Debond Process

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, T, corresponds to the maximum debond stress, crj. The Zmax value is determined from Eq. (4.102) as 

Numerical treatment of Eq. (4.104) gives Zmax values for the different composite systems as shown in Table 4.3. It is worth emphasizing that for the SiC fiber-glass matrix composites, z, ax values are very small relative to values, irrespective of the fiber surface treatments and when compared to other epoxy matrix based composites. 

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 

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 

From the discussion presented above, it is clear that the stability of the debond process can be evaluated by a single parameter, Zmax, which is the shortest (remaining) bond length needed to maintain the debond process stable, and is a constant for a given composite system. Therefore, three different interface debond processes are identified in the following totally unstable, partially stable and totally stable debond processes. The schematic plots of the applied stress versus displacement curves are illustrated in Fig. 4.25 for these debond processes. 

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Fig. 1. (a) Adhesive vs. cohesive failure, (b) Close-up view of adhesive failure in the pre.sence of an interphase. The locus of failure may be adjacent to or within the interphase (as shown), and particles of material may be ejected during the debonding process. 

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)... 

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 ... 

Fig. 4.25. Schematic presentations of applied stress versus displacement (

One can easily note that Eq. (4.138) is similar to the solution given by Eq. (4.126), which is derived from the assumption of a constant friction and complete neglect of the Poisson expansion. The solution for Zma, which is the shortest bond length required to maintain a stable debonding process, is obtained from Eq. (4.137)... 

To evaluate the stability of the debond process, the instability parameter, z,nax, is compared, z ax values calculated based on Eqs. (4.104) and (4.139) respectively for fiber pull-out and fiber push-out give z ax = 6-5, 6.2 mm for coated steel wire-epoxy matrix and z ax = 0.5, 0.49 mm for the untreated SiC-fiber-glass matrix composite... 

Zmax maximum embedded fiber length for unstable debond process... 

In connection with this debonding process, the matrix material between the voids deforms more easily to achieve shear yielding. 

In composite propellants, the cavitation (or debonding) process, which has been shown to take place near (or at) the particle-matrix interface, is dependent on pressure, deformation, and additional viscoelastic and dissipative considerations (10). 

Thus, the transport of hydrated ions and chemical debonding processes can be studied by means of the SKP. Fig. 31.6 shows the potential distribution measured with the SKP when a thin electrolyte layer enters the interface between an adhesive and an iron surface covered by a thin (about 6 nm) nonconducting SiOx layer precipitated by a plasma-polymerization process [51, 52]. The SiO layer inhibits the electron-transfer reaction. Consequently, no corrosive degradation of the interface takes place (see Section 31.3.2.1). However, as the adhesion of the epoxy adhesive to the siUca-Uke layer is weak, the polymer is replaced by... 

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