Probabilistic theory for mixed mode fatigue crack growth in brittle plates with random cracks

Abstract

A probabilistic fracture mechanics theory is proposed for fatigue life prediction in which a mixed-mode fatigue crack growth model is combined with extreme value probabilistic methods. The Sih–Barthelemy fatigue crack growth criterion based on strain energy intensity factor under uniaxial loading has been slightly modified and extended to multiaxial loading including biaxial loading and torsion. A probability density function is computed for the number of cycles to failure, and scaling relations are also computed. Crack number, length, and orientation at the onset of fatigue are treated as random varixsables whose probability distributions are known. Numerical results are presented to demonstrate dependence on plate size, on the variance of the crack length distribution, on the multiaxial loading factors, and on the parameters of the fatigue model.