applied fracture mechanics

250Applied Fracture Mechanics aKI x'f( )(15)Q12 42 a2f ( ) sin cos c where a/c is 1, and specifies a particular position the stress level at around the tip of ahemispherical crack. Q is the shape factor of the defect or pit. The maximum value of KIoccurs for = 0°, where ƒ(√a/c, this is, near the surface over the major axis of the ellipse.Figure 18. Relationship between the transformed stress acting around a pit-like crack and theorientation angleThe value of the threshold stress intensity factor for load mode II (ΔKII ) and III (ΔKIII ) werecalculated using the solution proposed for long elliptical surface cracks under mixed loadmode [68]:2 1/2xy' 'aka / cKII0 (16)BKxy ' 'ak1 sin2 2 2Bsin ( a/ c) cos III 0 1/42(17)where k 2 = 1-(a/c) 2 , B =(k 2 -)E(k)+(a/c)2K(k) and E(k) is the second order elliptic integraldefined by:/2 2 2/20 02 2Ek ( ) Q 1 k sin d , Kk ( ) d1 k sin Equations 15, 16 and 17 were used to determine the stress intensity factor for load mode I, IIand III respectively developed at the pit contour defined by the angle φ: (φ = 0, φ = 45 and