Generalized model of fatigue crack propagation under multiaxial loading conditions

The problem of determination of the service life of gearing is directly related to the geometry of gears, loading, materials and appropriate models for prediction of the crack propagation. If a defect is found during the periodic inspection, the following question arises: how long can such a gear/gearing still safely operate. To be able to answer this question we have developed a stochastic model for the determination of service life of gears. Since the size of defects which can be detected is 0.5 - 1 mm we applied only the theory of long cracks, taken into account by means of the stochastic model of crack growth. Geometric particularities are taken into account by means of the shape factor, the real loading by means of mathematics modelling of actual gearing and in our model we propose a new parameter, the tooth stress intensity factor Z, by which we describe the fracture mechanics conditions in the tooth root where the defects causing destruction, occur statistically most frequently.