Complete debonding

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

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 yield stress taken from the stress-strain curves is compared with predictions in Figure 7. The upper bound is the prediction from equation 5 for a yielding angle of 70° and Hashing upper modulus bound. The lower bound in Figure 7 is obtained from Nielsen s approach for completely debonded parti-... 

For CNTs not well bonded to polymers, Jiang et al. [137] established a cohesive law for CNT/polymer interfaces. The cohesive law and its properties (e g. cohesive strength and cohesive energy) are obtained directly fiom the Lennard-Jones potential from the vdW interactions. Such a cohesive law is incorporated in the micromechanics model to study the mechanical behavior of CNT-reinforced composite materials. CNTs indeed improves the mechanical behavior of composite at the small strain. However, such improvement disappears at relatively large strain because the completely debonded nanotubes behave like voids in the matrix and may even weaken the composite. The increase of interface adhesion between CNTs and polymer matrix may significantly improve the composite behavior at the large strain [138]. 

The length of embedment plays a considerable role in the kind of failure. For short lengths, pull-out occurred in most cases after complete debonding and longer strands are rather fractured. 

Figure 6 illustrates the dependence of the engineering draw stress on filler content Like the peld stress, draw stress depends on adhesion between the polymer and the particles. The upper limit of the draw stress, equal to the draw stress of unfilled polymer, describes polymers filled with well-bonded particles. The lower border of the fork, corresponding to completely debonded particles in the )deld zone, is a straight line with the slope approximately equal to minus one. If particles are debonded partially, the draw stress is given by ... 

Figure 3.35 Modelling of the pull-out of hooked end steel fibre when being extracted from the matrix (a) hooked steel fibre at the onset of complete debonding, (b) hooked steel fibre during mechanical interlock with two plastic hinges, (c) mechanical interlock with one plastic hinge, (d) hooked steel fibre at onset of frictional bond (after Alwan etal. [68]) PH is plastic hinge.

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