Interfacial sliding near a free surface in a fibrous or layered composite during thermal cycling

Abstract This paper presents a simple shear lag model of interfacial sliding at a free surface in a layered or continuous fiber composite. The interface is characterized by a critical interfacial shear stress, τ 0 , which might represent the critical stress for frictional sliding at a weakly bonded interface, or the shear flow stress of a thin, ductile interface layer at a well bonded interface. We calculate the history during heating and cooling of the relative normal displacement of the reinforcing inclusions and the matrix on a free surface cut normal to the inclusions. The calculated history is shown to depend on both the absolute value and the temperature dependence of τ 0 , as well as on the magnitudes of the bulk residual stresses. Analytical results are obtained for the first few heating and cooling cycles and the equilibrium hysteresis loop under thermal cycling of uniform amplitude. The variety of possible displacement histories suggests that they are a rich source of information about τ 0 and the residual stresses. A discussion of feasible experiments and some results for continuous fiber titanium and titanium aluminide composites are presented in a companion paper.