13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Main crack φp=18° φp=20° Main crack Main crack φp=30° φp=26° Main crack Table 3. Values of the GSIFs (crack terminating at the interface) for δ=0.46391, F=10N/mm, ΔT=-1230°C. VATZ /VAMZ Hm [MPa.m1-δ] Hr (ΔT) [MPa.m1-δ] σxx (AMZ) (ΔT) [MPa] H=Hm+Hr 2/1 0.10 2.92 -795 3.02 5/1 0.11 1.58 -795 1.69 8/1 0.11 1.07 -795 1.18 For the calculation of δΠ (Eqs. (2), (4), (7), (8)) for different propagation directions (including single penetration and bifurcation type of propagation) values of SIFs, corresponding to the state, when the crack is arrested behind the interface, were used – see Figure 5. Observe that SIF decreases rapidly with increasing length of crack extension behind the interface. In Figure 6 a), b) a ceramic laminate with volume ratio of laminate components VATZ/VAMZ=8 is studied. Energetic condition for crack propagation (the additional energy ΔW ≥0 - see Eq. (1)) is satisfied for the loading force F≅100N. The referred figure shows a change in potential energy for case of single penetration and crack bifurcation (for ap=ab=25μm). One can see that crack bifurcation is a preferred propagation type in this case (due to higher change in potential energy). a) b) c) d) Figure 6. Variation of the change of the potential energy δΠ with the angle of the crack extension for a), b) volume ratio VATZ/VAMZ=8 and c), d) VATZ/VAMZ=5. For each volume ratio a case of single crack deflection - a), c) and case of the crack bifurcation - b), d) is calculated. δΠp,max(18°) =6.5·10-10 J/m δΠb,max(22°) = 7.5·10-10 J/m δΠp,max(30°) =3.44·10-10 J/m δΠb,max(26°) = 3.42·10-10 J/m
RkJQdWJsaXNoZXIy MjM0NDE=