Abstract :
The antiplane shear deformation of a bi-material wedge with finite radius is studied in this paper. Depending upon
the boundary condition prescribed on the circular segment of the wedge, traction or displacement, two problems are
analyzed. In each problem two different cases of boundary conditions on the radial edges of the composite wedge
are considered. The radial boundary data are: traction–displacement and traction–traction. The solution of governing
differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for
displacement and stress fields in the entire domain. The geometric singularities of stress fields are observed to be dependent
on material property, in general. However, in the special case of equal apex angles in the traction–traction problem,
this dependency ceases to exist and the geometric singularity shows dependency only upon the apex angle. A result
which is in agreement with that cited in the literature for bi-material wedges with infinite radii. In part II of the paper,
Antiplane shear deformation of bi-material circular media containing an interfacial edge crack is considered. As a special
case of bi-material wedges studied in part I of the paper, explicit expressions are derived for the stress intensity factor
at the tip of an edge crack lying at the interface of the bi-material media. It is seen that in general, the stress intensity
factor is a function of material property. However, in special cases of traction–traction problem, i.e., similar materials
and also equal apex angles, the stress intensity factor becomes independent of material property and the result coincides
with the results in the literature.
