On the calculation of moments of dislocation pile-ups from the stress intensity factor

Abstract

Abstract It is shown that the stress intensity factors associated with a one-dimensional crack subjected to a non-uniform applied stress can be obtained from the first derivative, with respect to crack length parameters, of the dipole moment of the geometrically equivalent double-ended pile-up of continuous dislocations. An analogous relationship is derived between the stress intensity factor associated with a penny-shaped crack subjected to a radial symmetric non-uniform applied stress and the derivative of the quadrupole moment of the geometrically equivalent circular dislocation pile-up. Based on these relationships an approximation scheme is proposed which permits the construction of the corresponding dislocation pile-ups, in terms of superdislocations, simply from the stress intensity factor. The relationships so obtained for the dipole moment and the quadrupole moment provide an opportunity to calculate for cracks subjected to non-uniform loading the crack opening area and crack opening volume, resp...