Fitting Curves to Toughness Data

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Abstract
Curve-fitting (regression) procedures for toughness data have been examined. Approaches using the normal probability function and the tanh function to model the transition between brittle and ductile behavior have been briefly reviewed. The objectives of fitting such curves have been summarized in the context of the study of nuclear pressure vessel steels as (1) convenient summarization of test data to permit comparison of materials and testing methods; (2) development of statistical statements concerning the data, and (3) the study of changes in material behavior, particularly radiation damage. These objectives impose differing demands on the curves, which result in several versions of each approach. The computational and mathematical procedures that can be used with the tanh function have been described in detail, with examples of the different curves that can be fitted to the data. Six different algorithms to be used for situations involving different constraints have been summarized. Weighted regression has been reviewed briefly, with emphasis on the use of models to describe the changes in variance between the different modes of material behavior.