applied fracture mechanics

Fracture Mechanics Based Models of Structural and Contact FatigueFracture Mechanics Based Models of Structural and Contact Fatigue 5149intensity factor k 1 can be approximated by the normal stress intensity factor for the case of asingle crack of radius l in an infinite space subjected to the uniform tensile stress σ, i.e. byk 1 = 2σ √ l/π.2.3. Fatigue crack propagationFatigue cracks propagate at every point of the material stressed volume V at which max (k 1) >Tk th , where the maximum is taken over the duration of the loading cycle T and k th is thematerial stress intensity threshold. There are three distinct stages of crack development:(a) growth of small cracks, (b) propagation of well–developed cracks, and (c) explosive and,usually, unstable growth of large cracks. The stage of small crack growth is the slowest oneand it represents the main part of the entire crack propagation period. This situation usuallycauses confusion about the duration of the stages of crack initiation and propagation of smallcracks. The next stage, propagation of well–developed cracks, usually takes significantly lesstime than the stage of small crack growth. And, finally, the explosive crack growth takesalmost no time.A relatively large number of fatigue crack propagation equations are collected and analyzedin [6]. Any one of these equations can be used in the model to describe propagation of fatiguecracks. However, the simplest of them which allows to take into account the residual stressand, at the same time, to avoid the usage of such an unstable characteristic as the stressintensity threshold k th is Paris’s equationdldN = g 0( max k 1) n , l | N=0 = l 0 , (4)−∞