where b is the Burgers vector, A = Gb/2n for screw dislocations, or A = Gb/2n(1 — vm) for edge dislocations, G, vm are the shear modulus and the Poisson's ratio of the matrix, respectively, and a is the applied stress.

If crack growth is considered to be a function of the CTOD, ^, through a Paris-type relationship, then Eq. 6.17 determines da/dN when Za = ni7 Zb = 1 [«i represents a dimensionless measurement of crack length, i.e., n1 = a/(iD/2 + d/2)]. In addition, Eq. 6.18 establishes the condition for crack propagation across the fiber row when the axial stress a3 acting around the fiber is equal to the stress required for debonding, a3d . Clearly, a3 = a3d acknowledges the condition when the clamping stress provided by the fibers to plastic displacements within the plastic zone are removed, since no or minimum interfacial shear stress is acting along the debond length.

Assuming that debonding is not a continuous process (propagation of a bimaterial interface crack), then the stress at the fiber zone required to debond a particular fiber length could be written as:

OdEc Ef

where ad is the tensile stress at the fiber required to debond a particular embedded fiber length, Ec and Ef are the elastic moduli of the composite and the fiber, respectively.

Equation 6.19 is obtained by considering a simple force balance in a fiber push-out test and strain compatibility between the fiber and the composite in the fiber zone. If the interfacial shear strength is taken as constant along the fiber-matrix interface and the shear-lag analysis is utilized, the stress applied at the fiber to cause debonding is obtained as:

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