J Mater Sci(2007)42:5046-5056 5053 Fig. 5 Typical fracture a)as-received HNL fiber; (b)1, 600C annealed HNL fiber: (e) as-received HNLS r,(d)1,600° C annea INLS TySA fiber;(f)1,900° annealed TySA fiber 2 um ce flaw Fracture mechanics predicts a relation between fiaw of=Am(rm)-05 (9) radius, fracture strength(af) and fracture toughness (Klc), where Klc is the mode 1 fracture toughness of where Am is the mirror constant the sic fiber Substituting of in Eq(8)with Eq(9), the fracture In Eq(8), Y is a geometric factor dependent (8 toughness, Klc, could be expressed ar(re)"-= YKlc=constant on the Kic= Am(e/rm)/Y critical flaw shape and location and its relative size The ratio of critical flaw size (r) to mirror size(rm)in compared to the fiber dimension. Y is 1.56 for a small, present work was measured to be about 0.39. In Fig.8. centrally located penny-shaped fiaw in a plane normal the tensile strength or versus(rm). are plotted for HNL to the tensile axis given in the Ref. 32 and HNLS fiber, respectively. The data were fit to a line Additionally, it has been observed that the product by linear regression analysis. The mirror constant A of strength, of, and the square root of mirror size defined as the slope of the fitting line in Fig8, was obeyed following formula 30-33 determined to be 3.93 MPam for hNl fiberFracture mechanics predicts a relation between flaw radius, fracture strength (rf) and fracture toughness (K1c), where K1c is the mode 1 fracture toughness of the SiC fiber. rf(rc) 1=2 = YK1c = constant ð8Þ In Eq. (8), Y is a geometric factor dependent on the critical flaw shape and location and its relative size compared to the fiber dimension. Y is 1.56 for a small, centrally located penny-shaped flaw in a plane normal to the tensile axis given in the Ref. [32]. Additionally, it has been observed that the product of strength, rf, and the square root of mirror size obeyed following formula [30–33] rf = Am(rmÞ 0:5 ð9Þ where Am is the mirror constant. Substituting rf in Eq. (8) with Eq. (9), the fracture toughness, K1c, could be expressed as: K1c = Am(rc/rm) 0:5 /Y ð10Þ The ratio of critical flaw size (rc) to mirror size (rm) in present work was measured to be about 0.39. In Fig. 8, the tensile strength rf versus (rm) –0.5 are plotted for HNL and HNLS fiber, respectively. The data were fit to a line by linear regression analysis. The mirror constant Am, defined as the slope of the fitting line in Fig. 8, was determined to be 3.93 MPam1/2 for HNL fiber, Fig. 5 Typical fracture surface observation in: (a) as-received HNL fiber; (b) 1,600 C annealed HNL fiber;(c) as-received HNLS fiber; (d) 1,600 C annealed HNLS fiber; (e) as-received TySA fiber; (f) 1,900 C annealed TySA fiber J Mater Sci (2007) 42:5046–5056 5053 123