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

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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.