The Fiber Composite With Nonlinear Interface—Part I: Axial Tension

Abstract

This paper treats the effective axial tension response of a composite consisting of fibers that debond from the matrix according to nonlinear Needleman-type cohesive zones. A second, related paper (Part II) treats effective antiplane shear response. The composite cylinders representation of a representative volume element (RVE) is employed throughout. For axial tension loading a simple rotationally symmetric boundary value problem for a single composite cylinder is solved. Bounds on the total potential energy and the total complementary energy are shown to coincide and an exact solution for axial extension and Poisson contraction of an RVE of the composite is obtained. Nonlinear interfacial debonding, however, is shown to have a negligible effect on extensional response and only a small, though potentially destabilizing, effect on Poisson contraction response. [S0021-8936(00)02004-3]

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

“…1992(Rae et al, , 1993Xu and Needleman, 1994;Camacho and Ortiz, 1996;Zhong and Knauss, 1997, 2000Espinosa et al, 1998;Geubelle and Baylor, 1998;Huang and Gao, 2001;Zhang et al, 2002;Kubair et al, 2002Kubair et al, , 2003Samudrala et al, 2002Samudrala et al, , 2003Thiagarajan et al, 2004aThiagarajan et al, , 2004b. A cohesive zone model assumes a relation between the normal (and shear) traction(s) and the opening (and sliding) displacement(s), and is capable of capturing the debonding process of particle/ matrix interfaces.…”

“…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.…”

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.…”

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).…”