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Realistically, o2 in Eq. 6.36 represents a time-dependent parameter. This is due to the fact that the flow resistance of the material ahead of the crack tip could take significantly high and significantly low values during crack propagation. In fact, when the plastic zone is small, the contribution of the fibers is negligible and therefore o2 — o'ym. Larger plastic zones, on the other hand, especially those corresponding to cracks above the crack arrest curve (Fig. 6.26), the contribution of the fibers is significant and Eq. 6.21 should be employed. Such representation of the flow resistance will remain the same until the crack is long enough to claim fiber failure within the plastic zone. In this case the effective Vf will start to decrease. The decrease will continue, probably following an asymptotic descent, until the fiber reaches a length smaller than its critical value. At this stage, the Vfeff should be taken as negligible and the flow resistance equal to o'ym(1 — Vf). Equation 6.36 also makes clear that if all fibers ahead of the crack tip are fractured, then o3d ^ 0, and instability will occur due to oins — oym(1 — Vf), which signifies conditions of general yielding [47]. Figure 6.29 shows a typical crack instability curve.

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