HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I e. Ao'Pexpl=pgs fiber-creep activation energies for those particular (2)fibers, respectively. The agreement is best for Hi-C and less good for CG-C. Fabrication differences in Nicalon-CG fibers over the years may be one cause In equation(2), E is the creep strain, A is a constant, of this discrepancy. The single fiber-creep data indi- o is the applied stress, n is the stress exponent, t is cate that the d'o term should be significantly differ time, @e is the true activation energy, p is the time- ent for the Nicalon-CG and Hi-Nicalon fibers(Table temperature exponent, and the other symbols have 4), which is also observed in the experimental fits their usual meanings. Values for these parameters are The time-temperature exponent, P, for CG-C and Hi listed in Table 4. DiCarlo et al.[34] report activation C composites is similar in the crack-growth fits. How energies of 600 kJ/mol for Hi-Nicalon fibers and 500 ever, since the observed deformation is transient, and kJ/mol for Nicalon-CG fibers between 1473 to 1673 other parameters are involved, such as the stress K in air, up to 1% strain at stresses ranging from 200 exponent, these comparisons must be done with care to 400 MPa. This activation-energy determination is Nonetheless, the agreement between the activation based on the transient creep analysis of Sherby and energies for fiber creep and subcritical crack growth Don [49], from which one obtains the power-law (or displacement) supports the hypothesis that fiber unctional form used by DiCarlo. This approach avo- creep controls the rate of crack extension in these ids the assumption that the activated process has composites. reached a steady state, which is probably not true for Others have also investigated high-temperature either fiber creep of Hi-Nicalon fibers (Table 5), but the acti- Therefore, our displacement-time data were fit to vation energies shown in Table 5 differ widely. Part of the discrepancy is related to observations regarding apparent steady-state creep versus transient-creep A'σpexp (3)egimes. The analysis for determining activation ener- ies depends greatly on this interpretation [50]. Note that for the Sherby-Dorn analysis, the product of p, the time-temperature exponent, and @c, the true acti- where 8mp is the midpoint displacement of the speci- vation energy, equals the apparent activation energy mens.For the fit, the term a" was treated as a single one would obtain assuming a steady-state creep rate parameter, and the three parameters(Ao" @e, and p) Another explanation is that the creep characteristics were simultaneously determined for each material of Hi-Nicalon fibers are sensitive to oxygen concen- type from the displacement, time, and temperature tration. The differences in values reported by these data. Since all the composite data were obtained at a groups may be a result of variable experimental con- obtained for a stress exponent. The fit parameters in the material propenes o ed ment, or variations gle stress-intensity level, no information was ditions, especially the test enviro rs among separate Table 4)are in good agreement with those obtained manufacturing batches by DiCarlo et al. [34, 36, 37, 4648] using single- The increased creep of the hi-Nicalon data. In particular, measured activation fibers improves the th resistance of the energies for crack growth in composites with either composites [13, 25 displacement-time Hi-Nicalon or Nicalon -CG fibers agree with measured curves for the Hi-C materials reflect the reduced dis- Table 4. Fiber creep data and composite crack growth data Fiber: experimental fit Creep parameters f=Ao"Pexp(-po kn) A(MP asp) P @.(kJ/mol) Nicalon-CG Composite. experimental Displacement-time fit parameters A'ofrexp(-QJkn Ao(m s-p) G-C long-term(Fi CG-C short-term(Fig. 2) 8.2+0.6 430±3 Fitting equation and parameters from DiCarlo et al.[34] b Fitting equation shown, but term Ao treated as a single parameter.HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I 3733 ec Asn t p exp

pQc kT (2) In equation (2), ec is the creep strain, A is a constant, s is the applied stress, n is the stress exponent, t is time, Qc is the true activation energy, p is the time– temperature exponent, and the other symbols have their usual meanings. Values for these parameters are listed in Table 4. DiCarlo et al. [34] report activation energies of 600 kJ/mol for Hi-Nicalon fibers and 500 kJ/mol for Nicalon-CG fibers between 1473 to 1673 K in air, up to 1% strain at stresses ranging from 200 to 400 MPa. This activation-energy determination is based on the transient creep analysis of Sherby and Dorn [49], from which one obtains the power-law functional form used by DiCarlo. This approach avo￾ids the assumption that the activated process has reached a steady state, which is probably not true for either fiber. Therefore, our displacement–time data were fit to the following: dmp Asn t p exp

pQ kT (3) where dmp is the midpoint displacement of the speci￾mens. For the fit, the term Asn was treated as a single parameter, and the three parameters (Asn , Qc, and p) were simultaneously determined for each material type from the displacement, time, and temperature data. Since all the composite data were obtained at a single stress-intensity level, no information was obtained for a stress exponent. The fit parameters (Table 4) are in good agreement with those obtained by DiCarlo et al. [34, 36, 37, 46–48] using single- fiber creep data. In particular, measured activation energies for crack growth in composites with either Hi-Nicalon or Nicalon-CG fibers agree with measured Table 4. Fiber creep data and composite crack growth data Fibera : experimental fit Creep parameters e = Asn t p exp(
pQc/kT) A (MP a
n s
p ) npQc (kJ/mol) Hi-Nicalon 121 1.8 0.58 600 Nicalon-CG 1.5 1.2 0.40 500 Compositeb : experimental Displacement–time fit parameters fit dmp = Asn [t exp(
Qc/kT)]p Asn (m s
p ) p Qc (kJ/mol) Hi-C long-term (Fig. 4) 340±60 0.40±0.004 614±8 CG-C long-term (Fig. 3) 0.2±0.03 0.41±0.005 374±6 CG-C short-term (Fig. 2) 8.2±0.6 0.49±0.003 430±3 a Fitting equation and parameters from DiCarlo et al. [34]. b Fitting equation shown, but term Asn treated as a single parameter. fiber-creep activation energies for those particular fibers, respectively. The agreement is best for Hi-C and less good for CG-C. Fabrication differences in Nicalon-CG fibers over the years may be one cause of this discrepancy. The single fiber-creep data indi￾cate that the Asn term should be significantly differ￾ent for the Nicalon-CG and Hi-Nicalon fibers (Table 4), which is also observed in the experimental fits. The time–temperature exponent, p, for CG-C and Hi￾C composites is similar in the crack-growth fits. How￾ever, since the observed deformation is transient, and other parameters are involved, such as the stress exponent, these comparisons must be done with care. Nonetheless, the agreement between the activation energies for fiber creep and subcritical crack growth (or displacement) supports the hypothesis that fiber creep controls the rate of crack extension in these composites. Others have also investigated high-temperature creep of Hi-Nicalon fibers (Table 5), but the acti￾vation energies shown in Table 5 differ widely. Part of the discrepancy is related to observations regarding apparent steady-state creep versus transient-creep regimes. The analysis for determining activation ener￾gies depends greatly on this interpretation [50]. Note that for the Sherby–Dorn analysis, the product of p, the time–temperature exponent, and Qc, the true acti￾vation energy, equals the apparent activation energy one would obtain assuming a steady-state creep rate. Another explanation is that the creep characteristics of Hi-Nicalon fibers are sensitive to oxygen concen￾tration. The differences in values reported by these groups may be a result of variable experimental con￾ditions, especially the test environment, or variations in the material properties of the fibers among separate manufacturing batches. The increased creep resistance of the Hi-Nicalon fibers improves the crack-growth resistance of the composites [13, 25, 35]. The displacement–time curves for the Hi-C materials reflect the reduced dis-