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.
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]
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.
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