M.L. Antti et al. Journal of the European Ceramic Society 24(2004)565-578 this study shows a larger decrease in strength. This can as providing a means of strength prediction via Eq (1) at least partly be explained by the fact that Jurf and Thus the embrittlement of a composite can be expected Butner reported unnotched strength to lead to a reduction of both Ke and co In order to apply Eq.(1)to the present strength 4.2. Notch sensitivity values. these were first orrected for the finite width effect by applying the factor K/3, where K is the stress intensity As indicated earlier, the tensile fracture stress results factor for a hole in a plate with finite width: for the 0/90 materials were analysed in terms of the Waddoups model. The basis of the model is that the K=3.00-3 13(9)+3.66(9)-1.53( fracture stress, oF, of a centre-hole notched infinite plate is given by The corrected stress value is in effect the predicted strength of an infinite plate. The width- corrected value (1) for a nominal a/w=0. 25 are listed in Table 3 and for all a/w they are presented in Fig 8 The corrected values were used with Eq.(1) to find where a is the hole diameter, Ke is a critical stress the Ke and co values for each treatment condition. The ntensity factor and co is the length of each of two three a/w geometries for each condition permitted three cracks on opposite sides of and adjacent to the hole. independent solutions for these constants. In almost all In fibre composites it is assumed that the cracks are cases the values obtained lay very close to each other equivalent to the damage zones adjacent to the holes. It thus justifying the assumption that they were constant is also assumed that both Ke and co are constants, that is within the range of the experiments. Average values for ndependent of hole size, for a given material. The two the various heat treatments are included in Table 3 parameters cannot readily be related to actual physical together with the unnotched strength values estimated processes in the material but provided that they are by inserting the values of the constants into Eq (1)with found experimentally to indeed be constants then they offer a convenient means of comparing materials as well stern 150 -08 210225103 35104 4.510 LM=T(25+logt) [K-h a [ma Fig. 7. Larson-Miller plot of strength of heat-treated samples. ncluding literature data. 3The results are normalised with respect to ig. 8. Net section strength. corrected for finite width. versus hole oom temperature stren diameter for 0/90 fibre orientation. Table 3 Strength values corrected for finite width, and the results of the application of Waddoups model Corrected net-section Kc/] Estimated unnotched strength[MPa strength[MPa Fibre orientation: 0/900 Received A(RT) Sreceived B (RT) 17.5 210 200hat500°C(B) l00 h at 1000°C(B) 14.4 240hatl000°C(B) 20hatl100°C(A) l00hatl100°C(A) For nominal a/w=0.25this study shows a larger decrease in strength. This can at least partly be explained by the fact that Jurf and Butner reported unnotched strength. 4.2. Notch sensitivity As indicated earlier, the tensile fracture stress results for the 0/90 materials were analysed in terms of the Waddoups model. The basis of the model is that the fracture stress, F, of a centre-hole notched infinite plate is given by: Kc ¼ F ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 þ c0 r ð1Þ where a is the hole diameter, Kc is a critical stress intensity factor and c0 is the length of each of two cracks on opposite sides of and adjacent to the hole.19 In fibre composites it is assumed that the cracks are equivalent to the damage zones adjacent to the holes. It is also assumed that both Kc and c0 are constants, that is independent of hole size, for a given material. The two parameters cannot readily be related to actual physical processes in the material but provided that they are found experimentally to indeed be constants then they offer a convenient means of comparing materials as well as providing a means of strength prediction via Eq. (1). Thus the embrittlement of a composite can be expected to lead to a reduction of both Kc and c0. In order to apply Eq. (1) to the present strength values, these were first orrected for the finite width effect by applying the factor K/3, where K is the stress intensity factor for a hole in a plate with finite width:19 K ¼ 3:00 3:13 a w þ 3:66 a w 2 1:53 a w 3 ð2Þ The corrected stress value is in effect the predicted strength of an infinite plate. The width-corrected values for a nominal a/w=0.25 are listed in Table 3 and for all a/w they are presented in Fig. 8. The corrected values were used with Eq. (1) to find the Kc and c0 values for each treatment condition. The three a/w geometries for each condition permitted three independent solutions for these constants. In almost all cases the values obtained lay very close to each other thus justifying the assumption that they were constant within the range of the experiments. Average values for the various heat treatments are included in Table 3 together with the unnotched strength values estimated by inserting the values of the constants into Eq. (1) with Fig. 7. Larson–Miller plot of strength of heat-treated samples, including literature data.13 The results are normalised with respect to room temperature strength. Table 3 Strength values corrected for finite width, and the results of the application of Waddoups model21 Sample Corrected net-section strengtha [MPa] KC MPa ffiffiffiffi m   p c0 [mm] Estimated unnotched strength [MPa] Fibre orientation: 0/90
As-received A (RT) 163 18.9 2.7 205 As-received B (RT) 140 17.5 2.2 210 200 h at 500
C (B) – – – – 100 h at 1000
C (B) 135 14.4 2.0 182 3240 h at 1000
C (B) 84 8.9 1.7 122 20 h at 1100
C (A) 92 9.8 1.7 134 100 h at 1100
C (A) 30 2.7 0.3 88 a For nominal a/w=0.25. Fig. 8. Net section strength, corrected for finite width, versus hole diameter for 0/90 fibre orientation. M.-L. Antti et al. / Journal of the European Ceramic Society 24 (2004) 565–578 571