On the inverse power laws for accelerated random fatigue testing

Abstract

This paper addresses the usage of inverse power laws in accelerated fatigue testing under wide-band Gaussian random loading. The aim is not at predicting an absolute value of fatigue life but assessing the fatigue damage relative accumulation. The widely accepted inverse power scaling laws in fatigue damage assessment is discussed, reviewing the engineering standards and pointing out their inherent limitations. A physically consistent general scaling law is obtained by rigorous mathematical analysis in the framework of random vibration theory and the rules of safe-life fatigue analysis. Simplifications of the general scaling rule are presented, highlighting conditions under which the current standard practice could provide a correct an acceptable estimation of the relative fatigue damage accumulation.Key words: fatigue, inverse power law, random loading, cycle counting, accelerated testing Nomenclature T r -fatigue life in the operative environment;T s -fatigue life in the testing condition; g -acceleration root mean square value (RMS); g r -acceleration RMS in the operative environment;

A bandwidth correction to the Allegri-Zhang solution for accelerated random vibration testing

“…Although b, C virtually represent the parameters of the constant amplitude S-N curve, their value may change under a random stress, as also pointed out in [3] (this issue will be further discussed in Section 6).…”

“…Inverse power scaling laws are commonly used to correlate the time to failure in the accelerated laboratory test to the life estimated under real excitations. The following simple power law model is commonly used [1][2][3]: …”

“…In practical applications, however, α is often treated as an empirical factor (ranging from 5 to 8) that summarises all the uncertainties and approximations in Eq. (1) and its value is often adjusted based on previous experience [3]. Due to its simplicity, the scaling law (1) has been largely used in industry, especially at the design stage, and it is currently included in MIL Standard 810 [1].…”

“…It also ignores the structure dynamic behaviour, which may directly affect the output stress. In 2008, Allegri and Zhang published a research study [3] in which they contextualized the scaling law (1) in a more general theory based on finite element analysis and multiaxial spectral methods defined in the frequencydomain through a Power Spectral Density (PSD) matrix − their theory adopted the "equivalent von Mises stress" (EVMS) criterion. The Allegri-Zhang's study derived an exact solution of a general scaling law model, of which the empirical relationship (1) is only a simplified case.…”

Small-Sample Accelerated Life Test Method based on the Inverse Power Law Model

“…Some available life-stress models, such as numerical simulation method [1], Arrhenius, Eyring, and inverse power law model, are most commonly used for the accelerated life test: Nelson [2] and Bai [3] studied the accelerated life test with the inverse power law model about 30 years ago; Shin [4] developed the accelerated life test method using the inverse power law model for small DC motors; Rajkumar [5] used the life-stress relationship based on the inverse power law-Weibull model to predict reliability under the normal usage level; Nogueira [6] proposed an accelerated life model that involves temperature, humidity and current parameters to evaluate the reliability of LED; Zhang [7] studied the constant-step-stress accelerated life test under Weibull distribution case; Lee [8] discussed the parameter estimation method of Step-Stress Accelerated Life Testing model by utilizing Generalized Linear Model techniques; while Tang [9] focused on the general k-step step-stress accelerated life tests for two-parameter Weibull distributions; Besides, Allegri [10] provided an acceptable estimation of the relative fatigue damage accumulation based on the inverse power law model.…”