Quasi brittle fracture of the v notched specimens subjected to pure torsion (in Russian)

(1)

M ECH AN I KA TEORETYCZNA I STOSOWANA 3 - 4, 23 ( 198 5)

**KBA3HXPyiIKOE PA3PyiIIEHHE CKPy*fflBAEMI»IX OEPA3IJOB**

C V— OBPA3HWMH BŁIPE3AMH

H . H . ByraKOB (JlEHHiirpAff, C C C P )

3KOiepHAieHTaJiBHo H caieAOBaiibi ABe 3afla^H KpyqeniiH — oceciiM M erpiraiafl H aH -OnbiTbi npoBOfliinn Ha ijunnimpiraecKH X o6pa3uax H3 cTeKnoo6pa3H oro n o Jiiu iepa c V — oSpasHbiMH BŁipe3aMii. OrHOCHTejiŁuyio r.uy6nH y B W -pe3a H p a ^ n yc e r o Bepuim ibi ocTasjiHJiH Hen3MeBHi>iMH, a yroji pacrBopa BaptH poBajiH B HHTepBajie 15 - 150°. H 3yq en bi >KecTi<ocTb H npo^H ocTb o6pa3iioB₅

xapai<Tep pa3py-o6eiix

1 .

OAH OH H3 H anSojiee Tpy^H bix npo6neM MexaHHKH fle<J)opMH pyeMbix Teji HBJIHCTCH n po^n ocT H Ten c KOHneHTpaTopaMH HanpHJKeHHń. H MeeTca Sojibinoe IH CJIO H 3i<cnepiLMeHTajibHbix HCCJieflOBaHHśł B cjiyâax rjiaflraax KOH nempa-TopoB, c OAHOH cro po H bi, H pa3pe3OB (H aqaiiBH bix TpemH H ), c flpyroii. OflHaKO, 6OJHB-IIIOH H ay^H biH H n paim raecK H H HHTepec npeACTaBJiaiox H BceBO3MO>KHbre npoMOKyToq-H ue cjryâ BceBO3MO>KHbre npoMOKyToq-H j K o râ KO BceBO3MO>KHbre npoMOKyToq-Hi;e BceBO3MO>KHbre npoMOKyToq-HTpaTopbi BceBO3MO>KHbre npoMOKyToq-HMCIOT p e6p a, yraoBbie TO BceBO3MO>KHbre npoMOKyToq-H K BceBO3MO>KHbre npoMOKyToq-H , BceBO3MO>KHbre npoMOKyToq-H O OTJI BceBO3MO>KHbre npoMOKyToq-H BceBO3MO>KHbre npoMOKyToq-H BceBO3MO>KHbre npoMOKyToq-HBI OT Tpem im . A1O>KHO npH Becxii MHoro npH MepoB yraoBbrx KOHqeHTpaTopoB: 77 H V — 06pa3H bie rra3bi u KaHaBKH, L — o6 V — 06pa3H bie nepexoflbi BCTpeâiOTCfl B umoH OiH bix, IU JIH -, pe3b6oBbix, CBapH wx H npyrH X coeflHHeHHflx H B ajieMeirrax MauiHH, KOHcrpyK-coopy»ceH H fi.

TeMaTnqecKoro HCCJieflOBamiH Tan oro pofla 3aflau cBH3aHbi c pe3KHMH HanpH>KeHHił B OKpecraocTH BepuiH H bi yr a o Bo r o Bbipe3a. B paMKax iwe-KOHTHHyyMa n ojie HanpHH<eHHH B OKpecTHOCTH BepuiH H w cH H ryjiapno [ I ] . I I pH OTOM CTeneHŁ cHHryjiapHOCTH He paBH a 0, 5, KaK B arcyqae pa3pe3OB, a H3MemrxcH B n p e

-OT 0 pjo 0, 5, yM entuiaflCb c POCTOM yr a a pacrBopa n p n Bepm nH e. AjitTepHaTHB-noflxofl pa3pa6oTaH B MOHorpa<J)HH [ 2] .

KaCaeTCH npO^HOCTH, TO KpHTepHft rpH ^^H T C a MJW T0KHX 3aflai 0I<a3bIBaeTCH H naâTŁi HccjieflOBaHHH flpyrax KpH TepaeB pa3pyiueH iiH [ 3 - 6 ] . H e BbI3bIBaeT COMHeHHił OCTpaH Heo6xORHMOCTb HaKOIIJieHHH 3KCnepiIMeHTajIŁHbIX flaH H blX. c V—o6pa3H biM Bbipe3OM npHMeHHiOT flJiH or;eHKH BH 3KOCTH pa3pyM aTepnauoB n p n oceBO3KOCTH pa3pyM H BHeiêHTpemio3KOCTH pa3pyM pacTH>KeHHH, craTHêcKO3KOCTH pa3pyM H y# a p

(2)

-564 I. BOGAKOW

HOM iraraSe; yroji pacrBopa n e BapbwpyioT H *iam e sc e r o npiranviaiOT paBH bm 60°. I l p a 3T0.M TaKiie o6pa3u w o6biqH o npHMeiraiOT c neJibio 3aM enbi o6pa3i;oB c tiaqajibH oK ip e-m ie-m ofi. JI H I U B B pe^KHX cnyiaH X HcnwTaHHH o6pa3qoB c yriroBbM ii Koie-meHTpaTopaiviH paccMaTpH Baior i<ai< npe^cTaBJiH iomne caJWOCTOHTeJibHWft H H Tepec [ 3 - 5 , 7 - 9 ] . B pa-Gcnre [6] 3KcnepHMeHxaJiLnwe flaH H H e [ 8, 9] 6WJI H yflOBjieTBopjirejiŁH o oimcaH M npH

KpHTepHH HoBOJKHJioBa. B yKa3aHHbix paSoTax H ccneAOBana pacTH H teH iie HJIH

paSoxe 3KcnepHMeHtanŁHO crep>KHH H S creKJioo6pa3H oro

Bbipe3 6 H J I KOJiti;eBbiM 3aflaya).

B

B 03H0M

c V

_Bwpe30M.

B apyroiw npo-2 . 3KCHCpiIMCHT

O6pa3L(bi G bura H3roTOBJieHW H3 OT^H BKH snoKCHMHoro no^H M epa r o p n ' i e r o oTBep->K«eHHH '3JX- 20, Hcnojii>3OBaHHoro B n peflbm ym iix paSoTax [ 83 9 ] . 3 T O T nojiiiM ep HMeer

TpexMepHoe MOJiei<yjiHpHoe c rp o eraie, n pw KOMHaTHoń TeM nepaType HaxoRHTCH B creK-jioo6pa3HOM COCTOJIHHH H pa3pyiuaeTCH KBa3H xpym<o; M o^y.ib c^Biira p a se n I , I G P a, KO3(pcl3HqHeHT I lyaccoH a 0, 35.

<E>opMa H pa3Mepbi o6pa3i^oB ( B MHJUiHMeTpax) H3o6pa>KeHW n a P H C . 1. OTHOcHTejiB-n a a rJiy6H H a Bwpe3a B OSOHX cJiyqaax 6biJia paB. 1. OTHOcHTejiB-n a 0 , 5 ; p a ^ a yc e r o Bep. 1. OTHOcHTejiB-niH H bi . 1. OTHOcHTejiB-n e . 1. OTHOcHTejiB-n

pe-R7

PH C. 1.

Bbim an 0,03 MM. Yro ji pacTBopa a H3MCHHJICH B HHTepBajie 15° - 150°. Bwp e3bi H 3ro-pe3n,aMH Ha 4>pe3epHOM H TOKapHOM craH Kax. TexH oitorH H aH ajioraiH a nofl-onacaHHOH B [10]. Bcero SbiJio H cntiTaH O 15 o6pa3i^OB I H 16 o6pa3B(OB I I , Tem-n ep aryp a SbiJia paBH a 2 9 6 ± I K .

OnbiTBi 6Ł I JI H npoBefleH bi Ha n pocToił JiaSopaTopH oft ycraH OBKe, no3BOJisnoineH TOI H O ijenrpH poBaTB o 6p a3qw H npHKJiaflbiBaTB K pyT am n n MOMCHT M flo 50 N M

(3)

; MO-KWAZICHRUPKOJE RAZRUSZENIJE OHRAZCOW ₅₆₅

C03flaBariH rpysaM ii, a yr a r t 3aKpyt£HBaHiia..t? oTcurrM n an H n o nwaSy c nenoft 0, 5°. M O U U I O C T H ycTaiiOBKii HexBaTHJio, m- o6bi AOBCCTH AO pa3pyin eH iia 06-pa3n w H e Ai' ^ ^ e T P0 M

20 AIM, Kan y o6pa3UOB I , u noTOMy HX AHaMerp flO 15 M.M.

Pe3yjitTaTbi sKcn epiwieirroB 11 H X o6cy>KAeHHe npunoAHTCH H H JKC

3 . 3KccTKOCTb n

KpyrniU H H MOMeirr M — yro ji 3aKpyiH BaiiH a moupy 3axBaTa.wn & 06-I H I I AJIH pa3JiH tiH bix yrn o B p acrBo p a a npeflcraBJieH bi Ha p n c . 2. BH AH O, mo

n p n BH C O K H X H arpy3Kax Heju- iHenHbi, uamsuibiibie yq a c n u i jiHHeHirw, a I K

M[N- m]

• - 15° v- 90°

o- 30° + - 120°

• - 60°—A- 150°

MtNml

Puc. 2.

3aBHCiiT OT oc, n p H 3TOM c pocTOM a. jKecTKOCTb o6pa3i;oB 3aMeTHo n aflaei. C paB-AJIH O6OH X o6pa3i;oB noKa3WBaeT, ^ T O >KecrKocTb o6pa3qoB I SonBiue, a snaqeH H H p a 3p ym a io m e r o KpyTH mero MOMeirra Mc H y m a saKpy^H BaH H a n p a p a 3-pymeHHH &c M eH tm e, HCM. y o6pa3i;oB I I . I T pn STOM 3Ha^eHHH §c c pocroM « fljia 06-pa3U0B I yBeJiH iH BaioTCH , a flJia o6pa3ij(OB I I no^TH n e H3MeHHioTca.

An pH opn MO>KHO SbiJio npeAnojio>KHTb, TTO C POCTOM a n poun ocTb Syfler 3aMeTHO BospacTaTb, Kau OTO niweeT M ecro B cn yqae paciH rH Baewbix o6pa3qoB c Bbipe30M B BHfle JiyiiKH [8, 9] . Oi<a3aJiocB, qTO n po^n ocT b o6pa3E(OB I n pH a ^ 120° He 3aBiicHT OT a H JiHiub npH a = 150° naSjiioAaeTCH ee yBejraraemre. ITpouHOCTŁ o6pa3i;oB I I saweTHO c pocroM a , n pn ^eM rpa<f)HK cpeflH eii OTHOCHTCJIBHOH n p o qH o cru Mc(x) n oBT opn er r p a ^ H K /_f( a ) . 3Aeci> J_f — n ojin pH bui MOMCHT H H epmoi n o n ep ey-H oro ceieey-H ey-H ey-H j nojiyqeey-H ey-H Bift n o yr a y ey-H aicioey-H a npey-HMOJiey-Hey-Heiiey-Hbix yiacrKOB Aey-HarpaMM ey-Ha $ H r . 2. CjieflOBaTeJibHO, BJiHHHHe n ojiapH oro MOMeffra n a n po^n ocTb o6pa3iioB I

(4)

I oi<a-566 I. BUGAKOW

,; • • • • 4 . Xa p a K T e p p a 3 p ym e H H H

pa3pyiiienH Bix o5pa3i(OB. M aTepaaJi o6pa3U pB SBIJI npo3pa*ieH , «xo rro3BOJmjio paccAiaTpHBaxb He TOJIŁ -KO H3JIOMBI, HO H BHyTpeHHHe TpemH H Bi. BHfl (j)parMeHTOB oSpasu oB I I c

xpeuninaM H noi<a3aJi, *JTO n pH MajiBix yr n a x a , K or^a pa3pyuieH H e HOCHJIO

H BIH xapai<xep, OHO H aun n ajioct HOMTH oflHOBpeAieHiio BO M H orax x o w a x BAOJIŁ Bepmn-Hbi Bi>ipe3a. 3 T O cBH#exe.iibCTByex o BBICOKOH c r e n e m i OAHopoflHocxn Aiaxepiiajia, a Tai<->i<e H anpjD Kennoro COCTOJIHHH BROJIB npoflOJi&Hoń OCH o6pa3ija.

XO T H marpamihi H arpywenH H (CM. p «c . 2) saAiexHO H eJiH ueftH ti, pa3pym eH n e SBIJIO KBa3iixpym<HM. 0 6 3XOM CBHflexejiBCTByex i<ai< peJiBecJ) noBepxH Ocxeft pa3pym em ifi, xau H opH enxaqH H BH yxpeH i»ix xpemH H H H 3JIOM OB. H a H3JroMax BH AH W 3epi<ajiŁ HaH 3ona, a xai<>Ke cxynentKH , 6opo3flBi, rp eSro i, opH eH xapoBaaH Bie B HanpaBJieHHH

cf)poHxa5 KoxoptiH 6 B W KpHBoran- ieeH. O xu exm m o BbwejiaexcH 30H a ^ojiOM

I, IIojio>KeHHe BiiyxpeHHHX xpeiqH H H pe^BefJ) H 3JIOMOB CBHAexeJiBCXByex o TOM, HTO paspyiueH H e Bcerâ naîiH aôcB ox BepuiH H bi Bwpe3a.

P a3pymeiiH e npoHCXofliMO n o nepBOMy xim y (HopMaJibHBiił p a3p biB) : TpemHHbi pacnpocxpanjiJiH Cb He B n on epem iofi IIJIOCKOCXH, a n pim epH O n o ^ yr n a i i 45° K ruiocKocr-HM cHMMexpHH o6pa3i;oB. AHajiorHHHyio opH eirraił H io xpemH H p a sp yin e r r a n Ha6xnoflajin B cn yiiae KOJibueBbix H aflpe30B- xpemH H [ 11, 12]. Jluuih ROJIOM. n pon cxoflH

^ noA apy-pa3pymeH H H o6pa3u;oB I H I I BH eume n e oflHHaKOBŁ i (CM . HHH<e₃ n . 5). H jieexcji KopejmaaH H nempy pejibecJwM H n jiom afltio H 3JIOM OB, C O# H OH cxopoH bi, H pa6oxoii pa3pymeH H H , c flpyroii.

H 3BecxH 0, qxo pa6oxa pa3pyuieH i«i paBH a AonojiHHxeJibHOH paSoxe. B H

ameia cjry-nae 3io pa3iiocTB Me>KAy paSoxofi BH eiiiH ero KpyxH

iriero MOMeHxa u pafioxofi Ae4)op-MaqHH o6pa3i^a. OHa H3MepaexcH njiomaflBK) oSjiaciH , orpararaeH H oft OCBIO MOMCHXOB H AHarpaMMoft Harpy>KeHHH. I l o saiiHBiM 4} H r

2, OHa pacxex B o6pa3i;ax I c yBeuipreH -HeM a, a B o6pa3yax I I — c yAienBUieiraeM a. Upa 3TOM AonoJiH uxejiBH an paSoxa o6pa3-I;OB I I 3Ha^HxejiBHo SonBiue, qeM o6pa3i(OB I . CooiBeTcxBeiiH o, SoJiee rpySBiM asJisercfl

H3J10MOB o6pa3i;oB I I , a cxajio 6BIXB SojiBine H CKOpociH i p e u p r a B o6pa3t(ax I I . 6ojibiiie flono^H H iejiBH aH pagoxa, xeM AieHburyio OTHOcnxe^BHyio n jioin aflt H3JIOAIOB 3aiiHMaeT 3epKajiBHaH 30H a. C pocxoM sonoJiHHxeiiBHOH paSoxBi yBejia^H BaexcH MHCJIO OCKOJIKOB H rniouxaffb noBepxHOCTeS pa3pymeH H H o6pa3ijoB. I I p H OXO.M I H C JI O OCKOJIKOB H ruiomafli) noBepxH ocTeii pa3pyiueH H H o6pa3itoB I I . 6o.Tbuie o6pa3t(OB I H pe3K0 pacieT c yMeHbiueHiieAi yr a a a. ..._:

5 .

Bo Bcex cny^aH X o6pa3E(Ł i I n pH pa3pyiueH H H pa3AeiiH ^H Cb B 3on e H anSojiee cna-6o ro ceqeiiH H Ha jape IIOJIOBH H BI. B 3aBHCHM0cxH ox yrjia a. B OIH X o6pa3L[ax H aSjnoAaioxca TpH (J)OpMbI pa3pymeH H H : OflHOCXOpOHIMH ( a . = 15 H 30°), £ByXCXOpOHHHH (_a = 120 H 150°) H npoMeHcyTOHHaa, nepexoflH aa ( a = 60 H 90°).

(5)

KWAZICH RUPKOJE RAZRUS ZENtJE OBRAZCOW 567

I l p i ! ofliiocropOH H eM p a3p ym eiu o i OT Ka>KflOH nonoBH H bi OTflejiHJioci. JIH U IB n o op,-ocKOJiKy ( p u c . 3, a ) . C KOJI Ha BTopoił n on oBm ie pacnojioH ceH npOH3BOju>H0 n o oTHOiueHHio K CKOJiy n e p Bo ń .

ITpii flByxcropoH H eai pa3pyiueH H H OT KEDKAOH noJioBHHbi o6paaqa I OTflejimiocB n o ^Ba H 6ojiee OCKOJIKOB, n p H STOM Ha M ecre H anSoJiee crcaSoro CCTCHHJI o6pa30BaJiocB pe6po ( p a c . 3, B ) . Peji&ec|) O6OH X CKOJIOB paajitraen , H3 - qero cJicnyeT, 'OTO 06a CKOJia

b)

OM50"

I

PH C. 3.

l i p a npoMeHcyTOMHoił (jłopiwe OT OflHoił nojiosH H bi oSpaaua I oTflejiHJicn OAHH OCKO-JIOK, a OT flpyroii n Ba — TpH (Bee c o^H oro 6oKa), H n p n OTOM B TeJie i<a>K«OH H3 flByx

oSpaaoBajiHCB TpemH H bi npocTpaHCTBeHHoii 4>opMw, He ycneBiuH e BBIH TH Ha n oBepxH oerb o6pa3i;a, i<aK STO niwejio Aiecro n p a flByxcTopoH H eii (J)opjvie. IlOBepXHOCTB i<aM<floro H3Jioivia —- no^TH iuiocKaa, n o ^ yrJioM K Heft pacnojioH<eHa nJIOCKOCTB flOJIOMa.

P aap yin eiat e o6pa3qoB I I npoacxoflH Jio n o BHHTOBBIM noBepxH ocraiM. I I o Bnpy aaaSojiee K pyn n bix OSJIOMKOB MO>KHO 3aKJiioyHTB, nio n p n Bcex yrjiax a HMeioT Mecro 4>opMbi pacpyiueH H H : npoflOJiBHaH, n o n e p e i H a a a CMeinaHHaa. ^ a m

e Bcero Bcrpe-npoflOJiBHan ^ O P1

*1 3 1

pa3pymeH H e nponcxoflH T OKOJIO npoAOJiBHoS a noBepxHOCTB paspyuieH H H HMeeT B H ^ cryneH eK (pH c. 4, a ) .

a)

b)

PH C. 4.

nonepe^H OH 4>opiwe ( a < 150°) o6pa3yioTCH Tpem im bi BHyTpeHHHe H

urae Ha n oBepxaocTB. I lep Bbie HMCIOT BHO, 3aKpyqeH H bix jion acreii, BTopbie o6pa3yioT Ha inuiH H flpiraecKOH noBepxHOCTH o6pa3i;oB BiraroBbie JIH H H H (pac. 4, B ) . I l p n a =

(6)

568 I . BU G AK O W

6.

O S B WH O n pH p a c u e r a x H anpH >Keinroro COCTOHHIIH n p n ocecH M AierpnqH oii # e(j)op-II aHTHIIJIOCKOM CflBH re OqiaH H IH BaiOTC H BbiqH C JieilH eM KO3(J)Cj)imHeHTa HHTCH-CHBHOCTH nanpH >KeH irii K3. IlpH Be^eH H bie pe3yjitTaTi>i H apjm y c [ 1 1 , 12] noKa3f>iBaioT,

paCUeTbl HeJIL3tt npi- IMCHHTS K OUCHKC npO^HOCTH XpyilKHX o6pa3i;oB I n p ii oflHHaKOBbix yrjie et I I OTHOCHTCJILHOH rjiySn H e

HHHce n po^n ocT ii o6pa3H OB I I H cBoiicrBa o6pa3i;oB I ir I I BO M H O H K OTHOIUeHHHX npOTH BOnOJIOJKH H . JlH Tepaxypa 1. M. L. WILLIAMS, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, i. Appl. M ech., 19, 4, 526- 528, 1952. 2. H . N EU BEK, Kerbspannungskhre. Springer, Berlin 1958. 3. J . F . K N O T T , Fundamentals of fracture mechanics. Butterworth s, L o n d o n 1973.

4. V. WBISS, I n : Fracture. An Advanced T reatise (ed. by H . Liehovitz). Vol. 3. Acad . P ress. N . Y. & London 1971.

5. A. A. H JD KH KJ Bonpocu npUMenemm mxamatu pa3pyuteuun K attamay pa6omocnoco6noanu juamep-tuiJioe napottix mypówi npu IMJIWIUU deifiemiwa u mpettfwi. B : T lnebnueiiue uadezKHocmu u aanecmm MamepuaAot 9Hepioo6opydoeanun. Tpyflbi l|eH T p. KoT^:oTyp6. H H CT.J JlemfflrpaA) 160, 29 - 44,

1978.

6. H . <t>. M OP O30BJ Hcc/ iedotainte pa3pyuta}0Ufe& nazpyzmi dnu oSnacmu, ocna&Aemou zupizon s nude .tyjiKtt. floi(Jia«w AKBfleMHH Hayic C C C P , 253, 6, 1336 - 1338, 1980.

7. B. G ROSS, A. M EN D ELSON , Plate elastostatic analysis of V- notched plates. I n tern . J . F rac t u re M ech. 8, 3, 267- 276, 1972.

8. H . I'l. EyrAKoB, I i . H . JtEMHfloBA, Keasuxpy/ moe pa3pyutcuue o6pa3ifoa c eupeso.u, UMś fOUfUM yino-eue mo'iKu. H3BecTHH Aia^e.Mira H ayK C C C P , MexaHHKa TBepnoro Tejia, 3, 182 - 183, 1980.

9. I- I. I I . ByrAKoB, Kea3uxpymae pa3pyutcmie o6pa3ą oe c eape30M e eude jiyHKU. H 3Bec in a AKa^eMHH HayK C C C P . M exaH ima TBepfloro iem, I , 177 - 180, 1982.

10. J . L. M AR C H , W. J. R U P R E C H T, G . R E E D , Machining of notched tension test specimens. AST M Bull., 244, 52 - 55, 1960.

11. E . SOMMER, Formating of fracture,, lances" in gloss. E n g. F ract u re M ech ., 1, 3, 539- 546. 1969. 12. W. G . KN AU SS, An observation of crack propagation in anti- plane shear. I n t ern . J . F ract u re M ech., 6,

2, 183 - 187, 1970.

S t r e s z c z e n i e

KWAZIKRUCHE PĘ KAN IE PRÓBEK SKRĘ CAN YCH Z KARBEM W KSZTAŁCIE LITERY V

Badano doś wiadczalnie dwa przypadki skrę cania próbek walcowych z karbem obrą czkowym i karbem wzdł uż nym. Próby przeprowadzono na próbkach ze szkł opodobnego polimeru epoksydowego. G ł ę bokość karbu i promień dna karbu by!y stał e, zmieniano natomiast ką t rozwartoś ci karbu w granicach 15°- r- 150°. Wyznaczono sztywnoś ć, wytrzymał ość próbek oraz przedstawiono róż nice charakteru pę kania. Podano porównanie obydwu przypadków karbów.

(7)

KWAZICHROPKOK RAZRUSZENDE OBRAZCOW 5 6 9

S u m m a r y

QUASI BRITTLE F RACTU RE OF TH E V N OTCH ED SPECIMENS SUBJECTED TO PU RE TORSION Two types of specimens have been investigated, both cylindrical with circumferential and longitudinal V notches. Tests have been conducted on specimens made of glassy epoxy polimer. Depth of the notch and notch tip radius were constant while notch angle varricd from 15°- ł- 150°. Stiffness and strength of the specimens as well as character of fracture have been determined. Compari-son of both cases has been given.