ON THE CALCULATION OF MOMENTS OF DISLOCATION PILE-UPS FROM THE STRESSINTENSITY FACTOR

It is shown that the stress intensity factors associated with a one-di mensional crack subjected to a non-uniform applied stress can be obtai ned from the first derivative, with respect to crack length parameters , of the dipole moment of the geometrically equivalent double-ended pi le-up of continuous dislocations. An analogous relationship is derived between the stress intensity factor associated with a penny-shaped cr ack subjected to a radial symmetric non-uniform applied stress and the derivative of the quadrupole moment of the geometrically equivalent c ircular dislocation pile-up. Based on these relationships an approxima tion scheme is proposed which permits the construction of the correspo nding dislocation pile-ups, in terms of superdislocations, simply from the stress intensity factor. The relationships so obtained for the di pole moment and the quadrupole moment provide an opportunity to calcul ate for cracks subjected to non-uniform loading the crack opening area and crack opening volume, respectively, and with it the strength of e quivalent force dipoles from the stress intensity factor.