Fatigue crack propagation:

If it is assumed that no plastic deformation occurs around crack tip and law of fatigue crack propagation for place of above Example is da/dN =  10^{- 8} (Δ K_{I eff} )2.0 mm/cycle , find after how many cycles the plate will fracture.

Solution

Δ K I = ΔK _{I eff}     because there is no plastic deformation in crack tip neighbourhood.

a_c = 146.14 mm, a_i = 35 mm from above Example .

or, Nf   =2´10⁴ ln ( ac/ ai) =  2´10⁴ ln (146.14/35)

or, N f  = 2´10⁴ ln (4.175) = 28584 cycles