Statistical Theory of Fatigue Failure under a Complex State of Stress - 1.

The probability of fracture is accepted as the criterion of fatigue resistance. Based on this criterion, the condition of statistical equivalence of different states of stress is formulated. A formula is presented for calculating the probability of failure under the conditions of a complex state of stress according to particular probabilities of its failure under the appropriate linear states of stress. An analysis of the limiting conditions of an isotropic body under different states of stress is given and the type of the limiting surface of the probability of failure under three-dimensional state of stress is established. Based on the introduced quantitative characteristics of danger of one kind of state of stress in comparison with others, the danger of fatigue failure depending on the type of the state of stress is analyzed.