A crack at the interface between a Kane-Mindlin plate and a rigid substrate

The interface fracture of an elastic plate bonded to a rigid substrate is studied using Kane and Mindlin's kinematic assumptions for the quasi-three-dimensional (3-D) deformations of plates deformed in stretching. The stresses and deformations are computed for a semi-finite plate perfectly bonded to a rigid substrate and subjected to uniform in-plane normal tractions at infinity. These agree well with those obtained from the 3-D elasticity theory when the latter are averaged over the plate thickness. The Kane-Mindlin theory predicts a boundary layer adherent to the interface between the plate and the substrate and its thickness approximately equals the plate thickness. An interface crack between the elastic plate and the rigid substrate is investigated. The crack front average stress fields consist of a plane strain (not plane stress) oscillatory singular field and an antiplane shear inverse-square-root singular field, and the three fracture modes are coupled. These agree with the existing 3-D finite element results. The effect of the plate thickness on stress intensity factors and phase angles is studied. The antiplane shear stress intensity factor approaches zero for a vanishingly thin plate, but cannot be ignored otherwise. A path-independent integral including the thickness effects is deduced and is used to establish a fracture criterion for thin plates. Finally, the interface fracture criterion is discussed within the framework of the Kane-Mindlin theory. (C) 1997 Published by Elsevier Science Ltd.