Curve fitting impact test data: a statistical procedure

TLDR: In this paper, a curve fitting impact method is presented and discussed, where a mathematical model (usually a polynomial) is fitted to the test data so that the sum of squares of the deviations of the data points from the fitted curve is minimum.

Abstract: Quality assurance programs such as those related to nuclear pressure vessel materials usually require impact property measurements taken over a range of temperatures. These property measurements frequently include impact energy, fracture toughness, lateral expansion, or other quantities exhibiting the typical ductile-brittle transition. It is often difficult, however, to develop a suitable relationship between impact test data and temperature. Impact properties tend to vary in a sigmoidal fashion, starting at a fairly constant low value, increasing sharply over a short temperature range, and leveling off at a fairly constant higher value. The best approach to this task is through regression analysis. In this technique a mathematical model (usually a polynomial) is fitted to the test data so that the sum of squares of the deviations of the data points from the fitted curve is minimum. There are standard and relatively simple methods for fitting such equations which can handle transformations of the data before analysis. A curve fitting impact method is presented and discussed.