178 B. K Ahn et al 4 COMPARISON TO EXPERIMENT materials and the fracture surfaces were examined for evidence of interfacial crack deflection We have shown various predicted results for Ga/G,versus From the constituent property data shown in Table 2, fiber volume fraction Vand crack extension a. Here, we it is straightforward to determine that the elastic mis- compare those predictions to careful experiments on match in the F-glass is a=0.751. The only uncertain model composites parameter is the value of r. Here, we assume that the A glass matrix/SiC fiber model composite has been interface toughness is the same as the matrix toughness fabricated, as described in Ref 12. The glass matrix is a Ti= rm, since there is reasonable bonding between the home-made 'F-glass. The reinforcing fibers are Textron SiC and the glass; this is expected to be an upper bound SCS-0 SiC fibers, which are 67 um in radius and have on the true T. With these values, the ratio of Ti/Tcan no coatings. We have measured the elastic and tough- be formed and can be appropriately overlaid on the Ga ness properties of these materials, and they are shown in Gp versus a parameter space, as shown in Fig. 9. Also Table 2. The critical energy release rate or surface shown in Fig 9 is the HEH prediction for Ga/Gp, which nergy is calculated from the toughness Kl via lies above the experimental data point r=K(1-12)/E in each case. These constituents were hence predicts crack deflection. Our predictions for this combined to form a unidirectional composite with 35% specific system at the experimental volume fraction and volume fraction of fibers. Note that the coefficients of various ad=ap=a are also shown in Fig 9; all of the thermal expansion of the fibers and matrix materials are curves lie below the experimental data point and hence essentially equal for SCS-0/F-glass composites so that predict crack penetration. The observed fracture mode there are no significant thermal residual stresses present is crack penetration, as shown by the micrograph of the in the as-fabricated composites. This model composite is composite fracture surface(Fig. 10). Although there is thus well-suited for direct comparison against the pre- some structure to the fracture surface indicating that the dictions of the present work and the HEH results fibers do affect the overall propagation of the propa because of the absence of the complicating issue of resi- gating matrix crack, there is absolutely no evidence of dual stresses and the absence of intermediary fiber any crack deflection at any of the fiber/matrix interfaces coatings Uniaxial tension tests were performed on these across the entire composite. The HEH criterion thus appears to overestimate the tendency for crack deflec tion while the present results for finite crack extensions are consistent with the experimentally observed pene- tration. Another model composite (SCS-0/7040 glass has been fabricated and studied with similar results but nce the residual stresses are not negligible in those ap (in penetration)=a.010 systems, we have not discussed them here. Again, Table 2. Material properties of F-glass matrix and SCS-0 fiber E(GPa) KIC(MPam) r (/m2) 10-155 4230-15423 15-622 0.402000204060.81 HEH(->0,a=ap→ Present work (40 a 0.02! ent work (% 0.0t01 Present work [35%o: 0.025) :,,: 100.80.604020.00.2 Fig. 8.(a) GalGp versus a with ad ap assumption for Vr=40%;(b) GaGp versus a with adf ap assumption for Fig9. Comparison of the present study with experiment data =1% on SCS-0/F-glass composite4 COMPARISON TO EXPERIMENT We have shown various predicted results for Gd/Gp versus ®ber volume fraction Vf and crack extension a. Here, we compare those predictions to careful experiments on model composites. A glass matrix/SiC ®ber model composite has been fabricated, as described in Ref. 12. The glass matrix is a home-made `F-glass'. The reinforcing ®bers are Textron SCS-0 SiC ®bers, which are 67 m in radius and have no coatings. We have measured the elastic and tough￾ness properties of these materials, and they are shown in Table 2. The critical energy release rate or surface energy is calculated from the toughness KIc via ÿ ˆ K2 Ic…1 ÿ v2†=E in each case. These constituents were combined to form a unidirectional composite with 35% volume fraction of ®bers. Note that the coecients of thermal expansion of the ®bers and matrix materials are essentially equal for SCS-0/F-glass composites so that there are no signi®cant thermal residual stresses present in the as-fabricated composites. This model composite is thus well-suited for direct comparison against the pre￾dictions of the present work and the HEH results because of the absence of the complicating issue of resi￾dual stresses and the absence of intermediary ®ber coatings. Uniaxial tension tests were performed on these materials and the fracture surfaces were examined for evidence of interfacial crack de¯ection. From the constituent property data shown in Table 2, it is straightforward to determine that the elastic mis￾match in the F-glass is  ˆ 0:751. The only uncertain parameter is the value of ÿi. Here, we assume that the interface toughness is the same as the matrix toughness, ÿi ˆ ÿm, since there is reasonable bonding between the SiC and the glass; this is expected to be an upper bound on the true ÿi. With these values, the ratio of ÿi=ÿf can be formed and can be appropriately overlaid on the Gd/ Gp versus  parameter space, as shown in Fig. 9. Also shown in Fig. 9 is the HEH prediction for Gd/Gp, which lies above the experimental data point for ÿi=ÿf and hence predicts crack de¯ection. Our predictions for this speci®c system at the experimental volume fraction and various ad ˆ ap ˆ a are also shown in Fig. 9; all of the curves lie below the experimental data point and hence predict crack penetration. The observed fracture mode is crack penetration, as shown by the micrograph of the composite fracture surface (Fig. 10). Although there is some structure to the fracture surface indicating that the ®bers do a€ect the overall propagation of the propa￾gating matrix crack, there is absolutely no evidence of any crack de¯ection at any of the ®ber/matrix interfaces across the entire composite. The HEH criterion thus appears to overestimate the tendency for crack de¯ec￾tion while the present results for ®nite crack extensions are consistent with the experimentally observed pene￾tration. Another model composite (SCS-0/7040 glass) has been fabricated and studied with similar results but since the residual stresses are not negligible in those systems, we have not discussed them here. Again, Fig. 8. (a) Gd/Gp versus  with ad 6ˆ ap assumption for Vf ˆ 40%; (b) Gd/Gp versus  with ad 6ˆ ap assumption for Vf ˆ 1%. Table 2. Material properties of F-glass matrix and SCS-0 ®ber E (GPa) v  ( C)ÿ1 KIC…MPam† ÿ (J/m2 ) F-glass 59 0.20 4.25 0.79 10.155 SCS-0 423 0.15 4.23 2.60 15.622 Fig. 9. Comparison of the present study with experiment data on SCS-0/F-glass composite. 1782 B. K. Ahn et al