Transactions of the Japan Society of

Mechanical Engineers

57~ 536% A {f.,lffi

(:ijZgjz 344)=J)

f±EfIi:t)\. B *,f*JUflX~~

864

E3*jj!H~Cjti\'gifli::z~ (A m)57 § 536 -l5- (1991-4)

~"'~~-@;-~W~LD7J <D B E ]\I[ 'L: J: ~m1~mtJT$ Co -"E-<DLDm*

Simple Metbod to Analyze tbe Residual Thermal Stressof Disslmilar Material Joints and SomeApplications

Ryojl YUUKI.Jln-Quan Xu and Siegfried Schmauder

~x No. 90-0931 A

Residual stress seems to be a maln factor controlling the fracture ofdisslmllar materials such as met.al/ceramlc bonded materials. In thIs study,we develop a simple method to analyze the residual stress caused by thethermal mlsmatch of dlsslmllar materials, uslng the boundary element method.The present results present a stress slngularlty at the edge of the

Interface and therefore It can be supposed that a fracture occurs at theedge of the Interface into elther material. Thls fracture behavior isevaluated by CF em.x crlterion with the use of the obtained numericalresults on the stress distribution around the edge point and discussed Incomparison wlth the experimental results.

Key Words: Elastostatic Analysis, Residual Stress, Thermal Stress,Disslmllar Material, Interface, Boundary Element Method,Fracture, Ceramies.

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tJ' ff ll1i c tJ: iS .: c tß i± 13 ;!! ft 7., . 1J OC 7 ~ 1 5 0 (7) ij\ €;

I<:-:> \' -C iilii:L '1 './ A . B i!I {'i'ff (7) (J 9(7) 7T ~ ~ M -IITT 7., c

1Zl11 (7) d:. -j I<:tJ: "? t:. C (7)*fi !li!tJ> G A .<2,(7) :L '1 './ l;l \$

OC((.j I<:Iiiiil < -tz '7 , '1 7 7. {!!IJ" (7)liIlifj:i tJ' tt L -!>\\, tJ',

B R, {!!IJ1;1:?1 'ffJ IG 11 tJ' * iffi IC t'& tri ;!! ft, liIliW:ItJ' tt l n \'

Ce tJ'0tJ> 7.,. .: (7)tä !li!tJ, G, A ,<2,{!!I)L'fftm, B .<2.fJ!'j

L' ~ I \Ii<fJ ~ 'it Ij 7., d:. -j tJ: iJjJ If f!t i"i (7)~ €; I<:1;1:?\! i!jj ~ M

ib I~ -t iS c '!Sl!ll: fUJ J: tJ' M 1"f -c' 8 7.,.

l tJ, l, - tJi< ~ I \& f!t i"i (7)ij\ €; tJ: C L' l;l A ,<2,l;l • 1J (7)

ij\€;d:. fJ9.Jl\i'JIG;I]tJ'Iiiiil <, j$1<:'!SlOClftl'"tJ''f't"-;!!Ü

7.,. .: (7)~ €; , -t L' I<:m ~ (7) J:; 7., IZlI 3 I<:;f; -t .,t -j tJ: W

ilii lfHk tJ' ff ~ c "5 ;t G ft 7., {{ " . .: (7)~ €; (7)W i!jjJ: (7)

71 \i'J IG 11 7T 1li (7)~~ tJT f9ij~ IZlI 3 I<:;y; -t .• tJ, I<:?1 \i'JIG 11

~4.-c';f;lk •• Wilii(7)~€;ctt.l-riilii:L7'./c

h * iM I<: g \i'J lG 11 tJ' *" to ;!! ft -r \, 7., .: c tJ' 0 tJ> "'.

A

1.0

----7=0°-0- 7=15°~- 7 =3U'"

o

NORMALIZED DISTANCE ~ / L

-1.2&-1.0

1.6

- •.... 1.2~I "2"<:] ""'-'-cE 0.8'-.... ~~•...

::.. 004t:><r.lOx-'<r.l 0<r.l

~~ -004~:E -0.8

Mater_ E. v. aFracture Angle(J jLl.T

ialsGPa lO-ß;oCExper.BEMMPa°C

SF56/58,0.242, 8.8-29°,-31°-29°0-500

CaNa70,0.240, 8.6

SF56/58,0.242, 8.828°, 28°32°1.0-400

LF559, O.226,10. 3 (30°)

BK7/

81,0.208, 8.324°, 22°30°11.2-500CaNa

70, O.240, 8.6 1(25°)

SF53/

58, O.238, 9.324°, 22°33°7.6-400LF5

59 0.226,10.3 1(23°)

SF53/

58, O.238, 9.3-21°.-25°-32°-----400

SF5658, O.242, 8.8

LF5/59,0.226,10.3-17°,-17°-23°-----400

BaSF64105,O.262,8. 7

LF5/59, O.226,10. 3-30°,-31°-2800-400

BK781,0.208, 8.3

L' liIli~ l. liIli~ 1J OC1i2 3° I" E L' J:; "? to . .: (7) ~ €; (7)

1" ill'J1J !ll: 1:J:330 c tJ: fJ, 111!!Hfi !Il c -j& l tJ: \ \. l tJ,

l , .: (7)~ €; IHl- 11 f!t f,H: .,t 7., IG 11 ,Hf] ~ :>5!!!l:l -r 91

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tJ: 7.,. .: (7) • b €; b * I~ d:. fJ 1Zl1 0 I~ ;f; -t d:. -j I<: !:' - 7

tJ' '" 7 " cl • .: (7)1J oc l;l • lji *fi !Il c EI < - j& l t:.

.3(7)ti7~~Mttk~.1Joctln11f!t.~d:.7.,IG11

~ • b €; b * -r ~ iltlJl to (J 9m" C tJ: 7., 1J Ill: ~ ;f; -t.

JiU: (7)*fi !Il tl' G. tf '7 7. (7) d:. -j tJ: lIl'ilt H *'I L' ~ H W

jffi (7)fll' €; '!Sllll: tJ' \$ \ d~ €; I<:1;1:, '* .f. $ L' ~ ill'j l to liIli<$1

1Jlll:tl •• M!IlcEl<-j&-t7.,cc~.mL'8k. 1J

Ill: (7)~ ilt'jtJ' iiJ ~ c tJ: "? te tJ', '!Sllll: (7)~.!i!((.j tJ: 1W1ÜIi I<:-:>

\' -r 1;1: ;!! G I<: er i& (7) !;1; IT tJ' :12:, j1 c tJ: "'.

1Zl11 -tz'7"177./~Jiilm.f.

(7)~4 ib W iliLt (7)9j\i'J 1G11(7)7T~

-176-

869

~ fJ' g; <, I~ €1 ~ ~ g• ~ ~ -r liIIi~ ., iS c ., n I! , -t

':7 , '1 '7 A lIlrJ'" f.J 30° 15 fOJI<: liIIi~., iS c. c fJ' 'Y 't!! '" niS (2). i!! L, im 'ii; 1;19~~ i'l ~ ~ I<: liIIi~., iS ~ -r, 'C ~

±!>l~~M~~J;,?K'C~~~~~~.~~b1t~~~

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iS c. cfJ''Y,\!!'" niS.

L 2 q:.rrilJiil ~ <5 7.,t~€i

IXK ~ 14K ~., C u ~ cj:rr.' ~ c -t iS -t ':7 , '1 '7 A /

e •• €i~ •• ~~~Mfihft~~. MM~.~.2K ~ L to h ~ ~ ffl ~,to. c. c. -r 1;1cj:rr.' Ji!i~ ~ '" ~ ill'ft'" 1t -r M fi L to, cj:rr.' ~ ~ '" 0 ~ 0, 01 W ~ ±!>l€i I~ -::> ~,

-r, -t ':7 , '1 '7 A / C u W ~ :Iö J;, 1f C u / S 4 5 C W

~~~g.~~~~~~151<:~", ;!,toI3ElJ~I<:if}?

a x~~1!i~~161~~." c. n ~~fS~l;liiE*~ FE M

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~ 15 fJ' ~ -t ':7 , '1 '7 A / C u W ~ ~ '" '1 Y ~ ~ ~ ~

cj:rfJ':j!fL<, c.c.fJ'~~IiIIi~fJ''Y't!!'''niS. i!!L, 181

6~=ffi~±!>l€1cJtt2L-r, cj:rr"'Ji!il~Cu~AniSc.

cKJ;,~B.~~~~~~.~"iSC.c~~~iS. c.

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~ a .~ ~ 1!i ~ ~ '" iS c ~ 17 c tJ ~ to, C. ~ fS ~ fJ' ~ :J\!.

VI

STRAIGHT INTERFACE

CURVE INTERFACE

0.5 1. 0NOMALIZED DISTANCE S / So

w= 20 rnrn

=""'"'"

~ -0. 80==

~ 0.8"-

'Jl.: 0.4z'"

"'" --_<.:.-~ 0.0'.-------- /fNS

~"'"-0.4

S45C

E- 0.81 S45CI~S i3N4<l<oS<.-)- 0.4~c..:>

'--- 0" '"

-o"J ----11o=O.OlWW=20 mm

y

S 4 5 C

xS bN ~~r--

w~ 20 mmW

6

W

1.0o

NORMALIZED DISTANCE X/W

~ 16

~17 :J\!.~.i!IM-t':7''1'7A.~ ••

~~ C7" .~~~clilli~fIJJ3t~'Yill>J

-1.0

ue-- Ö=O.OlW

G,[C,C,TI 0.6 t r"'I

r=0.0025 W8

I

0.4 t

\ ~~

S45CS13N410.2

,.x ~ \ Vf=""~

Cu

r =0.005 We

0

30'60'90'

-0.2

w= 20 mm

- - - S 4 5 C/ C u Interface

0.6

ou:l=u:lu:l~ _ 0.2' - S i 3N 4/ C uu:lQE::'3·0.4

~ 0 0.1 0.2 0.3 0.4 0.5~ NORMALIZED DISTANCE y /W

~15 3ffi.M.*~~W~~~g.~~~~~

870

er

40'

30'

20'

(1) EIl<f1. BOUNDARY. 5 (1989), 31.

(2) Ij';j;j; li tJ> 3:g; 1IU~. 55-512, A (1989), 750.

( 3 ) ifJi ~ I;: tJ> 5 :g; • ~. 5 5 - 5 10 , A (1 98 9 ), 3 11.

(4) Dike J. J. and Johnson G.C., J. Appl. Mech ..

57 (1990), 11.

(5) Erdogan F. and Sih G. C., J. of Basic Engrg ..

85 (1963), 519.

1: ~ 0) '5 JIlI1. <f1r.~ JlliJ]j!~ 0 = o. 01 W 0) ~ €I -r- i5 <>tJi,

o~R~~mfi-r-~~~9m~~*IC~~~LC~

., ~. jjS] 18 11.<f1r.~ R!i J]j!~ ~ ,< -'7 ;I- - '7 c L -C, -tz -'7 ,

,1 A/C uWlliiliffiO)lli;i1~~ a80)J&*{i1!C{-0)!&

* C tJ. <>jlj oc e ,0) lliItf, ~ ;f,; T . .:: 0) a 8.' x ~ ~ iJ/j. c L

-C~. EIl<f1.; (12) tJij~ Ji1jL -C \, <> J: ? I~ lli; iI ~ ~ tJi!&

~cC<>~.C<f1M~J]j!~~~&T<>,::c~~m-r-1

~. ~.<f1MJlliO)~€i~~m~n<>l[l(ij!jljoc~~*c

0.2

0.0

W=29 mm

r=9.99SW

0.05jjS]1 8 <f1r.~JlliJ]j!~O)CT .maxc

I[l(ij! jlj oc I~ &,1;fT lI~!,\'!

10'

_ JL0.1 W

(6) Sih G. C., Mechanics of Fracture, Noodhoff

International Pub. Leydon, (1972).

(7) 9(111· ~Iaj, .IIN~~$I~J:<>~~~· 1 1) _

7·~jiiJI:Mfi, ->f1.J::/AU. (1985).

(8) ,all/(· Wf •• ~. 56-527, A (1990), 13.

(9) ~!i . Mll/(, ~W~$$~:)ClIL 4 (1989), 37.

(10) './li'!, 8*:JEJ1il"l'=~~~. 25 (1986).419.

( 11) 9( EIl I;: tJ> 4 :g, • j~. 5( - 5 08, A (198 8), 2128

(11) EIl<f1; ilfl!JJ. 62-1 (1990), 5-11

~M.€iMO).oc·.ij!~~~Cti~~&.~Tlli;i1

~~~M~~~AA.~~BEMmfiT<>~$~ •• L.

:JE Iii. / -tz -'7 , 'Y 1 A. €I tJ. cO) lli; iI ~ ~ 0) m fi ~ fT \'.

jJf tt -c lli; iI ~ ~ l~ J: <>• ij! '* iIJ 0) ~ i!lIJ$ c L -C a 8. ax

~ t;ji ~ •• L . .:: 0) ~ t;ji l~ J: <>• ij! jlj oc 0) ~ i!l'J~ ii\ 1J.

~. *~K-r- • .;n~~CM~~0TO)~~-r-~<>.

I ). * B E M ~HT 11.W im 1: &. cf W im liffijfr j~ 0) ~ iI ~

~ 9 m tJi AA. ~ tJ> ~ ~ fIi oc I~ *~.;n. W llii liffitJ> .; •

ij!~.~.ocwm~.AAc~~.;n<>.

2). lli;i1~~O)~~R,ctJ.<>WimliffitJ>';O).ij!jljfJt

0) ~ i!lIJ$ c L -C a 8. ax ~ j;ji I~ tl!i -j' < 1.i $ ~•• L. ti-'7A/ti-'7A.€iMO).~~J:~{-O) •• tt~ •• L

tc.

3). W im Jf~"* &. cf <f1r.~11 J]j! ~ ~ R ~ ~ ~ fi M fi filJ~

~ L-c. lli;i1~~tJi~fOT <>WimJf~,,*&.cf~.<f1r.~1i!!

J]j! ~ tJi ~ & T <> .:: c ~ •• L tc.

-178-