The moment of inertia method to calculate equivalent ranges in non-proportional tension–torsion histories

A critical issue in multiaxial damage calculation in non-proportional (NP) histories is to find the equivalent stress or strain ranges and mean components associated with each rainflow-counted cycle of the stress (or strain) path. A traditional way to find such ranges is to use enclosing surface methods, which search for convex enclosures, such as balls or prisms, of the entire history path in stress or strain diagrams. These methods only work for relatively simple load histories, since the enclosing surfaces lose information of the original history. This work presents an approach to evaluate equivalent stress and strain ranges in NP histories, called the moment of inertia (MOI) method. It is an integral approach that assumes the path contour in the stress diagram is a homogeneous wire with a 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. Experimental results obtained from the literature for 13 different multiaxial histories prove the effectiveness of the MOI method to predict fatigue lives.