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-interfacematrix 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 decohe sion 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.
|Original language||English (US)|
|Number of pages||8|
|Journal||Journal of Applied Mechanics, Transactions ASME|
|State||Published - 1996|
ASJC Scopus subject areas
- Mechanics of Materials
- Computational Mechanics