Total Fracture Toughness Theory

Marston et al. (1974) and Atkins (1975) have developed a theory based on the coexistence of the three major sources of fracture toughness, i.e., stress redistribution (/ r of Eq. (6.5)), fiber pull-out (/ po of Eq. (6.8)) and generation of new surfaces / s. Therefore, the total fracture toughness, / i, is given by 

R is regarded as the sum of the specific energies absorbed in creating new surfaces in fiber r, matrix Rm and at the interface G based on the nominal transverse area neglecting the cylindrical interface area 

The interface fracture toughness is implicit of the debond toughness R. In Eq. (6.11), Rt is neglected and R q is taken as approximately equal to / m- 

In using Eq. (6.10) to predict / , of a given composite system it is important that the said failure mechanisms all exist. If any one mechanism is apparently absent the corresponding toughness term must be excluded from the / t equation. It is also worth emphasizing that / , varies linearly with reciprocal of the frictional shear strength of the interface, i.e. l/tf, with the lower limit of (1 — Ff)/fm when if approaches infinity. This relationship has been shown to apply to many carbon fiber polymer matrix composites (CFRPs) (Harris et al., 1971 Beaumont and Phillips, 

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EWF is based on the theory that total fracture work W, to breakage is partitioned into essential work of fracture that takes place in process zone where fracture process takes place and plastic work of fracture that takes place in plastic zone where gross ductility occurs (Eq. 1), and then evaluates fracture toughness considering those corresponding elements of and (Eq. 2, Eq. 3). 

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