Life time estimation under probabilistic fatigue of cracked plates for multiple limits states

The fatigue failure is most critical factor in lifetime estimation of industrial elements. The failure of a device in fatigue is due to a crack growth becoming instable and leading to strength decreasing. Based on Paris equation and S-N curves of WhOler, the probabilistic fatigue crack growth is studied where each parameter can be considered as random variable. A reliability analysis was developed here for plates under fatigue crack; the failure event taken can be expressed by many performance functions called limits states depending on possible failure modes. We study 3 limit states, the first is the reaching of a critical value of crack width a_c,r. the second is the reaching of the capacity value of tenacity of materials Kjc, the third is the reaching of a critical number of cycles of applied stresses N_c,r. Between theses 3 modes, we choose the most critical one toward the reliability value. A model of crack growth with respect to time is chosen to evaluate the time-reliability variation and hence to estimate the life time corresponding to a desired level of reliability.