Model debonding

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

Gulino, R., Schwartz, P. and Phoenix, L. (1991). Experiments on shear deformation, debonding and local load transfer in a model graphite/ glass/epoxy microcomposites. J. Mater. Sci. 26, 6655-6672. 

Lacroix, Th., Tilmans, B., Keunings, R., Desaeger, M. and Verpoest, F. (1992). Modelling of critical fiber length and interfacial debonding in the fragmentation testing of polymer composites. Composites Sci. Technol. 43, 379-387. 

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 ... 

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)... 

Fig. 4.16. Variation of mean fiber fragmentation length, 2L, versus applied strain, , in the partially debonded interface model for Tb = 50 MPa. After Kim et al. (1993b).

Fig. 4.18. Variation of mean fiber fragment length, 2L. as a function of applied strain, e, predicted in the fully debonded interface model for constant fiber tensile strengths

Theoretical analyses of interfacial debonding and frictional pull-out in the fiber pull-out test were initially modeled for ductile matrices (e.g. tungsten wire-copper matrix (Kelly and Tyson, 1965, Kelly, 1966)) assuming a uniform IFSS. Based on the matrix yielding over the entire embedded fiber length, as a predominant failure mechanism at the interface region, a simple force balance shown in Fig. 4.19 gives the fiber pull-out stress, which varies directly proportionally to the cylindrical surface area of the fiber... 

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... 

One of the major differences between the results obtained from the micromechanics and FE analyses is the relative magnitude of the stress concentrations. In particular, the maximum IFSS values at the loaded and embedded fiber ends tend to be higher for the micromechanics analysis than for the FEA for a large Vf. This gives a slightly lower critical Vf required for the transition of debond initiation in the micromechanics model than in the FE model of single fiber composites. All these... 

In contrast, the single fiber composite model predicts that the IFSS concentration becomes higher at the embedded end than at the loaded end if fiber Kf is greater than a critical value, suggesting the possibility of debond initiation at the embedded fiber... 

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. 

Hutchinson, J.W. and Jensen, H.M. (1990). Models for fiber debonding and pullout in brittle composites with friction. Mech. Mater. 9, 139 163. 

Karbhari, V.M. and Wilkins, D.J. (1990). A theoretical model for fiber debonding incorporating both interfacial shear and frictional stresses. Scripta Metall. Mater. 24, 1197-1202. 

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