residual stress

Shot Peening Theory and Application, series ed. A. Niku-Lari,IITT-International, Gournay-Sur-Marne, France, 1990, pp. 81-93

X-RAY DIFFRACTION CHARACTERIZATIONOF RESIDUAL STRESSES PRODUCED

BY SHOT PEENING

Paul S. PrevyLambda Research

ABSTRACT

A brief overview of the theory and practice of x-raydiffraction residual stress measurement as applied toshot peened materials is presented.

The unique ability of x-ray diffraction methods todetermine both the macroscopic residual stress and thedepth and magnitude of the cold worked layerproduced by shot peening is described. The need toobtain a complete description of the subsurface residualstress distribution, in order to accurately characterizethe residual stress distributions produced by shotpeening, is emphasized.

Non-destructive surface residual stress measurementsare shown to generally be inadequate to reliablycharacterize the residual stresses produced by shotpeening. Practical applications of x-ray diffractionmethods for quality control testing are considered. Examples are presented for steel and nickel base alloys.

Keywords

X-ray diffraction, residual stress, shot peening,non-destructive

INTRODUCTION

SHOT PEENING IS COMMONLY USED to producea layer of compressive residual stress at the surface ofcomponents subject to fatigue or stress corrosionfailure. The shot peening process is controlled bymonitoring the Almen intensity. However, no simplerelationship exists between the peening intensitymeasured with the Almen strip and the residualstress-depth distribution produced. The Almen archeight depends upon the form of the residualstress-depth curve, and quite different stressdistributions can produce equivalent arc heights. Conversely, peening to the same Almen intensity with

different shot sizes will generally produce differentsubsurface residual stress distributions. The stressdistribution produced by shot peening depends uponthe properties of the material being shot peened, priorprocessing, and the specific peening parameters used. Shot peening can only be reliably controlled andoptimized by measuring the subsurface residual stressdistributions produced.

X-ray diffraction (XRD) is the most accurate and bestdeveloped method of quantifying the residual stressesproduced by surface treatments such as shot peening. XRD offers a number of advantages when compared tothe various mechanical methods, or thenon-linear-elastic ultrasonic or magnetic methodscurrently available. XRD is a linear-elastic method in which the residual stress in the material is calculatedfrom the strain measured in the crystal lattice. XRDmethods are not significantly influenced by materialproperties such as hardness, degree of cold work, orpreferred orientation. XRD is capable of high spatialresolution, on the order of millimeters and depthresolution on the order of microns, and can be appliedto a wide variety of sample geometries. Themacroscopic residual stress and information related tothe degree of cold working can be obtainedsimultaneously by XRD methods. XRD is applicableto most polycrystalline materials, metallic or ceramic,and is non-destructive at the sample surface. XRDmethods are well established, having been developedand standardized by the SAE(1) and ASTM(2).

The most common problems encountered in usingXRD techniques are due to the high precision requiredfor measurement of the diffraction angles, which in turnrequires accurate sample/instrument alignment andprecise methods of diffraction peak location(3). XRDmethods are limited to relatively fine-grained materialsand often cannot be applied to coarse-grained castings. The shallow depth of penetration of the x-ray beam, onthe order of 8 m, is an advantage for high resolutionsubsurface profiles but can be a disadvantage when

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X-Ray Diffraction Characterization of Residual Stresses Produced by Shot Peening Page -2-

trying to characterize a stress distribution produced byshot peening with only surface measurements. Rarely,extreme preferred orientation or near-surface stressgradients and associated shear stresses can cause errors.

XRD methods of residual stress measurement havebeen widely used for forty years in automotive andaerospace applications, and interest in the use of XRDstress measurement for quality control testing isincreasing. Specifications now exist requiringminimum levels of compression produced by shotpeening and limiting the tensile stresses produced byEDM and grinding. Commercial XRD residual stressmeasurement equipment, designed for both laboratoryuse and portable measurement in the field or shopenvironment, is readily available. However, a basicunderstanding of the theory and assumptions behindXRD techniques and caution in the interpretation ofthe results is necessary for reliable application.

This paper briefly describes the theory, methods, andlimitations of XRD residual stress measurement asapplied to the study of residual stress distributionsproduced by shot peening. Special mention is made ofproblems commonly encountered in both obtaining andinterpreting data from shot peened samples.

THEORY

Macroscopic Residual StressMeasurement

Because the depth of penetration of the x-ray beam isextremely shallow, the diffracting volume can beconsidered to represent a free surface under planestress. As shown in Fig. 1, the biaxial surface stressfield is defined by the principal residual and/or appliedstresses, 1 and 2, with no stress normal to the surface. The stress to be determined is the stress, , lying inthe plane of the surface at an angle, , to the maximumprincipal stress, 1. The direction of measurement isdetermined by the plane of diffraction. The stress inany direction (for any angle, ) can be determined byrotating the specimen in the x-ray beam. If the stress ismeasured in at least three different directions, theprincipal stresses and their orientation can becalculated.

Fig. 1 Plane Stress at a Free Surface

Consider the strain vector, , lying in the planedefined by the surface normal and the stress, , to bedetermined. is at an angle , to the surfacenormal, and can be expressed in terms of the stress ofinterest and the sum of the principal stresses as,

( )2121 +

+=

E

vSin

E

v

(1)

A typical metallic sample will consist of a large numberof small grains or crystals, nominally randomlyoriented, as shown schematically in Fig. 1. The crystallattice consists of planes of atoms identified by theirMiller Indices, (hkl). The spacing between a specificset of lattice planes, for example, the (211) planes in asteel, will be equal regardless of orientation relative tothe sample surface in a stress-free specimen and will beexpanded or compressed elastically by an amountdependent upon orientation by any stress present in thespecimen. The state of stress can, therefore, bedetermined by measuring the lattice spacing at differentorientations.

The only crystals which diffract x-rays are those whichare properly oriented relative to the incident anddiffracted x-ray beam to satisfy Bragg's Law,

Sindn 2=(2)

where is the x-ray wavelength, n is an integer(typically 1), is the diffraction angle, and d is thelattice spacing. XRD can be used to selectivelymeasure the lattice spacing of only those crystals of aselected phase which have a specific orientationrelative to the sample surface by measuring andcalculating d from Equation 2.




The lattice spacing can be determined for anyorientation, , relative to the sample surface by merelyrotating the specimen. It can be seen intuitively that if

is a tensile stress, the spacing between lattice planesparallel to the surface will be reduced by a Poisson'sratio contraction, while the spacing of planes tilted intothe direction of the tensile stress will be expanded. Ifwe express the strain in terms of the crystal latticespacing

o

o

d

dd =

(3)

where d is the stress-free lattice spacing, our "straingage" becomes the lattice spacing measured in thedirection , . Substituting Equation 3 into Equation 1and rearranging, the lattice spacing measured in anyorientation can be expressed as a function of thestresses present in the sample and the elastic constantsin the (hkl) crystallographic direction used for stressmeasurement,

( )( ) oo

ohkl

dd

E

vSind

E

vd

++

+

=

21

21,

(4)

It should be noted that the elastic constants in the (hkl)direction may differ significantly from the valuesobtained by mechanical testing because of elasticanisotropy and should be determined empirically(4).

0.0 0.1 0.2 0.3 0.4 0.5 0.61.2270

1.2275

1.2280

1.2285

1.2290

1.2295

1.2300

k s i5.2 1=

( )

+

=

211

h kl

ooE

dd

o

hkl

dE

vd

+=

1sin 2

d(311) vs. SIN2SHOT PEENED 5056 ALUMINUM

SIN2

Fig. 2 Linear Dependence of Lattice Spacing with Sine-Squared-Psi in Shot Peened Aluminum

Examination of Equation 4 shows that the latticespacing measured at any angle, , in the plane definedby in the surface normal, will vary linearly as afunction of Sin2. The actual lattice spacing of the(311) planes plotted as a function of Sin2 for shotpeened 5056 aluminum is shown in Fig. 2. Theintercept of the plot is equal to the unstressed latticespacing, d, minus the Poisson's ratio contractioncaused by the sum of the principal stresses. The stressis determined from the slope, knowing the elasticconstants, and the unstressed lattice spacing which isgenerally unknown. Because the value of the latticespacing measured at = 0 differs by not more than 0.1percent from the stress-free lattice spacing, theintercept can be substituted for d. The residual stresscan then be calculated without reference to a stress-freestandard.

XRD macroscopic residual stress measurementprovides the arithmetic average stress in a diffractingvolume defined by the size of the irradiated area andthe depth of penetration of the x-ray beam. Theresidual stress in that volume is assumed to be uniformboth along the surface and as a function of depth. Rapid variation of the stress within the depth ofpenetration of the x-rays is a significant source of error. The errors caused by the presence of a subsurfacestress gradient can be corrected if material is removedin thin layers by electropolishing (so as not to induceresidual stresses); and a series of measurements is madeas a function of depth. Correction may then benecessary for the stress relaxation caused byelectropolishing(5).




0 10 20 30 400

1

2

3

4

5

6 Tension Compression Ground + Tension Shot Peened + Tension

RENE 95 (420) BREADTH vs. COLD WORK420 HALF BREADTH DEGREE

COLD WORK %

Fig. 3 The Variation of the (420) Diffraction Peak Widthwith Cold Work (True Plastic Strain) for Rene 95

Line Broadening and Cold Working

When a metallic material is cold worked by a processsuch as shot peening, the crystals are severelyplastically deformed. The non-uniformity of thisplastic deformation with depth causes the compressivemacroscopic residual stresses produced by shotpeening. As the crystals are deformed, lattice defectsand dislocation tangles develop, producing microstrain(strain over the dimensions on the order of the crystallattice) and a reduction in the crystallite size (theperfect regions within the crystals which are free ofdefects).

Both the increase in microstrain and the reduction inthe crystallite size cause broadening of the diffractionpeak used for measuring the macroscopic residualstress. This line broadening information can be used toquantify the degree to which the material has beenplastically deformed by the shot peening process.

Fig. 3 shows an empirical line broadening curvedeveloped for the (420) diffraction peak of the nickelbase alloy, Rene 95. The peak half-breadth is a nearlylinear function of the amount of cold work, calculatedas the true plastic strain. Fig. 3 was developed using aseries of specimens deformed in tension, compression,and by prior grinding or shot peening followed bytension. Line broadening is independent of the mode ofdeformation and is additive as damage to the crystalstructure accumulates. Similar line broadening curves

have been developed for a variety of alloys to date. The degree to which the material has been cold workedcan be calculated from the width of the peak used forXRD residual stress measurement. The amount of coldwork, expressed as true plastic strain, can then be usedto determine the variation of such properties as yieldstrength as a function of depth after shot peening.

LIMITATIONS IN APPLICATION TOSHOT PEENED SAMPLES

Shot peened metallic alloys are nearly ideal specimensfor XRD residual stress measurement. However,problems do develop, some related to the method itself,and some related to the nature and form of the samples.

General

First, XRD methods require expensive precisionapparatus, usually computer controlled, and extensivedata processing, to reliably determine the position ofbroad diffraction peaks to the required accuracy on theorder of 0.01 deg. Technicians must be well-trainedwith an understanding of both basic crystallographyand stress analysis. These requirements may bedifficult to meet in the field or shop environment. Errors in XRD residual stress measurement may arisefrom a variety of sources and are often difficult todetect.

Second, the areas of primary interest, such as boltholes, fillets, the root area of gear teeth, dovetail slots,etc., are often inaccessible to the x-ray beam. In thesecases, sectioning is required to allow access to thesurface of interest. The likelihood of residual stressrelaxation during sectioning requires that the surface bestrain gaged without altering the near-surface residualstress distribution in order to measure the sectioningstress relaxation. Any sectioning stress relaxationwhich occurs can be calculated and used to correct theXRD results obtained on the sectioned part.

Stress Gradients

Near surface residual stress gradients, the rapid changeof residual stress with depth at the surface, is a primarysource of error(6), and impacts directly upon the use ofXRD methods for non-destructive surfacemeasurement. Many surface treatments produce




residual stress distributions which vary rapidly near thesurface of the material. Shot peening of workhardening materials, particularly after prior surfacedeformation caused by turning, grinding, etc., canproduce a pronounced "hook" in the form of a rapidincrease in compression just beneath the samplesurface. Typical subsurface residual stress gradientsare evident at the surface of the residual stress profilesshown for various methods of processing Inconel 718in Figs. 4, 5 and 6.

Fig. 4 Residual Stress and Cold Work DistributionsProduced by Abrasive Cutting of Inconel 718

0 50 100 150 200 250 300 350-1000

-800

-600

-400

-200

0

200

400

600

INCONEL 718SHOT PEENED

110 STEEL SHOT, 6-8A, 100%

RESIDUAL STRESS DISTRIBUTION

RESIDUAL STRESS MPa

DEPTH, MICRONS

0 50 100 150 200 250 300 3500

5

10

15

20

25

COLD WORK %

PERCENT COLD WORK DISTRIBUTION

DEPTH, MICRONS

Fig. 5 Residual Stress and Cold Work DistributionsProduced by Shot Peening (6-8A) Iconel 718

The rate of attenuation of the x-ray beam can bedetermined by calculating the linear absorptioncoefficient from the density and composition of thealloy. If XRD measurements are made at fineincrements of depth by electropolishing, the trueresidual stress distribution can be calculated from theapparent distribution(7). Failure to make the correctioncan lead to errors as high as 300 MPa and can evenchange the sign of the surface results. Non-destructivesurface XRD stress measurements cannot be correctedand must, therefore, be used with caution.

0 50 100 150 200 250 300 350-1000

-800

-600

-400

-200

0

200

400

600

INCONEL 718ABRASIVELY CUT

RESIDUAL STRESS DISTRIBUTION

RESIDUAL STRESS MPa

DEPTH, MICRONS

0 50 100 150 200 250 300 3500

5

10

15

20

25

COLD WORK %

COLD WORK DISTRIBUTION

DEPTH, MICRONS




0 50 100 150 200 250 300 350-1000

-800

-600

-400

-200

0

200

400

600

INCONEL 178SHOT PEENED

110 STEEL SHOT, 5-7C, 400%

RESIDUAL STRESS DISTRIBUTIONRESIDUAL STRESS MPa

DEPTH, MICRONS

0 50 100 150 200 250 300 3500

5

10

15

20

25

COLD WORK %

PERCENT COLD WORK DISTRIBUTION

DEPTH, MICRONS

Fig. 6 Residual Stress and Cold Work DistributionsProduced by Shot Peening (5-7C) Inconel 718.

Effects of Prior Processing

When employing residual stress measurement tomonitor shot peening, it is important to realize that theresidual stress distribution after shot peening willdepend not only on the peening parameters used, butalso on the prior processing of the material as well. Fig. 7 shows the near-surface residual stressdistributions produced by shot peening carburized 8620steel to 22A intensity with 230H steel shot for 200%coverage. The stress distributions are shownimmediately beneath the surface for areas on the samesample on the original surface, with a decarburizedsurface layer, and after electropolishing to remove thedecarburized layer. A reduction in surface residualstress is evident in the decarburized area, even thoughthe two areas were identically shot peened. Thepresence of the decarburized layer is evident in the(211) peak width distribution shown at the bottom ofFig. 7. Without subsurface residual stressmeasurement, the anomalous results would likely beattributed to the shot peening process rather than theprior heat treating.

0.000 0.025 0.050 0.075 0.100-1500

-1250

-1000

-750

-500

-250

0

250

LONGITUDINAL RESIDUAL STRESSDISTRIBUTION

RESIDUAL STRESS MPa

DEPTH (mm)

0.000 0.025 0.050 0.075 0.1000

2

4

6

8

DECARB/PEEN ELP/PEEN

HALF-WIDTH (deg)

(211) PEAK WIDTH DISTRIBUTION

DEPTH (mm)

Fig. 7 Residual Stress and Peak Width DistributionsProduced by Shot Peening (22A) Decarburized andElectropolished Surfaces of 8620 Steel.

Ambiguity of Surface Results

Non-destructive surface XRD residual stressmeasurement is often inadequate to characterizeresidual stresses produced by shot peening or othersurface treatments. Virtually all cold-abrasiveprocesses, such as grinding, wire brushing, polishing,sand blasting, shot peening, etc., will producecompressive surface stresses, often of comparablemagnitude. The desirable compressive residual stressdistributions produced by shot peening arecharacterized not only by the surface stress, but also bythe magnitude of the peak subsurface compressivestress and the depth of the compressive layer. Figs. 5and 6 show the residual stress and percent cold workdistributions produced by shot peening Inconel 718 to6-8A and 5-7C intensities, respectively. The surfaceresidual stresses are virtually identical, approximately-600 MPa; and the surfaces have both been cold




worked to approximately 20%. The surface stress,even on the abrasively cut specimen shown in Fig. 4,would be nearly identical if a few microns wereremoved by etching. Fig. 8 shows comparable surfaceresidual stresses developed by shot peening to an 18Aintensity and grinding the surface of the same couponof 8620 steel.

0.000 0.025 0.050 0.075 0.100-1500

-1250

-1000

-750

-500

-250

0

250

LONGITUDINAL RESIDUAL STRESS DISTRIBUTION

RESIDUAL STRESS (MPa)

DEPTH (mm)

0.000 0.025 0.050 0.075 0.1000

2

4

6

8

GROUND SHOT PEENED

HALF-WIDTH (deg)

(211) PEAK WIDTH DISTRIBUTION

DEPTH (mm)

Fig. 8 Residual Stress and Peak Width DistributionsProduced by Shot Peening (18A) and Grinding of Carburized8620 Steel.

The interpretation of surface results is furthercomplicated by the fact that the greatest variation instress will generally occur at the surface of shot peenedor machined specimens. Surface residual stressmeasurements alone are simply inadequate to properlycharacterize the residual stress distributions producedby shot peening or other surface treatments.

CONCLUSIONS

1. X-ray diffraction (XRD) residual stressmeasurement is the best developed and most accuratemethod available for the characterization of theresidual stress distributions produced by shotpeening. However, a thorough understanding of themethod and proper technique are required to achieveaccurate results. Caution is warranted in interpretingthe results obtained, particularly non-destructivesurface measurements.

2. The residual stress distributions produced by shotpeening will depend upon the priorthermal-mechanical history of the surface layers. Residual stress measurement alone may be inadequateto verify that shot peening was performed to aspecific specification. Subsurface measurement,coupled with line broadening information, offers themost reliable tool for quality control of shot peening.

3. A given level of surface compressive residualstress is a necessary, but not sufficient, condition toindicate that shot peening was performed properly. Many surface treatments other than shot peeningproduce similar levels of surface compression, as willshot peening to different Almen intensities.

4. Subsurface residual stress measurement, withcorrection for penetration of the x-ray beam andstress relaxation caused by electropolishing, isnecessary to accurately and reliably characterizeresidual stress distributions produced by shotpeening.

REFERENCES

1. Hilley, M. E., ed., "Residual Stress Measurementby X-ray Diffraction," SAE J784a, Society ofAutomotive Engineers, Warrendale, PA (1971).

2. ASTM, "Standard Method for Verifying theAlignment of X-ray Diffraction Instrumentationfor Residual Stress Measurement," E915, Vol.3.01, Philadelphia, PA, 809-812, (1984).

3. Prevy, P. S., "The Use of Pearson VIIDistribution Functions in X-Ray DiffractionResidual Stress Measurement," Adv. in X-RayAnalysis, Vol. 29, Plenum Press, NY, 103-112,(1986).




4. Prevy, P. S., "A Method of Determining theElastic Properties of Alloys in SelectedCrystallographic Directions for X-ray DiffractionResidual Stress Measurement," Adv. in X-rayAnalysis, Vol. 20, Plenum Press, NY, 345-354,(1977).

5. Moore, M. C. and EVANS, W. P.,"Mathematical Corrections for Stress inRemoved Layers in X-Ray Diffraction ResidualStress Analysis," SAE Trans., Vol. 66, (1958).

6. Hilley, M. E., ed., SAE J784a, 61, (1977).7. Koistinen, D. P. and Marburger, R. E., Trans

ASM, Vol. 51, 537, (1959).



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