15 20 25 30 35 40 0 2 4 6 8 Crack extension [mm] Deflection Angle [degrees] 0.7 0.5 0.5 Bridged 0.3 where x is the distance from the crack tip. These were then used to determine the hoop stress around the crack tip: 2 cos K sin 2 3 2 K cos 2r 1 II 2 I q úû ù êë é q - q s = qq (3) The angle of crack deflection, q, was then determined by calculating the value of q for which sqq was maximum. Following this another model was constructed in which the crack was incremented ~1 mm in the direction of the calculated deflection and the process repeated. Figure 4: Model of crack showing bridging fibre and nomenclature used in calculations Figure 5: Crack deflection angles as a function of crack extension for bridged and unbridged cracks as calculated in FE model. Figure 5 shows the calculated deflection angles as a function of crack extension for an unbridged crack with initial positions of 0.3, 0.5 and 0.7 and for a bridged crack with initial position of 0.5. It can be seen that the crack deflects towards the polymer as observed in the experiments. It can also be seen that for the unbridged crack models that the deflection angle increases as the crack propagates. This is in contrast to the experiment where the deflection angle decreased with crack extension. However, when crack bridges are incorporated into the model then the crack deflection is less than an unbridged crack and, as crack extension becomes large, begins to decrease. This analysis presents only a qualitative comparison with the experimental work as elastic constants and bridge geometry are dissimilar. Crack edge node s s t t Bridge (beam) -px py 2v 2u y x q sqq
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