Shape change of surface crack during fatigue growth

Approximate analytical solutions of the differential equation controlling the shape change of a semielliptical surface crack during tension and bending fatigue growth are presented. These solutions reduce the prediction of the shape change of a surface crack to the calculation of elementary functions and reduce the prediction of fatigue life to the calculation of a definite integral. The solutions are compared with more than 680 pairs of experimental data for 22 different metallic materials published in the literature and the agreements are excellent. A multipoint analysis procedure combining the Paris relation and the requirement that the surface crack remain semielliptical during fatigue growth has been developed.