10.1002==9781118061992.ch143

ii ACKNOWLEDGEMENTS This research could not have been completed without the support of many individuals. Their contributions in various ways to my work and the making of this thesis deserve special mention. It is a pleasure to convey my gratitude to them all in my humble acknowledgement. I am deeply grateful to Professor Makhlouf M. Makhlouf for giving me the opportunity to work with him during my journey at Worcester Polytechnic Institute. It has been an honor to be his student. I would like to deliver my special gratitude to him for sharing his invaluable insight, advice and knowledge with me for nearly six years. His words of encouragement and motivation came a long way in bringing this work to completion. I would like to thank Professor Diran Apelian for his advice, guidance and friendship throughout these years. He has been a great mentor not only in my academic performance, but also in my personal life. Thanks are also extended to the members of my dissertation committee, Professor Richard D. Sisson Jr. and Mr. Christof Heisser for their time and assistance in this work. It is my pleasure also to pay tribute to all the WPI faculty and staff. I would like to express my great gratitude to my wife and parents, without their never- ending love, understanding and support, this thesis would be impossible. Collective and individual acknowledgements are also due to my colleagues, classmates and friends whose enthusiasm and support in one way or another was helpful and memorable. The group at Advanced Casting Research Center has contributed immensely to my personal and professional experience at WPI. The team has been a wonderful source of friendships, good advice and collaboration. I want to thank the Metals Processing Institute and the Department of Materials Science and Engineering at WPI who gave me the opportunity to be a part of them. Finally, I thank everyone who supported and believed in me, and I express my apology to anyone who I did not mention personally. Chang Kai (Lance) Wu Worcester Polytechnic Institute

v LIST OF FIGURES Fig. 1 . Block diagram describing the Integrated Heat Treatment Model. .......... 3 Fig. 2. Typical Ct function and its use in calculating the quench factor. ............ 5 Fig. 3. The process diagram for the Shercliff-Ashby aging model. .................... 7 Fig. 4. SEM micrograph of the A356 alloy solutionized, quenched in 80 o C (176 o F) water, and then aged at 155 o C (311 o F) for 4 hours. ..................... 11 Fig. 5. Location of Energy Dispersive Spectrometer (EDS) scanning. ............ 11 Fig. 6. Energy Dispersive Spectrometer (EDS) scan at the Location labeled “Spectrum 3” in Fig. 5. ............................................................................. 12 Fig. 7. Stress-strain curves for supersaturated A356 alloy at elevated temperatures. ............................................................................................. 14 Fig. 8. Stress-strain curve for supersaturated A356 alloy samples at room temperature. Strain rate = 0.005/s. ............................................................ 15 Fig. 9. Schematic representation of the apparatus used to measure thermal conductivity. .............................................................................................. 16 Fig. 10. Measured, software generated and public available thermal conductivities of A356.2 alloy. ................................................................. 16 Fig. 11. Schematic representation of the quenching system . ............................ 18 Fig. 12. The newly-designed cylindrical quenching probe. .............................. 19 Fig. 13. The newly-designed disk quenching probe. In this disk probe the ratio of the bottom surface area to the total surface area of the disk is 79.7%.. 19 Fig. 14. Metal-Fluid HTCs measured by the newly designed probe and disk quenched in hot water (80 o C). .................................................................. 20 Fig. 15. Metal-Air and Air HTCs measured by the newly-designed probe. ..... 20 Fig. 16. Measured creep-rupture data adapted from reference [22]. ................ 21 Fig. 17. Measured creep-rupture data adapted from reference [22]. ................ 22 Fig. 18. Measured creep-rupture data adapted from reference [22]. ................ 22 Fig. 19 . Measured hardness as a function of aging time for A356 alloy that was

viii air quenched + T7. .................................................................................... 62 Fig. 56. Model-predicted yield strength (MPa) for the casting (a) quenched in hot water + T6, (b) quenched in hot water + T7, (c) air quenched + T6 and (d) air quenched + T7. ............................................................................... 64 Fig. 57. Model-predicted UTS (MPa) for the casting (a) quenched in hot water + T6, (b) quenched in hot water + T7, (c) air quenched + T6 and (d) air quenched + T7 ........................................................................................... 66 Fig. 58. Model-predicted T6 aging curves for strength at location (2) of Fig. 42 (water quenched part). .............................................................................. 66 Fig. 59. Model-predicted T7 aging curves for strength at location (2) of Fig. 42 (water quenched part). .............................................................................. 67 Fig. 60. Model-predicted and CMM measured total length increments for T6 aged casting. .............................................................................................. 69 Fig. 61. Model-predicted and measured total length increments for T7 aged casting. ...................................................................................................... 69 Fig. 62. Model-predicted and measured total length increments during the only aging step for T6 aging condition. ............................................................ 70 Fig. 63. Model-predicted and measured total length increments during the only aging step for T7 aging condition. ............................................................ 70 Fig. 64. Location of measurements made by x-rays diffraction (red dot). ....... 72 Fig. 65. Model-predicted residual stress on the X-ray measured location after water quenching (110.1MPa ~ 97.92MPa). .............................................. 73 Fig. 66. Model-predicted residual stress on the X-ray measured location after T6 aging (65.19MPa ~ 58.7MPa). ............................................................ 73 Fig. 67. Model-predicted residual stress on the X-ray measured location after T7 aging (18.24MPa ~ 16.65MPa). .......................................................... 74 Fig. 68. Measured and model-predicted residual stresses. ............................... 74

2 2. METHODOLOGY Plan of Research The commercially available finite element analysis software ABAQUS was used to construct the model. The structure of the model is divided into two parts: Part 1 and Part 2, as shown in Fig. 1. In Part 1, the focus is on predicting the response of the casting to only the quenching step of the heat treatment schedule. Simulating heat transfer during quenching is performed by a thermal analysis module and the calculated transient thermal fields are used by a stress analysis module for stress and deformation calculations. In addition to the initial conditions, and the boundary conditions on the casting, these analyses require a material database that includes the necessary temperature-dependent quenching heat transfer coefficients, the thermal properties of the casting, its physical properties and its mechanical properties. Part 1 of the model produces three outputs at each node: (1) the geometric distortion, (2) the magnitude and type of residual stresses, and (3) the thermal profile during quenching. In a parallel calculation, a user-developed quenching subroutine and a quenching database that is based on Quench Factor Analysis [2] compute the unique Quench Factor which is later used by the model to predict the heat- treated mechanical strength and the hardness at each node within the cast component. Part 2 of the model focuses on calculating the changes that occur in the component in response to the aging step of the precipitation hardening heat treatment. Within the context of Part 2 is a creep analysis module with a creep database and a specially developed dilation subroutine that makes use of outputs from Part 1 of the model. That is, predicting the overall distortion, the overall volumetric dilation and the residual stresses caused by the aging step will build upon the calculated changes that develop during the quenching step. Similarly, for predicting the mechanical properties and hardness after aging, a user-developed aging subroutine and database (this database is constructed by means of the Shercliff and Ashby aging model [3]), make use of the determined Quench Factor parameter that was computed earlier. These user-developed subroutines are written in the FORTRAN language.

5 material spends at the specific temperature ( ∆ t i ) divided by the critical time that is required for a certain amount of transformation to occur at that temperature ( Ct i ). The incremental quench factor values are then summed up over the entire transformation temperature range in order to produce the cumulative Quench Factor, as shown in Eq. (2). ܳ ൌ ෍ q ୤ ൌ ෍ ∆t ୧ Ct ୧ T ౠ T ౟ (2) In order to use Eq. (2) in calculating the cumulative Quench Factor (Q), the cooling path taken by the material during quenching and the critical time at each temperature step must be known. One way of representing the critical time is via a time-temperature- precipitation (TTP) curve. This curve is often referred to as the ‘C’ curve of the material. The TTP curve, an example of which is shown in Fig. 2, is a graphical representation of the transformation kinetics that influences the material’s strength or properties and defines the time that is required to precipitate sufficient solute to alter the strength or properties of the material by a specified amount. Fig. 2. Typical Ct function and its use in calculating the quench factor.

8 The Shercliff-Ashby aging model assumes that the strength (or hardness) of precipitation hardened material is a sum of the intrinsic property of the material ( σ i ), hardening due to formation of a solid solution ( ∆σ ss ), and hardening due to second phase precipitates ( ∆σ ppt ), as shown in Eq. (5) σሺt, Tሻ ൌ σ ୧ ൅ ∆σ ୱୱ ൅ ∆σ ୮୮୲ (5) Moreover, the contribution by solid solution hardening can be described by microstructure variables in terms of an equilibrium solute concentration at the aging temperature as shown in Eq. (6). ∆σ ୱୱ ሺt, Tሻ ൌ ൜∆σ ୱୱ଴ ଷ ଶ ሺTሻ ൅ exp ሺ െt τ ଵ ሺtሻ ሻ ൤∆σ ୱୱ୧ ଷ ଶ െ ∆σ ୱୱ଴ ଷ ଶ ሺTሻ൨ൠ ଶ ଷ (6) In Eq. (6), ∆σ ୱୱ୧ ൌ σ ୯ ൅ σ ୧ (7) ∆σ ୱୱ଴ ሺTሻ ൌ σ ୭ୟ ሺTሻ െ σ ୧ (8) σ ୭ୟ ሺTሻ ൌ σ ୧ ൅ ൫σ ୯ െ σ ୧ ൯exp െ2Q ୱ 3R ൬ 1 T െ 1 T ୱ ൰ (9) τ ଵ ሺTሻ ൌ KP ୮ Texpሺ Q ୟ RT ሻ (10) The contribution to hardening by second phase precipitates may be given by Eq. (11) ∆σ ୮୮୲ ሺt, Tሻ ൌ 2Sሺt, TሻሾP כ ሺt, Tሻሿ ଵ ଺ 1 ൅ ሾP כ ሺt, Tሻሿ ଵ ଶ (11) In which P כ ሺt, Tሻ ൌ Pሺt, Tሻ P ୮ (12) Pሺt, Tሻ ൌ t T exp ൬ െQ ୟ RT ൰ (13) Sሺt, Tሻ ଶ ൌ ሺS ଴ ሻ ୫ୟ୶ ଶ ൤1 െ exp െQ ୱ R ൬ 1 T െ 1 T ୱ ൰൨ ൤1 െ exp ሺ െt τ ଵ ሺtሻ ሻ൨ (14)

11 5%H 2 O) [12]. In order to detect Mg 2 Si particles, Transmission Electron Microscopy (TEM) is recommended. These microstructure observations are in agreement with previous findings [13-15]. Fig. 4. SEM micrograph of the A356 alloy solutionized, quenched in 80 o C (176 o F) water, and then aged at 155 o C (311 o F) for 4 hours. Fig. 5. Location of Energy Dispersive Spectrometer (EDS) scanning.

12 Fig. 6. Energy Dispersive Spectrometer (EDS) scan at the Location labeled “Spectrum 3” in Fig. 5. Table II. Chemical analysis of the particle labeled “Spectrum 3” in Fig. 5 obtained from Energy Dispersive Spectrometer (EDS) scan. Al Si Fe Mg Atomic % 49.54 28.21 5.01 17.24 Weight % 47.27 28.02 9.9 14.82 Determination of the Physical Properties of A356 Alloy The physical property database that is required for the Thermal-Stress Analysis module includes the density, specific heat, Poisson’s ratio and thermal expansion coefficient of the alloy. These temperature-dependent properties can be generated by JMatPro software. The database used in this work is shown in Table III. Within the range between the solidus temperature of 538 o C (1000 o F) and room temperature, all the physical properties of this alloy vary linearly with temperature. Determination of the Mechanical Properties of the Supersaturated Solid Solution A356 Alloy At the beginning of quenching and before any precipitation has occurred, thermal-stresses and distortion develop in the alloy when it is still a supersaturated solid solution.

13 Therefore, in order to determine the deformation throughout quenching, the mechanical properties of the supersaturated solid solution must be known. This information is needed by the Thermal-Stress Analysis module to compute the stresses and deformations that develop in the cast part during quenching. The mechanical properties of the supersaturated solid solution A356 alloy at elevated temperatures are courtesy of Maijer, et al. [16]. These measurements were performed on tensile samples that were previously heated and quenched. Subsequently, the samples were re-heated in a Gleeble 4 to 540 ° C (1004 ° F) for 30 seconds in order to re-create a supersaturated solid solution, and then the samples were cooled at a rate of 5 ° C/s to the required temperatures by means of water-cooled platens. Results were generated with two different strain rates: 0.1 and 0.001 s -1 and the stress-strain curves are shown in Fig. 7. It was found from preliminary quenching simulations that strain rate is 0.004 s -1 ; therefore, only the results obtained at a strain rate of 0.001 s -1 were used in the model. An Instron universal testing machine 5 was used to generate the mechanical properties of the supersaturated solid solution A356 alloy at room temperature. The elastic modulus, yield stress, and plastic strain of the alloy were calculated from these measurements. Standard-size round tensile specimens (2 inch gage length – ASTM-E8 [17]) were cast in a steel mold. The samples were solutionized at 538 ° C (1000 ° F) for 12 hours and then rapidly quenched in room temperature water. The tensile measurements were performed at an extension rate of 5% per minute (strain rate of 0.005 /s). A 2-inch gage extensometer 6 was used to monitor the extension. Measurements were performed without dwell, and sufficient measurements were made in order to obtain accurate representation of these properties. The measured stress-strain curve is shown in Fig. 8. The yield stress and elastic modulus measured at room temperature as well as elevated temperature are shown in Table IV. 4 Developed and manufactured by Dynamic System Inc. 5 Instron, 825 University Ave, Norwood, MA 02062-2643, USA 6 MTS Part no. 634.25E-24.

14 Table III. Physical properties of A356 alloy generated by JMatPro Software. Property Temperature: 25 o C (77 o F) – 538 o C (1000 o F) Specific Heat (T) 886 – 1300 (J/Kg ° C) Density (T) 2674 – 2576 (Kg/m 3 ) Expansion Coefficient (T) 21.13 – 26.2 (1/ ° C 10 -6 ) Poisson’s Ratio (T) 0.330 – 0.359 Table IV. Measured mechanical properties for supersaturated A356 alloy. Temperature ( o C) Yield Stress (MPa) Elastic Modulus (MPa) 25 90.4 57381 200 75.2 47287 300 51.5 46934 400 16.8 27249 500 7.7 2134 Fig. 7. Stress-strain curves for supersaturated A356 alloy at elevated temperatures. Strain rates = 0.001/s and 0.1/s measured in Gleeble.

15 Fig. 8. Stress-strain curve for supersaturated A356 alloy samples at room temperature. Strain rate = 0.005/s. Determination of Thermal Conductivity of A356 Alloy Thermal conductivity is an important parameter required for heat transfer analysis and it can be determined by either one of the following three methods: It can be directly measured from a thermal gradient induced in the material as per ASTM standard E1225-04 [18]. The apparatus used is shown in Fig. 9. It can be obtained from electrical conductivity by Wiedemann-Franz Law. The thermal conductivity for A356 alloy as calculated from measured electrical conductivity is available in [19]. It can be predicted by commercially available software such as JMat Pro. Fig. 10 shows a comparison of the thermal conductivity of A356 as obtained by these three methods. The measured data and data calculated from electrical conductivity are in good agreement, but are significantly different from the values predicted by JMat Pro. Hence, the measured thermal conductivity values were used in all the heat transfer simulations.

16 Fig. 9. Schematic representation of the apparatus used to measure thermal conductivity. Fig. 10. Measured, software generated and public available thermal conductivities of A356.2 alloy.

17 Determination of the Quenching Heat Transfer Coefficients The quenching heat transfer coefficients (HTCs) are important boundary conditions used by the thermal analysis module to compute the heat that is transferred out of the cast part during quenching. The apparatus shown in Fig. 11 [20] was used to measure the HTCs during quenching. Measuring the quenching HTCs involved quenching a heated cylindrical probe that is machined from a cast piece of A356 alloy and equipped with a k- type thermocouple connected to a data acquisition system into the quenching fluid and acquiring the temperature-time profile at a scan rate of 1000 scans/sec. Prior to quenching, the probes are heated at the solutionizing temperature for 12 hours. A heat balance analysis (usually referred to as a lumped parameter analysis [21]) performed on the system (probe + quenching medium) results in Eq. (15), which yields the quenching HTC. hሺTሻ ൌ െ ρVC ୮ A ୱ ሺT ୱ െ T ୤ ሻ dT dt (15) In Eq. (15), h(T) is the quenching heat transfer coefficient at the surface of the probe, ρ , V, C p , and A s are the density, volume, specific heat at constant pressure, and surface area of the probe, respectively. T s is the temperature at the surface of the probe, which, due to the geometry of the probe, is approximately equal to the measured temperature at the center of the probe. T f is the bulk temperature of the quenching medium. The derivative of temperature with respect to time is calculated from the measured data. For the lumped parameter analysis to be valid, the probe dimensions must be chosen such that the Biot number for the quenching process is less than 0.1. This insures that significant thermal gradients will not be present in the radial direction in the probe. When Biot number less than 0.1 the error associated with the calculation of the quenching HTC is less than 5%.

18 Fig. 11. Schematic representation of the quenching system . In the earlier measurements, a small cylindrical probe was cast from a standard A356.2 alloy. A blind hole was then drilled down to the geometrical center of this probe and a thermocouple was inserted for measuring the time-temperature data. Graphite powder was packed into the hole before the thermocouple was inserted in order to ensure intimate contact between the probe and the thermocouple. However, there are two drawbacks in this design: (1) although graphite powder was tightly packed into the space between the thermocouple and the probe, full contact between the two was not always guaranteed. An air gap may exist between the thermocouple and the probe before or during the measurements; and (2) the connecting rod introduces an error into the measurements as it absorbs some of the heat from the probe by conduction. In this research, a new design was used. The thermocouple is placed in the molds during casting the probe and molten metal is poured around it after solidification, the probe is machined to the accurate tolerances. Before casting, the thermocouple wires are exposed to guarantee full contact with the metal, and the surface contamination was burned off. Two new probes were cast and machined from standard A356.2 alloy: a cylindrical

19 quenching probe, 0.367 inch (9.32 mm) in diameter and 1.2 inch (30.48 mm) in length, and a quenching disk, 1.1 inch (27.94 mm) in diameter and 0.3 inch (7.62 mm) in thickness, as shown in Fig. 12 and Fig. 13, respectively. During measurements, both the cylindrical probe and the disk probe were quenched from 538 o C (1000 o F) into three different quenching media: (i) hot water that is maintained at 80 o C (176 o F), (ii) static room temperature air, and (iii) room temperature forced-air obtained by an industrial fan. Fig. 14 shows the measured HTCs from two quenching probes that were quenched in hot water. The data from disk probe shows delay HTC compared to data from cylinder probe, as a result of more surface area in contact with air entrapment underneath the probe during quenching. The measured HTCs for quenching in static room temperature air range between 14~41 W/m 2 , and that for quenching in forced-air range between 168~181 W/m 2 , as shown in Fig. 15. Three iterations were made for each experiment, and results were averaged from measurements. Fig. 12. The newly-designed cylindrical quenching probe. Fig. 13. The newly-designed disk quenching probe. In this disk probe the ratio of the bottom surface area to the total surface area of the disk is 79.7%.

20 Fig. 14. Metal-Fluid HTCs measured by the newly designed probe and disk quenched in hot water (80 o C). Fig. 15. Metal-Air and Air HTCs measured by the newly-designed probe.

21 Determination of the Creep Properties Creep deformation is unavoidable in cast parts that experience stress at elevated temperature resulting in gradual stress relaxation and strain accumulation. Suitable modeling tools and databases are essential for satisfactory prediction of the creep behavior during heat treatment. There are several creep models available, but generation of reliable creep databases is costly and time consuming. Holt [22] measured and published temperature-dependent creep-rupture data for A356-T61 alloy. His data is shown graphically in Fig. 16, Fig. 17 and Fig. 18. Legend indicates the sample number with testing stress. This database was used to develop the creep parameters needed for calculating the contribution by creep to part deformation during the aging step of heat treatment. Fig. 16. Measured creep-rupture data adapted from reference [22].

22 Fig. 17. Measured creep-rupture data adapted from reference [22]. Fig. 18. Measured creep-rupture data adapted from reference [22].

23 ABAQUS software provides several built-in nonlinear viscoplastic models for modeling the creep behavior of metals. Among them, the Bailey-Norton Law, sometimes called the Power Law model, can be used in creep calculations for isotropic materials, and it is the most suitable for simulating the aging response of aluminum alloys. The constitutive equation of isotropic Power Law is given by Eq. (16). It applies to both the primary stage and the secondary stage of creep. ε ሶ ؠ dε dt ൌ ܣσ ௡ t ௠ (16) In Eq. (16), ε ሶ is the uniaxial equivalent creep strain rate, σ is the uniaxial equivalent deviatoric stress, t is the total time and A , n , and m are temperature-dependent creep parameters. Two sets of creep parameters were generated: (1) Power Law creep without time hardening, i.e., m =0; and (2) Power Law creep with time hardening. (1) Power Law creep without time hardening – In this case, the Norton Creep Law [23] is used with the time hardening parameter m = 0, which assumes that the secondary creep rate ሺε ሶ ୫୧୬ ሻ is a straight line as shown in Eq. (17). Therefore, by using the creep-rupture database, the parameters, A and n, can be determined by fitting a trend line to the data points in a secondary creep rate vs. stress plot. The calibrated creep database generated for Power Law without time hardening is shown in Table V. ε ሶ ୫୧୬ ؠ dε dt ൌ ܣσ ௡ (17) Table V. Creep database generated for Power Law creep without time hardening. A n m Temperature ( o C) 9.155E-23 6.0184 0 149 6.416E-20 5.7514 0 204 8.096E-15 3.8194 0 260

24 (2) Power law with time hardening – In this case, the creep strain, ε , is determined by integrating Eq. (13) with respect to time and constant stress, where A and n must be positive, and -1< m ≤ 0, as shown in Eq. (18). By taking the logarithm of both sides, as shown in Eq. (19), the average time hardening parameter, m , can be determine by the slope in each test under different test stresses. Similarly, using the y-intercept, the average parameter, A , can be determined with known test stress, m , n and in each test. The calibrated creep database generated for power law with time hardening parameters is shown in Table VI. ε ൌ A ݉ ൅ 1 σ ଴ ௡ t ௠ାଵ (18) ln ε ൌ ሺ݉ ൅ 1ሻln t ൅ log ܣ ݉ ൅ 1 σ ௡ (19) Table VI . Creep database generated for power law with time hardening A n m Temperature ( ° C) 4.69 × 10 -19 6.0184 -0.383168 149 1.72 × 10 -16 5.7514 -0.2639 204 3.60 × 10 -13 3.8194 -0.22685 260 Determination of the Quench Factor Analysis Constants The required kinetics parameters K 1 , K 2 , K 3 , K 4 , and K 5 that appear in the C t function described in Eq. (3), are measured and calibrated for hardness, yield strength and ultimate tensile strength separately. The calibrating process consists of three steps: (1) determining the maximum ( σ max ) and minimum ( σ min ) attainable strength and hardness, (2) measuring the strength and hardness with matched thermal data for different quenching paths, and (3) calibrating the K constants based on the measurements. These steps are described in the following paragraphs.

25 (1) Determining the maximum and minimum attainable strength For hardness – The aging curve was obtained by measuring the Rockwell Hardness F scale (HRF) of the alloy. The HRF measurements were performed with a steel ball indenter that is 1/16 inch (1.59 mm) in diameter and minor and major loads that are 98N and 491N, respectively. The measured results are shown in Fig. 19 where the error bars indicate standard deviations. The smoothed curve was averaged by the adjacent averaging method over 10 points. In order to obtain this data, small identical samples of A356 alloy were solutionized at 538 o C (1000 o F) for 12 hours and then quenched into ice water. These samples represent the maximum possible quenching rate. Subsequently, the samples were aged at 155 o C (311 o F) for different periods of time and their hardness was measured. The HRF hardness values were averaged from 20 to 40 measurements and the maximum value was found to be 93.3 HRF (achieved after 19 hours of aging). This number represents the maximum hardness ( σ max ). The value for the minimum hardness ( σ min ) was obtained by furnace cooling the samples after solutionizing, and it was found to be 20.7 HRF. The cooling rate in the furnace was less than 0.2 o C/s. Fig. 19 . Measured hardness as a function of aging time for A356 alloy that was solutionized for 12 hours at 538 ° C (1000 ° F) and quenched in ice water.

26 For yield strength and ultimate tensile strength – The standard tensile test specimens and the testing parameters described previously were employed. Since the aging time required for maximum strength is known from the hardness measurements. The maximum tensile strength ( σ max ) was obtained from tensile specimens that were quenched in ice-water, and then aged at 155 o C (311 o F) for 19 hours. Similarly, the minimum strengths ( σ min ) were obtained by furnace cooling the samples after solutionizing. The measured values are shown in Table VII. (2) Measuring the hardness and strength with matched thermal data for different quench paths For hardness – The Jominy End Quench test described in ASTM-A255 [24] was used to reduce the testing effort. Jominy End Quench bars that are 1 inch (25.4mm) in diameter and 4 inches (101.6 mm) long were cast from A356 alloy in a permanent mold. The cast bars were then instrumented with k-type thermocouples at seven different locations along their length in order to record the local cooling data during quenching. The thermocouples were equally spaced at 0.5 inch (12.7 mm) increments along the length of the bar. The cast bars were solutionized for 12 hours at 538 o C (1000 o F) and then quenched from one end by cold tap water while the time-temperature data was being recorded. The apparatus is shown in Fig. 20(a). The unidirectional heat transfer thus created results in a progressively decreasing cooling rate along the length of the bar. The recorded cooling curves and cooling rates are presented in Fig. 21 and Fig. 22, respectively. Cooling rate curves indicate moving averages. After end quenching, bars were aged at 155 o C (311 o F) for 19 hours. Small flat surfaces were then made along the length of each Jominy End Quench bar by rubbing the surface with fine sand paper in order to allow for accurate hardness measurements on the surface of the bar. HRF measurements were then performed around the perimeter at the thermocouple locations as shown in Fig. 20(b). HRF values were averaged from 15 to 30 measurements. Because the measured Rockwell hardness is an arbitrary number with no

27 physical meaning, the HRF measurements were converted into Meyer hardness [25] for the purpose of computer calculations 7 and then they were converted back to HRF for result presentation. (a) (b) Fig. 20. (a) Apparatus for performing Jominy End Quench test, and (b) measuring HRF on the Jominy End Quench bars at the thermocouple locations. 7 Meyer hardness is the amount of work required for indenting the material in MPa.

28 Fig. 21. Recorded cooling curves at different thermocouple locations along the length of the Jominy End Quench bar. Fig. 22. Recorded cooling rates for different thermocouple locations along the length of the Jominy End Quench bar.

29 For yield strength and ultimate tensile strength – Unfortunately, the Jominy End Quench test cannot be applied for measuring tensile strength. Therefore, in order to measure the cooling rate of the tensile specimens during quenching, first, specimens were cast around a k-type thermocouple that was placed in the center of their gage section. Before casting, the thermocouple wires were exposed to guarantee full contact with the metal. The instrumented tensile bars were solutionized at 538 o C (1000 o F) and then quenched in different quenching media: water at 24 o C (76 o F), 48 o C (119 o F), 100 o C (213 o F), ice water, and room temperature forced-air. Cooling data were averaged from three iterations, and the measured cooling rates vs. temperature are shown in Fig. 23. As expected, the results indicate that the maximum cooling rate decreases as the water temperature increases. Fig. 23. Measured cooling rates as function of temperature for tensile bars that were quenched in different media. Next, in order to measure the mechanical properties matched to the measured cooling curves, the tensile specimens were quenched in quenching media as described above, and then immediately transferred to a furnace where they were aged at 155 o C (311 o F) for 19 hours. The room temperature tensile properties of the specimens were then measured.

30 Tensile properties for as ice-water quenched specimens were also measured without aging. The as-quenched specimens were tested after quenching without delay, and the total testing time was less than 5 minutes. The measured tensile properties are shown in Table VII. Table VII. Measured tensile properties. YS (MPa) UTS (MPa) Elongation (%) As solutionized 46.34 143.19 12.85 As 0 ° C water quenched 80.13 247.72 12.86 Air quenched + 155 ° C 19h aged 266.32 330.08 3.2 100 ° C water quenched + 155 ° C 19h aged 289.35 364.42 3.66 48 ° C water quenched + 155 ° C 19h aged 290.6 386.25 5.35 24 ° C water quenched + 155 ° C 19h aged 287.7 393.66 5.51 0 ° C water quenched + 155 ° C 19h aged 303.36 395.95 5.55 (3) Calibrating the K constants based on the measurements In order to determine the kinetics parameters K 1 to K 5 , note that Eq. (4) can be re-written as follows, ܳ ൌ 2 ln ൬ σ െ σ ୫୧୬ σ ୫ୟ୶ െ σ ୫୧୬ ൰ 1 K ଵ (20) According to Eq. (20), the Quench Factor ( Q ) can be determined from the measured maximum and minimum values ( σ max and σ min ) provided the constant K 1 is known. K 1 is easily found since it is the natural log of the fraction of material that is untransformed during quenching. Similarly, the Quench Factor ( Q ) can be determined from the local cooling data and the C t function. The C t function is given by Eq. (3), which can be re- written as follows, ܳ ൌ ෍ ۏ ێ ێ ۍ ∆t ୧ െK ଵ K ଶ exp ൤ K ଷ K ସ ଶ RTሺK ସ െ Tሻ ଶ ൨ exp ቂ K ହ RT ቃ ے ۑ ۑ ې T ౠ T ౟ (21)

31 The kinetics parameter K 4 is the solvus temperature. However, recent findings suggest that the solution temperature would be a more accurate representation of K 4 [26]. The kinetics parameter K 5 is the activation energy for aging the precipitates, and it was found to be 78 (kJ/mol) in the aging experiments, as shown in the following section. Therefore, the calculated Quench Factor from Eq. (20) was plotted against the Quench Factor calculated from Eq. (21). Three out of the five unknown kinetics parameters; namely, K 1 , K 4 , and K 5 , were fixed. Then the remaining unknown kinetics parameters K 2 and K 3 in Eq. (21) were continuously adjusted until the scatter show the least distance to the line X=Y. This procedure allowed obtaining all the QFA kinetics parameters (K 1 through K 5 ) as shown in Table VIII. With this procedure, a TTP curve for grain refined A356 alloy was generated according to hardness as shown in Fig. 24. Table VIII. The determined kinetics parameters for A356.2 alloy K 1 K 2 K 3 (J/mol) K 4 (K) K 5 (kJ/mol) For Hardness -0.00501 2.87 × 10 -10 5043 813 78143.72 For Yield Strength -0.00501 6.36 × 10 -24 30522 813 78143.72 For Ultimate Tensile Strength -0.00501 3.02 × 10 -10 3758 813 78143.72 Fig. 24. TTP curve for A356.2 alloy with 0.2 wt% TiB grain refinement (Hardness).

32 Determination of the Shercliff-Ashby Aging Parameters An alloy-specific aging database is necessary for accurately modeling the heat-treated strength for complete heat treatment. Generating such an extensive database can be very time-consuming and labor-intensive. However, Shercliff and Ashby [3] developed an efficient method for populating the aging database and since its introduction in 1990, their aging model has been employed successfully to obtain the as-aged properties (e.g., corrosion resistant, hardness, strength, etc.) of many wrought and cast aluminum alloys, as described in background section. In order to determine the aging parameters required for the Shercliff-Ashby aging model, the aging curves were produced by measuring the Rockwell hardness F scale (HRF) of the alloy after exposure to different aging times and temperatures. Measured curves are shown in Fig. 25. For obtaining aging curves, small identical samples of A356 alloy with 0.2 wt% TiB grain refiner were solutionized at 538 o C (1000 o F) and then quenched in ice water. Subsequently, quenched samples were aged at different aging conditions (time and temperature). The samples were aged in a fluidized bed right after quenching in order to ensure that the maximum possible heating rate is attained. Once the aging peaks were determined, the peak tensile properties were then measured. The measured tensile properties and hardness at aging peaks are shown in Table IX. The measured peak hardness decreases as aging temperature increases, but it ceases to decrease after 330 o C (626 o F), as shown in Fig. 26. Therefore, this temperature was determined to be the metastable solvus temperature (T s ) of precipitation.

33 Fig. 25. Measured aging curves for A356 alloy. Fig. 26 Measured aging curve for A356 alloy. Table IX. Peak tensile properties for A356 alloy grain refined with 0.2 wt% TiB Harness (HRF) YS (MPa) UTS (MPa) Elongation (%) 155 o C Aged peak at 19 hours 94 303.4 396.0 5.55 210 o C Aged peak at 42 min 91 299.0 353.0 3.28 250 o C Aged peak at 6 min 86 271.6 315.8 2.43 315 o C Aged peak at 4.5 min 73 194.6 253.4 3.57

34 The detailed calibration procedure for the Shercliff-Ashby aging model is described in [3, 11, 27]; and the calibrated model parameters are presented in Table X. The as-quenched strength ( σ q ) was measured values of quenched samples without dwell. According to Eq. (13), the activation energy for second phase precipitation was determined by using the time required to reach the aging peak under different aging temperatures in an Arrhenius plot as shown in Fig. 27. This value was also used in the Quench Factor Analysis. The aging model reconstructed aging curves together with the measured data points for Meyer hardness are shown in Fig. 28. Table X. Calibrated or measured aging model parameters for A35 alloy. Aging Model Parameters Symbol For Meyer Hardness For Yield Strength For Ultimate Tensile Strength Intrinsic strength (MPa) σ i 114.6 46.3 143.2 As-quenched strength (MPa) σ q 463.4 80.1 247.7 Activation energy for aging (kJ/mol) Q a 78.1 78.1 78.1 Peak temperature-corrected time (s/K) P p 3.34×10 -8 3.34×10 -8 3.34×10 -8 Metastable solvus temperature ( o C) T s 330 330 330 Solvus enthalpy (J/mol) Q s 9520.5 16052.4 6886.7 Max strength parameter at 0 K (MPa) (S 0 ) max 1238.2 331 247.6 Constant coefficient relating τ 1 to t p K 1 0.4496 0.4013 0.6327

35 Fig. 27. Arrhenius plot for obtaining the activation energy for precipitation. Fig. 28. Reconstructed aging curves and measured data points for Meyer hardness.

36 4. MODEL CONSTRUCTION Among the many finite element codes that are commercially available, ABAQUS enables a wide range of linear as well as nonlinear engineering simulations. Because of its popularity and its ability to perform the required simulations accurately and efficiently, it was selected for this project. Moreover, it has the feature that allows the user to create user-defined material properties and analysis parameters that can vary with time and/or temperature. These user-defined subroutines are written in the FORTRAN language and are compiled before the model is run. In this work, this function was used extensively to develop the module of volumetric dilation and the module of strength and hardness. Commercially available software MAGMA5 8 is a simulation tool that is widely used in the casting industry. The newly developed MAGMA5 Heat Treatment (HT) module was also used in this work without any alteration, but only its thermal predictions were compared to the measured results. Thermal-Stress Module In order to calculate the heat treatment response of cast components during quenching and aging, two separate simulations were executed in sequence in ABAQUS. First, a heat transfer analysis calculates the time-temperature profile in the component as it cools down from the solutionizing temperature and as it is reheated to the aging temperature. Next, a stress analysis calculates the evolution of stresses and the deformations in the component by using the pre-calculated thermal profiles. Heat Transfer Analysis – Heat transfer across the metal/fluid interface is the most important aspect of the heat treatment process because it controls the rate of cooling, which in turn determines all outcomes. Heat transfer across the metal/fluid interface is described by a heat transfer coefficient on the component’s surfaces. In ABAQUS, the rate of heat loss due to convection (q c ) is determined from Eq. (22): 8 Headquarters, MAGMA Gießereitechnologie GmbH

37 q ୡ ൌ h ୡ ሺT െ T ஶ ሻ ୟ ሺT െ T ஶ ሻ (22) In Eq. (22), h c is the convective heat transfer coefficient from the component surface to the quenching medium. T is the surface temperature and T ∞ is the fluid’s temperature. The exponent, a, has a value of zero for forced convection, and a value of 0.25 for free convection. Numerical modeling of quenching poses several challenges. This is primarily due to the intensive thermal changes that are involved in the process. For decades, many researchers have tried to determine heat transfer coefficients for various quenching processes analytically [28] and many have tried to determine them experimentally [29]. However, quenching heat transfer coefficients are very much dependent on part geometry and the quenching medium; and this makes its determination approximate at best. More recently, a computer program has been developed for determining heat transfer coefficients in casting and quenching processes [30]. However, quenching a hot object into a fluid involves complex thermodynamic, fluid dynamic and phase transformation interactions that occur simultaneously and make the necessary simulations require a prohibitive amount of time even with the fastest state-of-the-art computer processors. For these reasons, we focused on developing a new efficient method for obtaining quenching heat transfer coefficients for complex castings. Before discussing our effort towards this end, it is necessary to briefly review what happens during quenching. There are three distinct stages during quenching. These are basically two types of boiling: pool boiling and flow boiling. Pool boiling is boiling on a heating surface that is submerged in a pool of initially quiescent liquid. Flow boiling is boiling in a flow stream of fluid where the heating surface may be the wall of the channel that confines the flow [21]. Of the two types, pool boiling best describes the quenching conditions. There are three critical stages during quenching. These are: (1) formation of a vapor blanket, (2) nucleate boiling, and (3) convective cooling. Each of these 3 stages is associated with a distinct cooling regime, as shown in Fig. 29. During stage (1), the liquid is first in contact with the hot surface and it boils intensely. The HTC at this stage is low due to the low thermal conductivity of the vapor layer.

38 During stage (2), the liquid near the material surface of the solid is superheated and tends to evaporate forming bubbles. These bubbles transport the latent heat of the phase change and also increase the convective heat transfer by agitating the liquid near solid surface. The HTC at this stage is at its maximum as the hot solid surface is constantly contacting cold water. During stage (3), the temperature of the solid surface approaches the boiling temperature of the fluid. This causes the rate of liquid vaporization to decrease and the rate of heat transfer from the solid surface to decrease, as shown in Fig. 30 [31]. It is thus clear that the distinct cooling regime and heat transfer from the solid surface are very much dependent on small variations in the conditions of the quenching bath and the state of the metal surface. Particularly, the formation of the vapor blanket around the solid surface creates a problem in modeling the quenching process: Since air is insulating compared to quenching fluids, it significantly reduces the extraction of heat from the part and lowers the heat transfer coefficient at this location. Therefore, contact of the solid surface with air bubbles decreases HTC while its contact with cold water increases it. Fig. 29. Three critical stages during quenching.

39 Fig. 30. The associated with critical stages during quenching. The cylindrical changes in HTC quenching probes used for measuring the HTCs were designed so that the three stages of quenching are reflected and so that no feature of the geometry blocks the motion of the vapor or traps the air bubbles. This is not the case in typical castings where some features may trap the vapor phase and other features may restrict the movement of the quenching fluid causing the fluid in contact with these areas to heat up locally. These effects can reduce the local rate of cooling. A new method is thus needed to obtain local quenching heat transfer coefficients (HTCs) for complex shape castings. Since the various surfaces of the cast component can be easily classified into groups by the user in a computer simulation, each of the surfaces can be assigned a different HTC: (i) on the surfaces where air pockets exist, an Air HTC is used, (ii) on the surfaces where fluid flows freely; Metal-Fluid HTC is used. There are two important advantages in locally applying the quenching heat transfer coefficients before computer calculations. These are: (1) the boundary conditions for the model become more representative of the physical situations, and (2) the computational time is significantly reduced.

40 The new modeling technique of using local quenching heat transfer coefficients was preliminary tested on simple cast components with simple shapes that were equipped with k-type thermocouples at their geometric center. These parts were solutionized at 538 o C (1000 o F) and then quenched into water that is maintained at 80 o C (176 o F). In each case, the measured cooling curve was compared to its computer-calculated counterpart. The cooling data were extracted from the geometric center of the component. In the computer calculations the surfaces were assigned either a measured Metal-Fluid HTC or an Air HTC depending on the local quenching conditions. Three different part geometries were used: (a) a cone shape, (b) a combination cylinder and cube, and (c) a cylinder with a cavity as shown in Fig. 31. During quenching, the cavity volume is completely filled with air from the start of the quenching event until its end. For each part, several repetitions were made and the results together with model predictions are shown in Fig. 32, Fig. 33 and Fig. 34. For better visualization, the results are shown as temperature vs. cooling rate. Cooling rate curves indicate moving averages. The Figs. show excellent agreements between the measured and computer-calculated cooling curves indicating that the newly developed method is valid. For the purpose of demonstrating the importance of assigning the correct HTC locally on the component’s surface, the yellow curve in Fig. 34 is a model predicted cooling curve obtained by using the Metal-Fluid HTC on the inside surfaces of the cavity instead of using the Metal-Air HTC. Clearly in this case the model-predicted cooling curve is significantly higher than the measured cooling curve. (a) (b)

41 (c) (d) Fig. 31. Instrumented cast probes used to test the importance of assigning local HTC’s on a component’s surface. (a) A cone, (b) A combined cube + cylinder, (c) a cylinder with a cavity, and (d) the cylinder with cavity sectioned in half in order to show the cavity geometry and the location of the thermocouple tip (indicated by the red dot). Fig. 32. Measured and computer-predicted cooling rates for the part shown in Fig. 31 (a).

42 Fig. 33. Measured and predicted cooling rates for the part shown in Fig. 31 (b). Fig. 34. Measured and predicted cooling rates for the part shown in Fig. 31 (c).

43 Stress Analysis – In the thermal analysis module, the temperature is the unknown variable. However, in the stress analysis module, the displacement and stress are the unknown variables. The thermal fields affect the mechanical fields through thermal expansion and temperature-dependent material properties during quenching. The relationship is given by Eq. (23). ε ୲୦ ൌ αሺθሻሺθ െ θ ଴ ሻ െ αሺθ I ሻሺθ I െ θ ଴ ሻ (23) In Eq. (23), α ( θ ) is the temperature-dependent coefficient of thermal expansion, θ is the current temperature, θ I is the initial temperature, and θ 0 is the reference temperature for the expansion coefficient; at this temperature the thermal expansion is assumed to be zero [32]. In stress analysis, all residual stresses that were introduced into the part during its previous manufacturing processes are assumed to be removed during solutionizing. An elastic-plastic analysis is therefore performed in order to account for material yielding as the part is cooled from the high solutionizing temperature where the mechanical properties of the alloy are severely reduced. The stress analysis uses the same time increment that is used in the thermal module, but if desired, the time increment can be refined to enhance the accuracy of the stress analysis. Nodal constraints are required in order to prevent rigid body displacement and rotation. Therefore, three nodes are constrained from moving, and this setup applies to all the process steps. Creep Module Two factors contribute to dimensional changes during aging. These are: (1) precipitation of the strengthening phase, which invariably has a different specific volume from that of the matrix; and (2) creep. As stated previously, in order to account for the contribution of creep to the overall distortion and residual stresses, the high temperature creep during artificial aging was simulated by the nonlinear viscoplastic module built-in ABAQUS together with temperature-dependent creep parameters that were calibrated from data in the open literature.

44 Volumetric Dilation Module In addition to the completely reversible changes that are caused by thermal expansion and contraction, and irreversible dimensional changes and distortion that are caused by quenching, aluminum alloy components experience permanent volume changes during aging [33]. This volumetric dilation is of concern to designers and manufacturers, particularly when the application calls for maintaining tight tolerances. Therefore, a dilation module is developed for predicting transformation-induced dilation during the aging step. In order to account for the contribution of precipitation of second phase particles to the overall volumetric dilation, we assume that precipitation of the second phase follows the classical nucleation and growth theory, and that the volumetric dilation is proportional to the volume fraction of second phase particles, then the famous Avrami (Johnson-Mehl-Avrami-Kolmogorov [7]) equation may be used to simulate the volumetric dilation, as shown in Eq. (24). ε ൌ ε ୲୭୲ୟ୪ ൈ ൣ1 െ exp ൫െkሺTሻ t ୬ሺTሻ ൯൧ (24) In Eq. (24), ε is the dilation, ε total is the total dilation after precipitation is complete, k is a temperature-dependent constant, t is time, and n is a temperature-dependent exponent. Provided that k and n are known, the dilation during aging step can be calculated as a function of aging time. Rooy and Kauffman [33] have documented the dilation of many aluminum alloys during aging heat treatments In their data, the growth of cast alloy, 356-T4, are shown in Fig. 35. The measured extensions ( ∆ l ) per unit linear dimension (l 0 ) for 356 alloy after aging at different temperatures was used as database for the dilation module. The samples used to obtain this data were rods made in a permanent mold. The rods were 1.125 inches (28.575 mm) in diameter and 12 inches (304.8 mm) long. According to Eq. (24), data were then fitted to an Arrhenius plot to yield the temperature-dependent constant (k) and the exponent (n). The calibrated results are shown in Table XI. Notice that k increases with aging temperature; and n, which is known to vary with the nucleation rate and the precipitate morphology, shows a maximum peak near 226 o C (440 o F).

45 Fig. 35. Growth (dilation) curves for aluminum cast alloy 356-T4. Table XI. Material constants (k) and (n) as a function of aging temperature. Temperature ( o C) n k 149 0.597 0.000205 176 0.765 0.000079 204 0.791 0.000272 226 0.814 0.000432 260 0.394 0.040555 343 0.241 0.382472 Before incorporation into the integrated model, the volumetric dilation module was tested. Bars (3.5 inches (88.9 mm) in length and 0.5 inch (12.7 mm) in diameter) cast from A356 alloy in a permanent mold were used for this purpose. The bars were solutionized at 525 o C (980 o F) for 12 hours and quenched in boiling water. The lengths of the bars were measured by a micrometer (accuracy of ± 0.0001 inch) right after quenching and the bars were found to show no sign of distortion. The bars were then aged in a box furnace at 215 o C (420 o F) for up to 100 hours and their dilation was measured. In order to ensure that the measured dilations are not a result of the bars creeping during the lengthy

46 exposure to heat, two groups of bars were placed in the furnace (one set vertically, the other horizontally), and there was no significant difference between the two groups, which indicates that there was negligible creep caused by gravity. The measured and computer-predicted dilations that occurred during aging at 215 o C (420 o F) are shown in Fig. 36. It is clear that the measured and computer-predicted values are in good agreement. If the measured dilation was due solely to formation of second phase particles of a different volume from the matrix as the model assumes, then the dilation would be completely irreversible. This was found to be the case. Indeed, samples that were re- solutionized at 525 o C (980 o F) for 12 hours and furnace-cooled to room temperature did not revert to their pre-aging dimensions. Fig. 36. Dilation curve for specimen aged at 215 o C (420 o F). Strength and Hardness Module In order to be able to predict the resulting strength and hardness, a quenching subroutine and aging subroutine were developed to perform the Quench Factor calculations and to

47 include the Shercliff-Ashby aging model as a database. Both subroutines use only the calculated time-temperature data. In this work, a new approach was adopted to facilitate coupling the Quench Factor Analysis with the Shercliff-Ashby aging model. In this approach, instead of measuring the maximum achievable strength (i.e., σ max ) for each one of the aging conditions under consideration, the as-aged strength as given by the Shercliff-Ashby aging model is used. This was accomplished by re-defining ( σ max ) in Eq. (4) so that it becomes available to the Quench Factor Analysis. The new property prediction, σ (dT/dt ,t, T) is dictated by the quenching rate and aging conditions, as shown in Eq. (25). By physical definition, the minimum value of the property that is achievable ( σ min ) and the intrinsic property of the material ( σ i ), are assumed to be the solutionized values. Thus, the final integrated equation can be described by three terms: the first term is controlled by the quenching process, the second term is controlled by the aging conditions and the final term is a material constant, as shown in Eq. (26). ߪሺݍݑ݄݁݊ܿ ݎܽݐ݁, ܽ݃݅݊݃ ݐ, ܽ݃݅݊݃ ܶሻ ൌ ሾ݁ݔ݌ሺܭ ଵ ܳሻሿ ଵ ଶ ൣߪ ௜ ൅ ∆ߪ ௦௦ ൅ ∆ߪ ௣௣௧ െ ߪ ௠௜௡ ൧ ൅ ߪ ௠௜௡ (25) ߪ ሺݍݑ݄݁݊ܿ ݎܽݐ݁, ܽ݃݅݊݃ ݐ, ܽ݃݅݊݃ ܶሻ ൌ ሾ݁ݔ݌ሺܭ ଵ ܳሻሿ ଵ ଶ ሺܿ݋݊ݐݎ݋݈݈݁݀ ܾݕ ݍݑ݄݁݊ܿሻ ൣ∆ߪ ௦௦ ൅ ∆ߪ ௣௣௧ ൧ ሺܿ݋݊ݐݎ݋݈݈݁݀ ܾݕ ܽ݃݅݊݃ሻ ൅ߪ ௠௜௡ ሺܿ݋݊ݏݐܽ݊ݐሻ (26)

48 5. VALIDATION OF THE INTEGRATED MODEL Two cast parts were chosen to demonstrate the model and verify the accuracy of its predictions: (1) a lab-manufactured cast part and (2) a commercially cast part. The model predictions were verified by comparing them to measurements of corresponding properties for parts made using processing conditions identical to those used in the simulations. The computer models were created using both ABAQUS and MAGMA5 HT software platforms. The lab-manufactured part contains thin and thick sections as well as a blind cavity as shown in Fig. 37, and its symmetrical shape reduces both quenching and measuring difficulties. The part was cast with two k-type thermocouples permanently inserted in it, and the cavity features were created by machining. The computer-generated renditions of the lab-manufactured cast part in ABAQUS and MAGMA5 are shown in Fig. 38 and Fig. 39, respectively. The thermocouple locations are indicated by locations (1) and (2). (a) (b) Fig. 37. The lab-manufactured part used for verification: (a) front view and (b) back view.

49 Fig. 38. An ABAQUS generated rendition of the lab-manufactured part. Fig.39. A MAGMA5 generated rendition of the lab-manufactured cast part. The commercially cast part 9 is shown in Fig. 38 to 41. It is a hub of a motorcycle wheel made by the gravity semi-permanent mold casting process wherein both bolt flange ends are formed with metal mold sections and the external surfaces between the flanges, as well as the internal hollow cavity for the axle section, are formed by sand cores. In the as- cast condition, the central hollow cavity is sealed at one end as shown in Fig. 39. Computer-generated renditions of this part are shown in Fig. 40 and Fig. 41. Locations (1) and (2) shown in Fig. 42 indicate locations where cooling data was extracted. 9 Courtesy of Harley-Davidson Motor Company, 3700 W. Juneau Avenue. Milwaukee, WI 53208, USA

50 (a) (b) Fig. 38. Commercial casting used for validating the model. Fig. 39. Sectioned commercial casting used for validating the model. Fig. 40. ABAQUS model of the commercial casting used for validating the model.

51 Fig. 41. MAGMA5 HT model of the commercial casting used for validating the model. Fig. 42. Locations where data was extracted. Heat Treatment Quenching – Two different quenching processes were used to verify the computer- predictions. The cast parts were solutionized at 538 o C (1000 o F) for 12 hours and then either (1) quenched in 80 o C (176 o F) water, or (2) quenched by room temperature forced- air. Quenching models were created for both quenching conditions, and temperature- dependent local quenching heat transfer coefficients were assigned on the casting surfaces according to the local surface quenching conditions.

52 In the case of the lab-manufactured part, for hot water quenching, the part was immersed in the hot water so that the front face is down into hot water and the blind cavity shown in Fig. 37 (a) is filled with air as the part cools down to the temperature of the water. For air quenching, the part was cooled by room temperature forced-air directed onto its front face. For simulating hot water quenching, the surface indicated by pink color in Fig. 38 was assigned the Metal-Fluid HTC (as measured by the disk probe), the surfaces indicated by yellow color in Fig. 38 were assigned the Air HTC, and all the remaining surfaces were assigned the Metal-Fluid HTC (as measured by the cylindrical probe). For simulating forced-air quenching, the surfaces indicated by pink color in Fig. 38 were assigned the Metal-Air HTC and the remaining surfaces were assigned the Air HTC. In the case of the commercially cast part, for hot water quenching, the part was quenched by immersing its open end down into the water so that the blind hollow cavity shown in Fig. 39 was filled with air as the part cooled down to the temperature of the water. For air quenching, the part was quenched by forced-air impinging directly onto its open end. For simulating the part’s response to quenching, local temperature-dependent quenching heat transfer coefficients were assigned on the casting surfaces in the same manner employed for simulating the lab-manufactured part. Aging – Two standard aging conditions, namely T6 and T7, were used to verify the computer-predictions. T6 aging is the most widely used condition, and T7 is often used for components that are intended for high temperature applications. Both parts were aged without delay. T6 aging was done by holding the part at 155 o C (311 o F) for 4 hours. T7 aging was done by holding the part at 227 o C (440 o F) for 8 hours. Aging was performed in a fluidized bed in order to ensure that the maximum possible heating rate is attained. A constant heat transfer coefficient, namely 1000 (W/m2) was used to simulate the aging step and at the end of aging, the model assumes that the parts are air-cooled to room temperature. Predicting the thermal profiles in the lab-manufactured part – The time-temperature data recorded from both thermocouple locations are reported and compared to the model- predicted data from the same locations. The results of cooling curves and cooling rate vs. temperature are shown in Fig. 43, Fig. 44 and Fig. 45 for the hot water quenched part,

53 and are shown in Fig. 46 and Fig. 47 for the forced-air quenched part. Cooling rate curves indicate moving averages. All measured data are averages obtained from five adjacent points in order to minimize noise. In all cases, the results show good agreement between the model-predictions and the measurements. Fig. 43. Measured and computer-calculated cooling curves for the hot water quenched part at thermocouple locations (1) and (2). Fig. 44. Measured and computer-predicted quenching rate curves for the hot water quenched part at thermocouple location (1).

54 Fig. 45. Measured and computer-predicted quenching rate curves for the hot water quenched part at thermocouple location (2). Fig. 46. Measured and computer-predicted cooling curves for the air quenched part at thermocouple locations indicated by (1) and (2).

55 Fig. 47. Measured and computer-calculated quenching rate curves for the air quenched part at thermocouple locations (1) and (2). Predicting the thermal profiles in the commercially cast part The model-predicted cooling curves are shown in Fig. 42. The model-predicted cooling curves and cooling rate vs. temperature for the hot water quenching simulation are shown in Fig. 48 and Fig. 49, respectively, and the model-predicted cooling rate vs. temperature for the forced-air quenching simulation is shown in Fig. 50. Cooling rate curves indicate moving averages. Fig. 48. Computer-predicted cooling curves of the hot water quenching simulation of the commercially cast part.

56 Fig. 49. Computer-predicted cooling rate curves vs. temperature for the hot water quenching simulation. Fig. 50. Computer-predicted cooling rate curves vs. temperature of air quenching simulations. Predicting the Heat-treated Tensile Strength and Hardness Standard-size plate type tensile specimens (2 inch gage length with 0.3 inch thickness (ASTM standard E8 [17]) were machined from the as-cast as well as from the heat- treated commercial part, and then they were used to measure the room temperature tensile properties and hardness of the casting. Four tensile specimens were extracted from each

57 cast part as shown in Fig. 51. The hardness and tensile measuring conditions are as described earlier. These measurements are compared to their computer-predicted counterparts from the same location – location (2) in Fig. 42 – and the results are reported in Table XII. For better visualization, the results are shown graphically in Fig. 52, Fig. 53 and Fig. 54 wherein the error bars indicate standard deviations. Fig. 51. Cast part and machined tensile samples. Table XII. Model-predicted and measured as-cast and as-heat-treated strength and hardness from location (2) in Fig. 42. Measurements Model-predictions Hardness (HRF) YS (MPa) UTS (MPa) Hardness (HRF) YS (MPa) UTS (MPa) Water quenched + T6 aged (4 hours) 78.0 238.9 288.5 89.7 266 338 Air quenched + T6 aged (4 hours) 77.2 181.8 231.8 80.4 209 311 Water quenched + T7 aged (8 hours) 58.0 127.0 185.3 87.5 257 250 Air quenched + T7 aged (8 hours) 60.3 127.3 182.9 79 203 236 As cast 69.4 101.8 169.4

58 Fig. 52. Measured and model-predicted hardness (HRF scale). Fig. 53. Measured and model-predicted yield strength.

59 Fig. 54. Measured and model-predicted ultimate tensile strength. Screen captures from the computer simulations are shown in Fig. 55, Fig. 56 and Fig. 57 for the heat-treated hardness, yield strength and ultimate tensile strength, respectively. The computer-predicted values vary from location to location within the casting due to the unique local cooling at each location. The model-predicted minimum and maximum values throughout the casting for each heat treatment condition are shown in Table XIII. The computer-predicted aging curves from location (2) of Fig. 42 for parts quenched in hot water and parts quenched by room temperature forced-air, and then aged following the T6 and T7 schedules are shown in Fig. 58 and Fig. 59 for yield stress and ultimate tensile stress, respectively. In each case, the computer-predicted curves clearly show the aged-peak strength and the subsequent decrease in strength caused by over-aging.

60 Table XIII. Model-predicted minimum and maximum values within the casting. Hardness (HRF) YS (MPa) UTS (MPa) Min Max Min Max Min Max Water quenched + T6 aged (4 hours) 89.71 89.74 265.3 266.1 337 338.7 Air quenched + T6 aged (4 hours) 87.93 88.02 256.9 257.1 248.8 252.5 Water quenched + T7 aged (8 hours) 80.41 80.44 209 209.6 310.3 311.8 Air quenched + T7 aged (8 hours) 78.52 78.61 202.7 202.9 234.2 237.4 (a)

61 (b) (c)

62 (d) Fig. 55. Model-predicted hardness (HRF) for the casting (a) quenched in hot water + T6, (b) quenched in hot water + T7, (c) air quenched + T6 and (d) air quenched + T7. (a)

63 (b) (c)

64 (d) Fig. 56. Model-predicted yield strength (MPa) for the casting (a) quenched in hot water + T6, (b) quenched in hot water + T7, (c) air quenched + T6 and (d) air quenched + T7. (a)

65 (b) (c)

66 (d) Fig. 57. Model-predicted UTS (MPa) for the casting (a) quenched in hot water + T6, (b) quenched in hot water + T7, (c) air quenched + T6 and (d) air quenched + T7. Fig. 58. Model-predicted T6 aging curves for strength at location (2) of Fig. 42 (water quenched part).

67 Fig. 59. Model-predicted T7 aging curves for strength at location (2) of Fig. 42 (water quenched part). Predicting dimensional changes A Starrett coordinate measuring machine (CMM) was used to measure the dimensional changes and distortion caused by the heat treatment process. In order to characterize the amount of distortion in the parts after heat treatment, a fixture was made to hold the part at the same location in the CMM. The total length of the commercial part, 7 inches (177.8 mm), was measured before quenching, after quenching, and after aging. Before heat treatment, the top and bottom surfaces of the part were ground with sand paper in order to make true flat surfaces. Sufficient measurements (125) were made in order to obtain accurate values and the results were averaged from all measurements. In the computer simulations, both sets of creep parameters, with and without time hardening, were used. The model-predicted and measured changes in length for the hot water quenched parts followed by T6 and T7 aging conditions are shown in Table XIV and Table XV, respectively. The model-predictions made by the two sets of creep parameters show similar results. For better visualization, the results are shown graphically in Fig. 60 and Fig. 61. The model-predicted changes during aging are

68 contributed by both volumetric dilation and creep. Model-predicted total length increments during the aging step, together with the measured values are shown in Fig. 62 and Fig. 63, for predictions made by the creep module only and by the dilation module + creep module for both T6 and T7 aging. The predictions made by the creep module only are significantly different from the measured values, which confirm the importance of the volumetric dilation module. However, it is believed that better predictions can be made with up-to-date creep and volumetric dilation databases. Table XIV . Model-predicted and measured change in length for T6 aged castings. Table XV. Model-predicted and measured change in length for T7 aged castings. Change in total length (10 -4 mm/mm) T6 (155 o C for 4 hours) Model-predicted without time hardening Model-predicted with time hardening Measured After quenching 6.636 6.636 4.195 Dilation after aging 0.5279 0.5279 0.323 Creep after aging 0.0012 0.0257 Total change in length 7.166 7.190 4.518 Change in total length (10 -4 mm/mm) T7 (227 o C for 8 hours) Model-predicted without time hardening Model-predicted with time hardening Measured After quenching 6.636 6.636 3.057 Dilation after aging 5.8465 5.8465 15.928 Creep after aging -0.1720 -0.2290 Total change in length 12.310 12.253 18.985

69 Fig. 60. Model-predicted and CMM measured total length increments for T6 aged casting. Fig. 61. Model-predicted and measured total length increments for T7 aged casting.

70 Fig. 62. Model-predicted and measured total length increments during the only aging step for T6 aging condition. Fig. 63. Model-predicted and measured total length increments during the only aging step for T7 aging condition.

71 Predicting Residual Stresses There are several methods for measuring residual stress. Some are destructive, while others can be used without damaging the part. In this work, the standard X-ray diffraction method for measuring residual stresses in metallic components was used. In this method, line shifts due to a uniform strain in the component are measured and then the stresses in the component are determined by a calculation involving the elastic constants of the material [34]. By knowing the strain-free inter planar spacing d and do, the modulus of elasticity in a specific crystal direction, E, and Poisson’s ratio in that crystal direction, ν , and the two components of the biaxial principle stress can be obtained from Eq. (27). d െ d ଴ d ଴ ൌ ൬ 1 ൅ ݒ E ൰ σ ׎ sin ଶ φ െ ݒ E ሺσ ଵ ൅ σ ଶ ሻ (27) Due to restrictions imposed by the part geometry, bi-axial stress analysis is difficult. Therefore, uni-axial residual stress analysis was used, which is the standard method for measuring residual stresses in large size samples. Measurements were made in an X-ray diffractometer equipped with a stress analysis module 10 . The X-ray measurements were focused on the spot where the highest magnitude of compressive residual stress is expected, and the location where the measurements were made is shown in Fig. 64. 10 Model Empyrean Diffractometer manufactured by PANalytical, Inc., Natick, MA, USA.

72 Fig. 64. Location of measurements made by x-rays diffraction (red dot). The model predictions were made by using both sets of creep parameters, with and without time hardening. Screen captures on the X-ray targeted location are shown in Fig. 65, Fig. 66 and Fig. 67, for predictions after water quenching, after T6 and after T7 aging, respectively. The measured and model-predicted residual stress values are shown in Fig. 68. Error bars for model predictions are residual stress variation on the X-ray scanned location. The X-ray measurements show negative values for residual stress, which confirms the presence of a compressive stress at this location, and the magnitude of residual stress compares well to the model-predicted magnitude. The predictions made by using the creep database with time hardening are in better agreement with measurements than the ones made by using the creep database without time hardening.

73 Fig. 65. Model-predicted residual stress on the X-ray measured location after water quenching (110.1MPa ~ 97.92MPa). Fig. 66. Model-predicted residual stress on the X-ray measured location after T6 aging (65.19MPa ~ 58.7MPa).

74 Fig. 67. Model-predicted residual stress on the X-ray measured location after T7 aging (18.24MPa ~ 16.65MPa). Fig. 68. Measured and model-predicted residual stresses.

75 6. SUMMARY AND CONCLUSIONS A heat treatment model has been developed and computer simulations using the model were performed with the finite element analysis software (ABAQUS) in order to predict the response of cast aluminum alloy components to a complete precipitation hardening heat treatment, including solutionizing, quenching, and aging. The necessary database for A356 alloy was generated. The model is unique in its ability to capture variations in part properties from location to location within the same casting by incorporating local cooling rates reflected in local quenching heat transfer coefficients. The model calculates the temperature profiles for the quenching processes using a database of temperature- dependent heat transfer coefficients and the new method of locally assigning them to regions on the surface of the cast part. The model-predicted temperature profiles for both hot water and air quenching were found to be in good agreement with measurements. The model also predicts the magnitude and sense of residual stresses and the magnitude and profile of distortion caused by quenching and aging steps. Model predictions were validated by comparing them to measurements made on heat-treated commercial cast parts. Distortion and residual stresses were measured on heat treated parts and compared to the computer predictions. The distortion was measured with a coordinate measuring machine (CMM), and residual stress was measured with the standard X-ray diffraction method. The model-predictions of dimensional change and distortion show reasonable agreement with measurements considering the fact that quenching operations involve complex thermodynamic, fluid dynamic, and phase transformation interactions that occur simultaneously and make it difficult to control these phenomena. Even in a laboratory- controlled environment, quenching experiments performed under identical conditions tend to yield significantly different (more than 25%) magnitudes of distortion and dimensional change. The model predictions of residual stresses were found to be in good agreement with measured values, and predictions made by using a creep database with time hardening show a better match to X-ray measurements. However, it is believed that a more accurate creep database is needed in order to improve the ability of the creep module to predict the magnitude of the residual stress and distortion caused by artificial aging, especially for high temperature aging conditions. The ABAQUS built-in power

76 law creep model used in this thesis has provided a simple yet well performing tool to predict residual stress relaxation and creep strain during aging. Other more sophisticate creep models could have improved the accuracy of the predictions, but those models require a large database, and improvements will probably be limited. Lastly, the model demonstrates the computational utility of the strength predictions in describing the essential mathematical equations using the user-developed subroutines. This part of the model is based on the Quench Factor Analysis method together with the Shercliff-Ashby aging model. All required kinetic parameters and material constants were measured and calibrated. The model was successfully applied to a lab-manufactured cast part and a commercial cast component to confirm its validity. The model-predicted strength and hardness were found to be in good agreement with measurements made on heat-treated parts. However, without considering the prior casting conditions, including porosity and defects, all model perditions will be invariably higher than their measured counterparts.

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78 the Guarded-Comparative-Longitudinal Heat Flow Technique," vol. E1225-04, ed: ASTM International. [19] S. Bakhtiyarov , et al. , "Electrical and thermal conductivity of A319 and A356 aluminum alloys," Journal of Materials Science, vol. 36, pp. 4643-4648, 2001. [20] M. Maniruzzaman , et al. , "CHTE Quench Probe System - a new quenchant characterization system," presented at the the 5th International Conference on Frontiers of Design and Manufacturing, ICFDM, Dalian, China, 2002 [21] L. S. Tong and Y. S. Tang, "Boiling Heat Transfer and Two-Phase Flow," 1997. [22] M. Holt, "Creep-Rupture Properties of Aluminum Alloy A356-T61," Journal of Testing and Evaluation, vol. 5, 1977. [23] F. H. Norton, Creep of steel at high temperatures . New York.: McGraw-Hill Book Co., 1929. [24] ASTM, "Standard Test Methods for Determining Hardenability of Steel," ed: ASTM International. [25] M. Tiryakioglu and J. Campbell, "On macrohardness testing of Al-7wt.% Si-Mg alloys I. Geometrical and mechanical aspects.," Materials Scence and Engineering, vol. A361, pp. 232-239, 2003. [26] M. Tiryakio ğ lu and R. Shuey, "Modeling Quench Sensitivity of Aluminum Alloys for Multiple Tempers and Properties: Application to AA2024," Metallurgical and Materials Transactions A, vol. 41, pp. 2984-2991, 2010. [27] L. Wu and W. G. Ferguson, "Computer modelling of age-hardening for isothermally aged Al-Mg-Si alloys," International Journal of Modern Physics B, vol. 20, pp. 4177-4182, 2006. [28] R. G. Hills and E. C. H. Jr., "One-dimensional nonlinear inverse heat conduction technique.," Numerical Heat Transfer vol. 10, pp. 369-393, 1956. [29] K. Ho and R. D. Pehlke, "Metal-Mold interfacial heat transfer " Metallurgical and Materials Transactions B, vol. 16, pp. 585-594, 1985. [30] M. L. a. J. E. Allison, "Determination of thermal boundary conditions for the casting and quenching process with the optimization tool OptCast," Metallurfical and Materials Transactions B, vol. 38B, pp. 567-574, August 2007. [31] C. H. Gür and J. Pan, Handbook of Thermal Process Modeling of Steels : CRC Press, 2008. [32] K. Hibbitn and I. Sorensen, "Heat Transfer and Thermal-Stress Analysis with ABAQUS Training," 2002. [33] J. G. Kaufman and E. L. Rooy, "Aluminum alloys castings, Properties, process, and applications," 2004. [34] P. S. Prevey , " A method of Determining Elastic Constants in Selected Crystallographic direction for X-Ray diffraction residual stress measurement ," Advances in X-Ray Analysis , vol. 20, pp. 345-354, 1977 .

79 APPENDIXES

80 Appendix A Predicting the Response of Aluminum Casting Alloys to Heat Treatment

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86 Appendix B A Mathematical Model and Computer Simulations for Predicting the Response of Aluminum Casting Alloys to Heat Treatment

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93 Appendix C Modeling the Response of Aluminum Alloy Castings to Precipitation Hardening Heat Treatment

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