An improved multiaxial rainflow algorithm for non-proportional stress or strain histories – Part II: The Modified Wang–Brown method

The objective of this work is to develop a simple multiaxial rainflow algorithm that allows the proper calculation of multiaxial damage in NP histories. Enclosing surface methods are usually employed to obtain the equivalent ranges necessary for damage calculation, as discussed in Part I of this 2-part paper. Part I also presented a new approach to evaluate equivalent ranges in NP histories, called the Moment Of Inertia (MOI) method. This second and last part 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. It is shown that Wang–Brown’s (WB) multiaxial rainflow algorithm has a few idiosyncrasies that can lead to non-conservative predictions, incorrectly filtering out significant events within a multiaxial loading cycle. An improved multiaxial rainflow algorithm is proposed, called Modified Wang–Brown (MWB). It has two main improvements over the WB algorithm. First, the criterion to choose the point where the count is started is modified. Examples are shown to prove that the original criterion can overlook the most damaging event from the history, as opposed to the modified version. And second, the algorithm implementation is significantly simplified when formulated in a reduced five-dimensional Euclidean space. Under plane stress conditions, the algorithm is further simplified using a three-dimensional Euclidean space based on the deviatoric stresses or strains. A simple pseudo-code is presented in a flowchart to efficiently implement the multiaxial count, allowing a fast and efficient calculation of fatigue damage even for very long non-periodic NP histories.