J. Ma et al. /Journal of the European Ceramic Society 24(2004)825-831 Ri= RI (3) The fracture energy ratio, R/Rm, for the various volume fraction of porosity in the porous interlayers to where v. is the volume of pores in the porous the dense layers, were computed and summarized in layers. Putting Eq (2), Clegg et al. pro- Table 3. The results are plotted in Fig 3 to compare posed that the criterion deflection should be with previous works in the literature and also Eq (4)as R proposed by Clegg et al. The figure show that Eq .(4) Rn (4) provides a good prediction on the deflection criteria of cracks in layered systems. It is also shows that the I mr Fig. 2. Crack deflection of the layered systems for different volume fraction porosity in the porous interlayers, (a)30.2 vol %,(b)39.8 vol %,(c) 48.7vol.%,(d)576vol.%,(e)65.2volRi ¼ Rlig 1
Vp
ð3Þ where Vp is the volume fraction of pores in the porous interlayers. Putting Eq. (3) into (2), Clegg et al. pro￾posed that the criterion for crack deflection should be Ri Rm 1
Vp
< 0:57 ð4Þ The fracture energy ratio, Ri/Rm, for the various volume fraction of porosity in the porous interlayers to the dense layers, were computed and summarized in Table 3. The results are plotted in Fig. 3 to compare with previous works in the literature and also Eq. (4) as proposed by Clegg et al. The figure show that Eq. (4) provides a good prediction on the deflection criteria of cracks in layered systems. It is also shows that the Fig. 2. Crack deflection of the layered systems for different volume fraction porosity in the porous interlayers, (a) 30.2 vol.%, (b) 39.8 vol.%, (c) 48.7 vol.%, (d) 57.6 vol.%, (e) 65.2 vol.%. 828 J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831