a.a. garcia-granada,^ v. lacarac,^ dj. smith ... - wit press · a.a. garcia-granada,^ v. lacarac,^...

3D residual stresses around cold expanded

holes in a new creep resistant aluminium alloy

A.A. Garcia-Granada, V. Lacarac, DJ. Smith/*' MJ Pavier,

R. Cook,**' P. Holdway

Department of Mechanical Engineering, University of Bristol,Bristol BS81TR, UK

EMail: David. Smith@bristol ac. uk

™Structured Materials Centre, DERA, Farnborough, GUI 4 6TD, UK

Abstract

Hole cold expansion is used frequently to enhance the fatigue endurance ofcomponents. The cold expansion process introduces compressive residual stressat the periphery of the hole and tensile stress further away. To understand howthese residual stresses enhance the fatigue life, it is essential that we have anaccurate description of the three dimensional distribution of the stresses. In thispaper we describe the results of experimental studies and finite element analysesused to determine detailed residual stress distributions in a new creep resistantalloy. The near surface residual stresses at the mandrel entrance and exit faceswere measured using an X-ray diffraction technique. The results show significantdifferences between residual stresses at the two faces. The residual stresses arealso shown to vary as a function of position around the hole. To take account ofthis variation a new approach, called the Garcia-Sachs method, was used tomeasure residual stress averaged through the thickness of the component. Forfinite element simulations, a combined hardening material model was used toreproduce the Bauschinger effect exhibited by the aluminium alloy. Using thisnew model, excellent agreement was found between predicted and measurednear surface residual stresses. Finally there is also good agreement between themeasured mid-thickness residual stress and the FE predictions.

Transactions on Engineering Sciences vol 25, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533

104 Surface Treatment

1 Introduction

Cold expansion is a well-known method^ frequently employed particularly inaircraft structures to improve fatigue life of components. The techniqueintroduces a compressive residual stress in the material surrounding the hole.One such cold expansion process involves the use of a split-sleeve which isplaced over the mandrel, and inserted into the hole. Plastic deformation of thematerial occurs as the mandrel is drawn through the hole, thus inducingcompressive residual stresses around the hole when the mandrel is withdrawn.

Many experimental^ and numerical^ studies have been undertaken todetermine the distribution of the residual stresses. Finite element (FE)simulations^ have shown that cold expansion introduces a complex 3Ddistribution of residual stresses. Experimental measurements of the residualstress distribution have been carried out using non-destructive techniques such asX-ray'*, and neutron diffraction methods. Destructive methods, like Sachs'boring^, have also been used to measure average through thickness residualstresses. In general, the trends of the residual stress distributions obtained usingvarious experimental techniques and numerical methods agree. However, thereis conflicting information about the detailed three-dimensional (3D) distributionaround a hole that has been cold worked using the split sleeve process. Forexample, Cook and Holdway\ measured the most compressive surface residualstresses at a location that corresponds to the position of the split in the sleeveduring cold expansion. In contrast, Edwards and Wang^ found that the mostcompressive residual stresses were at a location 90° to the split in the sleeve. Inaddition, Leftheris and Schwarz^ measured the largest surface hoop strain at theposition of the split. Link and Sanford^ also noted that the greatest amount ofexpansion occurred at positions adjacent to the location of the split in the sleeve.

In this paper, results are presented where both experimental measurement andFE analysis were used to characterise the residual stress field around coldworked holes. Two experimental techniques, X-ray and the new Garcia-Sachsmethod^, which is based on Sachs' boring technique, were used. Finite elementanalysis was employed, using a material model, which takes account ofasymmetry in the material stress-strain response. Comparisons betweenexperimental measurements and FE analyses are presented and discussed. It isshown that, contrary to the conventional Sachs approach, the Garcia-Sachsmethod measured the angular variation of the residual stresses. Overall, it isshown that complementary experimental and numerical studies are required todetermine the residual stress distribution. It is demonstrated that significantdifferences in the residual stresses exist between entrance and exit faces as wellas between various angular positions around cold expanded holes.

2 Residual stress measurements

2.1 Material and SpecimensThe material used for the study was aluminium alloy Al 2650, with the chemicalcomposition, 94.55% Al, 2.76% Cu, 1.74% Mg, 0.34% Mn, 0.41% Si, 0.11% Fe,


Surface Treatment 105

0.09% Ti. The yield and tensile strength are 430 and 460 MPa respectively,Young's modulus 72 GPa, and Poisson's ratio 0.33.

SECTIONA-A'

6=16

All dimensions in mm

Figure 1: Dimensions of cold expanded specimens.

To apply residual stress measurement techniques, discs were manufacturedinitially with 32mm outside diameter and 6mm thick, and holes, 6mm indiameter, were drilled in the centre. The discs were then subjected to nominal4% cold expansion using the split-sleeve cold expansion process developed byFatigue Technology Incorporated (FTI). The location of the split in the sleeveduring cold expansion is defined as 9=0 degrees, with increasing 9 clockwise asshown in Figure 1. The cold expanded holes were then reamed to removeextraneous material generated at the location of the split in the sleeve. Fourfaces are defined on the discs, the inner disc edge, the outer disc edge, the discface corresponding to the mandrel entrance face, and the disc face at the mandrelexit.

2.2 X-ray measurementsX-ray residual stress measurements were made using a Bruker D500diffractometer using Cu K« radiation at 40 kV and 40 mA. X-ray readings weremade at the aluminium {422} peak at 137.5°, and using a position sensitivedetector to reduce data collection times. The X-ray beam was collimated to givean irradiated area of about 1x1 mm. After background subtraction, the peakposition was determined from the midpoint of a line at 70 % of the maximumpeak intensity. A stress analysis package was used to calculate stresses,assuming a biaxial stress state and employing the sinV technique^.

X-ray measurements were made on the mandrel entrance and exit faces of thediscs. Two angular positions were examined, 9=0 and 9=90°. At each angle,measurements were made at various radial locations, moving from the edge of



the central hole towards the edge of the disc, to a distance of about 3.5mm fromthe edge of the discs. Since the beam size was Ixlmm, residual stresses within0.5mm of the hole edge could not be measured. Measurements were made ofsurface hoop residual stresses, and no radial residual stress measurements weremade.

Surface hoop residual stresses are shown in Figure 2 for the mandrel exit andentrance faces, at 8=0 and 0=90°. The most compressive residual stress (-350MPa) was found about 1mm from the hole edge on the mandrel exit face atthe position of the split in the sleeve (6=0°). The least compressive hoop residualstress (about -lOOMPa) was measured on the mandrel entrance face along aradial line at 90 degrees to the position of the split in the sleeve.

C30*

CQ3138

oo

100

0

-100

-200

-300

-400

_<nn

r x-n

: •

: o

1 vV

oT f#

: #

- , , , , i

ay mea

Exit, (

Entrar

v

0T#

suremenl

)=0°

ice, 8=0°

vv

00

T7 ## _

ts

T Exit, 8=90°

v Entrance, 0=90°

v ^

0 *T#

Typical error bar on

X-Ray measurement

i

-

-

3 4 5 6 7 8

Distance from hole centre, r [mm]

Figure 2: Hoop residual stresses measured using X-ray diffraction

The results in Figure 2 show that there is a significant difference in the hoopresidual stresses on the surface of the mandrel entrance and exit faces. Residualstresses on the mandrel exit face were more compressive and differencesbetween stresses on the mandrel exit and entrance faces were more pronouncedat 90° than at 0°. For example, the largest difference between residual stresses onthe two faces is 200 MPa and 100 MPa at 90° and 0° respectively. The hoopresidual stresses also vary as a function of position around the hole and are morecompressive at 0° than at 90°.

2.3 Destructive measurementsResidual stresses were also measured using the Garcia-Sachs method^,developed from the conventional Sachs boring technique. The conventionalSachs' method*° assumes that the residual stresses are independent of angular



position. In the new method, angular variations in strain are measured. Thisrequires that strain gauges at different locations are used, and a Fourier analysisof the angular strain distribution undertaken. The detailed theoretical analysis isgiven in^.

The Garcia-Sachs method was used to measure residual stresses in the coldexpanded discs used for the X-ray measurements. To use the Garcia-Sachsmethod five strain gauges were bonded at 8=0, 45, 90, 135, and 180° on the edgeof the discs, as shown in Figure 1. The strain gauges were orientated on the edgeof the disc to measure hoop strains during boring. Cold expanded holes werebored out incrementally using a boring machine. A number of specimens weretested and a feed rate of 1 mm/sec was selected as it gave the greatestrepeatability. In performing the machining, a sharp tool and a slow cutting speedwith copious amounts of coolant were employed to minimise the possibility ofgenerating further residual stresses in the exposed surface during metal removal.For each increment of boring the strains at each of the strain gauges weremeasured. Cuts were made in increments of about 0.05 mm and readings weretaken typically every 0.2 mm increasing to up to 0.5 mm at about 6 mm from thehole edge. A micrometer was used to measure the hole diameter correspondingto each strain reading.

To determine the residual stresses from the measured strains, first a Fourieranalysis was performed on the strains. Equation (Al) describing the measuredstrain increments, r((r,8), is given in the appendix. The analysis of strain wasrestricted to the first five Fourier terms of the cosine coefficients, rj^ for n=0 to4. The residual stresses corresponding to each of the coefficients weredetermined using equations (A3) to (A5), given in the appendix for the first threecoefficients. Equations for the remaining two terms are similar to Equation (A5),and are expressed in a general form in equation (A6). The complete residualstress distribution for the hoop, aee(r,9), radial, cr,-r(r,8) and shear stresses, Tre(r,6)was found by summing the residual stress terms using equation (A2).

Results for the measured hoop, radial and shear residual stresses are shown inFigure 3. Hoop residual stresses at 9=0, 90 and 180° are shown in Figure 3a, andradial residual stresses are shown Figure 3b for the same angles. Also shown inFigure 3a are measured shear residual stresses at 9=90°. The maximumcompressive hoop residual stress occurred at 8=0°, and at about 0.5mm from theedge of the hole. It is also evident that there was a significant variation of hoopresidual stresses with angular position adjacent to the hole. For example at thehole edge the hoop residual stress varied from about -420MPa at 9=0° to-140MPa at 9=180°. This variation becomes less significant with increasingdistance away from the hole, so that at about 5.5mm from the centre of the holethe residual stresses were essentially axisymmetric.

As might be expected the radial stresses, shown in Figure 3b, also exhibited adependence on angular position. Radial stresses were entirely compressive overthe measured range and reached a maximum at about 5.5mm from the centre of ahole. The largest compressive radial residual stress of-120MPa was found at 0°and the least compressive stress of-80MPa at 180°.



"3

oo

100

0

-100

-200

-300

-400

-500

100

50

0

-50C v•2 1 -100

: (a)

Garcia-Sachsmeasurements

- - Ow, 8=0°

..v • 098,8=90°

4 5 6 7


a =-

-150

(b) Garcia-Sachs measurements__o__ er ,6=0° Q_a , 8=180°rr ' rr '

. . v • <*„ , 9=90° ..-*.. T^Q , 8=90°

^ T .^. .^-'V ?' T

4 5 6 7


Figure 3: Residual stresses measured using the new Garcia-Sachsmethod, (a) Hoop, (b)Radial and Shear

The shear residual stresses were relatively small, as shown in Figure 3b for8=90°. Although not shown a similar distribution was found at 45°. At 9=0° and180° shear residual stresses were approximately equal to zero, and are notincluded in the figure.



3 Finite Element simulations

3.1 Material and finite element modelPrevious analytical ' and finite element studies^ of the cold expansion processstress the importance of introducing an accurate material model. In particular, itis important to include the Bauschinger effect . Cyclic loading experiments,including reversed compressive loading, were carried out to obtain the materialstress-strain curve, shown in Figure 4. In the finite element analysis, threematerial models were used, isotropic hardening, kinematic hardening andcombined hardening.

500

400 r

• Experimental

FE models— Combined

KinematicIsotropic

2Strain, f [%]

Figure 4: Stress-strain behaviour for Al 2650 and FE hardening models.

The stress-strain curves for these models are also shown in Figure 4. Thecombined hardening model allows both expansion and translation of the yieldsurface and gives the best representation of the material response. The materialparameters for this model were identified iteratively.

An axisymmetric FE model was employed, similar to that used by Pavier etar\ The analysis included a simulation of the mandrel being pulled through thehole containing the sleeve. Since an axisymmetric model was used, thesimulation did not include the opening of the sleeve. The mandrel and sleevewere simulated as a rigid surface moving in the z direction as indicated in Figure1. The rigid surface included the dimensions of mandrel plus sleeve to provide a4 % radial expansion of the aluminium plate. The disc was modelled using 80by 50 (in the radial and axial directions respectively) first order, 4 nodedaxisymmetric elements. Contact elements were placed between the rigid surfacesimulating the moving mandrel and the disc. The boundary conditions wereapplied to the mandrel in 240 steps to complete an axial displacement that



allowed the mandrel to be pulled through the hole. A means of constraining thedisc from moving in the z direction during the simulation of cold expansion wasprovided by non-linear springs placed around the hole periphery. Reid and co-workers^ also used this method for constraining the disc.

cq

Q.OOSB

100

0

-100

-200

-300

-400

-500

ITypical error bar on

Sachs' measurement

Garcia-Sachs

measurement

o 8 = 90"

FE results— Combined

KinematicIsotropic

83 4 5 6 7


Figure 5: Hoop residual stresses measured using the new Garcia-Sachsmethod compared to FE axisymmetric simulations.

_ 100CQa-

-100

-200CQ3si -300

oo33

-400

-500

X-ray FE combinedo Entrance, 8=90° Entrance

• Exit, 8=90" Exit

iTypical error bar on

X-ray measurement

3 4 5 6 7 1


Figure 6: Hoop residual stresses measured using X-ray diffractioncompared to FE axisymmetric simulations.



The axisymmetric FE simulation of the cold expansion process provided theresidual stress distribution as a function of radial (r) and through thickness (z)position. The reaming process was not simulated. Previous studies have shownonly a small redistribution of residual stresses due to reaming.

3.2 ResultsThe residual stresses resulting from a 4% cold expansion are very similar thoseobtained for aluminium alloy 2024 by Pavier et al*. Reversed yielding, as aresult of unloading during the cold expansion process, was obtained adjacent tothe hole edge. This is the region where there is a significant influence of thematerial hardening model. Predicted hoop residual stresses, averaged throughthe thickness, are shown in figure 5. Results for each of the three differentmaterial models are shown. The most compressive residual stress was foundusing the isotropic model, while the least compressive residual stress wasobtained using the combined hardening material model.

As reported in previous studies^ the predicted residual stresses variedthrough the thickness of the plate. The least compressive residual stresses werefound close to the mandrel entrance face, irrespective of the material model used.In Figure 6, the FE hoop residual stresses at the mandrel entrance and exit facesare shown. These results were obtained from averaged nodal values for throughthickness depths up to 0.1 mm from the mandrel entrance and exit faces. Thedepth of O.lmm is intended to represent the maximum depth of penetration forthe X-ray measurement method.

At the mandrel entrance face the predicted near surface hoop residual stresswas approximately constant at about -lOOMPa, while at the mandrel exit face thenear surface residual stress wass much more compressive and similar to thepredicted residual stress averaged through the thickness.

4 Discussion

Measurements using X-ray and the Garcia-Sachs methods revealed an angularand through-thickness variation of the residual stresses around a cold expandedfastener hole. Both techniques show that the most compressive hoop residualstress adjacent to the hole edge at the position of the split in the sleeve usedduring cold expansion. The FE analysis cannot confirm these results since detailof the split in the sleeve was not included in the model. Nevertheless, the resultsof the axisymmetric analysis support the experimental findings whencomparisons are made between experiment and FE analysis at 0=90°.

The Garcia-Sachs method obtains residual stresses averaged through thethickness of the cold expanded discs, with measurements as a function of angleand radius. Figure 5 shows the results from measurements using this method at0=90°. This distribution is very similar to the FE predictions using the combinedhardening model. The kinematic and isotropic material models result in largerpredicted compressive residual stresses. Further away from the edge of the hole,the differences between the various models and the experimental results arerelatively small.



Near surface FE predictions and X-ray measurements of the residual stressesat 0=90° are shown in Figure 6. There is excellent agreement between results atthe mandrel entrance face, while at the exit face X-ray results face are slightlyless compressive than predicted from the FE analysis. It is notable that themeasured and predicted residual stress distributions at the mandrel exit face aresimilar to the average through thickness residual stresses.

Application of the Garcia-Sachs method illustrated the significance of theangular dependence of the residual stresses. This is not the case if the traditionalSachs method is applied. If the strains measured at each angle during boring areanalysed independently of each other using the traditional Sachs analysis,erroneous results arise. This is illustrated in Figure 7, where hoop residualstresses at 8=0° and 90° measured using the conventional and new methods areshown. The results at 0=90° indicate that the new method measured lesscompressive residual stresses than measured using the conventional method.The converse occurs at 0=0°, with less compressive residual stresses measuredusing the conventional Sachs method compared to the new method. The resultsfrom the new method are also in better agreement with the FE results, especiallywhen a combined hardening material model.

&

3

573

aooa

100

0

-100

-200

-300

-400

-500

Garcia-Sachs Conventional Sachs—o__ 8=0° —+— 8=0°..^.. 8=90° ..^..8=90°

Distance from hole centre, r [mm)Figure 7: Hoop residual stresses measured using the new Garcia-Sachs

method compared to the conventional Sachs.

The results obtained from measurements using X-ray and the Garcia-Sachsmethods confirm earlier surface residual stress measurements*. The mostcompressive hoop residual stresses were obtained at cold expanded holes usingthe split-sleeve process at 0° and the least compressive at 180°. Furthermore, theresidual stresses were shown to be a function of angular location, distancethrough the thickness and radial distance from the hole edge. The resultspresented here indicate that split-sleeve cold expansion of holes induces anasymmetric residual stress field. Importantly, the conventional Sachs method is



not able to resolve residual stress variation around a hole. Results obtained inearlier investigations , using the conventional technique to obtain the angulardistribution, are incorrect. In contrast, the new Garcia-Sachs method can be usedto calculate the angular variation of hoop, radial and shear stresses.

Concluding remarks

• Measurements of residual stresses generated during cold expansion offastener holes have been shown to be a function of position around the hole,distance through the plate thickness and radial distance from the hole edge.

• The X-ray method and a new method, called the Garcia-Sachs method, havebeen used to measure the three dimensional distribution of the residualstresses.

• Finite element analyses, utilising a combined hardening material model,were used to simulate the cold expansion process, and predict the residualstress distributions.

• Excellent agreement between the predictions and measurements wereobtained, particularly at the entrance and exit faces of the plate containingthe cold expanded hole.

Acknowledgements

This work was financially supported by a grant from the UK Department ofTrade and Industry (Air Division 4).

Appendix

Relevant equations used in the Garcia-Sachs method are given below, togetherwith relevant notation.

Notation:a Radius at which the boring process is started.b Radius at which strains are measured.

rjfj (r, 0) - A£0 (r, 0) Measured strain at radius b.

M = E Elastic constant for plane stress.

M = r- Elastic constant for plane strain.\-v

The measured strains must be described using a Fourier equation where:

»<>(r)sin(/i0) (Al)H=0 H=0

The corresponding stresses are also described using Fourier equations, where



cr»(r,0)= £aJ'''>(r)cosM+ £cH=0 M=0

(A2)

W=0 77=0The coefficients for the first three terms in the Fourier equations for the stressesare as follows:

_(o)_M62-r\(

dr

(A3)

4

T"

en ' = ( o

(A4)

cr ' =cr): /4-r-wy

-/F

'+ —2

The general solution for all the coefficients are:



n dc

(A6)

References

1. Petrak, G.J. and Stewart, R.P., "Retardation of Cracks Emanating fromFastener Holes", Engineering Fracture Mechanics, 6, pp. 275 - 282, 1974.

2. Mann, J.Y., and Jost, G.S., "Stress Fields Associated with InterferenceFitted and Cold-Expanded Holes", Metal Forum, 1983, Vol.6, No.l, pp.43-53, 1983.

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6. D.J. Smith, C.G.C. Poussard and M.J. Pavier, "An Assessment of Sach'sMethod for Measuring Residual Stresses in Cold Worked Fastener Holes",Journal Strain Analysis, Vol. 33, No. 4, pp263-274, 1998.

7. Hermann, R., "Three-dimensional stress distribution around cold expandedholes in aluminium alloys", Engineering Fracture Mechanics, Vol. 48, No.6,pp. 819-835, 1994.

8. Forgues, S.A., Bernard, M., and Bui-Quoc, T., "3D AxisymmetricNumerical Analysis and Experimental Study of the Fastener ColdworkingProcess", Computer Methods and Experimental Measurements for SurfacerreafmeMf E0Ws, pp.61-67, 1993.

9. Pavier, M.J., Poussard, C.G.C., and Smith, D.J., "A Finite ElementSimulation of the Cold Working Process for Fastener Holes", Journal of#ram /fWyjzj, Vol. 32, No.4, pp. 287-299, 1997.

10. Sachs, G., "Der Nachweis Innerer Spannungen in Stangen and Rohren",Zg c/zrz/?ywrA W/A:wWg, 19, pp. 352-357, 1927.

11. Leftheris, B.P, and Schwarz,R., "Residual Stresses in 2024-T81 AluminiumUsing Caustics and Moire Interferometry", Journal of Aircraft, Vol.24,No.7, pp. 474-476, 1987.



12. Link, R. E., and Sanford, R. J., "Residual Strains Surrounding split-SleeveCold expanded holes in 7075-T651 Aluminum", Journal of Aircraft, Vol.27, No 7, 1990.

13. Garcia-Granada,A.A., Pavier,M.J., and Smith, D.J., "A new procedure basedon Sachs' boring for measuring non-axisymmetric residual stresses" In Press,Journal of Mechanical Sciences.

14. Noyan. I.C., Cohen, J.B., "Residual Stress-Measurment by Diffraction andInterpretation", MRE, Springer-Verlag, 1987.

15. Chen,P.C.T., "The Bauschinger and hardening effect on residual stresses inan autofrettaged thick-walled cylinder" Journal of Pressure VesselTechnology, Vol. 108, pp. 108-112, 1986.

16. Ball,D.L., "Elastic-plastic stress analysis of cold expanded fastener holes"Fatigue and Fracture of Engineering Materials and Structures, Vol.18, No.l1995, pp. 47-63, 1994.

17. Bauschinger, J., "Ueber die Veranderungen der Elastizitatsgreze und derFestigkeit des Eisens und Stahls durch Strecken, Quetschen, ErwarmenAbkuhlen und durch Oftmals Wiederholte Belastung" Mitt: Mech-Tech Lab.,XIII Munchen, Germany, 1886.

18. Reid, L., Marrese, V., and Easterbrook, E.T., "Residual stress analysis ofcold expanded bushings" Procedings of the 19th Symposium of theInternatinal Committee on Aeronautical Fatigue, Edinburgh, 18-20 June1997,pp.871-882, 1997.


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