Page 130 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress transfer 113

4.2.4.2. Interface debond and fiber fragmentation criteria
In the shear strength criterion, the debond crack propagates when the maximum
IFSS at the debond crack tip z = &(L - e) reaches the shear bond strength, Tb, i.e.

Ti(a, (L - e)) = Tb . (4.67)
By substituting Eq. (4.67) into Eq. (4.60), the debond crack tip stress, CJ~, is
expressed as a function of the material properties and CT. Thus,

(4.68)

Therefore, by combining Eqs. (4.66) and (4.68), one can derive the stress applied to
the matrix at the remote ends, oa(= (b2 -a2)/a2) =God, for debond crack
propagation

(4.69)

where R3 is given in Appendix C.
Based on the same average fiber tensile strength model as that employed in
Section 4.2.3, the fiber fragmentation criterion is derived in terms of the external
stress, ca(= (h2 - .')/a2) = c,,f, for the partially debonded interface:

(4.70)

4.2.4.3. Three diferent interjace conditions
Depending on the applied stress relative to the fiber tensile strength and the
interfacial properties for given elastic properties of the constituents and the
geometric factors of the composite model, three distinctive cases are considered with
regard to the fiber-matrix interface condition: namely full bonding, partial
debonding and complete debonding or full frictional bonding. The conditions
required to satisfy each interface state are systematically identified in the following
in terms of the relationship between the applied stress and the properties of the
constituents and the interface. The stress distributions in the constituents are also
characterized for each interface state, and the important factors governing the stress
fields are identified. Therefore, the fiber fragmentation criterion is applied to each
interface condition to derive the mean fiber fragment length, 2L, as a function of the
applied stress.
(i) Full bonding: Let us first consider the perfectly bonded interface over the
whole fiber length where the stress transfer is purely elastic. The FAS and IFSS
normalized with u are plotted along the axial direction, z/a, for the half the fiber