Debond stress

Impurities and flaws have a detrimental effect on the fibre strength. Due to shear stress concentrations at structural irregularities and impurities, the ultimate debonding stress r0 ( rm) or the critical fracture strain / may be exceeded locally far sooner than in perfectly ordered domains. Thus, during the fracture process of real fibres the debonding from neighbouring chains occurs preferably in the most disoriented domains and presumably near impurities. At the same time, however, the chains in the rest of the fibre are kept under strain but remain bonded together up to fracture. 

Determination of the crack tip debond stress, ae, at a debond length, , is contingent to the condition that the fiber axial strain is equivalent to the matrix axial strain at the boundary between the bonded and debonded regions (i.e. duf z)/dz — diP a,z)/dz at z = (L — )). Within the debonded region, the matrix axial strain at the interface is greater than the fiber axial strain due to the relative slip between fiber and matrix. Therefore, combining Eqs. (4.8), (4.9) and (4.61) at the boundary, is obtained from... 

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)... 

Tf is the crack tip debond stress at the boundary between the bonded and debonded regions at z = f, as defined in Section 4.2.3. It should be noted, however, that the actual values of (Tf are different for different specimen geometry even for an identical debond length, t Therefore, the solutions of FAS, and the corresponding MAS, MSS and IFSS are obtained for the bonded region ( [Pg.129]

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)... 

It follows that consists of two stress components a crack tip debond stress, at, and a friction stress component, at is not only a function of the interfacial fracture toughness, G c, but is also dependent on the debond length, t, relative to the total... 

Fig. 4.23. Plot of parlial debond stress, as a function of debond length, (. for a carbon fiber-epoxy matrix composite. After Kim ct al, (1992).

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 ... 

Details of the instability conditions of the debond process and Zmax are discussed in Section 4.3.4. Further, the solution for the initial frictional pull-out stress, (T, upon complete debonding is determined when the debond length, , reaches the embedded length, L, and the crack tip debond stress, ai, is zero ... 

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... 

Fig. 4.26. Comparisons between experiments and theory of (a) maximum debond stress, trj, and (b) initial frictional pull-out stress for carbon fiber-epoxy matrix composites. After Kim et al. (1992).

In these equations, the crack tip debond stress, at the boundary between the bonded and debonded regions is given by... 

Similarly, the initial debond stress, oq, is obtained for the infinitesimal debond length, the maximum debond stress, debond length becomes = L - Zmax and the post-debond initial friction pull-out stress, [Pg.153]

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