We consider a solitary circular elastic inclusion bonded to an infinite elastic matrix
through a linear viscous interface. Here the viscous interface with vanishing thickness
can simulate the Nabarro–Herring or Coble creep of a thin interphase layer
between the fiber and the matrix. The interface drag parameter is varied along
the interface to reflect the real thickening and thinning of the interphase
layer. In particular, we consider a special form of the interface function that
yields closed-form solutions in terms of elementary functions under four
loading conditions: the matrix is subjected to remote uniform antiplane
shearing; a screw dislocation is located in the matrix; a screw dislocation is
located inside the inclusion; and uniform eigenstrains are imposed on the
inclusion.
Our results show that a nonuniform interface parameter will induce an
intrinsically nonuniform stress field inside the inclusion when the matrix
is subjected to remote uniform shearing or when uniform eigenstrains are
imposed on the inclusion, and will also result in a noncentral image force acting
on the screw dislocation. In addition, the nonuniformity of the interface
will increase the characteristic time of the composite. More interestingly
our results show that there coexist at the same time a transient stable and
another transient unstable equilibrium positions for a screw dislocation in the
matrix when the viscous interface is extremely nonuniform and when the
inclusion is stiffer than the matrix. Also discussed is the overall time-dependent
shear modulus of the fibrous composite by using the Mori–Tanaka mean-field
method.
