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A more efficient procedure is proposed to speed up the Carpinteri-Spagnoli (CS) algorithm in numerical computations. The goal is accomplished by deriving the exact solution for the spectral moments and expected maximum peak of normal/shear stress in any rotated plane orientation. The algorithm then avoid the use of “for/end” loops to identify the five rotations that locate the critical plane in CS method. The procedure is especially advantageous if applied to three-dimensional finite element analysis, in which the stress spectra in thousands of nodes need to be processed iteratively. The procedure is based on theoretical results that have, however, a more general validity, being applicable to any multiaxial criterion that makes use of angular rotations to identify the critical plane.

An efficient procedure to speed up critical plane search in multiaxial fatigue: Application to the Carpinteri-Spagnoli spectral criterion