Page 266 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. Interface mechanics and,fracture toughness theories 241

(1974). For high interface bond strength, cr, is determined based on LEFM where
the stress intensity factor, or the composite strength, oc, of a brittle material is
proportional to the square root of the strain energy release rate, Le., 0,’ K Rt. For
low q, oc decreases almost linearly with l/q. They proposed that both high strength
and high toughness cannot be achieved simultaneously in (brittle fibre-brittle
matrix) composites although these properties can be optimized as indicated by the
peak point in Fig. 6.4.

6.1.7. Fracture of ductile jibers and ductile matrices

The descriptions presented in the foregoing sections are concerned mainly with
composites containing brittle fibers and brittle matrices. If the composite contains
ductile fibers or matrix material, the work of plastic deformation of the composite
constituents must also be taken into account in the total fracture toughness
equation. If a composite contains a brittle matrix reinforced with ductile fibers, such
as steel wireecement matrix systems, the fracture toughness of the composite is
derived significantly from the work done in plastically shearing the fiber as it is
extracted from the cracked matrix. The work done due to the plastic flow of fiber
over a distance on either side of the matrix fracture plane, which is of the order of
the fiber diameter d, is given by (Tetelman, 1969)

(6.12)
If a ductile matrix is reinforced with brittle fibers as in most thermoplastic and metal
matrix composites, the matrix forms ‘bridges’ in the plane of the broken fibers and
the work of matrix shearing R,, is given by (Cooper and Kelly, 1967; Tetelman,
1969; Cooper, 1970)

(6.13)

6.2. Toughness theories for short and randomly oriented fiber composites

6.2.1. Introduction

The foregoing discussion on the theories of fracture toughness is primarily
concerned with unidirectional continuous fiber composites. While these theories can
generally be employed for short fiber composites, particularly those due to
debonding, post-debonding friction, fiber pull-out and matrix surface energy, some
modifications are required. Although short fiber composites normally have poorer
in-plane mechanical properties than continuous fiber composites, they have
advantages of low production costs, and more variety in the selection of thermal,
mechanical and chemical properties of the matrix material. The evolution of many
engineering thermoplastics as high performance matrix materials has made it