This study presents a method to achieve a concise description of multidimensional loading histories for fatigue analysis using the stochastic process theory. For purposes of this study, the load history is considered to have stationary random and non-stationary mean and variance content. The stationary variations are represented by a vector Autoregressive Moving Average (ARMA) model while Fourier series are used to model the non-stationary variations.
Justification for this method is provided by comparing the dynamic characteristics of the original loading and reconstruction through their power spectral densities. Further justification is obtained by comparing histograms of principal strain and the corresponding orientation for original loading and reconstruction. Final justification is provided using the resulting fatigue lives of original and simulated loading. To this end, a multi-axial fatigue damage model, valid for approximately proportional loading, is employed and two fatigue failure modes are considered:failure due to normal strain and failure due to shear strain. The shortest predicted life is reported.
A concise description of complex loadings is achieved due to the relatively small number of Fourier coefficients needed and the use of ARMA models. The overall frequency content, correlations, and sequential information of the load history are statistically preserved.