Refinement of fatigue curve parameters using fuzzy set theory and tomography images processing of censored composite samples

Abstract

The fatigue curve is important in engineering practice. Since the task of constructing a fatigue curve is characterized, among other things, by the presence of qualitative (not numerical), inaccurate and incomplete information, the question arises of the appropriateness of applying the theory of fuzzy sets. To clarify information on censored, namely, removed from testing upon reaching the test base specimens, the use of computed tomography to study the degree of their damage is proposed. A fuzzy regression model has been developed to consider linguistic variable that describes the status of a sample (broken or censored). With fuzzy dependent variables of the of regression model, the coefficients of the equation also turn out to be fuzzy. For the fuzzy dependent variable of the time before failures of censored samples, the degree of damage is additionally evaluated based on the rating of experts by the analysis of tomography images. The model made it possible to estimate the interval of expected life for a given stress amplitude using an uncertainty accounting method that differs from the classical statistical description. An example of constructing a fuzzy fatigue curve for polymer composite materials is considered.