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 Youngs592 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. Mono￾lithic 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 measure￾ment 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 determina￾tion 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. An￾other reason for this choice was that, analysing the results of an European round robin test, Damani et al.16 have con￾cluded that this method seemed to deliver the most repro￾ducible results. The toughness was calculated from the mea￾surement 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 rela￾tion: 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 measure￾ments of the toughness and Young’s modulus from the re￾lation: 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 de￾termination 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