A general regression model for lifetime evaluation and prediction

A particular form of a probabilistic model for materials under fatigue which embodies Weibull features and the size effect in a weakest-link framework is derived. The parametric and functional form of the model arises from a certain set of assumptions, as the weakest-link principle, stability, limit behavior, limited range and compatibility, which can be justified as being consistent with experimental features of fatigue (mainly of highly drawn steel wires) and the mathematics of extreme value theory. These assumptions, which are discussed, can be used to rule out other possible forms as being fundamentally inconsistent. The authors also discuss estimation procedures for the parameters based on two steps: a non-linear regression step, in which the threshold lifetime and stress range values are determined, and a second step in which the Weibull parameters are estimated by pooling data from different stress levels and using a probability-weighted moments approach or the Castillo-Hadi estimators. Next, the damage accumulation problem is dealt with and two different proposals for the damage index are given. The model, originally developed to handle a fixed load parameter (such as the stress range in cyclic fatigue), is extended to handle a block load sequence involving many load levels, as well as random load programs. Some formulas for calculating the accumulated damage index for constant, block and random loading are given. Finally, the model and methods are applied to a particular fatigue program on concrete to illustrate all concepts and the practical use of formulas.