Cold extruded rods : residual stresses and mechanical properties [PDF]

interface could significantly affect the state of residual stress in the extruded rods. It has also been indicated that

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Loughborough University Institutional Repository

Cold extruded rods : residual stresses and mechanical properties This item was submitted to Loughborough University's Institutional Repository by the/an author.

Additional Information:



A Doctoral Thesis.

Submitted in partial fulfillment of the requirements

for the award of Doctor of Philosophy of Loughborough University.

Meta

10 or drawn materials expressed .

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Fig. 3.4.3

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Lead mOlimum shear stress / yield strength

The "ulidity III thf! IUnximum-tihcnr Illw (ur lhe rdief of the rc::tidual

~II t~dl:l.

*

see Reference [101]

Fig. 3.4.4 .

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air (fRACTIONS Of allJJ TEST STRESSES

_ Fig. 3.4.5

Change in size of residual stresses in the surface layers of rolled samples depending on the working conditions of the test.

Number of cycles in testing - 2,000,000 except in specified cases,

--- -_. -

..

_---------

CHAPTER

4

Detennination of Residual Stresses

92 4.1

INTRODUCTION

After Heyn' s [lJ pioneering work in 1912, on the importance and measurement of Residual Stresses, a number of methods have been proposed by various researchers for determination of these stresses. The basic princip.le under-lying most of these meth?ds is the same; that residual stresses are the result of mismatch of different regions of a body.

Due to this mismatch, they are under elastic

strain and when a stressed portion of the body is removed, the remaining portion undergoes partial stress relaxation resulting in change in dimensions.

From this change of dimensions or strain the /

stresses existing in the removed portion can be calculated from elastic theory formulae. 'All mechanical methods of residual stress detennination are based on this principle.

X-ray diffraction

technique, however, is based on the measurement of the change of interatomic distance of surface lattice, caused by the residual micro or macro

St

resses.

Vast literature exi sts on the various

experimental techniques on residual •stress determination and these have been reviewed by several workers, perhaps the latest being by Den ton [ll1J, in -1966.

~or

a complete determination of the magnitude and nature

of residual stresses in solid bars, Sach' s boring method gives the most dependable re'sults and, therefore, it was decided to use this method in the present investigation.) The mechanical methods of residual stress determination are not direct methods in the sense that in these methods the residual stresses in a particular region of the body are d~termined

93 from the strains which are induced in the remainder of the body by the ,removal of the former part.

A more direct approach would be

to find out the state of stress in the body just before the unloading takes place after the deformation that introduces the residual stresses, and to determine the stresses left over in the body (residual stress) as a result of the stress relaxation after the forming load is removed.

In this approach the accuracy of the ~

residual stress determination depends on the accuracy with which the stress distribution in the deformation zone of the body is arrived at.

Several methods are available for the determination of the

state of stress in the deformation zone of the body but in all these certain simplifying assumptions are made about the material and the way in which it is deformed. the

In spite of these assumptions some of

methods are claimed to give good agreement with the experimental

results.

By making use of such methods it should be poss'ihle to

determine the state of residual stress 'in a body which, although it may not be very accurate, can still reveal the nature of the stress distribution along the cross-section of the body and can provide a .'

useful check on the experimentally determined residual stresses.

94 4.2

SACH'S BORING METHOD

4.2.1

GENERAL Bauer arid Heyn

[112J

worked out equations relating

longitudinal residual stresses with change in length of specimen. These \-Iere subsequently replaced by the more rigorous equations due to Mesnager

[2J

and, then, later simplified by Sachs

[3J.

The general technique of boring out a cylinder or tube in stages and measuring the resulting longitudinal and circumferential

strains at the outer surface caused by the release of residual stress is no~v knov..T!1 as "Sachs boring method".

The following assumption's arc implicit Ln this method:

1.

The metal is effectively isotropic and has a constant value of Young's modulus and Poisson's ratio.

2.

The residual stresses are distributed with rotational symmetry about the axes of the bar and the principal axes coincide \"ith the axial, radial and circumferential directions.

3.

After the boring operation, the tube' left is circular in section and inner and outer \o1al1 surfaces are concentric.

4 •. The spedmen is sufficiently long to prevent lateral bending.

The stress equations derived by Sachs are:

D, . ~

=

" E , [( Fa - F ) df, _ ,~ dP

./

95

at

a

where,

r

~

E' [(Fa - F)

de dF

Fa + F 2F

eJ

-- E' [Fa 2F- F eJ E

(4.2.2)

(4.2.3)

, v being the Poisson's ratio and E Young's

E'

~

Fa

~

1f

R2, R being the external radius of cylinder

F

~

1f

r2, r being the current radius of cylinder

A

~

1 - v2

modulus.

and

A + vG A and

e

0

~

e+

.vi' ,

being the longitudinal and circumferential

strains

aR-' at & a r are longitudinal, tangential and radial stresses respectively.

A derivation of these equations is given in Appendix 11.

4.2.2 1.

LIHITATIONS OF THIS l1ETHOD It is limited to cylindrical parts in which stresses vary in one cartesian direction (radial) and are constant in the other two (longitudinal and circumferential).

2.

In order to obtain the value of stresses from the above equations, it is necessary to plot A and

0

as functions of F.

Between the final cut in boring, and the outside diameter, there are no experimental points on such curves and surfac.e stresses

must be obtained by extrapolation.

This introduces large errors

in some cases, particularly where the difference in Fa aTid F is

large.

This can be quite significant with surface hardened specimens

where it is not easy to machine the hardened layer.

Many attempts

have been made in the past to overcome this difficulty. Hardy

[113[

Barker and

suggest that Sachs equations can be re,Jritten thus:

o~

°t

d dF [(Fa - F)

;

E'

;

E' d 2 dr

~a

:

F

~

(4.2.4)

0J

(/•. 2.5)

the expression for radial stress remains unchanged. Fa - F

The values of the functions (Fa - F)A and

I;)

r

are

zero at both inner and outer surfaces, so that extrapolation is to zero instead of an Unkn01

639

pi'!AO

63, 200'

GO iO 2Qn1 '", =N.' ('0 173 tC4~E,,1

1.(IS?FC.F.Q.o.OR.!~PF~.EQ.1iGO

4'

.1~r.ASES

READ C1,1noo, rEAD (1, '2> K

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FOR~'A'j'(!?) ~EAD(1,16)D~

16

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22

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27 I='.'!

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IF (ISW3) '6~,'6~,'67 165 IF (NQRO-LAST) 17',167,'7' ;67 TF(I~n.eQ.~,nR.I~0.e0.6.0R.140.E~.Q)GO TO ?99 W~ITE(2",OO)

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299

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169

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~TLI1~r,(I\=~2.552'EU6q«F-X(I».OynX-S')

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651

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110 TO 9901> 56

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TO 9998

STTAN(I)=-32.552'Ev6.«X(I)~X(N».OYDX+(X(I)+X(N».S'1(Z.O.X(I») ~TRAD(I)=-32.552'EU6.(X(I)-X(N».S1/(2.0*X(I» IF(I,~E.')GO TO 99'18 STTAN~=12.55?'E06·tX(I)·X(~»·S"(2.0·X(I»)

9991'.

STRH~=O. 0 S3=Y(t>-~1 WRITE(2,1040)X(I),Y(I),S1,S3.~TLONG(I).STTAN(I),STPAD(I)

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403

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11

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r.O TO ... , FORM., (:'1,,,3) ~ORMAT(I"!.12.11.2F4.0,1') FnRMAT(1~.13.~X,E'b.'2) FOR~AT(4~ ND.lnX11HcnEFFICIENT//) FnRMAT('nXl~y8~'HVbX5~OCALC7X5HEQROR6X6HSTLONG6X5HSTTAN7X5HSTRAO)

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A4(1l=0:OOO 1-\4(1).0.000 ~o

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3(;,

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~TTANG(I+')=STTAM(l) ~'rRADrCl .. 1)=RTPA~(1)

:;;0'

CONT I ~,'UF GO TO 99Q~

603

WIDTH(7)c(X(~)-.POUO')/(K-')

w

=

---a

('·V'~· ...

STLON(1)nSTLANG(1) )lIojI:W=O,O 00 304 J,,2,K XNE 11=)lN FIJ+!J I nT H C'1l

CALL INTRPL(KA,S'LANG,N1,XNEW,YN~W' SiLC1NCJ)"YNEP 304

r.O~T1':U~

AQ F A( 71

"li TS!!

( ~ , S T LUN( 1 , , WI "T k ( 7) )

STRESS=AnFA(7)/(F-~(N»

STRe~S I.J~

67,

Lr.M"A=32,5S~'E06.ALEMr.A

I TE (2, fii'1)

~ORMRT('~YII' ~RIT~(2,~72)~TRESS,STRES~

672

LEMOA

FORMATCF?O,4, HlnTH(8)=(RS(N)-,OUUOO')ICK~1) 5'RON(I)=sTRAOG(~)

~N~W=O;O

no

305

Jh2,K

X~~W",~F~+WIBTH(R)

~OS

CALL lNTPPL(~)A,STRADG,N1,XNFW,YNEW) C;rR(1"1 (J 1) =YN~~I Cf)NT1Nl)F r.c4.RS(~).RS'NI~ST~ON(K)/(Da·DB·4*PS(N)·RSCN» I) I)

61) ~

I" 1 , tl

~rAN(I)=C*('~(DBaD~/(nS(').D5(1»» ~u~

~~AD(')~r.('~cnB.O~/(OS(l)*Ds(r)I»

.J 1 6H1

=,

'F(STLANn(J11:~E,STLON(K»GO

J1=Jl .. ,

no

TO 6H1

T(1 fi82

b 1)2

r.•) 641

=

1 1,N

~TI.ANG(J'-'+I)=STLUN~(N+'-I)-STRFSS ~TT~NO(JI-'+I)=STTAN(N+I-I)-STAN(~+I-I) STQ~~r.(JI-'+I)=STRAD(N.'·I)-SRAD(N+'-I}

XAIJ1.'+II=XIN+'.11 DSAIJ'-'+l)=n~(N.'·I) .'A(.I'·'+')=~S(~.'·J)

641

A4(J'.,.,,=A4(N+I-I) R4(J'.'+!)=B4(N+,.I) lA n= J I + N ~TLA~G(Mn)=STLnNF-~TQ~SS ~TTANG(Mn)=STT~~~-~.C ~T~Anr,(M~l=S~~Anc

)(~(l.1b)=F

r>SA('ln)=n~ P~.~ (1~[) =~R/2.

n

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STRA1~'X"HLONG

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STRESS/6.5H(DS~)6X5H(RSA)5X4~(XA

2)6X8H~EA'ING.3XbHR~ADINGS3X9H(REVISED)2X9H(REVISED)'X'OHRAD

3'

ST~ESS

1'10 .S2S J =1, '~n WQTTFI2,~?~) J,D~AtJ),RSA(J),XA(J).A4(J),B4(J),STLANG(J),STTANG(J)

, , S T R1\ 0 G ( J 1 3~6

3i

~

FOR.~AT(I'.OP~F'O.6'~F".7.3GI2.4'

r. 0 NT I fl UE

~IQITF(2,331l

351

FORMAT('~XII)

l1=Mn/2 ~lDTH(')c(MAtL')·.UOOO')/«~1)

341

1.IRITEC2,~411 XACL11,WIDTII(1) F0RM~TC2r,O.AI STLOi,(1I"STL~NG(11 )cN~W=O.1)

r,O

61l~

Jc2,K

XNEW=XNP~.WI~TH('1

rALL

INTRPL(~A,STLANG,MD,XNEW,VNPWI

5TLON(J)"v~Ei·' ob~

CONTlNUF.

="

~ RE A( , ) TS8 , I( • S T LUN( 1 ) , 1:11 0 TH( 1 ) WIOT~(2)~(XA(~DI-XA(LI»/(K-I)

)

L=2*K-1 XNHI=XA(Lll

01) 306

J~I(+1.L

X~EW=X~eu.wlnTH(?) CALL INTRDL(~A,STLANG,MO,XNEW,VNFW)

3\1~

STLn~ rJ laVNEIJ r.O"JTINUF.

AREA(~)=UTS8(~,STLUN(K),WIDTH(2)1

UIDTH(3lc(RSA(L1)·,on001)/(K·1) WRITF.(2,34?)pS~(L11,WIDTH(3) 3~?

~ORMAT(2r.10.A) RTTON(1)c~TT~NG(')

xNE.,=O :()

no 31, Ja2,1( XNEW=KNEu.WlnTH(~l

311

CALL INTcPL(RSA.~TTANG,Mn,XNeW,V~Ew) r.TTON(J) cYNcll CONT I NUF. AREA(3)=IJTS8(~,STTUN('),WIDTH(3»

WIDTHr4'a(RSA(MDI-RSA(L1»/CK-1) ~~E'.oI=RS~ r Ll ' no 313 J=K+1.L ~NEW=XNFW.WI~THC')

31'1

73~

rALL INTROL(pSA,~TTANG,Mn,XNEW,YNEW) CONTINUF. 'qTON (J) aVNft' .~ REA ( t.) =IJ T~ 8 CK, S TT UNC() , l·) I DTH( 4 I ) WRIH(?,734) ~ORflATI'Y3HNr.3X~HSTLONG1jX5~STTAN/6X12HINTERPOLATED5X12HINTERPOLA

1 iF D)

no 317 Jc1,L WRITE(2,~2H'J,STLON(J),STTON(J)

3lR 327

CONTINUE

352

'J~ITEC?,332) FORMATC1~XII)

FORMATC't.~12.4,~K.G12.4)

WRITE(2.329) 3~9

. ARE_(1).AREA(21.AREA(~).AREA(4)

FORMATI,~x,OPF12.4,3XOPF12~,,3x,npF'~.4,3x,OpF12.4) ~O 351 le1,Mf') STLANGIIl=68Q44E-Of*STLANGCI) ATTANnll)c68 0 44E-Of·STTANGCI)

~TRAnG(I)c68Q44E-Of*STRAOr,(I)

RSACI)=2l.4*PSA(I) DSA(I)=7~.4*nSA(I)

3;1

YP(I)=XA(I).~5.4*t'.4

IIRITF.(?,741l 74.

FURMAT('~XII)

00 ?4~ I c1 ,M~ WR I TF ( 2 , 742) T • 0 S A( I ) , RSA ( I I , XA( I ) , S Tt ANG( I )

,

S TT ANG( I ) , S TRAD G( I )

-- -

74~ 74~

FORMAT(I~,np3~'O,3,3G12,4)

CONT'tJUE XMAX=UT~?(~D.R~~(')

Xr·lIN=O,O YMAX=1I50*?S4/200 VMIN=.'3~n·2~4/?on ~ALL lITP'AIXrlIN,XMAX,YMIN,VMAX,XAXIS,VAXIS,X4TITLE,1,V4TITLE,2)

rALL CU L CALL CALL CALL 9903 9995 9"'94

UTP~R(R,~,STLANG,MD,O)

11 TP t. A(

X" IN, XHA X, YMIN, VMA X, XAX'S, YAXIS. )( 2 TIT LE, , , Y2 TIT LE, 2 )

lIT~I·RCR~A,STTANr"MD.O) UTp&~CXMIN,XMAX,VMI~,VMAX,XAXIS,VA)(IS,)(3TITLE,',Y3TITLE.2)

UTP~R(~SA,STP.AOG,MD.O)

'F«140.~A).nE,C) ~ONTlNUE

~O

TO Q994

r..oiLL UTPCL ~TOP

END ~ UR Q!) UTI " nIM~N~!O,'

F i "IT q PI. ( K , V • N , )( NF W, Vt~ HI)

XC1nO),Y'100)

D0777Jc',r~

GV TO 778 (X"Fi.l. CT, Y. (J» ~O TO 777 TFCJ.FO,1,GO TO 7~U 'F(XN~W,~o,X(J»

IF

VN~lf=V(J-1)+IKN~W-K(J-'»*CY(J)-Y(J-'»)/(X(J)-X(J-')'

TO 7/1v>;E'I=yCJ) ~(l TO 711' YNEW=Y(J'.XNFW/XCJ) r,,) TO 7i11 r.UNT I'WE

r,()

77i>. 7~n

777

,8'

R.E.ulil. ...

6..-1>

t=,,..,,.s.,.,

----------~-

313 PROGRAM 3

I~AS"FR

RES I [lUAL 11 HII' N S I ON X T , TL ~ (1 ) • X1 T I TL E (1 ) , Y 5 T I Tl E ( 3 ) , Y 6 TI TL E ( 3 ) , Y 7 T I TL E ( 3 ) !) 111 ENS I OIJ R R ( 40) • F ( 40) , TT R Z ( 40) , TT RR ( 40) • TT R T H ( 1.0) , SUM ( 40) , RES Z ( 40

" ) , RE ~ R (40) • ~ F S T Il ( 4 0) , V 111 AX (3) , V 1tH N ( 3) , X B (40) , VB (40) , I MA X C4 0) Illr~ENSloN Xr,RAF(40) .ZSUll(40) .THSlJH(40) - and (} are the longitudinal and circumferential strains, and e=y"-+(}. The residual stresses found by equations (2) have to be corrected for the effect of producing the internal bore. Eighth-degree polynomials were fitted to A=A(F) and @=@(F),and the residual stress patterns were produced by the computer in the form of curves of 01, 00' and Or as functions of r. A blank test carried out on the annealed specimen gave residual stresses that were zero to within

±30 MN/m'. The derivation of the residual stresses from the experimental data identically ensures the fulfilment of the various equilibrium conditions, for example, the condition that there should be no net longitudinal force transmitted across any section perpendicular to the rod axis:

t) r'+d, (~-m) r+mdl

.......... (4)

respectively: that is, for each exit boundary CQD, the corresponding entry boundary is determined by the parameter m. The deformation boundaries CQD and APBcorrespond, in three dimensions, to surfaces on which the velocity of a particle changes discontinuously. In practice such discontinuities cannot occur, but a more or less smooth transition may be realized by the superposition of a large number (in practice, 50 is adequate 9,11) of basic flow patterns. In order to derive the stress and strain distribution associated with any given flow pattern, the flowfunction method was used. Since the flow is steady-state and axisymmetric, the metal may be imagined to flow

r

A

(a)

'F

j olotdF=O

f\

Checks were made that the equilibrium conditions were satisfied, but these do not, unfortunately, provide any confirmation of the validity of the original data. In the figures showing longitudinal stresses, these have been plotted against radial position rather than against For r2, and the total area under the curves is not, therefore, zero. More complete details, and a derivation of equations (2), which have been quoted incorrectly in a number of publications, have been given elsewhere.1 6

I

\\ \

I

'.

\ \ \

I I

I I

!

1 . 1 1

i

\. "

I

Reference (b)

16.

and G. F. MODLEN: Preprint of 4th International Cold Forging Meeting, 231; 1970, Dusseldorf, Verein Deutsche Ingenieure. P. S. MIDHA

Metals Technology

April1976

8 a basic flow pattern; b range of boundary positions taken in superimposing basic flow patternsll

Midha and Mod/en

Residual stresses in cold·extruded rods

500r-------------------------,

500r-------------------------,

.. b'y..'

250

250

.€

,-250

::;:

Vl

~

tii

-750 ~OOO7L

1

/!

\\

i//

i. 1/1/

11'

V)

a

\.

'>-f-.-.-.-~- ---~ ,. ,I: .... ............. ~ '-:'-,"-" . ,,-~.

J

~

z-250

./

\.

!./

Z

E

d

~

O~-f--~,~~----------~~~~~

N N

205

i·-· I

a

".

ill -500 -750

________________________

axis

radial position

~

-'OOOL-________~--------------~ axis

surfac~

a experimental residual stress; b residual stress calculated from optimum friction less upper bound (seo Table 2); e residual stress calculated from velocity field displaced by friction (see Table 2); d residual stress calculated from velocity field displaced in direction opposite to friction: d,=

0'302. d e c O'604, m=2'256

6 Longitudinal stresses: 4:1 extrusion ratio, 120 e included angle: horizontal axis=radial position from centre to surface

consequently the magnitude of the longitudinal residual stresses, were found to depend on surface finish in the following way: Length of slit from leading end of extrudate, mm 34-92 Thickness of saw, mm 0'30 Surface finish of die, /-tm (centre-line average) 0·2 0·64 1·55 4 Approximate coefficient of friction (ring test lO ) 0·024 0'028 0·035 0'055 Opening of slit, mm 1·141·291'351·37 On this basis, it is therefore considered possible that modification to the pattern of metal flow in extrusion will give rise to corresponding changes in the pattern of residual stresses and that one cause of such modification may be the existence of friction at the die surface. It is suggested that the estimation of residual stresses by examination of experimentally determined flow functions is worthy of further study. The possibility also arises of determining residual stresses theoretically or semi.empirically if data relating to friction conditions at the metal/die interface are available.

Conclusions J. The longitudinal residual stresses in cold·extruded mild steel rods are similar to those found in hydrostatically extruded rod and in drawn bar, namely, compressive on the axis with a maximum tensile value near the surface. As in drawn bar, the residual stresses can be modified by a small reduction of approximately 2% immediately following the main die. This causes the surface longitudinal residual stresses to become compressive.

radial position

surfac~

a experimental residual stress; b residual stress calculated from optimum frictionless upper bound (see Table 2); e residual stress calculated from velocity field displaced by friction (see Table 2); d residual stress calculated from velocity field displaced in direction opposite to friction: d, =

0'302,

d~"'0·604,

m=2'256

7 Circumferential stresses: 4:1 extrusion ratio. 120· included angle: horizontal axis=radial position from centre to surface

2. An attempt to correlate the observed residual stresses with those predicted by the use of various velocity fields to describe the metal flow indicates that the residual stresses depend upon the details of the velocity field selected and that friction at the die surface, as one of the factors affect~ ing the velocity field, may consequently also affect the pattern of residual stresses.

Acknowledgment

The authors acknowledge with thanks the receipt of a Science Research Council Grant that enabled this work to be carried out.

References I. J. MCKENZIE: Sheet Metallnd., 1964,41,379. 2. S. MIURA et al.: Metals and Materials, 1973, 7, 441. 3. S. MIURA etal.: ibid., 547. 4. K. OSAKADA et al.: J. Inst. Metals, 1971.99,341. 5. A. A. DEl'ITON: Metallurgical Rev., 1966, 11, (101), I. 6. J. FRISCH and E. G. THOMSEN: Trans. ASME, 1957,79,155. 7. R. J. FIORENTINO et al.: M('tai Forming, 1969,36,243. 8. E. BUHLER and E. H. SCHULTZ: Slah! u. Eisen, 1950,70, 1147. 9. E. R. LAMBERT and s. KOBAYASHI: 'Advances in machine tool design and research', 253; 1969, Oxford, Pergamon. 10. s. SOHRABPOUR et al.: TraIlS. ASME, Ser. B, J. Eng. Ind., 1970,

92,461. 11. E. R. LAMBERT

and s.

KOBAVASHI:

J. Mech. Eng. Sei., 1968.

10,

367. 12. c. H. LEEetal.: Trans. ASME. Ser. B,J. Eng. Ind., 1973,95,283. 13. c. DONALDSON: Final year project report, Department of Engineering Production, Loughborough University of Tech· nology, 1974. 14. D. HART and o. F. MODLEN: Prod. Engineer, 1974, 53, 153. 15. A. T. MALE and M. o. COCKCROFT; J. Inst. Metals, 1964-5, 93, 38,

Metals Technology

April1976

Midha and Mod/en

Residual stresses in cold-extruded rods

207

bound for frictionless conditions is given by the P corres4 ponding to the lowest extrusion pressure. For each lp, therefore, the radial, axial, and circumferen· tial stresses are calculated on each of the mesh points.

RESIDUAL STRESS CALCULATION radial flow

parallel! flow 9 Alternative velocity fields for extrusion

through pipes of circular cross-section, the flowrate down any pipe being constant and equal to IjI. The intersection of a plane containing the axis of symmetry with any given pipe gives a flow line associated with a particular constant value of if. Thus each basic flow pattern corresponds to a family of flow lines, each of constant IjI. The superposition of the basic flow patterns to smooth out the velocity dis~ continuities may be performed in any way that satisfies the boundary conditions; in fact, the method selected was simply: In '1'= -2:.p, .................................. (5) n i =l where ifl represents the flow functions corresponding to the basic patterns, and P is the smoothed flow function. Radial and axial velocities are then given by 11=

I 0'1' 2"r 8Z

.................................. (6)

The normal axial, radial, and circumferential stress com~ ponents (a;,/', ar", and ao", respectively) at the exit boundary of the deformation zone are calculated by interpolation from known stresses at the mesh points on either side of the exit boundary. These then constitute the state of stress at the instant when the loading is interrupted, that is, when the material is about to leave the deformation zone and be~ come the extruded rod. On emerging from the deformation zone the material undergoes elastic stress relaxation. Be~ cause of the non~uniform distribution of stress, the material remains residually stressed after the elastic stress relaxation has taken place. Let al:, ao, and ar be the residual longitudinal, circum~ ferential, and radial stresses in the extruded bar. Then static equilibrium requires that

f: J:

217

I

0'1'

a; ................................ (7)

respectively. The circumferential velocity is, of course, zero. For each extrusion condition (die angle and extrusion ratio), 25 smoothed flow functions, P, were generated by taking 5 values of dl in equal steps from dlmln.= 1·05 b cota to dlma:ot.=1·5 b cota, each with 5 values of rn, again in equal steps, from mmln.= VTfb-0'2 to mma:ot.= ,/l/b+0·2. The 50 basic flow patterns making up each P had entry boundaries equally spaced between dl (giving IjIt) and dn= md, (giving .pn, where n=50) (Fig.8b). The values of .p, were calculated on a mesh of points, the mesh size being the minimum possible within the limits set by the com~ puter's capacity, and the if! combined, according to equation (5), to give P. Velocities, strain rates, axial, radial, and circumferential stresses and extrusion pressure may then be calculated for each lp, a mean yield streSS being taken for each extrusion ratio.· The optimum upper -The mean yield stress values for the calculated curves in Figs.4-7 were taken from McKenzie. 1

aodr=O

ao=a,+r

da,

dr ................................ (8)

Assuming elastic stress relaxation to be uniform and denoting the changes in stress caused by elastic relaxation by a/, an', and ar', the residual stress components are given by al:=az " -Ul: , where

al:'=~

I:

ul:"rdr . ............................... (9)

ao"=uo-a,/ where

ao'=~I>odr ................................ (10)

and

v= - z"r

al:rdr=O

and ar is calculated as follows. Solving the last equation of (8) for ar we have

d d;(ru)=uo or

1ra," I:

=

where R is any radius at which Then

a,= ~

Ur

is to be determined.

J: aodr ................................

(11)

because (ar)r_b=O In general, residual stresses calculated from the optimum upper bound for friction less extrusion did not give good agreement with those found experimentally, and flow patterns with exit and 'entry boundaries on either side of the optimum upper~bound pattern were then examined, and the corresponding residual stresses were determined.

Metals Technology

April1976

Technical note W. G. Ferguson N. E. Clark B. R. Watson

Effect of austenitizing temperature On toughness of martensitic steels ©1976 The A1etals Society. Manuscript received 29 April 1975. The authors are in the Department a/Chemical and Materials Engineering, University of Auckland, New Zealand.

Recent studies l _.5 have shown that the fracture toughness of martensitic steels can be improved by austenitizing at higher temperatures than are conventionally used in the heat treatment of such steels. Austenitizing AISI 4340 at 1200 ClC instead of the usual temperature of 870°C. increased the plane-strain fracture toughness for the asquenched state by about 100%. Conventional heat-treatment practice is to heat into the lower austenite range to keep the grain size small and the 'toughness', as measured with a Charpy-type test, high. Dulieu 6 has reported a rise in plane-strain fracture toughness with increasing austenitizing temperature without an increase in the Charpy impact absorbed energy. In the present investigation the 'toughness' of a tempered martensitic steel austenitized at 850° and 1200°C is determined using Charpy V-notched specimens and Charpy fatiguecracked specimens and compared with plane-strain fracture-toughness data obtained previously by Clark and Ferguson. 7 The energy measured in a Charpy V-notch impact test . arises from three main sources: (a) energy for crack initiation, (b) energy for crack propagation, and (c) losses. Under the heading of 'losses' are included mechanical losses in the test machine (vibrational and frictional losses) and the kinetic energy of the broken test pieces. Chipperfield 8 has found that the crack opening displacement for crack initiation SI in mild steel is a linear function of the notch root radius down to a radius approximately equal to the inclusion spacing, below which it remains constant. The value of Si for fatigue-cracked specimens was determined by this constant value. Hence SI for Charpy V-notched specimens, which contain relatively blunt notches, will be much greater than that for Charpy fatigue-cracked specimens and consequently the energy absorbed will be very much greater in initiating a crack in the former type of specimen than in the latter type. Hence Charpy fatigue-cracked specimens will basically give the energy for propagation and in this respect the results from this type of specimen should, apart from strain-rate effects, approximate to the behaviour found using standard fracture-toughness specimens.

Experimental procedure The specimen material was Consteel En25, supplied in the form of centreless-ground bars, 25 mm dia., of the following composition (wt-%): 0·27C-O·30Si-O·63Mn-2·63NiO' 70Cr-0. 55Mo-O'021 S-O ·023 P. The Charpy V-notched specimens were standard but the fatigue-cracked specimens which had the same dimensions had, instead ofa V-notch, a slot 0·25mm wide and 1·67 mm deep from which a fatigue crack was grown after heat treatment. Samples of both types of specimen were austenitized at 208

Metals Technology April1976

either 850° or 1200°C. Austenitizing at 850°C was carried out in a salt bath for 1 h before oil quenching, whereas at 1200°C austenitizing was carried out in an inert atmosphere furnace for 1 h before oil quenching. For the latter heat treatment the quench was interrupted at 850°C for 1 min to reduce quenching stresses. Two samples of each spedmen type were tempered at the following temperatures (with subsequent oil quenching): 2000, 300°, 400°, and 600°C. The fatigue-cracked specimens were fatigued in threepoint bending until the crack was 3·33 mm long, the final stages of crack growth being carried out in accordance with ASTM E 399-72. All impact testing was done at room temperature in a standard Charpy impact tester, and the fractured area of the fatigue-cracked specimens was measured. The hardness of each specimen was measured and a selection of heattreated specimens etched in a 3% Nital solution in order to determine the prior austenite grain size.

Results and discussion The average grain size for specimens austenitized at 850°C was 17 ,urn, and for those austenitized at 1200°C was 184,um. With the etch used it was relatively easy to detect the prior austenite grain boundaries for the 850°C heat treatment, but very difficult for the 1 200°C heat treatment. Clark et al. 9 attributed this effect to grain-boundary segregation for they found that grain boundaries readily grooved when segregated and that the degree of segregation decreased as the austenitizing temperature increased. provided that the specimens were quenched from the austenitizing temperature. The hardness (HRC) as a function of tempering temperature is shown in Fig.la: The hardness data indicate that the two austenitizing heat treatments give approximately the same tensile strength. Lai et al. 4 reported a similar result for as-quenched 4340 steel. The Charpy V-notched impact energy and the Charpy fatigue-cracked impact energy for the 850° and 1 200°C heat treatments are given in Fig.l b. Each point represents the mean of two tests. From now on the Charpy V-notched. impact energy will be referred to as C\· and the fatiguecracked impact energy as Cr. For purposes of comparison, the fatigue-cracked data have been corrected by multiplying the measured values by: fracture area for Cv fracture area for Cr This allows comparison on the basis of the Charpy Vnotch test and was done because the two areas are different, being 0·8 cm 2 for the V-notched specimens and about 0·68 crn 2 for the fatigue-cracked specimens. The results show that for both heat treatments Cv is greater than Cr for all tempers. For the 850°C heat treatment the minimum

Made and printed in Great Britain by Lund Humphries London and Bradford

Rr..:JIDUAL S'IRFSS RELIEF IN COLD-EX'ffiUDED ROD

§y'!!0psis. The residual stresses in cold-extruded mild steel rods have. been estimated by the longitudinal slitting method; and the effect of lOH-tmeperatur'e annealing on the residual stress level has been investigated.

For the extrusion ratios used (2.78:1 and 4:1), .

0

residual stress relief appears first at about 250 C, and is .. substantially complete by approximately 500 0 c, the tensile strength havir~

decreased over this temperature range by less than 10 percent.

A correction factor is proposed that allows the determination of resj.dual stresses by the longitudinal slitting method to become

independe~t

of

slit length. Introduction. Although there is considerable eVidence(l) that residual stresses introduced by cold work may be substantially reduced in certain cases by heat-treatment at temperatures that do not cause extensive loss of the increase in strength imparted by the cold work, there appears to be little information regardip..g the·temperatures required for the relief of residual stresses in mild steel . subjected to large strains, or regarding the resultant mechanical·properties. The present work was therefore undertaken to investigate residual-stress relief in heavily cold-worked (extruded) mild steel, and also to investigate whether it \'/ould be feasible to aim for a more-or-less complete removal of residual stresses

\~ithout

incurring a drastic loss in strength.

Experimental.

The material used was a mild steel to British Standard En 2E (0.09C, 0.39Mn, O.25Si, 0.o45S and 0.025 percent P).

1.5 inch (38

as follm'lS:

The steel, in the form of nominally

mm) diameter black bar, slightly oversize, was heat-treated o . 940 C, 1/2 h, furnace cool. Billets, 2 inches long x 1.5 inches

dia'1leter (51 x 38.1 mm) were machined from the black bar, shot-blasted and subjected to a proprietary phosphate + soap lubrication treatment. Extrusion was through conical dies having included angles of 60 0 . The billets v/ere extruded straieht through following durrmy billet.

~Ii thout

ejection by use of a

- 2 -

The specimens for'residual stress determination and tensile ,testing, were heat-treated together, (apart from those heat-treated at 500

0

e

and above) with the thermocouple in the centre of the bundle of pods. When the required temperature had been reached, the specimens were held for 45 minutes at temperature and then cooled in air. The level of residual stress in the extruded rods was determined by (!l.)2i,'t)

longitudinal slitting into two semicircular sections from the leading end of the extrusion, the slit width being 1/32 inch (rJo.8 mm) and theJength approximately 2.875 inches (-73 mm) or 3.875 inches (~98 mm) for the 2.78:1 and the 4:1 extrusion respectively. ' Some aspects of the method are discussed in the Appendix, and a method,of correction to make the residual stress determination independent of slit 'length is proposed. Tensile specimens were 0.564 inches (14.45 mm) in diameter, with a gauge length of 2 inches (50.80 mm). Results and Discussion. Table I gives the slit openings, f, found for the as-extruded and for the hear.-treated rods; Fig. I shows the same results plotted against heat-treat~er:t te~perature,

but as a percentage of the slit opening for

the as-extruded rods.

It can be seen that the residual stresses first o begin to relax at about 250 e, and that any given percentage relaxation occurs at a lower temperature for the 2.78:1 extrusion than fol:'. the 4:1 extrusion.

This result may appear anomalous, in that relaxation processes,

like recrysta1lization processes, might be expected to occur more readily in the more hig.l:!ly

~lOrked

material.

However, the peak residual stresses

are higher in the case of the 2.78:1 extrusion (see Table 2), and it is ·this factor that is here determining the relative positions'of the two curves. Fig. 2 shows that there is comparatively little change in tensile strength or 0.1% proof stress up to a heat-treatment temperature of ,

0

approximately 450- 500 C. extruded rods,

ap~

The tensile specimens were machined from the

hence the residual longitudinal stresses in them were

displaced from the vaH:es in the initial bar by some cor:stant stress ) •

J"

• F:.

)

I

to maintain the condition of zero net axial fo,rce ( ~f d...f =0 . Denoting the diameter of the test-piece by 2.R: ,and the diameter of the ini tial bar by 2. R..,i t may readily be shOlm that

cT~ (~R~) 1R:':_ ~ O);Af - (;

. . ~j

l '

(J

In this way, by making use of the residuo.l stress patterns previously determined (5) (Fig. 8), the peak tensile

longitudi~al residual stresses

in the 2.78:1 and 4:1 tes"C-pie.ce.!. were found to be approximately 140 and 150 MN/m~ respectively,

the ~ocation' of these peak stresses being

at the specimen surface. When a tensile stress is applied to a specimen containing residual stress, yielding will first occur where the effect of the applied stress plus that of the internal stress is such that the yield

~~A- ~$

fulfilled: in the present case, since-the peak residual stress occurs at the specimen sur'face, this merely reduces to the requirement that sum of the residual and applied stresses should exceed some critical value.

The initial deviation from linearity on the stress strain curve

is thus affected by the presence of residual stresses,', but as furthe'r plastic flow relieves the residual stresses, the higher proof stresses are little affected.

The form of the curves in Fig. 2 thus show little

change in 0.1% proof stress and UTS over a range of heat-treatment temperature that causes a marked increase in the 0.01% proof stress and o a marked decrease in the residual stress level ( 200,- 400 C). It should be noted that there was little evidence of any strain ageing effects, thy steel having been aluminium - killed.

In addition, it may

be seen that a combination of time and temperature

(45 mins at 2OOoC)

that would be expected to cause appreciable strain - ageing (if such effects

~lere

relevant), in fact does not cause any appreci'}ble change in

the O.Ol%·proof'stress.

It therefore appears reasonable to aseriJ5e the

increase in the 0.01% proof stress to the relaxation of those residual stresses which, when' the external stres's is applied, give rise to early local yielding in the tensile test.

As to ,the mechanism by which the

stress relaxation itself occurs, this must clearly involve the thermally activated_movement of dislocations, non-conservative motion possibly being assisted by the vacancies produced in the initial deformation. Metall'o.graphic exa'llination showed that the specimens heat-treated at o

600 and 615 C had undergone recrystallization, the rather high lower yield stress (380 MN/m ) corresponding to the small recrystallized grain size (apprOximately 6.5 I'JfI). 1«.rt.:1al re crystallization ~Ias observed in o

,the specimens heat-treated at SSI:) C (Fig. 3,1r) ,

wherees there ':lere

no Signs of recr~'stC)11i;c8tion in those heat-treated. at 500"'C

_'le. 3 ,3 \...

( p.

The form of "the tensile o

strength-temperature curves, in the region 500-550 C, does, however, indicate that recrystallization is more advanced in the specimens extruded' at the 4:1 ratio, in agreement world.ng.

~Iith

their greater degree of

1

-4The results of the present l'lork are compared

I~i th

existir.g data in Fig. 11

and Table 2. Some results concerning residual stresses introduced into Armco iron cylinders by quenching from 8500 C are included (1) : these are remarkable in that they

sho~1

appreciable stress relief at comparatively o

low temperature::;, for example, 150 C.

It is possible that processes

connected with diffusion of interstitial atoms are here contributing to the rapid stress relaxation.

In a rather similar situatlon, in steels

undergoing tempering, there is some evidence that residual stress relax-ation is accelerated. (7)

There-are two sets of data from previous investi-

gations of residual stress reUef in drawn bar:

whereas the results of the

present investigation and'those of Peiter's(3) appear to be mutually consistent, BUhler's(l, 6) results point to atures.

muc~ gre~ter

stress relief at low temper-

A possible reason for this discrepancy is the rather high value of

peak residual stress reported for the as-drawn bar:

600 MN/m2 for natural

strains of 0.082 and 0.085 respectively, details of die angle, etc., not being available.

If this initial value were too high, this would, of course,

cause an over-estimate of subsequent stress relief.

Peiter's (3) results

were obtained with a leaded free-cutting mild steel (Table 2) (C, .13 max;

Mn, .9 - 1.3; P, .035 - .1; S, .2 - .27; Fb, .15 - 30 %).

It may be seen

that the temperature required for a given percentage stress relief is lower for the higher initial peak residual stress, even though the higher stress was the result of a smaller initial deformation.

A comparison of the two

sets of data indicates that an increase in the initial strain over the range considered.(true strains from 0.085 to 1.386) also has the effect,of lower/

ing the temperature required for stress relief.



,

c

- 5 Conclusions. 1. In cold-extruded mild-steel rods (extrusion ratios, 2.78:1 'and 4:1, included.die angle 60°), residual stresses begin to be removed by heat-treatlhEmt at temperatures of approximately 250 - 300°C.

At

any given temperature, relief is more extensive in the 2."(8:1 extrusion, corresponding to the higher initial residual stress. 2. Heat-treatment at 500°C for 45 minutes results in rv90 percent relief of residual stresses with an approximately 10 percent fall in tensile strength. stress relief

It therefore appears feasible to obtain effective

~1i thout

appreciable loss of the strength acquired by

. cold work.

3. The UTS and 0.1 percent proof stress of the extruded material change little as a result of heat treatment at temperatures up to .

0

approximately 4co C: over the same range, the 0.01 percent proof stress rises as the residual stresses are relieved, to become approximately equal to the 0.1

pe~ccnt

proof stress.

4. Comparison with other data indicates that two factors determine the temperature required for a given percentage of stress relief. These are the initial peak residual stress and prior strain: an increase in either factor tends to reduce the temperature. required for stress relief. 5. A correction factor is proposed to make the determina-cion of./ "

residual stresses by the longitudinal slitting method independent of sli t length.

I.

- 6 APPENDIX. The longitudinal residual stresses in the (5)

previously been determi.ned

as-extl~ded

rods

p~d

by the Sachs borc-out method

(3 ;i))

and it was therefore of interest to compare the slit openings found in the present work with calculated values based on the previous )

work. 'If the width of the slit is neglected, the second moment of area of each half of semicircular cross-section about its neutral axis, I, .is given by is

M=

R4 (~ -

2J\ )

25: p2.(JJ!....rLp

,

where

the bending moment caused by s1i tting 2R = D

is the rod diameter, and

fJ

is the longtudinal residual stress at radial position slitting.

CY,l

before

Hence the neutral aXis of each half is bent into a circular -

r:1=

M

E

arc of radius ., ~ £:':r. where ~2.. ,E being Young's modulus and ~ Poisson's ra'tio (following Schepers and Peiter, (.2) the semicircular section is regarded as undergoing plane strain during bending ). In addition to the circular curvature giving rise to the opening f, there is also a region of elastic stress relief in advance of the slit, so that the slope

(~&)

-::j= 0 at

x = 0

(Fig. 5,a).

In order to evaluate

this slope, the slit \,:as clamped shut and a second slit made at. :sight angles to the original slit, but some distance back

(Fig. S, bi.

This causes a region of local stress relief, so that the portion

AB

of the rod (Fig. 5, b) undergoes a rotation equal to twice the rotation of each half section in Fig. 5, a being ignored). corrected to

,

f

~Iidth

(the

of the slit at A,

Hence the slit opening at any position I

corresponding to

~=O

at

ttx..

x

x = O.

section is deformed into a circular arc, then

J~ ~7'-1

straight line shculd be obtained by plotting

f'

6 mm,

may be If the half , and a

against

Fig. 6 shows such a diagram for the as-extruded 2.78: 1 rod. It can be seen that the initial section of the graph becomes linear as a result of the correction, indicating a r 0'

but for large

x

the values of

cor~tant I

f

radius of curvature,

are less than those given by

extrapolation of the initial linear section.

This is attributed to the

fact that the residual stresses build up from the leading end of the extrusion at B (Fig. 5,b) , so that r is greater at large

x.'

- r An equivalent increment of slit length, of r

o

b. , may be derived from the value

found from Fig. 6, such that the rotation

du.)

() =-(

lM

would "J

>(70

b. (Fig. 7) : that is, fJ=(!-!t:) -= (;Gl x. =0 I-~ ~ 0.29D. With the assumption that Ll is proportional to D, Tne But . f l r = x"- and hence f/=/ fA,:' fI(l -+ 0-53])/>

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