Total fracture toughness

Ac can be approximated to Cf if Cm is neglected in brittle matrix composites (Harris, 1980). It is shown that Rd( contributes substantially to the total fracture toughness of glass fiber-polymer matrix composites (Harris et al, 1975 Kirk et al., 1978 Beaumont and Anstice, 1980 Munro and Lai, 1988). 

Fig. 6.4. Relationship between composite strength, etc, and total fracture toughness, f i, or equivalently the inverse of frictional shear strength, Tf. After Marston et al. (1974).

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 libers, such as steel wire-cement 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)... 

Mai (1985) has also given a review of the fracture mechanisms in cementitious fiber composites. The total fracture toughness, / i, is given by the sum of the work dissipation due to fiber pull-out, fiber and matrix fraetures, fiber-matrix interfacial debonding and stress redistribution, i.e.. 

Fig. 6.10. Schematics of the dependence of total fracture toughness, on fiber volume fraction of short fiber reinforced thermoplastic composites at different loading rates (a) static loading (b) dynamic...

From a conjectural estimate of the total fracture toughness, the generation of new surfaces was the highest contributor to the overall toughness. 

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