APPLIED MECHANICS GROUP A NEW TECHNIQUE FOR ESTIMATING SYSTEM UNCERTAINTY IN DESIGN

Components operating in modern power plant, such as nuclear reactors, gas and steam turbines are subject to complex loading cycles at elevated temperatures so that combined creep/fatigue damage often occurs. Estimates of the life of these components are difficult because of the indefinite nature of the assumed constitutive model and also of the relevant material properties. In an attempt to handle this problem, a new predictive technique is presented which is based on the concept of 'fuzzy sets ' (1). The basic ideas behind fuzzy sets are simply explained and then applied to test results previously obtained (2) on a 1 Cr Mo V steel. A simple linear cumulative damage rule is used for illustration. Using the method, estimates of system uncertainty can be made which can then be combined with random uncertainty of the parameters to obtain a probability measure of the number of loading cycles to failure of a component. Cumulative distribution functions for the system uncertainty in the test results are produced and their usefulness to the designer discussed. NOTATION ordinary sets fuzzy sets constant constants number of cycles to failure number of cycles to failure under dwell period t number of cycles to failure under dwell period td probability of [] probability that no. of cycles to failure< N probability of simple event x E X relation time time-fraction of dwell period time to rupture sets elements of X, Y variable strain peak tensile stress relaxed stress after 30 min stress relaxed after 30 min stress relaxed after t membership level of x in A union of A and B intersection of A and B A is a subset of X x contained in X