Interfacial models in viscoplastic composites materials

The aim of the present work is to extend the concept of interphase and equivalent imperfect interface in the context of viscoplasticity. The interphase takes the form of a thin curved layer of constant thickness, made up of a rigid viscoplastic material located between two other surrounding materials. We aim at representing this interphase by an interface with appropriately devised interface conditions. To reach this objective, a Taylor expansion of the relevant physical fields in the thin region is used. It is shown that, depending of the degree of stiffness of the layer with respect to the neighboring media, this interphase can be replaced by an idealized imperfect interface involving the jump of the velocity field or the traction vector. The first kind of interface model, applicable to soft interphases, is the “spring-type” interface across which the traction are continuous but the velocity field exhibits a discontinuity which is given in term of the traction by a power-law type relation. Moreover, it is shown that the constant of the model can be expressed in terms of the material parameters of the interphase. When the interphase is stiffer than the two surrounding media, it can be replaced by an imperfect interface described by a generalization of the so-called Young Laplace model to viscoplastic solids.