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The hole-drilling strain gauge method for the measurement of uniform or non-uniform residual stresses

AIAS TR-01:2010 Page 1 of 70

Working Group on Residual Stresses

A.Ajovalasit, M.Scafidi, B.Zuccarello, University of PalermoM.Beghini, L.Bertini, C.Santus - University of Pisa

E.Valentini, A.Benincasa, L.Bertelli SINT Technology s.r.l.

AIAS TR01:2010

The hole-drilling strain gaugemethod for themeasurement of uniform or non-uniform residual

stresses

Revision: 02.09.2010


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PREFACE

This test method is the result of work by the AIAS Working Group on Residual Stresses over theperiod from 2006 to 2010.

The objective was to draw up a draft set of recommendations for the measurement of residual

stresses by the incremental hole-drilling technique, also known as the hole-drilling strain-gaugemethod. Both terms are used without distinction in this document.

The hole-drilling strain-gauge method is the test method which is the most widely used inindustry to determine near-surface residual stresses.

The technical standard on the subject (ASTM E 837-08), which is an indispensable reference,has a restricted field of application as it does not consider:

cases in which stresses exceed 50% of the yield stress.

corrections where the drilled hole is eccentric to the centre of the rosette;

the effects of plasticity within the hole boundary.

the effects of any fillet radius at the bottom of the hole.

All these effects, nevertheless, influence the quality and accuracy of measurement.

The latest revision of the standard, ASTM E837-08, introduced computation of non-uniformstresses, however, the static nature of the method means that it is impossible to evaluateresidual stresses in many practical cases.

While acknowledging the progress that has been achieved thanks to the ASTM E837-08standard, the purpose of this guide is to go a step further, integrating new methods of correctingand calculating residual stress values with the considerations set out in the ASTM standard.

This method presents detailed instructions for the test reports and provides considerationsregarding uncertainty analysis in residual stress measurement.

The contributions presented herein reflect the results of the work carried out on these subjectsby Italian researchers both in the theoretical-experimental field and in design and constructionof new measurement instruments.

Thanks go to the researchers of the University of Palermo, the University of Pisa and thecompany SINT Technology srl for the invaluable contributions they have given both to thescientific works developed over these years and to the preparation of this test method guide.

Emilio Valentini

Coordinator of the A.I.A.S.Residual Stress Working Group

Florence, July 2010


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CONTENTS

1 INTRODUCTION ......................................................................................................................... 72 SCOPE ........................................................................................................................................... 73 REFERENCED DOCUMENTS .................................................................................................. 74 SYMBOLS ..................................................................................................................................... 85 PRINCIPLE OF MEASUREMENT ......................................................................................... 106 PRACTICAL ISSUES ASSOCIATED WITH THE MEASUREMENT ............................... 13

6.1 APPLICABILITY OF THE METHOD................................................................................................. 136.1.1 PARAMETERS OF THE MATERIAL ......................................................................................... 136.1.2 ACCESSIBILITY OF THE MEASUREMENT AREA ..................................................................... 146.1.3 EFFECT OF NON-UNIFORMITY AND PLASTICITY ................................................................... 14

6.2 STRAIN GAUGE ROSETTE SELECTION .......................................................................................... 146.2.1 ROSETTE DESIGNS................................................................................................................ 146.2.2 ROSETTE DIMENSIONS ......................................................................................................... 156.2.3 OTHER FACTORS INFLUENCING SELECTION ......................................................................... 16

6.3 SURFACE PREPARATION AND INSTALLATION.............................................................................. 186.3.1 SURFACE PREPARATION....................................................................................................... 186.3.2 CHOICE OF ADHESIVE. ......................................................................................................... 18

6.4 STRAIN-MEASUREMENT INSTRUMENTATION .............................................................................. 186.5 ALIGNMENT. .................................................................................................................................. 196.6 PERPENDICULARITY ..................................................................................................................... 216.7 EFFECTS OF THE FILLET RADIUS AT THE BOTTOM OF THE HOLE. ............................................. 226.8 HOLE SPACING .............................................................................................................................. 246.9 DISTANCE FROM GEOMETRIC DISCONTINUITIES........................................................................ 246.10 ZERO DEPTH DETECTION.............................................................................................................. 24

6.10.1 ELECTRICAL CONTACT DETECTION ..................................................................................... 246.10.2 OBLIQUE OBSERVATION OF DRILLING ................................................................................. 25

6.11 HOLE-PRODUCING TECHNIQUES.................................................................................................. 256.11.1 HIGH-SPEED DRILLING ......................................................................................................... 266.11.2 MEDIUM-SPEED DRILLING ................................................................................................... 276.11.3 LOW-SPEED DRILLING.......................................................................................................... 276.11.4 ABRASIVE JET MACHINING .................................................................................................. 276.11.5 ELECTRO-CHEMICAL MACHINING........................................................................................ 286.11.6 HIGH-SPEED ORBITAL DRILLING .......................................................................................... 28

6.12 DRILLING CUTTERS....................................................................................................................... 286.13 VERIFICATION OF THE DRILLING PROCESS................................................................................. 306.14 SELECTION OF DRILL DEPTH INCREMENTS ................................................................................. 306.15 MEASUREMENT OF STRAIN........................................................................................................... 30

6.15.1 EFFECT OF THE TURBINE AIR SUPPLY TEMPERATURE.......................................................... 306.15.2 HEAT GENERATED DURING THE DRILLING PROCESS............................................................ 30

6.16

MEASUREMENT OF HOLE DIMENSIONS AND ECCENTRICITY

...................................................... 31

6.17 FINAL HOLE DEPTH MEASUREMENT CHECK ............................................................................... 326.18 PRACTICAL EXAMPLE OF APPLICATION...................................................................................... 33

7 RESIDUAL STRESS ANALYSIS TECHNIQUES .................................................................. 347.1 STANDARD ASTME837-08: GENERAL ........................................................................................ 35

7.1.1 STRAIN GAUGE ROSETTES.................................................................................................... 357.1.2 STRAIN RELIEF IN PROXIMITY TO THE HOLE ........................................................................ 357.1.3 NUMERICAL VALUES OF aAND b..................................................................................... 367.1.4 SENSITIVITY OF THE METHOD.............................................................................................. 36

7.2 STANDARD ASTME837-08: CALCULATION OF RESIDUAL STRESSES........................................ 38


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7.2.1 THIN WORKPIECE ................................................................................................................. 387.2.2 THICK WORKPIECE............................................................................................................... 387.2.3 RESIDUAL STRESS UNIFORMITY TEST .................................................................................. 397.2.4 CALCULATION OF UNIFORM RESIDUAL STRESSES ............................................................... 397.2.5 CALCULATION OF NON-UNIFORM RESIDUAL STRESSES ....................................................... 407.2.6 INTERMEDIATE THICKNESS WORKPIECE .............................................................................. 45

7.3 CALCULATION OF NON-UNIFORM RESIDUAL STRESSES.OTHER METHODS.............................. 457.3.1 INTEGRAL METHOD ............................................................................................................. 457.3.2 INCREMENTAL STRAIN METHOD (ALSO KNOWN AS THE SCHWARZKOCHELMANN METHOD)

487.3.3 HDMMETHOD .................................................................................................................... 497.3.4 NON-UNIFORM RESIDUAL STRESSES WITH AN OFF-CENTRE HOLE....................................... 50

7.4 CORRECTION FOR PLASTICITY (ELASTIC RELAXATION OF STRESSES) ..................................... 527.4.1 CORRECTION WITH A 3-ELEMENT ROSETTE......................................................................... 537.4.2 CORRECTION WITH A SPECIAL 4-ELEMENT ROSETTE........................................................... 55

7.5 CORRECTION FOR ECCENTRICITY ............................................................................................... 567.5.1 CORRECTION FOR ECCENTRICITY: THROUGH HOLE............................................................. 577.5.2 CORRECTION BY HDM TECHNIQUES ................................................................................... 597.5.3 CORRECTION USING THE SPECIAL 6-ELEMENT ROSETTE ..................................................... 59

8 RESIDUAL STRESS ANALYSIS SOFTWARE FEATURES ............................................... 609 TEST REPORT ........................................................................................................................... 62

9.1 CONTENTS OF THE TEST REPORT................................................................................................ 629.1.1 GENERAL ............................................................................................................................. 629.1.2 PRESENTATION OF THE RESULTS ......................................................................................... 63

10 UNCERTAINTY ANALYSIS .................................................................................................... 6410.1 SUMMARY OF THE SOURCES OF UNCERTAINTY .......................................................................... 6410.2 CORRECTION OF THE MAIN ERRORS AFFECTING MEASUREMENT............................................. 6410.3 EVALUATION OF UNCERTAINTIES ON STRESSES ......................................................................... 66

11 REFERENCES ............................................................................................................................ 68


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INDEX OF FIGURES

Figure 1 - Symbols used in this publication. (On the left the symbols necessary for determiningthe state of stress, on the right the symbols used for correct definition of the geometry of therosettes). 10

Figure 2 - Relaxation of residual stresses after hole-drilling. 11Figure 3 - Diagram of the measurement chain using a high-speed air turbine. 12Figure 4 - Designs of strain gauge rosettes recommended by standard ASTM E837-08. 15Figure 5 - On the left a CW numbering scheme, on the right a rosette with CCW gauge

identification. 15Figure 6 - Hole drilling apparatus with a high speed air turbine (MTS 3000 - SINT Technology) 20Figure 7 Hole drilling device: on the left alignment, on the right rotation of the drilling head. 21Figure 8 - Checking the vertical perpendicularity of the hole-drilling tool. 21Figure 9 - Hole sections: on the left and in the centre a hole made by high speed drilling with

inverted-cone tungsten carbide cutters, on the right a hole made by EDM. 23Figure 10 - 2D (left) and 3-D (right) BEM models for studying the effects of the hole-bottom fillet

radius. 23Figure 11 - Identifying the zero cutter depth by an electrical connection. 25Figure 12 - Types of holes that can be produced with the techniques studied by Flaman: 26Figure 13 - High speed drilling technique 26Figure 14 - Medium-speed drilling technique. 27Figure 15 - High-speed orbital hole-drilling 28Figure 16 - High-speed orbital hole-drilling technique. Detail of the cutting tool 28Figure 17 - Cutters used for high-speed drilling 29Figure 18 - Hardness ranges for which the three types of cutters are recommended 29Figure 19 - Measurement of hole diameter and eccentricity 31Figure 20 - Off-centre hole, parameters necessary for calculating hole-rosette eccentricity 32Figure 21 - Instrument for measuring hole depth 32Figure 22 - Graphical test of through-thickness stress uniformity (ASTM E837-08) 39Figure 23 - Schwarz Kochelmann method. 48Figure 24 - On the right, calibration functions Kx and Ky for the HBM rosette shown on the left. 49Figure 25 -. Symbols used in the HDM method. 50Figure 26- Assumed material constitutive law: bilinear isotropic hardening 53Figure 27- Ratio between the measured relaxed strains versus plasticity factor 54Figure 28 .HBM 4-element Rosette 0/90/157,5/225 (Left), Angles between gauges (Right) 56Figure 29: (a) Principal Angle (least squares minimisation); (b) Reconstruction of measured strain

versus angle. 56Figure 30 Equi-biaxial Stress Field: difference between the values of strain measured in the

absence (above) and presence (bottom) of eccentricity (e=0.1 mm) 57Figure 31 - Notations relating to a rosette with an off-centre hole 57Figure 32 - 6-element rosette for eccentricity correction 59Figure 33 - Hole-drilling software. Endmill Positioning Tool (left) and Drilling System Setup (right)

60Figure 34 - Measured and interpoled strains versus depth. 60Figure 35 - Residual stress evaluation: above analysis in accordance with ASTM E837-08, below

stress analysis with the Integral Method. 61


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INDEX OF TABLES

Table 1 - Symbols. 10Table 2 - Typical dimensions of type A, B and C rosettes described by standard ASTM E837-08. 16Table 3 - Rosettes produced by HBM and Vishay Measurement Group. 17Table 4 - Maximum and minimum workpiece thicknesses and hole diameters, and drilling depths

recommended by standard ASTM E837-08. 22Table 5 - Residual stress calculation methods: principal features. 34Table 6 - Numerical values of coefficients a and b provided by standard ASTM E837-08 for type

A, B and C rosettes for uniform stress evaluations with through holes and blind holes. 36Table 7 - Convention used for placement of angle (ASTM E837-08). 38Table 8 - Coefficients a and b for type A rosettes for non-uniform residual stress evaluations

(ASTM E837-08). 41Table 9 - Coefficients a and b for type B rosettes for non-uniform residual stress evaluations

(ASTM E837-08). 42Table 10 - Coefficients a and b for type C rosettes for non-uniform residual stress evaluations

(ASTM E837-08). 43Table 11 - Coefficients a and b of the integral method for type A, B and C rosettes. 47Table 12 - Errors due to hole-rosette eccentricity for some types of rosette considered in standard

ASTM 837-08 58Table 13 - Contributions of uncertainty in residual stress measurement. 65


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1 Introduction

Residual stresses are present in almost all structures. They may be caused by manufacturingprocesses or may be created during the life of a mechanical component. Residual stresses areoften a predominant factor contributing to structural failure, particularly of structures subject toalternating service loads or corrosive environments.

The effect on properties can also be beneficial, in which case residual stresses are createdpurposely to improve the behavior of a material, for example, the compressive stressesproduced by shot peening. In either case, it is important to determine the residual stresses inorder to be able to foresee static resistance and fatigue strength.

The hole-drilling method is a practical, inexpensive and widely used method for determiningresidual stresses near the surface of a component to be analysed. It can be applied to a widerange of materials.

It involves attaching a three-element strain rosette to the surface, drilling a hole in a series ofdepth increments through the centre of the rosette, and measuring the strains that are producedreflecting the stress relaxation which takes place with the removal of material.

2 ScopeThis test method specifies an incremental hole-drilling procedure for determining residual stressprofiles near the surface of an isotropic linearly elastic homogeneous material. The test methodis applicable also to plastic materials and composite materials: these materials present adifferent mechanical behavior from that of metal materials and also require particular attention inthe choice of hole-drilling procedure.

The test method may be considered semi-destructive because the damage that it causes islocalized and often does not affect use of the component to which it is applied.

The method, which is a development of the hole-drilling procedure specified by standard ASTME837-08 [1], may also be applied in cases where: a) residual stresses vary with depth, b) thereis a small eccentricity between the axis of the hole and the centre of the strain gauge rosette.

This test method is limited to cases where the maximum residual stresses do not exceed 50%of the material yield stress. A correction method is specified for stresses exceeding 50% of yieldstress, which can only be applied where the stresses remain constant with depth.

However, the limitation relating to the thickness of a component reported in the ASTM standardholds and if the thickness is between 0.4 D and 1.2 D the results have to be consideredapproximate.

3 Referenced documents

Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain GaugeMethod, ASTM E837-08.

Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain Gauge

Method, ASTM E837-01. Grant P.V., Lord J.D., Whitehead P.S., The Measurement of Residual Stresses by the

Incremental Hole Drilling Technique, NPL Materials Centre, Measurement Good PracticeGuide No.53, National Physical Laboratory, UK, 2002.

LU J., Handbook of Measurement of Residual Stresses, Society for ExperimentalMechanics, Fairmont Press, Lilburn, GA, 1996, Chapter 2.


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4 Symbols

The diagrams shown in Figure 1 are useful for understanding the majority of the symbols listedin Table 1.

Symbol Definition Units

a Calibration constant for isotropic stresses

b Calibration constant for shear stresses

jka Calibration matrix for isotropic stresses

jkb Calibration matrix for shear stresses

D Gauge circle diameter mm

GL Grid length mm

GW Grid width mmR1 Distance from the centre of the rosette to the internal edge of the grid mm

R2Distance from the centre of the rosette to the external edge of thegrid

mm

W Rated resistance of the strain gauge rosette

D0 Diameter of the drilled hole mm

E Youngs modulus MPa

Ep Plastic modulus of proportionality MPa

r Strain hardening ratio of the material

Poissons ratio

j Number of drilled hole depth steps

k Sequence number for hole depth steps

z Depth of drilling mm

P Uniform isotropic stress MPa

Pk Uniform isotropic stress within hole depth step k MPa

p Uniform isotropic strain m/m

pk Uniform isotropic strain after hole depth step k m/m

Q Uniform 45shear stress MPa

Qk 45shear stress within hole depth step k MPa

q Uniform 45shear strain m/m

qk 45shear strain after hole depth step k m/m

T Uniform shear stress in x-y direction MPa

Tk x-y shear stress within hole depth step k MPa

t Uniform shear strain in x-y direction m/m

tk x-y shear strain after hole depth step k m/m

P Regularization factor for P stresses


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Q Regularization factor for Q stresses

T Regularization factor for T stresses

Angle measured clockwise from r to max direction

Relieved strain for uniform stress case m/m

r Relieved strain measured by the gauge, in radial direction m/m

1,2,3 Relieved strains measured by the strain gauge grids m/m

j Relieved strain measured after j hole depth steps have been drilled m/m

0 Maximum relievable strain m/m

Angle of strain gauge from the x-axis

max Maximum principal stress MPa

min Minimum principal stress MPa

x Stress in x direction MPa

(x)k Stress in x direction within hole depth k MPa

y Stress in y direction MPa

(y)k Stress in y direction within hole depth k MPa

xy Shear xy-stress MPa

(xy)k Shear xy-stress within hole depth step k MPa

Ra Surface roughness m/m

S Sensitivity merit index

Biaxiality ratio

C Plasticity corrective coefficient

f(C) Dimensionless load parameter

X1,X2 Hole radiuses measured in x direction mm

Y1,Y2 Hole radiuses measured in y direction mm

Dx Hole diameter measured in x direction mm

Dy Hole diameter measured in y direction mm

D0,m Average diameter of the measured hole mm

ex Eccentric radius measured in x direction mm

ey Eccentric radius measured in y direction mm

e Eccentric radius mm

Eccentric angle

p(hj), q(hj),t(hj),

p, q and t values calculated for the hole depth steps by the integralfunctions proposed by Schajer

MPa

A(H,hj), B(H,hj) Influence functions of the integral method

Kx, Ky Numerical/experimental calibration functions

j(11)

,j(33)

,j(13)

Influence functions describing the state of stress (HDM)

Kj(11)

,Kj(33)

,Kj(13)

Coefficients for the calculation of strains (HDM)

Objective function

u(x) Uncertainty tied to factor x


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ci Weight of uncertainty associated with parameter x

Uc(y) Total uncertainty associated with the measurement

k Normal distribution of uncertainty coverage factor

y Quantity measured in the test

U Extended uncertainty associated with the measurement

V Result of the test

Table 1 - Symbols.

Figure 1 - Symbols used in this publication. (On the left the symbols necessary for determining the stateof stress, on the right the symbols used for correct definition of the geometry of the rosettes).

5 Principle of measurement

The hole-drilling method involves drilling a small hole into the surface of a component, at thecentre of a special strain gauge rosette, and measuring the relieved strains. The maximumdepth of hole is approximately equal to 0.4 D.

The single measurements represent the average values of surface strain in the area of the gridscaused by relaxation of the stresses and the value of the readings is more sensitive torelaxation of the material the closer they are taken to the surface. This sensitivity decreases asthe depth increases until it reaches zero. The residual stresses originally present at the holelocation are then calculated from the measured strain values.

The relieved strains depend on the stresses that originally existed at the boundaries of thedrilled hole (the residual stresses are assumed to act uniformly over the in-plane region aroundthe rosette and to vary only through the thickness of the material) and are not affected by thestresses beyond the hole boundary.


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It is also assumed that the drilling technique does not introduce plastic local strains: as will bepointed out later, the drilling operation calls for techniques and specific measures to eliminate

Figure 2 shows relaxation of the stresses after drilling a hole for measurement of residualstresses.

Strain Gauge

Modifiedstress due to hole

Stress before drilling

Relieved stress

Hole Diameter - Do

Hole Depth - h

Figure 2 - Relaxation of residual stresses after hole-drilling.

The relieved strains decrease rapidly with distance from the edge of the hole and the straingauges measure only a strain corresponding to 25% to 40% of the original residual stresspresent in the hole area.

The measurement involves the following steps, which are described in greater detail in Section6 of this guide:

Installation of a special strain gauge rosette, with a minimum of three grids, on thecomponent to be analysed for residual stress;

Connection of the rosette to suitable instrumentation for recording of strains;

Alignment and setting up of the drilling fixture;

Establishing zero depth, particularly important for incremental drilling;

Drilling in a series of depth increments to obtain data on the variation of stresses withdepth;

Recording of the strains measured at each depth increment;

Calculation of the residual stress state applying a series of equations to the measured

values. These calculations are described in Section 7.The typical rosettes used for these measurements are shown in Section 6.2: the size of the holestrictly depends on the size of the strain gauge used.

The maximum depth of a hole is approximately equal to 0.4 D. Any greater depths are pointlessbecause the surface strain gauges are not sensitive to contributions at subsequent depthincrements.

It is necessary to use an accurate alignment and drilling system for making thesemeasurements. Excellent results are achieved drilling with a high speed air turbine.


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It is always preferable to drill the hole in small increments of depth, recording the measuredstrains and hole depth at each increment.

It is advisable that the drilling system for the incremental method is automatic and electronicallycontrolled: for example, Figure 3 shows a typical diagram of the measurement chain using ahigh-speed air turbine.

Figure 3 - Diagram of the measurement chain using a high-speed air turbine.

(Restan MTS 3000, SINT Technology s.r.l.)

Also where stresses can be considered to be uniform, incremental hole drilling allowsconsiderations to be made on the uniformity of the stresses.

The basic method described in ASTM E837-08 and presented in Section 7.2 is strictly validwhere the stresses do not exceed approximately 50% of the yield strength. In these cases theexperimentally derived strain calibration coefficients experimentally developed from testspecimens with known stress fields can be used.

The numerical determination (finite element solutions) of calibration data (influence coefficients)has opened new possibilities for improving the calculation of non-uniform residual stresses fromincremental strain data using the so-called integral method [2]. With this method, thecontributions to the total measured strain relaxation of the stresses at all depths are consideredsimultaneously. It will be examined in greater detail in Section 7.3.1.


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6 Practical issues associated with the measurement

There are two major factors that influence uncertainty associated with the measurementsobtained by the hole-drilling method, which are:

the way the hole is produced,

the procedure used to evaluate the residual stresses originally present, based on thestrain measurements.

These factors will be considered separately in the following sections. Some of the practicalissues are considered below, and recommendations on the analysis methods are presented inSection 7.

The practical issues addressed in the following section include:

applicability of the method and planning of measurements,

strain gauge rosette selection,

surface preparation and installation,

strain gauge instrumentation,

alignment,

perpendicularity,

hole diameter,

effects of the fillet radius at the bottom of the hole,

hole spacing,

distance from geometric discontinuities,

zero depth detection,

hole-producing technique,

drilling cutters,

selection of drilling steps,

measurement of strain,

measurement of hole dimensions and eccentricity,

final hole depth measurement check.

6.1 Applicability of the method

Hole-drilling is a semi-destructive technique with relatively low sensitivity and can analyseresidual stress profiles in proximity to the surface of a material. It is the least expensive andmost widely used technique for measuring residual stress.

6.1.1 Parameters of the material

A component on which the test for determining residual stress is to be carried out should bemade of an isotropic material and the properties of the material should be known.

If possible, values for Youngs modulus (E) and Poissons ratio () experimentally determinedon a sample of the material under investigation should be used, particularly for non-standardalloys and materials where handbook data is not available.

Handbook values are correct only for some well-defined, homogenous materials.

Typical uncertainties in the mechanical properties of common steel and aluminium alloys areroughly considered to be in the 1 - 4% range and can therefore contribute significantly to theoverall uncertainty in the measurement.


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6.1.2 Accessibility of the measurement area

It is necessary to be able to access the areas of the component to be analysed both in order toapply the strain gauge rosette and to align and make the hole.

Ideally, the sample should be flat and the hole location far from any geometric discontinuity.

In practice, tests often have to be conducted on curved surfaces or at a location close to an

edge, hole or some other feature. In such cases, although the results may provide sufficientinformation, the validity of the stress values must be considered carefully.

In the most critical cases, departures from the ideal can be evaluated by using a finite element

model to calculate the influence functions ( a and b coefficients) for the specific installation.

6.1.3 Effect of non-uniformity and plasticity

Standard ASTM E837-08 is applicable to residual stress profile determinations where thestresses may be uniform or non-uniform through the thickness of the component underinvestigation.

In addition, the test method provides accurate results if the stresses are less than approximately50% of the yield stress.

There are many circumstances where these requirements are not met, for example, residualstress measurements on a shot peened surface, close to a weld or a hole. This does not meanthat the hole-drilling technique cannot be applied, but numerical corrections are required to takeaccount of these effects.

For example, the welding process generates high residual stress values that may reach andeven exceed the yield strength of the base metal being welded, and in this case the twoprincipal sources of error are:

the assumption of uniformity in the stress field,

the plasticity around the hole.

The methods of evaluating non-uniform through-thickness stresses are analysed in detail inSection 7.

The error in residual stress measurements due to the effect of localized yielding has beenanalysed in literature from both an experimental and an analytical point of view.

Beghini and Bertini [3,47,49] have studied the effects of plasticity in the region around the hole:if the value of the stresses in that area exceeds the yield strength of the material, some relationshave been proposed to correct the value of stresses, clearing obtained results of the effect ofplasticity.

The influence of plasticity is discussed in detail in Section 7.

6.2 Strain gauge rosette selection

6.2.1 Rosette designs

A number of commercial strain gauge rosette designs are available, designed specifically for thehole-drilling technique.

Rosettes are available with self-temperature-compensation for some materials.

All of the rosette designs incorporate centering marks for aligning the drilling tool precisely atthe centre of the gauge circle.

Standard ASTM E837-08 describes the three strain gauge designs which are shown in Figure 4.


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Figure 4 - Designs of strain gauge rosettes recommended by standard ASTM E837-08.

Standard ASTM E837-08 distinguishes rosettes also by the arrangement of the measurementgrids: the numbering scheme can follow a clockwise (CW) convention if a clockwise rotation isnecessary to go from grid 1 (or a) to grid 3 (or c); rosettes can have counter-clockwise (CCW)gauge numbering if a counter-clockwise convention is used.

Whether a rosette is CW or CCW type therefore depends on the location of grids 1 and 3:whereas the position of grid 2 determines the type of rosette (type A, B or C).

Figure 5 shows both identification schemes.

Figure 5 - On the left a CW numbering scheme, on the right a rosette with CCW gauge identification.

Type A (with grids in two quadrants) is recommended for general-purpose use, type B (with allgrids in a single quadrant) is used for measurements near an obstacle, such as a fillet radius orweld, and type C for situations where high strain sensitivity and high thermal stability arerequired.

The type C rosette consists of six grids forming three pairs, with radially and tangentially alignedgrid axes. The opposed grids (for example, 1T and 1R in Figure 4) are to be wired in half-bridgeconfigurations.The type C gauge has increased sensitivity (varying from +70% to +140%) inrelation to type A and B designs. The disadvantages in using this type include a higher cost,limited availability, and the extra preparation time and instrumentation associated with the sixstrain gauges (connected to three measurement channels).

Table 2 shows the typical geometric dimensions of type A, B and C rosettes described by

standard ASTM E837-08. A variety of sizes and types of strain gauge currently produced byHBM and Vishay Measurement Group are presented in Table 3.

6.2.2 Rosette dimensions

The first factor to be considered in selecting a strain gauge is size.

The size of strain gauge to use is dependent on the following factors:

the size of the available area on the component (proximity of edges, weld features, etc.),


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the depth required for the residual stress analysis (larger gauges are more suitable fordetermining the stress profile at greater depths whereas smaller gauges are suitable for anear-surface analysis),

acceptable damage (smaller holes are introduced with the smaller gauges).

The most widely used gauge size is the one with an individual gauge length measuring 1.5 1.57 mm. This size of gauge is capable of providing useful residual stress data to a depth ofapproximately 1 mm.

It should be noted that the experimental errors associated with the measurements from smallstrain gauges (hole eccentricity, control of depth, etc) are higher than those associated with thecorresponding measurements with larger gauges.

However, the larger strain gauges should be selected with caution because of the size of drillsrequired and the large amount of material to be removed during the drilling process.

Table 2 - Typical dimensions of type A, B and C rosettes described by standard ASTM E837-08.

6.2.3 Other factors influencing selection

Others factors to be considered in selecting the most suitable strain gauge rosette include:

the time required for installation and wiring,

temperature compensation,

the ease of handling,

availability,

cost.


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Encapsulated designs are available complete with soldering tabs. These are particularlysuitable for use in harsh environmental conditions where special protection for the gauge isrequired.

Gauge Pattern Designation ManufacturerASTM E837

Type

Re

sistance()

No

minalGauge

Factor

GridLenght(mm)

GridCtr'lineDia.

(mm)

Min.

dia.

hole-

dmin(mm)

Max.

dia.

hole-

dmin(mm)

CarrierLenght

(mm)

C

arrierWidth

(mm)

dmin/D

dmax/D

d/D

1-RY61-1,5/120S HBM Type A (CCW) 120 1.94 1.5 5.1 1.5 2.2 10.2 10.2 0.29 0.43

1-RY61-1,5/120K HBM Type B (CCW) 120 1.93 1.5 5.1 1.5 2.2 10.2 5.2 0.29 0.43

1-RY61-1,5/120R HBM Type B (CCW) 120 1.93 1.5 5.1 1.5 2.2 10.2 5.2 0.29 0.43

K-RY61-1,5/120R

(with pre-attached

leads)

HBM Type B (CCW) 120 1.93 1.5 5.1 1.5 2.2 10.2 5.2 0.29 0.43

1-VY61-1,5/120S HBM 120 1.93 1.5 5.1 1.5 2.2 10.2 5.2 0.29 0.43

N2K-XX-030 RR

Vishay -

Measurement

GroupType C (CW) 350 0.75 4.32 2.3 2.6 9.4 9.4 0.53

EA-XX-031 RE

Vishay -

Measurement

Group

Type A (CW) 120 2.01 0.75 2.56 0.8 1 7.4 7.4 0.31

EA-XX-062 RE

Vishay -

Measurement

GroupType A (CW) 120 2.08 1.57 5.13 1.5 2 10.7 10.7 0.29

CEA-XX-062 UL

Vishay -

Measurement

Group

Type A (CW) 120 2.05 1.57 5.13 1.5 2 12.7 11.7 0.29

CEA-XX-062 UM

Vishay -

Measurement

GroupType B (CW) 120 2.05 1.57 5.13 1.5 2 10.7 10.7 0.29

EA-XX-125 RE

Vishay -

MeasurementGroup Type A (CW) 120 2.05 3.18 10.26 3 4.1 19.8 19.8 0.29

Table 3 - Rosettes produced by HBM and Vishay Measurement Group.

Open-faced strain gauges are more suitable for installation on irregular surfaces where thestiffness of encapsulating layers precludes conforming the gauge to the workpiece surface.

Configurations with pre-attached leads considerably facilitate installation work avoidingsoldering on the strain gauge solder tabs and reduce strain gauge installation time and errors.


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6.3 Surface preparation and installation

Installation of the strain gauge rosette should be carried out by qualified personnel inaccordance with the strain gauge and adhesive manufacturers instructions. [4].

The instructions provided by the UNI 10478 standards [5-9] should be followed for correctinstallation of strain gauges.

Surface-preparation and gauge-installation procedures must be of the highest quality as theyhave a direct influence on the accuracy of the strain measurements.

As a rule, it is also useful to refer to material manufacturers instructions for surface-preparationand gauge-installation procedures.

6.3.1 Surface preparation

To ensure a high-quality bond between the strain gauge and the component, the surface mustbe properly prepared.

This is particularly important when using the incremental hole-drilling technique as the strainsmeasured are generally very small (typically only several m/m in the first depth increments).

The purpose of surface preparation is to develop a surface texture suitable for bonding without

altering the state of the surface stresses.

Nevertheless, any oxides, rust or paint should always be removed.

The UNI 10478-3 standard suggests a surface roughness (Ra) in the 2.0 4.0 m range forgauge bonding with a cyanoacrylate-based adhesive [6].

However, it is recommended that mechanical abrading be avoided as much as possible if theincremental hole-drilling method is to be used for determining near-surface stresses [10-11]

Surface abrasion influences only the range of depth nearest the surface and the importance of itdepends on the residual stress gradients and the measurement requirements.

It should be noted that extremely rough surfaces must be avoided due to ambiguity inestablishing the zero depth for incremental hole-drilling [12].

ASTM E837-08 also recommends restricting surface preparation to those methods that havebeen demonstrated to induce no significant residual stresses (particularly for workpieces thatcontain sharp near-surface stress gradients).

6.3.2 Choice of adhesive.

The simplest, quickest and most common method of bonding the strain gauge to the specimenis to use a conventional cyanoacrylate adhesive.

These adhesives consist of a single component with a short cure time (1-2 minutes), and arerealtively easy to use.

If the surface of the component is particularly rough, it is important that the chosen adhesive fillsthe asperities and irregularities to achieve a good bond. In such cases, a more viscous, two-

component epoxy adhesive may be more suitable.

6.4 Strain-measurement instrumentation

It is important that the instrumentation chosen for strain measurement is calibrated and suitableto be used for this application.

ASTM E837-08 stipulates that the instrumentation for recording of strains should have a strainresolution of 1 m/m and that stability and repeatability should also be 1 m/m.

Generally, most modern strain-measurement instrumentation has the required resolution andstability for measuring the small strains in incremental hole drilling.


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However, the following minimum requirements are believed to be advisable for incrementalhole-drilling applications: strain resolution of 0.25 m/m, stability 0.5 m/m, repeatability 0.5m/m.

With the more conventional rosettes (types A and B) a three-wire quarter bridge circuit shouldbe used (self-temperature-compensating for as far as regards apparent thermal strain of theleads) with conveniently short leadwires.

Half-bridge circuits should be used with type C rosettes.

A particularly high acquisition frequency is not necessary for these measurements.

It is advised that the average of the values measured (recommended value between 10 and 50acquisitions) be made for every measurement interval.

ASTM E837-08 recommends checking the integrity of the gauge installation by applying a smallload to induce strains and evaluating the mechanical hysteresis of the strain gauges forming therosette. The standard also recommends visual inspection of the rosette installation.

For the strain gauge installation, however, it is advisable to refer to the preliminary checksspecified by the standard UNI 10478-3 [7].

6.5 Alignment.

Eccentricity between the hole and gauge centre can introduce significant errors into themeasurement of residual stresses.

Alignment between these centres is normally achieved with the aid of a microscopeincorporating a reticle in the focus of the objective, the centre of which should coincide with thecentre of the endmill for drilling the hole.

After installation of the strain gauge rosette, the mechanical part of the measurement system ismoved close to the point where the measurement is to be made, and is positioned so that thestrain gauge centering marks are within the field of view of the microscope. Two adjustmentsset at 90 to each other are used for centering until the microscope reticle coincides with thestrain gauge centering marks.

A typical alignment and air turbine drilling system is shown in Figure 6. In this setup, themicroscope is incorporated in the measurement system and is not taken off duringmeasurements: all that is necessary is a rotation of the drilling head as it is aligned with themicroscope (Figure 7).

The drilling tool is fitted in front of the microscope after the alignment procedure. In othermeasurement systems the microscope is replaced with the drilling tool after alignment.

This reduces (but does not eliminate) eccentricity as alignment of the reticle does not allow theuncertainty in positioning the tool holder (in the region of a few microns) to be taken intoaccount.

ASTM E837-08 states that the centre of the drilled hole should be aligned concentric with thestrain gauge circle to within 0.004 D.


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1 - Stepping motor for fine positioning2 - Knob for slow manual feed3 - Eyepiece4 - Turbine release pushbutton5 - Compressed air connection6 - Air turbine7 - Chuck8 - Endmill

9 - Knob for fast vertical movement10 - Rear cap for closing the turbine11 - Threaded dowels for microscope alignment12 - Support feet13 - Microscope14 - Knob for horizontal movement15 - Eyepiece reticle16 - Vertical height adjustment

Figure 6 - Hole drilling apparatus with a high speed air turbine (MTS 3000 - SINT Technology)

15

1

12

2

16

149

5

87

6

10

13

11

4

3


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Figure 7 Hole drilling device: on the left alignment, on the right rotation of the drilling head.

The standard recommends using an optical system to align the axis of rotation of the cutter inrelation to the centre of the strain gauge rosette. In other cases it is necessary to align theapparatus using a microscope, then remove the microscope and fit the air turbine hole-drillingsystem. Section 7.5 deals with the influence of eccentricity and methodologies for correcting theeffect of eccentricity.

6.6 Perpendicularity

It is essential that the cutter is positioned perpendicular to the surface of the component to beanalysed.

Figure 8 - Checking the vertical perpendicularity of the hole-drilling tool.

For example, if a 2 mm. diameter hole is to be made using a rosette with strain gauges with 1.5 1.57 mm long grids, a 1angle off the perpendicular will lead to a difference in depth of 17 mbetween the outer edge and the centre of the cutter.


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This corresponds to a substantial error in depth in the typical increments that are used inincremental measurements: its effect will depend on the orientation between the angle axis andthe rosette configuration [12].

It is important that the drilling system be checked before any test to avoid any errors caused bythe drill not being perpendicular: this is not always easy, particularly for in-situ measurements.

It is therefore important that the drilling system incorporates a means of adjusting

perpendicularity to ensure that the cutter is correctly positioned. Apparatuses usually have threemagnetic feet that can be used for regulating perpendicularity.

This operation can be checked with precision squares and levels (Figure 8).

It is recommended that a margin of at least 0.30 mm be maintained between the hole and thestrain gauge grid endloops to protect the grids.

The need for this margin limits the maximum allowable diameter of the drilled hole D0.

The recommended minimum hole diameter is 60% of the maximum allowable diameter.

Table 4 indicates the maximum and minimum diameters recommended for standardized, typeA, B, and C rosettes.

Table 4 - Maximum and minimum workpiece thicknesses and hole diameters, and drilling depthsrecommended by standard ASTM E837-08.

As indicated in Section 7.1.4, it is important to note that as the ratio of D0/D increases, thesensitivity of the method increases in approximate proportion to (D0/D)

2.

Consequently, larger holes are recommended to achieve higher sensitivity.

Drilling diameters between 1.6 and 2.0 mm are normally used for rosettes with grids from 1.5 1.57 mm long.

If orbital drilling is used, the hole diamter is significantly larger than the drill diameter.

6.7 Effects of the fillet radius at the bottom of the hole.

The drilling techniques that can be used with the hole-drilling method for determining residualstresses generally produce a blind hole with a significant fillet radius at the bottom of the hole.

For example, if the high-speed drilling technique is used, the hole-bottom fillet radius variesbetween 4% and 20% of the hole diameter D0; whereas with electrical-discharge machining(EDM) or abrasive jet machining techniques the fillet radius can reach values greater than 30%.


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Figure 9 shows the section and hole-bottom radius of three holes made with different hole-drilling techniques and endmills.

Figure 9 - Hole sections: on the left and in the centre a hole made by high speed drilling with inverted-cone tungsten carbide cutters, on the right a hole made by EDM.

The hole-bottom fillet radius has an effect on residual stress values measured by the hole-drilling method. It is possible to study the effect with 2-D and 3-D BEM models (BoundaryElement Method, Beasy code) (Figure 10).

r

D0/2

D/2

ER

z

r

D0/2

D/2

ER

z

Figure 10 - 2D (left) and 3-D (right) BEM models for studying the effects of the hole-bottom fillet radius.

The study by M. Scafidi and B. Zuccarello [14] has shown that the hole-bottom fillet radiusranges from 0.04 D0 to 0.10 D0 using inverted-cone tungsten carbide cutters and is in the regionof 0.30 D0 with EDM techniques.

The effect of the hole-bottom fillet radius on relaxed strains was evaluated by numericalsimulations performed with the BEM models shown in Figure 10: it must be taken into dueaccount particularly in the initial drilling steps.

The effect increases as the hole-bottom fillet radius increases and decreases with hole depth.

The hole-bottom fillet radius can significantly influence the test specified by ASTM E837-08 forevaluating the uniformity of stresses.

For example, considering an equi-biaxial stress field, it is found that:

a hole-bottom fillet radius equal to r=0.10 D0

leads to a maximum deviation in relaxedstrains of 5%,

a hole-bottom fillet radius equal to r=0.30 D0 leads to a deviation in relaxed strains greaterthan 20%.

In both cases the bottom-hole fillet radius influences the stress uniformity test and thereforestress measurement by the ASTM E837-08 method: these deviations can actually influencedetermination of the stress field since uniformity of the field is guaranteed if the deviations instrain between the measured value and the theoretical value are lower than 3% according tothe standard.

rr


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6.8 Hole spacing

The presence of a hole in the vicinity of a new hole alters the residual stresses present in thematerial as the first hole-drilling process produces a relaxation of the residual stresses whichextends a certain area around the hole. The extension of the relaxed area depends on the typeand diameter of the hole.

It is recommended that the minimum spacing between holes should be equivalent to at least sixtimes the hole diameter. When possible, strain gauge grids should be installed well removedfrom adjacent holes, and not between adjacent holes. [15,16].

6.9 Distance from geometric discontinuities

ASTM E837-08 introduced a number of considerations relating to the minimum distancenecessary between the centre of a hole and the closest geometric discontinuity.

A geometric discontinuity means an abrupt geometric change or an abrupt change in thethickness of a component: these geometric discontinuities can locally influence the value ofresidual stresses present in a component.

The minimum distance from the nearest discontinuity depends on the diameter and type ofstrain gauge used. If type A strain gauge rosettes are used, the distance between the hole

centre and the discontinuity must be at least 1.5 D; this is reduced to 0.5 D using a type Brosette and positioning the grids diametrically opposed to the discontinuity.

6.10 Zero depth detection

Accurate detection of zero depth, ie, the point at which the drill is in initial contact with thesurface of the component, is particularly important in measuring residual stress variation withdepth (using the incremental hole-drilling technique).

Before actually drilling into the material, the drill should be lowered so that it cuts through thebacking film on the strain gauge without touching the surface below.

Zero depth is the point at which drilling and acquisition of the strain measurements start aftercutting through the backing film.

Exact identification of the zero point may be affected by the following causes of uncertainty:

surface roughness causing uncertainty in identifying a single zero depth;

any error in drill alignment (off perpendicular) leading to initial contact on one side of thehole;

a concave profile at the end mill cutting edge resulting in an initial ring contact around theend mill circumference rather than over the whole end face;

axial clearance in drill motor bearings (in particular those of air turbines) may cause someambiguity in the absolute position of the end mill cutting edge;

uncertainty relating to actual removal of strain gauge backing and encapsulation material.

These causes of uncertainty can affect the accuracy of stress measurements at initial depth

increments and cannot be identified or corrected by examination of the strain data.The techniques presented in sections 6.10.1 and 6.10.2 can be applied to determine the instantwhen the strain gauge backing is broken.

6.10.1 Electrical contact detection

Considering the zero point to be the point when the strain gauge backing is removed, it ispossible to use the electrical contact technique.


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This technique can be applied when analysing conductive materials and providing the airturbine conducts electricity [17]. Figure 11 shows zero depth detection by the electrical contacttechnique.

Figure 11 - Identifying the zero cutter depth by an electrical connection.

The advantages of this method are the simplicity in determining the initial contact, the short timerequired (a few seconds), the low cost (no auxiliary equipment is needed except for an electricallead) and automation of the method (managed by the electronic control system andmeasurement instrumentation software) [18,19,20]

The measurement system shown in Figure 11 has an automatic procedure for determining theinitial drilling point, removing the strain gauge backing and positioning the end mill cutter incontact with the workpiece metal surface.

6.10.2 Oblique observation of drilling

The technique consists in carrying out oblique observation of the drilling process through a minivideo camera, magnifying eyeglass or a microscope. The device should be held close to thehole location and cold light reflected from the strain gauge backing makes it possible to detectthe thinning and subsequent elimination of the strain gauge backing. A cold light source does notgenerate significant heat, whereas use of conventional inspection lamps may introduce undesiredthermal strains [12].

This technique for determining the zero position provides a less accurate detection of zerodepth than the electrical contact method. It may be applied to all types of materials and not justmaterials which carry electricity.

Oblique observation has the advantage of observing the drilling area in detail and consequently

the errors due to bad perpendicular alignment between the endmill and workpiece can beminimized [12].

6.11 Hole-producing techniques

The two key factors to be considered in selecting the hole-producing technique are thefollowing:

introduction of additional residual stresses during the machining process;

the ability of the technique to produce geometrically well-defined holes. In fact, calculation ofresidual stresses with one of the techniques available requires a cylindrical hole with a flatbottom.


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M.T.Flaman and J.A.Herring [21] studied four different techniques which were comparedquantitatively on the basis of induced stresses and hole geometry and qualitatively in terms ofportability and ease of use.

In addition, a fifth drilling technique, the orbital hole-drilling technique, was introduced and laterstudied by the aforementioned M.T.Flaman [22].

The main techniques are:

high-speed drilling,

low-speed drilling,

abrasive jet machining,

electro-chemical machining,

high-speed orbital drilling.

A diagram is provided in Figure 12 showing the geometric characteristics of the holes that canbe made by the four techniques studied by M.T.Flaman.

Figure 12 - Types of holes that can be produced with the techniques studied by Flaman:A High-speed drilling; B Conventional low-speed drilling; C Abrasive jet machining; D

Electro-chemical machining.

Figure 13 - High speed drilling technique

These methods for residual stress measurement are described and analysed in detail in thefollowing sections.

6.11.1 High-speed drilling

High-speed drilling was first used by M.TFlaman [21] employing an air turbine drilling systemrotating at speeds of up to 400,000 rpm (Figure 13). The typical cutting tool is an inverted-conetungsten carbide cutter, which produces a circular hole with straight sides and a flat bottom.


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High-speed drilling is considered suitable for most materials as it does not introduce significantmachining stresses due also to the modest torque applied to the tool during the drilling process.

6.11.2 Medium-speed drilling

The incremental hole drilling method can also be applied using a high speed electric motor(approx. 30000 RPM). Recent research shows that even lower speeds (14,000 40,000 rpm)

can produce reasonable results. [23].An electric motor system is an alternative when a compressed air supply for a high speedturbine is not available and with an automatic drilling system a high speed electric motor can beoperated automatically.

The electric motor drilling system can be housed in a special drilling head (Figure 14) and thecentering and measurement of the hole diameter can be done by changing the drillinginstrument holder with a microscope with a centering reticle.

The drill shank has a diameter of 2.35 or 3.0 mm. and the cutter diameter can be 1.6 to 1.8 mmor approx. 3 mm depending on the rosette diameter.

Figure 14 - Medium-speed drilling technique.

6.11.3 Low-speed drilling

The low-speed drilling was the first technique used for measuring residual stress by the hole-drilling method. Rendler and Vigness [24] introduced the low-speed drilling technique in 1966with specially developed endmills. The technique produces holes that are geometrically suitablefor determining residual stresses by the hole-drilling method.

However, the results of Flamans comparison of hole-producing techniques [21] showed that the

low-speed milling technique induces high stresses and therefore must be considered unsuitablefor the hole-drilling method.

6.11.4 Abrasive jet machining

Hole machining by the abrasive jet technique, proposed and developed by Beaney and Proctor,is achieved by directing a small diameter jet of cutting powder at high pressure at the surface ofthe workpiece. The jet of air and powder removes material and quickly produces a hole.

Abrasive jet machining produces a fairly irregular hole shape that is little suited to the hole-drillingmethod (type C in Figure 12): in fact, it allows little control of the hole diameter and shape.


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In addition, abrasive jet machining cannot be used for determining non-uniform residualstresses as it does not allow sufficient control of hole depth and diameter. It is notrecommended for the less hard materials. [12]

6.11.5 Electro-chemical machining

Electro-chemical hole-producing techniques refer to electrical discharge machining (EDM) and

electro-chemical machining (ECM).The hole shape they produce is acceptable for the hole-drilling method of measuring residualstress although convexities are formed on the bottom of the hole, as can be seen for type D inFigure 12, which can influence the measured value of residual stress.

Use of these hole machining processes is limited to electrically conductive materials: thepresence of high electric discharges that generate stresses on the surface layers of the materialplus the presence of chemical agents can cause problems for protection of the strain gaugegrids. These factors have prevented development and diffusion of these techniques inproducing holes for the measurement of residual stresses. [12]

6.11.6 High-speed orbital drilling

Another technique available for measurement of residual stresses by the hole-drilling method ishigh-speed orbital drilling. It was first introduced by Flaman [22].

With this technique, the drill is deliberately offset from the centre of the strain gauge and thehole is drilled with an orbital motion. The diameter of the cutting tool is smaller than the diameterof the hole (figures 15 and 16).

Figure 15 - High-speed orbital hole-drilling Figure 16 - High-speed orbital hole-drillingtechnique. Detail of the cutting tool

The orbital drilling technique is an effective method for drilling hard, highly abrasive materialssuch as spring and bearing steels and cast aluminium alloys with a silicon content greater than6% (for example AlSi9Cu3 and AlSi7Mg).

With the orbital drilling technique the removal and extraction of chips is facilitated and moreefficient. A further advantage are greater drilling diameters.

6.12 Drilling cutters

For high-speed drilling the recommended drill for most materials is the inverted-cone tungstencarbide type. An inverted-cone polycrystalline diamond coated cutter can be used for hardermaterials.


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The inverted-cone cutting tools that may be used for high-speed drilling with an air turbine areillustrated in Figure 17.

Figure 17 - Cutters used for high-speed drilling(on the left a tungsten carbide (TC) endmill, in the centre a TiAlN-coated tungsten carbide (TTC) endmill,

on the right a diamond-coated (D) cutting tool)

Milling cutters are available in a range of diameters (from 0.6 to 2.2 mm) and with 1.6 mmshanks (for an air turbine) or 2.3 mm shanks (for coupling to an electric motor). The end facecutting edge must be flat or slightly concave; the side relief of the inverted cone gives clearancefor chip removal without affecting the cutting surface.

To avoid ambiguities in hole diameter identification, ASTM E837-08 prescribes that the radialclearance angles of the cutting edges should not exceed 1(to avoid ambiguities in hole depthidentification by ensuring that the depth is uniform within at least 1% of the tool diameter) andthat the taper angle should not exceed 5 (to allow the diameter of the drilled hole to beidentified with certainty).

The cutting edge outer angle should be as sharp as possible. Excessive blunting or too high aradius can produce unacceptable errors (see 6.8)

Milling cutters should be visually inspected (for example, with a magnifying lens) prior to useand on completion of the drilling of a hole. It is advisable to change the cutter for every hole-drilling operation.

Figure 18shows the HV10 hardness ranges of metal materials for which tungsten carbide anddiamond-coated cutters are used.

Figure 18 - Hardness ranges for which the three types of cutters are recommended


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As can be noted, uncoated tungsten carbide cutters can be used on materials with a hardnessranging between 100 and 200 HV10. Tungsten carbide cutters with TiAlN coating can be usedwith materials with hardnesses up to 550 HV10.

Inverted-cone diamond-coated cutters (type D in Figure 17) are recommended for extremelyhard materials (cemented and nitrided steels, ceramics, glass, etc.).

Diamond-coated cutters do not cut a hole with a sharp angle; the small radius represents a

departure from the ideal case for which coefficients were evaluated, therefore the residualstress data from near-surface increments should be treated with caution as they are affected bygreater uncertainty.

6.13 Verification of the drilling process

Verification of the selected drilling technique is recommended, when no prior experience isavailable, in order to prevent any residual stresses induced by the drilling method fromsignificantly influencing the accuracy of the results.

Verification could consist in applying a strain gauge rosette identical to the rosette used in thetest method on a stress-free specimen of the same material, and then drilling a hole. If thedrilling method is satisfactory, the stresses produced by the drilling will be small.

According to standard ASTM E837-08 the drilling method is acceptable if the measured strainsare within 8 m/m. If necessary (or if the strains induced by the drilling process exceed 8m/m), it is possible to use coolants during the drilling process. The coolant used must beelectrically non-conductive (water-based coolants are not suitable).

The most common method for obtaining stress-free specimens consists of annealing heattreatment.

6.14 Selection of drill depth increments

It is recommended that the measurement system for the incremental hole-drilling techique havethe possibility of selecting the number and position of the depth increments to be drilled.

It may be useful to increase the number of increments in the area near the workpiece surface

and to reduce depth increments further from the surface.Modern automatic measurement systems make it possible to drill in increments even smallerthan 0.01 mm [17].

6.15 Measurement of strain

After the zero point corresponding to the workpiece surface is identified, strain at the set drillingdepth increments is measured by each strain gauge in a rosette.

6.15.1 Effect of the turbine air supply temperature

It is important that an air turbine drilling system have a side air exhaust to minimize the effectsof any difference between the air temperature and the temperature of the workpiece.

Should the exhaust not be in a lateral position, before beginning drilling the drill (if the air turbinetype) should be made to run for a period of time and then stopped while monitoring the straingauge outputs.

If any effect of the turbine exhaust on the strain gauge measurements is noted, it may benecessary to allow time for the strain gauge readings to stabilize.

6.15.2 Heat generated during the drilling process

Heat is generated during the drilling process and this causes localized heating of the straingauge area.


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It is therefore necessary to wait for undesired thermal strains to gradually reduce and for gaugeoutput to stabilize. This is particularly important for materials with poor thermal conductivity.

The delay time before acquisition of strain measurements depends on the material, the shape ofthe workpiece, and the ambient temperature.

Standard ASTM E837-08 prescribes waiting at least 5 seconds between the end of drilling andreading strain gauge output to allow the surface to cool. The cutter need not be retracted.

In practice, the signal stabilization time depends on the thermal conductivity and thickness ofthe material. In metal materials stabilization occurs in 3 to 10 seconds.

6.16 Measurement of hole dimensions and eccentricity.

After completion of the hole-drilling process it is necessary to measure all the geometriccharacteristics of the drilled hole.

Figure 19 - Measurement of hole diameter and eccentricity

The diameter and eccentricity are measured starting with measurement of four radiuses of the

hole in two directions perpendicular to each other.

An optical microscope incorporating a graticule may be of aid for obtaining an enlarged image ofthe drilled hole boundary, utilizing visible light.

The overall hole shape should be analysed to check for any irregularities. It is usual for thecutting edge of the gauge backing material to be irregular.

Displacement is measured at these four positions with two dial indicators (if possible withgraduations of 0.001 mm) (Figure 19).The four displacement measurements (X1,X2,Y1,Y2) are then used to calculate the measurementof the hole diameter (average value in the two directions) and eccentricity as indicatedherebelow (Figure 20)

Indeed, the hole diameter in the two orthogonal directions (X and Y) and the average diameter

have the following definitions:

)( 21 XXDX += ( 1 )

)(21 YYDY += ( 2 )

2

)(,0

YX

M

DDD

+=

( 3 )


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Figure 20 - Off-centre hole, parameters necessary for calculating hole-rosette eccentricity

while hole eccentricity and orientation are:

2

)( 21 XXeX

=( 4 )

2

)( 21 YYeY

=( 5 )

22

YX eee += ( 6 )

and the eccentric angle is expressed as:

=

180arctan

X

Y

e

e

( 7 )

6.17 Final hole depth measurement check

After removing the strain gauge, the final hole depth can be measured using a conventionaldepth gauge. A depth measuring instrument like the one shown in Figure 21 can be used.

Figure 21 - Instrument for measuring hole depth


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Any difference from the expected hole depth (recorded during drilling by the micrometer gaugeof the drilling apparatus) should be taken into consideration.

Cutter wear, the grip between the tool holder and cutter shank, and inadequate stiffnessbetween the component and the drilling apparatus can all contribute to hole depth errors.

6.18 Practical example of application

Automatic residual stress measurement systems are generally used having the advantage ofenabling numerous depth increments to be drilled with adequate accuracy.

Briefly summarized, the measurement procedure involves the following steps:

installation of the strain gauge rosette and wiring of the gauge grids,

connection to the strain recording instrumentation,

positioning of the measurement system,

centring of the drilling tool over the centre of the rosette (aligned with the microscope),

manual advancement of the cutter to the surface of the workpiece using the fast verticaladvance,

set-up of the test parameters. For example:

o Hole depth: 2.0 mm,o Number of drilling increments: 40,

o Hole drilling curve: linear.

An automatic procedure makes it possible to:

start the high-speed turbine by acting on the air supply system,

determine the initial drilling point (identification of the zero reference surface) by anelectrical contact that is made with removal of the strain gauge backing film and bringingthe endmill into contact with the metal surface,

zero-balance the strain gauge circuits by a command to the strain recording system.

The automatic system drills the hole automatically in the set depth increments.

On completion of each depth increment and the time interval, the system records the threestrain gauge readings.

Hole-drilling procedure example:

tool: 1.6 mm. diameter, inverted cone, surface-treated, tungsten carbide endmill,

speed of rotation (typical): from 350,000 to 400,000 rpm,

feed rate: 0.2mm/min,

depth increment: 0.05 mm,

delay time: 5 seconds.

Typical results are presented in section 8 (Residual stress analysis software features)


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7 Residual stress analysis techniques

The following analysis techniques are presented in this section:

methods proposed by standard ASTM E837-08 (uniform and non-uniform stresses),

other methods for analysing non-uniform stresses within the hole depth.

Treatment of uniform stresses substantially follows the recommendations of ASTM E837-08,making the following distinctions:

thin workpiece,

thick workpiece,

workpiece with a thickness between 0.4 D and 1.2 D (0.48 D and 1.44 D for type Crosettes).

With respect to the prescriptions of ASTM E837-08, in addition to considering the case ofrosettes which are not necessarily the types A, B or C contemplated by the standard, theprocedures are provided here for plasticity correction and hole-rosette eccentricity correction.Although a uniform stress profile is rare in reality, it is useful for study purposes and forevaluating uncertainties in the measurement procedure.

Other methods are also proposed for analysis of non-uniform stresses, for example, the integralmethod [2, 25, 26], the Schwarz Kochelmann method [27] and lastly the HDM method [28, 29,30, 31, 32, 33, 34, 35].

The methods are made more generally suitable considering:

the possibility of varying both the depth between two successive drilling increments and thenumber of measured acquisition points (Integral, Schwarz-Kochelmann, HDM),

the possibility of having an eccentric hole, a centred hole being a particular case (HDM),

the use of improved influence functions using a more accurate database and a betterrepresentation of influence functions versus Poissons ratio (HDM),

the possibility of describing the state of stress with various functions (HDM).

Feature

plate of

Intermediate

Thickness

thick plate

Drilling spacing and

depthsNo No No No No Yes Yes Yes

Optimization of

calculation stepsNo No No No No No No Yes

Type of rosettes Yes (*) Yes (*) Yes (*) Yes (*) Yes (*) Yes (*)HBM rosette

onlyYes

Eccentricity CorrectionYes

(Ajovalasit [38])Yes (**)

(Ajovalasit

[38])

Yes (**)(Ajovalasit

[38])

NoYes

(HDM)Yes

(HDM)No Yes

Plasticity CorrectionYes (***)

(Beghini-Bertini

[3,47])

Yes (***)

(Beghini-

Bertini [3,47])

Yes (***)

(Beghini-

Bertini [3,47])

No No No No No

ASTM E837-

08

ASTM E837-

08 Mod.IntegralThrough-hole

Blind hole in a

Stress State / Methods of calculation

(*) Any type of rosette can be used: however, the new coeff icients need to be calculated.

(**) In the case of blind hole, the correction is indicative.

(***) The accuracy of the correction depends on the stress state and on the type of rosette used in the test.

Uniform stresses Non-uniform stresses

Schwarz -

KochelmannHDM

Table 5 - Residual stress calculation methods: principal features.


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Table 5 summarizes the techniques and major features of the residual stress analysis methods.The main corrections that can be applied to the results are also indicated.

7.1 Standard ASTM E837-08: general

The ASTM E837-08 standard is the procedure that can be used for measuring residual stressesin homogeneous isotropic linear-elastic materials. Application of this test method is limited to

low levels of eccentricity.

The standard allows residual stresses to be calculated directly when using the rosettesspecified in the standard (A, B and C). Nevertheless, it is possible to extend the standard by re-calculating the coefficients for other rosettes.

The standard provides accurate results if:

the equi-biaxial component of the residual stresses is less than 50% of the yield stress,

shear stresses in any direction are less than 25% of the yield stress.

However, in practice satisfactory results are achieved providing the residual stresses do notexceed 60% of the material yield stress.

7.1.1 Strain gauge rosettesFigure 4 shows the geometry of the strain gauge rosette and the preferred numbering for thedirection of the principal stresses.

The centres of the three radially oriented gauges are D/2 from the gauge target and the centreof the hole.

Although, in theory, the angles between the strain gauges can be chosen arbitrarily, the majorityof commercially available rosettes are rectangular with gauges oriented at 0/45/90. The typesof strain gauge rosette standardized by ASTM E837-08 are presented in Table 2.

In the ASTM type A rosette design (gauges in two quadrants, ie, at 0/225/90), gauge 2 (or b)has been transposed to be diametrically opposite its original position to give more samplingabout the hole position and a larger grid size.

The type B rosette has all three gauges in a single quadrant, ie, at 0/45/90, to allow thegauge to be used closer to obstructions such as corners or welds.

The ASTM type C rosette has a circular configuration and is formed of six diametrically opposedcircumferential and radial grids. Compared to the other rosettes, this design provides greatersensitivity and accuracy.

7.1.2 Strain relief in proximity to the hole

Considering the state of uniform stress in proximity to the hole, schematically illustrated inFigure 2 surface strain relief is tied to residual stresses , ,x y xy by the following relationship:

( 8 )

The two calibration constants a and b are dimensionless, almost independent of theproperties of the material, and vary with hole depth, as indicated in Table 2.

In the case of a through-hole in a thin workpiece, a is independent of the Poissons ratio.

Whereas, considering the case of non-uniform stresses within depth, the surface strain reliefassociated with the hole depth step j ( jk1 ) is tied to the relieved principal stresses by the

following relationship:

( ) ( )

2sin1

2cos2

1

2

1+

+

+

+= xy

yxyx

r bE

bE

aE


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( ) ( )

2sin)(1

2cos2

1

2

1

111

kxy

j

k

jk

k

j

k

yx

jk

k

j

k

yx

jkj bE

bE

aE

===

+

+

++=

( 9 )

The two calibration constants jka and jkb indicate the strains relieved by the drilling process at

the depth associated with hole step j.

7.1.3 Numerical values of aandb

Table 6 shows the numerical values of a and b for a blind hole and through hole, for the type

A, B and C rosettes specified by the ASTM E837-08 standard.

Table 2 indicates the dimensions provided in standard ASTM E837-08 for type A, B and Crosettes.

Finally, Table 4 gives the hole diameters and depth steps recommended for each rosette.

Table 6 - Numerical values of coefficients a and b provided by standard ASTM E837-08 for type A, B

and C rosettes for uniform stress evaluations with through holes and blind holes.

7.1.4 Sensitivity of the method

The strain relieved by hole-drilling is a fraction of the maximum relievable strain.

For a uniaxial tensile stress field (2/1 = x/y = 0) relieved strain in direction =0 is obtained onthe basis of

2

1

2

1

2

1

2

1 11 ++

=++

= bE

aE

bE

aE

xx

r

( 10 )


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Whereas the maximum relievable strain is:

E

1=

0 ( 11 )

Assuming as the sensitivity merit index the equation:

0

r

S= ( 12 )

it follows that:

00

2

1

2

1

BAE

bE

aE

S +=

+

+

=

( 13 )

where the values of A0 and B0 are to be found in literature [37] ]:

( ) ( )( ) ( )2112

2

0

0

2

1

+= RRG

D

AW ( 14 )

( )( )( )

( )

+

+++

+= 11

2

1

0

2121

12

2

0

0 2cos2sin2

2sin22sin21

14

2

21

R

D

RRG

D

BW

+22

2

2

0

2cos2sin2

R

D

( 15 )

where:

1

12

arctanR

d= ( 16 )

2

22

arctanR

d= ( 17 )

To increase strain relieving efficiency it is necessary to [37] ]:

adopt high values for (D0/2)/R1, that is, drill holes with the biggest diameter possible,compatibly with the need to avoid parasitic effects on the inner edge of the strain gauge(paragraph 6.7),

use rosettes with a short gauge length (low R2/R1 values),

use rosettes with reduced grid width (low GW/R1 values),

have the usual S values around 0.3.

Special rosettes are also available (ASTM Type C) with six grids, three of which are radial andthree circumferential, which are wired in a half-bridge configuration (using a radial grid and thediametrically opposed circumferential grid).

This achieves a sensitivity equal to 2.3 times the sensitivity of the corresponding ASTMstandard Type A or B.


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7.2 Standard ASTM E837-08: calculation of residual stresses

7.2.1 Thin workpiece

For a thin workpiece or a through hole (thicknesss 0.4 D plane stres

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