An improved multiaxial rainflow algorithm for non-proportional stress or strain histories – Part I: Enclosing surface methods

The objective of this work is to develop a simple multiaxial version of a rainflow algorithm that allows the proper calculation of multiaxial fatigue damage induced by non-proportional load histories. One of the issues in such algorithm involves a complementary problem, how to properly quantify equivalent stress or strain ranges and mean components associated with each rainflow-counted cycle. A traditional way to estimate such ranges is to use enclosing surface methods, which search for convex enclosures like balls or prisms, of the entire history path in stress or strain diagrams. To treat these two intrinsically related problems, this work is divided into two parts. Part I deals with how to compute equivalent stress or strain ranges in multiaxial NP histories using enclosing surface methods. The available methods are first reviewed, and new enclosing surface models are proposed, based on Deperrois’ idea of longest chords. Then, these methods are compared using results from more than 3 × 106 Monte Carlo simulations of random and especially chosen path topologies in two to five-dimensional stress or strain diagrams. Moreover, a new simpler but powerful approach to evaluate equivalent stress and strain ranges in NP histories is presented, called the Moment Of Inertia (MOI) method. The MOI method is not based on enclosing surfaces, it assumes instead that the path contour in the stress or strain diagram is analogous to 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 for 15 different multiaxial histories prove the effectiveness of the MOI method to predict the associated fatigue lives, when compared to the existing enclosing surface methods. Part II of this paper presents a multiaxial rainflow counting algorithm that allows the MOI and enclosing surface methods to be generalized to non-periodic NP histories and to periodic NP histories formed by complex blocks with multiple cycles each.