1140 Journal of the American Ceramic Society--Gouadec et al Vol 84. No 5 Comp Comp#3 Pristine fiber 135280cm 1352 Coated fibe Extracted 1350 Composites #1 &3 te #2 Fiber extracted from Composite #2 16 Measurement Series Fig. 5. Hi-Nicalon D band wavenumber(corrected by a neon reference line)and bandwidth determined by fitting the spectra recorded in 180 s(A=514.5 nm, P= I mW)on cross sections of different samples(drawings on the right-hand side). Each point corresponds to a region seled sample. The number of recorded spectra is given. perimental wavenumber shift AvExD has three possible p-BN/SiC interphase apparently relaxes the residual stress(#2) It can result from a mechanical stress(Distress), but laser but not the silicon-doped one(#3). Besides, working with the (AVHeating)and/or chemical alterations(Avchemistry )must 514.5 nm line, we found that vp in a fiber surrounded by a also be considered preserved p-BN/SiC double coating was lower than in a nearby △p= fiber with a broken SiC ring, where p-BN layer had dissolved in the celsian. The BN layer acts as a compliant material which (10) protects the fibers and results in better o and m(Weibull modulus) values in the composite. The stress-related shift, the one we want to know, is given by The compressive stresses that we found(100 and 950 MPa) (11) are not exactly in the range anticipated from our micromechanical modeling(150-650 MPa). Yet, the modeling relied on many Concerning the laser heating, it is straightforward to write approximations and did not consider interphase materials at all. On the other hand, we possibly incorrectly estimated the value of s △ilan=P(S (12) Indeed, measurements on carbon and polymeric fibers revealed As for the chemical term. it can be neglected in our case. on a slight but steady softening when stresses are changed from ccount of the small bandwidth difference between embedded and reference fibers. This approximation is ascertained by the fact that means a correlative decrease of S; in compression. Equation(2)is AvEn 0 for the fiber extracted from composite 2 (it has the same only an approximation and second- or third-order polynomial wavenumber in Fig. 5 as the "stress-free"references of the expressions are necessary to unify compressive and tensile behav left-hand side), for which Avstress and AvHeating must vanish. All iors of Courtaulds Graphil (U. K )XAS carbon fibers. However, all, the residual compressive stress will be obtained from the e dependency remains linear for fully crystalline polydiacetylene following expression fibers"and the same must apply to Hi-Nicalon fibers. Indeed, ceramics consist of highly covalent bonds and have a 3D structure ()x-(1)(=) and no failure-initiating defects in compression. Besides, in the △o(GPa)=E△e= peculiar case of the Hi-Nicalon fibers, there is a uniform distribu- tion of C and SiC species. We therefore assume our Sp value is E△甲一P(S=mk- presland almost the same whatever the sign of the applied strain, at least in (13) the explored range ( C) Statistical Relevance of the Results: It must be pointed After Fig. 5, for which P is I mW, the experimental shifts are out that not only the recording conditions, but also the statistical dispersion between the fibers(batch, size, coating, environment, △=△=135365-1351.70=1.95cm ) must be taken into account to ascertain the effect of chemical degradation or stress concentration on the Raman spectra. For △BB=1352.80-1351.70 instance, core wavenumbers in Figs. 5 and 6 differ despite erfectly identical working conditions. Yet, there is good consis If we put these shifts into Eq.(13), E 70G tency in the series of experiments that we conducted on composites I and 2 (Fig. 5). The extreme values that we obtained with 488 nm 1.54cm (Table I), excitation on nine different fibers of the: ame part of a sampl the calculated stress is 110 MPa compression in composite 2, and were -1359.5 and 1360.3 cm. A tenth fiber, isolated from a 960 MPa compression in composites 1 and 3. Hence, the the others by at least 10 diameters, showed a higher value ofThe experimental wavenumber shift Dn#Exp D-band has three possible origins. It can result from a mechanical stress (Dn#Stress), but laser heating (Dn#Heating) and/or chemical alterations (Dn#Chemistry) must also be considered: Dn# Exp D 5 n#Sample 2 n#Free-standing fiber 5 Dn#Stress 1 Dn#Heating 1 Dn#Chemistry (10) The stress-related shift, the one we want to know, is given by Dn# Stress 5 SHi-Nicalon ε zDε% (11) Concerning the laser heating, it is straightforward to write Dn# Heating 5 P~Ssample P 2 SFree-standing P ! (12) As for the chemical term, it can be neglected in our case, on account of the small bandwidth difference between embedded and reference fibers. This approximation is ascertained by the fact that Dn#Exp D > 0 for the fiber extracted from composite 2 (it has the same wavenumber in Fig. 5 as the “stress-free” references of the left-hand side), for which DnStress and DnHeating must vanish. All in all, the residual compressive stress will be obtained from the following expression: Ds~GPa! 5 EfzDε 5 S Ef 100DDε% 5 S Ef 100DS Dn#Stress SHi-Nicalon ε D 5 Ef@Dn#Exp D 2 P~Ssample P 2 SFree-standing P !# 100SHi-Nicalon ε (13) After Fig. 5, for which P is 1 mW, the experimental shifts are the following: Dn# Exp #1 5 Dn#Exp #3 5 1353.65 2 1351.70 5 1.95 cm21 Dn# Exp #2 5 1352.80 2 1351.70 5 1.10 cm21 If we put these shifts into Eq. (13), taking Ef 5 270 GPa, SHi-Nicalon ε 5 22.7 cm21 /% (see above), SD in celsian P/514.5 nm 5 20.55 cm21 /mW, and SD Free-standing P/514.5 nm 5 21.54 cm21 /mW (Table I), the calculated stress is 110 MPa compression in composite 2, and a 960 MPa compression in composites 1 and 3. Hence, the p-BN/SiC interphase apparently relaxes the residual stress (#2), but not the silicon-doped one (#3). Besides, working with the 514.5 nm line, we found that n#D in a fiber surrounded by a preserved p-BN/SiC double coating was lower than in a nearby fiber with a broken SiC ring, where p-BN layer had dissolved in the celsian. The BN layer acts as a compliant material which protects the fibers and results in better sr and m (Weibull modulus) values in the composite.29 The compressive stresses that we found (>100 and 950 MPa) are not exactly in the range anticipated from our micromechanical modeling (150–650 MPa). Yet, the modeling relied on many approximations and did not consider interphase materials at all. On the other hand, we possibly incorrectly estimated the value of Si ε . Indeed, measurements on carbon30 and polymeric fibers31 revealed a slight but steady softening when stresses are changed from tensile ones to compressive ones (Etensile . Ecompression), which means a correlative decrease of Si ε in compression. Equation (2) is only an approximation and second- or third-order polynomial expressions are necessary to unify compressive and tensile behav￾iors of Courtaulds Graphil (U.K.) XAS carbon fibers.32 However, the dependency remains linear for fully crystalline polydiacetylene fibers8 and the same must apply to Hi-Nicalon fibers. Indeed, ceramics consist of highly covalent bonds and have a 3D structure and no failure-initiating defects in compression. Besides, in the peculiar case of the Hi-Nicalon fibers, there is a uniform distribu￾tion of C and SiC species. We therefore assume our SD ε value is almost the same whatever the sign of the applied strain, at least in the explored range. (C) Statistical Relevance of the Results: It must be pointed out that not only the recording conditions, but also the statistical dispersion between the fibers (batch, size, coating, environment, . . . ) must be taken into account to ascertain the effect of chemical degradation or stress concentration on the Raman spectra. For instance, core wavenumbers in Figs. 5 and 6 differ despite perfectly identical working conditions. Yet, there is good consis￾tency in the series of experiments that we conducted on composites 1 and 2 (Fig. 5). The extreme values that we obtained with 488 nm excitation on nine different fibers of the same part of a sample were ;1359.5 and 1360.3 cm21 . A tenth fiber, isolated from the others by at least 10 diameters, showed a higher value of Fig. 5. Hi-Nicalon D band wavenumber (corrected by a neon reference line) and bandwidth determined by fitting the spectra recorded in 180 s (l 5 514.5 nm, P 5 1 mW) on cross sections of different samples (drawings on the right-hand side). Each point corresponds to a region selected in the corresponding sample. The number of recorded spectra is given. 1140 Journal of the American Ceramic Society—Gouadec et al. Vol. 84, No. 5