It was shown that the stress intensity factors which were associated with a 1-dimensional crack that was subjected to a non-uniform applied stress could 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 was found to exist between the stress intensity factor that was associated with a penny-shaped crack which was subjected to a radial symmetrical non-uniform applied stress and the derivative of the quadrupole moment of the geometrically equivalent circular dislocation pile-up. On the basis of these relationships, an approximation scheme was described which permitted the construction of the corresponding dislocation pile-ups, in terms of super-dislocations, merely on the basis of the stress intensity factor. The resultant relationships for the dipole moment and the quadrupole moment provided the possibility of calculating the crack opening area and crack opening volume, respectively, for cracks that were subjected to non-uniform loading. It was also possible to calculate the strength of equivalent force dipoles from the stress intensity factor.

Calculation of Moments of Dislocation Pile-ups from the Stress Intensity Factor. P.Streitenberger, J.F.Knott: Philosophical Magazine A, 1997, 75[2], 469-83