Alternate expressions for the near-tip in-plane mixed-mode K-field stresses and displacements

Alternate expressions for the angular variation of the K-field stresses and displacements around a sharp-crack embedded in an elastic medium subjected to an in-plane mixed-mode (mode-1 and -2) loading are presented. The expressions are derived in terms of the mode-mixity angle instead of superposing the pure-mode fields. The alternate expressions are derived using complex potentials and the Kolosov-Muskhelishvili method. The mixed-mode stress and displacement fields are presented in the crack-tip Cartesian and polar coordinates. We have obtained the crack growth angle in terms of the mixity-angle assuming the maximum hoop- and principal-stress criterions.

doi: 10.1016/j.engfracmech.2010.07.011