Natalya Narkevich. Academy of Sciences/ Institute of Strength Physics and Materials Science, Tomsk, Russia,

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1 Intrnational Journal of Innovativ Rsarch in Enginring & Managmnt (IJIREM) ISSN: , Volum-, Issu-4, July-016 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns Yvgny Dryugin * Th Sibrian Branch of th Russian Acadmy of Scincs/ Institut of Strngth Physics and Matrials Scinc, Tomsk, Russia, d@ispms.tsc.ru Natalya Narkvich Th Sibrian Branch of th Russian Acadmy of Scincs/ Institut of Strngth Physics and Matrials Scinc, Tomsk, Russia, natnark@list.ru Natalya Antipina National Rsarch Tomsk Polytchnic Univrsity/ Tomsk, Russia, natalya_alx@mail.ru ABSTRACT A nw mthod is proposd to dtrmin fractur toughnss of structural matrials according to th tst data of non-standard small-siz chvron-notchd spcimns. Th analytical xprssions ar obtaind bing basd and drivd from th constitutiv quations of nginring fractur mchanics to dtrmin th crack-driving forc (spcific fractur nrgy) and th strss intnsity factor. Thr ar no mpirical constants and phnomnological dpndncis in th calculations. Th mthod allows us to xclud th priodic unloading of th spcimn applid. All ncssary calculation paramtrs ar dtrmind according to th xprimntal data. Th mthod allows us to us th low-powr tst machins and dos not rquir larg amounts of matrial for th production of spcimns, as wll as fatigu prcracking. Th mthod allows us to crtify fractur toughnss of th matrial without rstrictions rgarding th amount of plastic dformation and in front of th crack tip and in th spcimn as a whol. Th xampls ar givn to calculat th fractur toughnss critria for a numbr of structural matrials charactrizd by th ability to plastic dformation and by th Young s modulus valu. Th complianc of th calculatd fractur toughnss charactristics with tst data of standard mthods is obsrvd. Kywords Fractur toughnss, chvron-notchd spcimns, complianc, spcific fractur nrgy, strss intnsity factor 1. INTRODUCTION Various mthods for dtrmining fractur toughnss of matrials ar wll-known and widly usd whn tsting standard spcimns with inducd fatigu crack [1, ], whn tsting th Charpy notchd spcimns for fractur toughnss [, 4], by th micro indntation mthod [5, 6], t al. An ssntial fatur of ths mthods is that th charactristics of loading diagrams and th xisting fractur lngth ar masurd, and thn fractur toughnss charactristics of th matrial ar calculatd by th smi-mpirical formulas. As a rul, th critical strss intnsity factor (SIF) of th 1-st kind К 1с (for clavag crack) is takn for th main fractur toughnss charactristics of th matrial. Th plan strain stat condition of th loadd spcimn is rquird in th xprimnts. In this rgard, standard tsts ar conductd on spcimns at last 10mm thick. Disadvantags of usd mthods ar as follows: 1. Thr is no possibility to assss th fractur toughnss of th matrial whn tsting th small thicknss spcimns;. Complxity of th mchanical procssing and manufacturing of spcimns;. Rquirmnt for th fatigu pr-cracking on th notch; 4. Availability of spcial tst quipmnt; 5. Us of significant amount of th complx-shapd spcimns (cut out by layrs, hols, notchs); 6. Nd for th high powr load dvic; 7. High consumption of mtal; 8. Nd for priodic unloading of th spcimn to dtrmin th chang in spcimn complianc undr loading. 9. Availability of phnomnological constants in constitutiv quations, taking into account th gomtric shap and boundary loading conditions. As a rul, during a fractur toughnss tst of small-siz spcimns, th chvron-notchd spcimns ar usd [7-1]. Th spcimns with this configuration do not rquir th prliminary guidanc of a fatigu crack. Whn tsting th small-siz chvronnotchd spcimns, many of th abov-mntiond problms ar absnt. This papr proposs a nw mthod for fractur toughnss dtrmination of structural matrials using th small-siz chvronnotchd spcimns. Th mthod allows us to dtrmin fractur toughnss charactristics without svr rstrictions on th spcimn ability to plastic dformation. Thr ar no phnomnological dpndncis and mpirical constants in th calculations. Th fractur toughnss charactristics comply with th conditions of continuous loading of spcimns, without using th loading-unloading opration. Th important calculation works wr carrid out associatd with th us of chvron-notchd spcimns during tsting.. FRACTURE TOUGHNESS CALCULATION OF STRAIGHT- THROUGH NOTCHED SPECIMENS To dtrmin th global failur conditions, irrspctiv of th matrial stat and gomtrical dimnsions of th spcimn, th nrgy approach is appropriat [1-14]. Th ky point of th nrgy fractur critrion in fractur mchanics is formulatd as follows: th crack growth can occur if th systm can rlas nrgy rquird to initiat crack propagation to th lmntary distanc dl. Th nrgy ndd for crack growth, appars only du to th lastic dformation nrgy that occurs insid th matrial undr th applid xtrnal forc. Th rliabl fractur toughnss charactristic is th critical valu of th lastic nrgy rlas rat (ERR) during th crack Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 9

2 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns propagation G c. In th two-dimnsional vrsion, this charactristic is quivalnt to th valu of th J-intgral [1-14]. For brvity, th valu of G will b calld spcific fractur nrgy. Th spcific fractur nrgy (SFE) is dfind as nrgy that is spnt on th formation of a singular crack surfac. Th unit of masurmnt for SFE is J/m (Joul /m ). In practic, thr is a dcras in spcimn stiffnss or structur at initiation and propagation of th crack. Th spcimn stiffnss M is dfind as th ratio of load P, applid to th spcimn, to th displacmnt of load application point е at lastic dformation of th spcimn: М = P/ е. Th rciprocal of th stiffnss is dfind as a spcimn complianc η: η = е /P Th ncssary condition for through-crack propagation in th flat spcimn of unit thicknss obys th quation [1-14] G P d η, dl (1) whr dη/dl is th chang in spcimn complianc during crack propagation, dl is th short distanc, to which a straight-lin crack front propagats. At th stag of stabl crack propagation, this valu charactrizs th fractur toughnss G c of th matrial. As follows from (1), lastic nrgy pr unit of nw crack surfac at its propagation to dl in th spcimn in thicknss а is qual to P dη P dη G, adl ds whr ds = adl is th lmntary incrmnt of th crack surfac ara. Thr is a classic xampl for calculating th strss intnsity factor (SIF) K I to tst a doubl cantilvr bam spcimns with a straight-through notch [1, 14]. Th rlation btwn G and K I for th plan strss stat obys th quation G K I E. () Lt us considr th cas of doubl-cantilvr bam spcimns with a straight-through notch in dtail, sinc th rsult will b usd in th calculation of G for th chvron-notchd spcimns. Figur 1 prsnts th doubl-cantilvr bam spcimns with a straight-through notch. Distanc from th load application point P to th crack front is th initial crack lngth l 0. As follows from th cantilvr bnding thory [15], displacmnt of th load application point (Fig. 1) is qual to 4P l, Ea b whr E is th Young s modulus, b is th cantilvr thicknss. For th doubl cantilvr bam spcimn, displacmnt of load application point s ζ is. Thrfor, th spcimn complianc η is ζ 8 l η =. P Ea b Th complianc drivativ by th crack lngth is qual to d dl η 4 l. Eab () Substitution of () into (1) lads to th following xprssion for SFE [1, 14] 1P l G. Eb a (4) Fig. 1. Straight-through notchd spcimn. According to [15], th displacmnt е of th cantilvr nd undr lastic dformation for th spcimn in thicknss of a with a crack lngth l is providd by th load: E a b P 4 l Substituting this xprssion into (4), w obtain th quation for G that allows us to calculat fractur nrgy by th crack lngth l and by th lastic opning valu of th notch tips е : G b E. 4 4l. (5) (6) In th givn rprsntation, th valu of G dos not dpnd on th spcimn thicknss а. Equation (4) dtrmins SFE by th crack lngth l, and by th xtrnal load valu Р, at which spontanous crack propagation bgins. Basically, SFE can b calculatd according to th (4) whn tsting th small-siz spcimns. It should b notd that thr ar no any mpirical constants in (4). All ncssary valus can b takn from th xprimnt. To maintain th xprimntal intgrity, on can grow a fatigu crack at th tip of th notch. Howvr, this mthod has svral disadvantags. Equation (4) givs only a rough approximation of th SFE valu. Thr is a crtain divrgnc du to th fact that th cantilvrs nds ar fixd not absolutly rigidly, as in th cantilvr mbddd in th rigid bas. But this is not th most important thing. Th main disadvantag is that in practic crack propagation along th notch plan is not guarantd. Consquntly, dviations in crack propagation dirction caus shar dformations. Bsids, crack front straightnss is not prsrvd. To som xtnt, this problm is solvd by using th chvron-notchd spcimns. Fig.. Standard tst of th chvron-notchd spcimn. Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 40

3 Intrnational Journal of Innovativ Rsarch in Enginring & Managmnt (IJIREM) ISSN: , Volum-, Issu-4, July-016. FRACTURE TOUGHNESS CALCULATION OF THE CHEVRON- NOTCHED SPECIMENS Whn tsting th small-siz spcimns, gnrally, th chvron-notchd spcimns ar usd [6-8, 16]. For th first tim, a chvron-notchd spcimn was proposd by L.M. Barkr in 1977 to dtrmin fractur toughnss undr plan strain conditions [7, 17]. Standard tsts of th chvron-notchd spcimn ar conductd according to th schm prsntd in Fig.. Figur shows xampls of th chvron-notchd spcimns. Th spcimns of this configuration do not rquir th prliminary guidanc of a fatigu crack to th tip of th notch. From th momnt of loading, thr is a high strss concntration at th tip of th chvron notch that is sufficint to crack initiation. It is assumd that th dvlopmnt of plastic dformation in th chvron zon satisfis th plan strain stat condition. Th crack initiatd at th tip of th chvron, can propagat only along th notch plan. At th sam tim, thr is a high probability that th crack front during propagation, at th avrag, maintains a straight shap. Th chvron notch gomtry allows us to fix and xtnd th stabl crack propagation stag and, thus, to calculat th bginning of th spcimn catastrophic failur mor accuratly. As a rul, short circular spcimns ar usd in th xprimnts (Fig. a). Th disadvantag of th standard mthod for masuring fractur toughnss of th chvron-notchd spcimns is that in ordr to dtrmin th chang in spcimn complianc, th loading-unloading condition should b carrid out [18-0]. For this rason, th calculation formulas includ adjustabl cofficints considring th non-linar bhavior of th matrial and a complx gomtric shap of th notch. Fig.. Exampls of th chvron-notchd spcimns: short circular spcimn (a), longatd rctangular spcimn (b). This sction provids a nw mthod for calculating th fractur toughnss charactristics of matrials whn tsting th chvron-notchd spcimns. Th novlty is in th fact that th calculation of SFE is basd on calculation of th nrgy and powr paramtrs of th spcimn taking into account th complx gomtry of a chvron notch according to th strict laws of solid mchanics. It is convnint to mak calculations and xprimnts for th longatd rctangular spcimn (Fig. b). Th chvron-notchd spcimn has a shap of a doubl cantilvr bam configuration. Lt us dtrmin th rlation of th xtrnal forc Р with an lastic dflction of th singl cantilvr of th spcimn. Th cantilvr can b rprsntd as a st of lmntary cantilvrs (mini cantilvrs) of th infinitly small width dx. Figur 4 shows th projctions of th chvron-notchd spcimns. Th mini cantilvr lngth at a distanc х from th symmtry axis of th spcimn is l(x) = l 0 + x ctg(/), whr l 0 is th minimum distanc from th load application point to th chvron notch, is th chvron angl (Fig. 4). For ach mini cantilvr in th st, th wll-known lasticity thory formula is valid [15]: 4 dp( x) l( x), Edx b whr is th lastic dflction of th mini cantilvr, dp is th lmntary load, undr th action of which th cantilvr in thicknss of dx is dflctd to th valu of, b is th thicknss of th mini cantilvr. In viw of this, from (6) w obtain th lmntary load dpndnc dp, applid to th nd of th mini cantilvr on its width dx: ( ) E b dp x dx. 4 l( x) Intgration of lmntary forcs (8), affcting ach mini cantilvr across th spcimn width а, will clarly dtrmin th actual load Р, providing th mini cantilvr s dflction by : P Fig. 4. Projctions of chvron-notchd spcimn. a 0 ctg, a or b E P dx l x 4 Ea b a a Ea b 4 ctg ctg k 4 l0 l0 l0 4 l0 (9) This quation diffrs from (5) from th straight-through notch only by th factor a a k 4 ctg ctg. l l 0 0 According to (9), a singl cantilvr lastic dflction of a doubl cantilvr bam spcimn with a chvron notch is 4P l0 1 ( l0) k. Ea b During th loading, th momnt of crack initiation occurs at th tip of th chvron notch. Propagation of th initiatd crack to th distanc Δl incrass th ffctiv fractur lngth. Lt us prsnt th crack front as a straight lin (Fig. 5). Th lngth of this lin is h = Δltg(/). Basically, this spcimn with a crack is a st of two spcimns: with a straight-through notch in width of h and with a chvron notch in width of а h (Fig. 5). Lt us (7) (8) Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 41

4 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns dtrmin th forcs Р' and Р'' for ths spcimns, rspctivly, causing idntical dflction. Using (5), w find an xprssion for Р' acting on a straight-through notchd spcimn in width of h = Δltg(/): P El α b tg. 4 l (10) According to (9), for th chvron-notchd spcimn in width of а h, w obtain an xprssion for Р": Fig. 5. Prsntation of th spcimn with a crack as a sum two sampls: with th straight and chvron incision. On th basis of (10) and (11), an xprssion for е is dtrmind: whr Р= Р' + Р'', l = l 0 + Δl and k is l tg E b l l a l a P 1 tg 4 ctg ctg. 4 l a l l l l 4P l 1 ( l) k, Ea b (1) (11) l a l l a l a k tg ctg 1 tg 4 ctg ctg a l0 a l0 l0 l0 l0 It is asy to vrify that at Δl 0, th valu of k k'. Substituting (1) for е into (6), w obtain th xprssion for SFE G: G 1P l Eb a k. (1) This quation diffrs from th similar on for th straightthrough notch only by k -. In particular, if α = π, (1) gos ovr into (4) for th straight-through notch, sinc thn k is 1. As follows from (1), th charactristic of G dpnds on th Young s modulus E. Th highr E is, th lowr is th SFE valu undr all othr conditions bing qual. In contrast, according to (), charactristic of K I dos not dpnd on E, i.. SIF is invariant in rlation to th Young s modulus. 4. THEORETICAL DETERMINATION OF ELASTIC CRACK OPENING δ е Th spcimn prsntation in th form of a doubl cantilvr configuration allows us to dtrmin th lastic crack opning initiatd at th tip of th chvron. It is known that th lastic displacmnts of th cantilvr points oby [15] P x x l l υ ( x) 6 4, Ea b b b b (14) whr th x axis is dirctd along th cantilvr. At x = 0, (14) dtrmins th lastic dflction of th load application point P. Equation (14) is also valid for th doubl cantilvr bam spcimn with a straight-through notch. Thn lastic notch opning in th point x is δ (x) = υ (x). Th cantilvr displacmnt in th point x = l 0 is qual to Pl0l l υ ( l0). Eab l0 (15) Substituting (5) for P into (15), w obtain th cantilvr displacmnt in th point x = l 0 for th straight-through notchd spcimn: l l l υ. 0 ( l0 l) (16) Lt us find th cantilvr displacmnt in th point x = l 0 for th chvron-notchd spcimn. For this, w us (15), whr w plac th valu of Р' instad of P according to (10), and th width of th spcimn cntral part h = Δltg(/) shown in Fig. 5 instad of a. Lt us find th cantilvr dflction in th load application point Р': P l0 l. El tg( ) b (17) Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 4

5 Intrnational Journal of Innovativ Rsarch in Enginring & Managmnt (IJIREM) ISSN: , Volum-, Issu-4, July-016 Altrnatly, as follows from (16), υ ( l l). 0 (l0 l) l From (17) and (18),w obtain an xprssion for Р': (18) As follows from (11), υeb tg(α ). P (l l) l 4l l 0 ctg ( P P) a a l ctg 4 ctg. Eb ( a tg( )) l l l Taking in to account (19), w find a cantilvr point displacmnt at a distanc l 0 from th load application point P: l (19) P( l l) l Th valu of δ (l 0 ) = υ dtrmins th crack opning initiatd at th chvron. During th crack propagation, th incrmnt of th singl cantilvr lastic dflction occurs in th load application point P. Th incrmnt Δ = е (l 0 + Δl) е (l 0 ) (1) corrsponds to th crack lngth Δl. Figur 6 prsnts th curvs of th υ е dpndnc on th crack lngth Δl and on th incrmnt of th singl cantilvr lastic dflction Δ obtaind using (0), at following valus of th paramtrs: Е = 110GPa, l 0 = 18.1mm, Δl =.77m, P = 8N, α = π/9 (0º), а = b = 4.5mm. Th calculations show that thr is a parabolic dpndnc btwn Δl and υ е, which can b writtn as υ е = АΔl, whr А is th constant, which dpnds on th assignmnt of concrt paramtric valus in (0). In this cas, А is qual to.58. As sn from th plot, thr is a linar dpndnc Δ = Вυ е btwn Δ and υ е.th proportionality factor for th assignd valus of В is Th quations givn abov ar drivd from th constitutiv quations of nginring fractur mchanics for th first tim and can b usd for th calculation of SFE for th chvron-notchd spcimns. Th procsss of plastic dformation affct th cantilvr dflction valu and opning of crack sids in th point of its initiation. For this rason, th xprimntally masurd valus of th cantilvr dflction, xcpt for е, contain a part of th quation p = е that is not rlatd to th chang in spcimn complianc. Th crack opning valus of υ masurd in th sam way contain th plastic dformation contribution υ p = υ υ. Th valus of p and υ p ar vry important whn simulating th fractur procss in th chvron-notchd zon. Using (1), according to th xprimntally masurd valu of cantilvr dflction (Fig. 6), on can dtrmin th rlativ valu of (1 е )/ е = p / е as an additional fractur toughnss charactristic. It is obvious that th mor compliant a matrial is, th highr is its fractur toughnss. Th valu of p is not associatd with chang in spcimn complianc sinc it is dtrmind only by th lastic dflction of th spcimn. Th strss distribution in th plastic dformation zon is significantly diffrnt from th strss fild in an lastic mdium with a crack. On th way of crack propagation, th matrial is always subjctd to a crtain dgr of plastic dformation. This mans that crack is always surroundd by a layr of th plastically dformd matrial. Th calculations mad in [1] by th mthod l( l l)( a ltg( )) l 4l actg( ) l υ. Eb tg( ) 4l0l tg( ) l0 actg( ) Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 4 (0) of rlaxation lmnts showd that strss fild in th plastic dformation zon diffrs significantly from th crack strss fild in th lastically dformabl mdium. Plastic dformation lads to strss rlaxation. Forth is rason, thr is no singularity in th crack mouth. Th maximum strss concntration is obsrvd in th plastic dformation zon. Fig. 6. Dpndnc crack half-opning υ from Δl and Δ. Th abov quations ar drivd without any assumptions about th plastic proprtis of th matrial. Thrfor, thy can b usd to calculat fractur toughnss of any structural matrials whrin th crack initiation at th tip of th chvron notch is obsrvd. Th product of ЕG dos not dpnd on th Young s modulus sinc SFE G is invrsly proportional to th Young s modulus valu E (s(1)). Thrfor, irrspctiv of plastic proprtis of th matrial, th quation K Pl ab 1 I EG k / () Dtrmins th strss intnsity factor (SIF) for th small-siz chvron-notchd spcimns. Th standard tst on complianc chang of th chvronnotchd spcimns is mad using th loading-unloading oprations [7, 8, 18-0]. As a rsult, th fractur toughnss of th matrial is dtrmind undr th low-cycl loading conditions, rathr than undr constant loading. It is known that th curv typ

6 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns load-displacmnt changs significantly dpnding on th prvious loading history. This is du to th fact that th plastic dformation rat and strain hardning of th matrial ssntially dpnd on th xtrnal load and tim during which th load is acting. To dfin th mchanisms of failur of structural matrials, first of all, th valus ofsfe and SIF undr continuous loading ar significant. Equations (1) and (14) allow us to calculat ths charactristics without using th load-unload condition. It is nough to know th crack lngth Δl initiatd at th chvron. Fig. 7. Th two cantilvr spcimn dflction. Th xampls of th fractur toughnss analysis of a numbr of structural matrials, which diffr in thir ability to crack formation and th Young s modulus, ar prsntd blow. 5. Fractur toughnss of structural matrials This sction prsnts th calculation rsults of th fractur toughnss charactristics of VT6 alloy, F-5.4% Ni and 1GBA tub stl. Th spcimns 1х10х6mm in siz wr cut from th work pic by th lctrorosion mthod. Thn a notch 0.mm thick was mad with a chvron angl = 60º (s. Fig.4). Th crack lngth at th pr-fractur stag was dtrmind by th spcimn imags. Alloys with diffrnt ability to plastic dformation and with diffrnt valus of th Young s modulus E wr tstd. Th loading of spcimns mad of VT6 and F+4.6%Ni alloys was prformd by th intrusion of a narrow wdg into th notch at a motion rat of 5 µm/s (Fig. 8).Th 1GBA tub stl loadings wr prformd by application of opposit forcs to th tips of th notch (Fig. 1 and ). Figur 8 shows th imag (a) and schm (b) of th spcimn wdging. Th constant motion rat of th wdg provids th prolongd stag of stabl crack propagation initiatd at th chvron. Th quation for th calculation of P bnding th cantilvr is obtaind from th condition of quilibrium of forcs: F cosγ P, β β sin κ cos () whr F is th load on th wdg, κ and γ ar th friction factor and intr planar angl btwn th wdg and cantilvr, rspctivly, β is th angl of wdg opning. a b Fig. 8. Imag (a) and schm (b) of th chvronnotchd spcimn wdging. As sn from (), in ordr to dtrmin th bnding forc P, it is important to calculat th friction factor κ. Substituting () in to (9) instad of P, w obtain th following quation for κ: a cosγ ctg F l0 b β L β a l0 κ tg, sin 4 ctg ae l0 whr ΔF/ΔL is th dclin of th initial lastic sgmnt of th xprimntal loading diagram load P wdg displacmnt L. Th calculations showd that κis qual to 0.08 to an accuracy of 10%. Tabl 1 shows th fractur toughnss charactristics of th studid matrials. 5.1 VT6alloy (Ti-6Al-4V) Th structural VT6 alloy is mainly usd for th manufacturing of larg wldd and built-up aircraft structurs, balloons working undr intrnal prssur ovr a wid tmpratur rang from 196 C to 450 C, and a numbr of othr structural lmnts. Th studis wr conductd using th matrial in th initial coars-crystallin (CC) stat (grain siz of 7-5 µm) and with ultrafin graind (UFG) structur (grain siz of 500 nm) obtaind by th svr plastic dformation []. Th loading was carrid out by a wdg with β qual 0º (Figur 8). Figur 9 shows a typical loading diagram of th UFG VT6 alloy. Th load-pak corrsponds to th momnt of crack initiation at th tip of th chvron. A suddn strss drop is causd by th spontanous crack propagation to a crtain lngth along th chvron notch. Aftr that thr is slow and stabl crack propagation to th critical lngth, which dtrmins th final fractur of th matrial. In th calculations for th VT6 alloy, E was qual to 110GPa [-5]. Th masurd valus ofl 0 and Δl ar qual to 18.1 and.767mm, rspctivly, а = b = 4.5mm. Th sam valus wr usd for calculating th fractur toughnss of thvt6 alloy in th coars-crystallin stat (CC). Tabl 1 shows that plastic dformation dos not affct th displacmnt of th notch sids prior to th crack initiation in th UFG VT6 alloy ( p / = 0). This mans that th spcimn is dformd only lastically prior to crack initiation. At th stag of pr-fractur, th influnc of Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 44

7 Intrnational Journal of Innovativ Rsarch in Enginring & Managmnt (IJIREM) ISSN: , Volum-, Issu-4, July-016 plastic dformation was obsrvd: p / = Th contribution of plastic dformation to th crack opning at th tip of th chvron is comparabl with that of lastic dformation: υ p /υ = 0.5. Fig. 9. Loading diagram of UFG VT6 alloy. Spontanous crack propagation from th momnt of its initiation is accompanid by th rduction in th lastic dflction of a singl cantilvr of th spcimn and rduction in th fractur toughnss charactristics of G and K I. This alloy shows quit diffrnt fractur rgularitis in th coars-crystallin stat. A qualitativ viw of th loading diagrams and consistnt pattrns of crack propagation in th chvron-notch zon (Fig. 10) show th following. Th bginning of crack initiation and propagation occurs long bfor th xtrnal load rachs a maximum. This is markd with an arrow 1 shown in Fig. 10. Crack initiation is prcdd by th plastic dformation of th matrial in th chvron-notch zon. Th contribution of plastic dformation p to th displacmnt of load application point P up to th momnt of crack initiation is comparabl with that of lastic dformation: p / = 0.54 (s Tabl 1). Paks and plataus on th loading diagram ar causd by abrupt natur of crack propagation. Th spcific fractur nrgy of G and K I is almost unchangd until it rachs th maximum load P max markd with an arrow in Fig. 10. Thus, a fractur toughnss critria for th CC VT6 alloy ar th valus of SFE G c = 4.±0.kJ/m and SIFK Iс = 68.9±0.MPa m 1/. Th SIF valu coincids with th valu of 66.4MPa m 1/ to an accuracy of.6% in [4] for standard tst conditions. Fig. 10. Loading diagram of th CC VT6 alloy. During crack propagation, a contribution of plastic dformation to th displacmnt of th notch tips incrass. Th quation p / = 0.81 corrsponds to th maximum load. Th contribution of plastic dformation to th crack opning at th tip of th chvron is tims highr than that of lastic dformation: υ p /υ =.1. Th subsqunt loading lads to a drop in th xtrnal load and to th rduction of G and K I charactristics. In this cas, th р / е ratio gos up du to th р incras and dcras. A comparison shows that th mthod usd to obtain th UFG structur in th VT6 alloy lads to a strong dcras in complianc, crack initiation strss (two tims) and strss of stabl crack propagation (thr tims). For this rason, th SMC VT6 alloy is charactrizd by th low fractur toughnss. Th bhavior of th SMC VT6 alloy can b xplaind as follows. Th low complianc of th alloy practically liminats th strss rlaxation factor in th chvron-notch zon and, as a consqunc, rducs th crack initiation strss in th chvron. Stabl propagation is dtrmind by th strss concntration at th tip of th crack, which is highr than that at th tip of th chvron prior to crack initiation. In this connction, a strss dcras taks plac. Th calculations hav shown that th fractur toughnss critria for th SMCVT6alloy ar th valus of SFE G c = 4.58±0.kJ/m and SIF K Iс =.5±0.MPa m 1/ at th stag of stabl crack propagation. Tabl 1. Fractur toughnss charactristics of structural matrials Alloy P, N,mm,mm p / υ,μm υ,μm υ p /υ G, kj/m K I, MPa m 1/ UFG VT6 77.7(max) (stabl) CC VT6 5.6(Δl=0) (max) Ni-F 96.0(Δl=0) (max) GBA 776(max) Th F+4.6%Ni-alloy Tabl 1 also includs th data for th iron-nickl invar F+4.6% Ni, which is widly usd in modrn industry and tchnology as an alloy with thrmal linar xpansion cofficint (TLEC) clos to zro. Whn loading th spcimn, a wdg with β = 40º was usd. Th structural stat of th alloy corrsponds to that aftr th multi-axial forging. Th alloy has a polycrystallin structur with an avrag crystallit siz d = 8µm. Th valu of Young s modulus E in th calculation is 10GPa. Figur 11 shows a loading diagram of this alloy. Th momnt of crack initiation at th tip of th chvron is markd with an arrow 1. Th bginning of crack initiation and propagation occurs long bfor th xtrnal load rachs a maximum. According to (1), th SFE from th momnt of crack propagation (at Δl = 0) is qual to G =.6±0.0kJ/m. Th corrsponding valu of K Ic is 70.5±0.1MPa m 1/. Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 45

8 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns Fig. 11. Loading diagram of th F-Ni alloy. Th intrmittnt natur of th loading curv dmonstrats that crack propagation occurs abruptly. Exprimntally masurd displacmnt of th load application point up to th momnt of crack initiation is = 0.47±0.0mm. According to (11), th portion of displacmnt that taks plac du to th spcimn lastic dformation is = 0.4±0.0mm. Thrfor, within th limits of th xprimntal rror, th rlativ valu of p / dos not xcd 10%. Thus, th plastic dformation prior to th momnt of crack initiation in th chvron maks a minor contribution to th displacmnt of th load application point. Th obsrvations show that th crack propagats along a complx trajctory, sharply changing th motion dirction (Fig. 1). Th maximum valu of SFE G с = 0.8±0.kJ/m corrsponds to th maximum load. Th corrsponding valu of K Iс is qual to 80.4±0.MPa m 1/. Not that th valu obtaind practically coincids with thos of K c = 81.MPa m 1/, obtaind for th F-17%Ni alloy [6]. Th critical valu of crack opning δ = υ = 61.56µm can also b usd as a fractur toughnss charactristic. Th xprimntal valu of δ is 179.8µm. Hnc, υ p /υ is qual to 1.9. Thus, at th stag of pr fractur th crack opning in th chvron-notch zon contains a significant contribution rlatd to th plastic dformation, which is almost twic gratr than that of th lastic dformation of th spcimn. A subsqunt incras in crack lngth lads to a drop in th valus of G с and K Iс. In this cas, th υ p /υ ratio incrass du to th incras of υ p contribution and dcras in υ contribution. 5. Th 1GBA tub stl Th low-carbon low-alloy 1GBA stl is widly usd in th construction of main oil and gas piplins. Th matrial was subjctd to plastic dformation by rolling to th finit crosssction of bars of 8х8mm for svral passs with stp-lik tmpratur dcras from 750ºС to 550ºС [7]. Aftr svr plastic dformation, th stl has a fibrous UFG structur with a latral fragmnt siz of 0.5µm. In th longitudinal dirction, th lngth of fragmnts is 15-0µm. Th 1GBA tub stl loading was prformd by opning of th chvron-notch sids (Fig. ). Figur 1 shows a loading diagram forc P displacmnt of notch tips for th 1GBA tub stl. Crack initiation at th tip of th chvron notch is prcdd by considrabl plastic dformation. A crack initiats at th momnt whn th load rachs practically rachs a maximum (markd with an arrow). First, th crack slowly grows, and thn its propagation vlocity incrass sharply. Th calculations by (5) dtrmin th valu of K Iс = 104kJ/m for 1GBA, which is much highr than for th F-Ni alloy (75.51MPa/m 1/ ). a b Fig. 1. Crack in th chvron-notch zon prior to th fractur (a) and th spcimn fractur aftr 4s (b). Fig 1. Th loading diagram of 1GBA stl. Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 46

9 Intrnational Journal of Innovativ Rsarch in Enginring & Managmnt (IJIREM) ISSN: , Volum-, Issu-4, July-016 Fig. 14. Crack propagation bhavior in th chvron-notchd zon. Th 1GBA tub stl in th UFG stat. Th р / е ratio can srv as a quantitativ charactristic of viscosity. For ths matrials, it diffrs quit considrably; in particular, at th load pak р / е is.6 for 1GBA and р /е is 0.81 for th CC VT6 alloy. Ths xampls show that at fractur toughnss crtification of th matrial, xcpt for SFE, it is important to know th charactristics of р / е andυ p /υ, which dtrmin th ffct of plastic dformation on th displacmnt of load application points and crack opning, rspctivly. Th proposd mthod allows us to study th fractur toughnss of matrials without rstrictions on th plastic zon siz at th crack tip. 6. CONCLUSION This papr prsnts a nw mthod for dtrmining fractur toughnss of matrials according to th tst data of non-standard small-siz chvron-notchd spcimns. Th analytical xprssions ar obtaind bing basd and drivd from th constitutiv quations of nginring fractur mchanics to dtrmin th crack-driving forc G (spcific fractur nrgy) and th strss intnsity factor (SIF) K Ic. Exprimntal dtrmination of crack lngth Δl is of principl importanc in calculations. During tsting, loading diagrams and photographic imags of th spcimns takn in tim intrvals ar obtaind. Th displacmnt of th notch sids, crack opning at th tip of th chvron notch and crack lngth during its initiation and propagation ar masurd. This allows us to distinguish th plastic dformation contribution to th displacmnts that is not rlatd to th chang in spcimn complianc and thrfor dos not affct th fractur toughnss charactristics of th matrial. Du to th fact that chang in spcimn complianc with incras in th crack lngth is analytically considrd in constitutiv rlations, th priodic unloading of th spcimn applid undr standard tst conditions of th chvron-notchd spcimns is xcludd in th xprimnts. Thr ar no mpirical constants and phnomnological dpndncis in th calculations. All ncssary calculation paramtrs ar dtrmind according to th xprimntal data.th mthod allows us to us th low-powr tst machins and dos not rquir larg amounts of matrial for th production of spcimns, as wll as fatigu pr-cracking. Th mthod allows us to crtify fractur toughnss of th matrial without rstrictions rgarding th amount of plastic dformation and in front of th crack tip and in th spcimn as a whol. Th thortical analysis has shown that G c compard to K Ic dpnds on th Young s modulus E of th matrial. Th highr E is, th lowr is G с undr all othr conditions bing qual. For this rason, th rlativ valus of G c and K Ic charactristics can diffr ssntially. Thus, th valu of G c for th F-Ni alloy is lowr that for th CC VT6 alloy, and th valu of K Ic is, on th contrary, highr (Tabl 1). It is proposd to considr th р / е ratio as an additional fractur toughnss charactristic that dtrmins th plastic dformation contribution to th displacmnt of load application point in rlation to th lastic dformation. Thrfor, in ordr to mak fractur toughnss crtification of th matrial mor complt, it is rcommndd to dtrmin thr fractur toughnss charactristics of th matrial: SIF, SFE and th р / е ratio. According to this mthod, th fractur toughnss charactristics of th VT6, F-5.4%Ni alloy and th 1GBA tub stl ar dtrmind, which diffr in th ability to fractur toughnss and th Young s modulus. REFERENCES [1] ASTM Dsignation E 99-09: Standard Tst Mthod for Linar-Elastic Plan-Strain Fractur Toughnss K IC of Mtallic Matrials. PA, USA: Wst Conshohockn, 009. [] GOST Mthods of mchanical tsting of mtals. Dtrmination of fractur toughnss charactristics undr static loading, Moscow: Izdatlstvo standartov. [] GOST (STSEV ) Moscow: IPK Izdatlstvo standartov, [4] Lis, B.N. 01. Th Charpy impact tst and its applications. Journal of Piplin Enginring. 1 (), [5] Krn, A.P. and Rudnitskiy, V.A Us of nrgy approach to dtrmin fractur toughnss of polymthyl mthacrylat by indntation. Industrial Laboratory. Diagnostics of Matrials. 74 (1), [6] Glzr, A.M., Prmyakova, I.E., and Fdorov, V.A Crack rsistanc and plasticity of amorphous alloys at microindntation. Nws of th Russian Acadmy of Scincs, Physical Sris. 70 (9), [7] Barkr, L.M Thory for dtrmining K Ic from small, non-lefm spcimns, supportd by xprimnts on aluminum. Int. J. of Fractur. 16 (6), [8] Wang, C.T. and Pillar, R.M Short-rod lastic-plastic fractur toughnss tst using miniatur spcimns. J. Matr. Sci. 4, [9] Grant, T.J., Wbr, L., and Mortnsn, A Plasticity in Chvron-notch fractur toughnss tsting, Enginring Fractur Mchanics. 67, [10] Drozdovskiy, B.A., Polischuk, T.V. and Volkov, V.P Chvron notch as a mthod of thicknss dcras of th spcimn at dtrmining of К Ic valu. Zavodskaya Laboratoriya. 6, [11] Rakhimkulov, R.R Matching of fractur toughnss valus of К1с, obtaind in chvron-notchd spcimns and basd on standard tchniqu for a stl Stsp. Nftgazovodlo., Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 47

10 Nw Mthod of Dtrmin Fractur Toughnss Charactristics of Small-Siz Chvron-Notchd Spcimns [1] Hrtzbrg, R.W Dformation and Fractur Mchanics of Enginring Matrials. rd d., Nw York Wily. [1] Matvinko, Yu.G Modls and critria of fractur mchanics, Moscow: FIZMATLIT,. [14] Brok, D Elmntary nginring fractur mchanics, Lydn. [15] Timoshnko, S.P. and Goodir, J.N Thory of Elasticity, Nw York, Toronto, McGraw-Hill Book Company. [16] Salm, J.A., Shannon, J.I., and Jnkins, M.G Som Obsrvation in Fractur Toughnss and Fatigu Tsting with Chvron-Notchd Spcimns. In K.R. Brown and F.I. Baratta (ds). Chvron-Notch Fructur. Tst Exprinc Mtals and Non-Mtals. ASTM STP 117, Amrican Socity for Tsting and Matrials. Philadlphia, 9-5. [17] Barkr, L.M A simplifid mthod for masuring plan strain fractur toughnss. Enginring Fractur Mchanics. 9, [18] Ruggiri, C. and Mathias, L. 01. Fractur-rsistanc tsting of piplin girth wlds using bnd and tnsil fractur spcimns, Journal of Piplin Enginring, 1 (), [19] Roy, H., Ray, A., Barat, K., Hochmuth, C., Sivaprasad, S., Tarafdr, S., Glatzl, U., and Ray, K.K. 01. Structural variations ahad of crack tip during monotonic and cyclic fractur tsts of AISI 04LN stainlss stl. Matrials Scinc & Enginring A. 561, [0] Bartisch, M., Zang, Z.F., Schu, C., Rühl, M., and Mssrschmidt, U Fractur paramtrs of chvronnotchd Al O /Nb sandwich spcimns. Z. Mtallkd. 95, [1] Dryugin, E.E Improvd modl of th Griffith crack. J. of Appl. Mchanics and Tchnical Physics, 9 (6), [] Zhrbtsov, S.V., Salishchv, G.A., Galyv, R.M., Valiakhmtov, O.R., Mironov, S.Yu., and Smiatin, S.L Production of submicrocrystallin structur in larg scal Ti-6Al-4V billt by warm svr dformation procssing, Scripta Matrialia. 51, [] Physical Quantitis. Rfrnc Book Editd by I.S. Grigor v, B.Z. Milikhova. Enrgoatomizdat, Moscow, Russia. [4] Titanium Alloys. Composition, structur, proprtis Rfrnc Book. Moscow, VILS-MATI,. [5] Dryugin, E.E. and Suvorov, B.I. 01. Dfining th Fractur Toughnss for Small-sizd Sampls of Matrials with Submicrostructur, Vstnik SamGU. Tchnicalscincs. 4 (6), [6] Prokopovich, K.A Static fractur toughnss of th xtratrrstrial F-17%Ni alloy. In Works of XII Intrnational Scintific and tchnical Ural school-sminar of mtallographrs-young mtal scinc scintists. Ekatrinburg: UrFU, [7] Safarov, I.M., Srgv, S.N., Korznikov, A.V., Galyv, R.M., and Gladkovsky, S.V. 01. Fibrous Ultrafingraind Structur and Proprtis of Rolld Low carbon Stl 1 GBA. Lttr on Matrials., -6. Copyright 016. Innovativ Rsarch Publications. All Rights Rsrvd 48