Estimating the parameters of the impact energy variation in the ductile/brittle transition region from complete and sparse data

A numerical method is proposed for estimating the systematic variation of the Charpy impact energy in the ductile/brittle transition region of low-carbon weld steels from sparse data sets. The parameter estimates obtained by the proposed method are practically unbiased, i.e., the means of the parameters produced by multiple runs of the numerical procedure converge to the values of the parameters from which the sparse data sets were generated. An advantage of the numerical method proposed is its simplicity and the precision with which the parameters are estimated, even in the case of very large scatter bands of the absorbed impact energy. The method allows to determine precisely the transition temperature corresponding to a specified impact energy level, which is necessary for quantifying the deterioration of properties due to embrittlement factors. Various aspects associated with fitting the systematic variation of the impact energy from complete data sets and problems concerning Avrami plots are also considered. It is demonstrated that what appears to be the best linear fit on double logarithm Avrami-type plots is not necessarily the best fit for the untransformed data. Weights are needed to improve the fit even if all data points are characterised by equal variances.