5054 J Mater Sci(2007)42:5046-5056 Fig 6 Magnified SEM graphs on the fracture surface of TsA fiber. a)as-received; (b)annealed at1900°C 4.33 MPam for HNLS fiber, respectively. From where Y is a geometric constant, E the modulus of Klc=Am(re/rm)/Y, using rc a 0.39 rm and Y= 1.56, elasticity (270 GPa for HNL, 420 GPa for HNLS the calculated Klc is 1.56 MPam" for as-received HNL respectively). By substituting the fracture strength amorphous ceramics is 0.5to1MPam2图3 For the 7s=8自 fiber, 1.74 MPamfor as-received HNLS fiber. Since Eq.(12) with Eq.( 8), the critical fracture energies Am is an average value, the Klc value determined for could be simplified as: these fibers also is an aver erage value. The Klc for poly- crystalline Sic is a 2 MPa m", while that for most annealed fibers the resultant value of fracture toughness was listed in Table 1. The fracture toughness decreased The critical fracture energy calculated with Eq(13)is with increasing the annealing temperature, but it did not 4.5 J/m for as-received HNL fiber, 3.6 J/m" for as show strong dependence on the annealing temperature. received hnls fiber, which are on the same magnitude with those of other glass materials 31. The low critical Critical fracture energy fracture energy for HNLS fiber could be attributed to the low strain to failure(HNL: 1%o, HNLS: 0.65% Attempts have been made to relate the critical flaw [11). As for the critical fracture energies for annealed radius to the critical fracture energy, ,e, which can be fibers, were listed in Table 1 obtained from the following equations 30, 311 The Griffith theory presents a criterion for propa- gation of preexisting flaws that generally determines re=y'2E , do (11) the failure of brittle materials and can be used to explain the features of fracture surface [31]. For the (12) as-received fibers, the carbon layer covered on the urface of fibers can blunt the critical flaw and reduce the stress concentration on the surface flaw. However. O HNL this carbon layer can be removed by reaction witi ●HNLs residual oxygen from fiber itself and atmosphere. In this case, the propagation of preexisting surface flaws will become easy. In addition, flaws produced by decomposition, active oxidation and large grain depo- sition can exist on the fiber's surface at high tempera ture resulting in the low fracture toughness. Generally this flaw is sub-critical size. At fairly high strain rate (0.3 mm/min)at which the strengths were measured, this flaw would propagate gradually until it becomes critical because of stress concentration around the flaw Combining the fracture properties with microstruc Critical flaw size, rc/um ture characterization of sic-based fibers it is clear that Fig. 7 The dependence of tensile strength on critical flaw size in he strength of sic fibers is associated with the thermal as-received HNL and HNLS fibers; the slops of fitting lines are decomposition of amorphous phase, grain coarsening and active oxidation However we still can not deny the 2 Springer4.33 MPam1/2 for HNLS fiber, respectively. From K1c = Am(rc/rm) 0.5/Y, using rc  0.39 rm and Y = 1.56, the calculated K1c is 1.56 MPam1/2 for as-received HNL fiber, 1.74 MPam1/2 for as-received HNLS fiber. Since Am is an average value, the K1c value determined for these fibers also is an average value. The K1c for poly￾crystalline SiC is  2 MPa m1/2, while that for most amorphous ceramics is  0.5 to 1 MPa m1/2 [33]. For the annealed fibers, the resultant value of fracture toughness was listed in Table 1. The fracture toughness decreased with increasing the annealing temperature, but it did not show strong dependence on the annealing temperature. Critical fracture energy Attempts have been made to relate the critical flaw radius to the critical fracture energy, cc, which can be obtained from the following equations [30, 31], rc = Y2 2E c c/r2 f ð11Þ rf r 1=2 c = Y ffiffiffiffiffiffiffiffiffiffiffiffiffi 2E c c p ð12Þ where Y is a geometric constant, E the modulus of elasticity (270 GPa for HNL, 420 GPa for HNLS, respectively). By substituting the fracture strength in Eq. (12) with Eq. (8), the critical fracture energies could be simplified as: cc = K2 1c 2E ð13Þ The critical fracture energy calculated with Eq. (13) is 4.5 J/m2 for as-received HNL fiber, 3.6 J/m2 for as￾received HNLS fiber, which are on the same magnitude with those of other glass materials [31]. The low critical fracture energy for HNLS fiber could be attributed to the low strain to failure (HNL: 1%, HNLS: 0.65% [11]). As for the critical fracture energies for annealed fibers, were listed in Table 1. The Griffith theory presents a criterion for propa￾gation of preexisting flaws that generally determines the failure of brittle materials and can be used to explain the features of fracture surface [31]. For the as-received fibers, the carbon layer covered on the surface of fibers can blunt the critical flaw and reduce the stress concentration on the surface flaw. However, this carbon layer can be removed by reaction with residual oxygen from fiber itself and atmosphere. In this case, the propagation of preexisting surface flaws will become easy. In addition, flaws produced by decomposition, active oxidation and large grain depo￾sition can exist on the fiber’s surface at high tempera￾ture resulting in the low fracture toughness. Generally, this flaw is sub-critical size. At fairly high strain rate (0.3 mm/min) at which the strengths were measured, this flaw would propagate gradually until it becomes critical because of stress concentration around the flaw. Combining the fracture properties with microstruc￾ture characterization of SiC-based fibers, it is clear that the strength of SiC fibers is associated with the thermal decomposition of amorphous phase, grain coarsening and active oxidation. However, we still can not deny the Tensile strength, σ/GPa 0 1 2 3 4 5 6 0 0.5 1 1.5 HNL HNLS Critical flaw size,rc/um 2 Fig. 7 The dependence of tensile strength on critical flaw size in as-received HNL and HNLS fibers; the slops of fitting lines are approximate –0.5 Fig. 6 Magnified SEM photographs on the fracture surface of TSA fiber: (a) as-received; (b) annealed at 1,900 C 5054 J Mater Sci (2007) 42:5046–5056 123