On the applicability of the paris law to the growth of fatigue surface cracks

Linear Elastic Fracture Mechanics (LEFMhas been traditionally used to model growth of fatigue cracks under cyclic loads. Paris Law [1] created a strong link between fatigue and LEFM and made the numerical prediction of crack propagation possible. The scope of applicability of the Paris Law for one-dimensional edge and through cracks (the Griffith crack has been studied extensively using fatigue crack growth experiments. However, in the case of the surface cracks in thick plates and tubular sections, unlike thin sections containing one dimensional cracks, crack shape or aspect ratio has a profound effect on crack front stress intensity factor and any resulting Paris Law based life prediction. Nevertheless, the applicability of the Paris Law to the problem of the growth of surface cracks is sometimes taken for granted without taking into account the caveats and limitations that are intrinsic to the surface crack. The transition of the state of stress from a near plane strain mode at the deepest point of the surface crack to a plane stress situation at the surface point is one of the limiting factors that should be considered while applying the Paris Law in its current form to the deepest and surface points. In this paper, the problem of the growth of surface cracks is analysed from a mathematical point of view, and it is shown that not only does the Paris Law coefficient depend on the geometry of the surface crack-As believed previously, but also that the surface crack Paris Law coefficient depends on loading. Unlike the shape dependence of the surface crack Paris Law coefficient, which can be found from purely geometrical considerations and assumptions such as semi-elliptical crack growth hypothesis, the load-dependent nature of the Paris Law coefficient makes the application of the law in its simple form inaccurate.