Size and crack length effects on fracture toughness of polycrystalline graphite

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1 Engineeing Solid Mehanis 2 ( Contents lists available at GoingSiene Engineeing Solid Mehanis homepage:.goingsiene.om/esm Size and ak length effets on fatue toughness of polyystalline gaphite J. kbadoost Faulty of Engineeing, haazmi Univesity, Mofatteh venue, P.O. Box , Tehan, Ian R T I C L E I N F O B S T R C T tile histoy: Reeived Januay 20, 204 Reeived in Revised fom pil, 0, 204 epted 25 pil 204 vailable online 24 pil 204 eyods: Polyystalline gaphite Fatue toughness Size effet Cak length effet Highe ode tems Modified maximum tangential stess iteion In this pape, the effets of speimen size and ak length on the fatue toughness of polyystalline gaphite ae studied. The expeimental esults epoted in the pevious studies shoed that the fatue toughness of gaphite inease in bigge speimen. It has been also demonstated that the fatue toughness of gaphite is nealy idential in speimens ith ak length atio less than but deeases fo gate ak length atios. To justify the size and ak length dependeny of fatue toughness, the modified fom of maximum tangential stess (MMTS iteion, hih makes the use of highe ode tems in alulating the stess field aound the ak tip is employed. It is shon that the MMTS iteion an povide good estimates fo the fatue toughness of gaphite obtained fom speimen ith diffeent sizes. It is also indiated that the MMTS iteion an pedit vey good the epoted expeimental fatue toughness data fo samples ith the ak length atios less than. 204 Going Siene Ltd. ll ights eseved.. Intodution Sine gaphite has good themal stability, lo pemeability, high oosion esistane, good pefomane in eletial and themal ondutivity and good themal shok esistane, it is employed fequently in diffeent engineeing omponents suh as sliding uent onneto, efatoy gaphite pats, sealing ings, abon bushes, gaphite eletodes, heating elements, et. Hoeve, gaphite is pone to mehanial o themal failue, espeially hen gaphite pats ontain stess onentatos suh as aks o nothes. In othe ods, the gaphite pats might ontain aks, inheent disontinuities and flas, hih play the ole of stess aise and make the gaphite pats vey suseptible to suddenly fatue. The aks ae often eated duing the manufatuing o mahining poesses, o due to the mehanial o themal loads applied unde sevie onditions. Theefoe, it is ugently equied to study the mehanial failue of aked gaphite omponents. Reseahes and Coesponding autho. Tel./Fax: addesses: kbadoost@khu.a.i (J. kbadoost 204 Going Siene Ltd. ll ights eseved. doi: /j.esm

2 84 enginees have used fequently a fundamental paamete so-alled fatue toughness fo detemining the stength of aked omponents. Fatue toughness pesents the esistane of mateials against ak goth unde mode I o opening mode loading. Fatue toughness of gaphite is usually measued fom standad laboatoy speimens ith speifi geomety, shape and size limits. It is expeted that the fatue toughness obtained fom laboatoy speimen of diffeent sizes and shapes is nealy idential. Hoeve, expeimental esults have shon that the fatue toughness of gaphite is signifiantly dependent on the size, length of initial ak and geomety of speimen (Chi, 20; Li et al., 20; Sakai & uita, 996; Sakai & Nonoyama, 2005; Yamauhi et al., 2000, 200; Yoon et al., 20. Fo example, Li et al. (20 shoed expeimentally that the fatue toughness of NBG gaphite obtained fom the single-edge-noth beam samples ineases by ineasing the size of speimen. Fo anothe example, Yamauhi et al. (2000, 200 demonstated that the fatue toughness of gaphite measued fom to test onfiguations inluding edge-aked semi-iula bend (SCB speimen subjeted to thee-point loading and aked Bazilian disk (CBD ae signifiantly diffeent. Moeove, Sakai and Nonoyoma ( 2005 shoed that the length of initial ak has the influene on the fatue toughness of gaphite hen the ak length atio is moe than. Thus, in ode to use the fatue toughness obtained fom the laboatoy-size speimen fo pediting the onset of ak goth in eal size and geomety gaphite pats, the effets of speimen size, initial ak length and geomety on fatue toughness should be onsideed. On the othe hand, thee ae seveal iteia fo investigating the size effets on mode I fatue toughness of quasi-bittle mateials suh as oks, onetes, eamis, et. Fo instane, Bazant's size effet la (SEL poposed by Bazant (984is a ell-knon iteion hih has been used fequently fo taking into aount the speimen size effets on fatue toughness of gaphite (Li et al., 20; Sakai & uita, 996; Sakai & Nonoyama Hoeve, almost all of the size effet iteia (e.g. SEL ae not able to onside simultaneously the geomety and ak length effets on the fatue toughness. The aim of this pape is to investigate the size and ak length effets on the fatue toughness of gaphite simultaneously. Fo this pupose, test data epoted by Sakai and uita(995 is used. They shoed expeimentally that the fatue toughness fo a type of polyystalline gaphite (IG- depends signifiantly on the size and ak-length of speimen. In ode to justify the size and ak-length dependene of fatue toughness, a modified fom of the maximum tangential stess (MMTS iteion is used. This iteion takes into aount the influene of the highe ode tems in alulating the stess field aound the ak tip in addition to the singula tems. s an impotant paamete in the MMTS iteion, the itial distane is assumed to be size dependent and a fomula poposed eently by yatollahi and kbadoost ( 202 is employed fo desibing the size dependene of. The values of fo speimens ith diffeent ak lengths ae also pedited using the MMTS iteion based on the onstant value of itial distane. It is shon that the MMTS iteion is able to povide good estimates fo the fatue toughness of gaphite by taking into aount the effets of speimen size and the length of initial ak. 2. Modified MTS iteion Based on the lassial MTS iteion poposed by Edogan and Sih (96, fatue ous adially fom the ak tip and pependiula to the dietion of the maximum tangential stess θ m. Moeove, the ak ill be extended hen the tangential stess omponent σ θθ along θ m and at a itial distane fom the ak tip eahes a itial value σ θθ (Edogan & Sih 96. The tangential stess aound the ak tip unde pue mode I loading an be itten fom the William's seies expansion (Williams, 957: n n n n n 2 n n, os ( os n n (

3 J. kbadoost / Engineeing Solid Mehanis 2 ( hee and θ ae the onventional ak tip o-odinates, n is the ode of tem in the seies expansion and the onstant oeffiients n ae dependent on the speimen geomety and loading onditions. These oeffiients an be geneally itten in tems of dimensionless paametes n as: n N ( n / 2 n (2 in hih N is the nominal stess and is a haateisti dimension like the idth of single-edge nothed beam (SENB speimens. Moeove, the dimensionless oeffiients n depend only on the onfiguation paametes like the ak length atio (a/ and the loading span to idth atio (S/. These paametes ae independent of the load and the dimensions of samples. Due to symmety in mode I loading, the ak goth takes plaes along the ak dietion, i.e. m =0. Theefoe, the tangential stess along the fatue dietion is obtained fom Eq. ( by setting =0: (, / 2... ( The paamete is elated to the mode I stess intensity fato I as / 2.The onventional MTS iteion (Edogan & Sih, 96 onsides only the fist stess tem and ignoes the highe ode tems. It has been eently demonstated that the highe ode tems of ak tip asymptoti field ae no longe negligible and they should be taken into aount to haateize the tangential stess moe auately (aji & Sato, 978; yatollahi & kbadoost, 202; yatollahi & liha, 20; liha & yatollahi, 2009, 20; Misaya et al., 204; liha et al., 200, 20. By taking the fist to tems in Eq. ( into onsideation, the maximum tangential stess omponent at the itial distane an be obtained fom: (4 2 hee is the itial value of and is the itial stess intensity fato o appaent fatue toughness hih is onsideed to be dependent on the size and geomety of aked speimen. By substituting Eq. (2 into Eq. (4 fo n= and n=, Eq. (4 simplifies to: ( (5 2 oding to pevious studies and onsideing the intinsi featues of gaphite (yatollahi & liha, 20; Li et al., 20; Sakai & uita 996, the itial value of σ θθ an be assumed to be the tensile stength of mateials, f t. Thus, the mode I bittle fatue ous hen: ft ( (6 2 In ode to use Eq. (6 fo pediting the onset of fatue, one should fist detemine the itial distane. Thee ae seveal fomulations in the liteatue fo alulating the value of (Bazant et al., 99; Bazant & Planas 998; aihaloo, 999; Shmidt, 980. Reently, yatollahi and kbadoost (202 poposed a modified fom of Shmidt s fomula (Shmidt, 980 fo detemining the value of. The poposed fomula an be itten as: f t 2 2 2f t (7

4 86 In this fomula, is the mode I fatue esistane, and ae the dimensionless paametes fo the oeffiients of fist and thid stess tems in pue mode I loading. It has been also shon (Bazant & Planas, 998; aihaloo, 995 that the value of depends on the size of speimen and ineases by ineasing the speimen size. Theefoe, the size dependent value of should be onsideed in the poposed method. Hee, a simplified fomula poposed eently by yatollahi and kbadoost (202 is used fo desibing the size dependeny of : B (8 hee the onstant oeffiients and B ae alulated by a linea egession on fatue esistane obtained fom mode I tests onduted on speimens of diffeent sizes. Fo alulating and B, the value of oesponding to eah speimen size is fist detemined by eplaing the fatue toughness ( obtained fom the expeiment into Eq. (7. Then a linea egession based on Y=M X + Q, in hih: Y, M B, X, Q is used (see moe details in yatollahi and kbadoost (202. By simplifying Eq. (6, the vaiations of fatue toughness vesus the speimen size an be obtained fom: ft 2 ( (9 in hih the value of is detemined aoding to speimen size fom Eq. (8. Sine the poposed iteion is a modified fom of the MTS iteion, it is named the MMTS iteion. In the next setion, the size dependent values of fatue toughness fo a polyystalline gaphite epoted by Sakai and uita (995 ill be justified using the MMTS iteion. It ill be also shon that the fatue toughness of gaphite obtained fom speimens of diffeent ak lengths an be pedited using the MMTS iteion.. Gaphite expeiments Sakai and uita (995onduted seveal expeiments on the single-edge nothed beam (SENB fo investigating the dependeny of size and ak length on the fatue toughness of gaphite. The shemati of the SENB sample and geometi notations ae shon in Fig.. The gaphite employed by Sakai and uita (995 as an isotopi polyystalline gaphite (IG- ith the folloing mehanial popeties: bulk density of.76 g/m,young's modulus of 9 GPa and tensile stength of 27 MPa. The samples ee lassified into to ategoies: the speimen having simila geomety but diffeent sizes, 2 the speimens ith simila haateisti dimension, i.e., but diffeent ak lengths a. In the fist ategoy, the idths of speimens ee =2.5, 5, 7.5, 0, 2.5, 7.5, 20 mm and thei ak length atio as onstant and equal to 0.5. The seond ategoy as pefomed on the speimens ith the onstant idth of 2.5 mm but diffeent ak lengths of a =.25, 2.5,.75, 5, 6.25, 7.5, 8.75, 0,.25 mm. Fo all speimens, the thikness t as 0 mm and the span to idth atio S/ as equal to 4.The dimensions of samples and loading onditions fo the fist and seond test ategoies ae listed in Table and Table 2, espetively. The fatue toughness fo the SENB samples is often alulated fom: Pu S 2, 2 2 t (0

5 J. kbadoost / Engineeing Solid Mehanis 2 ( hee P u is fatue load. Sakai and uita (995 did not epot the fatue loads of tested speimens and they only pesented the values of fatue toughness as displayed in Table and Table 2. s seen fom Table, the fatue toughness of gaphite depends on the speimen size and ineases by ineasing the size of speimen. Meanhile, the fatue toughness of tested gaphite is nealy onstant fo speimens lage than =2.5 mm. Theefoe, one an obtained the sizeindependent value of by testing the speimen lage than the idth of 2.5 mm. Table 2 also shos that the fatue toughness of gaphite is nealy onstant fo speimens ith ak lengths of a=.25, 2.5,.75, 5, 6.25 and 8.75 mm and deeases fo lage ak lengths. It means that the fatue toughness of gaphite depends on the ak length hen the ak length atio is lage than. P a S=4 L Fig.. The shemati of SENB speimen and its dimension notations Table. Gaphite speimens and thei fatue paametes fo size effet analysis Categoy I (Size effet analysis S/=0.4, a/=0.5 Speimen Dimensions (in mm (MPa.m 0.5 (L t(sakai and uita 995 (Sakai and uita (mm Table 2. Gaphite speimens and thei fatue paametes fo ak length effet analysis Categoy II (ak length effet analysis S/=0.4, =2.5 mm Speimen Dimensions (in mm (L a t(sakai and uita 995 (MPa.m 0.5 (Sakai and uita

6 88 4. Results and disussion In ode to employ the MMTS iteion fo size and ak length effets studies, the dimensionless fom of the oeffiients of fist to tems in ak tip stess field, i.e. and, should be knon. The non-dimensional paametes and, hih ae funtions of S/ and a/, an be detemined analytially fo simple geometies and numeially fo ompliated aked bodies. aihaloo and Xiao (200 poposed the folloing equations fo alulating the values of and fo thee-point bend speimens ith S/ of 4: ( 2 ( ( / 2 ( ( 5 ( (2 hee in Eq. ( and Eq. (2 is ak length atio, i.e. α = a/. These equations ill be used fo pediting the fatue onset of gaphite speimens by taking into aount the effets of speimen size and ak length. 4.. Size effet analysis fte alulating the values of and in Eq.(9, the value of itial distane should be detemined. The values of fo eah tested speimens ae obtained fom Eq. (7. Fo using this fomula, the tensile stength (f t and mode I fatue toughness ( should be knon. The tensile stength of IG- gaphite f t as found to be 27MPafom(Sakai and uita 995. The mode I fatue toughness ( as also extated fom Table elated to the size of speimen. The values of alulated fom Eq. (7 fo eah tested samples ae shon in Table. oding to this Table, the values of depends on the speimen size and ineases fo bigge samples. Theefoe, the size dependeny of should be onsideed. Eq. (8 is employed hee fo desibing the vaiations of vesus the speimen size. Fo using Eq. (8, the values of and B should be detemined fom a linea egession of the test esults. The linea egession plot, as shon in Fig. 2, gives = 0.06 mm and B =.806 mm. It is noteothy that the values of and B ae alulated based on the fist fou test data and the expeimental esults fo othe speimen sizes (i.e. =2.5, 7.5 and 20 mm ae assumed to be unknon and ill be pedited using the MMTS iteion. fte the alulation of and B, the itial distane an be itten as a funtion of speimen size. Fig. illustates the vaiations of vesus the speimen size obtained fom Eq. ( y 7.0x mm; B.806mm / 4 (mm Expeiment (Sakai & uita / Fig. 2. Linea egession fo alulating and B in Eq. ( (mm Fig.. The vaiations of itial distane vesus the speimen size fo gaphite

7 J. kbadoost / Engineeing Solid Mehanis 2 ( No, the size-dependent behavio of an be pesented using Eq. (9as an asymptoti uve. Fig. 4 displays the vaiations of elative to the speimen size togethe ith the expeimental esults. s shon in this Figue, the MMTS iteion an povide good estimates fo the fatue toughness of speimens hit idth of =2.5, 7.5 and 20 mm hih ee assumed to be unknon. Moeove, Fig. 4 indiates that the mateial fatue esistane fo infinitely lage speimens is independent of speimen size and appoahes a nealy onstant value. The size-independent value of an be obtained dietly fom Eq. (9 by taking as infinity. oding to Eq. (9, hen the value of is alulated as MPa.m 0.5. This value of, hih is denoted by I an be onsideed as the inheent fatue toughness of IG- gaphite. One might ague that the value of I fo IG- is less than those values obtained fom the speimen sizes of =7.5 and 20 mm (see Table. This is beause I as alulated based on the linea egession of 4test data and the moe auate value of I an be ahieved by using all test esults. all test data ee used in the linea egession fo detemining the values of and B, the value of I ould be alulated as I =2 MPa.m (MPa.m MMTS iteion Expeiments (Sakai & uita (mm Fig. 4. The vaiations of fatue toughness of gaphite ith espet to the speimen size 4.2. Cak length effet analysis The MMTS iteion o Eq. (6is employed hee to pedit the fatue toughness of gaphite obtained fom the seond test ategoy. The speimens in the seond test ategoy have the same idth but diffeent ak lengths (see Table 2. By onsideing the tensile stength f t as a onstant mateial popety, the left hand side of Eq. (6 ould be a onstant value fo any given mateial. Thus, the folloing elation an be itten fo to speimens ith diffeent ak length atios: f t 2 ( 2 ( a/ a/ 2 ( In ode to deive a elation beteen the values of mode I fatue toughness fo to speimens ith diffeent ak lengths, Eq. ( an be eitten as:

8 90 a/ a/ ( ( a/ 2 a/ (4 The dimensionless paametes and in Eq. (4 an be espetively obtained fom Eq. ( and Eq. (2 fo the SENB speimens ith diffeent ak length atio. Table shos these paametes fo eah speimen in the seond test ategoy. Sine all speimens in this test ategoy have the same idth of 2.5 mm, the itial distane in Eq. (4 is taken to be as 0.02 mm aoding to the value obtained fom SENB speimen of =2.5 mm. By eplaing the values of / oesponding to the speimens of the seond test ategoy and the value of =0.02 mm in Eq. (4, the fatue toughness fo these speimens ae estimated as shon in Table. It should be noted that the efeene fatue toughness in Eq. (4 is taken to be MPa.m 0.5 obtained fom speimen ith the idth of =2.5 mm. Table. The values of dimensionless paametes and fatue toughness pedited by MMTS iteion fo gaphite speimens in the seond test ategoy (MPa.m 0.5 Speimen Dimensions =a/ / (L a t (in mm Expeiment MMTS (Sakai and uita Eo (% Table indiates that the MMTS iteion an povide good estimates fo the fatue toughness obtained fom speimens ith the ak length atios of =0. to. It is also shon in Table that thee is a disepany of moe than 0% beteen the values of fatue toughness obtained expeimentally fom speimens ith ak length atios of 0.8 and 0.9 and those values pedited by the MMTS iteion. The main eason fo this disepany an be that the itial distane employed in this setion is taken to be onstant fo diffeent ak length atios. The pevious studies (Bazant & Planas 998; Wittmann & Hu 99 have shon that the fatue poess zone aound the ak tip is affeted by the bak bounday hen >. Theefoe, the MMTS iteion annot pedit the auate fatue toughness fo speimens ith >. It is noted that the stess field aound the ak tip is affeted by the bak boundaies hen α is lage than and thus the William s seies expansions annot haateize the nea tip stess omponents. Theefoe, the laboatoy speimens ith > ae not usually employed fo detemining the fatue popeties of mateials(hu & Wittmann, Moeove, the eal gaphite stutues ill be failed befoe the ak length atios eahes to and, theefoe, the omponents ith α> ae patially invalid. Consequently, one an onluded that the MMTS iteion is able to pedit the onset of fatue in eal gaphite stutues. 5. Conlusions The size and ak length effets on the fatue toughness of gaphite as studied using the modified maximum tangential stess (MMTS iteion hih takes into aount the tem in the

9 J. kbadoost / Engineeing Solid Mehanis 2 (204 9 Williams seies expansion in addition to the onventional singula tem of stess. The itial distane is also assumed to be size dependent in the MMTS iteion hen the size effet on fatue toughness is investigated. It as shon that the theoetial estimates obtained fom the MMTS iteion ae in good ageement ith the expeimental esults epoted in the pevious studies. To analyze the ak length effet on the mode I fatue esistane of gaphite by using MMTS, the itial distane as taken to be the same value fo speimens ith diffeent ak lengths. Compaison beteen the fatue toughness pedited by MMTS and those expeimental values epoted in pevious studies indiated that the MMTS iteion an povide good estimates fo fatue toughness of speimen ith ak length atios less than, i.e. α. Sine the ak tip is lose to the bak boundaies fo >(hih affets the stess field aound the ak tip, the MMTS iteion is not able to pedit auately the value of obtained fom the expeimental esults. Refeenes liha, M. R. M., & yatollahi, M. R. (2009. Bittle fatue evaluation of a fine gain ement mota in ombined tensile shea defomation. Fatigue & Fatue of Engineeing Mateials & Stutues, 2(2, liha, M. R. M., & yatollahi, M. R. (20. To-paamete fatue analysis of SCB ok speimen unde mixed mode loading. Engineeing Fatue Mehanis, 0, 5-2. liha, M. R. M., Hosseinpou, G. R., & yatollahi, M. R. (20. ppliation of Caked Tiangula Speimen Subjeted to Thee-Point Bending fo Investigating Fatue Behavio of Rok Mateials. Rok Mehanis and Rok Engineeing, 46(5, liha, M. R. M., yatollahi, M. R., Smith, D. J., & Pavie, M. J. (200. Geomety and size effets on fatue tajetoy in a limestone ok unde mixed mode loading. Engineeing Fatue Mehanis, 77(, aji, H., & Sato, S. (978. Combined mode fatue toughness measuement by the disk test. Jounal of Engineeing Mateials and Tehnology, 00(2, yatollahi, M. R., & kbadoost, J. (202. Size effets on fatue toughness of quasi-bittle mateials ne appoah. Engineeing Fatue Mehanis, 92, yatollahi, M. R., & liha, M. R. M. (20. Fatue analysis of some eamis unde mixed mode loading. Jounal of the meian Ceami Soiety, 94(2, Bazant, Z. P. (984. Size effet in blunt fatue: onete, ok, metal. Jounal of Engineeing Mehanis, 0(4, Bažant, Z. P., Gettu, R., & azemi, M. T. (99, Januay. Identifiation of nonlinea fatue popeties fom size effet tests and stutual analysis based on geomety-dependent R-uves. In Intenational Jounal of Rok Mehanis and Mining Sienes & Geomehanis bstats (Vol. 28, No., pp Pegamon. Bazant, Z. P., & Planas, J. (997. Fatue and size effet in onete and othe quasibittle mateials (Vol. 6. CRC pess. Chi, S. H. (20. Speimen size effets on the ompessive stength and Weibull modulus of nulea gaphite of diffeent oke patile size: IG-0 and NBG-8. Jounal of Nulea Mateials, 46(, Edogan, F., & Sih, G. C. (96. On the ak extension in plates unde plane loading and tansvese shea. Jounal of basi engineeing, 85(4, Hu, X., & Wittmann, F. (2000. Size effet on toughness indued by ak lose to fee sufae. Engineeing fatue mehanis, 65(2, aihaloo, B. L. (995. Tension softening diagams and longitudinally einfoed beams. Fatue of bittle disodeed mateials: onete, ok and eami, aihaloo, B. L. (999. Size effet in shallo and deep nothed quasi-bittle stutues. Intenational Jounal of Fatue, 95(-4,

10 92 aihaloo, B. L., & Xiao, Q. Z. (200. Highe ode tems of the ak tip asymptoti field fo a nothed thee-point bend beam. Intenational Jounal of Fatue, 2(2, -28. Li, H., Li, J., Singh, G., & Fok,. (20. Fatue behavio of nulea gaphite NBG-8. Cabon, 60, Misaya, M. M., liha, M. R. M., & Samaei,. T. (204. On fatue initiation angle nea bimateial nothes Effets of fist non-singula stess tem. Engineeing Fatue Mehanis, 9, 24-. Sakai, M. & uita, H. (995 Defomation and fatue in the fontal poess zone and the akfae ontat egion of a polyystalline gaphite. In: Bake G, aihaloo BL (eds Fatue of Bittle Disodeed Mateials: Conete, Rok and Ceamis. E & FN Spon, London pp Sakai, M., & uita, H. (996. Size Effet on the Fatue Toughness and the R Cuve of Cabon Mateials. Jounal of the meian Ceami Soiety, 79(2, Sakai, M., & Nonoyama, R. (2005. Nonlinea Fatue of a Polyystalline Gaphite Size-Effet La and Iin s Similaity. In Fatue Mehanis of Ceamis (pp Spinge US. Shmidt, R.. (980, Januay. mioak model and its signifiane to hydauli fatuing and fatue toughness testing. In The 2st US Symposium on Rok Mehanis (USRMS. meian Rok Mehanis ssoiation. Williams, M. L. (957. On the stess distibution at the base of a stationay ak. Jounal of pplied Mehanis, 24, Wittmann, F. H. & Hu, X. (99. Fatue poess zone in ementitious mateials. Intenational Jounal of Fatue, 5(, -8. Yamauhi, Y., Nakano, M., ishida,. & Okabe, T. (2000. Measuement of fatue toughness fo bittle mateials unde mixed mode impat loading using ente-nothed disk speimen. Jounal of the Soiety of Mateials Siene, Japan, 49 (2, Yamauhi, Y., Nakano, M., ishida,. & Okabe, T. (200. Measuement of mixed-mode fatue toughness fo bittle mateials using edge-nothed half-disk speimen. Jounal of the Soiety of Mateials Siene, Japan, 50 (, Yoon, J. H., Byun, T. S., Stizak, J. P. & Snead, L. L. (20. Chaateization of tensile stength and fatue toughness of nulea gaphite NBG-8 using subsize speimens. Jounal of Nulea Mateials, 42 (, 5-20.