THE DOUBLE SLIP PLANE MODEL FOR THE STUDY OF SHORT CRACKS

Apart from crack closure which has been employed extensively to explain apparent differences in the behaviour of short and long cracks, dislocation crack tip shielding is investigated as an additional contributing factor. The double slip plane (DSP) crack model is employed and a numerical approach is followed for the calculation of the dislocation density distributions on the crack and the slip planes and the plastic zone size. By accounting for dislocation crack tip shielding, the critical stress sigma(cr) and applied stress intensity factor K-A,K-cr which define the onset of crack advance, exhibit a crack length dependence which is a manifestation of the anomalous short crack behaviour. It is shown, that below a critical crack length K-A,K-cr is not constant, but rather decreases with decreasing crack length. Furthermore, a critical stress smaller than that predicted by linear elastic fracture mechanics is found. A method to calculate crack propagation rates based on dislocation density distributions is also presented. It is shown that under cyclic loading, a short crack propagates below the threshold stress intensity of a long crack and exhibits faster crack growth rates for the same nominal crack driving force. For the mild crack growth regime, Paris power-law exponents of 2 and 2.7 are predicted, depending on the value of an adjustable parameter in the configuration of the DSP model.