Multiscale statistical analysis of the tin-lead alloy solidification process

Abstract This paper presents a quasi-two-dimensional solidification benchmark experiment with controlled thermal boundary conditions. The experiment consists in solidifying a rectangular ingot of Sn-3wt.%Pb using two lateral heat exchangers to extract the heat flux from one or both vertical sides of the sample. The aim is to assess the reproducibility of the solidification experiments performed under rigorously identical conditions. The temperature difference ( ΔT ) between the two vertical sides is 40 K and the cooling rate (CR) is 0.03 K/s. This slow-cooling condition favours segregation formation. A lattice of fifty thermocouples placed on the front of the sample between the two vertical sides is used to determine the instantaneous temperature distribution. During solidification, the time evolution of the temperature field is recorded and analyzed. This allows us to estimate the time evolution of the temperatures due to natural convection and assess the velocity field, the solidification macrostructure and the segregation behaviour. Post-mortem segregation patterns are obtained both by X-ray radiography and induction coupled plasma analysis. The recorded data is analyzed statistically. An ensemble average procedure is applied to both instantaneous temperature and post-mortem composition measurements. This makes it possible to determine the mean values of the solidification parameters as well as their standard deviations. Temperature fluctuation standard deviations are deterministic and characterize the solidification dynamics. Among other results, it is shown that mesoscale segregation locations are not fully predictable.