Availableonlineatwww.sciencedirect.com SCIENCE E噩≈S Journal of the European Ceramic Society 24(2004)825-831 www.elsevier.com/locatejeurceramsoc Effect of porous interlayers on crack deflection in ceramic laminates J. Ma Hongzhi Wang, Luqian Weng, G.E. B. Tan a school of Materials Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore bDSO National Laboratories, 20 Science Park Drive, Singapore 118230, Singape Received 13 March 2003: received in revised form 10 April 2003; accepted 27 April 2003 Abstract Ceramic layered systems with interlayers of various porosities were fabricated using tape casting technique. Submicron size alu nina powders were used to make the tapes for both the strong dense laminae and the weak porous interlayers. Porosity was ntroduced into the interlayers by the addition of PMMa powders. The pores generated were found to be spherical and uniformly distributed. The crack deflection capability of the layered systems with interlayers of different porosity were then investigated. To acilitate the study, the fracture energies of the different porosity monolithic porous layers, and also the dense alumina layer, were quantified using four point bending tests. It was observed that there exists an optimum porosity that the crack deflection, hence the fracture energy of the system, can be maximized. Theories proposed in the literature on crack deflection in layered systems were also discussed and compared with the present experimental findings C 2003 Elsevier Ltd. All rights reserved Keywords: Al2O3; Crack deflection: Fracture: Laminates; Porosity 1. Introduction presence of residual stresses, they proposed that the cri- tical interface to bulk fracture energy ratio for crack Ceramic layered systems have attracted wide attention deflection is 0. 25. In their subsequent work, they in recent years as such configurations have shown to be incorporated the effect of in-plane and residual stresses effective in improving the toughness of the ceramic in their model to illustrate the influences of these stres components. ,2 It is noted that such enhancement in ses in crack deflection of layered systems. The results of fracture property is mainly attributed to the crack their studies were also found to be consistent with that deflection capability in the interlayers of such systems. computed numerically by other researchers. 10 Both experimental and theoretical works reported in the The above studies have shown that to build a tough literature have indicated that the ability to deflect crack ness enhanced layered system, not only a weak interface lepends on the fracture energy ratio of the interlayer is required to promote crack deflection, a chemically and the laminae in the layered systems. 3-7 Cook and compatible interface is also required to avoid the build Gordon have analyzed the problem based on the stres- ing up of internal stresses. An easy way to construct ses at a crack tip and suggested that a crack will be such a system has been proposed by Clegg et al deflected at an interface if the strength of the interface is where a porous interlayer of the same material as that of about 1/5 of that of the matrix. Based on an energy the bulk is to be employed as the weak interface. In their approach, Kendall, on the other hand, has proposed work, natural starches, such as rice and potato starch that crack deflection will occur if the fracture energy of were used to generate the pores in the porous interlayer the interface is less than 10 to 20% of the matrix, where via burnt-off during sintering. In the present work, the exact value depends on the thickness ratio of the however, PMMa powders are used to generate the interface and the matrix layer In a theoretical study by desired porosity in the porous interlayers. It is found He and Hutchinson% for layered systems without the that the PMMa powder particles produce uniformly distributed spherical pores after they burnt out during Corresponding author. Tel +65-67906214; fax: +65-67900920. sintering. Both the dense and porous layers were E-mail address: asima(@ ntu.ed u sg (J. Ma). fabricated using tape casting technique 0955-2219/03/S. see front matter C 2003 Elsevier Ltd. All rights reserved. doi:10.1016S0955-221903)00338-8
Effect of porous interlayers on crack deflection in ceramic laminates J. Maa,*, Hongzhi Wanga , Luqian Wenga , G.E.B. Tanb a School of Materials Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore bDSONational Laboratories, 20 Science Park Drive, Singapore 118230, Singapore Received 13 March 2003; received in revised form 10 April 2003; accepted 27 April 2003 Abstract Ceramic layered systems with interlayers of various porosities were fabricated using tape casting technique. Submicron size alumina powders were used to make the tapes for both the strong dense laminae and the weak porous interlayers. Porosity was introduced into the interlayers by the addition of PMMA powders. The pores generated were found to be spherical and uniformly distributed. The crack deflection capability of the layered systems with interlayers of different porosity were then investigated. To facilitate the study, the fracture energies of the different porosity monolithic porous layers, and also the dense alumina layer, were quantified using four point bending tests. It was observed that there exists an optimum porosity that the crack deflection, hence the fracture energy of the system, can be maximized. Theories proposed in the literature on crack deflection in layered systems were also discussed and compared with the present experimental findings. # 2003 Elsevier Ltd. All rights reserved. Keywords: Al2O3; Crack deflection; Fracture; Laminates; Porosity 1. Introduction Ceramic layered systems have attracted wide attention in recent years as such configurations have shown to be effective in improving the toughness of the ceramic components.1,2 It is noted that such enhancement in fracture property is mainly attributed to the crack deflection capability in the interlayers of such systems. Both experimental and theoretical works reported in the literature have indicated that the ability to deflect crack depends on the fracture energy ratio of the interlayer and the laminae in the layered systems.37 Cook and Gordon8 have analyzed the problem based on the stresses at a crack tip and suggested that a crack will be deflected at an interface if the strength of the interface is about 1/5 of that of the matrix. Based on an energy approach, Kendall,3 on the other hand, has proposed that crack deflection will occur if the fracture energy of the interface is less than 10 to 20% of the matrix, where the exact value depends on the thickness ratio of the interface and the matrix layer. In a theoretical study by He and Hutchinson4 for layered systems without the presence of residual stresses, they proposed that the critical interface to bulk fracture energy ratio for crack deflection is 0.25. In their subsequent work,9 they incorporated the effect of in-plane and residual stresses in their model to illustrate the influences of these stresses in crack deflection of layered systems. The results of their studies were also found to be consistent with that computed numerically by other researchers.10 The above studies have shown that to build a toughness enhanced layered system, not only a weak interface is required to promote crack deflection, a chemically compatible interface is also required to avoid the building up of internal stresses. An easy way to construct such a system has been proposed by Clegg et al.,1,11 where a porous interlayer of the same material as that of the bulk is to be employed as the weak interface. In their work, natural starches, such as rice and potato starch, were used to generate the pores in the porous interlayer via burnt-off during sintering. In the present work, however, PMMA powders are used to generate the desired porosity in the porous interlayers. It is found that the PMMA powder particles produce uniformly distributed spherical pores after they burnt out during sintering. Both the dense and porous layers were fabricated using tape casting technique. 0955-2219/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0955-2219(03)00338-8 Journal of the European Ceramic Society 24 (2004) 825–831 www.elsevier.com/locate/jeurceramsoc * Corresponding author. Tel.: +65-67906214; fax: +65-67900920. E-mail address: asjma@ntu.ed.u.sg (J. Ma)
J. Ma et al. /Journal of the European Ceramic Society 24(2004)825-831 2. Experimental procedure fine-polished cross-section face of the samples using Scanning Electron Microscope (Jeol, JSM5310) The ceramic powders used in the present work were ne-grained high purity alumina powders(AKP 30 Sumitomo Chemicals, Japan) with a average particle 3. Results and discussions size of 0.4 um. The PMMa powders(Acrylic Powder, Buehler) used to generate pores in the porous inter- 3. 1. Sintering behavior layers, on the other hand, have an average particle size of 40 um. Tapes for forming the respective layers in the Fig. I shows the cross-section SEM micrograph of the layered systems were produced by tape casting of a layered system formed with 60% PMMA addition. It aqueous slurry containing 58 wt. of alumina powders, can be seen that the layers were very well integrated I wt. of fish oil, 6.5 wt. of polyethylene glycol 400, without any delamination between the dense and por- 4.5 wt. of benzyl butyl phthalate, 7 wt. of polyvinyl ous layers. The dense layers have been fully densified butyral and 23 wt. of ethanol(99.86%). For the os nation using SEM and image analyzer showed that or- during the sintering process and microstructural exami ous tapes, various volume percent of PMMA powde were added to the slurry with respect to the amount of relative density of more than 97% has been achieved. It the alumina powder in the slurry. The different volume is also observed that the addition of PMMa produced percent added were 40, 50, 60, 70 and 80 vol % The uniformly distributed large spherical pores throughout slurries were then de-gased in a pressure de-gas system the por he ize of these large pores and finally tape casted using a continuous feed tape (70 um) is measured to be more than two orders of casting machine (Unique, USA)onto a polypropylene magnitude larger than the average grain size of alumina carrier tape running at a speed of 20 cm/min. The (0.4 um). These large pores introduced from the burnt thickness of the dense and porous tapes fabricated was out PMMa powders are termed as"macropores"in the both 0.3 mm. After drying, the tapes were cut into a subsequent discussions for clarity. It is also noted from rectangle of size 60 4 mm. The dense and porous layers the microstructural examinations that the actual volume were then stacked and pressed together at room tem- fraction of porosity in the porous layer, which is mainly perature to a final thickness of 3.3 mm. For layered contributed by the large macropores since the matrix is systems, dense and porous layers were stacked alter- almost fully densified, is lower than that of the initially nately. The stacked green samples were then trimmed to added PMMa volume percent. For example, in the 50x4x3.3 mm block before sintering at 1550C for 3 h. sample shown(Fig. 1), although the added amount of The sintered layered systems and the monolithic sam- PMMA was 60 vol % the porosity result obtained from les were finally subjected to microstructural exami- image analysis showed a porosity of 48.7%. Similarly nations and four point bending tests with a loading span the final porosity after sintering for samples with other of 30 mm to evaluate the fracture energies of the volume fraction of PMMA addition was found to be samples. Microstructural studies were performed on the lower than the actual PMMA volume fraction (Table 1) 2kU75 1m141129 Fig. I. SEM cross-section micrograph of a layered system with 60 vol. PMMA
2. Experimental procedure The ceramic powders used in the present work were fine-grained high purity alumina powders (AKP 30, Sumitomo Chemicals, Japan) with a average particle size of 0.4 mm. The PMMA powders (Acrylic Powder, Buehler) used to generate pores in the porous interlayers, on the other hand, have an average particle size of 40 mm. Tapes for forming the respective layers in the layered systems were produced by tape casting of a aqueous slurry containing 58 wt.% of alumina powders, 1 wt.% of fish oil, 6.5 wt.% of polyethylene glycol 400, 4.5 wt.% of benzyl butyl phthalate, 7 wt.% of polyvinyl butyral and 23 wt.% of ethanol (99.86%). For the porous tapes, various volume percent of PMMA powders were added to the slurry with respect to the amount of the alumina powder in the slurry. The different volume percent added were 40, 50, 60, 70 and 80 vol.%. The slurries were then de-gased in a pressure de-gas system and finally tape casted using a continuous feed tape casting machine (Unique, USA) onto a polypropylene carrier tape running at a speed of 20 cm/min. The thickness of the dense and porous tapes fabricated was both 0.3 mm. After drying, the tapes were cut into a rectangle of size 604 mm. The dense and porous layers were then stacked and pressed together at room temperature to a final thickness of 3.3 mm. For layered systems, dense and porous layers were stacked alternately. The stacked green samples were then trimmed to 5043.3 mm block before sintering at 1550 C for 3 h. The sintered layered systems and the monolithic samples were finally subjected to microstructural examinations and four point bending tests with a loading span of 30 mm11 to evaluate the fracture energies of the samples. Microstructural studies were performed on the fine-polished cross-section face of the samples using Scanning Electron Microscope (Jeol, JSM5310). 3. Results and discussions 3.1. Sintering behavior Fig. 1 shows the cross-section SEM micrograph of the layered system formed with 60% PMMA addition. It can be seen that the layers were very well integrated without any delamination between the dense and porous layers. The dense layers have been fully densified during the sintering process and microstructural examination using SEM and image analyzer showed that a relative density of more than 97% has been achieved. It is also observed that the addition of PMMA produced uniformly distributed large spherical pores throughout the porous layer. The average size of these large pores (70 mm) is measured to be more than two orders of magnitude larger than the average grain size of alumina (0.4 mm). These large pores introduced from the burntout PMMA powders are termed as ‘‘macropores’’ in the subsequent discussions for clarity. It is also noted from the microstructural examinations that the actual volume fraction of porosity in the porous layer, which is mainly contributed by the large macropores since the matrix is almost fully densified, is lower than that of the initially added PMMA volume percent. For example, in the sample shown (Fig. 1), although the added amount of PMMA was 60 vol.%, the porosity result obtained from image analysis showed a porosity of 48.7%. Similarly, the final porosity after sintering for samples with other volume fraction of PMMA addition was found to be lower than the actual PMMA volume fraction (Table 1). Fig. 1. SEM cross-section micrograph of a layered system with 60 vol.% PMMA. 826 J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831
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%, expression
This 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 general 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 thermodynamically stable and will remain. In our present situation, the size of the induced macropores are two orders in magnitude larger than the grain size surrounding 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 literature37 that crack deflection in layer systems is mainly determined by the relative fracture energy of the adjacent layers, which is, in turn, dependent on the volume fraction 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 monolithic 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 bending 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 substantial 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 interlayer continues to increase, the amount of deflected crack propagation also increases in the porous interlayer. Theoretical models proposed in the literature have predicted that if there is no elastic mismatch, the interfacial 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 material. 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 immediately kink out of the porous interface. Nevertheless, practically, it is noted that in the porous interlayers, there exists an interaction effect between the homogeneously distributed pores.16,17 Taking this pore interaction 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
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)65.2vol
Ri 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. proposed 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
iropean Ceramic Society 24(2004)825-831 present results are in good agreement with that obtained value than that of the monolithic sample due to the by Clegg et al. on Al2O3 I and that by Blanks et al. on introduction of porosity in the component. On the other hand, it is also noted that for systems with crack deflection mechanism operating, i.e., the layered systems 3.3. Optimum configuration in layered systems with 39.8, 48.7, 57.6 and 65.2% of porous volume frac- tion in the porous interlayers, the fracture energy In the previous sections, the fabrication of a layered increases as the amount of porosity increases in the system with porous interlayer and the verification of the porous interlayer. However, when the porosity is further crack deflection criteria have been discussed. In the increased to 65.2%, the fracture energy of the system present section, the mechanical performance of the decreased again. Hence, there exists an optimum overall layered system with the different configuration is amount of porosity in the porous interlayers, or an investigated. The fracture energies of the layered sys- optimum value of R/Rm, to achieve the best fracture tems with different volume fraction of porosity in the toughness for such systems. This is attributed to the fact porous interlayers were quantified by four point bend- that as the amount of porosity in the porous interlayers ing tests. Fig. 4 shows the load-displacement curve for increases, despite the promotion of crack deflection the layered system(60% porosity in interlayer) and that mechanism, the overall mechanical strength of the of the monolithic alumina sample. It can be seen that component has been weakened. This strength weaken with effective crack deflection, the component possesses ing effect from the porosity hence becomes a competi higher fracture toughness. Fig. 5 shows the results of the tive factor to the toughening mechanism effect resulting racture energies of the layered systems with various from crack deflection. Eventually, as the porosity in the volume fraction of porosity in the porous interlayers. It porous interlayers exceeds a certain threshold where the can be further deduced that, in general, the layered sys- component becomes too weak, the overall fracture tems without crack deflection during the bending test energy of the system will deteriorate. This phenomenon possessed a lower value of fracture energy compared to can also be verified by estimating the total energy that with crack deflection occurring in the system. In absorbed from that contributed by crack deflection and fact, such system even possessed lower fracture energy that contributed by porosity, using the experimental Table 3 Fracture energy ratios between the dense and porous interlayers for cred systems with different amount of porosity volume fraction the porous interlayers Fig. 4. Load-displacement curve of a layered system with 60% Crack Deflection 0 100 Volume fracture of ceramic in interlayer Volume Fraction of Porosity (%) bols represent data fro Fig. 5. Fracture energy of various layered systems as a function of volume fraction porosity in the porous interlayers
present results are in good agreement with that obtained by Clegg et al. on Al2O3 11 and that by Blanks et al. on SiC.2 3.3. Optimum configuration in layered systems In the previous sections, the fabrication of a layered system with porous interlayer and the verification of the crack deflection criteria have been discussed. In the present section, the mechanical performance of the overall layered system with the different configuration is investigated. The fracture energies of the layered systems with different volume fraction of porosity in the porous interlayers were quantified by four point bending tests. Fig. 4 shows the load-displacement curve for the layered system (60% porosity in interlayer) and that of the monolithic alumina sample. It can be seen that with effective crack deflection, the component possesses higher fracture toughness. Fig. 5 shows the results of the fracture energies of the layered systems with various volume fraction of porosity in the porous interlayers. It can be further deduced that, in general, the layered systems without crack deflection during the bending test possessed a lower value of fracture energy compared to that with crack deflection occurring in the system. In fact, such system even possessed lower fracture energy value than that of the monolithic sample due to the introduction of porosity in the component. On the other hand, it is also noted that for systems with crack deflection mechanism operating, i.e., the layered systems with 39.8, 48.7, 57.6 and 65.2% of porous volume fraction in the porous interlayers, the fracture energy increases as the amount of porosity increases in the porous interlayer. However, when the porosity is further increased to 65.2%, the fracture energy of the system decreased again. Hence, there exists an optimum amount of porosity in the porous interlayers, or an optimum value of Ri/Rm, to achieve the best fracture toughness for such systems. This is attributed to the fact that as the amount of porosity in the porous interlayers increases, despite the promotion of crack deflection mechanism, the overall mechanical strength of the component has been weakened. This strength weakening effect from the porosity hence becomes a competitive factor to the toughening mechanism effect resulting from crack deflection. Eventually, as the porosity in the porous interlayers exceeds a certain threshold where the component becomes too weak, the overall fracture energy of the system will deteriorate. This phenomenon can also be verified by estimating the total energy absorbed from that contributed by crack deflection and that contributed by porosity, using the experimental Table 3 Fracture energy ratios between the dense and porous interlayers for layered systems with different amount of porosity volume fraction in the porous interlayers Porosity Vp (%) Ri/Rm 30.2 0.60 39.8 0.29 48.7 0.18 57.6 0.13 65.2 0.09 Fig. 3. Relationship between relative fracture energy between the dense and adjacent porous layers and the porosity in the porous interlayers. Circle symbols represent data from Clegg et al., and delta symbols are from present work. Filled symbols indicate cracked deflection is observed. Fig. 4. Load–displacement curve of a layered system with 60% porosity interlayer and that of the monolithic sample. Fig. 5. Fracture energy of various layered systems as a function of volume fraction porosity in the porous interlayers. J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831 829
J. Ma et al. Journal of the European Ceramic Society 24(2004)825-831 Table 4 Total energy absorbed estimation in various layered systems Crack deflectio Energy absorbed vp(%) energy Ed (J/m) Ea( /m) flection(L Lo) E(/m) Dense 398 85.1 97.3 163.3 decrease in the fracture energy of the layered system from 57.6% to 65.2% of interlayer porosity, the frac ture energy of the system at 65. 2% interlayer porosity is still much higher than that of the monolithic sample (400% higher). As a result, in general, it can be con cluded that crack deflection mechanism significantly enhances the fracture toughness of the component It is also noted in the process that the porous inter- layer systems studied in the present work are different from that introduced by Clegg et al. as in the pre- sent systems, there exists two contributing mechan Fig. 6. Final energy absorbed in the layered systems as a function of nterlayer porosity estimated after considering the effect from crack isms, namely, crack deflection and porosity. Although deflection length and porosity the porosity has shown to be fracture energy dete- riorating factor. it should be noted that it could be an essential parameter when strength to weight ratio is concerned results obtained. The averaged crack deflection length for various porosity laminates were first estimated using the SEM micrographs, and the factor increase com- pared to that without crack deflection can then be 4. Conclusions omputed. Using results from Table 2, the reduction in energy due to porosity for each porosity laminate sys e present work, the addition of PMMA in raw tem can also be evaluated by considering the amount of ceramic powders is found to be an easy and effective porous volume fraction in each system. The final energy way to generate uniform porosities in porous ceramic absorbed for the various systems was calculated and materials. Ceramic layered systems with interlayers of presented in Table 4 and Fig. 6. It can be seen that the different porosities were successfully fabricated. Theo energy variation trend estimated is in good agreement retical models on crack deflection criteria for layered with that from the experimental determined fracture systems reported in the literature were studied and energy values. With no crack deflection, the 30.2% compared with the present experimental results. It is interlayer porosity sample experienced a decrease in found that pore interaction effect in the porous inter- fracture energy compared to the monolithic sample. layers cannot be neglected. It is also shown that an However, as crack deflection started to occur, the increase of porosity in the porous interlayers promotes enhancement in energy from longer crack path has crack deflection, and hence the fracture toughness of the resulting in an overall improvement in systems fracture system. However, as the porosity in the porous inter nergy. Nevertheless, the increasing trend stops after layers increases beyond a critical volume fraction, the 57.6 porosity interlayer system, as beyond this point, the overall system will be weakened due to the large amount amount of crack deflection shown almost no increase. of porosity introduced and finally result in a decrease in As a result, the reduction of the energy due to higher the fracture toughness. Despite that, it is noted that porosity took over in significance, resulted in sub systems that promote crack deflection will possess sequent decrease in overall fracture energy level. It higher fracture toughness than that of the monolithic hould be noted that despite the observation of a sample
results obtained. The averaged crack deflection length for various porosity laminates were first estimated using the SEM micrographs, and the factor increase compared to that without crack deflection can then be computed. Using results from Table 2, the reduction in energy due to porosity for each porosity laminate system can also be evaluated by considering the amount of porous volume fraction in each system. The final energy absorbed for the various systems was calculated and presented in Table 4 and Fig. 6. It can be seen that the energy variation trend estimated is in good agreement with that from the experimental determined fracture energy values. With no crack deflection, the 30.2% interlayer porosity sample experienced a decrease in fracture energy compared to the monolithic sample. However, as crack deflection started to occur, the enhancement in energy from longer crack path has resulting in an overall improvement in system’s fracture energy. Nevertheless, the increasing trend stops after 57.6 porosity interlayer system, as beyond this point, the amount of crack deflection shown almost no increase. As a result, the reduction of the energy due to higher porosity took over in significance, resulted in subsequent decrease in overall fracture energy level. It should be noted that despite the observation of a decrease in the fracture energy of the layered system from 57.6% to 65.2% of interlayer porosity, the fracture energy of the system at 65.2% interlayer porosity is still much higher than that of the monolithic sample (400% higher). As a result, in general, it can be concluded that crack deflection mechanism significantly enhances the fracture toughness of the component. It is also noted in the process that the porous interlayer systems studied in the present work are different from that introduced by Clegg et al.1 ; as in the present systems, there exists two contributing mechanisms, namely, crack deflection and porosity. Although the porosity has shown to be fracture energy deteriorating factor, it should be noted that it could be an essential parameter when strength to weight ratio is concerned. 4. Conclusions In the present work, the addition of PMMA in raw ceramic powders is found to be an easy and effective way to generate uniform porosities in porous ceramic materials. Ceramic layered systems with interlayers of different porosities were successfully fabricated. Theoretical models on crack deflection criteria for layered systems reported in the literature were studied and compared with the present experimental results. It is found that pore interaction effect in the porous interlayers cannot be neglected. It is also shown that an increase of porosity in the porous interlayers promotes crack deflection, and hence the fracture toughness of the system. However, as the porosity in the porous interlayers increases beyond a critical volume fraction, the overall system will be weakened due to the large amount of porosity introduced and finally result in a decrease in the fracture toughness. Despite that, it is noted that systems that promote crack deflection will possess higher fracture toughness than that of the monolithic sample. Table 4 Total energy absorbed estimation in various layered systems Porosity Vp (%) Crack length L (mm) Factor increase due to crack deflection (L/L0) Crack deflection energy Ed (J/m2 ) Energy reduction due to porosity El (J/m2 ) Energy absorbed Ea (J/m2 ) Dense 3.0 1.00 – – 62.3 30.2 3.2 1.07 66.5 11.1 55.4 39.8 4.1 1.37 85.1 20.0 65.1 48.7 5.8 1.93 120.5 23.2 97.3 57.6 9.1 3.03 189.0 24.5 164.5 65.2 9.1 3.03 189.0 25.7 163.3 Fig. 6. Final energy absorbed in the layered systems as a function of interlayer porosity estimated after considering the effect from crack deflection length and porosity. 830 J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831
J Ma et al. Journal of the European Ceramic Society 24(2004)825-831 References 9. He. Y. M.. Bartlett. A. Evans. A. G. and Hutchinson, J. W. Kinking of a crack out of an interface: role of in-plane stress. J. 1. Clegg endall, K. Alford. N. M. Birchall, J. D. and Am. Ceran.Soc.1991,74.767-771 Button, T.W., A simple way to make tough ceramics. Nature. 10. Mammoli, A. A. Graham, A. L. Reimanis, I. E and Tullock 1990,347,455-457 D. L, The effect of flaws on the propagation of cracks at bi 2. Blanks, K.s., Kristoffersson. A, Carlstrom. E and Clegg. w.J materials interfaces. Acta Mater. 1995.. 1149-1156 Crack deflection in ceramic laminates using porous interlayers.J. 11. Davis. J. B. Kristoffersson, A. Carlstrom, E and Clegg. w.J Eur.cerm.Soc.1998,18,1945-1951. Fabrication and crack deflection in ceramic laminates with por- 3. Kendall. K. Transition between cohesive and interfacial failure interlayers. J. Am. Ceram. Soc., 2000. 8. 2369-2374 n a laminate. Proc. R. Soc. London. 1975. A344. 287-302. 12. Kellett, B J and Lange, F. F, Thermodynamics of densification 4. He M. Y. and Hutchinson. J. w. Crack deflection at an inter- sintering of simple particle arrays, equilibrium configurations, pore face between dissimilar elastic materials. Int. Solids Struct stability, and shrinkage. J. Am. Cera. Soc., 1989. 72. 725-734. 1989,25,1053-1067 13. Kingery, W.D. and Francois, B, The sintering of crystallin 5. Martinez, D and Gupta, V. Energy criterion for crack deflection ides, I. interactions between grain boundaries and pores. In at an interface between two orthotropic media. J. Mech. Phys. Sintering and Related Phenomena, ed. G. C. Kuczynski Solids.1994.42.1247-1271 N. A. Hooton and C. F. Gibbon. Gordon and Breach Science In Key Engineering Materials, Vol 116-117. ed. T. w. Clyne. 14. Lange, F. F. Sinterability of agglomerated powders. J. Am Trans Tech. Publications. Aedersmannsdorf. Switzerland. 1996 Ceran.Soc.1984,67,83-89 93-208. 15. He, Y. M. and Hutchinson, J. W.. Kinking of a crack out of an 7. Lee, W., Howard, S. J. and Clegg. W.J.. Growth of interface interface. J. App. Mech., 1989, 56, 270-278 defects and its effect on crack deflection and toughening criteria. 16. Clegg, w.J., Design of ceramic laminates for structural applica- Acta mater,1996,44,3905-3922 ns. Mater. Sci. Tech. 1998. 14. 483-495. 8. Cook. J. and Gordon. J. E. A mechanism for the control of 17. Sida, G.R., On the determination of stress intensity factors for crack propagation in all-brittle systems. Proc. R. Soc. London me common structural fract. Mech. 2 Problems. 1970. En 1964,A282,508-520
References 1. Clegg, W. J., Kendall, K., Alford, N. M., Birchall, J. D. and Button, T. W., A simple way to make tough ceramics. Nature, 1990, 347, 455–457. 2. Blanks, K. S., Kristoffersson, A., Carlstrom, E. and Clegg, W. J., Crack deflection in ceramic laminates using porous interlayers. J. Eur. Ceram. Soc., 1998, 18, 1945–1951. 3. Kendall, K., Transition between cohesive and interfacial failure in a laminate. Proc. R. Soc. London, 1975, A344, 287–302. 4. He, M. Y. and Hutchinson, J. W., Crack deflection at an interface between dissimilar elastic materials. Int. J. Solids Struct., 1989, 25, 1053–1067. 5. Martinez, D. and Gupta, V., Energy criterion for crack deflection at an interface between two orthotropic media. J. Mech. Phys. Solids, 1994, 42, 1247–1271. 6. Lee, W. and Clegg, W. J., The deflection of cracks at interfaces. In Key Engineering Materials, Vol 116–117, ed. T. W. Clyne. Trans Tech. Publications, Aedersmannsdorf, Switzerland, 1996, pp. 193–208. 7. Lee, W., Howard, S. J. and Clegg, W. J., Growth of interface defects and its effect on crack deflection and toughening criteria. Acta Mater., 1996, 44, 3905–3922. 8. Cook, J. and Gordon, J. E., A mechanism for the control of crack propagation in all-brittle systems. Proc. R. Soc. London, 1964, A282, 508–520. 9. He, Y. M., Bartlett, A., Evans, A. G. and Hutchinson, J. W., Kinking of a crack out of an interface: role of in-plane stress. J. Am. Ceram. Soc., 1991, 74, 767–771. 10. Mammoli, A. A., Graham, A. L., Reimanis, I. E. and Tullock, D. L., The effect of flaws on the propagation of cracks at bimaterials interfaces. Acta Mater., 1995, 43, 1149–1156. 11. Davis, J. B., Kristoffersson, A., Carlstrom, E. and Clegg, W. J., Fabrication and crack deflection in ceramic laminates with porous interlayers. J. Am. Ceram. Soc., 2000, 8, 2369–2374. 12. Kellett, B. J. and Lange, F. F., Thermodynamics of densification: sintering of simple particle arrays, equilibrium configurations, pore stability, and shrinkage. J. Am. Ceram. Soc., 1989, 72, 725–734. 13. Kingery, W. D. and Francois, B., The sintering of crystalline oxides, I.: interactions between grain boundaries and pores. In Sintering and Related Phenomena, ed. G. C. Kuczynski, N. A. Hooton and C. F. Gibbon. Gordon and Breach Science Publisher, NY, 1967. 14. Lange, F. F., Sinterability of agglomerated powders. J. Am. Ceram. Soc., 1984, 67, 83–89. 15. He, Y. M. and Hutchinson, J. W., Kinking of a crack out of an interface. J. App. Mech., 1989, 56, 270–278. 16. Clegg, W. J., Design of ceramic laminates for structural applications. Mater. Sci. Tech., 1998, 14, 483–495. 17. Isida, G. R., On the determination of stress intensity factors for some common structural Fract. Mech., 2 Problems, 1970, Eng, 61–79. J. Ma et al. / Journal of the European Ceramic Society 24 (2004) 825–831 831