0 10 20 30 40 50 60 0 5 10 15 20 Crack Extension [mm] Deflection Angle [degrees] 0.75 0.5 It can be seen that as the crack propagates the deflection angle decreases. The fracture surface revealed evidence of crack bridging by the polymer phase with ligaments appearing to debond from the ceramic. Figure 2: Fractured sample showing crack deflection, q, with 'interface' and nomenclature used to define position of initial crack within the interface (0.0, 0.5 and 1.0 positions). Figure 3: Experimentally determined crack deflection angle as a function of crack extension for initial cracks at the 0.75 and 0.5 position FINITE ELEMENT MODELLING A two-dimensional finite element model of the test piece was made using the Ansys FEM package. Plan2 elements were used in plane strain. These elements can handle the singularities associated with a crack tip. Cracks were introduced at 0.3, 0.5 and 0.7 positions with the Young's moduli of the Al2O3 and polyester taken to be 440 and 4.5 GPa, respectively, with Poisson's ratios of 0.4 and 0.22. An effective mean approximation was used to calculate the Young's modulus of the composite region, Ec, as 87.05 GPa and Poisson's ratio taken to be 0.3 with volume fraction of ceramic taken as 0.6. Crack bridges were introduced in the 0.5 crack position model as Beam3 elements with a diameter of 0.2 mm and initial length of 0.5 mm and with elastic properties of the polymer. Using the co-ordinate system shown in Fig. 4, KI and KII for the crack were calculated from displacements of the crack face nodes in the directions perpendicular and in-plane to the crack direction, v and u, by solving: ( ) p -n = 8x E K 1 v c 2 I (1) ( ) p -n = 8x E K 1 u c 2 II (2) q Ceramic Interface Region Polymer 0.0- - 1.0- - 0.5- - 3 mm
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