On the introduction of a mean stress in kinetic damage evolution laws for fatigue

An evolutive mean value of z is defined for complex loadings. It is shown to be independent from the loading shape and it tends toward the classical mean value zmean for a periodic loading. The proposed definition applies to quantities encountered in the fatigue modeling of different materials: mean stress or mean hydrostatic stress for metals, mean damage driving force or mean equivalent strain for quasi-brittle materials or for composites. It gives the possibility to introduce the adequate mean stress effect in kinetic (rate) damage evolution laws. This point is illustrated for woven interlock composites in two steps, (i) by proposing an original modeling of the asymptotic Haigh diagram and (ii) by the descrip- tion of full mean stress effect from kinetic damage evolution laws. The concept of evolutive mean stress gives the possibility to model fatigue under complex loading with no need to define a cycle. It applies to random fatigue as shown in different examples.