Prediction of non-proportionality factors of multiaxial histories using the Moment Of Inertia method

• Moment Of Inertia method predicts the non-proportionality of multiaxial histories.
• Accounts for the contribution of every single segment of the plastic strain path.
• Estimated factor is independent of the stress or strain coordinate system.
• Eigenvectors represent the principal axes of the plastic strain path.
• Associated eigenvalues account for the non-proportionality of the history.

This work studies further an approach originally proposed to evaluate equivalent stress and strain ranges in non-proportional (NP) load histories, called the Moment Of Inertia (MOI) method. The MOI method assumes that the path contour in the deviatoric stress or strain diagram is a homogeneous wire with unit mass. The center of mass of such wire gives then the mean component of the path, while the moments of inertia of the wire can be used to obtain the equivalent stress or strain ranges. The MOI method is an alternative to convex enclosure methods, such as Dang Van’s Minimum Ball or the Maximum Prismatic Hull methods, without the need for computationally-intensive search algorithms or adjustable parameters. The MOI method is extended here to calculate as well the non-proportionality factor Fnp of generic multiaxial load histories, formulated in an alternative sub-space of the deviatoric plastic strains. Experimental results for 14 different multiaxial histories prove the effectiveness of the MOI method to predict the observed non-proportionality factors. Hence, it can be a most useful tool for the computation of multiaxial fatigue damage in practical applications.