Generalization of energy-based multiaxial fatigue criteria to random loading

Results from a review of energy-based criteria of multiaxial fatigue indicate that they may be divided into three groups, depending on the kind of strain energy density per cycle which is assumed as a damage parameter. They are: criteria based on elastic strain energy for high-cycle fatigue, criteria based on plastic strain energy for low-cycle fatigue, and criteria based on the sum of plastic and elastic strain energies for both low-and high-cycle fatigue. Lately, special attention has been paid to criteria taking into account strain energy density on the critical plane. However, in the energy approach to multiaxial fatigue there is an important unsolved problem, namely, the evaluation of energy, especially plastic strain energy density, from the closed stress-strain hysteresis loops under random loading. In this paper, energy parameters defined for random loading are introduced. Under uniaxial loading we distinguish between the strain energy density for tension (positive) and the strain energy density for compression (negative). As a consequence, if there is no mean component in the random loading, we obtain a random history of strain (elastic and plastic) energy density with a mean of zero. Next, some known energy criteria of multiaxial cyclic fatigue were generalized for the random loading. The new criterion has been successfully used for fatigue life calculation under uniaxial and biaxial random tension-compression of plane specimens made of 10HNAP steel. For this material the equivalent strain energy density on the critical plane, Weq (t), seems to be an efficient parameter under nonproportional random loading in the range of a great number of cycles. The equivalent strain energy density is derived from the new criterion.