Overall Elastic and Elastoplastic Behavior of a Partially Debonded Fiber-reinforced Composite

Abstract

In order to quantitatively evaluate the effect of partial debonding on the reduction of overall elastic moduli and overall elastoplastic strength of a fiber-reinforced composite, a combined homogenization and finite-element study is carried out to examine how the debonding angle affects these mechanical properties. In the development of the elastichomogenization theory, the relative strain concentration tensors of the interfacial cracks and fibers with respect to that of the matrix are first determined from Toya’s complex-variable solution [Toya, M. (1974). A Crack Along the Interface of a Circular Inclusion Embedded in an Infinite Solid, J. Mech. Phys. Solids., 22: 325–348.], and then the fibers, cracks, and matrix are assembled together to form the composite. Extension of the elastic formulation to the nonlinear elastoplastic behavior is accomplished through a secant-moduli approach in conjunction with a field-fluctuation method. The developed theory is intended primarily for conditions with low fiber concentration. The finite-element method makes use of the ANSYS program with a carefully constructed mesh near the crack tips. Both the homogenization and the finite-element calculations disclose significant effect of the debonding angle on the overall transverse Young’s modulus along the debonding direction, and on the plane-strain tensile bulk modulus of the composite. In the plastic range the transverse tensile stress–strain curves of the debonded composite are found to be significantly lowered due to the presence of the interfacial cracks.