Cohesive tractions

The mathematical approaches pertaining to the full-shielded case (Keff = 0) for time-dependent bridging are very similar. In this case, Eqn. (19) still holds, but for a particular p(u) relation holding over a portion of the crack, the extent of that zone is determined by the Keff = 0 condition. For example, if, as in Eqn. (19), the cohesive tractions act over the entire crack, then the crack length itself is determined by that condition. 

A common representation of the behavior implied by (4.31) within a continuum framework is that of separation of adjacent planes of otherwise elastic materials, with that separation being resisted by a cohesive traction... 

Fig. 4.14. A hierarchical point of view of interface fracture advance, whereby the complexities of material separation are lumped into a representative phenomenological cohesive rule that is representative of the system its essential features are the work per unit area Fo required for separation of the surfaces and the maximum cohesive traction <7 that arises in the process. The cohesive traction must be imposed by the surrounding film and substrate materials, viewed as elastic-plastic continua. The tendency for significant plastic deformation in either material is determined by the ratio of a to the yield stress of that material. The driving force necessary to effect separation is characterized by an energy release rate Q. To sustain crack growth, its value must be large enough to overcome Fq plus plastic dissipation per unit area Fp. Adapted from Hutchinson and Evans (2000).

Figure 2. Cohesive failure model variation of the normal (a) and tangential (b) components of the cohesive traction vector T with respect to the normal (A ) and shear (A,) crack opening displacements, showing the coupling between tensile and shear failure.

As discussed earlier, the area under the traction-separation curve Fi and Fiio) and the peak stress (a and f) are the important parameters that describe the cohesive tractions. The precise shape of the traction-separation law does not strongly influence the behavior of the system. For example, one generally useful form of a mode-I traction-separation law is shown schematically in Fig. 4. It should be appreciated that while the area and peak stress are the two important parameters from a mechanics point-of-view, they may not necessarily represent the fundamental parameters from a materials perspective. In some ways, the peak... 

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