CYCLIC PLASTICITY OF A CRACKED STRUCTURE SUBJECTED TO MIXED MODE LOADING

Abstract. Cyclic plasticity in the crack tip region is at the origin of various history effects in fatigue. For instance, fatigue crack growth in mode I is delayed after the application of an overload because of the existence of compressive residual stresses in the overload’s plastic zone. Moreover, if the overload’s ratio is large enough, the crack may grow under mixed mode condition until it has gone round the overload’s plastic zone. Thus, crack tip plasticity modifies both the kinetics and the crack’s plane. Therefore modeling the growth of a fatigue crack under complex loading conditions requires considering the effects of crack tip plasticity. Finite element analyses are useful for analyzing crack tip plasticity under various loading conditions. However, the simulation of mixed mode fatigue crack growth by elastic-plastic finite element computations leads to huge computation costs, in particular if the crack doesn’t remain planer. Therefore, in this paper, the finite element method is employed only to build a global constitutive model for crack tip plasticity under mixed mode loading conditions. Then this model can be employed, independently of any FE computation, in a mixed mode fatigue crack growth criterion including memory effects inherited from crack tip plasticity. This model is developed within the framework of the thermodynamics of dissipative processes and includes internal variables that allow modeling the effect of internal stresses and to account for memory effects. The model was developed initially for pure mode I conditions. It was identified and validated for a 0.48%C carbon steel. It was shown that the model allows modeling fatigue crack growth under various variable amplitude loading conditions [1]. The present paper aims at showing that a similar approach can be applied for mixed mode loading conditions so as to model, finally, mixed mode fatigue crack growth