I.. Davies et al. Composites Science and Technology 59(1999)801-811 which is vulnerable to degradation during fibre and approximations for So and m with the correct form of composite processing. That fracture initiation does not the relationship being [5] normally occur within the fibre bulk suggests the aver- ge flaw size and or flaw density to be significantly lar- F=l ger on the fibre surface compared to that within the fibre bulk. A common equation linking mirror radius, with S" and m being the uncorrected Weibull strength Im, to fibre strength, S is of the form parameters In order to obtain the relevant in situ fibre strength S (2) parameters, So and m, it is required to use correction factors that have been determined [5 to be of the form shown in Fig. 2. It may be observed from Fig. 2 that Eqs (1)and (3)gives similar results when m A 4 but values for So and m obtained from Eq (1)for the case of m< 4 will Am= bric respectively underestimate and overestimate actual valu where Am and Bm are empirical constants and Kic is the It should be noted that Eq 3)assumes no knowledge racture toughness of the fibre. a value of Kic a 1 of the specimen gauge length. However, the value of S MPa m/ 2 has been estimated for Nicalon"SiC-based obtained depends strongly on the specimen gauge length fibres [ 8] whilst values of 3. 5 [10]and 2.51 [11] have been with large specimens having reduced strengths com- suggested for Bm. Although values of Bm and Kic have not pared to smaller specimens. It is thus necessary when been determined for Tyranno Si-Ti-C-O fibres, they comparing S, for different data sets to normalise differ might be expected to be similar to those for Nicalon" ent gauge lengths to a standard gauge length, Lo, by fibres as the microstructure and chemistry of Tyranno" using the relationship [9] and Nicalon"fibres are alike in many respects. It has recently been shown that Eq. (1) provides only where S, is the predicted value of S, at the standard gauge length, L', and Lo is the gauge length for a spe cimen with Weibull strength parameters So and m It has been suggested that Lo=10-3 m is an appro priate standard gauge length for CMCs as this is the order of the fibre pull-out length. The reason why fibre th is significant for CMCs is that fo posites that fail as a result of multiple matrix cracking as is the case for most“good”CMCs, the gradual transfer of stress from matrix to fibre away from the sam2 4 um 1.1 (b) E0.8 0.7 0.6 um Weibull modulus . m Fig. 1. Scanning electron micrographs illustrating a typical fractu Fig. 2. Relationship between Weibull scale parameters(S, mr) mirror observed on the surface of Tyranno" Si-TiC-O fibres:(a) mined from fracture mirror data and underlying fibre strength general view, and(b) detailed view of fracture mirror. meters(So, m)[5which is vulnerable to degradation during ®bre and composite processing. That fracture initiation does not normally occur within the ®bre bulk suggests the aver￾age ¯aw size and/or ¯aw density to be signi®cantly lar￾ger on the ®bre surface compared to that within the ®bre bulk. A common equation linking mirror radius, rm, to ®bre strength, S, is of the form: S ˆ Am  rm p …2† with Am ˆ BmKIC where Am and Bm are empirical constants and KIC is the fracture toughness of the ®bre. A value of KIC  1 MPa m1/2 has been estimated for Nicalon1 SiC-based ®bres [8] whilst values of 3.5 [10] and 2.51 [11] have been suggested for Bm. Although values of Bm and KIC have not been determined for Tyranno1 Si±Ti±C±O ®bres, they might be expected to be similar to those for Nicalon1 ®bres as the microstructure and chemistry of Tyranno1 and Nicalon1 ®bres are alike in many respects. It has recently been shown that Eq. (1) provides only approximations for So and m with the correct form of the relationship being [5]: F ˆ 1 ÿ eÿ S … † S m …3† with S and m being the uncorrected Weibull strength parameters. In order to obtain the relevant in situ ®bre strength parameters, So and m, it is required to use correction factors that have been determined [5] to be of the form shown in Fig. 2. It may be observed from Fig. 2 that Eqs. (1) and (3) gives similar results when m  4 but values for So and m obtained from Eq. (1) for the case of m < 4 will respectively underestimate and overestimate actual values. It should be noted that Eq. (3) assumes no knowledge of the specimen gauge length. However, the value of S obtained depends strongly on the specimen gauge length with large specimens having reduced strengths com￾pared to smaller specimens. It is thus necessary when comparing So for di€erent data sets to normalise di€er￾ent gauge lengths to a standard gauge length, L0 o, by using the relationship [9]: S0 o ˆ So Lo L0 o  1 m …4† where S0 o is the predicted value of So at the standard gauge length, L0 o, and Lo is the gauge length for a spe￾cimen with Weibull strength parameters So and m. It has been suggested that L0 o ˆ 10ÿ3 m is an appro￾priate standard gauge length for CMCs as this is the order of the ®bre pull-out length. The reason why ®bre pull-out length is signi®cant for CMCs is that, for com￾posites that fail as a result of multiple matrix cracking (as is the case for most ``good'' CMCs), the gradual transfer of stress from matrix to ®bre away from the Fig. 1. Scanning electron micrographs illustrating a typical fracture mirror observed on the surface of Tyranno1 Si±Ti±C±O ®bres: (a) general view, and (b) detailed view of fracture mirror. Fig. 2. Relationship between Weibull scale parameters (S, m) deter￾mined from fracture mirror data and underlying ®bre strength para￾meters …So; m† [5]. 802 I.J. Davies et al. / Composites Science and Technology 59 (1999) 801±811