A Metric for the Quantification of Macrosegregation During Alloy Solidification

A metric for quantifying the degree of solidification macrosegregation is proposed that statistically fits compositional data from experiments and simulations to a three-parameter Weibull distribution. The method for fitting such a distribution is described and examples are presented. The new metrics are compared to existing macrosegregation measures and the Weibull distribution is shown to be the best fit to data. The fitted three-parameter Weibull distribution is generally found to have better agreement with the composition data than a Gaussian distribution, upon which the macrosegregation number is based, because the Weibull better accounts for asymmetry in the dataset. Trends in macrosegregation results are identified using the new metrics, specifically the normalized Weibull deviation, and compared to the trends identified by the macrosegregation number. A grid dependence study is performed using both metrics as tests for convergence. The utility of the Weibull distribution is demonstrated by comparing composition data with different degrees of asymmetry due to different solidification cooling rates. The difference between the values of the two metrics is a measure of the asymmetry in the compositional distribution.