13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- bridging cases, however, the compliance could be reduced by the bridging fibers, which results in a larger wrong value of χ. According to [8], experimental data for the crack length within significant bridging zone should be excluded during the fitting procedure to get the correct χ value. Figure 1. Illustration of fiber bridging zone for DCB specimen A bridging zone model to calculate the bridging stress σb versus the CTOD δ was derived by Tamuzs et al. [18]: * c b 0 0 ( )d G G (8) where G0 and Gc indicate the initial and total SERR, respectively. δ * is the crack opening displacement at the pre-crack tip. The distribution of bridging stress could thus be experimentally determined by differentiating Eq. (8) with respect to δ*. 2.4. Tri-linear interface element model To simplify the numerical model, the fiber bridging behavior is described by a tri-linear constitutive law shown in Fig. 2, although the real function of bridging stress is nonlinear. Figure 2. Illustration of the tri-linear cohesive constitutive law
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