AD-761 455

PROBLEM OF CALCULATING BOLTED JOINTSUNDER STRESS RELAXATION AND CREEPCONDITIONS DURING VIBRATIONS

D. Ya. Br.gin, et al

Foreign Technology DivisionWright-Patterson Air Force Ba se, Ohio

7 May 1973

I Ill l'-

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Natnd Technical Informamln ServiceU, S. DEPARTMENT OF COMMERCE5285 Port Royal Road, Springfield Va. 22151

-8 " I II II

fTPI-lr-P 3-1-2 76-7 3

FOREIGN TECHNOLOGY DIVISION

PROBI3I4 OF CALCULIAT~lrO IJOLThP) JOINTS UNIMEP 5V)TRE.118RET.AXATIOll ANID CHEEP CON1DITIONS DUFRII1r VIBRAP1O1J1-1$

hv af~. a .,Ia~n, 1. '1. Shkanov, 1. . Vasil'vev

Ee~roducod by

NATIONAL TECHNICALINFORMATION SERVICE

UI S DepartmentI of CommercqSp,rloyflod VA 221.1

'11- tribjuti~un unlIimitud.

' ~I!

FTD-HT- 23-0276-73 i

EDITED TRANSLATION

,r)-[T-23-0276-73 I

PRO3LEM 010' CALCUCATIP'J BOLTED JOINTS UNDER STRESSELAXATIOJ ANT) CREEP CONDITIONS DURING

VIBRATIONS

By: D. Ya. rlrafin,T. 1T. hkanov,G, V. iasi.I'yev

Enrlish pages: 8

Source: Kazan. Avtatsionnyy Institut. TrudyNo. 136, 19711 np. 34-41.

Country of origin: USSR ITranslated by: Tgrt Victor Iesenzeiff

Peeq ues ter: FTD/P P''A

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Anr•,ovod .for public release;dis1tribution unlimited.

THIS TRANSLATION IS A RINDI TION OF THE ORIGI.NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OREDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BYiADVOCATED ON IMPL.IED ARE THOSE OF THE SOURCEAND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION

ON OPINION OF THE FOREIGN TECHNOLOGY 01. POREIGN TECHNOLOGY DIVISIONVISION. 'FPAPS. OHIO.

R AT-NI- 2-?3-276-73 Date7 "av 197I/I _III

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Foreiqpn Technology Divisi on UNCLASSIPIEDFAlir I orce Sys tems Command sb. GRUU. S. Air Force

PROBIEN1 OF CALCUYLATING BOLTED JOINTS UNPER STRESS REL.AXATIONAND CREEP CONDITIONJS DURING VIBRATIONS

* 06SgIP TIve No fee (fte of som am Ae~has" dow

D. Ya* Bragin, I. N, Shkanov, 0. V. Vasil'yev

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FTL)-HTr-•3-02?6-y3

4 ~~U. S. BOARD ON GEOGRAPHIC NAMES TRANLITERTION L'"ISTEX)

IBlock Italic Transliteration Block Italic TransliterationA a A a As a P p P p R, r136 556 Bs b CO C C S, 8

r r re 6,g Y y Y y U, ufl 7 Do Dd 0. F,go B Ye. ye; E, e* Xx )( X Kh,(hX 5 1 Zh, zh U U U i Tso ts

a a. 3 Z.,z 4 VCh, chH~ M HM U iti WW 111w Sho shR IN Ra Y, y W IL U1 3hch, shch

-X K Kx K,kb .Jut fl a L,0 bi Whr / Y, YM N M M M ,m b b haHu N H N,0i n3 e

00, 0. O 10 D ~w Yu,y11

*Iyen write as in Rusin tasieAt as ya u

initially, after vowels, and after 'b, b; e elsewh-re.The use of diacritical mark~s is preferred, but Lsuch tnav-I.;may be omitted when expediency dictates.

jFTD-HT-23-0276-3 tV

FOLL.OuING ARE THE GIMSPON4DING RUSSIAN AaD ENGLISH

MEIGRATIONS~ OF THE TRIOONONSTRIC FUNCTIONS

Ripguiam English

ts tanatg Got

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kiTD-I.iT-23-O27 6-73

I

UNDER STRESS RELAXATION AND CREEP

CONDITIONS DURING VIBRATION~S

D. Ya. Bragiri, 1. N. Shkanov, and0. V. Vavil.yev

I ",

The existing methods for calculating tight bolted joints for

stress relaxation are based on equations cor-respond~ing to a

particular theory of creep which gives the most accurate quant~ita-

I> tive description of the creep and 5tress relaxation of fastening

materials in the examined specific oonditions. Thus, for example,

1. A. Birger [11 uses the flow theory developed by L. M. Kachanov

J. for calculating bolted joints; other authors use the theories of

Yu. N. Rabctnov and N. M. belyayev. Howaver, the calculation

9L relationships for describing the ireep and stress relaxation,

Ii f

obtained on the basiD of these theories, are in good agreement

with the experimental data only for the pure metals and alloys

structurally stable at Increasedu temperatures and are less suitable

for describing these processes in the heat resistant aging alloys

based on nickel, working under conditions of vibrmo tionsc especially

in the temperature range of their aging intensified by vibrations

I; and progressive with a decrease in the specific volume of the

material. In our opinion the following equation of stress

relax. tion proposed by B. H. Rovinskiy [2, 3, '1] Is mby i . tKable

for these purposes:

FTD-IIT-213-C)276-731

ýWichý#" jenia.± lzes, thrQ kno wn Maxwell equation when

E (2)

altou~i 4 i~.exresesa more complex dependence of the material's

viscoýs Ity. fatr a as, ~ oip are ih4~Jqain u it.describes the..stress relaxation process more accurately for theheat rebist_*SrI. a~lloys tested by us, used for manufacturing

'ieq. ht ions.(I' and: (2), ar and aT are the primary stress_ý 0

arid;_strtess- att the Imoment' of time T, respecively; p is the material's'index- of rla~xationaL. p~liabil'ity;, kP is the coefficient character-

*znghe ý". decreas~e in-t he i ni tial period; E is the modulusof loigtd~ileat-.yof. the material. Using th Ie value--, ofco fficierits-',ki and .it is; possible7'.to make a practical calcula-tion ýLotkh b the. s~tress relaxation as' well as f or cre Iep. Th ehie t hc0` O'Or, de termining; the.: coefficients taking into account theneculiatr"Ities' of cotress relaxatlion in heat re~si~stant alloys underc:n'di%;.ons .3f vibrations.i~dscie in work' F-5.

1'P-izeon"miftion 'ftightness fo0r--a 'bolted -joint wi L. t I atSfct :certa-ri time 'by the constancy in the dimenslon-

flt~and bolt Cmi the case of'the absolutely rigid flalig- whur3in.tighi.ness of' the junction under the effect of' t~he ant: 7led

1.-,,d Is broken due,. ',o the relaxation of stresses in the bolt-I C,'uth':. case of' pliable flange.,) by the cl~ani I'n thc' d*.Ile,..,'r!,

',iir he limits corresocndin.; to a tight unicl1. wheni as 1 3

_i,ý bolt creep under the *ef ~ect of the apl-'i~ed 'cu)d and(!icv'caý;ed e~mpe.au~ t-here wi) 1 occura 1.rihtn<oTe

FTV f-23-9276-13

c u 11p r uijetl Vlaugeo.ýi Itha case, even thiough the~ creep of LhuL,

fitinguu~ and t~ho boli_ will, be dif fererit , the Lotal relative vlingai-

tiuzi (ela~tla a1I16 plnistlc V should b e idet.-1 .cal. Then f~um. thu

*condition of~ sxualr corpat Lbi~lty of' the Uolt anm' flanges wecap writu uic coxiditiuzi whiuh satiafites Liicir tight mmtual U1nion:

In thIL3 caLu for~ the flange tnior; I t,, is valid to pose thib requirw'-

*e t'it~ L Or (oofl tant ra~t Io between~ j~4w Li~e, L to lt; 4.ald

and CzatulW, r.,tio of'tie- coefficients -of iscoot)

J ~Thei,. ;Ltfto,ý (J4) and ()anid aV ~I

(.9) it wi1n. aausrie t he f orm:

I0 +

X1't.vr integrating equation (7) within, t he Ii ml it, ftCi tuo t htrcrsdr~ oio ,r1I..~j

:ind fxmn! 0 oTwt i. oodrto fdf w mlc!

trid dL:L IgnaL i n~ , ig

Ii: IFA

ES.(. & C 2 *

I .47-J.

T-1I

w o ubt.:tiu the Vullow Lng relatio'nship tin Lhu Virial rurnii

T1hu. intI'LOduced ]'21aýlt1 oluhl (9) I. rb LIP' gL'riI~':Ll CtAok.

os L r~' co~ini h bolt takli ijItgiccut ~i ~oufe!iaJ iclt-y and •'r'ep of LhQ intermediatu parto. Pot, a 111011L,

accurate calculation Lhe itll v.1.5coiJ.y iauotu (A' L1iV

inturmediate par'ts -4)uld Lie detorm'ndz.. by 'the values; of puranht, -s

enturlug exprussi lou (2') whS.ui weru ublri Ined I'rorn tho L'xierimcrita L

cui'vus on striess :oc'laxatlon or cro~en -Juririg 'comprc~s.'on. Ilowvvui',

due to the fact thai. LheveuJ, a t~tal. ablueice of thu for-mer and

3cantiness OT thu lE,';ter' in the. )lturatux'e, we van u:3c Ut., da~ij

on Btress relaxation and cre-ep during extension, whilch Is valid

for' .%mall deformati )ns. which do riot exceed 1-2111 [6)] '1'iit o -

parlsoii of Iie curves of creep for alloy I3'.143b d'uvl h: cUrfipiws I .r,,1d

ipres';-rited In , ;or'k [7 J with those fur L1113 allo)y (114'. g'1eil'

spe'oeZz in 1ii r of' t~iis a~ssrtioru. A uomewhat ;31iltic -Jufoivrruatj0 m

''C~ tti i '*J recp durinig extLon.lion, as com;)pavuk wi. 1Lii 1. tie 2oum-~

orco6sion apil '-ablc' ':o I'langes (1ntevi-udlate p'r'ts) , y.1.;k1L. thu4

'u2ITI '2 U1 .tt V' 1 LiUS )Ltairied by f'ormulas ( 2 ), (,) , :idk (6~) a,; a

oat'c'y f;yc.'.' ~Iit;fl oulating thrz end struosu~s.

1Vlgure 1 sie'aL; :he Lexperimeintal curves on u tI'uU1 IC l1xal-1oi(A, te El1481 i I.L~arlthmrio. cuor-diriate:ý qL -. t~ tn- w I 'i,

and w~ithout vit :-atS ii. for thrue prima~ry sLtru:LL . 'liii Le

rt. layat~lori char;j.6ý.vv tics 1founid using thuse curvei8 zr' t;Li

TUb Ie U k , Wh i .V h11ow J t he i r de . (,ri de i i o~ ti I, Ii in.. v

01 A lupui ki3e SI with a. curtain dort'u cci'* ( ;AOWlvoC±'1 lsa t, "3 a ' 'Ov, for' ,-ngliiecrinC- CcUlCU tat- [-I]u rPCiII~n;

for Lh raded to r oiviuot1. ris), arc, ass umed to be 1 mooir i '

d':L~crlbud 1.\ i~rmi i a J'Oim~U laswh .11Q1 jh ~j'mljtS OneQ tLu Chid Q'I

p.et 1)clnd11 for inyv primary t ri Liic exartilnWdpv~1

2K I i ., - lI -:l..

3a)

1 m W .

- - - Fig. 2. Stress relaxationb) characteristics of steel Ei481

as a function of the primary.stress CT - 650 OC);

. - with vibrationsO O without vibrations

44 48 J2 66 4T

Fig. I. Stress relaxation curvesfor steel E1481 with T - 650°Cand primary stresses: a) a 0. 30 kgf/mm;2 b) a 20 k 2f/mmC) 1o 10 kgf/mm2 2

- - with vibrations0 - -without vibrations

5

Tab le 1.

fkt/mm2 With vibrations Without vibrations

______ P KP P K- -i

30 0,353 0,132 0,410 0,074

20 0.20 0,112 0,310 0,056

10 0,212 01F6 U0 104, 0,120 jTable 2.

Material Tempera- Range ofture, in applica-

according

to theprimarystressesC(o, kgf/nm2 -

650 10-30 -0,0024 0.,0,20* 0,0070. 4C,14" 455 8-5 -0,0025 Os 40,14 0,015303-0,06

550 10-35 -,o1 .5o,45" 0,00o01. 10,o09-o,o0430.0, 17 0,0=0 (Do 40,05 4

E1437B 700 25-45 0,00035 5. 40,047' 0,017 00 -0,3"' 0,00C54 0iO,0,32 0,019 Go -0,46

800 10-30 0,0 .(5 ,01 0.0096 0, -0,1* -C,09 0,018 0, -0,19L1598 . ... ,=O6 50OO~ 10 -

700 2o-45 O'=C86 4 .0,004 0,occ (Do +0,05 1Note: Empirical formulas for kP and p with vibrations are

indicated with the asterisk.

Table 2 shows th( empirical formulas of the stress relaxation Icharacteristics of certain alloys, used in the manufacture of

FTD-HiT-23-0276-73 6

r,"..=

I•

fastening parts for gas turbine engines, at operating temperatures

and stresses. The range of their use according to primary stresses

is given for these formulas.

The selection of empircal formulas was accomplished by the

graphic method. The difference in the ocales of values plotted

along the axes of ordinates and abscissae is taken into account

in the angular coefficient of these formulas.

The presented formulas reflecting the experimental graphic

dependence are obtained on the basis of the tests carried out on

stress relaxation for the indicated alloys for a period of 60 - 100

h with and without vibrations; some of them were experimentally

checked for the reliability of extrapolation up to 200 h. It turns

out that the use of coefficients p and kP found by these formulas1!yields a totally reliable calculation for 200 h, both in the tests

with and without vibrations; the difference between the final

stresses calculated by formula (9) for the case of rigid flanges

and those obtained by the experiment for 200 h did not excd.;ed

10-15%; moreover, calculation by the formula gave a stress value

to within the safety factor. There is basis to assume that

extrapolation to even longer time is possible. However, in thc

majority of cases it is precisely during this period that the

fir-t, unstabilived, most intense with respect to the decrease

* in stress, section is totally completed in the relaxation curve

of heac-resistant alloys. With vibrations this section is

completed even faster.

Tests on the Jndicated all9ys with vibrations were carried

out at frequencies of 310, 470, and 7'00 Hz and vibration amplitudes

b from 1 to 1.8 kgi/ 2 . The tests were done on cylindrical samples

whose working section was 100 mm long and 10 mm in diameter, both

With and without vibrations. The sample blanks were heat processed

according to the series production technique.

FTD-HT-23-0 276`1- 7

BIBLIOGRAPHY

1. ar g p M. A. Paoqey posab~ohm Co".UmIMX..O6O-

:a&U3.NMVJ5w6W2 9 MITSDJIX. KANI CCCP, 0711, IM,4 A 2.3. P 0g am 03 36 a U5s , A1 V. - u ay . r. 1Pewotopm

gA~qT NaMytt4XAX pefUOSt~ WIPFW iii 9ui 3STBUM K 0fiU.5U

3CIS.. Pona"Suwamme aueaiws 5 motuai a cuan"I. N., U.-?lAtyProust, 1963.

4. Iiio povu ix em rgc., Pos mosso a sm..

?tauoatma nmnputomfU, uomyWmb N 0=000N30 paotumUeO; oft

N 6606 oodmoots Apotteooo. 11(9.188 8 *5.Sparume Ji.Saeon it box ommuugo-

P ooodesmoom Pi5@IuM3 omm4MmIA a ;spofpo'itW monSS

a yaaoau ONOPAws*. b oG.: Topsonpeqowmb velurumaos x mm-%*OTPIMUU MOMONT011, 80g.5. Knes, Nih~yxema syia", 19M.

5. C a saitaoaa H. A. Aarnume sapoflp0o fa'tefzb208 N 00SY" uos'uf u =mT*abaq OPOqaoi M. , "VInaooTpomie',

A Y ?A UNitNNBD. n-, A Y x z0 B. K.9 0ea6 0 0 . 9. MWoaAMUM16~ 111OIY'(@0YI cuseaa 2H4M~ ape oausti.oda.: Topmonyomamotsm qumsTPJ x itooaWTUpffmo SImesMH3.

I:..fuem, "Haymoma zJyuuiV' 1987.

Received

29 April 1971

FTL)-HT-23-027 6 -738