An exact theory of interfacial debonding in layered elastic composites

Abstract

a b s t r a c tAn exact theory of interfacial debonding is developed for a layered composite system consisting of distinct linear elastic slabs separated by nonlinear, nonuniform decohesive interfaces. Loading of the top and bottom external surfaces is defined pointwise while loading of the side surfaces is prescribed in the form of resultants. The work is motivated by the desire to develop a general tool to analyze the detailed features of debonding along uniform and nonuniform straight interfaces in slab systems subject to general loading. The methodology allows for the investigation of both solitary defect as well as multiple defect interaction problems. Interfacial integral equations, governing the normal and tangential displacement jump components at an interface of a slab system are developed from the Fourier series solution for the single slab subject to arbitrary loading on its surfaces. Interfaces are characterized by distinct interface force-displacement jump relations with crack-like defects modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which account for rigid body translation and rotation, are sought by eigenfunction expansion of the solution of the governing interfacial integral equations. Applications of the theory to the bilayer problem with a solitary defect or a defect pair, in both peeling and mixed load configurations are presented.

A theory of one-dimensional fracture

“…Several recent research works on the topic are quoted here among many others. These are Chen et al [7], Chen [8], Zou et al [9], Wang and Qiao [10], Li et al [11], Nguyen and Levy [12], Yan and Shang [13] and Ouyang and Li [14].…”

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

“…It is therefore possible to track the evolution of the debonding process from its initial onset to complete separation and subsequent formation of voids. Nonlinear interfaces were considered by Levy and Dong (1988), Levy (2000), Nguyen and Levy (2009). An asymptotic simulation of the imperfect bonding was presented by Andrianov et al (2007Andrianov et al ( , 2010.…”

Partition of mixed modes in layered isotropic double cantilever beams with non-rigid cohesive interfaces

“…Positive u corresponds to positive interface shear stress s τ which is determined using Eqs (12), (13) and (14). (18) The mode II ERR can now be found using J-integral below.…”

“…[12] also reported a study on opening mode fracture between bonded dissimilar materials [13]. Nguyen and Levy [14] reported an exact theory of interfacial debonding in layered elastic composites using Fourier series solutions. The theory in Ref.…”

“…The theory in Ref. [14] results in a system of nonlinear algebraic equations, and numerical solution procedures are required. A mixed-mode partition theory was given in Ref.…”