On the Saint-Venant torsion of composite bars with imperfect interfaces

The Saint-Venant torsion problem of composite cylindrical bars with imperfect interfaces between the constituents is studied. Two kinds of imperfect interfaces are considered: one which models a thin interphase of low shear modulus and one which models a thin interphase of high shear modulus. In the former case, the traction on the interface is continuous but the axial warping displacement undergoes a discontinuity proportional to the axial shear traction. In the latter case, the warping displacement at the interface is continuous but the axial shear traction undergoes a discontinuity proportional to a differential operator of the warping function. The imperfect interfaces are characterized by certain interface parameters given in terms of the thickness and the shear modulus of the interphase. A derivation of these interface conditions is presented, and the Saint-Venant torsion of cylindrical composite bars with both types of imperfect interfaces is formulated in terms of the warping function and in terms of a stress potential. An example of the application of imperfect interfaces is the construction of 'neutral inhomogeneities' in torsion problems. These are cylindrical inhomogeneities which can be introduced in a cylindrical bar without disturbing the warping function in it and without changing its torsional stiffness. Neutrality is achieved by a proper design of an imperfect interface with a variable interface parameter. Analytical expressions are derived for the variable interface parameter at neutral elliptical inhomogeneities in an elliptical bar. The paper concludes with a study of the decay of end effects in composite bars with imperfect interfaces. The simplest example of a concentric cylinder is chosen to illustrate that the decay length increases as the degree of the imperfectness at the interface increases.