3736 HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I linear least squares fit(dashed curves). The fit para- 4.4. Crack velocities meters are in close agreement to the fits obtained fror the displacement-time curves and the fiber creep data, The crack velocity as a function of time is shown ga for the Cg-C materials calculated from th Table 4). Of course, since the specimen strain is pro- crack length as a function of the time curve of fig portional to the specimen displacement, this connec- tion is expected. However, it is not obvious that this 7b. Crack velocities are in the range of 10-9 m/s after would also hold for crack length e further checked the hypothesis short times. This is compared with a calculated crack controlling crack extension and permanent strain in velocity curve using an effective elastic crack nese materials by comparing the permanent strain as odology presented in previous studies [24, 13, 35, 601, based on the use of specimen compliance [61] a function of time(Table 2)with the calculated creep There is no calculable relation between compliance strain of Nicalon-CG and Hi-Nicalon fibers for the and crack length(damage zone extent) without a same time period using equation(2). The result shown in Fig. 8 for Nicalon-CG. This comparison is priori knowledge of the crack density and crack-face forces as a function of time, temperature, and applied approximate, but the observed reasonable agreement load. In general, these are not known. Making the suggests our rough strain calculations are of the cor- rect magnitude. The comparison assumes a uniform appropriate connection between crack length and compliance requires an explicit crack-bridging model good for the single Hi-C data point(Table 2)but is argument. This is particularly true when multiple within a factor of two(5.7x10-3 calculated and cracking occurs. The linear-elastic compliance-crack length relation [3] should underpredict actual crack 2x10-2 for specimen Hi-C-2). Therefore, it seems lengths since the bridging forces stiffen a mode-I reasonable to suggest that the strain in the damage crack relative to an unbridged crack( Fig. 9b).Since zone can be accounted for by fiber creep Finally, we qualitatively analyzed the hysteres this is not observed, we conclude that the multiple loops for changes in loop width. We observed no changes in loop widths as a function of time for any (a) of the specimens for which hysteresis loops were btained, although we note that these loops lack the fidelity of loops from tensile tests. Si Ince loop crack length data(Fig. 7b) width is sensitive to the value of the sliding stres [39-41, 58], we conclude that there is no time-depe dence for the sliding stress in this experiment, with the above caveat. a change in width would sugges pend was operative. Therefore, it is unlikely that any other -- time-dependent mechanism, such as interphase oxi- elastic crack length dation or viscous sliding between the fiber and matrix, is operable in argon [5]. This turns out not to be the ase for those materials tested in argon-oxygen mix- Time(s) tures 14, 42, 59](Fig. 5b) for which loop width changes in bending are readily observed (b) Crack 0.0025 0.015 4105 810 Time(s) 2105 6105 8 10 Fig. 9.(a)Experimental crack velocity, calculated from the privative of the fitted crack length vs. time curve in Fig. 7b compared to an effective elastic-crack calculation 3].(b) Fig 8. Experimental strains(Table 2)compared to calculated Experimental crack length compared to effective elastic creep strain for Nicalon-CG fibers at 1373 K. The calculated length calculation. Data are from CG-C material at 1373K in curve assumes a uniform fiber stress of 800 MPa argon(Table 3 and Fig. 7b)3736 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I linear least squares fit (dashed curves). The fit para￾meters are in close agreement to the fits obtained from the displacement–time curves and the fiber creep data (Table 4). Of course, since the specimen strain is pro￾portional to the specimen displacement, this connec￾tion is expected. However, it is not obvious that this would also hold for crack length. We further checked the hypothesis that fiber creep is controlling crack extension and permanent strain in these materials by comparing the permanent strain as a function of time (Table 2) with the calculated creep strain of Nicalon-CG and Hi-Nicalon fibers for the same time period using equation (2). The result is shown in Fig. 8 for Nicalon-CG. This comparison is approximate, but the observed reasonable agreement suggests our rough strain calculations are of the cor￾rect magnitude. The comparison assumes a uniform fiber stress of 800 MPa and indicates good agreement for the CG-C materials (Fig. 8). The agreement is less good for the single Hi-C data point (Table 2) but is within a factor of two (5.7×10
3 calculated and 1.2×10
2 for specimen Hi-C-2). Therefore, it seems reasonable to suggest that the strain in the damage zone can be accounted for by fiber creep. Finally, we qualitatively analyzed the hysteresis loops for changes in loop width. We observed no changes in loop widths as a function of time for any of the specimens for which hysteresis loops were obtained, although we note that these loops lack the fidelity of loops from tensile tests. Since the loop width is sensitive to the value of the sliding stress [39–41, 58], we conclude that there is no time-depen￾dence for the sliding stress in this experiment, with the above caveat. A change in width would suggest that a time-dependent interphase damage mechanism was operative. Therefore, it is unlikely that any other time-dependent mechanism, such as interphase oxi￾dation or viscous sliding between the fiber and matrix, is operable in argon [5]. This turns out not to be the case for those materials tested in argon–oxygen mix￾tures [4, 42, 59] (Fig. 5b) for which loop width changes in bending are readily observed. Fig. 8. Experimental strains (Table 2) compared to calculated creep strain for Nicalon-CG fibers at 1373 K. The calculated curve assumes a uniform fiber stress of 800 MPa. 4.4. Crack velocities The crack velocity as a function of time is shown in Fig. 9a for the CG-C materials, calculated from the crack length as a function of the time curve of Fig. 7b. Crack velocities are in the range of 10
9 m/s after long times, but are quite substantial (
5×10
8 m/s) at short times. This is compared with a calculated crack velocity curve using an effective elastic crack meth￾odology presented in previous studies [2–4, 13, 35, 60], based on the use of specimen compliance [61]. There is no calculable relation between compliance and crack length (damage zone extent) without a priori knowledge of the crack density and crack-face forces as a function of time, temperature, and applied load. In general, these are not known. Making the appropriate connection between crack length and compliance requires an explicit crack-bridging model and cannot be accomplished by a simple elastic crack argument. This is particularly true when multiple cracking occurs. The linear-elastic compliance-crack length relation [3] should underpredict actual crack lengths since the bridging forces stiffen a mode-I crack relative to an unbridged crack (Fig. 9b). Since this is not observed, we conclude that the multiple Fig. 9. (a) Experimental crack velocity, calculated from the derivative of the fitted crack length vs. time curve in Fig. 7b, compared to an effective elastic-crack calculation [3]. (b) Experimental crack length compared to effective elastic-crack￾length calculation. Data are from CG-C material at 1373 K in argon (Table 3 and Fig. 7b)