.G., Suyitno, Katgerman, L., 2004. Progress in Materials Science, 49, pp. 629-711. 10. Lahaie, D. J., Bouchard, M., 2001. Metallurgical and Materials Transactions B, 32B, 8, pp. 697-705. 11. Fortier, M., Lahaie, D. J., Bouchard, M., Langlais, J., 2001. TMS Light Metals 2001, pp. 839-846. 12. Farup, I., Drezet, J.-M., Rappaz, M., 2001. Acta mater., 49, pp. 1261-1269. 13. Pellini, W. S., 1952. Foundry, 80, pp.125-199. 14. van Haaften, W. M., Kool, W. H., Katgerman, L., 2002, Journal of Materials Engineering and Performance, 11, 5, pp. 537-543. 15. D.G. Eskin and L. Katgerman, Metallurgical and Materials Transactions A, Volume 38A, July 2007, pp1511-1519 16. Langlais, J., Gruzleski, J.E., 1999. Met. Soc. Light Metals '99, pp. 247-263. 17. Feurer, U., 1976. Giesserei-forschung, 28, pp. 75-80. 18. A.B. Phillion, S.L. Cockcroft and P.D. Lee, Scripta Materialia, 55, (2006), pp 489-492. 19. Rappaz, M., Drezet, J.-M., Gremaud, M., 1999. Metallurgical and Materials Transactions A, 30A, pp. 449-455. 139  20. Drezet, J.-M., Rappaz, M., 1999. Sixth Australian-Asian Pacific Conference on Aluminium Cast House Technology, pp.197-206. 21. J.F. Grandfield, C. J. Davidson and J.A. Taylor: in Light Metals 2001, J.L. Anjier, ed., TMS, Warringdale, PA, 2001, pp.895-901 22. Suyitno, W.H. Kool and L. Katgerman: Mater. Sci. Forum, 2002, vols. 396-402, pp. 179-84 23. Singer, A. R. E., Cottrell, S. A., 1946. J. Inst. Metals, 73, pp. 33. 24. Singer, A. R. E., Jennings, P. H., 1947. J. Inst. Metals, 73, 5, pp. 273. 25. Clyne, B. A., Davies, G. J., 1975. British Foundrymen, 68, pp. 238-244. 26. Novikov, I. I., Grushko, O. E., 1995. Materials Science and Technology, 11, pp. 926-932. 27. S. Lin, C. Aliravci and M.O. Pekguleryuz: Metallurgical and Materials Transactions A, May 2007, Volume 38A, pp 1056-1068 28. Instone, S., StJohn, D., Grandfield, J., 1998. Proceedings of Materials '98, pp. 125-130. 29. C. Davidson, D. Viano, L. Lui and D. StJohn: in The John Campbell Symposium, M. Tiryakioglu and P. Crepeau, eds., TMS, Warringdale, PA, 2005, pp175-182 30. C. Olivier, C. Yvan and B. Michel, Journal of Engineering Materials Technology, April 2008, vol. 130 31. Abu, A.A.-H, Thesis, The University of British Columbia, 2001. 32. L.J. Colley, M.A. Wells, and D.M. Maijer: Materials. Science &. Engineering., A, 2004, vol. 386, pp. 140–48. 33. James, J.D. Spittle, S.G.R. Brown, R.W. Evans and M.E. Keeble, "ASSET- The Advanced Semi-Solid Elongation Test for Determining Properties of Alloys in the Mushy Zone", COMPASS 99, Swansea, UK, 1999 34. Van Haaften, W. M., Kool, W.H., and Katgerman, L., 2002, Materials Science and Engineering A, A336, pp. 1-6 35. Dahle, A.K., Instone, S., Sumitomo, T., 2003. Metallurgical and Materials Transactions A, 34A, pp. 105-113. 36. Magnin, B., Maenner, L., Katgerman, L. and Engler, S., Mat. Sci. Forum, Vol. 217-222, pp. 1209-1214, 1996  140  37. Dickhaus, C H; Ohm, L; Engler, S, Trans. Am. Foundrymen's Society, Vol. 101; 24-27 Apr. 1993. pp. 677-684. 1994. 38. Larouche, D., Langlais, J., Wu, W. and Bouchard, M., Met. & Mat. Trans. B., Vol. 37B, pp. 431-443, June 2006 39. Martin, C.L., Favier, D., SueÂry, M., Int. J. of Plasticity, 15, pp. 981-1008, 1999. 40. Correlated Solutions, Columbia, SC, USA, 2005 41. LaVision GmBH, Goettingen, Germany, 2008 42. Sengupta, J., Cockcroft, S. L., Maijer, D. and Larouche, A., Materials Science and Engineering A, Volume 397, Issues 1-2, 25 April 2005, pp. 157-177. 43. Mills, K.C., “Recommended values of thermo-physical properties for selected commercial alloys”, ASM International, Woodhead Publishing, Cambridge, England. 44. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., “Transport Phenomena”, 2nd Edition, John Wiley & Sons, Inc., New York, USA, 2007. 45. Considine, J.M., Scott, C.T., Gleisner, R., Zhu, J.Y., 13th Fundamental Research Symposium, Cambridge, September 2005. 46. Phillion, A.B., Cockcroft, S.L. and P.D. Lee, Acta Materialia, 56, pp.4328–4338, 2008. 47. Vo, P., M.A.Sc. Thesis, The University of British Columbia, 1999.  141  Appendix A – UBC Experimental Set-up Images  Figure 8-1: Complete casting setup showing water cooling.  Figure 8-2: Interior of mould showing thermocouple locations relative to the chill surface, casting restraining bolts and ceramic fibre insulation required to create the hot-spot in the centre of the casting.  142  Figure 8-3: Interior of the mould showing the steel insert modification which was necessary to divert incoming liquid metal away from the glass during pouring.  Figure 8-4: Rear of the mould showing thermocouple connector placement.  143  Appendix B – Subroutine for Chill/Casting Heat Transfer SUBROUTINE GAPCON(AK,D,FLOWM,TEMP,PREDEF,TIME,CINAME,SLNAME, 1 MSNAME,COORDS,NOEL,NODE,NPRED,KSTEP,KINC) C INCLUDE 'ABA_PARAM.INC' C CHARACTER*80 CINAME,SLNAME,MSNAME C DIMENSION AK(5),D(2), FLOWM(2), TEMP(2), PREDEF(2,*), 1 TIME(2), COORDS(3), hR(4), hL(4), ZT(4) C C C C  user coding to define AK(1) -- AK(5) AK(2)=0.D0 AK(3)=0.D0  C C C  Input heat transfer coeff hR(1)=500.D0 hR(2)=9000.D0 hR(3)=21000.D0 hR(4)=26000.D0  C hL(1)=500.D0 hL(2)=5000.D0 hL(3)=17000.D0 hL(4)=22000.D0 C ZT(1)=100.D0 ZT(2)=640.D0 ZT(3)=654.D0 ZT(4)=660.D0 C C C  determine position if(COORDS(3).le.0.088D0)then  C C C  define temp dependent gap conductances for right end if (TEMP(2).gt.ZT(4)) then AK(1)=hR(4)  C else if (TEMP(2).le.ZT(4).AND.TEMP(2).gt.ZT(3)) then AK(1)=((hR(4)-hR(3))/(ZT(4)-ZT(3)))*TEMP(2)+hR(3) C else if (TEMP(2).le.ZT(3).AND.TEMP(2).gt.ZT(2)) then AK(1)=((hR(3)-hR(2))/(ZT(3)-ZT(2)))*TEMP(2)+hR(2) C else if (TEMP(2).le.ZT(2).AND.TEMP(2).gt.ZT(1)) then AK(1)=((hR(2)-hR(1))/(ZT(2)-ZT(1)))*TEMP(2)+hR(1) C else  144  if (TEMP(2).le.ZT(1)) then AK(1)=hR(1) end if end if C else C C C  define temperature dependent gap conductances for left end if (TEMP(2).gt.ZT(4)) then AK(1)=hL(4)  C else if (TEMP(2).le.ZT(4).AND.TEMP(2).gt.ZT(3)) then AK(1)=((hL(4)-hL(3))/(ZT(4)-ZT(3)))*TEMP(2)+hL(3) C else if (TEMP(2).le.ZT(3).AND.TEMP(2).gt.ZT(2)) then AK(1)=((hL(3)-hL(2))/(ZT(3)-ZT(2)))*TEMP(2)+hL(2) C else if (TEMP(2).le.ZT(2).AND.TEMP(2).gt.ZT(1)) then AK(1)=((hL(2)-hL(1))/(ZT(2)-ZT(1)))*TEMP(2)+hL(1) C else if (TEMP(2).le.ZT(1)) then AK(1)=hL(1) end if end if C C  END ALL end if  C RETURN END  145  Appendix C – Digital Image Correlation Digital image correlation is a non–intrusive technique which can be used to investigate deformation on the surface of a strained specimen. It is particularly useful for non-contact strain measurement. It can be used for a large range of specimen sizes, ranging from 10-9 to 102 m over time scales which range from static to 200MHz. Various commercial image correlation software is currently available to perform this type of analysis however this work utilised Vic-2d by Correlation Solutions and DaVis by LaVision.  The basic technique involves tracking the position/movement of specific features on a reference image to their position on subsequently deformed images (Figure 8-5). These features can be naturally occurring or artificially added, such as paint speckles on the specimen surface. Tracking is usually carried out by analysing the grey-scale values of certain pixels or sets of pixels within small windows or elements of a predetermined size in the reference image. After which the location of these pixels is determine in the deformed image by maximising a similarity function (correlation function) in the scanning algorithm.  Time t  Time t’  Time t”  Tracking Tracking  Figure 8-5: Tracking of point on a deforming surface over time, from t to t″.  146  However there is generally insufficient information to track individual pixels as they do not provide a unique enough signature, for example the greyscale value of a pixel may be exactly the same as its neighbour. It is therefore more appropriate to include groups of pixels which neighbour each other making it easier to then search for that group in the deformed images i.e. a subset or window (Figure 8-6).  Time t  Time t”  d  Figure 8-6: Tracking the movement of pixels as a group, usually called a window or subset. The associated displacement is shown as d.  Additionally, to make these so called signatures unique the surface pattern must be non-repetitive, isotropic and high contrast. For example, a set of close parallel lines on the surface of the specimen would not work, however very random speckle patterns or textures overcome this constraint. In addition to this it is usual that the scale of the pattern or speckle is constrained so that it is smaller than the window/subset size, if the pattern is larger than the window size then it is possible that all greyscale values will be recorded as the same value. In other words there must some contrast within the pattern.  Figure 8-7 shows a simple schematic of how greyscale is interpreted by correlation software. It shows a simple black cross on a white background. Each white pixel is recorded to memory as an integer value of 100. Each black pixel is stored in memory as an integer value of 0 (zero). Clearly in a real situation grey values of between 0 and 100 will be recorded.  147  White pixels have a grey level = 100 Black pixels have a grey level = 0 Therefore the image is a matrix of natural integers.  Pixels  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  Figure 8-7: Example of greyscale interpretation in digital image correlation. White pixels are registered as 100 and black as 0, to form a matrix of natural integers.  Figure 8-8 shows an image of the same black and white cross after displacement has taken place. In this case the centre of the cross has moved up and to the right and new greyscale values have been committed to memory.  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  100  100  100  100  0  0  0  100  100  When the image moves the greyscale values of each pixel change in memory.  Figure 8-8: New greyscale values are recorded after deformation, these are stored in memory.  As previously mentioned, a single pixel does not lend itself to be a unique enough pattern for the purposes of image correlation, we therefore have to analyse groups of pixels together. Figure 8-9 shows two 9x9 pixel grids showing greyscale data for our cross shape before and after deformation. Also indicated on the “before motion” grid is a 5x5 pixel subset. Now that the correlation algorithm has committed the reference image data to memory it must determine the new location of the subset in the deformed image. To do this it must check various locations on the deformed image and check possible  148  matches. Each possible match is graded and receives a similarity score or correlation function. It is this function that generally needs to be minimised indicating a good fit. The classic correlation function is the sum of squared differences of the pixel values.  5x5 subset 100  100  100  0  0  0  100  100  100  100  100  100  100  0  0  0  100  100  100  100  100  0  0  0  100  100  100  100  100  100  100  0  0  0  100  100  100  100  100  0  0  0  100  100  100  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  100  100  100  100  0  0  0  100  100  100  100  100  0  0  0  100  100  100  100  100  100  100  0  0  0  100  100  100  100  100  0  0  0  100  100  100  100  100  100  100  0  0  0  100  100  100  100  100  0  0  0  100  100  100  100  100  100  100  0  0  0  100  100  ?  After motion  Before motion  Figure 8-9: Schematic of greyscale values before and after motion with a 5x5 subset neighbourhood defined. A correlation algorithm is required to determine the new position of the subset.  Equation 8-1 below shows the sum of squared differences correlation function: Pixel coord., reference image  C ( x, y , u , v ) =  n/2  ∑ ( I ( x + i, y + j ) − I  i, j =−n / 2 Displacement Pixel value at (x+i; y+j) (disparity)  *  (x + u + i, y + v + j )) 2  8-1  Pixel value at (x+u+i; y+v+j)  where C, is the correlation function, n is the subset size in pixels, I is the image number before displacement and I* the image after displacement. In reality there will be situations where this function cannot find a near enough match to the original image. This may be because the shape of the window may have changed in addition to its location. Both of the commercial correlation software packages used in this work are robust enough to account for this by including a window (or subset) shape function.  149  

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