A quasi-three-dimensional crack problem of an elastic plate subjected to in-plane shear loading

Abstract

A quasi-three-dimensional analysis for a through crack in an elastic plate subjected to in-plane shear loading is conducted. The analysis shows that the quasi-three-dimensional crack tip stress fields are composed of a plane strain Mode II singular field and an antiplane Mode III singular field. The Mode III problem is coupled with the Mode II one. The antiplane stress near the crack tip is significant within the scale of one plate thickness. The Mode III stress intensity factor tends to zero when the nondimensional thickness , where a is half the crack length and h is half the plate thickness, becomes vanishingly small and reaches a maximum value around . The antiplane shear effect may not be neglected for plates which are not very thin.