This paper provides a direct method to determine the critical plane orientation for biaxial random vibration. The critical plane is obtained by finding the direction that maximizes the normal stress variance. It is found that the shear stress is uncorrelated with the normal stress in this orientation. Furthermore, the direction of maximal normal stress is shown to coincide with the principal direction in the case of proportional stress components. Spectral fatigue damage methods proposed in recent literature involve a Monte Carlo enumeration step to find the critical plane orientation. By using the proposed technique, computationally expensive enumeration methods are avoided and greater accuracy in the fatigue damage estimate may result.
McNeill, S., “A Method for Determining the Fatigue Critical Plane for Biaxial Random Vibration in the Frequency Domain,” Fatigue and Fracture of Engineering Materials and Structures Journal 33(6), 390-394, 2010.