Stress intensity factors for half-elliptical surface cracks subjected to complex crack face loadings

The disagreement in the literature on the stress intensity factors for surface cracks is considerable. It is also noted that not enough attention has been given to the behaviour of surface cracks in stress fields more complex than uniform tension and bending, although such solutions are needed for crack problems in, e.g. thermal and residual stress fields.In the present paper, stress intensity factors (Mode I) are presented for nine crack geometries in combination with six load cases. The finite element method using 20-node collapsed quarter point singular elements was employed. By a proper modelling of the problem, the number of degrees of freedom was significantly reduced and high accuracy achieved. For the cases of uniform stress and bending, the results agree very well with those of Refs. [8,10], (1–3% for most cases) except one, ($\text{a}\text{c = 0.2}$, $\text{a}\text{t = 0.75}$) for which the present results are 10–17% lower than those in [8]. (For this case other published results deviate up to ± 50%). The K-factors for the more complex loadings will be useful in analysing surface cracks in complex stress fields.