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

•An evaluative mean value is defined for complex fatigue loadings of different materials.•It allows for introducing mean stress effect in kinetic damage evolution laws.•Transient fatigue of woven interlock composites is modeled in two steps.•(i) By a original modeling of the asymptotic Haigh diagram.•(ii) By the description of mean stress effect from kinetic damage evolution laws.

An evolutive mean value z̆ is defined for complex loadings. It is shown to be independent from the loading shape and it tends toward the classical mean value zmean=z‾=12zmin+zMax 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 description 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.