Abstract: A significant scatter of cyclic stress-strain responses is observed for a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. This implies that a random fatigue strain applied history should be introduced under any of loading modes even a deterministic loading history. To assure safety of design evaluation, a modeling of so-called probability-based cyclic stress-strain curves is suggested. A method for estimating the curves and their confidence bounds is developed by a linear regression technique and a maximum likelihood principle. In the method, a verified appropriate assumed distribution, namely normal distribution, is introduced to describe the material random cyclic stress amplitude data. The curves are approximated by the mean value and standard deviation cyclic stress-strain curves of Ramberg-Osgood law. Then, analysis at an arbitrary given reliability should be conveniently made according to the normal distribution function. Availability of the method has been indicated by an analysis to the test results of the present material.

Key words: Low cycle fatigue, Maximum likelihood method, Modelling Linear regression, Random cyclic stress-strain response