S. Bueno et al. /Journal of the European Ceramic Society 28 (2008)1961-1971 A10-1550 30 0000010020,030,040,05 Displacement [mm] Displacement [mm] the procedure followed for R-curve deter- Fig. 3. Characteristic load-displacement curves recorded during the SENVB mination and Jc calculation. 27 The curve correspond to the A10 composite ending tests. Specimens tested with an initial relative notch length a/w=0.5. sintered at 1550C and tested with a relative notch depth a/W=0.6.For R table fracture is observed for both composites and semi-stable fracture is determination, the arrow marks the point where the non-linear beha observed for both aluminas selected as the onset of crack propagation. From this point, the increments in the Ci+1). For Jic calculation(Eq. (5)), the areas under the curves corresponding for the monophase alumina specimens and only semi-stable frac- to specimen tested with the notch(A)and to an unnotched specimen(AE)are ture was obtained for a limited number of tests of specimens shown with relative notch depths of 0.5(Fig. 3). The introduction of larger notches led to the failure of the specimens during machin- the compliance( Ci, Ci+1, Fig 4). An example of the graphics used to calculate Jic is depicted in Fig 4 The fracture toughness parameters are summarized in For the monophase materials, the Kic values were lower Table 2. Kic values were calculated using Eq (1)and the values than those reported for aluminas with similar grain sizes of the maximum loads attained during the tests and Gic was (KIC 235-4. MPam/), determined from unstable tests 35-37 calculated according to Eq (3)from Kic values and Young's and, in some cases, using specimens with notch radii larger modulus(E, Table 1)and using the poisson ratio of dense and than those utilized in this work, o and similar to those deter- fine-grained alumina(v=0.22) mined by Sbaizero et al. 38(KIC MPam)for hot-pressed In order to determine the increments in crack length aluminas using stable fracture tests. As discussed by Bar-On et (Aa=di+1-ai)to build the R curves, the common criterion al., unstable crack extension results in apparent increases of relating the onset of crack propagation in the load-displacement fracture toughness values compared to those determined during curves with the point where the non-linear behaviour starts quasi-static crack growth. Therefore, the semi-stable crack prop- (arrow in Fig 4)18. 24. 34 was used. From this point, the increments agation obtained in this work for the alumina specimens(Fig 3) in crack length(Aa=ai+1-ai) would produce the changes in would give values closer to the actual fracture toughness Table 2 Fracture toughness parameters of the materials: critical stress intensity factor (Kic), critical energy releasing rate(Gic), critical J-integral (ic) and work of fracture (ywoF) KiC(S D )MPam/2 GIC(S D)(J/m-) JiC(S D )(/m-) JIC/GIC (SD) yWoF(SD)(J/m2) 29 1.0 2.8 196 189 1.0 A-1550 3.2(0.1) 26.2(0.7) 29.9(3.0) 1.1(0.1) 20.1(20)2 A10-1450 3.5(0.1) 384(0.8) 21(3.7) 1.1(0.1) 34.7(1.3) 3.5(0.2) 38.6(2.9) 1.1(0.1) 33.4(23) 3.5(0. 37.6(1.2) 45.9(3.3) 1.2(0.1) 35.1(1.7) A10-1550 33(0.1) 38.4(1.2) 50.8(6.0) 1.3(0.2) 40.6(1.2) 0.5 33(0.1) 374(26) 554(4.1) .5(0.1) 41.9(3.0) 0.6 33(0.2) 379(20) 53.1(2.3) .4(.1) 39.6(2.1) S D. standard deviation. For monophase alumina materials valid tests were obtained only with a relative notch depth of 0-5. The values of the two tests obtained on pecimens of alumina sintered at 1450C are shown Semi-stable tests1966 S. Bueno et al. / Journal of the European Ceramic Society 28 (2008) 1961–1971 Fig. 3. Characteristic load–displacement curves recorded during the SENVB bending tests. Specimens tested with an initial relative notch length a/W = 0.5. Stable fracture is observed for both composites and semi-stable fracture is observed for both aluminas. for the monophase alumina specimens and only semi-stable frac￾ture was obtained for a limited number of tests of specimens with relative notch depths of 0.5 (Fig. 3). The introduction of larger notches led to the failure of the specimens during machin￾ing. The fracture toughness parameters are summarized in Table 2. KIC values were calculated using Eq. (1) and the values of the maximum loads attained during the tests and GIC was calculated according to Eq. (3) from KIC values and Young’s modulus (E, Table 1) and using the Poisson ratio of dense and fine-grained alumina (ν = 0.22). In order to determine the increments in crack length (a = ai + 1 − ai) to build the R curves, the common criterion relating the onset of crack propagation in the load–displacement curves with the point where the non-linear behaviour starts (arrow in Fig. 4) 18,24,34 was used. From this point, the increments in crack length (a = ai + 1 − ai) would produce the changes in Fig. 4. Schematic representation of the procedure followed for R-curve deter￾mination and JIC calculation.27 The curve correspond to the A10 composite sintered at 1550 ◦C and tested with a relative notch depth a/W = 0.6. For R-curve determination, the arrow marks the point where the non-linear behaviour starts, selected as the onset of crack propagation. From this point, the increments in the crack length (a = ai+1 − ai) would produce the changes in the compliance (Ci, Ci + 1). For JIC calculation (Eq. (5)), the areas under the curves corresponding to specimen tested with the notch (AI) and to an unnotched specimen (AE) are shown. the compliance (Ci, Ci + 1, Fig. 4). An example of the graphics used to calculate JIC is depicted in Fig. 4. For the monophase materials, the KIC values were lower than those reported for aluminas with similar grain sizes (KIC ∼= 3.5–4.5 MPa m1/2), determined from unstable tests35–37 and, in some cases, using specimens with notch radii larger than those utilized in this work,36 and similar to those deter￾mined by Sbaizero et al.38 (KIC ∼= 3 MPa m1/2) for hot-pressed aluminas using stable fracture tests. As discussed by Bar-On et al.,39 unstable crack extension results in apparent increases of fracture toughness values compared to those determined during quasi-static crack growth. Therefore, the semi-stable crack prop￾agation obtained in this work for the alumina specimens (Fig. 3) would give values closer to the actual fracture toughness. Table 2 Fracture toughness parameters of the materials: critical stress intensity factor (KIC), critical energy releasing rate (GIC), critical J-integral (JIC) and work of fracture (γWOF) KIC (S.D.) MPa m1/2 GIC (S.D.) (J/m2) JIC (S.D.) (J/m2) JIC/GIC (S.D.) γWOF (S.D.) (J/m2) A-1450 0.5 2.9 20.4 19.2 1.0 10.5a 2.8 19.6 18.9 1.0 9.8a A-1550 0.5 3.2 (0.1) 26.2 (0.7) 29.9 (3.0) 1.1 (0.1) 20.1 (2.0)a A10-1450 0.4 3.5 (0.1) 38.4 (0.8) 42.1 (3.7) 1.1 (0.1) 34.7 (1.3) 0.5 3.5 (0.2) 39.2 (0.6) 38.6 (2.9) 1.1 (0.1) 33.4 (2.3) 0.6 3.5 (0.1) 37.6 (1.2) 45.9 (3.3) 1.2 (0.1) 35.1 (1.7) A10-1550 0.4 3.3 (0.1) 38.4 (1.2) 50.8 (6.0) 1.3 (0.2) 40.6 (1.2) 0.5 3.3 (0.1) 37.4 (2.6) 55.4 (4.1) 1.5 (0.1) 41.9 (3.0) 0.6 3.3 (0.2) 37.9 (2.0) 53.1 (2.3) 1.4 (0.1) 39.6 (2.1) S.D.: standard deviation. For monophase alumina materials valid tests were obtained only with a relative notch depth of 0.5. The values of the two tests obtained on specimens of alumina sintered at 1450 ◦C are shown. a Semi-stable tests