Application of Maximum Entropy in Estimating the Reliability Functions for Creep Failure Modes of Engineering Materials at High Temperatures 670648

The principle of maximum entropy is used to obtain the prior probability distribution functions for critical creep-strain and creep-rupture characteristics of engineering materials, operating at known high temperatures and uniaxial stresses. From the prior distribution function obtained, reliability function which is simply the probability of successful operation of the material, can be derived for specified critical creep-strain and creep-rupture modes of failure. An attempt is made to derive the reliability functions from prior considerations of the mechanics of failure, and the mechanical and physical characteristics of engineering materials. This work assumes that mechanical creep design reliability functions for creep-rupture and critical creep-strain modes of structural elements can have values such that the failure of the elements can occur either by any of the modes of failure or by the assumed combined modes of failure. It is also pointed out that the prior probability distribution functions from which the reliability functions are derived, can be improved by the use of Bayes' theorem in order to obtain a posterior probability distribution function, whenever more creep data are made available. The posterior probability distribution functions can then be used to derive more accurate reliability functions. Finally, these considerations and procedures which yield the reliability design criteria, are illustrated by an application to the stress analysis of a structural member, with given mechanical, physical, environmental and creep characteristics.