On the heuristic extension of Haigh’s diagram for the fatigue of elastomers to arbitrary loadings

A new approach is proposed for the prediction of multiaxial fatigue of elastomers. This approach is inspired in principle, if not in details, from Dang Van’s work on a criterion for non-initiation of fatigue cracks in metals subjected to arbitrary periodic loadings. It consists of heuristically extending Haigh’s diagram, which provides the experimental fatigue lifetime for 1D cyclic loadings as a function of the mean stress and the stress amplitude, to completely arbitrary 3D loadings. This is achieved by defining, for every arbitrary periodic loading, some “equivalent” 1D loading. To do so, one considers the smallest sphere containing the closed path of some suitably chosen stress variable in the 6D stress space, and approximately characterizes this path through the norm of the center and the radius of this so-called Dang Van sphere. These parameters, which are equivalent in the 1D case to the mean stress and the stress amplitude, are then heuristically used as entries of Haigh’s diagram to predict the fatigue lifetime. Multiaxial fatigue experiments performed by Mars and Saintier are used to critically assess this proposal, and it is found to improve upon previous ones.