April 2001 Communications of the American Ceramic Society analysis reduces to the problem of a spring under uniform Hence, the modified fiber end displacement become compression. Since the axial strain in an unbonded fiber, E(), is AEr TrEt 验(m it follows that I 2Tr/ This is still a linear relationship between fiber force and displace nent with the same slope(independent of Ts )as Eq (2). Therefore all recession length determinations were made by a least-squares F甲p< Fubon linear regression fit of Eq.(4)to the compliance- push-in loading curves(omitting nonlinear regions at low loads) where 8 is the fiber end displacement, Iox is the interface recession For long recession lengths, when there was too mucl ength, Fapp is the applied force, Debond is the force required to from debonding events during initial loading, the recession length initiate debonding along the remaining unoxidized interface, rr is was determined by fitting to t the first reloading curve instead of the the fiber radius, and er is the fiber modulus. initial loading curve While Eq(2)is valid for short recession lengths, at longer recession lengths most fibers tended to move to one side of the gap left by interphase oxidation(Fig. 1(a)) so that there was at least Il. Results intermittent contact between the fiber and matrix producing some sliding friction. It was assumed that this localized sliding friction (Optical Microscopy could be treated as an equivalent uniform sliding friction, Ts, that The recession of the carbon interphase from the surface of counteracted the axial applied force, Fapp, on the fiber, ecimens was readily apparent after oxidation at 1073K(Fig I(b)). The interphase recession distance increased linearly with F(2)=F甲p-2mr (3) time, up to between 5.4 and 7.2 ks. These observations are in agreement with those of other investigators who have studied the oxidation behavior of carbon interphases. 8-20 The recession distance measured at 7.2 ks, by either the optical or push-in techn ques, was er than that predicted by the linear rate observed for times up to 5.4 ks. Although the reason for this discrepancy could not be determined, it is possibly due to the formation of interconnected pathways within the material that could provide a shortcut for oxygen transport relative to the channel caused by oxidation of the interphase (2) Push-In Testing Typical fiber push-in load-displacement curves for oxidation times,at1073K,of1.5,3.6,5.4,and7.2ks(25,60,90,andl20 min) are shown in Fig. 2. Consistent with Eq. (4), these curves are linear(except at low loads for long recession lengths) with slopes that decrease with longer oxidation times. Table i summarizes the recession lengths determined using Eq. (4)for the different oxidation times(9 to 18 tests per specimen) and compares these values with the optical measurements IV. Discussion The interphase recession distances calculated from push-in testing exhibited more scatter than those made optically. There ar two likely contributions to this scatter. As shown in Fig. 1(a), the gap due to the oxidized interphase is relatively large, hence the oxidized fibers are not laterally restrained and may experience buckling under the push-in load. This could result in a component of the nter phase Fig. 1. Examples of interphase oxidation: (a) SEM micrograph of a the distinction between oxidized and unoxidized interphases( the typical Fig. 2. Typical fiber push-in initial loading curves for various oxidationanalysis reduces to the problem of a spring under uniform compression. Since the axial strain in an unbonded fiber, ε(z), is ε~z! 5 F AfEf 5 F prf 2 Ef (1) it follows that d 5 E 0 lox ε~z! dz 5 S lox prf 2 Ef DFapp (2) for Fapp , Fdebond where d is the fiber end displacement, lox is the interface recession length, Fapp is the applied force, Fdebond is the force required to initiate debonding along the remaining unoxidized interface, rf is the fiber radius, and Ef is the fiber modulus. While Eq. (2) is valid for short recession lengths, at longer recession lengths most fibers tended to move to one side of the gap left by interphase oxidation (Fig. 1(a)) so that there was at least intermittent contact between the fiber and matrix producing some sliding friction. It was assumed that this localized sliding friction could be treated as an equivalent uniform sliding friction, ts, that counteracted the axial applied force, Fapp, on the fiber, F~z! 5 Fapp 2 2prftsz (3) Hence, the modified fiber end displacement becomes d 5 E 0 lox ε~z! dz 5 S lox prf 2 Ef DFapp 2 tslox 2 rfEf 5 S lox prf 2 Ef DFapp 2 d0 (4) for 2prftslox , F , Fdebond 1 2prftslox This is still a linear relationship between fiber force and displace￾ment with the same slope (independent of ts) as Eq. (2). Therefore, all recession length determinations were made by a least-squares linear regression fit of Eq. (4) to the compliance-corrected fiber push-in loading curves (omitting nonlinear regions at low loads). For long recession lengths, when there was too much interference from debonding events during initial loading, the recession length was determined by fitting to the first reloading curve instead of the initial loading curve. III. Results (1) Optical Microscopy The recession of the carbon interphase from the surface of specimens was readily apparent after oxidation at 1073 K (Fig. 1(b)). The interphase recession distance increased linearly with time, up to between 5.4 and 7.2 ks. These observations are in agreement with those of other investigators who have studied the oxidation behavior of carbon interphases.18–20 The recession distance measured at 7.2 ks, by either the optical or push-in techniques, was larger than that predicted by the linear rate observed for times up to 5.4 ks. Although the reason for this discrepancy could not be determined, it is possibly due to the formation of interconnected pathways within the material that could provide a shortcut for oxygen transport relative to the channel caused by oxidation of the interphase. (2) Push-In Testing Typical fiber push-in load–displacement curves for oxidation times, at 1073 K, of 1.5, 3.6, 5.4, and 7.2 ks (25, 60, 90, and 120 min) are shown in Fig. 2. Consistent with Eq. (4), these curves are linear (except at low loads for long recession lengths) with slopes that decrease with longer oxidation times. Table I summarizes the recession lengths determined using Eq. (4) for the different oxidation times (9 to 18 tests per specimen) and compares these values with the optical measurements. IV. Discussion The interphase recession distances calculated from push-in testing exhibited more scatter than those made optically. There are two likely contributions to this scatter. As shown in Fig. 1(a), the gap due to the oxidized interphase is relatively large; hence the fibers are not laterally restrained and may experience buckling under the push-in load. This could result in a component of the Fig. 1. Examples of interphase oxidation: (a) SEM micrograph of a push-in test fiber from an oxidized specimen (5.4 3 103 s at 1073 K, in air) showing a fiber leaning to one side of gap, and (b) a micrograph showing the distinction between oxidized and unoxidized interphases (the typical fiber diameter is 12 mm). Fig. 2. Typical fiber push-in initial loading curves for various oxidation times at 1073 K in air. April 2001 Communications of the American Ceramic Society 867