The present work aims to predict the fatigue life of 18G2A steel, in the time and frequency domain, using the method known as projection-by-projection-PbP, applied mainly in multiaxial loadings. The method used is based on the use of stresses invariants and from projections in the direction of maximum variance, independent uniaxial loadings are obtained, being possible to estimate the damage through the rainflow technique or through the analysis of the power spectrum. In order to evaluate the PbP method, predictions were made on 18G2A steel considering the experimental tests available in the literature for various tension-torsion stress states and with different correlation coefficients. For the estimates performed, 94 and 90 of the specimens were within the scatter band of three, in the frequency and time domain, respectively, and the predictions in the temporal model were more variable, in the spectral model the estimates were more stable not showing significant variations. After studying the behavior of fatigue life estimates by the PbP method, the computational costs to execute the predictions in each domain were analyzed considering a test for each correlation level and different sampling times. The processing time of the PbP method in the frequency domain does not depend on the degree of correlation or on the sampling time of the signals, remaining the same in all situations analyzed. In the time domain, the computational cost increased in the same proportion as the sample time and the case with correlation equal to 1 presented a longer processing time than the other cases.
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