Estimating Charpy transition temperature shift using Weibull analysis

Abstract

A primary consideration for operation of commercial nuclear light-water reactors is the fracture toughness of the reactor pressure vessel. One of the tests conducted for toughness determinations of the pressure vessel materials is the Charpy V-notch impact test. The tests are conducted over a range of test temperatures and the total impact energy required to break each specimen is determined and plotted vs test temperature. The impact energy values for a fixed temperature and radiation exposure are usually assumed to be Weibull distributed. This assumption was validated by a statistical selection process. An important parameter in the evaluation of reactor vessel materials is termed the ductile-to-brittle transition temperature shift (ΔT 4) and is the temperature shift between the unirradiated and irradiated Charpy V-notch curves at the 41-J (30-ft-lb) energy level. The purpose of this paper is to introduce a methodology for estimating the ΔT 41 value and to place limits on the error of estimation. This has been accomplished by assuming that the scale parameter in the Weibull distribution is a function of temperature (and neutron fluence for the irradiated Charpy V-notch data). An inverse regression technique is then used to solve for the temperature corresponding to an impact energy of 41 J. To obtain error bounds on this estimate, the parameters of the equation describing the scale parameter are resampled assuming a normal distribution and the inverse regression is repeated several times. This leads to several estimates of the temperature, and the variance of these values can be used to give bounds on the error of estimation.