The numerical solutions of stress and strain components on the critical plane of tungsten carbide coating were solved based on the critical plane method in three-dimensional coordinate system, and accordingly three strain energy density parameters (Smith-Watson-Topper, Nita-Ogatta-Kuwabara and Chen parameters) were determined to reveal the fretting fatigue characteristics of tungsten carbide coating. In order to predict the fretting fatigue life based on the strain energy density criterion, the expressions between the strain energy density parameter and the fretting fatigue life was obtained experimentally. After the comparison of the three strain energy parameters, it was found that all three parameters could accurately predict the crack initiation position, but only the Smith-Watson-Topper parameters could accurately predict the crack initiation angle. The effects of cyclic load, normal load and friction coefficient on fretting fatigue damage behaviors were discussed by using the Smith-Watson-Topper criterion. The results show that the fretting fatigue life decreases with the increase of cyclic load; an increase in the normal contact load will cause the Smith-Watson-Topper damage parameters more concentrated at the outer edge of the bridge foot; a decrease in the friction coefficient will increase the Smith-Watson-Topper damage parameters in the middle of the contact surface.

The paper contains a review of energy-based multiaxial fatigue failure criteria for cyclic and random loading. The criteria for cyclic loading have been divided into three groups, depending on the kind of strain energy density per cycle which is assumed as a damage parameter. They are: a) criteria based on elastic strain energy for high-cycle fatigue, b) criteria based on plastic strain energy for low-cycle fatigue. and c) criteria based on the sum of plastic and elastic strain energies for both low- and high-cycle fatigue. The criterion for random loading is based on the new definition of energy parameter which distinguishes plus and minus signs in history or specific work of stress on strain along chosen directions in the critical fracture plane. The criteria which rake into account strain energy density in the critical plane dominate in the energy description or multiaxial fatigue. Parameters dependent on loading and factors dependent on a kind or marcrial and inlluencing selection of the critical plane have been given. The author presented the mathematical models or the criteria and next distinguished those including influence of mean stresses and stress gradients as well as proportional and non-proportional loading. It has been emphasised that the generalized criterion of maximum shear and normal strain energy density in the critical plane seems to be the most efficient in practice and it should be developed and verified in a future.