Partial debond stress

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... 

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)... 

Equation 1 assumes that the shear stress at the interface is constant as a result of complete interfacial debonding. With good adhesion, only partial debonding or other micro-mechanical events such as transverse matrix cracking are observed, which invalidate the assumption of a constant interfacial shear stress. As a result, alternative data reduction techniques have been developed. For example, Tripathi and Jones developed the cumulative stress-transfer function, which deals with the limitations given above. This has been further refined by Lopattananon et al into the stress-transfer efficiency from which an ineffective length of that fibre in that resin can be determined. In this model, the matrix properties and frictional adhesion at debonds can be included in the analysis. It is also possible to use the three-phase stress-transfer model of Wu et al to include the properties of an interphase. 

Figure 3.36. Microsphere cross sections with relative stress components in the vicinity of the crack tip and corresponding Mohr circles under plane-strain (a) fully bonded for ME, (b) partially debonded for ME, and (c) fully bonded for MEH. The shear stress is denoted by r [37]...

Wu W, Jacobs E, Verpoest I and Vania J (1999) Variational approach to the stress-transfer problem through partially debonded interfaces in a three-phase composite, Compos Sci Technol 59 519-535. 

Figure 3.6 Partially debonded fibre configuration and the interfacial shear stresses to calculate combined elastic and frictional resistance to pull-out.

In the fiber pull-out test, a fiber(s) is partially embedded in a matrix block or thin disc of various shapes and sizes as shown in Fig 3.6. When the fiber is loaded under tension while the matrix block is gripped, the external force applied to the fiber is recorded as a function of time or fiber end displacement during the whole debond and pull-out process. There are characteristic fiber stresses that can be obtained from the typical force (or fiber stress). The displacement curve of the fiber pull-out... 

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. 

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

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