Transport Phenomena During Equiaxed Solidification of Alloys

Recent progress in modeling of transport phenomena during dendritic alloy solidification is reviewed. Starting from the basic theorems of volume averaging, a general multiphase modeling framework is outlined. This framework allows for the incorporation of a variety of microscale phenomena in the macroscopic transport equations. For the case of diffusion dominated solidification, a simplified set of model equations is examined in detail and validated through comparisons with numerous experimental data for both columnar and equiaxed dendritic growth. This provides a critical assessment of the various model assumptions. Models that include melt flow and solid phase transport are also discussed, although their validation is still at an early stage. Several numerical results are presented that illustrate some of the profound effects of convective transport on the final compositional and structural characteristics of a solidified part. Important issues that deserve continuing attention are identified

Modeling of macrosegregation: Applications and future needs

of alloy species due to the relative movement or ow of segregated liquid and solid during solidi cation. Modelling and simulation of macrosegregation There are numerous causes of uid ow and solid has experienced explosive growth since the pioneering studies of Flemings and co-workers in movement in casting processes: melt, separated from a mould wall or free surface, or melted oV dendrites; the solid can either oat The author is in the Department of Mechanical and or settle depending on its density relative to th

Effects of Simplified Enthalpy Relations on the Prediction of Heat Transfer during Solidification of a Lead-Tin Alloy

An investigation into the effects of enthalpy junctions that vary with both concentration and temper

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during solidification of an assemblage of equiaxed dendritic crystals. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology (i.e., tip radii, branch spacings, etc.) and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of initial supercoolings and, thus, interaction "strengths" between the crystals. The experiment thus extends the microgravity measurements of Glicksman and coworkers for steady growth of a single dendrite [Isothermal Dendritic Growth Experiment (IDGE), first flown on USMP-2] to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation more close to actual casting conditions. Corresponding earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will primarily be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt

Casting Yield Survey)

Abstract The results of a casting yield survey of steel foundries taken in the first quarter of 1997 are presented. Data collected in the survey includes the average, best case, and worst case castings yields for steel castings, and statistical data on the factors which influence casting yield. The average casting yield was found to be 53.3%, and the average best and worst case casting yields were found to be 72.7% and 33.2% respectively, based on a per response average. The response rate for this survey was 40% of the North American steel foundries contacted. Production, end-use, steel type, geometry, and risering methodology factors were identified and ranked in importance affecting casting yield. The following were statistically identified as important positive factors on casting yield, where yield increases with their increase: tons produced per pattern, amount of railroad and wear resistant end-use production, average section thickness, and use of risering rules developed in-house. A negative impact on yield was found to be related to pump and valve enduse production, and corrosion resistant steel production. The quantitative contributions of these factors on casting yield are presented. Unconventional yield improvements were rated very low relative to methods currently in use. Induction heating, compressed air cooling and stacking of castings were indicated as unconventional methods which had been attempted in foundries. Hardin, R.A., and Beckermann, C., "The Current State of Casting Yield: Results from the 1997 SFSA Yield Survey," in Proceedings of the 51 st SFSA Technical and Operating Conference, Paper No. 3.5, Steel Founders' Society of America, Chicago, IL, 1997. lNTRODUCTlON It is commonly believed that the average metal yield in the steel casting industry is approximately 50 to 55 percent. A primary goal of conducting the casting yield survey is to determine the yield with statistical accuracy for steel casting foundries. Regardless of the precise average yield, it can be safely assumed that most foundries must melt about twice as much steel as will be shipped as finished products. The resulting negative consequences of lower casting yield include additional costs in remelting scrapped steel (estimated to account for 7% of the total casting cost), the need for increased capacities for melt furnaces and melt handling, and increased costs associated with additional labor, molding and sand use. Increasing casting yield is therefore a major research priority for the Steel Founders' Society of America (SFSA). As part of that research plan, the SFSA is currently supporting a research project to achieve increased casting yield through new directional solidification techniques. The present casting yield survey was developed and conducted with the goals that it would assess the current yield performance among SFSA member companies, provide quantitative data on the casting process variables which affect yield (and to what extent), and poll the membership on promising yield improvement methods. From operational experience, it is understood that casting yield depends on factors such as type of casting (i.e. size, shape complexity, weight, and section thickness), alloys used, molding media and methods, and foundry practice (i.e. risering methods). The survey was designed to produce quantitative data on the relative importance of these factors. Finally, to further support the ongoing research project, it is hoped that the survey results will help identify types of castings and foundry practices as good candidates for application of the yield improvement techniques being developed as part of the project. Important objectives for the survey are summarized below: Obtain quantitative data on the current level of casting yield in steel foundries. Obtain data on the current methods of risering and yield improvement used. Acquire input from steel foundries on best yield improvement methods to pursue and important issues to consider in research. Use acquired data to correlate casting yield with casting variables. Use survey results in identifying and prioritizing yield improvement techniques. SURVEY DESCRIPTION The survey questionnaire was developed with input from the SFSA and SFSA member foundries. The result was a compact survey considering the amount of information collected. Following its development and approval, the survey was mailed from the SFSA to a pool of 93 foundries located in the U.S. and Canada. The response rate for the survey was 40%. The survey was divided into four sections; a general information section for contact data, and three sections of questions. The three question sections include general foundry characterization questions (section II with questions 1 through 9), current yield information questions (section Ill with questions 10 through 13), and questions regarding yield improvement methods (section IV with questions 14 through 18). The general foundry characterization questions covered information on tonnage, number of units of production, molding methods, typical casting geometry, and type of steels cast. For geometry data, participants were asked to give the minimum, maximum and average section thicknesses and the maximum dimensions for their typical castings' length, width, and height for a typical casting they produce. Annual energy usage for melting, and melting practice by weight percent of tonnage was also requested. Participants were directly asked for their average casting yield, which can be checked with the computed yield in the previous section for answer consistency. They were also asked to provide their highest possible yield on a "best case" casting and their worst yield on a "worst case" casting. The questions in the 2 final section were developed to collect data on issues dealing with yield improvement; identifying obstacles and looking for solutions. Causes of lowered casting yield and defects which limit yield were rated for importance, and conventional and unconventional methods of increasing casting yield were rated for effectiveness. Data in the SFSA Directory of Steel Founders and Buyers Guide was used to collect the foundries' end-use as percentage of their tonnage. RESULTS FOR THE SURVEY OF STEEL CASTING YlELD Data from the survey was entered into an Excel spreadsheet "database", and selected data from the spreadsheet was analyzed using the SAS statistical. The SAS program was used to produce the linear regression, ANOVA analysis (single and multivariate). Results from the survey's general foundry characterization section (section II) were also compared with results from two previous studies undertaken by the SFSA, the 1995 Capacity Study and the 1995 End-Use Survey, to confirm that the pool of respondents is representative of the industry. Extensive detail of the survey results is given in the survey report submitted to the SFSA (Steel Founders' Society of America 1997 Casting Yield Survey). Survey Production Data and Sample Pool Comparisons Data for the respondents' yearly production in tonnage and units produced per casting weight class are summarized in The percentage of tonnage produced by steel type and molding method is presented Product end-use data collected from the survey responses in combination with data in the SFSA Directory was used to produce the data given in A summary of averages and standard deviations from the section I survey data discussed above is given in Casting Geometry Data The reported minimum, maximum and average section thickness data (in inches) for a typical casting are plotted in Energy Use, Melting and Pouring The survey respondents' melting practice as a percentage of total was compared with the melt practice data reported in the 1995 SFSA Capacity Study. This showed the yield survey sample to be somewhat more highly skewed to the electric arc melting. The average reported energy (kW-hr) used per ton of metal melted was found to be 592 kW-hr per ton, and from the reported tonnage of castings shipped, the energy used per ton of metal shipped was found to be 1219 kW-hr per ton shipped. The average energy usage per ton of castings shipped is remarkably close to the value of 1300 kW-hr/ton as reported by McNaughton (1977), and is about 6% less. Also, there was a statistically significant relationship (found by ANOVA testing at the 0.15 level) between decreasing power usage per ton for foundries with increasing total tonnage; this data and its linear regression are shown in Responses to Yield Improvement Questions In the yield improvement section of the survey, respondents were asked to evaluate reasons for lower yield, relative importance of various defects to casting yield and various conventional and unconventional yield improvement techniques. In The evaluation of conventional and unconventional yield improvement techniques are presented in Tables VII and VIII. This feedback identified worthwhile yield improvement methods. Respondents were also 5 asked to indicate whether or not their foundry had used a given technique. For unconventional yield improvement methods, only induction heating of risers, compressed air chilling, and stacking were indicated as having been used by 1, 2, and 6 foundries respectively. The conventional improvement method evaluations are given in The ratings for unconventional yield improvement methods are presented in 6 Casting Yield Data The reported (average yield as reported directly in the survey) and computed (from the tonnage shipped and melted) casting yields averaged per survey response were 53.3% and 52.1%, respectively. They are remarkably close, as they should be. This serves as a check on this critical figure reported in the survey. The distribution of the reported average yield is given in When yields are computed on the basis of steel tonnage produced by risering method as shown in 7 Casting simulation is one of the lower resulting yields. This could be explained by the fact that casting simulation is generally used on the toughest parts a foundry casts, and the foundries which use it are casting difficult and complex parts. Hence, the comparison is not fair. Here, again, note that a high average yield appears to go hand-in-hand with a high minimum yield while the maximum yield appears to have little effect on the average yield. The average, maximum, and minimum casting yields averaged on a per tonnage produced by steel type, by molding method and for a given end use are also given in For steel type Carbon and wear resistant steel show the highest average casting yields, and carbon in particular shows the highest worst case (minimum) yield. Heat resistant steel shows the highest maximum yield on average. Corrosion resistant steels show the lowest average casting yield, which is also indicated by its very low value of worst case yield. The maximum casting yield values vary by about 10% while the minimum (or worst case) casting yield show a 21% variation. 9 For molding type There is the least degree of variation between yields when averaged by tonnage produced by molding method. However, green sand casting molding tonnage produces on average a noticeably higher yield. It should be noted that, green sand casting shows a high correspondence with railroad end-use. For casting end-use A dramatically higher casting yield is observed in railroad producers. As observed in The next highest yields appear in the mining and truck producing categories. These categories also revealed to have the next highest minimum observed yields. This is more evidence that higher average yield is achieved by increasing the yield of worst case castings (rather than getting the best possible yield out of best case castings). The lowest average and worst case (minimum) casting yields were noted in the pump and valve categories, and the oil, military, construction and industrial categories were not much better. The military production best case (or maximum) observed yield is the lowest of any category. This may not be too surprising owing to the standards which are required. In ANALYSIS OF FACTORS INFLUENCING CASTING YIELD In the yield survey results of the previous section the relative importance and interactions between factors affecting casting yield were not statistically prioritized or identified. By using the analysis of variance (ANOVA) and multivariate ANOVA analysis technique, the data gathered in the survey regarding casting geometry and production data are added to the analysis to search for the most important factors affecting casting yield. In ANOVA analysis, the possible sources of variation of a variable (say casting yield in our case) are tested for the significant factors contributing to its observed variation. If a factor or source of variation is found to be a statistically important contribution to that variation, the ANOVA analysis produces two figures of merit which signify the factor's importance. One of these, the F-ratio (or Fisher ratio) is a measure of the statistical significance of a factor; the higher the F-ratio is, the greater the probability that a given factor has a significant effect on the variation of casting yield. The second figure, the significance (or p-value), is an indicator of how random the effect of a given factor is on the variation in the variable of interest. A high significance indicates a high probability that a factor has a random effect, and the lower the significance the greater the probability that the factor's effect is not random. The ANOVA analysis also provides the contribution to the variation in the variable of interest due to a given factor. In this case, the ANOVA analysis gives the contribution in percentage of the variation in casting yield due to factor of interest. The ANOVA analysis is used here with linear regression to indicate the manner and degree to which the casting yield is effected by a given factor. Here the dependence of casting yield on a factor is prescribed to 10 be linear, and ANOVA analysis will be used to detect which of the hypothesized effects (or their interactions) are statistically significant. The results of the one-way ANOVA tests with no interactions on factors affecting average, minimum, and maximum casting yield are given in The effect of a variable's influence on increasing or decreasing yield can be determined by the regression formula given in the final column of each table. The linear regression formulas contain the SAS variables V1, V2, and V3 for average, maximum and minimum yield respectively. The independent variable is the variable being considered in that table row. Tables in the complete survey report also detail all variables considered which were found not to have a statistical effect on yield. For consistency the ANOVA table results given here were computed without discarding any observations. Results of ANOVA for Average Casting Yield Variables with the strongest statistical influence on average casting yield are summarized below (in order of significance): Factors of Strong Significance on Average Yield 1, Tonnage per pattern (yield increases with its increase) 2. Percentage of pump and valve production (yield decreases with its increase) 3. Percentage of rail production (yield increases with its increase) 4. Percentage use of in-house risering rules (yield increases with its increase) 5. Percentage of industrial production (yield decreases with its increase) 6. Percentage of corrosion resistant production (yield decreases with its increase) 7. Minimum section thickness (yield increases with its increase) Factors of Significance on Average Yield 8. Average section thickness (yield increases with its increase) 9. Percentage of wear resistant production (yield increases with its increase) 10. Typical casting "box" volume/average casting weight (yield decreases with its increase) The most significant factor influencing average casting yield is a variable related to mass production, tonnage per pattern. This variable does not distinguish between many casting made of a single smaller pattern, or fewer castings made of larger/heavier patterns. In both cases foundries are able to refine and optimize their process leading to higher yields. The number of units per pattern did show a weak statistical significance when all observations were included, and average casting weight (formed by the tonnage per pattern divided by the number of units per pattern) showed no statistical influence on casting yield. However, when one influential observation was discarded, the number of units per pattern was found to be significant 11 12 with p = 0.0011, and was associated with a positive effect on yield with its increase. It was already shown in Since corrosion resistant steel production showed a strong statistical association with both pump and valve production (p-value = 0.0015), it remains to be determined whether this is due to the type of steel itself or a dependence on the end use of many corrosion resistant steel castings. An analysis using induction melting showed a strong statistical correlation with corrosion resistant steel (p-value = 0.0010) and weak association with pumps and valves (p-value = 0.0506), and was shown to have no effect on yield. This is evidence that the deleterious effect of corrosion resistant steels is due to their association with pump and valve castings rather than the inherent properties of corrosion resistant steel. However, the results of Varga et al. (1958) among others show clearly the additional difficulties involved with feeding castings of increasing alloying elements. On their face the survey results directly support the poor casting yield/feeding characteristics of corrosion resistant steels. Two thickness variables appear next in the list; minimum thickness which has a strong significance with average yield and average section thickness which has an effect, but in the statistical class below "strong". Note that minimum thickness appears to be more important than the average thickness, and that these geometric variables, though identified as important, are less important than "production" related variables. Maximum thickness was not identified as a significant effect on average casting yield. Following percentage of wear resistance production in the list, is a variable derived from responses to geometric questions as to casting size and weight. By taking the reported typical casting's length, width and height and then multiplying them to create a casting "box" volume, and then dividing this volume by the foundry's average casting weight, a specific volume for the casting's rangyness was formed. For castings whose dimensions were large, but the average weight was small; this factor has a large value, and it is assumed that such a casting is rangier than a casting whose overall box dimensions are smaller and whose weight is higher. It was found that this derived variable proved a statistically significant factor, and that its effect is as one would logically expect, when its value increases (i.e. a rangier casting) it is associated with a slight decrease in average casting yield. It is also important to note the factors which do not have an influence on casting yield, according to the survey responses. Average casting weight had no influence, and only a weak influence was observed with the number of different casting patterns produced each year. Molding practice had no discernable effect. In the risering rules category, only "in-house rules" was found to have an important influence and it was positive. All other risering methodologies either had "no effect" or "not much", and when the effect was found it was negative (for SFSA Guidelines, in-house rules based software and casting simulation). Variables which might be expected not to have an effect on yield by themselves such as casting length, width and height, and melting practice; did not. Minimum and maximum casting yield data were also analyzed for factors influencing them. Unlike average yield and minimum yield few statistically defendable factors influencing maximum casting yield were found. The dependence between the three reported yields were also examined, and the only dependence found was between average and minimum reported casting yields. As shown in Results of ANOVA for Minimum Casting Yield A number of the factors which were found to have a strong influence on average yield appeared as strong factors on minimum casting yield. The factors influencing minimum casting yield are listed below in order of significance: Factors of Strong Significance on Minimum Yield 1. Tonnage per pattern (yield increases with its increase) 2. Minimum section thickness (yield increases with its increase) 3. Percentage of rail production (yield increases with its increase) 4. Percentage of pump and valve production (yield decreases with its increase) 5. Number of units per pattern (yield increases with its increase) Factors of Significance on Minimum Yield 6. Percentage use of in-house risering rules (yield increases with its increase) 7. Percentage of oil end-use production (yield decreases with its increase) 8. Percentage of industrial end-use production (yield decreases with its increase) 9. Typical casting "box" volume/average casting weight (yield decreases with its increase) As with average yield, variables dealing with mass production and production end-use appear to be the most important variables effecting minimum casting yield. The tonnage per pattern is the most important factor contributing to minimum casting yield accounting for 50% of the variatio

In-situ measurements of dendrite tip shape selection in a metallic alloy

The size and shape of the primary dendrite tips determine the principal length scale of the microstructure evolving during solidification of alloys. In-situ X-ray measurements of the tip shape in metals have been unsuccessful so far due to insufficient spatial resolution or high image noise. To overcome these limitations, high-resolution synchrotron radiography and advanced image processing techniques are applied to a thin sample of a solidifying Ga-35wt.%In alloy. Quantitative in-situ measurements are performed of the growth of dendrite tips during the fast initial transient and the subsequent steady growth period, with tip velocities ranging over almost two orders of magnitude. The value of the dendrite tip shape selection parameter is found to be $\sigma^* = 0.0768$, which suggests an interface energy anisotropy of $\varepsilon_4 = 0.015$ for the present Ga-In alloy. The non-axisymmetric dendrite tip shape amplitude coefficient is measured to be $A_4 \approx 0.004$, which is in excellent agreement with the universal value previously established for dendrites.Comment: 9 pages, 6 figures, submitted to "Physical Reviews Materials

SIMULATION OF DEFORMATION AND HOT TEAR FORMATION USING A VISCO-PLASTIC MODEL WITH DAMAGE

Abstract A three-phase model is presented that predicts solid deformation and damage as well as melt pressure, feeding flow and shrinkage porosity during metal casting. A visco-plastic constitutive theory with damage is used to model the solid deformation. Damage created by mechanically induced voiding is used as a hot tear indicator. The absence of liquid feeding determines when damage starts to form. The model has been implemented in general-purpose simulation codes. Novel steel casting experiments have been designed and performed which measure the deformation and force from solidification to shakeout. The measured and predicted deformations show generally good agreement with the simulation results. Furthermore, the damage predictions show good correspondence with hot tear indications on a radiograph of the test casting

Growth of equiaxed dendritic crystals settling in an undercooled melt, Part 1: Tip kinetics

Abstract Experiments are conducted to measure the dendrite tip growth velocities of equiaxed crystals of the transparent model alloy succinonitrile-acetone that are settling in an undercooled melt. The tip velocities are measured as a function of the crystal settling speed and the Eulerian angle between the dendrite arms and the flow direction relative to the crystal. The ratio of the settling speed (or flow velocity) to the tip growth velocity ranges from 62 to 572. The ratio of the measured tip velocity to that predicted from a standard diffusion theory for free dendritic growth ranges from almost zero for dendrite tips growing in the wake of the crystal, about unity for dendrite tips with an orientation close to normal to the flow direction, and up to two for dendrite tips growing into the flow. Despite the relatively strong flow relative to the crystal, the average tip growth velocity of the six primary dendrite arms of an equiaxed crystal is found to be in excellent agreement with the standard diffusion theory result. The individual tip velocities are correlated using a boundary layer model of free dendritic growth in the presence of melt flow that is modified to account for the flow angle dependence. Using the same dendrite tip selection parameter, s à , as established previously under purely diffusive conditions (0.02), good agreement is achieved between the measured and predicted tip velocities. The model is also found to predict well the variations in the tip velocity that occur during settling due to crystal rotation and settling speed changes.