October 2004 Shear Strength as a Function of Test Rate 1917 80 SIC/MAS-5 SIC/MAS-5 (DNS/110C) DNs/1100) 50 n=8.3 000=ga Best fit 6 10 104103102101 10110010110210310410510°107108 Applied shear stress rate, t [MPals Time to failure, t,[s] Fig. 9. Results of (a) constant stress-rate and (b)constant stress (stress rupture) testing for 2-D SiC /MAS.5 composite in double-notch shear at 1 100C in air. A life prediction based on the constant stress-rate data in(a) is shown as a solid line in(b) would also be dominant in shear, regardless of loading configura- n.+1 log T+ log D (12) tion(constant stress rate or constant stress loading) and that life prediction in shear from one loading configuration to another which is identical in form to Eg.(3)of Mode I loading. SCG could be made analytically or numerically depending on the parameters n, and D, in shear can be determined from slope and complexity of loading configurations. A phenomenological, sim- ntercept of a linear regression analysis of the log(individual shear plified life prediction is proposed based on the following relation trength with units of MPa) vs log (individual shear stress rate hat accounts for shear loading (modified from a relation primarily th units of MPa/s)databased on Eq. (12). The SCG parameter a used for brittle monolithic ceramics in tension". can be estimated from Eq.(I1) with appropriate constants and ameters associated D Figure 8 shows the results of shear strength as a function of +1 applied shear stress rate plotted based on Eg.(12): this plot is nalogous to the shear strength as a function of applied test rate plotted in Fig. 4, but with displacement rate converted to shear where t is the time to failure, T is the applied shear stress, and n, stress rate. The scG eters were determined as n.= 11.2+ and D. are SCG parameters determined in constant stress-rate 2.2 and D=1924 +0.91 for the interlaminar direction and n= esting in shear. Equation (13) determines the life for a given 11.4= 1.9 and D,=33. 27+ 1.35 for the in-plane direction. The applied constant shear stress. Statistically, the prediction repre orresponding coefficients of correlation (e of curve fit for sents the time to failure at a failure probability of- 50%e nterlaminar and in-plane directions were 0. 8442 and 0.8850 respectively, showing reasonably good data fit to Eq. (12).It is constant stress(stress rupture)testing must be conducted in shear noteworthy that the values of n, were identical to each other. using the same SiC /BSAS composite. However, the material was no longer available, so that an alternative composite material was regardless of material direction. The value of SCG parameter n," chosen to validate Eq(13). The material chosen was Nicalon I 1 in shear also compares reasonably with that of n=7 in tension for a similar 2-D SiC/BSAS composite tested at 1 C in air. fiber-reinforced(2-D)crossply magnesium aluminosilicate(desig- Constant stress-rate testing in tension was shown as a possible verage fiber diameter of 10-15 um. The nominal dimensions of alternative to life prediction testing, as verified with constant DNS test specimens prepared from laminates were 12 mm X 25 (stress rupture)testing for various CFCCs at elevated temperature mm x 3 mm in width, length, and thickness, respectively, and the of 1 100 to 1200C 6, 7 The results indicated that the same failure notch distance was 6 mm. Both constant stress-rate and constant mechanism might have been operative, independent of loading stress rates and three constant shear stresses were used in their loading or in static(constant stress)loading In the same way, it is respective loadings. Three test specimens were used at each test expected that a single failure mechanism, slow crack growth rate in constant stress-rate testing under force control, while two sed at each applied testing. The overall geometry and dimensions of DNS test speci mens were followed in accordance with ASTM test method C1425.A specially designed guide fixture was used to prevent ' If average shear strength and average shear stress rate were used, the coefficients buckling of test specimens. The results of both constant stress-rate 画m时 and constant stress testing in shear are shown in Fig 9. Significant ns. Hence, the difference in sCG parameters between individual data and slow crack growth in shear was observed from constant stress-rate testing with SCG parameter n,=8.3+ 1.5, and D, was found to be 31.54+ 1. 96. The value of rt = 0.9283 was indicative of a be used in regression analysis for improved statistical accurac ery reasonable data fit to Eq(12). Using the values of n, and D,October 2004 Shear Strength as a Function of Test Rate 80 70 •7 60 ra ^ 50 1r 40 O) 30 c (1) (0 o (A 10 10^ StC^MAS-5 (DNS/1100°C) n=8.3 10-3 10-^ 10^ 10° 10^ Applied shear stress rate, r [MPa/s] Q. ess, 50 40 30 20 :^ 8 I ^ SiC/MAS-5 (DNS/1 lOO'C) Best fit Prediction n=8.3 10° 10' 10^ lO^' 10* 10' 10« 10' 108 Time to failure, t,[s] (a) (b) Fig. 9. Resuits of (a) constant stress-rate and (b) constant stress (stress rupture) testing for 2-D SiCf/MAS-5 composite in double-notch sheiir at in air. A life prediclion based on the constant stress-rate data in (a) is shown as a solid line in (b). log Tf - + 1 log f + log D.. (12) which is identical in fonrs to Eq. (3) of Mode I loading. SCG parameters n^ and D^ in shear can be detetnilned from slope and intercept of a linear regression analysis of the log {individual shear strength with units of MPu) vs log (individual shear stress rate with units of MPa/s) databased on Eq. (12). The SCG parameter a, can be estimated from Eq. (11) with appropriate constants and parameters associated. Figure 8 shows the results of shear strength as a function of applied shear stress rate plotted based on Eq. (12); this plot is analogous to the shear strength as a function of applied test rate plotted in Fig. 4, but with displacement rate converted to shear stress rate. The SCG parameters were determined as «., = 11.2 ± 2.2 and D^ = I9.24±O.9I for the interlaminar direction and «.,= 11.4 ± 1.9 and D, - 33.27 ± 1.35 for the in-plane direction. The corresponding coefficients of correlation [r^^,^^) of curve fit for interlaminar and in-plane directions were 0.8442 and 0.8850, respectively, showing reasonably good data fit to Eq. (12).** It is noteworthy that the values of n^ were identical to each other. regardless of material direction. The value of SCG parameter n^ — 11 in shear also compares reasonably with that of n - 7 in tension for a similar 2-D SiCj/BSAS composite tested at I lOOX in airj indicating that the SiC,/BSAS composite exhibited a significant susceptibility to slow crack growth in both shear and tension. Constant stress-rate testing in tension was shown as a possible alternative to life prediction testing, as verified with constant stress (stress rupture) testing for various CFCCs at elevated temperatures of 1100" to I2OO°C.''-^ The results indicated that the same failure mechanism might have been operative, independent of loading configuration that was either in monotonic (constant stress rate) loading or in static (constant stress) loading. In the same way, it is expected that a single failure mechanism, slow crack growth. 'if average shear strength and average shear stress nite were used, the cucfficjenis of correlation were r^.,^, = 0.9708 and 0.9723, respectively, for intetlaminar and in-plane direciions. The corresponding SCG parameters were found to be n^- 12 and D^ = 19.4 and n, = 11 and D, = 33.5. respectively, for intetlaminar and in-plane direciion.s. HL-nue. ihe differenLf in SCG parameters between individual daia and average data apprnache-. WLIS negligible; however, thf difference in Ihc codficieni of correlation was somewhai amplified. It is recommended thai individual daia appriwch be used in regression analysis for improved statisiica! atctiracy.'"*'^ would also be dominant in shear, regardless of loading configura￾tion (constant stress rate or constant stress loading) and that life prediction in shear from one loading configuration to another could be made analytically or numerically depending on the complexity of loading configurations. A phenomenological, sim￾plified life prediction is proposed based on the following relation that accounts for shear loading (modified from a relation primarily used for brittle monolithic ceramics in ^'^ (13) where /, is the time to failure, T is the applied shear stress, and n^ and D^ are SCG parameters determined in constant stress-rate testing in shear. Equation (13) determines the life for a given applied constant shear stress. Statistically, the prediction repre￾sents the time to failure at a failure probability of —50%. To verify the life prediction relation proposed in Eq. (13), constant stress (stress rupture) testing must be conducted in shear using the same SiC/BSAS composite. However, the material was no longer available, so that an alternative composite material was chosen to validate Eq. (13). The material chosen was Nicalon￾flbcr-reinforced (2-D) crossply magnesium aluminosilicate (desig￾nated SiC|/MAS-5). fabricated by Corning, Inc." The SiC/MAS-5 composite had a fiher volume fraction of 0.39, 16 plies, and an average fiber diameter of 10-15 |i,m. The nominal dimensions of DNS test specimens prepared from laminates were 12 mm X 25 mm X 3 mm in width, length, and thickness, respectively, and the notch distance was 6 mm. Both constant stress-rate and constant stress testing were conducted at 1 lOO^C in air, where three shear stress rates and three constant shear stresses were used in their respective loadings. Three test specimens were used at each test rate in constant stress-rate testing unAcT force control, while two test specimens were used at each applied stress in constant stress testing. The overall geometry and dimensions of DNS test speci￾mens were followed in accordance with ASTM test method C1425.'' A specially designed guide fixture was used to prevent buckling of test specitncns. The results of both constant stress-rate and constant stress testing in shear are shown in Fig. 9. Significant slow crack growth in shear was observed from constant stress-rate testing with SCG parameter n^ = 8.3 ± 1.5. and D, was found to be 31.54 ± 1.96. The value of r^^f = 0.9283 was indicative of a very reasonable data fit to Eq. (12). Using the values of «, and D^