Analysis of Deformation Fields near an Interfacial Crack Tip in Locking Materials

We study plane strain deformations near a crack tip between two isotropic and homogeneous Hookean bodies and assume that deformations obey the constraint that the volume of a material element cannot become zero. The constraint is imposed by requiring that the dilatation everywhere in the body must be greater than or equal to a constant. The region where the dilatation equals the constant is called the locking region. It is shown that when the locking region occurs in only a part of one body, the index of the singularity near the interfacial crack tip is l/2, and the size of the locking region is determined by the values of the material parameters for the two bodies.