Availableonlineatwww.sciencedirect.com DIRECT E噩≈3S SEVIER Journal of the European Ceramic Society 25(2005)589-597 www.elsevier.com/locate/jeurceramsoc Mechanical properties and mechanical behaviour of Sic dense-porous laminates C. Reynaud a F. Thevenot a T. Chartier b, *.J.-L. Besson b Dept. Ceramiques Speciales, E.N.S. des Mines de Saint-Etienne, 42023 Saint-Etienne, france b SPCTS, U.M.R. C.N.R.S. 6638, E.N.S. de Ceramiques Industrielles, 87065 Limoges, france Received 3 December 2003; received in revised form 23 February 2004; accepted 28 February 2004 Available online 15 June 2004 Abstract Porous laminar materials and alternate laminates of silicon carbide dense and porous layers have been elaborated by tape casting and liquid phase sintering processing. Porosity was introduced by incorporation of pore forming agents(corn starch or graphite platelets) in the slurry. Homogeneous distributions of porosity have been obtained for both monolithic and composite laminates. The microstructure of the SiC matrix was equiaxed and was not affected by the porosity. The porosity(P) dependence of Young s modulus(e), modulus of rupture(or), toughness (Kic)and fracture energy(Gic)was found to be well described on the entire range of porosity by relations of the form Xo(1-P)x proposed by Wagh et al. from a model that takes into account the tortuosity of the porosity In the case of our materials, mE= 2.7, mog Kic= mE +0.5 and mGIc =mE+ 1. All the ex-corn starch composites behaved in a brittle manner, even those having weak interlayers with a porosity content higher than the critical value of about 0. 4 predicted by the model developed by Blanks et al. A non-purely brittle behaviour started to be obtained with ex-graphite laminar composites in which the pores are elongated and oriented parallel to the interfaces Keywords: Composites; Porosity; Mechanical properties; SiC; Laminates 1. Introduction As a necessary condition for the interfacial material that it must be chemically compatible with the material of Among the strategies developed to improve the flaw tol- the strong layers, Clegg and co-workers studied ceramic erance of non-transforming ceramics, the designing of lami- laminates with alternating dense and porous layers made nar structures with weak interfaces or interphases promoting of silicon carbide or alumina. This approach has also the crack deflection mechanisms have proved to be a successful advantage of avoiding the building up of any internal stresses way to increase fracture energy. The weak interfaces most due to difference in thermal expansion coefficients which mmonly used are either graphite or boron nitride. 2,3 For can be the source of delamination during cooling. 9 instance, in the case of graphite interfaces, Clegg et al. have According to theoretical analysis by He and Hutchinson obtained an apparent toughness and a fracture energy re- of the kinking of a crack out of an interface, 0 crack deflec- spectively 5 and 200 times higher than the typical values of tion is to occur when the ratio between the fracture energy monolithic a-SiC. However, since graphite and boron ni- of the homogeneous weak interphase, Gi, and the fracture tride have a low oxidation resistance and cannot be used at energy of the strong layer, Gs, is lower than 0.57. However high temperature in oxidising atmosphere without a protec- in the case of dense-porous laminates, the porous layer is tive barrier, other systems have been investigated, specially inhomogeneous, and the fracture energy to be considered is with oxidation resistant weak interphases such as monazite, 4 that of the ligament of matter between the crack and the pore fluorophlogopite or MoSi2+ Mo2 B5.6 ahead of it, Glig?. Than the criterion for crack deflection in the weak interphase becomes Glig/Gs <0.57. Though these ligaments of matter are made of the same material as Corresponding author the dense layers, and might be expected to have the same E-mail address: t chartier(aensci fr (T. Chartier). fracture energy, theoretical analyses show that if the tip of a 0955-2219/s-see front matter o 2004 Published by Elsevier Ltd doi: 10.1016/j jeurceramsoc 2004.02.009
Journal of the European Ceramic Society 25 (2005) 589–597 Mechanical properties and mechanical behaviour of SiC dense-porous laminates C. Reynaud a, F. Thévenot a, T. Chartier b,∗, J.-L. Besson b a Dept. Céramiques Spéciales, E.N.S. des Mines de Saint-Etienne, 42023 Saint-Etienne, France b S.P.C.T.S., U.M.R. C.N.R.S. 6638, E.N.S. de Céramiques Industrielles, 87065 Limoges, France Received 3 December 2003; received in revised form 23 February 2004; accepted 28 February 2004 Available online 15 June 2004 Abstract Porous laminar materials and alternate laminates of silicon carbide dense and porous layers have been elaborated by tape casting and liquid phase sintering processing. Porosity was introduced by incorporation of pore forming agents (corn starch or graphite platelets) in the slurry. Homogeneous distributions of porosity have been obtained for both monolithic and composite laminates. The microstructure of the SiC matrix was equiaxed and was not affected by the porosity. The porosity (P) dependence of Young’s modulus (E), modulus of rupture (σR), toughness (K1C) and fracture energy (G1C) was found to be well described on the entire range of porosity by relations of the form X0(1 − P)mX proposed by Wagh et al. from a model that takes into account the tortuosity of the porosity. In the case of our materials, mE = 2.7, mσR = mK1C = mE + 0.5 and mG1C = mE + 1. All the ex-corn starch composites behaved in a brittle manner, even those having weak interlayers with a porosity content higher than the critical value of about 0.4 predicted by the model developed by Blanks et al. A non-purely brittle behaviour started to be obtained with ex-graphite laminar composites in which the pores are elongated and oriented parallel to the interfaces. © 2004 Published by Elsevier Ltd. Keywords: Composites; Porosity; Mechanical properties; SiC; Laminates 1. Introduction Among the strategies developed to improve the flaw tolerance of non-transforming ceramics, the designing of laminar structures with weak interfaces or interphases promoting crack deflection mechanisms have proved to be a successful way to increase fracture energy. The weak interfaces most commonly used are either graphite1 or boron nitride.2,3 For instance, in the case of graphite interfaces, Clegg et al. have obtained an apparent toughness and a fracture energy respectively 5 and 200 times higher than the typical values of monolithic -SiC.1 However, since graphite and boron nitride have a low oxidation resistance and cannot be used at high temperature in oxidising atmosphere without a protective barrier, other systems have been investigated, specially with oxidation resistant weak interphases such as monazite,4 fluorophlogopite5 or MoSi2 + Mo2B5. 6 ∗ Corresponding author. E-mail address: t.chartier@ensci.fr (T. Chartier). As a necessary condition for the interfacial material is that it must be chemically compatible with the material of the strong layers, Clegg and co-workers studied ceramic laminates with alternating dense and porous layers made of silicon carbide7 or alumina.8 This approach has also the advantage of avoiding the building up of any internal stresses due to difference in thermal expansion coefficients which can be the source of delamination during cooling.9 According to theoretical analysis by He and Hutchinson of the kinking of a crack out of an interface,10 crack deflection is to occur when the ratio between the fracture energy of the homogeneous weak interphase, Gi, and the fracture energy of the strong layer, GS, is lower than 0.57. However, in the case of dense-porous laminates, the porous layer is inhomogeneous, and the fracture energy to be considered is that of the ligament of matter between the crack and the pore ahead of it, Glig7. Than the criterion for crack deflection in the weak interphase becomes Glig/GS < 0.57. Though these ligaments of matter are made of the same material as the dense layers, and might be expected to have the same fracture energy, theoretical analyses show that if the tip of a 0955-2219/$ – see front matter © 2004 Published by Elsevier Ltd. doi:10.1016/j.jeurceramsoc.2004.02.009
C. Reynaud et al. /Joumal of the European Ceramic Sociery 25 (2005)589-592 growing crack comes sufficiently close to a microcrack or De tip of th tic parameters of the two PFAs used increased and then, the apparent fracture energy of the liga- ment is reduced This reduction varies with the relative den- GP Blanks et al derived a minimum level of porosity equal to 37% to ensure Corn starch Graphite platelet ds0=14μm 8m×8pmx3um crack deflection, in good agreement with their experimental Aspect ratio 67 results for silicon carbide. Assuming that the fracture energy of the dense ligament is related to that of the porous layer GP, by the relation cosity and the rheological behaviour of the slurry and com- plement one another to produce handleable ceramic tapes Glig 1-P (1) The optimum concentrations for the binder and the plasti cizer were determined to be 8wt% for both additives on where P is the volume fraction of porosity, Davis et al. 8ex- the base of the ceramic powder. The third step corresponds pressed the criterion for continued crack deflection in terms to the incorporation, into the suspension, of the pore form- of easily measurable variables ing agent(PFA): corn starch(Roquette-France)or graphite platelets (Union Carbide-US)(Table 1). The PFA volume 0.57(1-P) (2) fraction, referred to the sum of the ceramic volume and pFA G volume, was 45 and 50% for graphite platelets and varied The experimental results obtained by Clegg's group with from 5 to 55% for corn starch. We were unable to fabricate ther alumina or silicon carbide were consistent with re- sound parts when larger PFA volume fraction were incor lation(2), crack deflection being observed when the ratio porated. A mixing time of 3.5 h leads to an uniform distri Gp/Gs falls under the line 0.57(1-P), that occurs for a bution of the PFA. Finally the slurry was de-aired at a low lume fraction of porosity of 0.37 rotation speed during 24 h The aim of the work presented in this paper was to deter Then the slurries were tape cast onto a Mylar" film using mine the porosity dependence of the mechanical properties a moving double blade device on a laboratory tape casting of a SiC material densified by liquid phase sintering on a bench(Elmeceram-France ). The tapes had smooth surfaces wide range of porosity, and to compare the mechanical be- and uniform thicknesses, which could be varied between haviour of dense-porous laminates to that obtained by Blanks 100 and 150 um. Sheets were punched in the green tapes et al. for silicon carbide densified by solid state sintering and stacked on each other using two types of stacking se- quence: (i) stacking of identical layers to obtain monolithic dense or porous specimens, and(ii) alternate stacking of 2. Processing and materials microstructure PFA free and PFA containing layers to obtain symmetrical dense/porous laminar composites. The outer layers were al 2. 1. Processing ways dense layers. The number of tapes was chosen to lead to a final thickness of about 3-4 mm after sintering. The The materials were made by stacking layers obtained by thickness of the layers was varied by stacking several tapes tape casting and co-sintering. The ceramic powder must of the same nature. This led to different architectures that al- ave a narrow particle size distribution and a rather low lowed to study the influence of the dense to porous thickness mean diameter dso was 1 um for the starting a-SiC powder ratio (Sika Tech FCP13, Norton-Norway) and the specific sur- After stacking, the specimens were pressed under 60 MPa face area(BEt)was 13 m/g. The densification aids(5 wt. at 65C. The burnout of organics was performed by heat- of the total ceramic content) for the liquid phase sinter ing very slowly(6 C/h)up to 550oC in air. Sintering was ing of SiC were Y203(Rhone-Poulenc-France)and Al203 conducted in a graphite furnace (VAS, France)under ar- (CR15 Baikowski-France)in a ratio corresponding to the gon at atmospheric pressure during I h at 1950C. The rel- YAG-Al2O3 eutectic composition(40 wt. Y203-60 wt ative density of the PFA free monolithic specimens was AlO3) 98% The first step of the elaboration of the suspensions for tape-casting consists in the dispersion of the ceramic pow- 2. 2. Microstructure ders in a solvent containing a dispersant. This was performed by planetary milling with alumina balls during 4 h in the a detailed description of the sintered microstructures of MEK -ethanol azeotrope containing 0.6wt. of a phosphate the monolithic and laminated Sic materials have been al ester(CP213, Cerampilot-France). Then, an acrylic binder ready published. So, only the main results will be briefly (Degalan" LP51701, Rohm and Haas-US) and a phtalate eported here plasticizer (DPB, Prolabo-France)were added to the suspen The microstructures were homogeneous. and in the case sion and mixed during 16h. They allow to optimise the vis- of the laminar composites, the layers were parallel with an
590 C. Reynaud et al. / Journal of the European Ceramic Society 25 (2005) 589–597 growing crack comes sufficiently close to a microcrack11 or a pore,12 the stress intensity factor at the tip of the crack is increased and then, the apparent fracture energy of the ligament is reduced. This reduction varies with the relative density, and for a cubic array of spherical pores, Blanks et al.7 derived a minimum level of porosity equal to 37% to ensure crack deflection, in good agreement with their experimental results for silicon carbide. Assuming that the fracture energy of the dense ligament is related to that of the porous layer, GP, by the relation: Glig = GP 1 − P (1) where P is the volume fraction of porosity, Davis et al.8 expressed the criterion for continued crack deflection in terms of easily measurable variables: GP GS < 0.57(1 − P) (2) The experimental results obtained by Clegg’s group with either alumina or silicon carbide were consistent with relation (2), crack deflection being observed when the ratio GP/GS falls under the line 0.57(1 − P), that occurs for a volume fraction of porosity of 0.37. The aim of the work presented in this paper was to determine the porosity dependence of the mechanical properties of a SiC material densified by liquid phase sintering on a wide range of porosity, and to compare the mechanical behaviour of dense-porous laminates to that obtained by Blanks et al.7 for silicon carbide densified by solid state sintering. 2. Processing and materials microstructure 2.1. Processing The materials were made by stacking layers obtained by tape casting and co-sintering. The ceramic powder must have a narrow particle size distribution and a rather low mean diameter d50 was 1m for the starting -SiC powder (Sika Tech FCP13, Norton-Norway) and the specific surface area (BET) was 13 m2/g. The densification aids (5 wt.% of the total ceramic content) for the liquid phase sintering of SiC were Y2O3 (Rhone-Poulenc-France) and Al2O3 (CR15 Ba¨ıkowski-France) in a ratio corresponding to the YAG–Al2O3 eutectic composition (40 wt.% Y2O3–60 wt.% Al2O3). The first step of the elaboration of the suspensions for tape-casting consists in the dispersion of the ceramic powders in a solvent containing a dispersant. This was performed by planetary milling with alumina balls during 4 h in the MEK-ethanol azeotrope containing 0.6 wt.% of a phosphate ester (CP213, Cerampilot-France). Then, an acrylic binder (Degalan® LP51/01, Röhm and Haas-US) and a phtalate plasticizer (DPB, Prolabo-France) were added to the suspension and mixed during 16 h. They allow to optimise the visTable 1 Characteristic parameters of the two PFAs used PFA CS GP Chemical nature Corn starch Graphite platelet Dimension d50 = 14 m 8m × 8m × 3m Aspect ratio 1.2 2.67 cosity and the rheological behaviour of the slurry and complement one another to produce handleable ceramic tapes. The optimum concentrations for the binder and the plasticizer were determined to be 8 wt.% for both additives on the base of the ceramic powder. The third step corresponds to the incorporation, into the suspension, of the pore forming agent (PFA): corn starch (Roquette-France) or graphite platelets (Union Carbide-US) (Table 1). The PFA volume fraction, referred to the sum of the ceramic volume and PFA volume, was 45 and 50% for graphite platelets and varied from 5 to 55% for corn starch. We were unable to fabricate sound parts when larger PFA volume fraction were incorporated. A mixing time of 3.5 h leads to an uniform distribution of the PFA. Finally the slurry was de-aired at a low rotation speed during 24 h. Then the slurries were tape cast onto a Mylar® film using a moving double blade device on a laboratory tape casting bench (Elmeceram-France). The tapes had smooth surfaces and uniform thicknesses, which could be varied between 100 and 150m. Sheets were punched in the green tapes and stacked on each other using two types of stacking sequence: (i) stacking of identical layers to obtain monolithic dense or porous specimens, and (ii) alternate stacking of PFA free and PFA containing layers to obtain symmetrical dense/porous laminar composites. The outer layers were always dense layers. The number of tapes was chosen to lead to a final thickness of about 3–4 mm after sintering. The thickness of the layers was varied by stacking several tapes of the same nature. This led to different architectures that allowed to study the influence of the dense to porous thickness ratio. After stacking, the specimens were pressed under 60 MPa at 65 ◦C. The burnout of organics was performed by heating very slowly (6 ◦C/h) up to 550 ◦C in air. Sintering was conducted in a graphite furnace (VAS, France) under argon at atmospheric pressure during 1 h at 1950 ◦C. The relative density of the PFA free monolithic specimens was 98%. 2.2. Microstructure A detailed description of the sintered microstructures of the monolithic and laminated SiC materials have been already published.13 So, only the main results will be briefly reported here. The microstructures were homogeneous, and in the case of the laminar composites, the layers were parallel with an
C. Reynaud et al. /Journal of the European Ceramic Society 25(2005)589-597 50 um 50 um Fig. 2. Optical micrographs showing the morphology of the porosity.(a) Monolithic laminate, (b) laminar composite Fig. 1 SEM micrographs; grain microstructure revealed by plasma etcl (a) Dense SiC,(b) porous SiC obtained by the incorporation of 45 tween the porous monoliths and the corresponding porous layers in the laminates remained low, that allowed the prop- erties of the porous layers to be obtained from tests on their monolithic counterparts without introducing a noticeable uniform thickness. The thickness was about 70 um for the error dense layers, 80-90 um for the ex-corn starch porous layers and 20-30 um for the porous layers where graphite platelets were used. No migration of pores from porous to dense lay ers was observed. Dense layers and skeletons in the porous layers were constituted by the same homogeneous, fine and 20um equiaxed microstructure with a mean equivalent diameter of about 1.25 um(Fig. 1). The pore characteristics were the same in the porous layers of the laminates and in their monolithic counterparts(Fig. 2). Whereas the pores intro- duced by corn starch had a low aspect ratio, those coming from graphite platelets were elongated and mostly oriented rallel to the interfaces(Fig. 3). The porosity of the mono- liths reached a maximum and levelled off for corn starch amounts higher than 40%. When the porous layers were co-sintered with dense layers, the amount of final porosity followed the law established by Slamovich and Lange+for thermodynamically stable pores shrinking the same amount as the matrix(Fig. 4). The lower shrinkage of the dense lay ers introduced tensile internal stresses in the highest porous Fig. 3. Optical micrograph showing the morphology of the porosity re- layers. However, the difference in volumetric shrinkage be- sulting from the incorporation of 50 vol. of graphite platelets
C. Reynaud et al. / Journal of the European Ceramic Society 25 (2005) 589–597 591 Fig. 1. SEM micrographs; grain microstructure revealed by plasma etching. (a) Dense SiC, (b) porous SiC obtained by the incorporation of 45 vol.% corn starch. uniform thickness. The thickness was about 70 m for the dense layers, 80–90 m for the ex-corn starch porous layers and 20–30m for the porous layers where graphite platelets were used. No migration of pores from porous to dense layers was observed. Dense layers and skeletons in the porous layers were constituted by the same homogeneous, fine and equiaxed microstructure with a mean equivalent diameter of about 1.25 m (Fig. 1). The pore characteristics were the same in the porous layers of the laminates and in their monolithic counterparts (Fig. 2). Whereas the pores introduced by corn starch had a low aspect ratio, those coming from graphite platelets were elongated and mostly oriented parallel to the interfaces (Fig. 3). The porosity of the monoliths reached a maximum and levelled off for corn starch amounts higher than 40%. When the porous layers were co-sintered with dense layers, the amount of final porosity followed the law established by Slamovich and Lange14 for thermodynamically stable pores shrinking the same amount as the matrix (Fig. 4). The lower shrinkage of the dense layers introduced tensile internal stresses in the highest porous layers. However, the difference in volumetric shrinkage beFig. 2. Optical micrographs showing the morphology of the porosity. (a) Monolithic laminate, (b) laminar composite. tween the porous monoliths and the corresponding porous layers in the laminates remained low, that allowed the properties of the porous layers to be obtained from tests on their monolithic counterparts without introducing a noticeable error. Fig. 3. Optical micrograph showing the morphology of the porosity resulting from the incorporation of 50 vol.% of graphite platelets.
C. Reynaud et al. /Joumal of the European Ceramic Sociery 25 (2005)589-592 E 000 , 0102030405060 Pore Forming Agent (%o) 5101520 Fig. 4. Volume fraction of porosity after sintering vs PFA content. Mono- Square root of the notch radius(um) lithic laminates:(O)corn starch; laminar composites: (O)corn starch, Fig. 5. Dependence of toughness measured by the SENB-s method (A)graphite platelets. The dotted line corresponds to the equation from the square root of the notch radius for dense monolithic laminates.The Slamovich and Lange. 4 The solid line corresponds to the critical porosity doted curve corresponds to Eq (5)with Y= 1. 12 and Sa= 10 um for crack deflection according to Refs. 7, 8 ness, Kic, is related to the measured toughness by the rela 3. Experimental procedures tanh 2) Youngs modulus, E, was calculated from the measure- ment of the velocity of longitudinal, VL, and shear, Vs ultrasonic waves using a pulse echo overlap technique in where y is a geometric correction factor and da is the size the approximation of an homogeneous isotropic infinite finite of the small defect at the notch-tip, under the influence of the stress interaction field of the notch In order to assess if it was possible to use Eq. (5)for 3V-4v the correction of our experimental data, the toughness of VS 22 (3) Sic dense monolith was measured for three different root radii (100, 300 and 1000 um) and fitted by Eq. (5). In the where p is the density case of this dense, fine grained material, the defect at the The modulus of rupture, OR, was measured in 3-point notch-tip was assumed to result from machining, i.e., an edge bending at a cross-head speed of 0. 2 mm/min crack configuration(r= 1. 12)and machining scratches, The experimental method for the toughness determina- &a, of 10 um were adopted. 6 Fig. 5 shows that a goo tion must be applicable to highly porous materials, that agreement was obtained, giving an extrapolated value atr eliminates indentation based methods. So, the single edge 0 of 3.82 MPam/, which falls nicely in the values between notch beam-saw cut method(SENB-S)was selected. An- 3 and 4 MPam/2 usually obtained for a-SiC with this kind other reason for this choice was that, analysing the results of microstructure In the case of the porous monoliths, the of an European round robin test, Damani et al. 6 have con- crack defects at the notch-tip were assumed to have also an cluded that this method seemed to deliver the most repro- edge crack configuration and their size was taken equal to ducible results. The toughness was calculated from the mea- 10 um or to the mean average Feret diameter of the porosity surement of the modulus of rupture in 3-point bending and when it was greater than 10 um. 8 the depth of the initial notch, a, according to the following The fracture energy was calculated from the measure- ments of the toughness and Young's modulus from the re- lation k器=[4(= IC here w is the height of the sample and A; are coefficients given by: Ao=1.9+0.0075L/; A1=-339+0.08L/w, 4. Mechanical properties A2=154-0.2175Lhw;A3=-26.24+0.1825Lh;A4= 2638-0. 145L/ with L being the span The experimental data for dense and porous monoliths are However, this method leads to an overestimated value of reported in Fig. 6. Seven specimens were used for the de- the toughness when the notch root value, r, is larger than a termination of the modulus of rupture and of the toughness critical value of the order of a few microns. Damani et al. 16 The data were fitted by a(1- Py form, since Blanks suggested and verified experimentally that the true tough- et al. have obtained for SiC a good description of Youngs
592 C. Reynaud et al. / Journal of the European Ceramic Society 25 (2005) 589–597 0 10 20 30 40 50 0 10 20 30 40 50 60 Pore Forming Agent (%) Porosity (%) Fig. 4. Volume fraction of porosity after sintering vs. PFA content. Monolithic laminates: () corn starch; laminar composites: () corn starch, () graphite platelets. The dotted line corresponds to the equation from Slamovich and Lange.14 The solid line corresponds to the critical porosity for crack deflection according to Refs. 7,8. 3. Experimental procedures Young’s modulus, E, was calculated from the measurement of the velocity of longitudinal, VL, and shear, VS, ultrasonic waves using a pulse echo overlap technique in the approximation of an homogeneous isotropic infinite medium:15 E = ρV2 S 3V2 L − 4V2 S V2 L − V2 S (3) where ρ is the density. The modulus of rupture, σR, was measured in 3-point bending at a cross-head speed of 0.2 mm/min. The experimental method for the toughness determination must be applicable to highly porous materials, that eliminates indentation based methods. So, the single edge notch beam-saw cut method (SENB-S) was selected. Another reason for this choice was that, analysing the results of an European round robin test, Damani et al.16 have concluded that this method seemed to deliver the most reproducible results. The toughness was calculated from the measurement of the modulus of rupture in 3-point bending and the depth of the initial notch, a, according to the following equation:17 KSENB 1C = σR √a 4 i=0 Ai a w i (4) where w is the height of the sample and Ai are coefficients given by: A0 = 1.9 + 0.0075L/w; A1 = −3.39 + 0.08L/w; A2 = 15.4−0.2175L/w; A3 = −26.24+0.1825L/w; A4 = 26.38 − 0.145L/w with L being the span. However, this method leads to an overestimated value of the toughness when the notch root value, r, is larger than a critical value of the order of a few microns. Damani et al.16 suggested and verified experimentally that the true tough- 0 2 4 6 8 10 12 14 0 5 10 15 20 25 Square root of the notch radius (µm1/2) Toughness (MPa.m1/2 ) Fig. 5. Dependence of toughness measured by the SENB-S method on the square root of the notch radius for dense monolithic laminates. The doted curve corresponds to Eq. (5) with Y = 1.12 and a = 10 m. ness, KT 1C, is related to the measured toughness by the relation: KT 1C = KSENB 1C tanh 2Y a r (5) where Y is a geometric correction factor and a is the size of the small defect at the notch-tip, under the influence of the stress interaction field of the notch. In order to assess if it was possible to use Eq. (5) for the correction of our experimental data, the toughness of SiC dense monolith was measured for three different root radii (100, 300 and 1000 m) and fitted by Eq. (5). In the case of this dense, fine grained material, the defect at the notch-tip was assumed to result from machining, i.e., an edge crack configuration (Y = 1.12) and machining scratches, a, of 10 m were adopted.16 Fig. 5 shows that a good agreement was obtained, giving an extrapolated value at r = 0 of 3.82 MPa m1/2, which falls nicely in the values between 3 and 4 MPa m1/2 usually obtained for -SiC with this kind of microstructure. In the case of the porous monoliths, the crack defects at the notch-tip were assumed to have also an edge crack configuration and their size was taken equal to 10m or to the mean average Féret diameter of the porosity ˆ when it was greater than 10 m.18 The fracture energy was calculated from the measurements of the toughness and Young’s modulus from the relation: G1C = K2 1C E (6) 4. Mechanical properties The experimental data for dense and porous monoliths are reported in Fig. 6. Seven specimens were used for the determination of the modulus of rupture and of the toughness. The data were fitted by a (1 − P) m form, since Blanks et al.7 have obtained for SiC a good description of Young’s
C. Reynaud et al. /Journal of the European Ceramic Society 25(2005)589-597 50 051015202530354045 051015202530354045 Porosity(vol%) Porosity(vol%) 3.5 30 3221100 051015202530354045 051015202530354045 Porosity (vol%) Porosity(vol%) Fig. 6. Dependence on porosity of the mechanical properties of monolithic laminates(PFA= CS).(a) Youngs modulus; (b)modulus of rupture;(c) toughness;(d) fracture energy. The solid lines correspond to the best fit with Wagh's equations modulus with Ep= Eo(1-P)2. Such an equation was also Wagh et al. this value of 2 is characteristic of ceramics established by Wagh et al. 19 for a model derived from an densified without additives or applied pressure. However, previous analytical one developed by Wong et al.20 in ef- for materials hot-pressed or densified using sintering aids forts to explain charge and mass transport through the ran- leading to an intergranular glassy phase, mE takes value dom pore structure of rocks. The assumed ceramic structure reater than 2 is a three-dimensional. intertwined continuous network of Wagh et al. 22 derived, for the fracture properties, power are interconnected by small channels oore i A 3 material chains and open-pore channels. This assumption is laws with different exponents connected together by based on the fact that it is possible to fabricate ceramics with a very high porosity, as high as 93%, and that oper mog=mIC =mE+0.5 and mGIc =mE+I exist even at very low porosity(6%). This is consistent with The results from fits done with the exponents put at their the mainly open nature of the porosity in the present mate- neoretical values are reported in Table 2. The correlation rials where the pores introduced by the factors are fairly good The model developed by Wagh et al. 9. that takes into The fitting parameters obtained using a classical mean account the tortuosity of the porosity, describes the whole square method, are reported in Table 2 set of our experimental data of the mechanical properties The mE parameter(2.68), is greater than the value of over the entire porosity range(from P=0%to P=42%) 2 obtained experimentally by Blanks et al. 7 According to and appears to be well adapted to the present porosity mor- Table 2 Fi ers for the mechanical properties using Wagh's model Property Correlation 5. Fracture behaviour 2.68±0.08 5.1. Experimental results 590±15 0.98 4.34±0.09 The fracture behaviour of the laminar composite (LC) 46.4±2.0 was studied in 3-point bending for unnotched and notche
C. Reynaud et al. / Journal of the European Ceramic Society 25 (2005) 589–597 593 Fig. 6. Dependence on porosity of the mechanical properties of monolithic laminates (PFA = CS). (a) Young’s modulus; (b) modulus of rupture; (c) toughness; (d) fracture energy. The solid lines correspond to the best fit with Wagh’s equations. modulus with EP = E0(1 − P)2. Such an equation was also established by Wagh et al.19 for a model derived from an previous analytical one developed by Wong et al.20 in efforts to explain charge and mass transport through the random pore structure of rocks. The assumed ceramic structure is a three-dimensional, intertwined, continuous network of material chains and open-pore channels. This assumption is based on the fact that it is possible to fabricate ceramics with a very high porosity, as high as 93%,21 and that open pores exist even at very low porosity (6%). This is consistent with the mainly open nature of the porosity in the present materials where the pores introduced by the pore forming agents are interconnected by small channels.13 The fitting parameters obtained using a classical mean square method, are reported in Table 2. The mE parameter (2.68), is greater than the value of 2 obtained experimentally by Blanks et al.7 According to Table 2 Fitting parameters for the mechanical properties using Wagh’s model Property Extrapolated at P = 0 m Correlation factor E (GPa) 407 ± 7 2.68 ± 0.08 0.995 σR (MPa) 590 ± 15 3.18 0.98 K1C (MPa m1/2) 4.34 ± 0.09 3.18 0.99 G1C (J/m2) 46.4 ± 2.0 3.68 0.96 Wagh et al. this value of 2 is characteristic of ceramics densified without additives or applied pressure. However, for materials hot-pressed or densified using sintering aids leading to an intergranular glassy phase, mE takes value greater than 2. Wagh et al.22 derived, for the fracture properties, power laws with different exponents connected together by: mσR = mK1C = mE + 0.5 and mG1C = mE + 1 The results from fits done with the exponents put at their theoretical values are reported in Table 2. The correlation factors are fairly good. The model developed by Wagh et al.19,22 that takes into account the tortuosity of the porosity, describes the whole set of our experimental data of the mechanical properties over the entire porosity range (from P = 0% to P = 42%) and appears to be well adapted to the present porosity morphology. 5. Fracture behaviour 5.1. Experimental results The fracture behaviour of the laminar composite (LC) was studied in 3-point bending for unnotched and notched