Multiaxial Haigh Diagrams from Incremental Two Scale Damage Analysis

In High Cycle Fatigue, plasticity and damage are localized at a microscale, a scale smaller than the Representative Volume Element (RVE) scale of continuum mechanics. An incremental two-scale damage model has been built on this basis by Lemaitre et al, and has been mainly applied to alternated loading with no plasticity at the RVE scale. A modified Eshelby-Kroner scale transition law is derived here, taking into account RVE mesoscale plasticity and also microscale plasticity and damage. The ability of the corresponding two-scale damage model to deal with multiaxiality in a wide range of load ratios (from -1 to 0.9) is then focused on. The crack initiation conditions for axisymmetric notched specimens loaded at different mean stresses are studied on the basis of several fatigue tests on TA6V specimens at a low temperature. Both the notch first loading pre-plastification and the biaxial stress state are naturally taken into account by the incremental analysis. Two multiaxial Haigh diagrams are finally drawn for TA6V at a low temperature. Their main features, such as a horizontal asymptote, are highlighted. A piecewise linear extension for a stronger mean stress effect is finally given within the two-scale damage framework considered.