J. Ma et al. /Journal of the European Ceramic Society 24(2004)825-831 Porosity volume fraction of the porous interlayers after sintering for Fracture energies for the monolithic samples with different amount of various amount of pmma additive Volume fraction Porosity Vp(%) Porosity Vp(%o) of PMMA (%) (J/m2) 57. This phenomenon, nevertheless, is expected as in the crack deflection were observed as shown in Fig. 2(b).It process of powder consolidation, natural small pores is also further noted that as the porosity of the inter between the particles will form. During the densification layer continues to increase, the amount of deflected of these natural small micropores, the particles in gen- crack propagation also increases in the porous inter eral have gone through some rearrangement and certain degree of local densification. After the micropores have Theoretical models proposed in the literature have fully sintered and resulted in the formation of a dense predicted that if there is no elastic mismatch, the inter matrix around the large macropores, the macroporous facial crack will not kink out of the interface when the system becomes stable. Researchers., I-4 have shown ratio of the fracture energy, Ri, to that of the matrix(or that pores with coordination numbers smaller than a adjacent layer), Rm, is less than 0.57[15],1.e critical number will sinter, otherwise, they are thermo- dynamically stable and will remain. In our present sit R, uation,the size of the induced macropores are two R, orders in magnitude larger than the grain size sur- rounding them, and resulted in a coordination number In our present studies, the entire layered system can much larger than the critical number. Therefore, all the be seen as a composite with Al2O3 as the matrix mate- macropores should remain stable after the matrix ha rial. Hence, we can assume that there is basically no fully densified. This, in turn, is consistent with our elastic mismatch between the layers, and the cracks are experimental observation in the present work. always moving in the dense Al2O3 material, regardless of whether they are in the dense or porous layer 3. 2. Crack defle Therefore, for the present configuration, in order for the crack to remain in the porous interlayer, which means It is noted from theoretical models in the literature3-7 that the ligaments of the Al2O3 matrix in the porous that crack deflection in layer systems is mainly deter- interlayer must fracture, Clegg [16] has rewritten Eq (1) mined by the relative fracture energy of the adjacent to be layers, which is, in turn, dependent on the volume frac- R tion of porosity present in the layers. As a result, in our 0.57 Rm (2) work, we first determined the fracture energy of the different porosity materials using homogeneous mono- where Rig is the fracture energy of the ligament of the lithic samples by four point bending test. These results Al2O3 matrix in the porous interlayer. Theoretically, the are summarised in Table 2, and will be discussed later ligament of the Al2O3 matrix in the porous interlayer is on their effects to crack deflection in layered systems. the same dense material as that of the adjacent dense Next, layered systems with interlayers of different Al2O3 layer in the layered system. Hence they will have volume fraction porosity, from 30.2 to 65.2% volume the same fracture energy and the crack should immedi- percent porosity after sintering, were fabricated and ately kink out of the porous interface. Nevertheless, their fracture energies evaluated using four point bend- practically, it is noted that in the porous interlayers, ing tests. The crack propagation results of the layered there exists an interaction effect between the homo- systems with different porosity interlayers are shown in geneously distributed pores. 16, 17 Taking this pore inter Fig. 2. It can be seen from Fig. 2(a) that interlayers action effect into account, Clegg et al. have proposed containing porosity volume fraction of 30.2% did not that the fracture energy of the porous interlayer, Ri,can show any effective crack deflection to provide sul be related to the fracture energy of the ligament of the stantial toughening. However, when the porosity Al2O3 matrix in the porous interlayer, Rlig, by the volume fraction of the interlayers increases to 39.8%, expressionThis phenomenon, nevertheless, is expected as in the process of powder consolidation, natural small pores between the particles will form. During the densification of these natural small micropores, the particles in gen￾eral have gone through some rearrangement and certain degree of local densification. After the micropores have fully sintered and resulted in the formation of a dense matrix around the large macropores, the macroporous system becomes stable.12 Researchers13,14 have shown that pores with coordination numbers smaller than a critical number will sinter, otherwise, they are thermo￾dynamically stable and will remain. In our present sit￾uation, the size of the induced macropores are two orders in magnitude larger than the grain size sur￾rounding them, and resulted in a coordination number much larger than the critical number. Therefore, all the macropores should remain stable after the matrix has fully densified. This, in turn, is consistent with our experimental observation in the present work. 3.2. Crack deflection It is noted from theoretical models in the literature3
7 that crack deflection in layer systems is mainly deter￾mined by the relative fracture energy of the adjacent layers, which is, in turn, dependent on the volume frac￾tion of porosity present in the layers. As a result, in our work, we first determined the fracture energy of the different porosity materials using homogeneous mono￾lithic samples by four point bending test. These results are summarised in Table 2, and will be discussed later on their effects to crack deflection in layered systems. Next, layered systems with interlayers of different volume fraction porosity, from 30.2 to 65.2% volume percent porosity after sintering, were fabricated and their fracture energies evaluated using four point bend￾ing tests. The crack propagation results of the layered systems with different porosity interlayers are shown in Fig. 2. It can be seen from Fig. 2(a) that interlayers containing porosity volume fraction of 30.2% did not show any effective crack deflection to provide sub￾stantial toughening. However, when the porosity volume fraction of the interlayers increases to 39.8%, crack deflection were observed as shown in Fig. 2(b). It is also further noted that as the porosity of the inter￾layer continues to increase, the amount of deflected crack propagation also increases in the porous inter￾layer. Theoretical models proposed in the literature have predicted that if there is no elastic mismatch, the inter￾facial crack will not kink out of the interface when the ratio of the fracture energy, Ri, to that of the matrix (or adjacent layer), Rm, is less than 0.57 [15], i.e., Ri Rm < 0:57 ð1Þ In our present studies, the entire layered system can be seen as a composite with Al2O3 as the matrix mate￾rial. Hence, we can assume that there is basically no elastic mismatch between the layers, and the cracks are always moving in the dense Al2O3 material, regardless of whether they are in the dense or porous layer. Therefore, for the present configuration, in order for the crack to remain in the porous interlayer, which means that the ligaments of the Al2O3 matrix in the porous interlayer must fracture, Clegg [16] has rewritten Eq. (1) to be Rlig Rm < 0:57 ð2Þ where Rlig is the fracture energy of the ligament of the Al2O3 matrix in the porous interlayer. Theoretically, the ligament of the Al2O3 matrix in the porous interlayer is the same dense material as that of the adjacent dense Al2O3 layer in the layered system. Hence they will have the same fracture energy and the crack should immedi￾ately kink out of the porous interface. Nevertheless, practically, it is noted that in the porous interlayers, there exists an interaction effect between the homo￾geneously distributed pores.16,17 Taking this pore inter￾action effect into account, Clegg et al.11 have proposed that the fracture energy of the porous interlayer, Ri, can be related to the fracture energy of the ligament of the Al2O3 matrix in the porous interlayer, Rlig, by the expression Table 1 Porosity volume fraction of the porous interlayers after sintering for various amount of PMMA additive Volume fraction of PMMA (%) Porosity Vp (%) 40 30.2 50 39.8 60 48.7 70 57.6 80 65.2 Table 2 Fracture energies for the monolithic samples with different amount of porosity Porosity Vp (%) Fracture energy (J/m2 ) Dense 62.3 30.2 37.9 39.8 18.2 48.7 11.2 57.6 8.4 65.2 5.8 J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831 827