The Effective Dilatational Response of Fiber-Reinforced Composites With Nonlinear Interface

Abstract

This paper presents a model of the dilatational response of fiber-reinforced composites for situations where the fibers interact with the matrix through a nonlinear interfacial separation mechanism. The solution to a planar solitary fiber-interface-matrix problem is employed together with the geometrically consistent composite cylinders model to obtain an exact solution for the bulk response of an elastic matrix reinforced with unidirectional elastic fibers. In the solitary fiber problem interface characterization assumes the form of a nonlinear force-separation law which couples the normal component of displacement jump to the normal component of interface traction and which requires a characteristic length for its prescription. Under decreasing values of characteristic length to inclusion radius ratio ductile or brittle decohesion or closure can occur provided the applied load, interface strength and elastic moduli of fiber and matrix are within the required bounds. Interaction effects due to finite fiber volume concentration, along with the phenomenon of brittle decohesion arising in the solitary fiber problem from the bifurcation of equilibrium separation at the fiber matrix interface, are shown to precipitate instability in the composite. An inequality relating the elastic moduli and interface properties is provided which governs the smooth or abrupt transition in composite response from rigid interface behavior to void behavior. The results are shown to apply equally well for composite geometry based on the three-phase model.

Defect propagation at a circular interface

“…In all of this work the approach taken is to capture interfacial behavior in nonlinear interfacial integral equations and to employ eigenfunction expansions to approximate solutions. This method makes the analysis of bifurcation straightforward and has the added benefit of allowing direct implementation in effective property models for estimation of effective composite response (Levy 1996(Levy , 2000aDong and Levy 2000). In this paper a similar approach is adopted except the constraint of interface uniformity is relaxed allowing for the modeling of interface defects.…”

The cohesive law for the particle/matrix interfaces in high explosives

“…Almost all analytic studies are limited to the linear cohesive law, i.e., a linear relation between the normal (and shear) traction(s) and the opening (and sliding) displacement(s) on particle/matrix interfaces (e.g., Mal and Bose, 1975;Benveniste and Aboudi, 1984;Benveniste, 1985;Achenbach and Zhu, 1989;Pagano and Tandon, 1990;Hashin, 1991aHashin, ,b, 2002Qu, 1993;Zhong and Meguid, 1997;Wu et al, 1999). There are very few analytic studies on the effect of nonlinear cohesive law (e.g., Levy, 1996Levy, , 2000.…”

Asymptotic study of imperfect interfaces in conduction through a granular composite material

“…Variational formulations with such imperfect bonding conditions were given by Hashin (1992) and Lipton & Vernescu (1995). Nonlinear interfaces were studied by Levy (1996Levy ( , 2000 and Levy & Dong (1998).…”