Partial debonding

As remarked earlier, in the example of Figs. 37 and 38 all chains longer than six units are partially debonded for a fibre strain of =0.03. Figure 39 shows that... 

Fig. 39 The tensile stress in a partially debonded chain as a function of the distance from the chain centre for chains consisting of 5,10 and 15 units and a fibre strain =0.03... 

Fig. 4.6. Schematic drawing of a partially debonded single fiber composite model subject to external stress, (Ta, in the fiber fragmentation test.

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, ffa(= (h = o er, for the partially debonded interface ... 

The basic requirement necessary to satisfy the partially debonded interface is that the crack tip debond stress, cr, (and the debond length, ) must be greater than zero. From the debond criterion given by Eq. (4.68)... 

Finally, the solution for the mean fiber fragmentation length, IL, which is the sum of the debonded and bonded lengths in the partial debond model, is derived from the fiber fragmentation criterion given by Eq. (4.70)... 

Fig. 4.16. Variation of mean fiber fragmentation length, 2L, versus applied strain, , in the partially debonded interface model for Tb = 50 MPa. After Kim et al. (1993b).

Fig. 4.21. Schematic drawing of the partially debonded fiber in fiber pull-out test.

Interface debond criterion and partial debond stress... 

Partial debond stress, is the applied fiber stress during the progressive debonding process that may be written as a function of the debond length, f, and the crack tip debond stress, <7f, from Eq. (4.89)... 

Fig. 4.24. Plot of partial debond stress, oJJ, as a function of debond length, f, for untreated SiC fiber-glass matrix composite. After Kim et al. (1991).

In light of the foregoing discussion concerning the functional partitioning of the partial debond stress, the characteristic debond stresses can be evaluated. The initial debond stress, ao, is obtained for an infinitesimal debond length where the frictional stress component is zero, i.e.,... 

The maximal debond stress, is determined immediately before the load instability (Karbhari and Wilkins, 1990 Kim et al., 1991) of the partial debond stress, (Tj, when the debond length becomes = L — z a ... 

The instability condition requires that the derivative of the partial debond stress with respect to the remaining bond length z = L — j k equal to or less than zero, i.e., dtr /dz O (Kim et al., 1991). Therefore, the fiber debond process becomes unstable if L - t) is smaller than a critical bond length, Zmax. where the slopes of the curves become zero in Figs. 4.23 and 4.24. At these bond lengths, the partial debond stress, maximum debond stress, crj. The Zmax value is determined from Eq. (4.102) as... 

To show clearly how and to what extent the parameter, Zmax. varies with the properties of the interface and the composite constituents, a simple fiber pull-out model by Karbhari and Wilkins (1990) is chosen here. This model is developed based on the assumption of a constant friction shear stress, Tfr, in the context of the shear strength criterion for interface debonding. In this model, the partial debond stress may be written as... 

Eq. (4.106) is essentially similar to the solution of the debond stress derived earlier by Takaku and Arridge (1973). The above instability condition for the partial debond stress of Eq. (4.105) gives a rather simple equation for z ax as... 

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