ABSTRACT
This chapter shows the influence of the primary loading cycles on the structure fatigue behaviour. It describes different models of stress-softening. The chapter also shows the influence of the loading history on an axisymmetrical notched sample dedicated to fatigue tests. It focuses on the importance of the Mullins effect for fatigue studies. Classically, fatigue tests are realized by a sequence of numerous identical cycles. Numerous models have been proposed since the stress softening phenomenon was pointed out. Models were based on material considerations. Marckmann et al. have proposed a new constitutive equation to describe the evolution of chain length of the material. By a study of the magnitude of the stress-softening according to the strain, Chagnon et al. have proposed a damage evolution law. As the local stress depends on the stress softening phenomenon, it is important to know what are the local stress and strain states after different loading histories.
