Debond criteria

Fig. 4.11. Plot of interface shear bond strength, ib, as a function of fiber length, 2L. showing the interface debond criteria, according to Eq. (4.71). After Kim et al. (1993b).

Debonding is assumed to be the effect of an intensive plastic deformation, either a tensile, shear, or combined one. Figure 22 illustrates the different debonding criteria, assuming pure load cases. 

Figure 22. Debonding criteria (a) for pure tension, (b) for pure shear, and (c) a corresponding equivalent stress-strain curve. ...

The interface debond criterion used in this analysis is based on the concept of fracture mechanics where the strain energy release rate against the incremental debond length is equated to the interface fracture toughness, Gk, which is considered to be a material constant... 

Substituting the solutions for the three major stress components determined in the bonded and debonded regions, a fiber-matrix interface debond criterion is derived as... 

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)... 

More recently, Stang and Shah (1986) derived a debond criterion based on a compliance analysis, and Wells and Beaumont (1985) took into account the effect of the Poisson contraction of the fiber and non-linear friction in the debonded region. 

Interface debond criterion and partial debond stress... 

It is envisaged that the degradation of the frictional interface properties and the corresponding increase in the relative displacements eventually lead to debond crack growth once the debond criterion is satisfied. The debond criterion based on the energy balance theory given by Eq. (4,35) under monotonic loading can be rewritten as... 

The material behavior for debonding, based on the strain energy approach as an interface debonding criterion, is shown by the dotted line in Figure 22c,... 

In the shear strength criterion, the debond crack propagates when the maximum IFSS at the debond crack tip z = L - tj reaches the shear bond strength, tb, i.e. 

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 ... 

Based on the shear strength criterion for the interface debonding, the condition for the fully bonded interface requires that the maximum IFSS be obtained at the... 

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)... 

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... 

There are many features in the analysis of the fiber push-out test which are similar to fiber pull-out. Typically, the conditions for interfacial debonding are formulated based on the two distinct approaches, i.e., the shear strength criterion and the fracture mechanics approach. The fiber push-out test can be analyzed in exactly the same way as the fiber pull-out test using the shear lag model with some modifications. These include the change in the sign of the IFSS and the increase in the interfacial radial stress, (o,z), which is positive in fiber push-out due to expansion of the fiber. These modifications are required as a result of the change in the direction of the external stress from tension in fiber pull-out to compression in fiber push-out. 

The earliest works of trying to model different length scales of damage in composites were probably those of Halpin [235, 236] and Hahn and Tsai [237]. In these models, they tried to deal with polymer cracking, fiber breakage, and interface debonding between the fiber and polymer matrix, and delamination between ply layers. Each of these different failure modes was represented by a length scale failure criterion formulated within a continuum. As such, this was an early form of a hierarchical multiscale method. Later, Halpin and Kardos [238] described the relations of the Halpin-Tsai equations with that of self-consistent methods and the micromechanics of Hill [29],... 

Another important result from the atomistic simulations was that the stress-strain response of a region of material around an interface that debonded could be represented by an elastic fracture analysis at the next higher size scale if the interface was assumed to be larger than 40 A. Hence, an elastic fracture criterion was used in the microscale finite element analysis, which focused on void-crack... 

The development of a criterion for debonding mechanism, which assumes that the debonding stress is proportional to the strength of adhesion and depends on the particle size of the filler, might explain the experimental observations on toughness. 

The failure behavior of composite propellants, which are filled elastomers, is complicated by the presence of filler particles. Under loading, phenomena such as cavitation and debonding can arise at or near the filler-matrix interface. (1, 2) Identification of a practical failure criterion for such... 

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