《复合材料 Composites》课程教学资源（学习资料）第二章 增强体_carbon fiber_Fracture toughness of PAN-based carbon fibers estimated from strength–mirror size relation

CARBON PERGAMON Carbon41(2003)979984 fracture toughness of pan-based carbon fibers estimated from strength-mirror size relation Kuniaki Honjo National Institute of Advanced Industrial Science and Technology, 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan Received 26 July 2002; accepted 4 December 200 Abstract Fracture toughness(Kic)of representative high-strength type PAn (polyacrylonitrile)-based carbon fibers, Torayca T300 and t800H. with or ut artificial surface defects, were estimated to be ca. 1 MPam- from the tensile strength vs fracture mirror size relation, assuming a constant crack-to-mirror size ratio. The corresponding critical energy release rat T)was ca. 7.4Jm, which was close to the value derived from the reported surface energies for a graphite crystal. Similar Kic values were obtained for the old-type PAN-based carbon fibers from the reported data by the use of the estimation procedure C 2003 Elsevier Science Ltd. All rights reserved Keywords: A Carbon fibers; C. Scanning electron microscopy (SEM); D. Fracture, Mechanical properties 1. Introduction size of a sharp edged crack. From fractographic observa tions on cracks, Whitney and Kimmel [3 estimated the Though fracture toughness, Kic, is one of the fundamen- surface energy (y), which is half of the critical energy tal properties of carbon fibers, which are reinforcements release rate(r), for old types of PAN-based carbon fiber widely used for composites, only a few data were reported with Youngs moduli ranging from 138 to 272 GPa, on this value. Helmer et al. [1] estimated a value of 1 assuming the fibers to be isotropic. The Kic values MPam for a PAN-based carbon fiber Torayca T800H converted from those y values are 2.67 to 4.7 MPam/2 (Toray Co. )from the dependence of tensile strength on the The problem of that method is how to identify a sharp thickness of a pyrolytic carbon coating, implicitly assum- dged crack on a fracture surface; a crack they considered ing Young's modulus of the coating is the same as that of seems to be a fracture mirror as will be mentioned later in the carbon fiber. This assumption, however, may not be this paper If-evident, because the in-plane Youngs modulus of a In the present study, Kic values of carbon fibers were pyrolytic carbon film, in which the basal planes of estimated from the size of a mirror region at the fracture turbostratic carbon crystallites are preferentially parallel to origin instead, because defects or cracks at the origin were the surface, is representatively 50 GPa[2], whereas the in many cases too small or featureless to be observed by ial Youngs modulus of the T800H carbon fiber is 293 scanning electron microscopy(SEM). The same method GPa. Therefore estimations by other methods would be was used for polycarbosilane-based SiC fibers(such Nicalon fiber of Nippon Carbon Co., Tokyo, Japan) by Fracture toughness, Kic, will be estimated from the several authors [4, 5]. Fig. I shows a schematic sketch of a Griffiths(Irwins)relation between tensile strength and fracture surface of glass cited from a paper of mechlosk et al. [6]. As suggested by many authors [6-9], the rH/c Tel:+81-727-519-535;fax:+81-727-519-637. ratio is a constant for a material, where rH, called the outer E-mail address. k-honjo @aist. go. jp(K. Honjo) mirror radius, is the distance from the origin to the onset of Also, 65 GPa by our three-point bending measurement for a hackle, and c is the radius of a sharp edged crack("source 200C-deposited 30-]m-thick film. of failure'in Fig. 1). Mechlosky et al. [7 and Bansal and 0008-6223/03/S-see front matter 2003 Elsevier Science Ltd. All rights reserved doi:1o.1016/S0008-6223(02)00444x

Carbon 41 (2003) 979–984 F racture toughness of PAN-based carbon fibers estimated from strength–mirror size relation Kuniaki Honjo* National Institute of Advanced Industrial Science and Technology, 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan Received 26 July 2002; accepted 4 December 2002 Abstract Fracture toughness (K ) of representative high-strength type PAN (polyacrylonitrile)-based carbon fibers, Torayca
T300 IC 1/2 and T800H, with or without artificial surface defects, were estimated to be ca. 1 MPam from the tensile strength vs. fracture mirror size relation, assuming a constant crack-to-mirror size ratio. The corresponding critical energy release rate 22 (G ) was ca. 7.4 J m , which was close to the value derived from the reported surface energies for a graphite crystal. Similar K values were obtained for the old-type PAN-based carbon fibers from the reported data by the use of the present IC estimation procedure.  2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Carbon fibers; C. Scanning electron microscopy (SEM); D. Fracture, Mechanical properties 1. Introduction size of a sharp edged crack. From fractographic observa￾tions on cracks, Whitney and Kimmel [3] estimated the Though fracture toughness, KIC, is one of the fundamen- surface energy (g ), which is half of the critical energy tal properties of carbon fibers, which are reinforcements release rate (G ), for old types of PAN-based carbon fiber widely used for composites, only a few data were reported with Young’s moduli ranging from 138 to 272 GPa, on this value. Helmer et al. [1] estimated a value of 1 assuming the fibers to be isotropic. The K values IC 1/2 1/2 MPam for a PAN-based carbon fiber Torayca T800H converted from those g values are 2.67 to 4.7 MPam . (Toray Co.) from the dependence of tensile strength on the The problem of that method is how to identify a sharp thickness of a pyrolytic carbon coating, implicitly assum- edged crack on a fracture surface; a crack they considered ing Young’s modulus of the coating is the same as that of seems to be a fracture mirror as will be mentioned later in the carbon fiber. This assumption, however, may not be this paper. self-evident, because the in-plane Young’s modulus of a In the present study, K values of carbon fibers were IC pyrolytic carbon film, in which the basal planes of estimated from the size of a mirror region at the fracture turbostratic carbon crystallites are preferentially parallel to origin instead, because defects or cracks at the origin were 1 the surface, is representatively 50 GPa [2], whereas the in many cases too small or featureless to be observed by axial Young’s modulus of the T800H carbon fiber is 293 scanning electron microscopy (SEM). The same method GPa. Therefore estimations by other methods would be was used for polycarbosilane-based SiC fibers (such as necessary. Nicalon
fiber of Nippon Carbon Co., Tokyo, Japan) by Fracture toughness, K , will be estimated from the several authors [4,5]. Fig. 1 shows a schematic sketch of a IC Griffith’s (Irwin’s) relation between tensile strength and fracture surface of glass cited from a paper of Mechlosky et al. [6]. As suggested by many authors [6–9], the r /c H ratio is a constant for a material, where r , called the outer *Tel.: 181-727-519-535; fax: 181-727-519-637. H E mirror radius, is the distance from the origin to the onset of -mail address: k-honjo@aist.go.jp (K. Honjo). 1 Also, 65 GPa by our three-point bending measurement for a hackle, and c is the radius of a sharp edged crack (‘‘source 1200 8C-deposited 30-mm-thick film. of failure’’ in Fig. 1). Mechlosky et al. [7] and Bansal and 0008-6223/03/$ – see front matter  2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0008-6223(02)00444-X

K. Honjo Carbon 41(2003)979-984 HACKLE REGION tive high-strength(HT) type PAn (polyacrylonitrile)-based carbon fibers, which are less graphitic than high-modulus MIST REGION SOURCE OF (HM) type fibers such as the Torayca M40 fiber(Toray Co. )with a modulus of 390 GPa. PAN-based carbon fibers SMOOTH MIRROR consist of fibrils of turbostratic carbon, whose basal planes orient preferentially parallel to the fiber axis. The degrees of axial orientation of the fibrils of the t300 and t800H fibers [11](partially in Ref. [12) are similar, as indicated by the full-width-at-half-maximum, FWHM, of 34.5 and 30.3, respectively, of the intensity profile l(o)of 00. 2 X-ray diffraction which centers on the equator, and differ Fig. 1. Shape and general arance of fracture mirror and from that of the more highly oriented M40 fiber with a related features on typical glass fracture surface (cited from FWHM of 17.7. Since the orientations of the basal planes Mecholsky et al. 6) are random and the crystallite sizes are uniform in a transverse section especially in the HT type fibers [13, 14 we can consider them to be mechanically axially aniso- Duckworth[8] also considered that this ratio, which is ca. tropic with transverse isotropy having properties in Table 13 according to Ref. [7, is material-independent for 1, which are based on bulk measurements many polycrystalline or amorphous ceramics To obtain fiber filaments with a variety of Tensile strength, o, is related to c by Griffith's(Ir- surface defects were introduced by rubbing abrasive: a 1-um diamond coated abrasive film g,=Kic/F(rc)(F: geometric constant for a crack Sic powder, or by an etching reaction to them during chemical vapor deposition of TiC or TiN. (The TiC and (1) TiN were dissolved away in a mixture of nitric acid and hydrofluoric acid, 4: 1, at a room temperature for I h before Thus, using a constant ru/c value, o is related to ru by testing. ) The filaments were tensile- fractured in glycerol, a damper to avoid secondary fractures, on an Instron-type F=A/r (2) filament testing machine(Type UTM-I1-20, Orientec Co Tokyo, Japan) with a gauge length of 10 mm and a cross head speed of 2 mm min, and then, rinsed with water KAESA (3) and ethanol. Those filaments which were not secondary where fractured, i.e., whose recovered two fragments matched in the fracture position, were lightly Au-coated and observed by SEM. The distance from the fracture origin to the onset of"hackle'"region of a filament on a SEM micrograph and A is called a mirror constant. The geometric constant F was taken as ru (outer mirror radius ) The tensile strength is 0.75 according to Bansal [10] for a semi-circular o of the filament was determined using its cross sectional surface crack with an alb, ratio of lengths of axes in Fig. area measured on the micrograph 1, between 0.2 and 3. Then, Kic will be determined from A using Eqs. (3)and (4) 3. Results and discussion 2. Experimen All filaments fractured from the surface. Fig. 2 shows some SEM photographs of the fracture surface of the T300 carbon T300 and and t800H carbon fiber filaments with different strengths fibers(Toray Co. These selected photographs are exceptions in a sense that s moduli and 294 GPa( 1), respective- they show a defect at the fracture origin, though it was not ly. They were supplied without sizing. Both are representa- visible on most of the filaments. The boundary between the mirror” and the“ hackle” regions is clear for the t300 SImilar values are expected from the a/kic ratios of ca 2 for fiber, and the lower the filament strength, the less the several ceramics in Refs. [8]and [9] change of roughness amplitude is between these region A value of 0.71 was used by olsky et al. 6. Care should be The boundary is clear for the T800H fiber filaments with taken not to confuse K with k in K=tk=Fofac)";some high strengths, but it is less clear for a weak filament with times they are confused a strength as low as 2.4 GPa, because fracture traces are The so-named T800 and T800HB fibers are identical to the more obvious in the""(or"mist")region on this T800H fiber, according to Toray Co fiber than on the T300 fiber. For the HM type M40 carbon

980 K. Honjo / Carbon 41 (2003) 979–984 tive high-strength (HT) type PAN (polyacrylonitrile)-based carbon fibers, which are less graphitic than high-modulus (HM) type fibers such as the Torayca
M40 fiber (Toray Co.) with a modulus of 390 GPa. PAN-based carbon fibers consist of fibrils of turbostratic carbon, whose basal planes orient preferentially parallel to the fiber axis. The degrees of axial orientation of the fibrils of the T300 and T800H fibers [11] (partially in Ref. [12]) are similar, as indicated by the full-width-at-half-maximum, FWHM, of 34.58 and 30.38, respectively, of the intensity profile I(f) of 00.2 X-ray diffraction which centers on the equator, and differ from that of the more highly oriented M40 fiber with a Fig. 1. Shape and general appearance of fracture mirror and FWHM of 17.78. Since the orientations of the basal planes related features on typical glass fracture surface (cited from Mecholsky et al. [6]). are random and the crystallite sizes are uniform in a transverse section especially in the HT type fibers [13,14], we can consider them to be mechanically axially aniso￾Duckworth [8] also considered that this ratio, which is ca. tropic with transverse isotropy having properties in Table 2 13 according to Ref. [7] , is material-independent for 1, which are based on bulk measurements. many polycrystalline or amorphous ceramics. To obtain fiber filaments with a variety of strengths, Tensile strength, su, is related to c by Griffith’s (Ir- surface defects were introduced by rubbing with an win’s) relation: abrasive: a 1-mm diamond coated abrasive film or 6-mm SiC powder, or by an etching reaction to them during 1/2 s 5 K /hF ? (pc) j (F: geometric constant for a crack) u IC chemical vapor deposition of TiC or TiN. (The TiC and (1) TiN were dissolved away in a mixture of nitric acid and hydrofluoric acid, 4:1, at a room temperature for 1 h before Thus, using a constant r /c value, s is related to r by: testing.) The filaments were tensile-fractured in glycerol, a Hu H damper to avoid secondary fractures, on an Instron-type 1/2 s 5 A/r (2) u H filament testing machine (Type UTM-II-20, Orientec Co., Tokyo, Japan) with a gauge length of 10 mm and a cross and: 21 head speed of 2 mm min , and then, rinsed with water KIC 5 SA (3) and ethanol. Those filaments which were not secondary fractured, i.e., whose recovered two fragments matched in where: the fracture position, were lightly Au-coated and observed 1/2 1/2 by SEM. The distance from the fracture origin to the onset S ; Fp /(r /c) (4) H of ‘‘hackle’’ region of a filament on a SEM micrograph and A is called a mirror constant. The geometric constant F was taken as r (outer mirror radius). The tensile strength, H 3 is 0.75 according to Bansal [10] for a semi-circular s , of the filament was determined using its cross sectional u surface crack with an a/b, ratio of lengths of axes in Fig. area measured on the micrograph. 1, between 0.2 and 3. Then, KIC will be determined from A using Eqs. (3) and (4). 3. Results and discussion 2. Experimental All filaments fractured from the surface. Fig. 2 shows some SEM photographs of the fracture surface of the T300 Fibers for this study were the Torayca
T300 and and T800H carbon fiber filaments with different strengths. 4 T800H carbon fibers (Toray Co., Tokyo, Japan) with These selected photographs are exceptions in a sense that Young’s moduli of 230 and 294 GPa (Table 1), respective- they show a defect at the fracture origin, though it was not ly. They were supplied without sizing. Both are representa- visible on most of the filaments. The boundary between the ‘‘mirror’’ and the ‘‘hackle’’ regions is clear for the T300 fiber, and the lower the filament strength, the less the 2 Similar values are expected from the A/K ratios of ca. 2 for IC change of roughness amplitude is between these regions. several ceramics in Refs. [8] and [9]. 3 The boundary is clear for the T800H fiber filaments with A value of 0.71 was used by Mecholsky et al. [6]. Care should be 1/2 1/2 high strengths, but it is less clear for a weak filament with taken not to confuse K with k in K5p k5Fs(pc) ; some￾a strength as low as 2.4 GPa, because fracture traces are times they are confused. 4 The so-named T800 and T800HB fibers are identical to the more obvious in the ‘‘mirror’’ (or ‘‘mist’’) region on this T800H fiber, according to Toray Co. fiber than on the T300 fiber. For the HM type M40 carbon

K Honjo /Carbon 41(2003)979-98 Table I Typical properties of carbon fibers hear modulus, CTE Pon sIsson s Density P Diameter, D strength, o. modulus, E Geran (mean: 300-1273 K)d, a FWHM(002),Adn ratio (kg m -) (um) (GPa) (GPa) 1. 12(axial) 03{2-e2)21.76×1 6.9 TS00H 294(axial 1.07(axial) 03(42=m2)1.81×1 5.1 20(radial)- 2.74 392(ax 0.51(axial) 177 81×10-36 Producer's data sheet. Assumed from G, for PAn based fibers with similar E in Ref. [21] Refs. [11, 12] Ref. [ 22] Assumed: the same values as for the t300 fiber fiber, which is not included in this paper, measurement of A thermodynamic Y(y: surface energy, G: graphite) rH was difficult, because the mirror region was obscured value of 4.8J m- was given by Abrahamson [16]for a by rough morphologies, probably owing to a higher lateral surface of a graphite crystal. According to Perret graphitic texture and Ruland [181, a PAN-based carbon fiber filament Fig.3 shows the o, of the fiber filaments, vS rH. The consists of axially oriented wrinkled fibrils of turbostratic slopes of straight lines for the plots determined by the least carbon separated by axially elongated pores [18, 19] with quare method so as to pass the origin give mirror diameter, the 00. 2 inter plane distance of the onstants, A,of 2.2 and 2.1 MPam, respectively, for the carbon being larger than that of graphite. Thus the 2y T300 and T800H fibers. The methods for creating surface CF: carbon fiber) for these fibers are ca. 7.4 Jm defects, mechanical or chemical, do not show marked considering that the packing density of graphitic basal differences in the o-rH relation. The a,, rH, c. and rH/c slanes in a transverse section of a carbon fiber would be values(co: length in depth of a defect at the fracture origin, less than that on a lateral surface of a graphite crystal as in cases observed) for all of these filaments are tabulated in Table Al in Appendix A. 2yp=2%×(pclp)×(cos(d) The rH/c. ratios for the T300 and T800H fibers and =5, respectively, which differ from 13 in Ref [7] for where Pcr(ca 1.8X10 kg m )and 66×10 materials. Using these rH/c, values, Kic values for kg m )are the densities of the carbon fiber and a graphite fibers are estimated to be 1 11 and 1. 25 MPam crystal, respectively, and (cos()), of ca. 0.97, is the espectively. Even if the observed defects are not sharp average of cos() for carbon crystallites whose basal edged, we can consider them as upper-bound values of planes incline by to the fiber axis. The 2yr value of 7.4 KIc. If the rH/c of 13 is correct, Kc values may be 0.8 J m is close to the I values of 8.6 and 7.4 J m Summarizing, the kic value for these fibers obtained for these fibers would be≈ I MPan1 Table 2 shows the re-estimated K values for the fibers The critical energy release rates, I, which correspond to in Whitney and Kimmel's paper [3]. As well as the the kic of 1 MPam, are 8.6 and 7.4 Jm for the T300 specified B, C and E fibers, the A and D fibers also are and T800H fibers, respectively, using Sih et al.'s relation most probably PAN-based, from the heat treatment tem- between I and Kc for a crack whose plane is on the axis perature, Youngs moduli and the producer's name. The of an orthotropic body [15] fibers a and e are those for which a set of strength, "crack r=K12(s15212)I(s2/s1)2 size"and micrograph was given or cited. Using the y +(2s,+S)/(2s,(plane stress) (5) Incze et al. gave y values of 5. 33(relaxed configuration) where s,=1/E, S22=1/E,, Su2= relaxed)J m- from ab-initio calculation [17] G.(E is Youngs modulus, G shear modulus, and This is determined by focos(o).1(o)do/fo cos( Poisson's ratio for a strain in the r-direction by a strain in in which the profile of 00.2 X-ray diffraction intensity direction; the subscripts“z” indicates the axial and“r measured from the equator) is approximated to be gaussia FWHM in Table I the radial directions)

K. Honjo / Carbon 41 (2003) 979–984 981 Table 1 Typical properties of carbon fibers a b d be Fiber Tensile Young’s Shear modulus, CTE Azimuthal Poisson’s Density , r Diameter , D d 23 strength, s modulus, E G (mean: 300–1273 K) , a FWHM(002), Df ratio (kg m ) (mm) u u z5rz 1/2 26 21 (GPa) (GPa) (GPa) (10 K ) (8) b c f 23 T300
3.53 230 (axial) 25 1.12 (axial) 34.5 0.3 (y ) 1.76310 6.9 rz5u z f f 20 (radial) 0.42 (y ) ru 5u r b c g 23 T800H
5.59 294 (axial) 25 1.07 (axial) 30.3 0.3 (y ) 1.81310 5.1 rz5u z g g 20(radial) 0.42 (y ) ru 5u r b c 23 M40
2.74 392 (axial) 22 0.51 (axial) 17.7 – 1.81310 6.5 a Torayca
fibers. b Producer’s data sheet. c Assumed from G for PAN based fibers with similar E in Ref. [21]. u z d Refs. [11,12]. e From mass and r. f Ref. [22]. g Assumed: the same values as for the T300 fiber. fiber, which is not included in this paper, measurement of A thermodynamic g (g : surface energy, G: graphite) G 22 r was difficult, because the mirror region was obscured value of 4.8 J m was given by Abrahamson [16] for a H 5 by rough morphologies, probably owing to a higher lateral surface of a graphite crystal . According to Perret graphitic texture. and Ruland [18], a PAN-based carbon fiber filament 21/2 Fig. 3 shows the s of the fiber filaments, vs. r . The consists of axially oriented wrinkled fibrils of turbostratic u H slopes of straight lines for the plots determined by the least carbon separated by axially elongated pores [18,19] with square method so as to pass the origin give mirror nano-metric diameter, the 00.2 inter plane distance of the 1/2 constants, A, of 2.2 and 2.1 MPam , respectively, for the carbon being larger than that of graphite. Thus the 2gCF 22 T300 and T800H fibers. The methods for creating surface (CF: carbon fiber) for these fibers are ca. 7.4 J m , defects, mechanical or chemical, do not show marked considering that the packing density of graphitic basal differences in the s –r relation. The s , r , c and r /c planes in a transverse section of a carbon fiber would be u H uH o Ho values (c : length in depth of a defect at the fracture origin, less than that on a lateral surface of a graphite crystal as: o in cases observed) for all of these filaments are tabulated in Table A1 in Appendix A. 2g 5 2g 3 (r /r ) 3 kcos(f)l (6) CF G CF G The rH o /c ratios for the T300 and T800H fibers are ¯7 23 23 23 and ¯5, respectively, which differ from 13 in Ref. [7] for where rCF G (ca. 1.8310 kg m ) and r (2.266310 23 other materials. Using these r /c values, K values for kg m ) are the densities of the carbon fiber and a graphite H o IC 1/2 these fibers are estimated to be 1.11 and 1.25 MPam , crystal, respectively, and kcos(f)l, of ca. 0.97, is the 6 respectively. Even if the observed defects are not sharp average of cos(f) for carbon crystallites whose basal edged, we can consider them as upper-bound values of planes incline by f to the fiber axis. The 2gCF value of 7.4 22 22 KIC H IC . If the r /c of 13 is correct, K values may be 0.8 J m is close to the G values of 8.6 and 7.4 J m 1/2 MPam . Summarizing, the K value for these fibers obtained for these fibers. IC 1/2 would be ¯1 MPam . Table 2 shows the re-estimated K values for the fibers IC The critical energy release rates, G, which correspond to in Whitney and Kimmel’s paper [3]. As well as the 1/2 22 the K of 1 MPam , are 8.6 and 7.4 J m for the T300 specified B, C and E fibers, the A and D fibers also are IC and T800H fibers, respectively, using Sih et al.’s relation most probably PAN-based, from the heat treatment tem￾between G and K for a crack whose plane is on the axis perature, Young’s moduli and the producer’s name. The IC of an orthotropic body [15]: fibers A and E are those for which a set of strength, ‘‘crack 2 1/2 1/2 size’’ and micrograph was given or cited. Using the g G 5 K (s s /2) [(s /s ) IC 11 22 22 11 1/2 1 (2s 1 s )/(2s )] (plane stress) (5) 5 12 66 11 Incze et al. gave g values of 5.33 (relaxed configuration) and 6.45 22 (unrelaxed) J m from ab-initio calculation [17]. where s 51/E , s 51/E , s 52n /E , and s 51/ 11 r 22 z 12 rz z 66 6 p /2 2 p / 2 This is determined by e cos (f)?I(f)df/e cos(f)?I(f)df, G 0 0 rz rz rz (E is Young’s modulus, G shear modulus, and n in which the profile of 00.2 X-ray diffraction intensity I(f) (f: Poisson’s ratio for a strain in the r-direction by a strain in measured from the equator) is approximated to be Gaussian using z-direction; the subscripts ‘‘z’’ indicates the axial and ‘‘r’’ FWHM in Table 1. the radial directions)

K. Honjo Carbon 41(2003)979-984 d ou 2.1 GPa o, 3.4 GPa 16m605μm le6.4 r/c4.3 A 2.6 MPam /2 A 2.3 MPam/eun e 3.1 GPa FH 0.7 um 8.3 A 2.6 MPam/2 9 GP 1.3 lumh/o。10.1 0.. 1.6 GPa C. 2. 4 GPa 15 0.6 /c。5.4 r/c。5.1 A 2.0 MPam/ dumA 1.8 MPamI/ Fig. 2. Tensile fractured surface of carbon fibers on which a defect is observed at the fracture origin; o: filament strength, rH: mirror radius, ruc. ratio of mirror radius observed defect length from the filament surface (a-(c): T300 fiber, (d)-(f: T800H fiber value in Ref. 3,"crack sizes" for the filaments of the tograph(Fig. I in Ref [ 3]) of a filament (o of 1.55 fiber e with the o values of 3. 1 and 1. 8 GPa are estimated GPa), as well as that of a void adjacent to the"mirror to be 0.7 um and 1. I um, respectively; they agree with the Thus, they seem to have regarded a"mirror"as a mirror radii"on the micrographs in Ref. [20] cited crack". The K values re-estimated with the ru /c ratio Ref. [3]. The"crack size"estimated for the fiber A is of 6 (average of rH/c, for T300 and T800H fibers) and the similar to the radius of amirror"(0.9 um)on a F factor of 0. 75 range from 0.8 to 1. 4 MPam" they are

982 K. Honjo / Carbon 41 (2003) 979–984 Fig. 2. Tensile fractured surface of carbon fibers on which a defect is observed at the fracture origin; s : filament strength, r : mirror radius, u H r /c : ratio of mirror radius to the observed defect length from the filament surface. (a)–(c): T300 fiber, (d)–(f): T800H fiber. H o value in Ref. [3], ‘‘crack sizes’’ for the filaments of the photograph (Fig. 1 in Ref. [3]) of a filament (su of 1.55 fiber E with the s values of 3.1 and 1.8 GPa are estimated GPa), as well as that of a void adjacent to the ‘‘mirror’’. u to be 0.7 mm and 1.1 mm, respectively; they agree with the Thus, they seem to have regarded a ‘‘mirror’’ as a ‘‘mirror radii’’ on the micrographs in Ref. [20] cited in ‘‘crack’’. The K values re-estimated with the r /c ratio IC H Ref. [3]. The ‘‘crack size’’ estimated for the fiber A is of 6 (average of r /c for T300 and T800H fibers) and the H o 1/2 similar to the radius of a ‘‘mirror’’ (0.9 mm) on a F factor of 0.75 range from 0.8 to 1.4 MPam ; they are

K. Honjo Carbon 41(2003)979-984 Mirror radius: rH / um 21.51 0.5 abraded etched 84730 T800H ◇ line is for A=22MPa·m12 A (rH1m)-12 Fig. 3. Tensile strength vs. mirror radius for T300 and T800H carbon fibers, which fractured from filament surface. Circle: mechanically abraded or as-obtained, square: chemically damaged during deposition of TiC or TiN, which were removed by dissolution before testing. A line for 4=2.2 MPam is shown in the figure close to the value for the T300 and T800H fibers in the MPam". Corresponding I values are close to the 2yce present stud value estimated from the y value for a graphite crystal The Kic values re-estimated for the old PAN-based fiber in Whitney and Kimmel's paper are also close to the 4. Conelusions observed values. These K values are similar to those of polycarbosilane based SiC fibers (I MPam")[4, 5 and The Kic values of the PAN-based high strength type silicate glasses(ca 0.7 MPam")[6], and also to that of T300 and T800H carbon fibers are found to be polycrystalline graphite (1 MPam)[7 Table 2 Re-estimated Kic for the fibers in Whitney and Kimmel's paper 3] Identity y value"(Ref. [3]) Kc value for y in Ref [3] Re-estimated Kc; rH/e=6 name with F=l(m)(MPam) and F=0.75(MPam") 2.7 HT-S D 43439 Ref. 20 1.8and3.2 The fibers are assumed to be isotropic in Ref. [ 3] Celanese Research Company Great Lakes Carbon Co The filaments on Johnson's micrographs(Fig. 5a and b in Ref. [20)). Acrilan"( Chemstrand Ltd based

K. Honjo / Carbon 41 (2003) 979–984 983 Fig. 3. Tensile strength vs. mirror radius for T300 and T800H carbon fibers, which fractured from filament surface. Circle: mechanically abraded or as-obtained, square: chemically damaged during deposition of TiC or TiN, which were removed by dissolution before testing. A 1/2 line for A52.2 MPam is shown in the figure. 1/2 close to the value for the T300 and T800H fibers in the MPam . Corresponding G values are close to the 2gCF present study. value estimated from the g value for a graphite crystal. G The K values re-estimated for the old PAN-based fibers IC in Whitney and Kimmel’s paper are also close to the 4. Conclusions observed values. These K values are similar to those of IC 1/2 polycarbosilane based SiC fibers (1 MPam ) [4,5] and 1/2 The K values of the PAN-based high strength type silicate glasses (ca. 0.7 MPam ) [6], and also to that of IC 1/2 T300 and T800H carbon fibers are found to be |1 polycrystalline graphite (1 MPam ) [7]. Table 2 Re-estimated K for the fibers in Whitney and Kimmel’s paper [3] IC a Fiber Identity E s g u IC IC H value (Ref. [3]) K value for g in Ref. [3] Re-estimated K ; r /c56 22 1/2 1/2 name (GPa) (GPa) with F51 (J m ) (MPam ) and F50.75 (MPam ) b A – 255 1.3 14 2.7 0.8 c B 4T 271 2.6 31 4.1 1.3 d C HT-S 272 2.5 41 4.7 1.4 b D – 262 2.3 35 4.3 1.3 e E Ref. [20] 138 1.8 and 3.2 39 3.3 1.0 a The fibers are assumed to be isotropic in Ref. [3]. b Celanese Research Company. c Great Lakes Carbon Co. d Hercules, Inc. e The filaments on Johnson’s micrographs (Fig. 5a and b in Ref. [20]). Acrilan
(Chemstrand Ltd.) based

K Honjo /Carbon 41(2003)979-98 Table Al Tensile strength(o ), mirror radius (rH), observed flaw depth from surface (c)and rH/c, ratio for filaments in Fig. 3 500 fiber T800H fiber (GPa)(um) (GPa)(um)(um) (GPa)(um)(um) rHc。 Pa) (um) (um 24 .550.246 3.390.470.114 3.880.53 3.130.33 2.860.75 1.891.34 3.100.720.09 2.790.600.144 297093 1.941.280.1310 2.67 2.530.69 3.l10 1.76 3.14049 195169 770.76 2071.53 1.79 0.81 440.72 2.310.75 1.540.85 2040.56 960490.153 1.611.500.2852400.67 3.350.31 2.840.86 660.94 2.530.56 1931.51 1951650.2861.810. 4.040.20 001.86 560.115 1.34166 1.213.040.55 4.770.29 2420.73 2.8 3.070.67 2.770.85 4.490.20 304 3.510.46 3050.51 2.700.590.096 3.10 .51 206101 2.950.52 3.06 References [11 Yasuda E, Tanabe T, Machino H, Kimura S. Correlation etween thermal expansion coefficient and orientation func- [1] Helmer T, Peterlik H, Kromp K. Coating of carbon fibers- on of various types of carbon fibers. TANSO 1988; 132: 2- the strength of the fibers. J Am Ceram Soc 1995: 78(1): 133-6 5, in Japanese. [2] Bokros JC. Deposition, structure, and properties of pyrolytic [12] Yasuda E, Tanabe T, Machino H, Takaku A. Thermal carbon. In: Walker Jr. PL. editor. Chemi arbon, vol 5, New York: Marcel Dekker, 1969, pp. 1-1l8 1000C. In: Extended abstracts 18th biennial conference carbon, American Carbon Society, 1987, pp 30-1 [3] Whitney W, Kimmel RM. Griffith equation and carbon fibre [13] Paris O, Loidl D, Peterlik H. Texture of PAN- and pitch- strength. Nature Phys Sci 1972- 237- 93-4 4] Kondo M, Tezuka H, Kohyama A Characteristics of pcs-SIC ased carbon fibers. Carbon 2002:40- 551 fiber after fabrication of aluminum alloy matrix composite [14] Guigon M, Oberlin A, Desarmot G. Microtexture and es. In: Proc. 7th International Conference on Composite structure of some high tensile strength PAN-base carbon Materials, Guangzhou, Oxford: Intermational Academic Publ fibres. Fibre Sci Technol 1984- 20: 55-72 Beijing, Pergamon Press, 1989, pp. 55-61, vol. 2. [15] Sih GC, Paris PC, Irwin GR. On cracks in rectilinearly 5] Thouless MD, Sbaizero O, Sigl LS, Evans AG. Effect of anisotropic bodies. Int J Fracture Mech 1965, 1: 189-203 terface mechanical properties on pullout in a SiC-fiber- [16 Abrahamson J. The surface energies of graphite. Carbon einforced lithium aluminum silicate glass-ceramic. JAm 1973;1:337-62. Ceram soc1989;72(4):525-32. [17] Incze A, Pasturel A, Chatillon C. Ab initio study of graphite [6]Mecholsky JJ, Rice RW, Freiman Sw. Prediction of fracture matic surfaces. Appl Surf Sci 2001; 177: 221 [18 Perret R, Ruland w. The microstructure of PAN-base carbon nergy and flaw size in glasses from measurements of mirror size. J Am Ceram Soc 1974: 57: 440-3 fibres, J Appl Crystallogr 1970:3: 525-32 [19] Sasanuma Y, Kitano Y, J Mecholsky JJ, Freiman Sw, Rice Rw. Fracture surface analysis of ceramics. J Mater Sci 1976: 11: 1310-9 industrial materials by smal X-ray scattering. J Mater Sci1989;24:1133-9 [8] Bansal GK, Duckworth WH. Fracture stress as related to [20] Johnson JW, Thorne DJ. Effect of intemal polymer flaws on faw and fracture mirror sizes. J Am Ceram Soc 1977: 60(7- strength of carbon fibres prepared from an acrylic precursor. 8):304-10 9 Kirchner HP, Gruver RM, Sotter WA. Fracture stress-mirror 21] Sawada Y, Shindo A. Torsional properties of carbon fibers. relations for polycrystalline ceramics. Philos Mag Carbon1992;304):619-29 1976;33(5):775-80 [22] Ishikawa T, Koyama K, Kobayashi S. Elastic moduli of [10] Bansal GK. Effect of flaw shape on strength of ce carbon-epoxy composites and carbon fibers. J Composite m Ceram Soc 1976: 59(1-2): 87-8 Mater1977;11:332-44

984 K. Honjo / Carbon 41 (2003) 979–984 Appendix A Table A1 Tensile strength (su H o Ho ), mirror radius (r ), observed flaw depth from surface (c ) and r /c ratio for filaments in Fig. 3 T300 fiber T800H fiber s rcr /c s rcr /c s rcr /c s rcr /c u H o Ho u H o Ho u H o Ho u H o Ho (GPa) (mm) (mm) (GPa) (mm) (mm) (GPa) (mm) (mm) (GPa) (mm) (mm) 2.21 1.24 2.06 1.55 0.24 6 3.39 0.47 0.11 4 3.88 0.53 1.85 1.02 2.06 1.43 0.19 7 3.09 0.36 2.76 0.45 1.91 1.09 1.98 1.42 3.13 0.33 2.82 0.76 2.86 0.75 1.89 1.34 3.10 0.72 0.09 8 2.79 0.60 0.14 4 2.97 0.93 1.94 1.28 0.13 10 2.67 0.61 2.53 0.69 3.11 0.92 1.87 1.76 3.29 0.64 3.14 0.49 1.95 1.69 2.14 1.25 3.08 0.50 2.77 0.76 2.64 0.53 2.07 1.53 1.79 0.81 2.44 0.72 2.31 0.75 1.54 0.85 2.04 0.56 2.96 0.49 0.15 3 2.69 0.99 1.61 1.50 0.28 5 2.40 0.67 3.35 0.31 2.84 0.86 1.66 0.94 2.53 0.56 3.58 0.38 1.93 1.51 1.95 1.65 0.28 6 1.81 0.86 4.04 0.20 1.99 0.79 1.00 1.86 2.42 0.56 0.11 5 4.60 0.31 1.34 1.66 1.21 3.04 0.55 5 3.60 0.45 4.77 0.29 2.42 0.73 1.18 2.08 2.81 0.49 5.61 0.17 2.75 0.70 3.07 0.67 2.77 0.85 4.49 0.20 3.04 0.41 3.51 0.46 3.05 0.51 – – – – 2.64 1.01 3.46 0.40 2.70 0.59 0.09 6 2.53 0.60 3.10 0.51 2.68 0.67 2.06 1.01 2.95 0.52 3.06 0.49 2.97 0.55 References [11] Yasuda E, Tanabe T, Machino H, Kimura S. Correlation between thermal expansion coefficient and orientation func￾tion of various types of carbon fibers. TANSO 1988;132:2– [1] Helmer T, Peterlik H, Kromp K. Coating of carbon fibers— 5, in Japanese. the strength of the fibers. J Am Ceram Soc 1995;78(1):133–6. [12] Yasuda E, Tanabe T, Machino H, Takaku A. Thermal [2] Bokros JC. Deposition, structure, and properties of pyrolytic expansion behavior of various types of carbon fibers up to carbon. In: Walker Jr. PL, editor, Chemistry and physics of 1000 8C. In: Extended abstracts 18th biennial conference on carbon, vol. 5, New York: Marcel Dekker, 1969, pp. 1–118. carbon, American Carbon Society, 1987, pp. 30–1. [3] Whitney W, Kimmel RM. Griffith equation and carbon fibre [13] Paris O, Loidl D, Peterlik H. Texture of PAN- and pitch- strength. Nature Phys Sci 1972;237:93–4. based carbon fibers. Carbon 2002;40:551–5. [4] Kondo M, Tezuka H, Kohyama A. Characteristics of pcs-SiC [14] Guigon M, Oberlin A, Desarmot G. Microtexture and fiber after fabrication of aluminum alloy matrix composite structure of some high tensile strength PAN-base carbon wires. In: Proc. 7th International Conference on Composite Materials, Guangzhou, Oxford: International Academic Publ. fibres. Fibre Sci Technol 1984;20:55–72. [15] Sih GC, Paris PC, Irwin GR. On cracks in rectilinearly Beijing, Pergamon Press, 1989, pp. 55–61, vol. 2. anisotropic bodies. Int J Fracture Mech 1965;1:189–203. [5] Thouless MD, Sbaizero O, Sigl LS, Evans AG. Effect of [16] Abrahamson J. The surface energies of graphite. Carbon interface mechanical properties on pullout in a SiC-fiber- 1973;11:337–62. reinforced lithium aluminum silicate glass-ceramic. J Am [17] Incze A, Pasturel A, Chatillon C. Ab initio study of graphite Ceram Soc 1989;72(4):525–32. prismatic surfaces. Appl Surf Sci 2001;177:221–5. [6] Mecholsky JJ, Rice RW, Freiman SW. Prediction of fracture [18] Perret R, Ruland W. The microstructure of PAN-base carbon energy and flaw size in glasses from measurements of mirror fibres. J Appl Crystallogr 1970;3:525–32. size. J Am Ceram Soc 1974;57:440–3. [19] Sasanuma Y, Kitano Y, Ishitani A. Characterization of [7] Mecholsky JJ, Freiman SW, Rice RW. Fracture surface industrial materials by small angle X-ray scattering. J Mater analysis of ceramics. J Mater Sci 1976;11:1310–9. Sci 1989;24:1133–9. [8] Bansal GK, Duckworth WH. Fracture stress as related to [20] Johnson JW, Thorne DJ. Effect of internal polymer flaws on flaw and fracture mirror sizes. J Am Ceram Soc 1977;60(7– strength of carbon fibres prepared from an acrylic precursor. 8):304–10. Carbon 1969;7:659–61. [9] Kirchner HP, Gruver RM, Sotter WA. Fracture stress–mirror [21] Sawada Y, Shindo A. Torsional properties of carbon fibers. size relations for polycrystalline ceramics. Philos Mag Carbon 1992;30(4):619–29. 1976;33(5):775–80. [22] Ishikawa T, Koyama K, Kobayashi S. Elastic moduli of [10] Bansal GK. Effect of flaw shape on strength of ceramics. J carbon–epoxy composites and carbon fibers. J Composite Am Ceram Soc 1976;59(1–2):87–8. Mater 1977;11:332–44