N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 (a) PLY BREAKING- MODE I b】T’AND" H CRACK|NG MIXED MODE I/II (C) INTERPLY SHEAR-MODE II Fig 4. Schematic figure showing the nature of crack extension in the crack arrester orientation when the specimen crack length is raried significantly. (a)Short crack lengths(a/w<0. 4). (b)intermediate crack lengths(0.4< a/w<0.55)and (c)longer crack lengths (a/W>0.6). Note the increasing extent of mode II fracture component with increasing crack length values. principal fracture event. The associated fibre bundle fracture is negligible(notice the very small sudden load drop(s)shown as A1 BI in Fig 3c) 3. 2. Plane strain fracture toughness (Klc) The plane strain fracture toughness(Klc)of the 2D silica-silica CFCC material was evaluated in the crack divider and crack arrester orientations according to the astm standard E-399 [20]. Specimens of varied crack length have been used for the determination of fracture toughness Figs 2 and 3 show the basic data of the load variation with displacement for the specimens in the two notch orientations. Table 1 provides the details of the specimens and the data derived from these fracture toughness tests. Though the specimens with varied a/W were tested, data corresponding to specimens with a/w values in the range of 0.45-0.55, as specified by ASTM standard E-399 [19], were only used to arrive at Klc. The values of K, and Ko derived for each test are also listed in Table 1. These data in Table l show that the material exhibits valid Kmax/Ko values(<1. 1)only when the crack lengths are smaller(a/W<0.44). At higher crack lengths. the material exhibits limited extent of stable crack extension, which yielded Kmax/ Ko values that are in excess of 1. 1. In view of these observations, the Ko values derived from specimens with a/w of 0.44 and 0.56 in the crack divider orientation and 0.52 in the crack arrester orientation(note only a small variation in the Ko values between different test specimens, see data in Table 1) are considered to yield valid KI Under such conditions, the CFCC material exhibits a significantly higher fracture toughness value in the crack divider orientation as compared to the crack arrester orientation. An average value of 2.03 MPavm (corresponding to the crack lengths of a/W of 0.44 and 0.56)obtained for the crack divider orientation is ore than 100% higher than the value obtained in the crack arrester orientation(Klc=0.98 MPa vm) econdly, the value of conditional fracture toughness(Ko) decreases significantly with increase in the crack length, especially in the crack divider orientation. This is due to the change in fracture mode. At higher
principal fracture event.The associated fibre bundle fracture is negligible (notice the very small sudden load drop(s) shown as A1B1 in Fig.3c). 3.2. Plane strain fracture toughness (KIc) The plane strain fracture toughness (KIc) of the 2D silica–silica CFCC material was evaluated in the crack divider and crack arrester orientations according to the ASTM standard E-399 [20].Specimens of varied crack length have been used for the determination of fracture toughness.Figs.2 and 3 show the basic data of the load variation with displacement for the specimens in the two notch orientations.Table 1 provides the details of the specimens and the data derived from these fracture toughness tests.Though the specimens with varied a=W were tested, data corresponding to specimens with a=W values in the range of 0.45–0.55, as specified by ASTM standard E-399 [19], were only used to arrive at KIc.The values of Kmax and KQ derived for each test are also listed in Table 1.These data in Table 1 show that the material exhibits valid Kmax=KQ values (<1.1) only when the crack lengths are smaller (a=W < 0:44).At higher crack lengths, the material exhibits limited extent of stable crack extension, which yielded Kmax=KQ values that are in excess of 1.1. In view of these observations, the KQ values derived from specimens with a=W of 0.44 and 0.56 in the crack divider orientation and 0.52 in the crack arrester orientation (note only a small variation in the KQ values between different test specimens, see data in Table 1) are considered to yield valid KIc. Under such conditions, the CFCC material exhibits a significantly higher fracture toughness value in the crack divider orientation as compared to the crack arrester orientation.An average value of 2.03 MPa pm (corresponding to the crack lengths of a=W of 0.44 and 0.56) obtained for the crack divider orientation is more than 100% higher than the value obtained in the crack arrester orientation (KIc ¼ 0:98 MPa pm). Secondly, the value of conditional fracture toughness (KQ) decreases significantly with increase in the crack length, especially in the crack divider orientation.This is due to the change in fracture mode.At higher Fig.4.Schematic figure showing the nature of crack extension in the crack arrester orientation when the specimen crack length is varied significantly.(a) Short crack lengths (a=W < 0:4), (b) intermediate crack lengths (0:4 < a=W < 0:55) and (c) longer crack lengths (a=W > 0:6).Note the increasing extent of mode II fracture component with increasing crack length values. 2594 N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605
N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 Table l Plane strain fracture toughness (KIc, MPa ym) data of the 2D silica-silica CFCC material f(a/w) Po and p (a) Crack divider orientation 123 9.76 7.23 3.12and0.32 234and246 2.15and2.26 993 4.39and0.44 205and206 2.43aand24 994 5.60and0.56 .25 89 and 101 1.63a and 1.84 7.26 6.35and0.65 4.63 52 and 58 1.36andl52 (b) Crack arrester orientation 7.74 7.53 58and66.5 0.78and0.89 23456 7.59 8.95 06and0.403 2.15 58 and 60 0.84and0.87 9.1 53 and 60 0.98aand1.10 976 4.84and0. 3.5 33 and 0.72and0.86 4.9and0.64 37 and 49 theo Decimen width, in mm; B-specimen thickness, in mm; L-specimen span length(fixed value of 40 mm); Pg--conditional load for nset of fracture, in N; Pmar-maximum load in the load-displacement curve, in N; Ko-conditional fracture toughness, in MPa vm; Kmar-maximum stress intensity factor, in MPa vm. Valid Klc. crack lengths, as discussed in the previous section, the fracture mode gradually changes to predominant shear, involving mode II (in-plane shear or sliding) fracture components. This is true for both test orien tations 3.3. Elastic-plastic fracture toughness (JIc) The procedure suggested by Landes and Begley [23] and the ASTM standard E-813 [24] provide details of the latest standard practice for the determination of elastic-plastic fracture toughness, Jic. Alternatively, another widely accepted methodology, again suggested by Landes and Begley [22], can also be employed for Jie determination. Both these methodologies are based on Rice proposed J-integral [21]. The later proce- dure principally involves the determination of fracture energy o) from the energy absorbed in the fracture process(Eini, area under the load-displacement, usually the displacement considered here corresponds to the load line) by specimens with different crack lengths, up to either a constant displacement or a constant load. In the present case, the load-displacement data given in Figs. 2 and 3 are used to calculate the energy for the crack initiation(Eini), which event is assumed to occur at the displacements corresponding to the peak load. Eini values thus determined are used to calculate the fracture energy, Jo as [21, 22 o=△Emn/B(△a), where(AEini)is the difference in the fracture energies(corresponding to peak loads in the load displacement curves)of two specimens with different initial crack lengths(their difference is Aa). The values of Jo, determined from the load-displacement curves in crack divider and crack arrester orientations, are shown as a function of crack length in Fig. 5. As to be expected, the material shows constant values of o in the crack divider(1.36 kJ/m")and crack arrester(0.66 kJ/m")orientations. The scatter in o values is higher for crack arrester orientation as compared to the crack divider orientation. However, all these values were found to satisfy the validity conditions and hence, can be termed as elastic-plastic fracture toughness, JIc of the CFCc As stated above, the lc corresponds to the peak load (assumed to correspond to the crack initiation) and ence would encompass only those fracture events that occur in the CFCC material before or up to the
crack lengths, as discussed in the previous section, the fracture mode gradually changes to predominant shear, involving mode II (in-plane shear or sliding) fracture components.This is true for both test orientations. 3.3. Elastic–plastic fracture toughness (JIc) The procedure suggested by Landes and Begley [23] and the ASTM standard E-813 [24] provide details of the latest standard practice for the determination of elastic–plastic fracture toughness, JIc.Alternatively, another widely accepted methodology, again suggested by Landes and Begley [22], can also be employed for JIc determination.Both these methodologies are based on Rice proposed J-integral [21].The later procedure principally involves the determination of fracture energy (JQ) from the energy absorbed in the fracture process (Eini, area under the load–displacement, usually the displacement considered here corresponds to the load line) by specimens with different crack lengths, up to either a constant displacement or a constant load.In the present case, the load–displacement data given in Figs.2 and 3 are used to calculate the energy for the crack initiation (Eini), which event is assumed to occur at the displacements corresponding to the peak load. Eini values thus determined are used to calculate the fracture energy, JQ as [21,22]: JQ ¼ DEini=BðDaÞ; ð1Þ where (DEini) is the difference in the fracture energies (corresponding to peak loads in the load displacement curves) of two specimens with different initial crack lengths (their difference is Da).The values of JQ, determined from the load–displacement curves in crack divider and crack arrester orientations, are shown as a function of crack length in Fig.5.As to be expected, the material shows constant values of JQ in the crack divider (1.36 kJ/m2) and crack arrester (0.66 kJ/m2) orientations.The scatter in JQ values is higher for crack arrester orientation as compared to the crack divider orientation.However, all these values were found to satisfy the validity conditions and hence, can be termed as elastic–plastic fracture toughness, JIc of the CFCC. As stated above, the JIc corresponds to the peak load (assumed to correspond to the crack initiation) and hence would encompass only those fracture events that occur in the CFCC material before or up to the Table 1 Plane strain fracture toughness (KIc, MPa pm) data of the 2D silica–silica CFCC material Specimen no. WB a and a=W f ða=W Þ PQ and Pmax KQ and Kmax (a) Crack divider orientation 1 9.76 7.23 3.12 and 0.32 1.6 234 and 246 2.15 and 2.26 2 9.93 7.54 4.39 and 0.44 2.22 205 and 206 2.43a and 2.43 3 9.94 7.17 5.60 and 0.56 3.25 89 and 101 1.63a and 1.84 4 9.76 7.26 6.35 and 0.65 4.63 52 and 58 1.36 and 1.52 (b) Crack arrester orientation 1 7.76 7.60 2.52 and 0.325 1.62 70 and 74 0.86 and 0.90 2 7.74 7.53 2.7 and 0.35 1.73 58 and 66.5 0.78 and 0.89 3 7.59 8.95 3.06 and 0.403 2.15 58 and 60 0.84 and 0.87 4 7.68 9.13 4.0 and 0.52 2.84 53 and 60 0.98a and 1.10 5 7.61 9.76 4.84 and 0.58 3.5 33 and 40 0.72 and 0.86 6 7.67 9.89 4.9 and 0.64 4.43 37 and 49 0.99 and 1.3 W ––specimen width, in mm; B––specimen thickness, in mm; L––specimen span length (fixed value of 40 mm); PQ––conditional load for the onset of fracture, in N; Pmax––maximum load in the load–displacement curve, in N; KQ––conditional fracture toughness, in MPa pm; Kmax––maximum stress intensity factor, in MPa pm. a Valid KIc. N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605 2595