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Measurement of Residual Stresses by the Hole-Drilling Strain Gage Method Table of Contents Introduction Residual Stress Fundamentals Hole-Drilling Method Principle and Theory Hole-Drilling Strain Gage Method Through-Hole Analysis Blind-Hole Analysis Determining Coefficients Introduction Experimental Calibration Residual Stress Rosettes Rosette Configurations Experimental Techniques Methods Strain Gage Selection and Installation Strain-Measurement Instrumentation Index: Residual Stress Determination http://www.measurementsgroup.com/guide/tn/tn503/503index.htm (1 of 2) [12/14/2000 11:14:21 AM]

Hole Drilling Strain Gauge Method

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Page 1: Hole Drilling Strain Gauge Method

Measurement of Residual Stressesby the Hole-Drilling Strain Gage

Method

Table of Contents

Introduction

Residual Stress Fundamentals

Hole-Drilling Method

Principle and Theory

Hole-Drilling Strain Gage Method

Through-Hole Analysis

Blind-Hole Analysis

Determining Coefficients

Introduction

Experimental Calibration

Residual Stress Rosettes

Rosette Configurations

Experimental Techniques

Methods

Strain Gage Selection and Installation

Strain-Measurement Instrumentation

Index: Residual Stress Determination

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Alignment

Boring

Mechanical Properties

Data Reduction and Interpretation

Blind Hole

Numerical Example

Sample Data

Limitations and Cautions

References

Bibliography

Additional References

Total of 36 Pages

http://www.measurementsgroup.com

A Measurements Group Hypertext Publication

Also available in printed form as Measurements Group Tech Note TN-503

Index: Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling* Strain Gage Method

Introduction

Residual Stresses and Their MeasurementResidual (locked-in) stresses in a structural material or component are thosestresses which exist in the object without (and usually prior to) the application ofany service or other external loads. Manufacturing processes are the most commoncauses of residual stress. Virtually all manufacturing and fabricating processes --casting, welding, machining, molding, heat treatment, etc. -- introduce residualstresses into the manufactured object. Another common cause of residual stress isin-service repair or modification. In some instances, stress may also be inducedlater in the life of the structure by installation or assembly procedures, byoccasional overloads, by ground settlement effects on underground structures, orby dead loads which may ultimately become an integral part of the structure.

The effects of residual stress may be either beneficial or detrimental, dependingupon the magnitude, sign, and distribution of the stress with respect to theload-induced stresses. Very commonly, the residual stresses are detrimental, andthere are many documented cases in which these stresses were the predominantfactor contributing to fatigue and other structural failures when the service stresseswere superimposed on the already present residual stresses. The particularlyinsidious aspect of residual stress is that its presence generally goes unrecognizeduntil after malfunction or failure occurs.

Measurement of residual stress in opaque objects cannot be accomplished byconventional procedures for experimental stress analysis, since the strain sensor(strain gage, photoelastic coating, etc.) is totally insensitive to the history of thepart, and measures only changes in strain after installation of the sensor.

In order to measure residual stress with these standard sensors, the locked-in stressmust be relieved in some fashion (with the sensor present) so that the sensor can

Introduction: Residual Stress Determination

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register the change in strain caused by removal of the stress. This was usually donedestructively in the past -- by cutting and sectioning the part, by removal ofsuccessive surface layers, or by trepanning and coring.

With strain sensors judiciously placed before dissecting the part, the sensorsrespond to the deformation produced by relaxation of the stress with materialremoval. The initial residual stress can then be inferred from the measured strainsby elasticity considerations. Most of these techniques are limited to laboratoryapplications on flat or cylindrical specimens, and are not readily adaptable to realtest objects of arbitrary size and shape.

X-ray diffraction strain measurement, which does not require stress relaxation,offers a nondestructive alternative to the foregoing methods, but has its own severelimitations. Aside from the usual bulk and complexity of the equipment, which canpreclude field application, the technique is limited to strain measurements in onlyvery shallow surface layers. Although other nondestructive techniques (e.g.,ultrasonic, electromagnetic) have been developed for the same purposes, these haveyet to achieve wide acceptance as standardized methods of residual stress analysis.

* Drilling implies all methods of introducing the hole (i.e., drilling, milling, air abrasion, etc).

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

The Hole-Drilling MethodThe most widely used modern technique for measuring residual stress is thehole-drilling strain gage method of stress relaxation, illustrated below.

Briefly summarized, the measurement procedure involves six basic steps:

A special three-element strain gage rosette is installed on the test part at thepoint where residual stresses are to be determined.

The three gage grids are wired and connected to a static strain indicatorthrough a switch-and-balance unit.

A precision milling guide (Model RS-200, shown above) is attached to thetest part and accurately centered over a drilling target on the rosette.

After zero-balancing the gage circuits, a small, shallow hole is drilledthrough the center of the rosette.

Readings are made of the relaxed strains, corresponding to the initial residualstress.

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Using special data-reduction relationships provided here, the principalresidual stresses and their angular orientation are calculated from themeasured strains.

The foregoing procedure is relatively simple, and has been standardized in ASTMStandard Test Method E837 (Ref. 1). Using commercially available equipment andsupplies, and adhering to the recommendations in the ASTM standard, thehole-drilling method can be applied routinely by any qualified stress analysistechnician, since no special expertise is required for making the measurements. Themethod is also very versatile, and can be performed in either the laboratory or thefield, on test objects ranging widely in size and shape. It is often referred to as a"semi-destructive" technique, since the small hole will not, in many cases,significantly impair the structural integrity of the part being tested [the hole istypically 1/32 to 3/16 in (0.8 to 4.8 mm) in both diameter and depth]. With largetest objects, it is sometimes feasible to remove the hole after testing is completed,by gently blending and smoothing the surface with a small hand-held grinder. Thismust be done very carefully, of course, to avoid introducing residual stresses in theprocess of grinding.

NOTE: In its current state of development, the hole-drilling method is intendedprimarily for applications in which the residual stresses are uniform throughout thedrilling depth, or essentially so. While the procedures for data acquisition andreduction in such cases are well-established and straightforward, seasonedengineering judgment is generally required to verify stress uniformity and othercriteria for the validity of the calculated stresses. This publication contains thebasic information for understanding how the method operates, but cannot, ofcourse, encompass the full background needed for its proper application in allcases. An extensive list of technical references is provided in the Bibliography as afurther aid to users of the method.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Principle and Theory

The Hole-Drilling Strain Gage MethodThe introduction of a hole (even of very small diameter) into a residually stressedbody relaxes the stresses at that location. This occurs because every perpendicularto a free surface (the hole surface, in this case) is necessarily a principal axis onwhich the shear and normal stresses are zero. The elimination of these stresses onthe hole surface changes the stress in the immediately surrounding region, causingthe local strains on the surface of the test object to change correspondingly. Thisprinciple is the foundation for the hole-drilling method of residual stressmeasurement, first proposed by Mathar (Ref 2).

In most practical applications of the method, the drilled hole is blind, with a depthwhich is: (a) about equal to its diameter, and (b) small compared to the thickness ofthe test object. Unfortunately, the blind-hole geometry is sufficiently complex thatno closed-form solution is available from the theory of elasticity for directcalculation of the residual stresses from the measured strains -- except by theintroduction of empirical coefficients. A solution can be obtained, however, for thesimpler case of a hole drilled completely through a thin plate in which the residualstress is uniformly distributed through the plate thickness. Because of this, thetheoretical basis for the hole-drilling method will first be developed for thethroughhole geometry, and subsequently extended for application to blind holes.

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Principle and Theory: Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Through-Hole AnalysisDepicted below is a local area within a thin plate which is subject to a uniformresidual stress, .

Stress states at ( , ) before the introduction of a hole.

The initial stress state at any point ( , ) can be expressed in polar coordinatesby:

(1a)

(1b)

(1c)

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(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Represented below is the same area of the plate after a small hole has been drilledthrough it.

Stress states at ( , ) after the introduction of a hole.

The stresses in the vicinity of the hole are now quite different, since , and must be zero everywhere on the hole surface. A solution for this case was obtainedby G. Kirsch in 1898, and yields the following expressions for the stresses at thepoint ( , ) : (Ref. 3)

(2a)

(2b)

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(2c)

where:

= hole radius

= arbitrary radius from hole center

Subtracting the initial stresses from the final (after drilling) stresses gives thechange in stress, or stress relaxation at point ( , ) due to drilling the hole.That is:

(3a)

(3b)

(3c)

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Substituting Eqs. (1) and (2) into Eqs. (3) yields the full expressions for the relaxed(or relieved) stresses. If the material of the plate is homogeneous and isotropic inits mechanical properties, and linear-elastic in its stress/strain behavior, theseequations can then be substituted into the biaxial Hooke's law to solve for therelieved normal strains at the point ( , ). The resulting expressions are asfollows:

(4a)

(4b)

The preceding equations can be written in a simpler form, demonstrating that alonga circle at any radius ( > ) the relieved radial and tangential strains vary in asinusoidal manner:

(5a)

(5b)

Comparison of Eqs. (5) with Eqs. (4) demonstrates that coefficients , , and have the following definitions:

(6a)

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(6b)

(6c)

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Thus, the relieved strains also vary, in a complex way, with distance from the holesurface. This variation is illustrated below, where the strains are plotted along theprincipal axes, at = 0 deg and = 90 deg.

Variation of relieved radial and tangential strains with distance (along theprincipal axes) from the center of the drilled hole -- uniaxial residual stress.

As shown by the figure, the relieved strains generally decrease as distance from thehole increases. Because of this, it is desirable to measure the strains close to theedge of the hole in order to maximize the strain gage output signal. On the otherhand, parasitic effects also increase in the immediate vicinity of the hole. These

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considerations, along with practical aspects of strain gage design and application,necessitate a compromise in selecting the optimum radius ( ) for gage location.Analytical and experimental studies have established a practical range of 0.3 < <0.45 where and is the radius to the longitudinal center of the gage.

It can be noticed from the illustration that for (along the axis of the majorprincipal stress) the relieved radial strain, , is considerably greater than thetangential strain, , in the specified region of measurement. As a result,commercial strain gage rosettes for residual stress analysis are designed withradially oriented grids to measure the relieved radial strain, . This being thecase, only Eq. (5a) is directly relevant for further consideration. It is also evidentfrom the figure that the relieved radial strain along the major principal axis isopposite in sign to the initial residual stress. This occurs because the coefficients and in Eq. (5a) are always negative, and (for ) cos .

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

The preceding treatment considered only the simplest case, uniaxial residual stress.In practice, however, residual stresses are more often biaxial, with two nonzeroprincipal stresses. This condition can readily be incorporated in the analysis byemploying the superposition principle, which is applicable to linear-elastic materialbehavior. Referring to the uniaxial stress state before and after the introduction of ahole, it is apparent that had the uniaxial residual stress been along only the axisinstead of the axis, Eqs. (1) and (2) would still apply, with cos replaced bycos , or by the equivalent, -cos . Thus, the relieved radial strain atthe point ( , ) due to uniaxial residual stress in only the direction can bewritten as:

(7)

And, employing the corresponding notation, Eq. (5a) becomes:

(8)

When both residual stresses are present simultaneously, the superposition principlepermits algebraic addition of Eqs. (7) and (8), so that the general expression for therelieved radial strain due to a plane biaxial residual stress state is:

(9a)

Or, in a slightly different form,

(9b)

Equations (9) represent the basic relationship underlying the hole-drilling methodof residual stress analysis. This relationship must be inverted, of course, to solve

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for the two principal stresses and the angle in terms of the measured strains thataccompany stress relaxation. Since there are three unknown quantities, threeindependent measurements of the radial strain are required for a complete solution.These three measurements can be substituted successively into Eq. (9a) or Eq. (9b)to yield three equations which are then solved simultaneously for the magnitudesand directions of the principal stresses.

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

The common procedure for measuring the relieved strains is to mount threeresistance strain gages in the form of a rosette around the site of the hole beforedrilling. Such a rosette is shown schematically below, where three radially orientedstrain gages are located with their centers at the radius from the center of thehole site.

Strain gage rosette arrangement for determining residual stress.

Although the angles between gages can be arbitrary (but must be known), a45-degree angular increment leads to the simplest analytical expressions, and thushas become the standard for commercial residual stress rosettes. As indicatedabove, is the acute angle from the nearer principal axis to gage no. 1, while

and , with positive angles measured in the

direction of gage numbering. It should be noted that the direction of gagenumbering for the rosette type sketched above is clockwise, since gage no. 2,

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although physically at position 2a, is effectively at position 2b for gage numberingpurposes. Equations (9) can be used to verify that both locations for gage no. 2produce the same result providing the residual stress is uniform over the area lateroccupied by the hole. For general-purpose applications, location 2a is usuallypreferred, since this provides strain sampling around the hole circumference. Whenspace for the gage is limited, as in measuring residual stresses near a weld orabutment, location 2b permits positioning the hole closest to the area of interest.

Equation (9b) can now be written three times, once for each gage in the rosette:

(10a)

(10b)

(10c)

When Eqs. (10) are solved simultaneously for the principal stresses and theirdirection, the results can be expressed as:

(11a)

(11b)

where is the angle from the nearer principal axis to gage no. 1 (in the direction ofgage numbering, if positive; or opposite, if negative).

Reversing the sense of to more conveniently define the angle from gage no. 1 tothe nearer axis, while retaining the foregoing sign convention,

(11c)

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(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

The following important comments about Eqs. (11) should be carefully noted.These equations are very similar in appearance to the data-reduction relationshipsfor conventional strain gage rosettes, but the differences are significant. Thecoefficients A and B not only incorporate the elastic properties of the test material,but also reflect the severe attenuation of the relieved strains relative to the relaxedstress. It can be observed, in addition, that the signs between terms in Eqs. (11a)and (11b) are opposite to those in the conventional rosette equations. This occursbecause and are always negative; and thus, since Eq. (11a) is algebraicallygreater than Eq. (11b), the former must represent the maximum principal stress.

Equation (11c) is identical to that for a conventional three-element rectangularrosette, but must be interpreted differently to determine which principal stress isreferred to gage no. 1. The following rules can be used for this purpose:

: refers to

: refers to

: = +

: at +

: at -

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Careful consideration must also be given to determining the appropriate values forcoefficients and . As defined algebraically in Eqs. (6), they apply only whenthe conditions imposed by the Kirsch solution are met. This solution gives thestress distribution at points with coordinates ( , ) around a circular hole througha thin, wide plate subjected to uniform plane stress. However, comparing thevariation in relieved strains with the strain gage arrangement illustrates that, sincethe strain gage grids in the rosette have finite areas, they sense varying straindistributions. Thus, the output of each gage tends to represent the average strainover the area of the grid. Moreover, because the grids are usually composed ofparallel lines, those lines which are not directly on the centerline of a radiallyoriented grid are not radial. Therefore, the gages are slightly sensitive to thetangential strain, as well as the radial strain. As a result, more accurate values forthe coefficients can be obtained by integrating Eqs. (4) over the areas of therespective gage grids. The coefficients thus determined, which account for thefinite strain gage area, are designated here by and to distinguish them fromthe values at a point as defined by Eqs. (6). An alternative method for obtaining and is to measure them by experimental calibration. The procedure for doing sois described in Section III, "Determining Coefficients and ." When performedcorrectly, this procedure is potentially the most accurate means for evaluating thecoefficients.

When employing conventional strain gage rosettes for experimental stress analysis,it is usually recommended that the strain measurments be corrected for thetransverse sensitivity of the gages. Correction relationships for this purpose aregiven in Measurements Group Tech Note TN-509, Errors Due to TransverseSensitivity in Strain Gages. These relationships are not directly applicable,however, to the relieved strains measured with a residual stress rosette by thehole-drilling method.

In the residual stress case, the individual gages in the rosette are effectively atdifferent locations in a spatially varying strain field. As a result, the relieved axialand transverse strains applied to each gage are not related in the same manner asthey are in a uniform strain field. Rigorous correction would require evaluation of

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the coefficient [actually, its integrated or calibrated counterpart, -- see Eqs.(6)], for both the through-hole and blind-hole geometries. Because of theforegoing, and the fact that the transverse sensitivities of Micro-Measurementsresidual stress rosettes are characteristically very low (approximately 1%), it is notconsidered necessary to correct for transverse sensitivity. Kabiri, (Ref 4) forexample, has shown that the error due to ignoring transverse sensitivity (in the caseof uniaxial residual stress) is negligible compared to the remaining uncertainties inthe measurement and data-reduction procedures.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Blind-Hole AnalysisThe theoretical background for the hole-drilling method was developed in thepreceding treatment on the basis of a small hole drilled completely through a thin,wide, flat plate subjected to uniform plane stress. Such a configuration is far fromtypical of practical test objects, however, since ordinary machine parts andstructural members requiring residual stress analysis may be of any size or shape,and are rarely thin or flat. Because of this, a shallow "blind" hole is used in mostapplications of the hole-drilling method.

The introduction of a blind hole into a field of plane stress produces a verycomplex local stress state, for which no exact solution is yet available from thetheory of elasticity. Fortunately, however, it has been demonstrated by Rendler andVigness (Ref. 5) that this case closely parallels the through-hole condition in thegeneral nature of the stress distribution. Thus, the relieved strains due to drilling theblind hole still vary sinusoidally along a circle concentric with the hole, in themanner described by Eqs. (9). It follows, then, that these equations. as well as thedata-reduction relationships in Eqs. (11) are equally applicable to the blind-holeimplementation of the method when appropriate blind-hole coefficients and are employed. Since these coefficients cannot be calculated directly fromtheoretical considerations, they must be obtained by empirical means; that is, byexperimental calibration or by numerical procedures such as finite-elementanalysis.

Compared to the through-hole procedure, blind-hole analysis involves oneadditional independent variable; namely, the dimensionless hole depth, (seebelow).

Thus, in a generalized functional form, the coefficients can be expressed as:

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(12a)

(12b)

For any given initial state of residual stress, and a fixed hole diameter, the relievedstrains generally increase (at a decreasing rate) as the hole depth is increased.Therefore, in order to maximize the strain signals, the hole is normally drilled to adepth corresponding to at least = 0.4 (ASTM E837 specifies = 0.4 forthe maximum hole depth).

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

The general variation of relieved strain with depth is illustrated below, where thestrains have been normalized, in this case, to 100% at = 0.4.

Relieved strain versus ratio of hole depth to gage circle diameter (strainsnormalized to 100% at = 0.4).

The data include experimental results from two different investigatorsdemonstrating the manner in which the relieved-strain function is affected by theratio of hole diameter to gage circle diameter ( ). Both cases involveuniform uniaxial (plane) stress, in specimens which are thick compared to the

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maximum hole depth. The curves plotted in the figure are considered representativeof the response to be expected when the residual stress is uniform throughout thehole depth.

An important contribution of the Rendler and Vigness work is the demonstrationthat, for any given set of material properties, and , coefficients and aresimply geometric functions, and thus constants for all geometrically similar cases.This means that once the coefficients have been determined for a particular rosetteconfiguration, the rosette size can be scaled upward or downward and the samecoefficients will still apply when the hole diameter and depth are similarly scaled(assuming, of course, the same material). Several different approaches have beentaken in attempting to remove the material dependency from and , leaving onlythe geometric dependence. One of these, proposed by Schajer (Ref. 7) is adopted inthis publication. Schajer introduced two new coefficients, denoted here as and

, and defined as follows:

(13a)

(13b)

By comparison with Eqs. (6), it can be seen that for the through hole, at least ismaterial-independent, and depends only weakly on Poisson's ratio. Schajer hasdetermined from finite-element calculations that for blind holes, and vary byless than 2% for the range of Poisson's ratio from 0.25 to 0.35.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Determining Coefficients and

IntroductionWhether the residual stress analysis application involves through-hole or blind-holedrilling, the coefficients and (or and ) must be determined to calculate thestresses from the relieved strains. In the case of the through hole, reasonablyaccurate values of the coefficients can be obtained for any particular case byanalytical means, if desired. This is done by integrating, over the area of the gagegrid, the component of strain parallel to the primary strain-sensing axis of the gage.Given the details of the grid geometry (line width and spacing, number of lines,etc.), slightly greater accuracy may be obtained by integrating along the individualgrid lines. This method cannot be applied to blind-hole analysis becauseclosed-form expressions relating the relieved strains to the residual stress, in termsof hole depth, are not available.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Experimental CalibrationThe needed coefficients for either through-hole or blind-hole analysis can alwaysbe determined by experimental calibration. This procedure is particularly attractivesince it automatically accounts for the mechanical properties of the test material,strain gage rosette geometry, hole depth and diameter, and the strain-averagingeffect of the strain gage grid. When performed correctly, with sufficient attention todetail, it is potentially the most accurate means for determining the coefficients. Itsprincipal disadvantage is that the calibration must be repeated each time a differentset of geometric parameters is involved.

Calibration for and is accomplished by installing a residual stress strain gagerosette on a uniaxially stressed tensile specimen which is made from the samematerial as the test part. The rosette should be oriented to align grid no. 3 parallelto the loading direction, placing grid no. 3 along the transverse axis of thespecimen. Care must be taken that the tensile stress is uniform over the crosssection of the test specimen; i.e., that bending stress is negligible. To minimizeedge and end effects, the specimen width should be at least ten times the holediameter, and the length between machine grips, at least five times the width.When determining and for blind-hole applications, a specimen thickness offive or more times the hole diameter is recommended. For through-hole calibration,the thickness of the calibration specimen is preferably the same as that of the testpart. It is also important that the maximum applied stress during calibration notexceed one-half of the proportional limit stress for the test material. In any case, theapplied stress plus the initial residual stress must be low enough to avoid the risk oflocal yielding due to the stress-concentrating effect of the hole.

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Basically, the calibration procedure involves measuring the rosette strains under thesame applied load or calibration stress, , both before and after drilling the hole.Such a procedure is necessary in order to eliminate the effect of the strain reliefwhich may occur due to the relaxation of any initial residual stress in thecalibration specimen. With this technique, the observed strain difference (beforeand after hole drilling) is caused only by the applied calibration stress, and isuniquely related to that stress. The steps in the calibration procedure can besummarized briefly as follows, noting that the strains in only grid no. 1 and grid no.3 need to be measured, since these grids are known to be aligned with the principalaxes of the specimen.

Zero-balance the strain gage circuits.1.

Apply a load, , to the specimen to develop the desired calibration stress,.

2.

Measure strains and (before drilling).3.

Unload the specimen, and remove it from the testing machine.4.

Drill the hole, as described in "Experimental Techniques".5.

Replace the specimen in the testing machine, re-zero the strain gage circuits,and then reapply exactly the same load, .

6.

Measure strains and (after drilling).7.

The calibration strains corresponding to the load, , and the stress, , are then:

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(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Calibration reliability can ordinarily be improved by loading the specimenincrementally and making strain measurements at each load level, both before andafter drilling the hole. This permits plotting a graph of , versus and , sothat best-fit straight lines can be constructed through the data points to minimizethe effect of random errors. It will also help identify the presence of yielding, if thatshould occur. The resulting relationship between the applied stress and the relievedstrain is usually more representative than that obtained by a single-pointdetermination.

Since the calibration is performed with only one nonzero principal stress, Eq. (5a)can be used to develop expressions for the calibrated values of and .Successively substituting = 0 deg (for grid no. 1) and = 90 deg (for grid no. 3)into Eq. (5a):

Solving for and ,

(14a)

(14b)

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

The procedure described here was applied to a through-hole specimen made from304 Stainless Steel, and the calibration data are plotted below.

Stress versus relieved strains for calibration of coefficients and on 304Stainless Steel (through-hole).

It can be seen from the figure that for this geometry ( = 0.35) and material, and are -90 microstrain and +39 microstrain, respectively, when is

10 000 psi (69 MPa). Substituting into Eqs. (14),

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(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Although the preceding numerical example referred to the through-holecoefficients, the same procedure is followed in calibrating for full-depth blind-holecoefficients. Once and have been obtained in this manner, the correspondingmaterial-independent coefficients, and , can be calculated from Eqs. (13) if theelastic modulus and Poisson's ratio of the test material are known. If desired, theprocedure can then be repeated over the practical range of to permitplotting curves of and for all cases of interest.

It should be noted that the values for the basic coefficients and obtained froma particular calibration test are strictly applicable only for residual-stressmeasurement conditions which exactly match the calibration conditions:

material with the same elastic properties.●

same rosette geometry (but rosette orientation is arbitrary).●

same hole size.●

same hole form (through hole or full-depth blind hole).●

uniform stress with depth.●

nominally uniform in-plane stress at the hole.●

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Coefficients for Micro-Measurements Residual Stress RosettesMicro-Measurements supplies special strain gage rosettes for residual stressanalysis in three basic configurations. Among other features, these rosette designsincorporate centering patterns for positioning the boring tool precisely at the centerof the gage circle. All RE and UL designs have geometrically similar gridconfigurations, with the gage-circle diameter equal to 3.25 times the active gagelength. The 062RE rosette, for example, has a gage-circle diameter of 0.202 in, or5.13 mm. Because of this similitude, the same material-independent coefficients and apply to all sizes of the RE rosette, and to the 062UL rosette, forgeometrically similar holes (i.e., for the same and ratios). The062UM rosette configuration has the same ratio of gage circle to grid length, butthe grids are narrower to permit their close grouping on one side of the hole. As aresult, the sensitivity of the gage to the relieved strains is slightly greater, andcoefficients specific to the 062UM are required for data reduction.

The and coefficients for Micro-Measurements residual stress rosettes areprovided graphically below, where the solid lines apply to full-depth blind holesand the dashed lines to through holes assuming, in both cases, that the initialresidual stress is uniform with depth. Through-hole coefficients for RE and ULrosettes were obtained by numerically integrating the expressions, for the relievedlongitudinal strains along the individual gridlines, as previously described. Becauseblind-hole coefficients cannot be calculated in the same manner, these have beendetermined for the RE and UL rosettes by both experimental calibration and finiteelement analysis (Refs. 5, 7, 8). Although results typically differ slightly from oneinvestigator to the next, the curves plotted in (a) are considered representative ofthe subject rosettes, and suitable for use in data reduction. Coefficients for the062UM rosette, calculated by extrapolation from the RE/UL data, are given in (b).

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Data-reduction coefficients and versus dimensionless hole diameter (typical) for Measurements Group residual stress rosettes.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Experimental Techniques

MethodsAs in all experimental methods, proper materials, application procedures, andinstrumentation are essential if accurate results are to be obtained. The accuracy ofthe hole-drilling method is dependent chiefly upon the following technique-relatedfactors:

strain gage selection and installation.●

hole alignment and boring.●

strain-indicating instrumentation.●

understanding the mechanical properties of the test material.●

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Strain Gage Selection and InstallationInstalling three individual strain gages, accurately spaced and oriented on a smallcircle, is neither easy to do nor advisable, since small errors in gage location ororientation can produce large errors in calculated residual stresses. Theconfigurations of the residual stress rosettes have been designed and developed bythe Micro-Measurements Division specifically for residual stress measurement.The rosette designs incorporate centering marks for aligning the boring toolprecisely at the center of the gage circle, since this is critical to the accuracy of themethod (Refs. 9, 10, 11). All configurations are available in a range of temperaturecompensations for use on common structural metals. However, only the RE designis offered in different sizes (031RE, 062RE, and 125RE), where the three-digitprefix represents the gage length in mils [0.001 in (0.0254 mm)]. The RE design isavailable either open-faced or with Option SE (solder dots and encapsulation).

The UL and UM configurations are supplied in 1/16 in (1.6mm) gage length, andboth types are fully encapsulated. Both configurations have integral, copper-coatedsolder tabs, and offer all advantages of the popular C-Feature strain gage series. Allresidual stress rosettes are constructed with self-temperature-compensatedconstantan foil, mounted on a flexible polyimide carrier. Gage resistance is 120ohms +0.4%.

Surface preparation for installing the rosettes is basically standard, as described inMeasurements Group Instruction Bulletin B-129, Surface Preparation for StrainGage Bonding. Caution should be observed, however, in abrading the surface ofthe test object, since abrasion can alter the initial state of residual stress (Ref. 12).In general, it is important that all surface-preparation and gage-installationprocedures be of the highest quality, to permit accurate measurement of the smallstrains typically registered with the hole-drilling method. As evidenced by thecalibration data, the relieved strains corresponding to a given residual stressmagnitude are considerably lower than those obtained in a conventionalmechanical test at the same stress level. Because of the small measured strains, anydrift or inaccuracy in the indicated gage output, whether due to improper gageinstallation, unstable instrumentation, or otherwise, can seriously affect thecalculated residual stresses.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Strain-Measurement InstrumentationThe residual stress rosettes described previously impose no special instrumentrequirements. When measurements are to be made in the field, a portable,battery-operated static strain indicator, supplemented by a precisionswitch-and-balance unit, is ordinarily the most effective and convenientinstrumentation. The Measurements Group Model P-3500 Strain Indicator andSB-10 Switch-and-Balance Unit are ideally suited for this type of application. Inthe laboratory it may be convenient to use a computerized automatic data systemsuch as the Measurements Group System 5000, which will rapidly acquire andrecord the data in an organized, readily accessible form. A special off-lineWindows-based computer program (RESTRESSTM) is also available to performand calculate residual stress magnitudes in accordance with ASTM E837. The database for the program includes values of the coefficients and for blind holes,and covers the full range of recommended hole dimensions applicable to allMicro-Measurements residual stress rosettes.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

AlignmentRendler and Vigness observed that "the accuracy of the (hole-drilling) method forfield applications will be directly related to the operator's ability to position themilling cutter precisely in the center of the strain gage rosette." More recent studieshave quantified the error in calculated stress due to eccentricity of the hole. Forexample, with a hole which is 0.001 in (0.025 mm) off-center of the 062RE or062UL rosette, the error in calculated stress does not exceed 3% (for a uniaxialstress state) (Refs. 9, 10, 11). In practice, the required alignment precision to within0.001 in (0.025 mm) is accomplished using the RS-200 Milling Guide shownbelow.

The milling guide is normally secured to the test object by bonding its three footpads with a quick-setting, frangible adhesive. A microscope is then installed in theunit and visual alignment is achieved with the aid of the four X-Y adjustmentscrews on the exterior of the guide.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

BoringNumerous studies on the effects of hole size and shape and machining procedureshave been published. Rendler and Vigness specified a specially dressed end millwhich is compatible with the residual stress rosettes. The end mill is ground toremove the side cutting edges, and then relieved immediately behind the cuttingface to avoid rubbing on the hole surface. It is imperative that the milling cutter berigidly guided during the drilling operation so that the cutter progresses in a straightline, without side pressure on the hole, or friction at the noncutting edge. These endmills generate the desired flatbottomed and square-cornered hole shape at initialsurface contact, and maintain the appropriate shape until the hole is completed. Indoing so, they fulfill the incremental drilling requirements as stipulated in ASTME837. Specially dressed end mills offer a direct and simple approach whenmeasuring residual stresses on readily machinable materials such as mild steel andsome aluminum alloys. The RS-200 Milling Guide with the microscope removedand the end-mill assembly in place is shown below.

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The end mill is driven through the universal joint at the top of the assembly, byeither a hand drill or variable-speed electric drill.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

In 1982, Flaman (Ref. 13) first reported excellent results for residual stressmeasurement using a high-speed (up to 400 000 rpm) air turbine and carbidecutters. This technique maintains all of the advantages (good hole shape,adaptability to incremental drilling, etc.) of the specially dressed end mill whileproviding for easier operation and more consistent results. Further, the air turbine ishighly recommended for use with test materials that are difficult to machine, suchas 304 Stainless Steel. Carbide cutters are not effective for penetrating glass, mostceramics, very hard metals, etc.; but diamond cutters have shown promise on thesekinds of test materials. The air turbine/carbide cutter assembly installed in the samebasic RS-200 Milling Guide is shown below.

Bush and Kromer (Ref. 14) reported, in 1972, that stress-free holes are achievedusing abrasive jet machining (AJM). Modifications and improvements were made

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to AJM by Procter and Beaney, (Ref. 10) and by Bynum (Ref. 15). Wnuk (Ref. 16)experienced good results by mechanically adapting AJM apparatus for use in theRS-200 Milling Guide. The principal advantage of AJM is its reported ability togenerate stress-free holes in virtually all materials. Its chief limitations center aboutthe considerable changes in hole shape as a function of hole depth. The initialshape is saucerlike, and the final is cylindrical with slightly rounded comers.During drilling there is also uncertainty as to the actual hole depth at any stage.These factors make AJM a less practical technique for determining the variation ofrelieved strain with hole depth, as recommended in ASTM E837.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Mechanical PropertiesAs in any form of experimental stress analysis, the accuracy of residual stressmeasurement is limited by the accuracies to which the elastic modulus andPoisson's ratio are known. But typical uncertainties in the mechanical properties ofcommon steel and aluminum alloys are in the neighborhood of 1 to 3% and, assuch, are minor contributors to potential errors in residual stress analysis. Muchlarger errors can be introduced by deviations from the assumptions involved in thebasic theory, as described previously. A key assumption, for instance, islinear-elastic material behavior. If the stress/strain relationship for the test materialis nonlinear, due to yielding or other causes, the calculated residual stresses will bein error.

When the initial residual stress is close to the yield strength of the test material, thestress concentration caused by the presence of the hole may induce localizedyielding. It is therefore necessary to establish a threshold level of residual stressbelow which yielding is negligible. This problem has been studied bothexperimentally and analytically, and there is substantial agreement among thedifferent investigations (Refs. 10, 17, 18). That is, errors are negligible when theresidual stress is less than 70% of the proportional limit of the test material -- forboth blind holes and through holes. On the other hand, when the initial residualstress is equal to the proportional limit, errors of 10 to 30% (and greater) have beenobserved. The error magnitude obviously depends on the slope of the stress/straindiagram in the post-yield region; and tends to increase as the curve becomes flatter,approaching the idealized perfectly plastic behavior (Ref. 18).

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Data Reduction and Interpretation

Blind HoleAs recommended in ASTM E837, it is always preferable to drill the hole in smallincrements of depth, recording the observed strains and measured hole depth ateach increment. This is done to obtain data for judging whether the residual stressis essentially uniform with depth, thus validating the use of the standard full-depthcoefficients and for calculating the stress magnitudes. If incrementalmeasurements are not taken, there is no means for making references about stressuniformity, and the calculated residual stress may be considerably in error. In suchcases, when the stress varies with depth, it should be realized that the calculatedstress is always lower than the actual maximum.

There is currently no absolute criterion for verifying stress uniformity from thesurface of the test piece to the bottom of a full-depth hole. However, theincremental data, consisting of relieved strain versus hole depth, can be used in twodifferent ways to aid in detecting a nonuniform stress distribution. The first of theseis to calculate, for each depth increment, the sums and differences of the measuredstrain data, and respectively (Ref. 1). Express each set of data asfractions of their values when the hole depth equals 0.4 times the mean diameter ofthe strain gage circle. Plot these percent strains versus normalized hole depth.These graphs should yield data points very close to the curves shown below.

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Percent strain versus normalized hole depth for uniform stress with depth (Ref. 1).

Data points which are removed from the curves shown above indicate eithersubstantial stress nonuniformity or strain measurement errors. In either case, themeasured data are not acceptable for residual stress calculations using thefull-depth coefficients and .

When a principal residual stress direction is closer to the axial direction of gage no.2 in the strain gage rosette arrangement than to either gage nos. 1 or 3, the strainsum , will be numerically larger than . In such a case, thepercent strain data check should be done using instead of .

NOTE: This graphical test is not a sensitive indicator of stress field uniformity.Specimens with significantly nonuniform stress fields can yieldpercentage-relieved-strain curves substantially similar to those shown above. Themain purpose of the test is to identify grossly nonuniform stress fields. Further, thegraphical comparison test using or becomes ineffective whenthe residual stress field approaches equal biaxial tension or compression (

) as expected in surface blasting and heat treating procedures.

Comparison to the plot is ineffective when (pure shear);

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however, this condition is relatively uncommon in the practical industrial setting.

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Preliminary judgments concerning the likely stress distribution, based on the percent-strain-relieved plot, can be supplementedwith additional analysis of the incremental data. This is done by calculating, at each depth increment, the equivalent uniform(E-U) principal residual stresses. By definition, the E-U stress is that stress magnitude which, if uniformly distributed, wouldproduce the same total relieved strain, at any depth, as measured during hole drilling.

In order to calculate the E-U stresses at each increment, the uniform-stress coefficients and , as functions of hole depth,must be available. These have been determined by Schajer (Ref. 23), based on finite-element studies. The partial-depthcoefficients obtained by Schajer have been plotted against the dimensionless hole depth, , for different values of thediameter ratio, , as shown below. When it is known that the residual stress is uniform with depth, the coefficientsapplicable to any combination of and can, in principle, be read directly from the graphs shown below and used tocalculate the residual stress by substitution into Eqs. (13) and then into Eqs. (11). In practice, however, drilling is normallycontinued to the full-hole depth ( = 0.4) as recommended in ASTM E837, since the relieved strains are greater and can bemeasured more accurately. Moreover, the full-depth coefficients for uniform stress are known quite reliably from numerousexperimental calibrations.

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Data-reduction coefficients and for RE and UL rosettes, as functions of nondimensional hole depth and diameter. Thecoefficients are derived from finite-element studies by Schajer (Ref. 23) for uniform stress with depth, and are used here to

calculate equivalent uniform stress.

When the residual stress apparently varies with depth, the stresses at partial depths (calculated with the coefficients shownabove) do not represent the actual residual stress, but the equivalent uniform stress (from the surface to depth ) which wouldproduce the same relieved strain at that depth. As demonstrated by the following numerical example, however, tabulation of thecalculated E-U stresses can provide at least qualitative information about the stress variation with depth. Furthermore, for thefirst small increment of depth, the calculated E-U stress is the best available estimate of the actual average stress in that layer.The E-U stresses calculated for the second and subsequent depth increments are ever less subject to quantitative interpretation.This is so because the cumulative relieved strain at any depth is affected in a complex way by the relaxed stresses at all lesserdepths.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Numerical Example of Data-Reduction Procedures*

A Micro-Measurements strain gage rosette, type CEA-062UL-120, was applied to

a cold-rolled steel bar. Elastic properties of the material are: = 29.5 x 106 psi,and = 0.29. Using the RS-200 Milling Guide and the High-Speed Accessory, a0.070-in diameter hole was drilled incrementally to a depth of 0.081 in. Since thegage circle diameter of the subject rosette is 0.202 in, the diameter ratio =0.347 for this example. The measured depths and strains for all increments arelisted in Columns 1 and 3 of Table 1.

The next step is to calculate the relieved strain parameters ( ) and ()** at each depth increment as shown in Columns 4-6 of Table 1. For this purpose,the strain parameters at the "full-depth" hole are defined as the 100% relievedstrain parameters.

Thus, at = 0.4 (full depth):

Columns 4-6 of Table 1

To calculate the percent relieved strain parameters (or normalized parameters) at = 0.050, for example:

Columns 4-6 of Table 1

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These and all other normalized strain parameters are listed in Columns 4-6 of Table1. As recommended in ASTM E837 the normalized strains are plotted versus (see below) for comparison with the uniform stress response. The experimentalpoints, ( ) in particular, fall well off the uniform stress response, andnonuniform stress is indicated.

Normalized relieved strains (from numerical example), compared to ASTM E837uniform stress response.

Purely for demonstration purposes, the residual stress will first be calculated usingonly the maximum measured strains at the full-hole depth (0.081 in). The resultingstresses are those which would be inferred (erroneously) from the strain data by anexperimenter who ignored the implications of Fig. 12, and assumed a uniformstress distribution.

Coefficients and for the full-depth hole can be read from Fig. 8a at thespecified value of = 0.347. Interpolating from the graph for the RE/UL

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rosettes:

= 0.147,

= 0.372

Substituting these values and the elastic properties of the steel into Eqs. (13):

Then, substituting 4 , 4 and the measured strains at = 0.4 (from Column3, Table 1) into Eqs. (11) yields:

= -33 deg from gage no. 1 to , since

= +25 000 psi

= +12 000 psi

* For simplicity and clarity in the presentation of this example, numerical values are given inU.S. customary units only. The procedure is, of course, unaffected by the units used.

** Use rather than when the direction angle ( ) is

(see ASTM E837).

(continued...)

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

The data in the first six columns of Table 1 will now be used, in conjunction withthe coefficients to calculate the equivalent uniform stresses at each increment ofdepth. This procedure will provide additional insight into the stress variation withdepth, and will yield an estimate of the average stress in the first increment.Calculations are performed as follows, starting with the first increment, for which

= 0.025.

Interpolating carefully from the data reduction coefficients (for = 0.347and = 0.025):

= 0.016,

= 0.030

Substituting these values along with the elastic constants, into Eqs. (13) as before:

The latter results are recorded in Columns 7 and 8 of Table 1, and the procedure isrepeated for all remaining depth increments. The equivalent uniform principalstresses and their direction can then be calculated at each increment, using Eqs.(11):

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The resulting stresses and directions are listed in Columns 9, 10, and 11 of Table 1,and the stresses versus the mid-depth of the respective increments are plottedbelow.

Equivalent uniform stress versus hole depth, with stresses plotted at mid-depths.

(continued...)

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Numerical Example of Data-Reduction Procedures (2): Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

If not previously so, it is now obvious that the stress varies significantly with depth.Had the stress been uniform, the data should have plotted as two straight,horizontal lines (except for experimental errors). It is also instructive to comparethe calculated stress in the first depth increment with that previously determined,assuming uniform stress distribution, and using only the full-depth and coefficients. From Table 1, the estimated average principal stresses in the firstdrilling increment are about 50 percent greater than those based on the uniformstress assumption. This example illustrates the necessity for incremental drilling(with proper hole geometry) to extract as much information as possible from thehole-drilling method.

The calculated stress data listed in Table 1 and plotted previously can be examinedin a different way by calculating the "apparent" equivalent uniform stress in eachincrement (Ref. 19). This is done separately for and as follows:

where:

= "apparent" equivalent uniform stress in the nth drilling increment.

, = equivalent uniform stress from the surface to depths ,

, = depths of drilling increments and

The preceding calculation is performed individually for each principal stress ateach depth increment. This procedure has been followed for the data in Table 1,with the results plotted below.

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Apparent stresses in depth increments, calculated from equivalent uniform stresses(see text).

It is important to keep in mind that neither the equivalent uniform stresses (given inTable 1 and shown in previous plot), nor the "apparent" stresses shown aboverepresent the actual residual stress, except when the stress is uniformly distributed.These calculated values can be very useful, however, in identifying the presence ofnonuniform stress and indicating the trend in stress distribution. Additionally, inthe first depth increment both of the preceding methods of analysis will produce thesame result which, if the increment is shallow and the measurements of strains andhole depth sufficiently accurate, should yield a good estimate of the average stressin that increment. But with each added increment in depth the calculated stressesmay depart farther from the actual stresses if there is sufficient variation in stresswith depth.

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Limitations and CautionsFinite-element studies of the hole-drilling method by Schajer and by subsequentinvestigators ( Refs. 20, 21, 22, 23) have shown that the change in strain producedin drilling through any depth increment (beyond the first) is caused only partly bythe residual stress in that increment. The remainder of the incremental relievedstrain is generated by the residual stresses in the preceding increments, due to theincreasing compliance of the material, and the changing stress distribution, as thehole is deepened. Moreover, the relative contribution of the stress in a particularincrement to the corresponding incremental change in strain decreases rapidly withdistance from the surface. As a result, the total relieved strain at full-hole depth ispredominantly influenced by the stresses in the layers of material closest to thesurface -- say, in the upper third, or perhaps half, of the hole depth. At hole depthscorresponding to > 0.2, the stresses in these increments have very little effecton the observed strains. This behavior is confirmed (for uniform stress) by theshape of the normalized strain graph, where about 80% of the total strain reliefnormally occurs in the first half of the hole depth. Because of these characteristics,little, if any, quantitative interpretation can safely be made of the incremental straindata for increments beyond = 0.2, irrespective of the analytical methodemployed for data reduction.

To summarize, the ideal application of the hole-drilling method is one in which thestress is essentially uniform with depth. For this case, the data-reductioncoefficients are well-established, and the calculated stresses sufficiently accuratefor most engineering purposes -- assuming freedom from significant experimentalerrors. Incremental drilling and data analysis should always be performed,however, to verify the stress uniformity. If the stress near the surface varies withdepth, the procedures given here for approximate incremental analysis offer asimple, convenient alternative to the more rigorous finite-element methods. Asillustrated by the example of the cold-rolled steel bar, the described procedures willnormally highlight the presence of stress variation with depth and indicate its trend,as well as providing a quantitative estimate of the average principal stresses in thefirst drilling increment.

Error and uncertainty are always present, in varying degrees, in all measurementsof physical variables. And, as a rule, their magnitudes are strongly dependent onthe quality of the experimental technique as well as the number of parameters

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involved. Since residual stress determination by the hole-drilling method involves agreater number and variety of techniques and parameters than routine experimentalstress analysis, the potential for error is correspondingly greater. Because of this,and other considerations briefly outlined in the following, residual stresses cannotusually be determined with the same accuracy as stresses due to externally appliedstatic loads.

(continued...)

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Limitations and Cautions: Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

(...continued)

Introduction of the small hole into the test specimen is one of the most criticaloperations in the procedure. The instruction manual for RS-200 Milling Guidecontains detailed directions for making the hole; and these should be followedrigorously to obtain maximum accuracy. The hole should be concentric with thedrilling target on the special strain gage rosette. It should also have the prescribedshape in terms of cylindricity, flat bottom, and sharp corner at the surface. It isparticularly necessary that the requirements on hole configuration be well-satisfiedwhen doing incremental drilling to examine stress variation with depth. Underthese same circumstances, it is important that the hole depth at each drillingincrement be measured as accurately as possible, since a small absolute error in thedepth can produce a large relative error in the calculated stress. Because ofpractical limitations on measuring shallow hole depths, the first depth incrementshould ordinarily be at least 0.005 in (0.13 mm). Accurate measurement of the holediameter is also necessary. Finally, it is imperative that the hole be drilled (milled)without introducing significant additional residual stresses. To the degree that anyof the foregoing requirements fail to be met, accuracy will be sacrificedaccordingly.

Strains relieved by drilling the hole are measured conventionally, with static straininstrumentation. The indicated strains are characteristically much smaller, however,than they would be for the same stress state in an externally loaded test part. As aresult, the need for stable, accurate strain measurement is greater than usual. Withincremental drilling, the strains measured in the first few depth increments can beespecially low, and errors of a few microstrain can cause large percentage errors inthe calculated stresses for those depths.

Beyond the above, it is also necessary that the underlying theoretical assumptionsof the hole-drilling method be reasonably satisfied. In full-depth drilling per ASTME837, the stress must be essentially uniform with depth, both in magnitude anddirection, to obtain accurate results. With finite-element and other procedures forinvestigating stress variation in subsurface layers, it is required only that thedirections of the principal stresses not change appreciably with depth. As for allconventional strain gage rosette measurements, the data-reduction relationshipsassume that the stress is uniformly distributed in the plane of the test surface.However, for residual stress measurements the effective "gage-length" is the hole

Limitations and Cautions (continued): Residual Stress Determination

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diameter rather than the relatively large dimensions of the overall rosette geometry.Consequently, uncertainties introduced by in-plane surface strain gradients aregenerally lower for residual stress determination than for conventional static loadtesting. No generalization can currently be made about the effects of steeplyvarying, nonlinear stress distributions in subsurface planes parallel to the rosette.

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Limitations and Cautions (continued): Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

References

Bibliography

"Determining Residual Stresses by the Hole-Drilling Strain-Gage Method."ASTM Standard E837.

1.

Mathar, J., "Determination of Initial Stresses by Measuring the DeformationAround Drilled Holes." Trans., ASME 56, No. 4: 249-254 (1934).

2.

Timoshenko, S. and J.M. Goodier, Theory of Elasticity, New York:McGraw-Hill (1951).

3.

Kabiri, M., "Measurement of Residual Stresses by the Hole-Drilling Method:Influences of Transverse Sensitivity of the Gages and Relieved StrainCoefficients," Experimental Mechanics 25: (252-256) (Sept. 1984).

4.

Rendler, N.J. and I. Vigness, "Hole-drilling Strain-gage Method ofMeasuring Residual Stresses." Proc., SESA XXIII, No. 2: 577-586 (1966).

5.

Kelsey, R.A., "Measuring Non-uniform Residual Stresses by theHole-drilling Method." Proc., SESA XIV, No. 1: 181-194 (1956).

6.

Schajer, G.S., "Application of Finite Element Calculations to Residual StressMeasurements." Journal of Engineering Materials and Technology 103:157-163 (1981).

7.

Redner, S. and C.C. Perry, "Factors Affecting the Accuracy of ResidualStress Measurements Using the Blind-Hole Drilling Method." Proc., 7thInternational Conference on Experimental Stress Analysis. Haifa, Israel:Israel Institute of Technology, 1982.

8.

Sandifer, J.P. and G.E. Bowie, "Residual Stress by Blind-hole Method withOff-Center Hole." Experimental Mechanics 18: 173-179 (May 1978).

9.

References: Residual Stress Determination

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Procter, E. and E.M. Beaney, "Recent Developments in Centre-holeTechnique for Residual-stress Measurement." Experimental Techniques 6:10-15 (December 1982).

10.

Wang, H.C., "The Alignment Error of the Hole-Drilling Method."Experimental Mechanics 17: 23-27 (1979).

11.

Prevey, P.S., "Residual Stress Distributions Produced by Strain GageSurface Preparation." Proc., 1986 SEM Conference on ExperimentalMechanics (1986).

12.

Flaman, M.T., "Brief Investigation of Induced Drilling Stresses in theCenter-hole Method of Residual-stress Measurement." ExperimentalMechanics 22: 26-30 (January 1982).

13.

Bush, A.J. and EJ. Kromer, "Simplification of the Hole-drilling Method ofResidual Stress Measurements." Trans., ISA 112, No. 3: 249-260 (1973).

14.

Bynum, J.E., "Modifications to the Hole-drilling Technique of MeasuringResidual Stresses for Improved Accuracy and Reproducibility."Experimental Mechanics 21: 21-33 (January 1981).

15.

Wnuk, S.P.. "Residual Stress Measurements in the Field Using theAirbrasive Hole Drilling Method." Presented at the Technical Committee forStrain Gages, Spring Meeting of SESA, Dearborn, Michigan, June, 1981.

16.

Delameter, W.R. and T.C. Mamaros, "Measurement of Residual Stresses bythe Hole-drilling Method." Sandia National Laboratories ReportSAND-77-8006 (1977), 27 pp. (NTIS).

17.

Nickola, W.E., "Post-Yield Effects on Center Hole Residual StressMeasurements." Proc., 5th International Congress on ExperimentalMechanics, 126-136. Brookfield Center, Connecticut: Society forExperimental Mechanics, 1984.

18.

Nickola, W.E., "Practical Subsurface Residual Stress Evaluation by theHole-Drilling Method." Proc., 1986 SEM Spring Conference onExperimental Mechanics, Brookfield Center, Connecticut: Society forExperimental Mechanics, 1986.

19.

Flaman, M.T. and B.H. Manning, "Determination of Residual StressVariation with Depth by the Hole-Drilling Method." Experimental

20.

References: Residual Stress Determination

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Mechanics 25: 205-207 (1985).

Niku-Lari, A.J. Lu and J.F. Flavenot, "Measurement of Residual StressDistribution by the Incremental Hole-Drilling Method." ExperimentalMechanics 25: 175-185 (1985).

21.

Flaman, M.T., B.E. Mills, and J.M. Boag, "Analysis ofStress-Variation-With-Depth Measurement Procedures for the Centre HoleMethod of Residual Stress Measurements." Experimental Techniques 11:35-37 (June 1987).

22.

Schajer, G.S., "Measurement of Non-Uniform Residual Stresses Using theHole Drilling Method," Journal of Engineering Materials and Technology,110, No. 4:Part 1, 338-343; Part 11, 344-349 (1988).

23.

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References: Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

Additional References

Ajovalasit, A., "Measurement of Residual Stresses by the Hole-Drilling Method:Influence of Hole Eccentricity." Journal of Strain Analysis 14, No. 4: 171-178(1979).

Beaney, E.M. and E. Procter, "A Critical Evaluation of the Centre-hole Techniquefor the Measurement of Residual Stresses." Strain, Journal of BSSM 10, No. 1:7-14 (1974).

Nawwar, A.M., K. McLachlan, and J. Shewchuk, "A Modified Hole-DrillingTechnique for Determining Residual Stresses in Thin Plates." ExperimentalMechanics 16: 226-232 (June 1976).

Nickola, W.E., "Weld Induced Residual Stress Measurements via the Hole-DrillingStrain Gage Method." Presented at the Winter Annual Meeting, ASME, NewOrleans, Louisiana, December 9-14, 1984.

Witt, F., F. Lee, and W. Rider, "A Comparison of Residual Stress MeasurementsUsing Blind-hole, Abrasive-jet and Trepan-ring Methods." ExperimentalTechniques 7: 41-45 (February 1983).

Schajer, G.S., "Judgment of Residual Stress Field Uniformity when Using theHole-Drilling Method," Proceedings of the International Conference on ResidualStresses II, Nancy, France. November 23-25, 1988, 71-77.

Flaman, M.T. and J.A. Herring, "SEM/ASTM Round-RobinResidual-Stress-Measurement Study -- Phase 1, 304 Stainless-Steel Specimen,"Experimental Techniques, 10, No. 5: 23-25.

Yavelak, J.J. (compiler), "Bulk-Zero Stress Standard -- AISI 1018 Carbon-SteelSpecimens, Round Robin Phase 1," Experimental Techniques, 9, No. 4: 38-41(1985).

Additional References: Residual Stress Determination

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Measurement of Residual Stresses by theHole-Drilling Strain Gage Method

EA-XX-062RE-120This geometry conforms to the early Rendler andVigness design (Ref. 5) and has been used in mostreported technical articles (see references). It isavailable in a range of sizes to accommodateapplications requiring different hole diameters ordepths.

CEA-XX-062UL-120This rugged, encapsulated design incorporates allpractical advantages of the CEA-Series of straingages (integral copper soldering tabs, conformability,etc.). Installation time and expense are greatlyreduced, and all solder tabs are on one side of thegage to simplify leadwire routing from the gage site.It is compatible with all methods of introducing thehole, and the strain gage grid geometry is identical to

the 062RE pattern.

CEA-XX-062UM-120Another CEA-Series strain gage, the 062UM gridwidths have been reduced to facilitate positioning allthree grids on one side of the measurement point asshown. With this geometry, and appropriatetrimming, it is possible to position the hole closer towelds and other irregularities. The user should bereminded, however that the data reduction equationsare theoretically valid only when the holes are wellremoved from free boundaries, discontinuities, abrupt geometric changes, etc.The UM design is compatible with all methods of introducing the hole.

Strain Gage Technology: Residual Stress Determination

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TABLE 1*

DEPTH MEASUREDSTRAIN

RELIEVED STRAINS COEFFICIENTSMulitplier of (10)-8

with and

Equiv.UniformStress toDepth

(1000 psi).

(in)% % %

0 0

e1 0

0

0%

0

0%

0

0%0 0

e2 0

e3 04 4

0.005 0.025

e1 -23

-37

16%

+9

13%

-19

12%

0.016 0.030

-32deg

+16 +37e2 -9 -0.035 -0.051

e3 -144

-0.1404

-0.204

0.010 0.050

e1 -49

-80

34%

+18

27%

-38

25%

0.036 0.067

-32deg

+16 +35e2 -21 -0.079 -0.113

e3 -314

-0.3154

-0.453

0.020 0.099

e1 -90

-145

61%

+35

52%

-85

56%

0.078 0.148

-34deg

+12 +30e2 -30 -0.171 -0.250

e3 -554

-0.6834

-1.000

0.030 0.149

e1 -118

-186

78%

+50

75%

-120

78%

0.111 0.227

-34deg

+11 +28e2 -33 -0.243 -0.384

e3 -684

-0.9724

-1.535

e1 -136 0.133 0.282

Table 1: Residual Stress Determination

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0.040 0.198-209

88%

+63

94%

-137

90%

-33deg

+10 +26e2 -36 -0.291 -0.477

e3 -734

-1.1654

-1.906

0.050 0.248

e1 -143

-219

92%

+67

100%

-143

93%

0.145 0.328

-32deg

+10 +24e2 -38 -0.318 -0.554

e3 -764

-1.2704

-2.217

0.060 0.297

e1 -146

-225

95%

+67

100%

-145

95%Beyond Range

e2 -40

e3 -794 4

0.081 0.40

e1 -152

-237

100%

+67

100%

-153

100%

0.147 0.374

-33deg

+12 +25e2 -42 -0.322 -0.632

e3 -854

-1.2884

-2.528

1 2 3 4 5 6 7 8 9 10 11

*Data rounded for tabulation.

Material: Cold Rolled Steel

Table 1: Residual Stress Determination

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