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TECHNICAL REPORT ARCCB-TR-94031, -

RESIDUAL STRESS ANALYSIS INSWAGE AUTOFRETTAGED THICK-WALLED

CYLINDERS BY POSITION-SENSITIVEX-RAY DIFFRACTION TECHNIQUES

S.L. LEE 6 L E .C-

AUGUST 1994

US ARMY ARMAMENT RESEARCH,DEVELOPMENT AND ENGINEERING CENTER

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4. TITLE AND SUWTITLE S. FUNDING NUMBERSRESIDUAL. STRLFSS ANALYSIS IN SWAGE_ AUTOFRLMAGED11-IICK-WAi -IN) CYLINDl)RS BY POSHION-SENSmTVE. AMCMS: 611 1.02.1-6 11.1X-RAY DIFFRA(710N T1&1-INIQUILS

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Prcsicutcd at the ASMl Int lzi ationaJ Conference on Pressure Vessels &Piping, Denver. Colorado. 2-5-29 July 1993. PublishedIn the 1rt-.ccding ot the ('onterence.

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13. ABSTRACT (Waxmum 200 words)Expenrtnental and theoretical invest ieat ions were moade for--wage autofrettaged partialy plasic ASTM A723steel cylinderswithan outside diameter (OD) to insidic diameter (ID) ratio of 2.75 and 74 percent overstrain. Residual stress radial distributionand angular stress distribution around the bore were analyzed using two position-sensitive x-ray diffraction stress analyzers.lhbeoieticai calculation was made by implementing an interactive, iterative Lotus Works spreadsheet reridual stress model onan IBM PC. The model was based on the classical solution to the elastic-plastic deformation problem of a symmetric thick-walled cyiiridvr under internal pressure, including reverse yielding effect. Angular stress distiibution data at the ID and ODindicated that non-axisyinmetric deformation had occurred during yielding of the cylinders. Excellent agreement was obtainedIi between ex~perimental results and theoretical1 predictions, including the Bauscliinger effect near the bore. By comparingcitpcrncrntal data with theoretical calculations for the 74 percent overstrained cylinders, the Bauschinger factor for the A72.3steel was determined to be close to 0.5. Residt',al stress analysis for the entirc cylinder is suggested in the future.

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TABLE OF CONTENTS

INTRO D U CTIO N ........................................................ 1

SPECIMEN PREPARATION ........................................... .... 2

EXPERIMENTAL METHOD ............................................... 2

X-RAY DIFFRACTION HOOP STRESS RADIAL DISTRIBUTION ANALYSIS ....... 2

X-RAY DIFFRACTION ANGULd,•.) STRESS DISTRIBUTION ..................... 3

CLASSICAL ELASTIC-PLASTIC DEFORMATION MODEL CALCULATIONS ........ 3

COMPARISON OF EXPERIMENTAL STRESSES WITH CALCULATIONS .......... 5

CO N C LU SIO N S ........................ ................................. 5

R E FE R E N C ES ........................................................... 6

Ta1bles

1. Theoretical Residual Stresses Including Effect of Reverse Yielding .................. 4

List of Illustrations

1, Hoop residual stress distribution in a symmetric cylinder ......................... 7

2. Reýsidual stress angular variation in a symmetric cylinder ......................... 8

3. Theoretical stress-strain curve for A723 steel ........ ......................... 9

4. Pressur, 'ed cylinderý after removal of internal pressure .......................... 10

5. Classical theoretical hoop and radial stress distribution .......................... 11

- I 6. Exper& nental and classical deformation model stresses including reverseyield, ag in a symmetric cylinder ........................................... 12

* 7. Baus(hinger effect factor (BEF) versus percent tensile overstrain .................. 13

8. Experimental and classical deformation model stresses including reverseyielding in an eccentriL cylinder ............................................ 14

2ist

---- i ii-- . . .. .....amlll OW h Ismlal

INTRODUCTION

It is a well-known fact that nearly all fatigue and stress corrosion failures originate at thesurface of a part, and that cracks do not propagate into a compressed layer of a component.Autofrettage, shot peen, and shrink fit are common processes to induce compressive stresses nearthe bore surface of a cylinder. In the manufacturing of high pressure vessel systems, steelcylinders made from ASTM A723 alloys are rotary forged, heat hardened through austeni~ingand quenching processes, tempered to improve toughness, rough and fine machined, swageau~ofrettaged, beam straightened, and thermally soaked to obtain desirable residual stressdistributions.

Excellent earlier developmental work for hydraulic and mechanical swage autofrettagemanufacturing processes were reported (refs 1,2). The hydraulic autofrettage process was slow,expensive, and dangerous. High pressures close to failure in the range of 1000 to 2000 mpa werenecessary. By driving a mandrel through the cylinder, the swage process eliminated the necessityof ultrahigh pressures required in the conventional hydraulic method to produce the same radial

A I Fforces and plastic deformation. Davidson and Kendall further reported results of residual stressinvestigation in swaged cylinders by Sack's boring out w~ thod (ref 3). Clark observed variationsin hoop residual stresses for a large caliber gun barrel forging (ref 4). Parker et al. studied thefatigue crack growth and safe design of gun tubes (ref 5). Results from our x-ray diffraction andfinite clement modeling investigation of an eccentric cylinder were reported (refs 6,7). Interestin the Bauschingcr effect in thick-walled cylinders is obvious (8-11), since there is littleexperimental data available.

With the recent development of position-scnisitivc x-ray diffraction instrumentation, fastand rcliable stress measurements are possible. The present work characterized residual stressdistribution in a symmetric prc-pressurized partially plastic thick-walled cylinder by swageautofrettage. Comparison of the prcsent theoretical calculation with our previous data for aneccentric cylinder of the same dimension was made. Measurements were made using both aposition-sensitive single-exposur-~ scintillation detection (PSSD) system and a position-sensitivemultiple-exposure proportional counter stress analyzer. Angular stress distribution measurementsaround the bore indicated that tion-axisymmetric deformation had occurred during yielding of asymmetric cylinder.

* Theoretical residual stress predictions were made assuming a classical model of asymmetric cylinder under internal pressure. An iterative Lotus Works spreadsheet residual stressprogram based on Parkri's model (ref 5) was designed and implemented on an IBM PC.Excellent agreement was found between experimental and theoretical results, including theBausehinger effect near the bore. The Bausehinger factor is defined as the ratio of yield strengthin compression to yield strength in tension. It can be described as a lowering of the elastic limitin compression subsequent to a previous stressing in tension beyond the elastic limit. Conversely.,he elastic limit in tension would be reduced for a material strained beyond the elastic limit incompression (ref 11). A qualitative comparison of our experimental data for the 74 percentoverstrained tube with model calculations indicated that the Bauschinger factor for the A723steel was close to 0.5.

~ _ I

SPECIMEN PREPARATION

In the swage process, the cylinder was subjected to plastic deformation by pushing anoversized mandrel through the bore under high pressure grease. Material constant, geometry ofthe ram, mandrel, and cylinder, and the shape and interference of the carbide tool determine theamount of plastic deformation under load. The thick-walled cylinder investigated was 74 percentoverstrained with an OD to ID ratio of 2.75. Slices of the tube 3.79 cm (1.5 in.) thick were cutfrom the cylinder, machine polished, and then electropolished. Electropolishing of the entirecross section of the ring was done by using a heated polishing solution of 50 percent sulfuric and50 percent phosphoric acid mixture with no external agitation device. It took approximately onehour to remove 0.13 mm (5 mils) from the surface of the ring. Surface material removal wasmade so that the effects due to sanding, machining, and oxidation would not influence theresidual stress measurements.

EXPERIMENTAL METHOD

Experimental analyses were made using both a prototype PSSD system from DenverX-Ray Instruments, and a position-sensitive multiple-exposure proportional counter stressanalyzer from Technology for Energy Corp (TEC). Experimental methods and calibration of theDenver stress analyzer have been described in another report (ref 12). The K-a from achromium x-ray tube reflects from the 211 plane of the body-ccnte red-cubic (BCC) steel at 20equal to 156.41 degrees. The fast single-exposure method was used in the radial stressdistribution analysis; the accurate multiple-exposurc method was used to analyze hoop and radialangular stress distribution around the bore.

The choice of zero degree for a normal cylinder was arbitrary. The surface was markedinto 32 ,zqual area pie slices at an 11.25-degree span each. For stress distribution determinationanalysis, a specimen stage with an x- and y-micrometcr slide was used. Angular stress variationmeasurements were made by manually rotating and positioning the specimen. Symphony, LotusWorks. and Freelance software were used for data analysis and graphics.

X-RAY DIFFRACTION HOOP STRESS RADIAL DISTRIBUTION ANALYSIS

In Figure 1, the x-ray diffraction experimental hoop residual stress radial distributionsalong radii at 0. 9), IN). and 270 degrees for a symmetric swaged cylinder are displayed.Experimental x..ray diffraction results for the swaged cylinders exhibited compressive residualstresses near the bore: the stresses gradually changed to tensile stresses near the outside surfaceof the cylinder. Closest to the bore, reduced compressive stresses were observed in allmeasurements. The solid curve in the figure represents the average stress from 0. 90. 180. and27/0 degree stress measurements in the symmetric ,ylindcr.

2

I-

X-RAY DIFFRACTION ANGULAR STRESS DISTRIBUTION

In Figure 2, hoop and radial stresses at the ID and OD of a symmetric swaged cylinder atvarious angular positions are plotted. Angular stress data showed a peak of reduced compressivestress around a random 290 degree plot. The data are in good agreement with Figure 1, wherethe 270 degree plot has less compressive stress near the bore. Hoop and radial stresses at the IDand OD of an eccentric cylinder with an 0.1-inch wall thickness variation measured on a TECposition-sensitive multiple-exposure stress analyzer have been reported (refs 6,7). A peak ofreduced compressive stress was observed around 180 degrees, which was the thinnest part of theeccentric cylinder. It is surprising to find non-uniform stress distribution ia both a symmetric andan eccentric cylinJer. Possible causes for this non-axisymrnmetric yielding are variations inmaterial properties, non-uniform heat treatment procedure, eccentricity, tribological problems,non-axisymmetric processing, unknown effects during manufacturing, or a combination of thesefactors. Another observation is that the radial stresses at the ID and OD are near zero for thesymmetric cylinder, as expected from Tresca's theoretical predictions shown in the next section.OD radial stresses for the eccentric cylinder peaked around 0 degree, which is the thickest partof the cylinder.

CLASSICAL ELASTIC-PLASTIC DEFORMATION MODEL CALCULATIONS

In the autofrettage process due to internal loading, the bore is plastically enlarged, andthe outer portion of the steel cylinder is elastically enlarged. As the internal pressure p isreleased, the outer portion contracts elastically to its original dimension, steel nearer the boreresists this action. This results in compressive hoop residual stresses near the bore that changesto tensile stress near the outer surface. However, closest to the bore, the Bauschinger effectcauses reversed plasticity and reduces the compressive stresses.

"To obtain theoretical stress predictions, a fast aaid versatile iterative Lotus Worksspreadsheet program was designed and implemented on an IBM PC. Assuming a thick-walledcylinder overstrained by direct internal pressure. our analysis was based on Parker's solution tothe classical elastic-plastic deformation problem using Lame's equations. Tresca's yield criteria,and reverse yielding (ref 5). Figure 3 is a stress-strain curve used in the analysis that assumed anelastic-perfectly plastic behavior during loading, and reduced yield stress during unloading. TheBauschinger factor is given by a. Figure 4 is a cross-sectional display of a pre-pressurizedautofrettaged cylinder after internal pressure has been removed, showing regions of elasticity,elastic-plastic interface, and rcvcrscd plasticity. The inside radius is a, the outside radius is b, theelastic-plastic interface radius is c. and the reversed plast' ity radius is d. Table I gives thecquaticrns used in the model. In Figure 5, predictcd resý ial stress distributions are given forBauschingcr factor a equal to 0.25. 0.5, and 0.75. Tihe calculation assumed a yield stress of 162Ksi.

H .3

Table 1. Theoretical Residual Stresses IncludingEffect of Reverse Yielding (ref 5)

Vanrable radius- r Elastic-plastic interfaces- 'c,dInside radius- a Interface pressure at c- p*Outside radius- b Interface pressure at d- pYield strength- YBauschinger factor- aHoop stress- 08Radial stress- a.

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a -uY (1 + Cn r/a))

a --aY in Cxr/a)

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4

COMPARISON OF EXPERIMENTAL STRESSES WITH CALCULATIONS

In Figure 6, experimental residual stress distributions for a symmetric cylinder displayedas data points are compared with theoretical stresses for a equal to 0.5 displayed as solidcurves. Excellent agreement was observed, indicating that the Bauschinger factor for A723 steelwas close to 0.5. The deviations between experimental and calculated results were the largest at270 degrees because of the non-uniform stress distribution in this region. A qualitativecomparison of the present experimental results with Chen's numerical residual stresses includingBauschinger and strain-hardening effects upon unloading (ref 10) indicated that the strain-hardening factor m' was near 0, and the Bauschinger factor a was between 0.4 and 1.0. Asshown in Figure 7, Milligan determined that for martensite structure, Zhe Bauschinger factor forpermanent tensile overstrain over 2 percent is approximately 0.35. This is in fair agreement withour determination of a = 0.5.

In Figure 8, theoretical stresses for a equal to 0.5 represented in solid lines are comparedwith our previous residual stress measurements of an eccentric cylinder plotted as data points.Again, excellent agreement was observed between experimental and theoretical hoop and radialstresses. The large deviations at 180 degrees, where the cylinder was the thinnest, may be due tomaterial property variations, eccentricity, or other factors.

Since residual stresses must form a balanced force system within the object, a slight shiftof the experimental stress distribution curves would render better agreement with calculations.This could be experimentally accounted for by zero powder stress corrections to the experimentalresults. Moreover, the difference in the nature of the induced stress conditions by the swageprocess as compared to the internal pressurization method should result in some differences inthe stress distributions.

CONCLUSIONS

Stress analysis of swaged components provides guidance to the pressure vessel system'sdesign. This is because controlled stress distribution improves the system's performance andfatigue life of the component. In this work, position-sensitive x-ray diffraction techniques wereapplied to characterize residual stresses in pre-pressurized thick-walled swaged autofrettagedcylinders. Excellent agreement was obtained with theoretical predictions obtained by assuming aclassical elastic-plastic deformation model including reverse yielding effect. For the 74 percentoverstrained cylinder, qualitative comparison of our experimental results with theoreticalcalculations determined that the Bausehinger factor for the A723 steel was 0.5. The non-uniformbore stress distribution around the random 290 degrees should be further investigated formanufacturing quality control purposes. Suggested future investigations include an improvedfinite element swage model, an analytical elastic-plastic deformation swage model, andexperimental investigations in residual stress, strain attenuation, hardness, and phasetransformation in the entire cylinder.

5

REFERENCES

1. T.E. Davidson, C.S. Barton, A.N. Reiner, and D.P. Kendall, "Overstrain of High Strength,Open End Cylinders of Intermediate Diameter Ratio," First International Congress onExperimental Mechanics, Pergamon Press, Oxford, 1963, pp. 335-352.

2. T.E. Davidson, C.S. Barton, A.N. Reiner, and D.P. Kendall. "New Approach to theAutofrettage of High-Strength Cylinders," Experimental Mechanics, 1962, pp. 33-40.

3. T.E. Davidson, arid D.P. Kendall, "Residual Stresses in Thick-Walled Cylinders ResultingFrom Mechanically-Induced O -rstrain," Experimental Mechanics, November, 1963, pp.2:)3-262.

4. G. Clark. "Residual Stresses in Swage-Autofrettaged Thick-Walled Cylinders," MaterialsResearch Laboratories Report MRL-R-847, 1982.

5. A.P. Parker. K.A. Sleeper, and C.P. Andrasic, "Safe Life Design of Gun Tubes--SomeNumerical Methods and Results," Proceedings of the Army Numerical Analysis andComputer Conference, 1981, pp. 311-333.

6. S.L. Lee, G.P. OHara, V. Olmstead, and G. Capsimalis, "Characterization of ResidualStresses in an Eccentric Swage Autofretraged Thick-Walled Cylinder," Proceedings of theASM International Conference on the Practical Applications of Residual Stress Technology,1991, pp. 123-129.

7. S.L. Lee, L. Britt, and G. Capsimalis, "Comparison of Residual Stress and Hardness in aSymmetric and an Eccentric Swage Autofrettaged Cylinder," NondestructiveCharacterization of Materials PI, to be published.

8. D.P. Kendall, '"he Influence of the Bauschinger Effect on Re-Yielding of AutofrettagedThick-Walled Cylinders," ASME Special Publication PVP Vol. 125, 1987, pp. 17-21.

9. J. He, G. Chen, H. Zhong, 'The Influence of Strain Hardening and Bauschinger EffectBehavior of the Material on the Autofrettage Residual Stresses of a Thick-WalledCylinder," ASME Special Publication PVP-Vol. 110, 1986, pp 49-54.

10. P.C.T. Chen, "Stress and Deformation Analysis of Autofrettaged High Pressure Vessels,"ASME Special Pub. PVP-Vol. 110, 1986, pp. 61-67.

11. R.V. Milligan, W.H. Koo, and T.E. Davidson, "The Bausch• ne•-r Efect in. a HighStrength Steel," Trans. ASME, Series D, June 1966, pp. 480-488.

12. S.L. Lee, M. Doxbcck, and G. Capsimalis, "X-Ray Diffraction Study of Residual Stressesin Metal Matrix Composite-Jacketed Steel Cylinder Subjected to Internal Pressure,"Nondestructive Characterization of Materials IV, 1992, pp. 419-427.

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41 Figure 3. Theoretical stress-strain curve for A723 steel.

9

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AMIa= Inside Radius, b= Outside Radius,c= Elastic-Plastic Interface Radius, d= Reversed Plasticity Radius

Figure 4. Pressurized cylinder after removal of internal pressure.

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