A closed expression for the Stress Intensity Factor of concave fatigue cracks in rotating shafts

Study of the propagation of concave semi-elliptical shaped breathing cracks in rotating shafts

“…We have developed a propagation algorithm to obtain the crack front evolution, considering that the points of the front advance according to the Paris Erdogan Law. The SIF has been computed using the four parametric expression for rotating concave cracks proposed by the authors in a previous work [34]. We aim to establish quantitatively the relationship among the shaft working cycles, its stress state and the crack characteristics (depth and shape), over time, during the crack propagation.…”

“…The shaft contains a semi-elliptical concave crack in its central section and it is submitted to rotary bending efforts. The diameter of the shaft is D = 20 mm and the total length is L = 900 mm [33,34]. We have applied two loads F = 100 N at a distande d = 225 mm from both ends of the shaft, to simulate pure bending.…”

“…The subindex γ refers to the position in the front. The nonsimensional SIF used by the algorithm has been obtained using the four parameter expression for concave cracks proposed by the authors in a previous work [34]. As mentioned before, the concave crack could become convex with the propagation, in this case, the nondimensional SIF used in the computations has been determined using the four parameter expression for convex cracks obtained in [17].…”

“…Rubio et al [17] determined a closed SIF expression for convex cracks in terms of the crack geometry characteristics (shape and depth), the relative position on the front and the rotation angle. In other work, Rubio et al [34] obtained a SIF expression for concave cracks in terms of the same variables. They also considered the gradual opening and closing of the crack.…”

“…For that, later, the studies were extended to semi-elliptical convex shaped cracks [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Nevertheless, although real cracks can also present semi-elliptical concave shape [19,20,21,22,23,24], there are fewer SIF studies in the literature related to these cracks [25,26,27,28,29,30,31,32,33,34]. [35,36].…”