The need for lighter weight vehicles to improve fuel efficiency is becoming increasingly imperative. Sheet magnesium alloys offer the potential as a light weight material for use in the transportation industry due to their high specific strength and stiffness. In fact, magnesium alloys have the highest strength-to-weight ratio of all the common structural metals. Though the demand for light weight materials is present and sheet magnesium is available, the use of these materials in automotive applications has been rather limited due to high production costs and poor corrosion performance and formability. A promising process to produce wrought magnesium sheet in a more cost effective manner is Twin Roll Casting (TRC). In addition, enhanced corrosion resistance and ductility may be realized in these sheet alloys with the possible introduction of a clad layer during the TRC process thereby producing a laminate sheet where the surface properties are different from the core. The focus of this research was to investigate the potential of cladding magnesium alloy AZ31 material during the TRC process. As part of this research, a thermal fluid mathematical model of the TRC process was developed, which was then further refined to include the addition of a clad layer during the process. The TRC model was validated through experimental work conducted at the Pohang Institute of Science and Technology (POSTECH University), where TRC experiments of AZ31 were conducted under various casting conditions. The as-cast microstructure of the AZ31 sheets were characterized and measurements of the secondary dendrite arm spacing (SDAS) made at the mid-region were compared to predicted microstructures from the TRC model based on solidification history. The predicted SDAS matched with the measured values, thus, validating the model. Using the validated TRC model the feasibility of adding a clad layer was assessed and various simulations were conducted to observe the effects of cast speed, cast thickness, and clad material on the thermal history and temperature profile in both the clad and core domains. The material properties and clad thickness did not seem to impact the temperature profiles significantly, while the cast speed and initial temperature dictated whether or not the cast would be successful. Using these operational parameters a process window was created (based on the CANMET facility) to illustrate the feasibility of casting and cladding during TRC. This window is beneficial for future experimentation and understanding the effects of these casting parameters.

Although Twin Roll Casting (TRC) process has been used for almost 60 years in the aluminum industry, TRC of magnesium is relatively new. In TRC, molten metal is fed onto water-cooled rolls, where it solidifies and is then rolled. Solidification of the molten metal starts at the point of first metal-roll contact and is completed before the kissing point (point of least roll separation) of the two rolls. The unique thermo-physical properties inherent to magnesium and its alloys, such as lower specific heat and latent heat of fusion and larger freezing ranges (in comparison with aluminum and steel) make it challenging for TRC of this alloy. Therefore, a comprehensive understanding of the process and the interaction between the casting conditions and strip final quality is imperative to guarantee high quality twin roll cast strip production. A powerful tool to achieve such knowledge is to develop a mathematical model of the process. In this thesis, a 2D mathematical model for TRC of AZ31 magnesium alloy has been developed and validated based on the TRC facility located at the Natural Resources Canada Government Materials Laboratory (CanmetMATERIALS) in Hamilton, ON, Canada. The validation was performed by comparing the predicted exit strip temperature and secondary dendrite arm spacing (SDAS) through the strip thickness with those measured and obtained by experiments. The model was developed in two stages, first a thermal-fluid model was developed followed by validation and then a thermal-fluid-stress model was developed. This is the first time a comprehensive thermal-fluid-stress model has been developed to simulate the TRC process for magnesium alloys. The work has led to new knowledge about the TRC process and its effects on magnesium strip quality including the following: 1) Using ALSIM and ANSYS® CFX® commercial packages a 2D mathematical model of thermal-fluid-stress behavior of the magnesium sheet during TRC was successfully developed and validated. 2) An average value of 11 kW/m2°C for the Heat Transfer Coefficient (HTC) was found to best represent the heat transfer between the roll and the strip during TRC casting of AZ31 using the CanmetMATERIALS facility. 3) Modeling results showed that increasing casting speed, casting thicker strips and applying higher HTCs led to less uniform microstructure through thickness in terms of SDAS. 4) Simulations showed the importance of casting parameters such as casting speed and set-back distance on the thermal history and stress development in the sheet during TRC; higher casting speeds led to deeper sumps and higher exit temperatures as well as lower overall rolling loads and lower total strains experienced during TRC. 5) The effect of roll diameter on the thermal history and stress development in the strip was also studied and indicated how larger roll diameters increased the surface normal stress and rolling loads but had little effect on the mushy zone thickness. 6) The correlation between the mechanisms of center-line and inverse segregation formation and thermo-mechanical behavior of the strip was performed. The modeling results suggested that increasing the set-back distance decreases the risk of both defects. Moreover, increasing the roll diameter reduces the propensity to inverse segregation but has a minor effect for center-line segregation formation.

Although Twin Roll Casting (TRC) process has been used for almost 60 years in the aluminum industry, TRC of magnesium is relatively new. In TRC, molten metal is fed onto water-cooled rolls, where it solidifies and is then rolled. Solidification of the molten metal starts at the point of first metal-roll contact and is completed before the kissing point (point of least roll separation) of the two rolls. The unique thermo-physical properties inherent to magnesium and its alloys, such as lower specific heat and latent heat of fusion and larger freezing ranges (in comparison with aluminum and steel) make it challenging for TRC of this alloy. Therefore, a comprehensive understanding of the process and the interaction between the casting conditions and strip final quality is imperative to guarantee high quality twin roll cast strip production. A powerful tool to achieve such knowledge is to develop a mathematical model of the process. In this thesis, a 2D mathematical model for TRC of AZ31 magnesium alloy has been developed and validated based on the TRC facility located at the Natural Resources Canada Government Materials Laboratory (CanmetMATERIALS) in Hamilton, ON, Canada. The validation was performed by comparing the predicted exit strip temperature and secondary dendrite arm spacing (SDAS) through the strip thickness with those measured and obtained by experiments. The model was developed in two stages, first a thermal-fluid model was developed followed by validation and then a thermal-fluid-stress model was developed. This is the first time a comprehensive thermal-fluid-stress model has been developed to simulate the TRC process for magnesium alloys. The work has led to new knowledge about the TRC process and its effects on magnesium strip quality including the following: 1) Using ALSIM and ANSYS® CFX® commercial packages a 2D mathematical model of thermal-fluid-stress behavior of the magnesium sheet during TRC was successfully developed and validated. 2) An average value of 11 kW/m2°C for the Heat Transfer Coefficient (HTC) was found to best represent the heat transfer between the roll and the strip during TRC casting of AZ31 using the CanmetMATERIALS facility. 3) Modeling results showed that increasing casting speed, casting thicker strips and applying higher HTCs led to less uniform microstructure through thickness in terms of SDAS. 4) Simulations showed the importance of casting parameters such as casting speed and set-back distance on the thermal history and stress development in the sheet during TRC; higher casting speeds led to deeper sumps and higher exit temperatures as well as lower overall rolling loads and lower total strains experienced during TRC. 5) The effect of roll diameter on the thermal history and stress development in the strip was also studied and indicated how larger roll diameters increased the surface normal stress and rolling loads but had little effect on the mushy zone thickness. 6) The correlation between the mechanisms of center-line and inverse segregation formation and thermo-mechanical behavior of the strip was performed. The modeling results suggested that increasing the set-back distance decreases the risk of both defects. Moreover, increasing the roll diameter reduces the propensity to inverse segregation but has a minor effect for center-line segregation formation.

Volume rendering is a research area within scientific visualisation, where images are computed from volumetric data sets for visual exploration. Such data sets are typically generated by Computer aided Tomography, Magnetic Resonance Imaging, Positron Emission Tomography or gained from simulations. The data sets are usually interpreted using optical models that assign optical properties to the volume and define the illumination and shading behaviour. Volume rendering techniques may be divided into three classes: object-order, image-order or hybrid methods. Image-order or ray casting methods shoot rays from the view plane into the volume and simulate the variation of light intensities along those rays. Object-order techniques traverse the volume data set and project each volume element onto the view plane. Hybrid volume rendering techniques combine these two approaches. A very popular object-order rendering method is called splatting. This technique traverses the volume data set and projects the optical properties of each volume element onto the view plane. This thesis consists of two parts. The first part introduces two new splatting methods, collectively called high-resolution splatting, which are based on standard splatting. Both high-resolution splatting methods correct errors of splatting by applying major modifications. We propose the first method, called fast high-resolution splatting, as an alternative to standard splatting. It may be used for quick previewing, since it is faster than standard splatting and the resulting images are significantly sharper. Our second method, called complete high-resolution splatting, improves the volume reconstruction, which results in images that are very close to those produced by ray casting methods. The second part of the thesis incorporates wavelet analysis into high-resolution splatting. Wavelet analysis is a mathematical theory that decomposes volumes into multi-resolution hierarchies, which may be used to find coherence within volumes. The combination of wavelets with the high-resolution splatting method has the two advantages. Firstly the extended splatting method, called high-resolution wavelet splatting, can be directly applied to wavelet transformed volume data sets without performing an inverse transform. Secondly when visualising wavelet compressed volumes, only a small fraction of the wavelet coefficients need to be projected. For all three versions of the new high-resolution splatting method, complexity analyses, comprehensive error and performance analyses as well as implementation details are discussed.

Volume rendering is a research area within scientific visualisation, where images are computed from volumetric data sets for visual exploration. Such data sets are typically generated by Computer aided Tomography, Magnetic Resonance Imaging, Positron Emission Tomography or gained from simulations. The data sets are usually interpreted using optical models that assign optical properties to the volume and define the illumination and shading behaviour. Volume rendering techniques may be divided into three classes: object-order, image-order or hybrid methods. Image-order or ray casting methods shoot rays from the view plane into the volume and simulate the variation of light intensities along those rays. Object-order techniques traverse the volume data set and project each volume element onto the view plane. Hybrid volume rendering techniques combine these two approaches. A very popular object-order rendering method is called splatting. This technique traverses the volume data set and projects the optical properties of each volume element onto the view plane. This thesis consists of two parts. The first part introduces two new splatting methods, collectively called high-resolution splatting, which are based on standard splatting. Both high-resolution splatting methods correct errors of splatting by applying major modifications. We propose the first method, called fast high-resolution splatting, as an alternative to standard splatting. It may be used for quick previewing, since it is faster than standard splatting and the resulting images are significantly sharper. Our second method, called complete high-resolution splatting, improves the volume reconstruction, which results in images that are very close to those produced by ray casting methods. The second part of the thesis incorporates wavelet analysis into high-resolution splatting. Wavelet analysis is a mathematical theory that decomposes volumes into multi-resolution hierarchies, which may be used to find coherence within volumes. The combination of wavelets with the high-resolution splatting method has the two advantages. Firstly the extended splatting method, called high-resolution wavelet splatting, can be directly applied to wavelet transformed volume data sets without performing an inverse transform. Secondly when visualising wavelet compressed volumes, only a small fraction of the wavelet coefficients need to be projected. For all three versions of the new high-resolution splatting method, complexity analyses, comprehensive error and performance analyses as well as implementation details are discussed.

Volume rendering is a research area within scientific visualisation, where images are computed from volumetric data sets for visual exploration. Such data sets are typically generated by Computer aided Tomography, Magnetic Resonance Imaging, Positron Emission Tomography or gained from simulations. The data sets are usually interpreted using optical models that assign optical properties to the volume and define the illumination and shading behaviour. Volume rendering techniques may be divided into three classes: object-order, image-order or hybrid methods. Image-order or ray casting methods shoot rays from the view plane into the volume and simulate the variation of light intensities along those rays. Object-order techniques traverse the volume data set and project each volume element onto the view plane. Hybrid volume rendering techniques combine these two approaches. A very popular object-order rendering method is called splatting. This technique traverses the volume data set and projects the optical properties of each volume element onto the view plane. This thesis consists of two parts. The first part introduces two new splatting methods, collectively called high-resolution splatting, which are based on standard splatting. Both high-resolution splatting methods correct errors of splatting by applying major modifications. We propose the first method, called fast high-resolution splatting, as an alternative to standard splatting. It may be used for quick previewing, since it is faster than standard splatting and the resulting images are significantly sharper. Our second method, called complete high-resolution splatting, improves the volume reconstruction, which results in images that are very close to those produced by ray casting methods. The second part of the thesis incorporates wavelet analysis into high-resolution splatting. Wavelet analysis is a mathematical theory that decomposes volumes into multi-resolution hierarchies, which may be used to find coherence within volumes. The combination of wavelets with the high-resolution splatting method has the two advantages. Firstly the extended splatting method, called high-resolution wavelet splatting, can be directly applied to wavelet transformed volume data sets without performing an inverse transform. Secondly when visualising wavelet compressed volumes, only a small fraction of the wavelet coefficients need to be projected. For all three versions of the new high-resolution splatting method, complexity analyses, comprehensive error and performance analyses as well as implementation details are discussed.

Volume rendering is a research area within scientific visualisation, where images are computed from volumetric data sets for visual exploration. Such data sets are typically generated by Computer aided Tomography, Magnetic Resonance Imaging, Positron Emission Tomography or gained from simulations. The data sets are usually interpreted using optical models that assign optical properties to the volume and define the illumination and shading behaviour. Volume rendering techniques may be divided into three classes: object-order, image-order or hybrid methods. Image-order or ray casting methods shoot rays from the view plane into the volume and simulate the variation of light intensities along those rays. Object-order techniques traverse the volume data set and project each volume element onto the view plane. Hybrid volume rendering techniques combine these two approaches. A very popular object-order rendering method is called splatting. This technique traverses the volume data set and projects the optical properties of each volume element onto the view plane. This thesis consists of two parts. The first part introduces two new splatting methods, collectively called high-resolution splatting, which are based on standard splatting. Both high-resolution splatting methods correct errors of splatting by applying major modifications. We propose the first method, called fast high-resolution splatting, as an alternative to standard splatting. It may be used for quick previewing, since it is faster than standard splatting and the resulting images are significantly sharper. Our second method, called complete high-resolution splatting, improves the volume reconstruction, which results in images that are very close to those produced by ray casting methods. The second part of the thesis incorporates wavelet analysis into high-resolution splatting. Wavelet analysis is a mathematical theory that decomposes volumes into multi-resolution hierarchies, which may be used to find coherence within volumes. The combination of wavelets with the high-resolution splatting method has the two advantages. Firstly the extended splatting method, called high-resolution wavelet splatting, can be directly applied to wavelet transformed volume data sets without performing an inverse transform. Secondly when visualising wavelet compressed volumes, only a small fraction of the wavelet coefficients need to be projected. For all three versions of the new high-resolution splatting method, complexity analyses, comprehensive error and performance analyses as well as implementation details are discussed.

The recent development of prototyping systems which can produce patterns for investment casting with significant time reduction from traditional techniques, has raised interest in the use of casting as a method to produce tooling for downstream prototype testing. However, the accuracy of the casting process remains a major obstacle to the use of these tools. Simultaneous development of numerical modelling techniques suggest that it will be possible to predict casting contraction and distortion. If this were possible, corrections could be made before castings are produced, resulting in time and cost savings, as well as potential improvement in the accuracy. Before these models can be applied, there is a need for both material property data and experimental data with which to validate the numerical models. The aims of this work are to: 1) Develop further understanding of the processes in investment casting that contribute to the dimensional changes and variability. 2) Develop the required data for numerical modelling and apply this to simulate the dimensional changes in investment casting. An apparatus has been designed to measure the dimensional and thermal history of investment castings with displacement transducers and thermocouples. Casting dimensions were also accurately measured to determine the final contraction of nominally unconstrained and thermally constrained castings. Numerical simulations of the temperatures, stress and distortion were compared with the experimental results and provide a detailed explanation of the processes involved. Data for these simulations were developed using a combination of direct measurement and iterative inverse modelling.

Mannheim, Univ., Diss., 2008.

Mannheim, Univ., Diss., 2008.