Residual Stresses in Thick-walled Cylinders

Wesuiting from Mechanically Induced Overstrain

Purpose of investigation is t o determine t he residual-stress d is t r ibut ion as a funct ion of magn i tude of overstrain a n d d iameter rat io, and how it af fects t he reyielding characteristics of cyl inders autofrettage by sl iding-wedged technique

T. E. Davidson, D. P. Kendall and A. N. Reiner

A H S I . K A C . I ' A~itofrettage 1s a process for Inducing elastic, response in thick-walled cylinders subjected to internal pressures w h i ~ h otheruise cause plastic strains. T o ex- tend the use of autofrettage to higher pressure applica- tions ~ n d lo ~ l ~ r n i n ~ t e many of the problems encountered in the use of the conventional process based on the use ,,f direct 1nterni:l hydrostatic pressure, a new technique has been developed ~ch lch u t ~ l i ~ e s the mechanical advantage o f a sl~clin: ~ v e d q . ~ to proclucc~ the dcs~red bore enlarqe- rnenr.

S1nc.e the ube of a sllciiny \vedze or nlanclrel ~ v i l l ~ n d u c e shefiring forces n t t h c mandrel cylinder interface, the reiultnnt revidu:~l-stress d ~ s t r ~ b u t i o n \ s i l l d~tl'er from that theoretically predicted as character~st ic of the direct hydrostatic process. I t is the purpose of this worL to determine the resicl~~al-stress distribution as a function oi' n w g n ; t ~ ~ c i e of overstrain and diameter ratio, and how i t af7'e:ts the reyielding ch:lr3cteristics of cylmders auto- frettaged by this technique.

Residual-stress distributions, determined b y the Sachs boring-out tet*hnique for diameter ratios ranging from 1.5 to 2 .3 and for severs1 different magnitudes of overstrain, are sho!:n. T h e shearing force associated with this technique induces substantial longi tud~nal residual S C I - P C - ; ~ ~ . T h e itlc~re,..;? in t l ? ~ n~:ignit~~rlcl of t h i - lonqi- t uclmnl reiidual stress with overstrain a n d t h e resultant decre3se in the tsngent id residusl stress are shown and discussed. Irydrostatic reyielding tests of autofrettaged cylinders are used to s u h t a n t i a t e the decrease of tangen- tial residual stress with increased overstrain. T h e sub- stantially lower opt i rn~tm o~ erstrnin 2s compared t o the ci~rect hydrostatic technique is shown and discussed. For opt imum overstrain, the elastic s t rength of cylinders au tofrettaged by swaging is comparable to that charac- teristic of the conventional process.

stress, psi bore ~ n d i u s outside radius radius of depth of material removal variable radlus radius of elastic plnst ic interface diamctei ratio, b a s t ra in Young's rnodulus of elastici ty Poisson's ratio E ( I - ,u')

O = e / + pt.i(,,, ,

'1 = c: + ~ € I I ( , , ~ , / = cl'oss-sectional ai'ea associated with dep th of ma-

terial removal ( rc ') f , = cross-sectional area associated with outside radius

( ~6') T = shearing stress P = pressul e, psi G , = yield stless. pi1

1. = I a d ~ n l dl1 ec.t Ion5 f = tangential d l i ~ c t ~ o n s z = longitudinal tlil~ections

R = i.esiduaI 12 = plastic zone e = elustic, zone

Autofrettage is a process for inducing elastic response in thick-waiied c y i l d e r s subjected to internal pres- sures whic.11 would otherwise cause plastic. s t ra i~ls . The proc?ss cgnsists of plastically enlarging the bore a predetermined amount by neans of internal hy- draulic or mechanical pressure. As this internal pressure is rtileased, the outer pzrtion of the tube attempts to resume its original size. T h e material near the bore, u.hic11 has been ctzformed a greater amount, resists this action, thus przducing a tan- gential residual stress that is compressive near the bcre and changes tr, tensile near the outer surface. This r~su l t ing strzss distributiqn is such t h a t i t o p p x e s the stresses prxluced by additio~lal applica- tions of internal pressure, thus increasing the pres- sure tha t the cylinder can withstand without further permanent expansion.

T h e conventiorlal autdre t tage process invalves w e of internal hydrostatic pressure of sufEcient magnitude to obtain the desired overstrain. This type of process has been used fcr several years in gun tube arid pressure-ve~sei construction. Cur- rently, pressures up to 200,000 psi are being used in the autofrettage of gun tubes and pressure vessels with yield strength levels of 160,000 t9 190,000 and 240,000 to 250,000 psi, respectively.

Autofrettage b-v the above technique is, for all practical purposes, litnitod to pressures not exceeding

200,000 psi. T o extend the use of auiofrettage t,o higher pressure applications and t o eliminate the many problems erxountered in the use of pressures in the range of 150,000 to 200,000 psi on a large-scale basis, a new autofrettage process has been developed. This new technique' uses the mechanical advantage of a wedge to produce the desired b x e enlargement, thus drastically reducing the pressure requirements to obtain a given amount of overstrain. This process, which is termed the swaging method of autofrettage, consists basically of passing an oversi~cd swaging tool (mandrel) through the bore of the cylinder t o produce the desired permanent enlargement. The force required to move the mandrel may be provided by direct hydraulic pressure applied behind the mandrel or by a mechanical loading device.

Because of the diference in the nature of the stress condition responsible for the inducement of t,he overstrain in the swaging method, as cxnpared to the direct pressure process, the resultant residual- stress distribution will be s m ~ e w h a t different. I t has been the purpose of this work to determine the residual-stress distribution as a function of the magni- tude of overstrain and i ts effect on elastic slrength chalacteristics. Diameter rati:, from 1.5 to 2.3 and yield strengtlls from 13C.000 t o 180,000 1 1 4 were investigated.

the-retical re5idual-stress d is t r ibut i~n. for a thick-walled cylinder o\ ersil-ained by direct internal pressure, has been repzr teci 1)y severai investi- gatcrs.? Based c1-1 tile Tresca ~7ield (*riieri:ln and assunjng the ol~en-end ccndition, i.e., a. = 0, the distribution of the residual stresses in the plastic region ( u 4 r I p J of a l ~ ~ x t i a l l y 01 erstrained cylinder is defined by the folicwing relationships:

I n the elastic region ( p 5 r < b ) , the residual-stress distribution is given by:

The theoretical longitudinal residua1 stress through- out the tube is assumed to he zero.

T h e residual-stress distribution which should, in theory, produce the greatest elastic strength of the cylinder is tha t associated with the 100 percent overstrain condition or the case where p = b. In

Fig. 1-Theoret ical res idua l s t resses for Tresca a n d Von M i s e s y ie id cr i ter ia

this condition, the cylinder is fully plastic and the re,<idual-stress distrjhutjon is given 1 3 1 :

The theoretical dislribu Lion of r e d ual stresses using the Von Mises yield criterion has been reported by Weigle and Pascwal.' Their salution for the residual stresses in a fully overstrained 2.0-diam ratio cylinder is shown in Fig. 1 along with t h a t computed using eqs (5) and (6). Due to the complexity of the method presented in the above reference and the small differences between the two methods, the residual stresses as computed from the Tresca yield criterion will be used a s a basis for comparison with the experimental results throughout this work.

Measurement of Residuul-stress Distribution

As material is removed from the bore of a thick- walled cylinder containing residual stresses, the force exerted by this stressed material on the remainder of the cylinder is removed, thus disturbing the condit,ion of equilibrium existing in the cylinder. In order to re-establish eyuilibriurn, elastic strains will occur throughout the cylinder. Strain gages mounted on the external surface will thus indicate

the strain prsdnced by the removal of tlic: ytrcssrd material. The relationship bct\veen this esterior surface strain and the stress existing in the removed material is develgped as follows:

Fram the Lame' equa t i~ns ' for elastic stresses in thick-walled cylinders, the change in stress a t the outside surface due to the removal of the material between a and c is given by:

From t h e general elastic stress-strain relationship:

Combining eqs (7) and (8) yields:

From the equilibrium equation for a thick-walled cylinder:

Substituting (9) into (10) yields:

DifTerentiation of eq (11 j and substitutjon of areas for radii yields:

T h e relationship for longitudinal stress is developed a s follows:

Removing a layer of stressed material produces an unbalance of force in the longitudinal direction of:

Assuming this force to he distributed evenly over the remainder of the cylinder:

F2 = u ~ i ( [ I - f ) (14)

From Hooke's law:

( T I = - ( 6 - + 1 = E ' \ ( l t5 i 1 - ,ui

Combining eqs j13j, (14). and (15) yields:

\ I = E I , - /) (16 I

DifTerentiating yields:

Computation of the stresses associated with each increment of material removed may be ac.c.omplished by either of two methods. The first ( tha t origil~ally pro1)osed by Sachs) uses the relatioi~ship in the form shown in cqs 112) and 118). Both the 0 and \ values were ])lotted vs. area i f ) .

Slopes of' these csurves idii df and d \ df I are taken

Fig. 2-Residual-stress mach in ing f ix ture wi th special ly gaged spec imen

Fig. 3-Tanger,tial-strain funct ion v c . r3dius s ' ionr ing actual data

a t several points and substituted in eqs (12) and (18) to determine the stress values a t each point.

The second method was proposed by Weiss'i and consists of plotting strain functions from eqs (1 1) and (171, namely: E'B j(b2 - r" 2 - 1 and E'.\ i f , - f ) , vs. r and f , respectively. The slope of' these curves then gives the stress values dire( tly .

The second method provides a slight simplification of the computing procedure and has been used throughoilt this work An exarnl~le of the ac4unl data for a typical slm.iinen is sl~own in Figs. 3 and 4.

Procedure

I n order t o fully evaluate the several variables in- volved in this ])rogram, residual-stress analysis of' a large number of specuimens was riqujrzd. To use operator and macahinc time 1 1 I ( )st e;fic.iently, it was

TABLE 1-RESIDUAL-STRESS DATA SUMMARY

Yield permanent residual- Longitudinal No r~ i l a i i zed Spec imen Diameter strength, bore stress residual permanent

number rat io ps i enlargement deviat ion stress bore strain

Fig. 4-Longitudinal-strain func t ion vs , bore area showing actual data

decided to remove the sl)ec*ilr,en from the lathe after each c'ut I ( ) r strain-gage rrladings. A spec+ial fix1 ure, a s shown in Fig. 2, was designed to allow quit k rc-

~rioval rJr sc~tup of a specimen. This f ix tv i z was mounted on a standard Monarch 16-in. hlodt.1 C engine lathe. I t consisted of a pair of' internal c ~ n i c frustl-urns each having a total included angle of' 70 deg. This angle was found to have the h i t centering effect while exerting a minimum of radial force on the specimen. One of these c - ~ n e s was mounted on the headsbock faceplate. T h e other was mounted in a ball beming ~ h i c h was ~ ~ ~ ~ ) p , ~ r t e d from the ways of the lathe and movable pwallel t o the asis. Originally t he sl~ecimens wcre driven by a key in t he headstock c3ne which engaged a imall groove a t t he end of the s1)ecin:en. I t was found, hr~w- ever, t ha t this key was not naeded since the fric Lion force between the cone and s l ~ c imen 1)rovidec-l suliicient driving force for the very light cuts taken. 'J'he 1.-ngitudinal c.lamping f'orcoe on the sl)ccimeii was limited t o about 60 1b. Th i s fixture a l l o ~ v ~ d very ra l~ id se tul) a n d removal of sl)ec.imens while maintziin- ing c*onc.ent ric-ity between the b:,re a n d the exterior 5urf'ac.e of' bct ler than 0.001 in.

'I'he cautting tool uscd was a c~:irI)itle-ti~)~)c.ci tool hvld in a slandard iteel 1):)ring bar. Yo liquid ( ~ ) o l -

TABLE 2-HYDROSTATIC YIELDING DATA

Diameter Y ie ld Percent permaner i t Reyield Spec. No. rat io strength bore en largement pressure

a n t was used bu t a siream of cornpl+essed air was directed on the tool through a hole in t h e bar. This served to prevent severe heating of the specimen and provided chip removal by blowing the chips out through the spindle of the lathe.

I n s t r t m ~ e n t a t i consisted of a 13aldwin SR-4 strain indicator, 'Fyl~e N. Specimen dimensions were measured using screw micl-ometers and tele- s ro lx gages.

r i I he test specimens used in this program were all of Type 4340 steel f~l-gings of the samc heat . The spec i r~en blanks were cut into 5-in. lengths from solid bars of about 4-in. OD and drilled to a n internal diameter of 1 in. They were then heat treated to the desired yic~ld-strength le\-el. 'I'he specimens M7ere then bored and graund on the inside diame:er t c ~ a nominal 1 .5-in. bare. Minor adjustments in the bore diameter were made to prr)vide the d e s i r d bcre enlargement for a (v l~s tan t mandrel diameter. T h e outside surface \vas machined to prcduce the desired diameter ratio. 'rhe specimens were then autof'rettagcd by s~vaging using a rj5-ton Ilydraulic arbor press to clrjve the mandrel.'

Mcs t s p e c h e n s were strain gaged w i t h two SK-4 'Fype AX-5, two element rcsette gagm mounted a t t h e mid-lengt 11 and diametricdl y o~)pc~sed . Con- nections were made t.) the <rain gages through banana jac-ks ~noun ted in word blocks whic~h were glued to the specaimen and sljring-tyl~r: banana plugs connec*ted to the st rain indicnatr~r. Two sl>ecimens, one of' w11ic.h is shown in Fig. 2, were s1)r~~ially gaged to determine the end eff'c-ct introduc*etl hy using a c~)rnjm.ativol y small lengt11-t o-tlim~~tftcr ratio. This c~onsisted of' mounting giig(!S at thc mid-length and ' a n 1 I . i t her i d of t I j o t . N o significant c1ifkrenc.e w:is f o u n d l ) c ~ t wchc~n t,lw residual-st ress d i s t r i l ~ u l i o ~ ~ a i ( . ; i I c ~ ~ i l ; i f ( ~ ( j frc,rn 11x1 1nid1)oint gages I i 1 0 ' in. c ~ i t llt~r i i c J i 3 . It w;iL, t 11cr-c~f'ore. as-

surncci tha t the mid-point was sufficiently free of end ef'fects.

Specimens were noi-mally run in groups of six. Two sets of strain-gage readings for each specimen were taken each morning. The specilnens were then placed in the machining fixture and a predetel-nlined amount of material was bored out. T h e cucting speed and feed \47ere maintained constant a t 494 rpm and 0.0042 in. per revolution, respecti\~eIy. The depth of cut was maintained a t ahout 0.005 in. per pass.

After machining, the specimens were r e ~ n ~ v e d froin the fixture and allowed t o stand overnight near the "dummy " specimen on which the compensating gage was mounted. This assured the most effective possible temperature compensation.

Bore and outside-diameter measurements were taken a t the same time the gages were read and as (.lose in location t:, the gages as pos4hle.

The average of both readings of both tangential and longitudinal gages was t,aken as the tangential and longitudinal strains 1 especiively. Corrections were made for transverse ~ensi t iv i ty of the gages and the tangct:tial. radial and In>giti~~!i>;al s i i - i . ~ distributions Ivere computed by the rneihcd dis- cussed previously.

Several specimens of various diameter ratios anti yield strengths were hydros ta t i~al ly tested to yield. These wele tested as open-end cylinders using a Harwood 200.000 psi infen~ifier pump and a restrailling press to support the prewure seals. The SR-4 Type A-7 strain gages wele mounted tan-

/I gentially on the outside surface a t the mid-length alld dian~etrically oppcs~ t l . 'l'hese gages were r t~ad L I L ~ I I ~

a Baldwin switc.hing and lxdanc.i~~q unit and an S.;R-,l strain indicator. Pressure was measured \ ~ i t h a manganin-wire pressure (*ell and Wheatstone bridge.

Discussion of Resuits

Tyj~ical experimental residual-stress distributions are sl~o\vn in Figs. 5 13. I h m these stress distl-ibu- tions it is evident tha t a subitantial longitudinal residual stress exists in cylinders autofrettaged by swaging. This stress increases in magnitude with increased amounts of' enla]-gcmcint and aljpcars to be ac.c.om[)anied by a pro1)ort ionate decrease in the tangential residual stress.

For the purpose of' ev21luaiing and com1):iring the ex1)erimental residual-stxess distributions of all s~)ec%-nens, a quantitat i\ie measure of' t he t heoretic ;I! effectiveness of' the ohiaincd stress ciisiributioll i \ utiliztvl. The quantiiy usod is t h ~ ii\)solute d i fk r - cncne hetween the exl)crimcl~t;il re.;iduitl strcss a n d t,he t l~eoretic~il o1)t imum st res\ ;it a1 I viilue:, of' radius averaged over the \ ~ i i l l I l ~ i ( lillc~ii. r I ' l ~ i ~ v i i I~~( ' was ohtaineci by l~loti ing tile cxl)c.rln~cbnt;il ;i1)(1 tl>eorc~tic.:ll resit1 u;il st resws 1;))- e;ic.h i l )c~c'inlc111 vi . radius ;intf

Fig. 5-Residual-stress distribution-1.5 diarn ratio, 0.49 percent bore enlargement

Fig. 6-Residual-stress distribution-1.5 diam ratio, 3.96 percent bore enlargement

Fig. 7-Residual-stress distribution-1.5 diam ratio, 5.71 percent bore enlzrgement

Fig. 8-Residual-stress distribution-1.9 diam ratio, 0.39 percent bore enlargement

",,o'i'- - - - - -A - c c 5 - I 0 I , 12 13 4

. . R h b l ~ S i N . -- > -

Frg 9-Res~dual-stress drstrrbutlon-1.9 dram ratro, 3 66 percent bore enlargement

Fig. 10-Residual-stress distribution-1.9 diam ratio, 5.53 percent bore enlargement

m e a s u r i n g t h e t o t a l a r e a between t h e ( w - v e s wi th whi{.h r . o r r e sponds t o t h e t o t a l wa l l thic.kness.

a 1)o lar 1)lanimetc.r . 'l'his a r e a w a s d i v i d d b y t h e T h i s q u a n t i t y was d e t e r m i n e d for t h e t angen t , i a l

ove r - a l l length of thtl ( * u r v e s 1)ri) j t i i ted on the :r l~sr . issa, a n d 1ongit.udin;ii residu;ll-s!.ress d is t r i1)u t ion Sound

2558 / ,YOL)~] ,~I / ,C~ 19fi.:

Fig. 11-Residual-stress distribution-2.3 d i a m ratio, 0.33 percent bore enlargement

Fig. 13-Residual-stress distribution-2.3 d i a m ratio, 5.66 percent bore enlargement

0 I -- -- - ----- - -- - -1 J * 2 L'6 - r , i lk ' :7C'+!C_LL xU_F_S_S_

d T 6

L l - ,

Fig. 14-Tangential res~dua l -s t tess d e v ~ a t ~ o n vs Iong~tudrna l residual stress

f j r each specimen. Si11c.e the tlheoretical longitudinal residual stress is assumed to be zero, t he longitudinal average difference value is equal to the average absolute value of the experimental longitudinal residual stress. All average difference values were normalized by dividing by the yield strength of the specimen and are given in Table I .

A theoretical analysis of the elastic plastic stress strain condition existing in the cylinder during the passage of the swaging tool (mandrel) will not be at tempted in this paper. However, it is obvious tha t the frictional forces between the mandrel and the cylinder bore, plus the longitudinal component of the normal force between the sloping surface of the mandrel and the bore, combine to produce a longi- tudinal shearing force on the cylinder.

In order to discuss the ef'fect of this longitudinal shearing stress on the over-all residual-stress distribu- tion, we refer to the generalized Von Mises yield equation, assuming 'I',, and 'I', equal zero:

( r , - o r ) ' + ( r r - c r z ) ' + ( g z - g ( , t 2 + GTr-' = 2c~,,'

This equation must he satisfied throughout the

plastic region of the cylinder during the passage of the mandrel. From this, i t can be seen tha t as T,, and a, assume values other than zero, either a, or ri, must decrease in absolute magnitude. Since the experimental values of the residual radial stress do not differ significantly in magnitude from the theo- retical, one may assume t h a t most of the change ov- curs in the tangential stress.

Figure 14 shows the tangential residual-stress deviation vs. the longitudinal residual stress. The expected change in the tangential residual stress with increasing longitudinal stress can be seen.

Figures 15, 16 and 17 show the average longitudinal residual-stress values and the tangential residual- stress deviations vs. normalized permanent bore strain for the 3 diam ratios considered. The values of tangential stless deviation appear to approach a particular minimum value for eaceh diameter ratio. For the case of the 2.3-diam ratio, a minimum value can be estimated. For the other diamcter ratios, this minimum is a t a pcrrnanent stmin value below the lowest value investigated. 'I'hese minimums

Fig. 15-Tangential resid- ual -s t ress deviat ion and longi tudinal res idual stress vs. p e r m a n e n t bore strain, 1.5 d i a m rat io

Fig. 16--Tangential resid- ual-stress deviat ion and longi tudinal res idual stress vs, p e r m a n e n t bore strain, 1.9 d ian i rat io

Fig. 17-Tangential resid- ual-stress deviat ion a n d longi tudinal res idual s t ress vs. permanent bore strain, 2.3 d i a m rat io

less than one. This is also true for the ibase of cylin- being i~onduc.t.ed by the auf hijrs. ders autofrettaged by the conventional hydrostatic Figure 19 shows thc normalized pe rma i~en t bol-e method. I t is due tm what is generally termed the strain required to produce 100 ~ ) e r ( ~ e i ~ t overstl-ain by "hysteresis" efTwt a n d , in the i-ase of t he 2.3-diam direct hydrostatii. pressure vs. diameter ratio.: Also ratio, reverse yielding 1)henomt~non. T h e hysteresis shown are t he estimated o11t~imun-i values of lJoye e f k r t was riducwl as rnu(.h a s 1):rssil)lr+ I)y sul>je(t inp i i rain found fi)r iyiiriders :iutofketb;igcd i j~r swaging all of' the hydr(iitwti(. yiclrling sl)e(*imens to a low- f'rom both the residual stress-a~ialyses nlrd Ilrdro- leml)rr;iturc th(~rma1 i reiitnrunt a t 675 F for 6 hr i ta i ic yielding tests. I n iht) (s :~sc of tlre 1 .5- ziI~d I.$)- r , I his has k e n s l~own l)y the a u t l ~ o r s t.o Iw o1)timurn diam ratios, the 1)oinis S I ~ O \ V I I rc*j)rew~li i11c ]inlit fi)r the rnatt~rial u~,ecl. of t hi. exlwrinienf a1 dilt a . ( : o i ~ s ( q ~ ~ c n t ly. the (levia-

A i .omj)lc~t(~ i tud y of l hew ~)lri.nornc~~la is (~urrcnf 1 y t io11 from f 1 1 ~ ( -urvc f'or 11 \>drostat i ( 8 j ~ r ~ s s ~ ~ r t ~ mzy l)e

even great,er as indicated by the arrows attached to the d a t a for these diameter ratios.

T h e seemingly large discrepancy bctween these optimum conditions can be attributed to the follow- ing:

(1) T h e theoretical cun7e sho\vn is derived as- suming completely elastic recovery 011 release of the 100 percent ovrrs! rain pressure. Act u d l y, some reverse yielding will occur in the 2.3-diam ratio and pxs ib ly , t o a lesscr extent,, in the 1.9-diam ratio. This :vould cause a decrease in the optimum perma- ncnt bore strain fram t h a t shown for the direct hydr- lat tic case.

(2: A further z.*plmaii -11 of this discrepancy can be seen by examii~ing the equatign for theoretical elastic breakd3wn f.)r a cylinder t h a t has been partially plastically def,,rrned by internal pressure.

From this equation,; i t can be determined that a cylinder 1)lastically cleforriled so t h a t the depth of plastic flow is equal to 60 pel-c>ent of the \ $ d l thick- ness has a n elastic breakdown pressure of about 93 p e i w n t of r h ~ 103 percent oversf rain prclcsure. This degree of plastic penetration is obtained a t a value of permanent bore t r a i n equal t o about 50 percent of t h a t required to produce 100 percent overstrain. It is, therefore, apparent t h a t the small benzfit t o be gained in increasing the amount of pel-manent

Fig. 19-Optimum permanent bore strain vs. d iameter ratio

bore strain from the exlminientnl optirm~un value to the theoretical optimum value is more t,han offset by the damaging effect of the increasing longitudinal stress.

It should be noted, however, t ha t the damaging effect of bore enlargements equal t o or slightly greater than the theoretical optimum value is very slight. Even for cbases where the b o x enlargen~enls greatly exceed the optinlum values, the strength of the cylinder is still greater than a comparable cylinder which is not autofrettaged.

D u e t o the hal-nlful effects of t>he longi tudi~~al shearing force prcduced in the swaging process, as sho\vn in this paper, a study has been initiated to detei-mine ways of decreasing this shearing force. Expected improvements in lubrication lnethods and mandrel geometry sllould cdnsiderably reduce the damaging effects noted.

Conclusions

I. For optimuln overstrain conditions, the tan- gential re~idual-stress distribution and the increase in elastic response of cylinders autofrettaged by ~ t : i2g;n g arc ccln1:)rLrz!31e io ? h i ~ i s c3h3rzctel-:',<I jc of the direct hydrostatic technique.

2. As the result of a longitudinal sliealing stress due t o the tapered mandrel, a substantial longitudinal residual stress exists in cylil~ders autofrettaged by swaging.

3. The magnitude of the longitudinal residual stress increases with increased overstrain u ~ i t h a resultant decrease in the tangential residual stress.

4. The reyielding pressure for cylinders auto- frettaged by swaging reac-hes a maximum and then decreases slightly with incwasing overstrain. This rnaxirnttm oi~cui-s a t suhstantinlly 1ov;c-r arno~:nts of overstrain than tha t charac'teri\tic of c.~~ljnc!e~s overstrained by direct internal hydrostatic pressure.

iZppreciatio11 is expressed t o G. E. Sogoian and R. Young whose skill as machinists and care in taking the experiment,al da ta made this investigation p~ss ib le .

Appreciation is also expressed to C. S. Barton for his assistance in the initiation and planning of this work.

I . I)cic~ic/.son, '1'. I:'., I!or/oti , C . S., Jic,invr, A . A'. (1110 h'c.ticicl//, I ) . I)., "A N e u ~ Approi ich I(, / / lc A U I O ~ , - ~ ' ~ I ( I ~ ~ , o/ Niglz-sir-c,ngili C,~~~linrlc~rs," i;.xllr,:ltr-

M I ~ ~ N 7 . A L MI<C13ANICS, I " , N O . 2 , : j : j '10 ( I . C ) m I . 2. Mncrc~c:, A . I;., " O v o s / r n i r i iri hdr,/rils," I-!. M S/rlliorro,:~~ Ofiicc~, I,or~-

don . 1 !!.YO. 3. IJrclgcr. MI. uncl I-lorlgo, 1'. C., " ' f ' / i c ~ ) r y o/ l ' r r / c ~ / l y lJ/o,s1ic~ Solids,"

./oh71 I i ' i l ~ y & ,C;o~i,s, Nvui Yorl:. 19: i l . . I . 11'1>iglr,, 11'. i:. clnd l'c~.sc~ucll, h f . , " Jic~,sidircll S ' l rc~ss t~ ,~ iti C,'ir.r.irlar '1'111~s

I-101,trrg o I-lislory o/ I'rc~ssrrrc~-lrrrl~~r~~~~l liln.slic~ I)c~/'or-n~c~lton," 1Ytrlr~rr~Irc~l A r,sc.nril ' f ' c ~ / l r i irril Jir,f)or/ 601.1-li , I!)iiO.

5. jr'rtrio,s/it~rii:o, S., " S / ~ I ~ I I K / / I o/ Rlcl/r~rlols, / ' ( I / - / I / , " I). C'clri No.s/rc~trr/, Itrc., l ' r ; n w / o ~ i , N . - J . , l!):iO.

6 . I l ' c~iss , \/., "Hr~.siclutil S / r c ~ s s ~ ~ . s i r i (',vlitrc/r~r.s," ,Y>~rr~c.ir.sc~ l i~r i~~r~t..si/ ,y I<(,- stvi 1-1.11 I rrst i/i,/rp J?c~l~ot-/ N o . Af 11'1' ,'I.l.i-:ili.7'1'2.

7 . I ) ~ i r ~ i d s o ~ i , 7'. I,,'., / ~ ( l r / o r l . C,'. .S., I ~ I , I I I ( J ~ , A . A'. o ~ i d 1i'1~11d1111, 1). I ) . , ' * f ) ~ ~ t ~ / - ~ / r ( ~ i r r o j l l i j ~ ~ i - , s / r ~ ~ r i ~ ~ / r , O I J ( ~ I I - ~ ~ ~ I ~ (',v/ir~cIc~rs I,/ 1 i ~ / c , r - r ~ i ~ ~ I i ( , / ( ~ 1)1(ir11- l,Ic2r Iio110," :l:j.> :).>?, / ' r ~ ~ ~ ~ c ~ c ~ / i r i ~ . s 01 1/11, lg'!r,\/ / r i / ~ ~ r ~ ~ ( ~ / ( o r i i i / ( 'OIIXIY*.S.\ O I I

/ - . ' t1~<.r~ur,rr/u/ Adr,r/,/,/iir.:,, I ' ~ , / - ~ , I J J I D ~ ) I ' r ~ ~ i h . O \ / o r ( / l:rrg11111(/ /!tli.'i.