ASTM E837-20

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

SIGNIFICANCE AND USE
5.1 Summary:  
5.1.1 Residual stresses are present in almost all materials. They can be created during the manufacture or during the life of the material. Residual stresses can be a major factor in the failure of a material, particularly one subjected to alternating service loads or corrosive environments. Residual stress may also be beneficial, for example, the compressive stresses produced by shot peening. The hole-drilling strain-gage technique is a practical general-purpose method for determining residual stresses.
SCOPE
1.1 Residual Stress Determination:  
1.1.1 This test method specifies a hole-drilling procedure for determining in-plane residual stresses near the surface of an isotropic linearly elastic material. It is applicable to residual stress determinations where the stresses do not vary significantly across the diameter of the drilled hole. The measured stresses are the in-plane residual stresses that exist within the depth of the drilled hole. Stress sensitivity rapidly decreases with depth from the measured surface and deep interior stresses cannot be evaluated. The measured residual stresses are described as “uniform” if they remain approximately constant within the hole depth, “non-unifom” if they vary significantly.  
1.1.2 In general, “blind” holes are used, where the depth of the drilled hole and therefore the depth of the residual stress evaluation is less than the workpiece thickness. However, for a thin workpiece, it is also possible to do through-thickness measurements of uniform (membrane) stresses using a through-hole.  
1.2 Stress Measurement Range:  
1.2.1 This test method applies in cases where material behavior is linear-elastic. When near-yeild residual stresses are present, it is possible for local yielding to occur due to the stress concentration around the drilled hole. Satisfactory measurement results can be achieved providing the residual stresses do not exceed about 80 % of the material yield stress for blind-hole drilling and about 50 % of the material yield stress for through-hole drilling.  
1.3 Workpiece Damage:  
1.3.1 The hole-drilling method is often described as “semi-destructive” because the damage that it causes is localized and often does not significantly affect the usefulness of the workpiece. In contrast, most other mechanical methods for measuring residual stresses substantially destroy the workpiece. Since hole drilling does cause some damage, this test method should be applied only in those cases either where the workpiece is expendable, or where the introduction of a small shallow hole will not significantly affect the usefulness of the workpiece.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Sep-2020
• ICS: 77.040.10 - Mechanical testing of metals
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.13 - Residual Stress Measurement

Relations

• Refers: ASTM E251-20a - Standard Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages
• Effective Date: 01-Jun-2020
• Refers: ASTM E251-20 - Standard Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages
• Effective Date: 01-May-2020
• Refers: ASTM E251-92(2014) - Standard Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages
• Effective Date: 15-Apr-2014
• Refers: ASTM E6-09be1 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 15-May-2009
• Refers: ASTM E6-09b - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 15-May-2009
• Refers: ASTM E251-92(2009) - Standard Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages
• Effective Date: 01-Apr-2009
• Refers: ASTM E6-09a - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Apr-2009
• Refers: ASTM E6-09 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Jan-2009
• Refers: ASTM E6-08a - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Oct-2008
• Refers: ASTM E6-08 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Feb-2008
• Refers: ASTM E6-07b - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Nov-2007
• Refers: ASTM E6-07a - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Jun-2007
• Refers: ASTM E6-07 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Mar-2007
• Refers: ASTM E6-06 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Apr-2006
• Refers: ASTM E6-03e1 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 10-Jun-2003

Overview

ASTM E837-20 is a widely recognized international standard developed by ASTM International for the determination of residual stresses in materials. The standard details the hole-drilling strain-gage method-a practical and general-purpose approach for measuring in-plane residual stresses near the surface of isotropic, linearly elastic materials. Residual stresses, which result from manufacturing or service conditions, can significantly influence a material's structural performance, potentially leading to failure under cyclic loads or corrosive environments. However, they may also be beneficial in controlled scenarios, such as in components that undergo shot peening.

The hole-drilling strain-gage method is considered semi-destructive, as it causes only localized damage, preserving much of the workpiece's utility-an important advantage over more destructive testing methods.

Key Topics

• Residual Stress Measurement: The standard specifies how to assess in-plane residual stresses near the test surface. The sensitivity of the method diminishes rapidly with depth; therefore, it is best suited for evaluating near-surface stresses.

• Blind and Through-Hole Techniques: Generally, "blind" holes-those that do not penetrate the entire workpiece-are used, allowing stress profiling without compromising the component's integrity. For thin workpieces, "through-holes" are permissible.

• Material Suitability: The method applies to isotropic, linearly elastic materials. When residual stresses approach the material's yield stress, localized plastic deformation may occur. Accurate results are typically obtained when stresses are within about 80% of yield strength for blind-hole drilling and 50% for through-hole drilling.

• Roquette Strain Gage Arrangement: The use of a strain gage rosette-a cluster of at least three strain gauges-is essential for capturing strain data around the drilled hole. Standardized rosettes simplify stress calculations and improve measurement repeatability.

• Localized Measurement: The technique provides a very localized measurement of stress, offering critical insight into specific high-stress regions on a component.

Applications

ASTM E837-20 finds application across various industries, including:

• Aerospace and Automotive: Assessing stresses in critical load-bearing parts to prevent fatigue failure or optimize design.
• Civil Engineering: Evaluating residual stresses in structural components, welds, or reinforcements.
• Manufacturing Quality Control: Verifying the effects of heat treatments, surface treatments (like shot peening), and other manufacturing processes intended to control residual stress distributions.
• Material Research: Comparing the effects of different fabrication or joining techniques on residual stress states in prototype or production materials.
• Failure Analysis: Investigating failed components to determine whether residual stress contributed to material degradation or fracture.

This method is particularly valued where non-destructive evaluation is required, but some degree of localized, controlled material penetration is acceptable.

Related Standards

• ASTM E6 – Terminology Relating to Methods of Mechanical Testing: Provides foundational definitions relevant to mechanical testing, including residual stress.
• ASTM E251 – Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages: Covers quality and performance assessment of strain-gage sensors used in the hole-drilling method.

Additional guidance is often aligned with the principles established by the World Trade Organization Technical Barriers to Trade (TBT) Committee, ensuring international relevance and harmonization.

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Keywords: ASTM E837-20, residual stress, hole-drilling strain-gage method, in-plane residual stresses, semi-destructive testing, stress measurement, strain rosette, mechanical testing, non-uniform residual stress, blind-hole, through-hole, ASTM standards.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E837 − 20
Standard Test Method for
Determining Residual Stresses by the Hole-Drilling Strain-
Gage Method
This standard is issued under the fixed designation E837; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The hole-drilling strain-gage method determines residual stresses near the surface of an isotropic
linear-elastic material. It involves attaching a strain rosette to the surface, drilling a hole at the
geometric center of the rosette, and measuring the resulting relieved strains. The residual stresses
withintheremovedmaterialarethendeterminedfromthemeasuredstrainsusingaseriesofequations.
1. Scope 1.3 Workpiece Damage:
1.3.1 The hole-drilling method is often described as “semi-
1.1 Residual Stress Determination:
destructive” because the damage that it causes is localized and
1.1.1 This test method specifies a hole-drilling procedure
often does not significantly affect the usefulness of the work-
fordeterminingin-planeresidualstressesnearthesurfaceofan
piece. In contrast, most other mechanical methods for measur-
isotropic linearly elastic material. It is applicable to residual
ing residual stresses substantially destroy the workpiece. Since
stress determinations where the stresses do not vary signifi-
hole drilling does cause some damage, this test method should
cantly across the diameter of the drilled hole. The measured
be applied only in those cases either where the workpiece is
stresses are the in-plane residual stresses that exist within the
expendable, or where the introduction of a small shallow hole
depth of the drilled hole. Stress sensitivity rapidly decreases
will not significantly affect the usefulness of the workpiece.
withdepthfromthemeasuredsurfaceanddeepinteriorstresses
1.4 This standard does not purport to address all of the
cannot be evaluated. The measured residual stresses are de-
safety concerns, if any, associated with its use. It is the
scribed as “uniform” if they remain approximately constant
responsibility of the user of this standard to establish appro-
within the hole depth, “non-unifom” if they vary significantly.
priate safety, health, and environmental practices and deter-
1.1.2 In general, “blind” holes are used, where the depth of
mine the applicability of regulatory limitations prior to use.
the drilled hole and therefore the depth of the residual stress
1.5 This international standard was developed in accor-
evaluation is less than the workpiece thickness. However, for a
dance with internationally recognized principles on standard-
thin workpiece, it is also possible to do through-thickness
ization established in the Decision on Principles for the
measurements of uniform (membrane) stresses using a
Development of International Standards, Guides and Recom-
through-hole.
mendations issued by the World Trade Organization Technical
1.2 Stress Measurement Range:
Barriers to Trade (TBT) Committee.
1.2.1 This test method applies in cases where material
behavior is linear-elastic.When near-yeild residual stresses are
2. Referenced Documents
present, it is possible for local yielding to occur due to the
2.1 ASTM Standards:
stress concentration around the drilled hole. Satisfactory mea-
E6Terminology Relating to Methods of Mechanical Testing
surement results can be achieved providing the residual
E251Test Methods for Performance Characteristics of Me-
stresses do not exceed about 80% of the material yield stress
tallic Bonded Resistance Strain Gages
for blind-hole drilling and about 50% of the material yield
stress for through-hole drilling.
3. Terminology
3.1 Definitions of terms common to mechanical testing:
This test method is under the jurisdiction of ASTM Committee E28 on
Mechanical Testing and is the direct responsibility of Subcommittee E28.13 on
Residual Stress Measurement. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Oct. 1, 2020. Published November 2020. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1981. Last previous edition approved in 2013 as E837–13a DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0837-20. theASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E837 − 20
3.1.1 The terms accuracy, calibration, lead wire, precision, 4. Summary of Test Method
residual stress, resolution, verification, and yield strength are
4.1 Workpiece:
used as defined in Terminology E6.
4.1.1 Aflatuniformsurfaceareaawayfromedgesandother
3.2 Definitions of Terms Specific to This Standard: irregularitiesischosenasthetestlocationwithintheworkpiece
of interest. Fig. 1 schematically shows the residual stresses
3.2.1 intermediate workpiece, n—a workpiece whose thick-
actingatthetestlocationatwhichaholeistobedrilled.These
ness is between that of thin and thick workpieces.
stresses are assumed to be uniform within the in-plane direc-
3.2.2 thick workpiece, n—a workpiece whose thickness is
tions x and y.
sufficiently large that its strain versus hole depth response is
independent of its thickness. NOTE 1—For reasons of pictorial clarity in Fig. 1, the residual stresses
are shown as uniformly acting over the entire in-plane region around the
3.2.3 thin workpiece, n—a workpiece whose thickness is
test location. In actuality, it is not necessary for the residual stresses to be
sufficiently small that its strain versus hole depth response is
uniform over such a large region. The surface strains that will be relieved
by drilling a hole depend only on the stresses that originally existed at the
proportional to its thickness.
boundaries of the hole. The stresses beyond the hole boundary do not
3.3 Symbols:
affecttherelievedstrains,eventhoughthestrainsaremeasuredbeyondthe
hole boundary. Because of this, the hole-drilling method provides a very
a¯ = calibration constant for isotropic stresses
localized measurement of residual stresses.
¯
b = calibration constant for shear stresses
4.1.2 Fig. 1(a) shows the case where the residual stresses in
a¯ = calibration matrix for isotropic stresses
jk
the workpiece are uniform in the depth direction. The in-plane
¯
b = calibration matrix for shear stresses
jk
stresses are σ , σ and τ throughout the thickness.
D = diameter of the gage circle, see Table1. x y xy
4.1.3 Fig. 1(b) shows the case where the residual stresses in
D = diameter of the drilled hole
the workpiece vary in the depth direction. The calculation
E = Young’s modulus
method described in this test method represents the stress
F = fractional workpiece thickness
f = fractional hole diameter profileasastaircaseshape,wherethedepthstepscorrespondto
h = hole depth at step j
the depth increments used during the hole-drilling measure-
j
H = stress depth at step k
ments.Withindepthstep k,thein-planestressesare(σ ) ,(σ )
k
x k y k
j = number of hole depth steps so far
k = sequence number for stress depth steps
P = uniform isotropic (equi-biaxial) stress
P = isotropic stress within hole depth step k
k
p = uniform isotropic (equi-biaxial) strain
p = isotropic strain after hole depth step k
k
Q = uniform 45° shear stress
Q = 45° shear stress within hole depth step k
k
q = uniform 45° shear strain
q = 45° shear strain after hole depth step k
k
T = uniform x-y shear stress
T = x-y shear stress within hole depth step k
k
t = x-y shear strain
t = x-y shear strain after hole depth step k
k
T = (superscript) matrix transpose
W = workpiece thickness
(a)
α = regularization factor for P stresses
P
α = regularization factor for Q stresses
Q
α = regularization factor for T stresses
T
β = clockwise angle from the x-axis (gage 1) to the
maximum principal stress direction
ε = relieved strain for “uniform” stress case
ε = relieved strain measured after j hole depth steps
j
have been drilled
ν = Poisson’s ratio
θ = angle of strain gage from the x-axis
σ = maximum (more tensile) principal stress
max
α = minimum (more compressive) principal stress
min
σ = uniform normal x-stress
x
(σ ) = normal x-stress within hole depth step k
x k
σ = uniform normal y-stress
y
(b)
(σ ) = normal y-stress within hole depth step k
y k
τ = uniform shear xy-stress
xy
FIG. 1 Hole Geometry and Residual Stresses, (a) Uniform
(τ ) = shear xy-stress within hole depth step k
xy k
Stresses, (b) Non-uniform Stresses
E837 − 20
and (τ ) . In cases where there is doubt about the uniformity
xy k
of the residual stresses, the stresses shall be assumed to be
non-uniform.
NOTE2—The "uniformstress"caseoccurswhenitisknowninadvance
that membrane type stresses dominate the residual stress distribution.
However, bending stresses and surface stresses may also be present and
cause significant deviations from stress uniformity. Thus, when in doubt,
a non-uniform residual stress calculation is a safe general choice. The
corresponding “uniform stress” value is an average of the stresses that
exist within the hole depth, weighted in favor of the stresses near the
measured surface. This value may be useful as an indicator of the general
residual stress level.
4.1.4 Aworkpiece of thickness up to 0.25D for a typeAor
B rosette, or 0.6D for a type C rosette (see Fig. 4) is described
as “thin”. The thickness of such a workpiece is sufficiently
small that its strain versus hole depth response is proportional
to its thickness. A blind hole can be used for “uniform” or
“non-uniform” measurements of near-surface residual stresses.
Alternatively,athrough-holecanbeusedforthrough-thickness
measurements of uniform membrane stresses.
4.1.5 Aworkpiece of thickness greater than 0.6D for a type
Aor B rosette (1, 2) , or 1.3D for a type C rosette (see Fig. 2)
is described as “thick”. The thickness of such a workpiece is
sufficiently large that its strain versus hole depth response is
independent of its thickness. A blind hole may be used for
“uniform” or “non-uniform” measurements of near-surface
residual stresses.
4.1.6 Aworkpiece of thickness between the limits specified
FIG. 2 Hole-Drilling Rosettes
for “thin” and “thick” workpieces is described as “intermedi-
ate”.Ablindholemaybeusedfor“uniform”or“non-uniform”
measurements of near-surface residual stresses. resistance to measurement noise can be achieved by aligning
rosette elements 1 and 3 with the principal residual stress
4.2 Strain Gage Rosette:
directions, if those directions are known in advance.Although
4.2.1 A strain gage rosette with three or more elements of
desirable, such alignment is not essential to achieving satisfac-
the general type schematically illustrated in Fig. 3 is attached
tory results.
to the workpiece at the location under consideration. Improved
4.3 Hole-Drilling:
4.3.1 A hole is drilled in a series of steps at the geometric
The boldface numbers in parentheses refer to the list of references at the end of
center of the strain gage rosette.
this standard.
4.3.2 The residual stresses in the material surrounding the
drilled hole are partially relieved as the hole is drilled. The
associatedrelievedstrainsaremeasuredataspecifiedsequence
of steps of hole depth using a suitable strain-recording instru-
ment.
4.4 Residual Stress Calculation Method:
4.4.1 The residual stresses originally existing at the hole
locationareevaluatedfromthestrainsrelievedbyhole-drilling
using mathematical relations based on linear elasticity theory
(3-7). The relieved strains depend on the residual stresses that
existed in the material originally within the hole.
4.4.2 For the uniform stress case shown in Fig. 1 (a), the
surface strain relief measured after hole-drilling is:
11ν σ 1σ
x y
ε 5 a¯ (1)
E 2
1 σ 2 σ
x y
¯
1 b cos2θ
E 2
¯
1 b τ sin2θ
xy
FIG. 4 Physical Interpretation of Coefficients a¯ E
jk
E837 − 20
j
11ν
ε 5 a¯ σ 1σ /2 (2)
~~ ! !
j ( jk x y k
E
k51
j
¯
1 b ~~σ 2 σ !/2! cos2θ
( jk x y k
E
k51
j
¯
1 b ~τ ! sin2θ
( jk xy
k
E
k51
¯
4.4.5 The calibration constants a¯ and b indicate the
jk jk
relieved strains in a hole j steps deep, due to unit stresses
within hole step k. Fig. 4 shows cross-sections of drilled holes
for an example sequence where a hole is drilled in four depth
steps. Within this sequence, calibration constant represents an
intermediatestagewheretheholehasreached3stepsdeep,and
has a unit stress acting within depth step 2. Numerical values
of the calibration constants have been determined by finite
element calculations (6) for standard rosette patterns, and are
tabulated in this test method.
4.4.6 Measurement of the relieved strains after a series of
holedepthstepsprovidessufficientinformationtocalculatethe
stresses σ , σ and τ withineachstep.Fromthesestresses,the
x y xy
(a)
corresponding principal stresses σ and σ and their
max min
orientation β can be found.
4.4.7 The relieved strains are mostly influenced by the
near-surface residual stresses. Interior stresses have influences
that diminish with their depth from the surface. Thus, hole-
drilling measurements can evaluate only near-surface stresses.
Deep interior stresses cannot be identified reliably.
4.4.8 When near-yield residual stresses are present, it is
possible for local yielding to occur due to the stress concen-
tration around the drilled hole. Satisfactory measurement
results can be achieved providing the residual stresses do not
exceed about 80% of the material yield stress for blind-hole
drilling (9), and about 50% of the material yield stress for
through-hole drilling.
(b)
5. Significance and Use
FIG. 3 Schematic Geometry of a Typical Three-Element Clock-
5.1 Summary:
wise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b) Detail of
5.1.1 Residual stresses are present in almost all materials.
a Strain Gage
They can be created during the manufacture or during the life
of the material. Residual stresses can be a major factor in the
failure of a material, particularly one subjected to alternating
¯
4.4.3 The calibration constants a¯ and b indicate the relieved service loads or corrosive environments. Residual stress may
strains due to unit stresses within the hole depth. They are also be beneficial, for example, the compressive stresses
dimensionless,almostmaterial-independentconstants.Slightly produced by shot peening. The hole-drilling strain-gage tech-
different values of these constants apply for a through- nique is a practical general-purpose method for determining
residual stresses.
thickness hole made in a thin workpiece and for a blind hole
made in a thick workpiece. Numerical values of these calibra-
6. Workpiece Preparation
tion constants have been determined from finite element
calculations (6, 8) for standard rosette patterns, and are 6.1 Requirements:
tabulated in this test method. 6.1.1 A smooth surface is usually necessary for strain gage
4.4.4 Forthenon-uniformstresscaseshowninFig.1(b),the application. Abrading or grinding that could appreciably alter
surface strain relief measured after completing hole depth step the surface stresses shall not be used. Alternatively, chemical
j depends on the residual stresses that existed in the material etching could be used, thus avoiding the need for mechanical
originally contained in all the hole depth steps 1 ≤ k ≤ j: abrasion.
E837 − 20
6.1.2 The surface preparation prior to bonding the strain 7.2.1 Several different standardized rosettes are available to
gages shall conform to the recommendations of the manufac- meet a wide range of residual stress measurement needs. The
tureroftheadhesiveusedtoattachthestraingages.Athorough use of standardized rosette designs greatly simplifies the
cleaning and degreasing is required. In general, surface prepa- calculation of the residual stresses. Fig. 2 shows three different
ration should be restricted to those methods that have been rosette types and Table 1 lists their dimensions.
demonstrated not to induce or remove significant residual
7.2.2 ThetypeArosetteshowninFig.2wasfirstintroduced
surface stresses. This is particularly important for workpieces
by Rendler andVigness (3).This pattern is available in several
that contain sharp near-surface stress gradients.
different sizes, and is recommended for general-purpose use.
NOTE 4—Choice of rosette size is a primary decision. Larger rosettes
7. Strain Gages and Instrumentation
tend to give more stable strain measurements because of their greater
7.1 Rosette Geometry:
capacity to dissipate heat. They are also able to identify residual stresses
7.1.1 A rosette comprising three single or pairs of strain
to greater depths. Conversely, smaller rosettes can fit smaller workpieces,
require smaller drilled holes, and give more localized measurements.
gage grids shall be used. The numbering scheme for the strain
gages follows a clockwise (CW) convention (10).
7.2.3 The type B rosette shown in Fig. 2 has all strain gage
gridslocatedononeside.Itisusefulwheremeasurementsneed
NOTE3—Thegagenumberingschemeusedfortherosetteillustratedin
Fig. 3 differs from the counter-clockwise (CCW) convention often used to be made near an obstacle.
for general-purpose strain gage rosettes and for some other types of
7.2.4 ThetypeCrosetteshowninFig.2isaspecial-purpose
residual stress rosette. If a strain gage rosette with CCW gage numbering
pattern with three pairs of opposite strain gage grids that are to
is used, the residual stress calculation procedure described in this test
be connected as three half-bridges. It is useful where large
method still applies. The only changes are that the numbering of gages 1
strain sensitivity and high thermal stability are required (11).
and 3 are interchanged and that the angle β defining the direction of the
most tensile principal stress σ is reversed and is measured counter-
max
7.3 Installation and Use:
clockwise from the new gage 1.
7.3.1 The strain gage rosette should be attached to the
7.1.2 The gages shall be arranged in a circular pattern,
workpiece surface such that its center is at least 1.5D from the
equidistant from the center of the rosette.
nearest edge, or the boundary of another material should the
7.1.3 The gage axes shall be oriented in each of three
workpiece comprise more than one material.
directions, (1) a reference direction, (2) 45° or 135° to the
7.3.2 When using a type B rosette adjacent to an obstacle,
reference direction, and (3) perpendicular to the reference
the center of the rosette should be at least 0.5D from the
direction. Direction (2) bisects directions (1) and (3), as shown
obstacle, with the set of strain gages diametrically opposite to
in Fig. 3.
the obstacle.
7.1.4 The measurement direction of gage 1 in Fig. 3 is
7.3.3 The application of the strain gage (bonding, wiring,
identified as the x-axis. The y-axis is 90° counterclockwise of
the x-axis. protective coating) should closely follow the manufacturer’s
recommendations, and shall ensure the protection of the strain
7.1.5 The center of the gage circle shall be clearly identifi-
able. gage grid during the drilling operation.
7.3.4 The strain gages should remain permanently con-
7.2 Standardized Rosettes:
nected and the stability of the installation shall be verified. A
resistance to ground of at least 20000 MΩ is preferable.
A
TABLE 1 Rosette Dimensions
7.3.5 Checks should be made to validate the integrity of the
B B B B
Rosette Type D GL GW R R
gage installation. If possible, a small mechanical load should
1 2
Type A
be applied to the workpiece to induce some modest strains.
Conceptual D 0.309D 0.309D 0.3455D 0.6545D
(SeeTest Method E251.)The observed strains should return to
1 zero when the load is removed. In addition, a visual inspection
⁄32 in. nominal 0.101 0.031 0.031 0.035 0.066
(2.57) (0.79) (0.79) (0.89) (1.68)
of the rosette installation should be made to check for possible
areas that are not well bonded. If incomplete bonding is
⁄16 in. nominal 0.202 0.062 0.062 0.070 0.132
observed, the rosette shall be removed and replaced.
(5.13) (1.59) (1.59) (1.77) (3.36)
1 7.4 Instrumentation:
⁄8 in. nominal 0.404 0.125 0.125 0.140 0.264
(10.26) (3.18) (3.18) (3.54) (6.72)
7.4.1 Theinstrumentationforrecordingofstrainsshallhave
Type B
-6
a strain resolution of 61×10 , and stability and repeatability
Conceptual D 0.309D 0.223D 0.3455D 0.6545D
-6
of the measurement shall be at least1×10 . The lead wires
⁄16 in. nominal 0.202 0.062 0.045 0.070 0.132
from each gage should be as short as practicable and a
(5.13) (1.59) (1.14) (1.77) (3.36)
three-wire temperature-compensating circuit (12) should be
Type C
Conceptual D 0.176D 30° 0.412D 0.588D
used with rosette typesAand B. Half-bridge circuits should be
sector
used with rosette type C, the resulting outputs of which are
1 designated ε , ε , and ε .
⁄16 in. nominal 0.170 0.030 30° 0.070 0.100 1 2 3
(4.32) (0.76) (30°) (1.78) (2.54)
A
Dimensions are in inches (mm). 8. Procedure
B
Rosette dimensions are defined in Fig. 3.
8.1 Suggested Preparatory Reading:
E837 − 20
8.1.1 References (13), (14), and (15) provide substantial possiblelocalizedresidualstresscreation.Toavoidambiguities
practical guidance about how to make high-quality hole- in hole diameter identification, the taper angle should not
drilling residual stress measurements. These publications are exceed 5° on each side.
excellent preparatory reading, particularly for practitioners 8.2.8 Some commercially available burs have diagonal
who infrequently make hole-drilling measurements. chamfers formed at the corners of the side and front cutting
edges. This adaptation produces holes with non-uniform depth
8.2 Drilling Equipment and Use:
andsonotbeusedexceptforthrough-thicknessmeasurements.
8.2.1 A device that is equipped to drill a hole in the test
8.2.9 Drilling can be done by plunging, where the cutter is
workpiece in a controlled manner is required. The device shall
advanced axially.Alternatively, an orbiting technique (18) can
be able to drill a hole aligned concentric with the strain gage
be used, where the rotation axis of the cutter is deliberately
circle to within 60.001in. (0.025mm). It shall also be able to
offset from the hole axis.The cutter is advanced axially, and is
control the depth of the hole to within 60.001in. (0.025mm).
then orbited so that the offset traces a circular path and the
8.2.2 Severaldrillingtechniqueshavebeeninvestigatedand
cutter creates a hole larger than its diameter. The direct plunge
reported to be suitable for the hole drilling method. The most
method has the advantage of simplicity. The orbiting method
common drilling technique suitable for all but the hardest
hastheadvantagesofholediameteradjustmentthroughchoice
materialsinvolvestheuseofcarbidebursorendmillsdrivenby
ofoffset,useofthecylindricalcuttingedgesaswellasthoseon
a high-speed air turbine or electric motor rotating at 20000 to
the end surface, and clearer chip flow.
400000 rpm (16). Low-speed drilling using a drill-press or
8.2.10 Table 2 indicates the target hole diameter ranges
power hand-drill is discouraged because the technique has the
appropriateforthevariousrosettetypes.Differentrangesapply
tendency to create machining-induced residual stresses at the
to uniform and non-uniform stress measurements.
hole boundary.
8.2.11 The size of the measured strains increases approxi-
8.2.3 For very hard materials, abrasive jet machining can
mately proportionally with the square of the hole diameter.
also be useful. This drilling method involves directing a
Thus,holesatthelargerendoftherangearepreferred.Ifusing
high-velocity stream of air containing fine abrasive particles
the plunging method, the cutter diameter should equal the
through a small-diameter nozzle against the workpiece (7).
target diameter. If using the orbiting method, the cutter
Abrasivejetmachiningcanbelesssuitableforsoftermaterials.
diameter should be 60 to 90% of the target diameter, with an
Itsuseshouldbelimitedtothrough-thicknessmeasurementsof
offset chosen to achieve a hole with the target diameter.
uniform (membrane) stresses because the hole geometry and
8.2.12 All drilling should be done under constant tempera-
depth cannot be controlled sufficiently tightly.
ture conditions. After each drilling step, the cutter should be
8.2.4 When using burs or endmills, carbide “inverted cone”
stopped to allow time for stabilization of any temperature
dental burs or small carbide endmills can be suitable as cutting
fluctuations caused by the drilling process and air turbine
tools. Commercially available cutters are designed for a wide
exhaust. Strain readings should attain their final values for at
range of applications, and not all types may be suited for hole
least five seconds before being accepted.
drilling residual stress measurements. Thus, a verification of
8.3 Drilling Procedure for a “Thin” Workpiece with Uni-
drillingtechniqueandchoiceofcuttershouldbedonewhenno
form Through-Thickness Stresses:
prior experience is available. Verification could consist of
8.3.1 For a “thin” workpiece, as defined in 4.1.3, obtain an
applying a strain gage rosette to a stress-free workpiece of the
initial reading from each gage before starting the drilling
same nominal test material produced by the annealing heat
operation.
treatment method (3, 7, 16, 17), and then drilling a hole. If the
8.3.2 Start the cutter and slowly advance it until it cuts
drilling technique and cutter are satisfactory, the strains pro-
through the entire thickness of the workpiece. If using the
duced by the drilling will be small, typically within 68µε.
orbiting technique, also orbit the cutter. Stop and retract the
8.2.5 If the drilling technique verification shows significant
cutter. Then measure one set of strain readings ε , ε and ε .
1 2 3
strains induced by the drilling process, or if the test material is
8.3.3 Measure the hole diameter and confirm that it lies
known to be difficult to machine, it can be helpful to lubricate
within the target range specified in Table 2.
the drilling cutter with a suitable lubricating fluid. The fluid
8.3.4 Check the hole concentricity and confirm that it lies
used shall be electrically non-conductive. Aqueous or other
within the tolerance specified in 8.2.1.
electrically conductive lubricants shall not be used because
8.3.5 Computeuniformresidualstressesasdescribedin9.2.
they can penetrate the strain gage electrical connections and
distort the strain readings. 8.4 Drilling Procedure for a “Thick” or “Intermediate”
8.2.6 Theradialclearanceanglesofthecuttingedgesonthe Workpiece with Uniform Stresses:
end face of the cutting tool should not exceed 1°. This 8.4.1 For a “thick” or “intermediate” workpiece, as defined
requirement avoids ambiguities in hole depth identification by in 4.1.4, obtain an initial reading from each gage before
ensuring that the depth is uniform within 1% of the tool starting the drilling operation. Start the cutter and slowly
diameter. advanceituntilitcutsthroughtherosettebackingmaterialand
lightlyscratchestheworkpiecesurface.Thispointcorresponds
8.2.7 “Inverted cone” cutters have their maximum diameter
to “zero” cutter depth.
at their end face, tapering slightly towards the shank. The
tapered geometry provides clearance for the cylindrical cutting
NOTE 5—Some practitioners use a technique that identifies the “zero”
edgesasthetoolcutsthehole.Thisfeatureisdesirablebecause
pointbythecompletionofanelectricalconnectionbetweenthecutterand
it minimizes tool rubbing on the side surface of the hole and the workpiece.
E837 − 20
A
TABLE 2 Workpiece Thicknesses, Hole Diameters and Depth Steps
Uniform Stresses Non-Uniform Stresses
Max. thickness Min. thickness
Rosette Type D of a of a
Min. hole Max. hole Practical Min. hole Max. hole Practical
“Thin” workpiece “Thick” workpiece
diameter diameter depth step diameter diameter depth step
Type A
Conceptual D 0.25 D 0.6 D 0.6 Max D Max D 0.02 D Min D Max D 0.01 D
0 0 0 0
⁄32 in. nominal 0.101 0.025 0.061 0.024 0.040 0.002 0.038 0.042 0.001
(2.57) (0.64) (1.54) (0.61) (1.01) (0.05) (0.96) (1.07) (0.025)
⁄16 in. nominal 0.202 0.050 0.121 0.060 0.100 0.004 0.076 0.084 0.002
(5.13) (1.28) (3.08) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
⁄8 in. nominal 0.404 0.101 0.242 0.132 0.220 0.008 0.152 0.168 0.004
(10.26) (2.56) (6.16) (3.35) (5.59) (0.20) (3.86) (4.27) (0.10)
Type B
Conceptual D 0.25 D 0.6 D 0.6 Max D Max D 0.02 D Min D Max D 0.01D
0 0 0 0
⁄16 in. nominal 0.202 0.050 0.121 0.060 0.100 0.004 0.076 0.084 0.002
(5.13) (1.25) (3.08) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
Type C
Conceptual D 0.60 D 1.30D 0.6 Max D Max D 0.024 D Min D Max D 0.012 D
0 0 0 0
⁄16 in. nominal 0.170 0.102 0.221 0.060 0.100 0.004 0.076 0.084 0.002
(4.32) (2.59) (5.62) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
A
Dimensions are in inches (mm).
8.4.2 Stop the cutter after reaching the “zero” point and changed. Use the new readings as the zero points for the
confirm that all strain gage readings have not significantly subsequent strain measurements.
changed. Use the new readings as the zero points for the 8.5.3 Start the cutter and advance it slowly by the Practical
subsequent strain measurements.
Depth Step listed in Table 2. Stop the cutter and record the
8.4.3 Start the cutter and advance it slowly by the Practical readings from each strain gage.
Depth Step listed in Table 2. If using the orbiting technique,
8.5.4 When working with a TypeAor B Rosette, repeat the
also orbit the cutter. Stop the cutter and record the readings
stepwise advance in hole depth followed by strain measure-
from each strain gage, ε , ε and ε . Other depth increments of
mentsinasequenceofequalPracticalDepthStepsuntilafinal
1 2 3
approximately similar size are also acceptable.
hole depth is reached, approximately equal to the minimum of
8.4.4 Repeat the stepwise advance in hole depth followed
0.2D or 0.6W.
by strain measurements in approximately similar hole depth
8.5.5 When working with a Type C Rosette, repeat the
steps until a final hole depth is reached approximately equal to
stepwise advance in hole depth followed by strain measure-
0.2D for a type A or B rosette, or 0.24D for a type C rosette.
mentsinasequenceofequalPracticalDepthStepsuntilafinal
hole depth is reached approximately equal to the minimum of
NOTE6—Thefinalholedepthissetat0.2Dor0.24Dbecausethislimits
0.24D or 0.05W.
thedamagedonetotheworkpiecebyleavingintactsomematerialsupport
below the hole to provide local reinforcement. This support reduces local
8.5.6 In circumstances where it may be desirable to
stress concentration effects and allows residual stress measurements to be
concentrate hole depth steps within a particular depth range, it
made to stresses up to 80% of the material yield stress. Up to about 20%
is permissible to use unequal hole depth steps. In this case, the
largerstrainscouldbemeasuredusingdeeperholes,butthispracticeisnot
total number of steps used should be in the range of 75%-
specified here because it increases workpiece damage and stress concen-
tration effects. 200% of the number of steps that would be made if using
equalPracticalDepthSteps,aslistedinTable2.Nostepshould
8.4.5 Measure the hole diameter and confirm that it lies
be larger than three times the listed Practical Depth Step.
within the target range specified in Table 2.
8.5.7 On completion of hole drilling, measure the hole
8.4.6 Check the hole concentricity and confirm that it lies
diameter and confirm that it lies within the target range
within the tolerance specified in 8.2.1.
specified in Table 2.
8.4.7 Computeuniformresidualstressesasdescribedin9.3.
8.5.8 Check the hole concentricity and confirm that it lies
8.5 Drilling Procedure for Workpieces with Non-Uniform
within the tolerance specified in 8.2.1.
Stresses:
8.5.9 Computenon-uniformresidualstressesasdescribedin
8.5.1 Obtain zero readings from each gage before starting
Section 10.
the drilling operation. Start the cutter and carefully advance it
until it cuts through the rosette backing material and lightly
9. Computation of Uniform Stresses
scratches the workpiece surface. This point corresponds to
“zero” cutter depth (see Note 5). 9.1 Assumption of Uniform Stress:
8.5.2 Stop the cutter after reaching the “zero” point and 9.1.1 A “uniform stress” calculation is appropriate when
confirm that all strain gage readings have not significantly priorinformationisavailable,forexample,basedonworkpiece
E837 − 20
geometry or processing procedure, that indicates the likely Et
T 5 τ 52 (10)
xy
presence of uniform residual stresses. This information should ¯
b
be recorded.
where:
9.1.2 If there is doubt as to whether or not the residual
P = isotropic (equi-biaxial) stress,
stresses that are present are substantially uniform, then a
Q = 45° shear stress, and
non-uniform residual stress measurement using the method
T = xy shear stress.
described in Section 10 shall be done.
9.1.3 Another purpose of doing a uniform stress calculation
9.2.5 Compute the in-plane Cartesian stresses σ , σ and τ
x y xy
istodeterminearepresentativesizeoftheresidualstressesthat
using:
arepresent.Inthiscase,the“uniformstress”willbeanaverage
σ 5 P 2 Q (11)
x
of the stresses that exist within the hole depth, weighted in
σ 5 P1Q (12)
favor of the stresses near the measured surface. y
τ 5 T (13)
xy
9.2 “Thin” Workpiece:
9.2.1 Compute the following combination strains for the
9.2.6 Compute the principal stresses σ and σ using:
max min
measured strains ε , ε , ε :
1 2 3
2 2
σ , σ 5 P6=Q 1T (14)
max min
p 5 ε 1ε /2 (3)
~ !
3 1
9.2.7 Themoretensile(orlesscompressive)principalstress
q 5 ~ε 2 ε !/2 (4)
3 1
σ is located at an angle β measured clockwise from the
max
t 5 ~ε 1ε 2 2ε !/2 (5)
3 1 2
directionofgage1inFig.3.Similarly,thelesstensile(ormore
9.2.2 Compute the fractional hole diameter f using:
compressive) principal stress σ is located at an angle β
min
measured clockwise from the direction of gage 3.
f 5 ~D ⁄ D 2 0.40!⁄0.10 ~forrosettetypesAorB! (6)
o
9.2.8 Compute the angle β using:
or
1 2T
β 5 arctan (15)
S D
2 2Q
f 5 D ⁄ D 2 0.48 ⁄0.12 ~forrosettetypeC!
~ !
o
9.2.9 Calculation of the angle β using the common one-
9.2.3 Use Table 3 and the following interpolation equation
argument arctan function, such as is found on an ordinary
to determine the numerical values of the calibration constants
¯
calculator, can give an ambiguity of 690°. The correct angle
a¯ and b corresponding to the hole diameter and type of rosette
may be found by using the two-argument arctan function
used.
(function atan2 in some computer languages), where the signs
a¯ D ⁄ D 5 0.5f 1 1 f a¯ (7)
~ ! ~ !
0 0.50
of the numerator and denominator are each taken into account.
Alternatively, the result from the one-argument calculation
1~1 1 f!~1 2 f! a¯
0.40
may be adjusted by adding or subtracting 90° as necessary to
20.5f 1 2 f a¯
~ !
place β within the appropriate range defined in Table 4.
0.30
9.2.10 Apositivevalueof β,say β=30°,indicatesthat σ
max
~forrosettetypesAandB!
lies 30° clockwise of the direction of gage 1.Anegative value
of β, say β = –30°, indicates that σ lies 30° counter-
¯ max
and analogously for b and for rosette type C.
clockwise of the direction of gage 1. In general, the direction
9.2.4 Compute the three combination stresses P, Q and T
of σ will closely correspond to the direction of the numeri-
max
corresponding to the three combination strains p, q and t using
cally most negative (compressive) relieved strain.
(6):
NOTE 7—The clockwise (CW) measurement direction for angle β
σ 1σ Ep
y x
defined in 9.2.10 applies only to a strain gage rosette with CW gage
P 5 52 (8)
2 a¯ 11ν
~ ! numbering, such as that illustrated in Fig. 3. The opposite measurement
direction for β applies to a counter-clockwise (CCW) strain gage rosette.
σ 2 σ Eq
y x
In such a rosette, the geometrical locations of gages 1 and 3 are
Q 5 52 (9)
2 ¯
b interchanged relative to the CW case. The new gage 1 becomes the
¯
TABLE 3 Through-Thickness Coefficients a¯ and b for Various Rosette Types and Hole Diameters
Rosette Coefficient D/D = 0.30 D/D = 0.40 D/D = 0.50
0 0 0
a¯ -0.090 -0.160 -0.250
A
¯
b -0.289 -0.478 -0.664
Rosette Coefficient D/D = 0.30 D/D = 0.40 D/D = 0.50
0 0 0
a¯ 0/096 -0.170 -0.266
B
¯
b -0.331 -0.542 -0.743
Rosette Coefficient D/D = 0.36 D/D = 0.48 D/D = 0.60
0 0 0
a¯ -0.265 –0.471 -0.736
C
¯
b -0.554 -0.806 -0.877
E837 − 20
TABLE 4 Placement of the Principal Angle β
9.3.1 Plot graphs of strains ε , ε , ε versus hole depth and
1 2 3
Q>0 Q=0 Q<0 confirm that the data follow generally smooth trends. Investi-
T < 0 45° < β < 90° 45° 0° < β < 45° gatesubstantialirregularitiesandobviousoutliers.Ifnecessary,
T = 0 90° undefined 0°
repeat the hole-drilling test.
T > 0 -90° < β < –45° –45° –45° < β<0°
9.3.2 For each set of ε , ε , ε measurements, calculate the
1 2 3
corresponding combination strains p, q and t using Eq 3-5.
9.3.3 Foreachoftheholedepthsh,j=.ncorrespondingto
reference gage. For a CCW rosette, a positive value of β, say β = 30°, j
indicates that σ lies 30° counter-clockwise of the direction of gage 1. the n sets of ε , ε , ε measurements, use the following
max
1 2 3
All other aspects of the residual stress calculation are identical for both
polynomial equation to determine the numerical values of the
CW and CCW rosettes.
¯
calibration constants a¯ and b for each of the three holes
9.2.11 If either of the computed principal stresses exceeds
dimaeters listed in Table 5. Use the polynomial coefficients for
50% of the material yield stress, then some localized yielding
workpiece thickness W/D= 0.6 for rosette types A and B, and
has possibly occurred in the material around the hole. In this
W/D=1.3forrosettetypeC.Thenumericalvaluesinthistable
case, the results are not quantitative, and shall be reported as
derive from finite element analyses (6).
“indicative” only. In general, the computed stresses whose
2 3 4 5
a¯ 5 C ~h ⁄ D!1C ~h ⁄ D! 1C ~h ⁄ D! 1C ~h ⁄ D! 1C ~h ⁄ D!
j 1 j 2 j 3 j 4 j 5 j
values exceed 50% of the material yield stress tend to be
(16)
overestimated. Their actual values are usually smaller than
¯
and analogously for a¯ and b for each of the three holes di-
indicated.
ameters in Table 5.
9.3 “Thick” Workpiece:
NOTE 8—The coefficients tabulated in Table 5, Table 6, Table 7, and
¯
TABLE 5 Polynomial Coefficients For Calibration Constants a¯ and b for Various Rosette Types, Hole Diameters And Workpiece
Thicknesses.
Data are applicable to hole depths in the range 0# h/D# 0.2 (#0.24 for type C).
¯
Rosette Polynomial Coefficients for Calibration Constant a¯ Polynomial Coefficients for Calibration Constant b
Type A
D/D W/D C1 C2 C3C4C5 C1 C2C3C4 C5
0.3 0.25 -.50362 -11.140 101.09 -319.99 402.56 -.81935 -12.734 87.089 -217.59 206.20
0.3 0.30 -.42321 -8.9426 74.746 -224.58 263.41 -.74914 -11.930 78.748 -193.69 185.87
0.3 0.40 -.33352 -7.2865 57.715 -170.69 194.44 -.67123 -11.294 71.862 -170.40 152.96
0.3 0.60 -.30948 -6.7619 54.91 -169.14 201.70 -.63325 -11.195 70.922 -167.49 148.52
0.4 0.25 -.86113 -19.711 169.71 -481.69 499.51 -1.4318 -21.788 153.77 -394.09 383.12
0.4 0.30 -.73061 -16.464 135.48 -388.12 412.48 -1.3121 -20.579 140.87 -346.97 309.78
0.4 0.40 -.60162 -13.605 107.70 -304.10 311.85 -1.1861 -19.766 132.33 -316.15 261.25
0.4 0.60 -.57899 -12.529 104.89 -323.22 374.46 -1.1344 -19.690 133.45 -325.40 279.39
0.5 0.25 -1.3214 -35.575 339.04 -1125.3 1399.7 -2.2249 -38.524 334.12 -1107.7 1438.6
0.5 0.30 -1.1574 -30.517 284.15 -951.32 1188.6 -2.0518 -37.085 317.13 -1030.5 1281.1
0.5 0.40 -1.0048 -26.130 241.63 -818.25 1028.0 -1.8786 -36.333 308.91 -998.97 1226.3
0.5 0.60 -1.0283 -22.771 219.75 -771.27 1002.3 -1.8255 -36.144 310.62 -1014.5 1258.2
¯
Rosette Polynomial Coefficients for Calibration Constant a¯ Polynomial Coefficients for Calibration Constant b
Type B
D/D W/D C1 C2 C3C4C5 C1 C2C3C4 C5
0.3 0.25 -.53572 -11.963 108.89 -345.92 435.69 -.89677 -14.486 97.399 -238.52 213.98
0.3 0.30 -.45097 -9.6437 81.038 -244.55 286.80 -.82656 -13.617 88.949 -215.84 200.10
0.3 0.40 -.35759 -7.8993 63.084 -187.45 213.48 -.74844 -12.930 81.943 -192.62 168.45
0.3 0.60 -.33297 -7.3189 59.985 -185.63 221.27 -.71045 -12.805 81.198 -191.21 166.82
0.4 0.25 -.91608 -21.388 186.48 -540.49 575.59 -1.5639 -25.004 175.87 -451.30 431.21
0.4 0.30 -.77905 -17.982 150.45 -440.98 481.04 -1.4431 -23.687 162.67 -404.14 361.30
0.4 0.40 -.64624 -14.925 120.51 -348.51 367.58 -1.3164 -22.787 153.97 -373.59 314.79
0.4 0.60 -.62400 -13.694 116.72 -365.77 429.85 -1.2647 -22.651 155.45 -386.21 339.5
0.5 0.25 -1.4114 -39.127 382.04 -1311.5 1692.6 -2.4244 -44.554 391.88 -1326.5 1748.0
0.5 0.30 -1.2463 -33.510 319.30 -1096.5 1403.1 -2.2485 -42.992 374.49 -1247.9 1587.5
0.5 0.40 -1.0907 -28.807 273.37 -950.25 1223.7 -2.0735 -42.136 366.11 -1216.8 1534.7
0.5 0.60 -1.1267 -24.700 243.88 -870.68 1146.0 -2.0213 -41.801 367.56 -1233.1 1569.7
¯
Rosette Polynomial Coefficients for Calibration Constant a¯ Polynomial Coefficients for Calibration Constant b
Type C
D/D W/D C1 C2 C3C4C5 C1 C2C3C4 C5
0.36 0.60 -.74676 -13.651 92.345 -238.45 238.02 -.90032 -17.049 83.732 -136.84 57.070
0.36 0.70 -.71128 -13.096 88.950 -231.18 231.99 -.93710 -17.319 86.252 -145.64 68.960
0.36 0.90 -.68292 -12.600 86.395 -226.61 229.03 -.98058 -17.658 89.221 -155.89 82.430
0.36 1.30 -.66901 -12.272 85.294 -225.90 229.79 -1.0250 -18.032 92.226 -166.02 95.450
0.48 0.60 -1.3720 -25.615 177.70 -457.43 441.18 -1.4956 -31.664 180.52 -364.85 242.46
0.48 0.70 -1.3180 -24.638 172.92 -452.35 443.63 -1.5604 -31.951 183.61 -375.94 257.75
0.48 0.90 -1.2739 -23.753 169.96 -454.11 455.39 -1.6374 -32.304 187.19 -388.86 274.53
0.48 1.30 -1.2528 -23.088 168.95 -459.52 468.10 -1.7164 -32.745 191.39 -403.93 294.70
0.60 0.60 -2.3772 -48.588 398.75 -1219.4 1386.8 -2.2042 -59.907 461.03 -1344.0 1458.1
0.60 0.70 -2.3161 -46.558 386.72 -1193.9 1366.3 -2.2973 -60.407 466.78 -1368.0 1494.3
0.60 0.90 -2.2751 -44.289 374.10 -1165.8 1340.4 -2.4142 -60.764 471.12 -1385.8 1520.6
0.60 1.30 -2.2761 -41.961 361.66 -1133.2 1302.3 -2.5374 -61.142 475.78 -1405.3 1548.7
E837 − 20
ˆ
TABLE 6 Polynomial Coefficients for Cumulative Calibration Matrices aˆ and b for Rosette Type A.
Data are applicable to hole depths in the range 0# h/D# 0.2.
Do/D W/D C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
0.30 0.25 -.50362 5.0067 -16.147 37.188 -61.903 125.82 84.311 -583.37 704.52 -525.47 31.254 -635.55 2320.9 -2310.7 996.67
0.30 0.3 -.42321 3.9914 -12.934 32.264 -55.045 97.527 48.985 -417.90 544.94 -400.61 73.582 -502.67 1570.1 -1603.6 726.00
0.30 0.4 -.33352 2.9995 -10.286 32.655 -52.266 77.326 58.941 -423.00 533.21 -339.84 118.14 -664.96 1697.7 -1619.7 663.26
0.30 0.6 -.30948 2.8003 -9.5622 34.712 -55.960 76.158 71.366 -456.15 575.24 -359.60 160.53 -834.97 1925.0 -1779.3 730.44
0.40 0.25 -.86113 6.4825 -26.193 66.247 -53.601 157.06 40.970 -843.17 785.80 -465.29 174.01 -871.06 3314.0 -2826.7 709.26
0.40 0.3 -.73061 5.5413 -22.005 59.199 -58.692 134.97 -1.5781 -617.30 679.83 -449.07 211.52 -687.92 2279.6 -2125.9 735.18
aˆ
0.40 0.4 -.60162 4.5507 -18.156 63.192 -67.979 112.49 18.615 -673.41 776.93 -426.24 285.27 -989.49 2667.8 -2459.2 807.47
0.40 0.6 -.57899 4.5728 -17.102 67.982 -81.364 118.27 48.715 -765.12 914.01 -520.83 373.96 -1372.6 3247.2 -2940.0 1065.9
0.50 0.25 -1.3214 9.5559 -45.131 104.67 -15.102 249.47 -141.42 -1095.6 690.07 -578.42 580.63 -981.97 4186.2 -2962.5 577.38
0.50 0.3 -1.1574 10.160 -40.677 84.342 -46.000 245.81 -122.69 -817.84 746.59 -757.38 486.93 -792.73 2936.8 -2546.9 1104.5
0.50 0.4 -1.0048 9.4354 -35.565 96.587 -77.249 222.29 -98.927 -965.68 1041.3 -794.94 620.85 -1294.1 3772.6 -3460.3 1388.9
0.50 0.6 -1.0283 10.722 -33.493 100.13 -113.86 233.48 -16.055 -1152.6 1384.9 -987.51 748.11 -2059.9 4999.1 -4627.6 1942.6
0.30 0.25 -.81935 4.5117 -17.246 67.304 -96.745 116.53 91.277 -740.10 936.13 -504.90 280.40 -1341.5 3092.4 -2840.9 1015.8
0.30 0.3 -.74914 3.7788 -15.709 65.387 -92.239 105.60 84.631 -705.89 887.74 -460.17 287.11 -1300.0 2949.9 -2683.3 932.16
0.30 0.4 -.67123 3.0908 -14.385 64.586 -88.974 96.250 83.440 -687.04 853.94 -420.74 278.49 -1272.2 2865.8 -2576.3 857.17
0.30 0.6 -.63325 2.7443 -13.939 65.991 -89.754 94.6
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E837 − 13a E837 − 20
Standard Test Method for
Determining Residual Stresses by the Hole-Drilling Strain-
Gage Method
This standard is issued under the fixed designation E837; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The hole-drilling strain-gage method determines residual stresses near the surface of an isotropic
linear-elastic material. It involves attaching a strain rosette to the surface, drilling a hole at the
geometric center of the rosette, and measuring the resulting relieved strains. The residual stresses
within the removed material are then determined from the measured strains using a series of equations.
1. Scope
1.1 Residual Stress Determination:
1.1.1 This test method specifies a hole-drilling procedure for determining in-plane residual stress profiles stresses near the surface
of an isotropic linearly elastic material. The test method It is applicable to residual stress profile determinations where in-plane
stress gradients are small. The stresses may remain approximately constant with depth (“uniform” stresses) or they may vary
significantly with depth (“non-uniform” stresses). The measured workpiece may be “thin” with thickness much less than the
stresses do not vary significantly across the diameter of the drilled hole or “thick” with thickness much greater than the diameter
hole. The measured stresses are the in-plane residual stresses that exist within the depth of the drilled hole. Only uniform stress
measurements are specified for thin workpieces, while both uniform and non-uniform stress measurements are specified for thick
workpieces.Stress sensitivity rapidly decreases with depth from the measured surface and deep interior stresses cannot be
evaluated. The measured residual stresses are described as “uniform” if they remain approximately constant within the hole depth,
“non-unifom” if they vary significantly.
1.1.2 In general, “blind” holes are used, where the depth of the drilled hole and therefore the depth of the residual stress evaluation
is less than the workpiece thickness. However, for a thin workpiece, it is also possible to do through-thickness measurements of
uniform (membrane) stresses using a through-hole.
1.2 Stress Measurement Range:
1.2.1 The hole-drilling method can identify in-plane residual stresses near the measured surface of the workpiece material. The
method gives localized measurements that indicate the residual stresses within the boundaries of the drilled hole.
1.2.1 This test method applies in cases where material behavior is linear-elastic. In theory, When near-yeild residual stresses are
present, it is possible for local yielding to occur due to the stress concentration around the drilled hole. Satisfactory measurement
This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.13 on Residual Stress
Measurement.
Current edition approved Sept. 15, 2013Oct. 1, 2020. Published October 2013November 2020. Originally approved in 1981. Last previous edition approved in 2013 as
E837 – 13E837 – 13a DOI: 10.1520/E0837-13A.10.1520/E0837-20.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E837 − 20
results can be achieved providing the residual stresses do not exceed about 80 % of the material yield stress for hole drilling in
a “thick” material blind-hole drilling and about 50%50 % of the material yield stress in a “thin” material.for through-hole drilling.
1.3 Workpiece Damage:
1.3.1 The hole-drilling method is often described as “semi-destructive” because the damage that it causes is localized and often
does not significantly affect the usefulness of the workpiece. In contrast, most other mechanical methods for measuring residual
stresses substantially destroy the workpiece. Since hole drilling does cause some damage, this test method should be applied only
in those cases either where the workpiece is expendable, or where the introduction of a small shallow hole will not significantly
affect the usefulness of the workpiece.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E6 Terminology Relating to Methods of Mechanical Testing
E251 Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gages
3. Terminology
3.1 Symbols: Definitions of terms common to mechanical testing:
a¯ = calibration constant for isotropic stresses
b¯ = calibration constant for shear stresses
a¯ = calibration matrix for isotropic stresses
jk
b¯ = calibration matrix for shear stresses
jk
D = diameter of the gage circle, see Table 1.
D = diameter of the drilled hole
E = Young’s modulus
j = number of hole depth steps so far
k = sequence number for hole depth steps
P = uniform isotropic (equi-biaxial) stress
P = isotropic stress within hole depth step k
k
p = uniform isotropic (equi-biaxial) strain
p = isotropic strain after hole depth step k
k
Q = uniform 45° shear stress
Q = 45° shear stress within hole depth step k
k
q = uniform 45° shear strain
q = 45° shear strain after hole depth step k
k
T = uniform x-y shear stress
T = x-y shear stress within hole depth step k
k
t = x-y shear strain
t = x-y shear strain after hole depth step k
k
T = (superscript) matrix transpose
α = regularization factor for P stresses
P
α = regularization factor for Q stresses
Q
α = regularization factor for T stresses
T
β = clockwise angle from the x-axis (gage 1) to the maximum principal stress direction
ε = relieved strain for “uniform” stress case
ε = relieved strain measured after j hole depth steps have been drilled
j
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
E837 − 20
ν = Poisson’s ratio
θ = angle of strain gage from the x-axis
σ = maximum (more tensile) principal stress
max
α = minimum (more compressive) principal stress
min
σ = uniform normal x-stress
x
(σ ) = normal x-stress within hole depth step k
x k
σ = uniform normal y-stress
y
(σ ) = normal y-stress within hole depth step k
y k
τ = uniform shear xy-stress
xy
(τ ) = shear xy-stress within hole depth step k
xy k
3.1.1 The terms accuracy, calibration, lead wire, precision, residual stress, resolution, verification, and yield strength are used as
defined in Terminology E6.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 intermediate workpiece, n—a workpiece whose thickness is between that of thin and thick workpieces.
3.2.2 thick workpiece, n—a workpiece whose thickness is sufficiently large that its strain versus hole depth response is independent
of its thickness.
3.2.3 thin workpiece, n—a workpiece whose thickness is sufficiently small that its strain versus hole depth response is proportional
to its thickness.
3.3 Symbols:
a¯ = calibration constant for isotropic stresses
b¯ = calibration constant for shear stresses
a¯ = calibration matrix for isotropic stresses
jk
b¯ = calibration matrix for shear stresses
jk
D = diameter of the gage circle, see Table 1.
D = diameter of the drilled hole
E = Young’s modulus
F = fractional workpiece thickness
f = fractional hole diameter
h = hole depth at step j
j
H = stress depth at step k
k
j = number of hole depth steps so far
k = sequence number for stress depth steps
P = uniform isotropic (equi-biaxial) stress
P = isotropic stress within hole depth step k
k
p = uniform isotropic (equi-biaxial) strain
p = isotropic strain after hole depth step k
k
Q = uniform 45° shear stress
Q = 45° shear stress within hole depth step k
k
q = uniform 45° shear strain
q = 45° shear strain after hole depth step k
k
T = uniform x-y shear stress
T = x-y shear stress within hole depth step k
k
t = x-y shear strain
t = x-y shear strain after hole depth step k
k
T = (superscript) matrix transpose
W = workpiece thickness
α = regularization factor for P stresses
P
α = regularization factor for Q stresses
Q
α = regularization factor for T stresses
T
β = clockwise angle from the x-axis (gage 1) to the maximum principal stress direction
ε = relieved strain for “uniform” stress case
ε = relieved strain measured after j hole depth steps have been drilled
j
ν = Poisson’s ratio
E837 − 20
θ = angle of strain gage from the x-axis
σ = maximum (more tensile) principal stress
max
α = minimum (more compressive) principal stress
min
σ = uniform normal x-stress
x
(σ ) = normal x-stress within hole depth step k
x k
σ = uniform normal y-stress
y
(σ ) = normal y-stress within hole depth step k
y k
τ = uniform shear xy-stress
xy
(τ ) = shear xy-stress within hole depth step k
xy k
4. Summary of Test Method
4.1 Workpiece:
4.1.1 A flat uniform surface area away from edges and other irregularities is chosen as the test location within the workpiece of
interest. Fig. 1 schematically shows the residual stresses acting at the test location at which a hole is to be drilled. These stresses
are assumed to be uniform within the in-plane directions x and y.
NOTE 1—For reasons of pictorial clarity in Fig. 1, the residual stresses are shown as uniformly acting over the entire in-plane region around the test
location. In actuality, it is not necessary for the residual stresses to be uniform over such a large region. The surface strains that will be relieved by drilling
a hole depend only on the stresses that originally existed at the boundaries of the hole. The stresses beyond the hole boundary do not affect the relieved
strains, even though the strains are measured beyond the hole boundary. Because of this, the hole-drilling method provides a very localized measurement
of residual stresses.
4.1.2 Fig. 1(a) shows the case where the residual stresses in the workpiece are uniform in the depth direction. The in-plane stresses
are σ , σ and τ throughout the thickness. Uniform residual stress measurements can be made using this test method with “thin”
x y xy
(a)
(b)
FIG. 1 Hole Geometry and Residual Stresses, (a) Uniform Stresses, (b) Non-uniform Stresses
E837 − 20
workpieces whose material thickness is small compared with the hole and strain gage circle diameters, and with “thick” workpieces
whose material thickness is large compared with the hole and strain gage circle diameters.
4.1.3 Fig. 1(b) shows the case where the residual stresses in the workpiece vary in the depth direction. The calculation method
described in this test method represents the stress profile as a staircase shape, where the depth steps correspond to the depth
increments used during the hole-drilling measurements. Within depth step k, the in-plane stresses are (σ ) , (σ ) and (τ ) .
x k y k xy k
Non-uniform residual stress measurements can be made using this test method only with “thick” workpieces whose material
thickness is large compared with the hole and strain gage circle diameters. In cases where there is doubt about the uniformity of
the residual stresses, the stresses shall be assumed to be non-uniform.
NOTE 2—The "uniform stress" case occurs when it is known in advance that membrane type stresses dominate the residual stress distribution. However,
bending stresses and surface stresses may also be present and cause significant deviations from stress uniformity. Thus, when in doubt, a non-uniform
residual stress calculation is a safe general choice. The corresponding “uniform stress” value is an average of the stresses that exist within the hole depth,
weighted in favor of the stresses near the measured surface. This value may be useful as an indicator of the general residual stress level.
4.1.4 A workpiece of thickness up to 0.25D for a type A or B rosette, or 0.6D for a type C rosette (see Fig. 4) is described as “thin”.
The thickness of such a workpiece is sufficiently small that its strain versus hole depth response is proportional to its thickness.
A blind hole can be used for “uniform” or “non-uniform” measurements of near-surface residual stresses. Alternatively, a
through-hole can be used for through-thickness measurements of uniform membrane stresses.
4.1.5 A workpiece of thickness greater than 0.6D for a type A or B rosette (1, 2) , or 1.3D for a type C rosette (see Fig. 2) is
described as “thick”. The thickness of such a workpiece is sufficiently large that its strain versus hole depth response is independent
of its thickness. A blind hole may be used for “uniform” or “non-uniform” measurements of near-surface residual stresses.
4.1.6 A workpiece of thickness between the limits specified for “thin” and “thick” workpieces is described as “intermediate”. A
blind hole may be used for “uniform” or “non-uniform” measurements of near-surface residual stresses.
4.2 Strain Gage Rosette:
4.2.1 A strain gage rosette with three or more elements of the general type schematically illustrated in Fig. 23 is attached to the
workpiece at the location under consideration. Improved resistance to measurement noise can be achieved by aligning rosette
elements 1 and 3 with the principal residual stress directions, if those directions are known in advance. Although desirable, such
alignment is not essential to achieving satisfactory results.
4.3 Hole-Drilling:
FIG. 34 Physical Interpretation of Coefficients a¯
jk
The boldface numbers in parentheses refer to the list of references at the end of this standard.
E837 − 20
FIG. 42 Hole-Drilling Rosettes
4.3.1 A hole is drilled in a series of steps at the geometric center of the strain gage rosette.
4.3.2 The residual stresses in the material surrounding the drilled hole are partially relieved as the hole is drilled. The associated
relieved strains are measured at a specified sequence of steps of hole depth using a suitable strain-recording instrument.
4.4 Residual Stress Calculation Method:
4.4.1 The residual stresses originally existing at the hole location are evaluated from the strains relieved by hole-drilling using
mathematical relations based on linear elasticity theory (1-3-57)).). The relieved strains depend on the residual stresses that existed
in the material originally within the hole.
4.4.2 For the uniform stress case shown in Fig. 1 (a), the surface strain relief measured after hole-drilling is:
11ν σ 1σ
x y
ε5 a¯ (1)
E 2
1 σ 2σ
x y
¯
1 b cos2θ
E 2
¯
1 b τ sin2θ
xy
E
4.4.3 The calibration constants a¯ and b¯ indicate the relieved strains due to unit stresses within the hole depth. They are
dimensionless, almost material-independent constants. Slightly different values of these constants apply for a through-thickness
hole made in a thin workpiece and for a blind hole made in a thick workpiece. Numerical values of these calibration constants have
been determined from finite element calculations (46, 8) for standard rosette patterns, and are tabulated in this test method.
4.4.4 For the non-uniform stress case shown in Fig. 1(b), the surface strain relief measured after completing hole depth step j
depends on the residual stresses that existed in the material originally contained in all the hole depth steps 1 ≤ k ≤ j:
E837 − 20
(a)
(b)
FIG. 23 Schematic Geometry of a Typical Three-Element Clockwise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b) Detail of a Strain
Gage
j
11ν
ε 5 a¯ σ 1σ /2 (2)
~~ ! !
j jk x y
( k
E
k51
j
¯
1 b σ 2σ /2 cos2θ
~~ ! !
( jk x y k
E
k51
j
¯
1 b ~τ ! sin2θ
( jk xy k
E
k51
4.4.5 The calibration constants a¯ and b¯ indicate the relieved strains in a hole j steps deep, due to unit stresses within hole step
jk jk
k.Fig. 34 shows cross-sections of drilled holes for an example sequence where a hole is drilled in four depth steps. Within this
sequence, calibration constant represents an intermediate stage where the hole has reached 3 steps deep, and has a unit stress acting
within depth step 2. Numerical values of the calibration constants have been determined by finite element calculations (46) for
standard rosette patterns, and are tabulated in this test method.
4.4.6 Measurement of the relieved strains after a series of hole depth steps provides sufficient information to calculate the stresses
σ , σ and τ within each step. From these stresses, the corresponding principal stresses σ and σ and their orientation β can
x y xy max min
be found.
E837 − 20
4.4.7 The relieved strains are mostly influenced by the near-surface residual stresses. Interior stresses have influences that diminish
with their depth from the surface. Thus, hole-drilling measurements can evaluate only near-surface stresses. Deep interior stresses
cannot be identified reliably, see reliably.Note 7.
4.4.8 In theory, When near-yield residual stresses are present, it is possible for local yielding to occur due to the stress
concentration around the drilled hole. Satisfactory measurement results can be achieved providing the residual stresses do not
exceed about 80 % of the material yield stress for hole drilling in a “thick” material blind-hole drilling (69)), and about 50% of
the material yield stress in a “thin” material.for through-hole drilling.
5. Significance and Use
5.1 Summary:
5.1.1 Residual stresses are present in almost all materials. They maycan be created during the manufacture or during the life of
the material. If not recognized and accounted for in the design process, residual Residual stresses can be a major factor in the
failure of a material, particularly one subjected to alternating service loads or corrosive environments. Residual stress may also be
beneficial, for example, the compressive stresses produced by shot peening. The hole-drilling strain-gage technique is a practical
general-purpose method for determining residual stresses.
6. Workpiece Preparation
6.1 Requirements:
6.1.1 For a “thin” workpiece, where a through-hole is to be used, the workpiece thickness should not exceed 0.2D for a type A
or B rosette, or 0.24D for a type C rosette (see Fig. 4).
6.1.2 For a “thick” workpiece, where a hole depth less than the workpiece thickness is to be used, the workpiece thickness should
be at least D for a type A or B rosette, or 1.2D for a type C rosette (see Fig. 4).
6.1.1 A smooth surface is usually necessary for strain gage application. However, abrading Abrading or grinding that could
appreciably alter the surface stresses must be avoided. Chemical shall not be used. Alternatively, chemical etching could be used,
thus avoiding the need for mechanical abrasion.
6.1.2 The surface preparation prior to bonding the strain gages shall conform to the recommendations of the manufacturer of the
adhesive used to attach the strain gages. A thorough cleaning and degreasing is required. In general, surface preparation should
be restricted to those methods that have been demonstrated not to induce no or remove significant residual surface stresses. This
is particularly important for workpieces that contain sharp near-surface stress gradients.
7. Strain Gages and Instrumentation
7.1 Rosette Geometry:
7.1.1 A rosette comprising three single or pairs of strain gage grids shall be used. The numbering scheme for the strain gages
follows a clockwise (CW) convention (710).
NOTE 3—The gage numbering scheme used for the rosette illustrated in Fig. 23 differs from the counter-clockwise (CCW) convention often used for
general-purpose strain gage rosettes and for some other types of residual stress rosette. If a strain gage rosette with CCW gage numbering is used, the
residual stress calculation procedure described in this test method still applies. The only changes are that the numbering of gages 1 and 3 are interchanged
and that the angle β defining the direction of the most tensile principal stress σ is reversed and is measured counter-clockwise from the new gage 1.
max
NOTE 3—It is recommended that the gages be calibrated in accordance with Test Methods E251.
7.1.2 The gages shall be arranged in a circular pattern, equidistant from the center of the rosette.
7.1.3 The gage axes shall be oriented in each of three directions, (1) a reference direction, (2) 45° or 135° to the reference
direction, and (3) perpendicular to the reference direction. Direction (2) bisects directions (1) and (3), as shown in Fig. 23.
7.1.4 The measurement direction of gage 1 in Fig. 13 is identified as the x-axis. The y-axis is 90° counterclockwise of the x-axis.
E837 − 20
7.1.5 The center of the gage circle shall be clearly identifiable.
7.2 Standardized Rosettes:
7.2.1 Several different standardized rosettes are available to meet a wide range of residual stress measurement needs. The use of
standardized rosette designs greatly simplifies the calculation of the residual stresses. Fig. 42 shows three different rosette types
and Table 1 lists their dimensions.
7.2.2 The type A rosette shown in Fig. 42 was first introduced by Rendler and Vigness (53). This pattern is available in several
different sizes, and is recommended for general-purpose use.
NOTE 4—Choice of rosette size is a primary decision. Larger rosettes tend to give more stable strain measurements because of their greater capacity to
dissipate heat. They are also able to identify residual stresses to greater depths. Conversely, smaller rosettes can fit smaller workpieces, require smaller
drilled holes, and give more localized measurements.
7.2.3 The type B rosette shown in Fig. 42 has all strain gage grids located on one side. It is useful where measurements need to
be made near an obstacle.
7.2.4 The type C rosette shown in Fig. 42 is a special-purpose pattern with three pairs of opposite strain gage grids that are to be
connected as three half-bridges. It is useful where large strain sensitivity and high thermal stability are required (811).
7.3 Installation and Use:
7.3.1 The strain gage rosette should be attached to the workpiece surface such that its center is at least 1.5D from the nearest edge,
or the boundary of another material should the workpiece comprise more than one material.
7.3.2 When using a type B rosette adjacent to an obstacle, the center of the rosette should be at least 0.5D from the obstacle, with
the set of strain gages diametrically opposite to the obstacle.
7.3.3 The application of the strain gage (bonding, wiring, protective coating) should closely follow the manufacturer’s
recommendations, and shall ensure the protection of the strain gage grid during the drilling operation.
7.3.4 The strain gages should remain permanently connected and the stability of the installation shall be verified. A resistance to
ground of at least 20 000 MΩMΩ is preferable.
A
TABLE 1 Rosette Dimensions
B B B B
Rosette Type D GL GW R R
1 2
Type A
Conceptual D 0.309D 0.309D 0.3455D 0.6545D
⁄32 in. nominal 0.101 0.031 0.031 0.035 0.066
(2.57) (0.79) (0.79) (0.89) (1.68)
⁄16 in. nominal 0.202 0.062 0.062 0.070 0.132
(5.13) (1.59) (1.59) (1.77) (3.36)
⁄8 in. nominal 0.404 0.125 0.125 0.140 0.264
(10.26) (3.18) (3.18) (3.54) (6.72)
Type B
Conceptual D 0.309D 0.223D 0.3455D 0.6545D
⁄16 in. nominal 0.202 0.062 0.045 0.070 0.132
(5.13) (1.59) (1.14) (1.77) (3.36)
Type C
Conceptual D 0.176D 30° 0.412D 0.588D
sector
⁄16 in. nominal 0.170 0.030 30° 0.070 0.100
(4.32) (0.76) (30°) (1.78) (2.54)
A
Dimensions are in inches (mm).
B
Rosette dimensions are defined in Fig. 23.
E837 − 20
7.3.5 Checks should be made to validate the integrity of the gage installation. If possible, a small mechanical load should be
applied to the workpiece to induce some modest strains. (See Test Method E251.) The observed strains should return to zero when
the load is removed. In addition, a visual inspection of the rosette installation should be made to check for possible areas that are
not well bonded. If incomplete bonding is observed, the rosette mustshall be removed and replaced.
7.4 Instrumentation:
-6
7.4.1 The instrumentation for recording of strains shall have a strain resolution of 61 × 10 , and stability and repeatability of the
-6
measurement shall be at least 611 × 10 . The lead wires from each gage should be as short as practicable and a three-wire
temperature-compensating circuit (912) should be used with rosette types A and B. Half-bridge circuits should be used with rosette
type C, the resulting outputs of which are designated ε , ε , and ε .
1 2 3
8. Procedure
8.1 Suggested Preparatory Reading:
8.1.1 References (1013)),(14), and (1115) provide substantial practical guidance about how to make high-quality hole-drilling
residual stress measurements. These publications are excellent preparatory reading, particularly for practitioners who infrequently
make hole-drilling measurements.
8.2 Drilling Equipment and Use:
8.2.1 A device that is equipped to drill a hole in the test workpiece in a controlled manner is required. The device mustshall be
able to drill a hole aligned concentric with the strain gage circle to within either 60.004D.60.001 in. (0.025 mm). It shall also be
able to control the depth of the hole to within either 60.004D. 60.001 in. (0.025 mm).Fig. 5 illustrates a typical hole-drilling
apparatus.
8.2.2 Several drilling techniques have been investigated and reported to be suitable for the hole drilling method. The most common
drilling technique suitable for all but the hardest materials involves the use of carbide burs or endmills driven by a high-speed air
turbine or electric motor rotating at 20 000 to 400 000 rpm (1316). Low-speed drilling using a drill-press or power hand-drill is
discouraged because the technique has the tendency to create machining-induced residual stresses at the hole boundary
boundary.(14).
8.2.3 For very hard materials, abrasive jet machining can also be useful. This drilling method involves directing a high-velocity
stream of air containing fine abrasive particles through a small-diameter nozzle against the workpiece (57, 14). Abrasive jet
machining can be less suitable for softer materialsmaterials. (Its7). Ituse should not be used for non-uniform stress measurements
be limited to through-thickness measurements of uniform (membrane) stresses because the hole geometry and depth cannot be
controlled sufficiently tightly.
8.2.4 When using burs or endmills, carbide “inverted cone” dental burs or small carbide endmills can be suitable as cutting tools.
Commercially available cutters are designed for a wide range of applications, and not all types may be suited for hole drilling
residual stress measurements. Thus, a verification of drilling technique and choice of cutter should be done when no prior
experience is available. Verification could consist of applying a strain gage rosette to a stress-free workpiece of the same nominal
test material produced by the annealing heat treatment method (13, 57, 1416, 1517), and then drilling a hole. If the drilling
technique and cutter are satisfactory, the strains produced by the drilling will be small, typically within 68 με.
8.2.5 If the drilling technique verification shows significant strains induced by the drilling process, or if the test material is known
to be difficult to machine, it maycan be helpful to lubricate the drilling cutter with a suitable lubricating fluid. The fluid used
mustshall be electrically non-conductive. Aqueous or other electrically conductive lubricants mustshall not be used because they
maycan penetrate the strain gage electrical connections and distort the strain readings.
8.2.6 The radial clearance angles of the cutting edges on the end face of the cutting tool should not exceed 1°. This requirement
avoids ambiguities in hole depth identification by ensuring that the depth is uniform within 1 % of the tool diameter.
8.2.7 “Inverted cone” cutters have their maximum diameter at their end face, tapering slightly towards the shank. The tapered
geometry provides clearance for the cylindrical cutting edges as the tool cuts the hole. This feature is desirable because it
E837 − 20
minimizes tool rubbing on the side surface of the hole and possible localized residual stress creation. To avoid ambiguities in hole
diameter identification, the taper angle should not exceed 5° on each side.
8.2.8 Some commercially available burs have diagonal chamfers formed at the corners of the side and front cutting edges. This
adaptation produces holes with non-uniform depth and so not be used except for through-thickness measurements.
8.2.9 Drilling maycan be done by plunging, where the cutter is advanced axially. Alternatively, an orbiting technique (1618)
maycan be used, where the rotation axis of the cutter is deliberately offset from the hole axis. The cutter is advanced axially, and
is then orbited so that the offset traces a circular path and the cutter creates a hole larger than its diameter. The direct plunge method
has the advantage of simplicity. The orbiting method has the advantages of hole diameter adjustment through choice of offset, use
of the cylindrical cutting edges as well as those on the end surface, and clearer chip flow.
8.2.10 Table 2 indicates the target hole diameter ranges appropriate for the various rosette types. Different ranges apply to uniform
and non-uniform stress measurements.
8.2.11 The size of the measured strains increases approximately proportionally with the square of the hole diameter. Thus, holes
at the larger end of the range are preferred. If using the plunging method, the cutter diameter should equal the target diameter. If
using the orbiting method, the cutter diameter should be 60 to 90 % of the target diameter, with an offset chosen to achieve a hole
with the target diameter.
8.2.12 All drilling should be done under constant temperature conditions. After each drilling step, the cutter should be stopped to
allow time for stabilization of any temperature fluctuations caused by the drilling process and air turbine exhaust. It is not essential
to retract the cutter. Strain readings should attain their final values for at least five seconds before being accepted.
A
TABLE 2 Recommended Workpiece Thicknesses, Hole Diameters and Depth Steps
Uniform Stresses Non-Uniform Stresses
Max. thickness Min. thickness
Practical Practical
Rosette Type D of a of a
Min. hole Max. hole Min. hole Max. hole
depth depth
“Thin” workpiece “Thick” workpiece
diameter diameter diameter diameter
B B
stepsstep stepsstep
Type A
Conceptual D 0.2 D D 0.6 Max D Max D 0.02 D Min D Max D 0.01 D
0 0 0 0
Conceptual D 0.25 D 0.6 D 0.6 Max D Max D 0.02 D Min D Max D 0.01 D
0 0 0 0
⁄32 in. nominal 0.101 0.020 0.101 0.024 0.040 0.002 0.037 0.040 0.001
⁄32 in. nominal 0.101 0.025 0.061 0.024 0.040 0.002 0.038 0.042 0.001
(2.57) (0.51) (2.57) (0.61) (1.01) (0.05) (0.93) (1.00) (0.025)
(2.57) (0.64) (1.54) (0.61) (1.01) (0.05) (0.96) (1.07) (0.025)
⁄16 in. nominal 0.202 0.040 0.202 0.060 0.100 0.004 0.075 0.085 0.002
⁄16 in. nominal 0.202 0.050 0.121 0.060 0.100 0.004 0.076 0.084 0.002
(5.13) (1.03) (5.13) (1.52) (2.54) (0.10) (1.88) (2.12) (0.05)
(5.13) (1.28) (3.08) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
⁄8 in. nominal 0.404 0.081 0.404 0.132 0.220 0.008 0.150 0.170 0.004
⁄8 in. nominal 0.404 0.101 0.242 0.132 0.220 0.008 0.152 0.168 0.004
(10.26) (2.06) (10.26) (3.35) (5.59) (0.20) (3.75) (4.25) (0.10)
(10.26) (2.56) (6.16) (3.35) (5.59) (0.20) (3.86) (4.27) (0.10)
Type B
Conceptual D 0.2 D D 0.6 Max D Max D 0.02 D Min D Max D 0.01D
0 0 0 0
Conceptual D 0.25 D 0.6 D 0.6 Max D Max D 0.02 D Min D Max D 0.01D
0 0 0 0
⁄16 in. nominal 0.202 0.040 0.202 0.060 0.100 0.004 0.075 0.085 0.002
⁄16 in. nominal 0.202 0.050 0.121 0.060 0.100 0.004 0.076 0.084 0.002
(5.13) (1.03) (5.13) (1.52) (2.54) (0.10) (1.88) (2.12) (0.05)
(5.13) (1.25) (3.08) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
Type C
Conceptual D 0.24 D 1.2D 0.6 Max D Max D 0.024 D Min D Max D 0.012 D
0 0 0 0
Conceptual D 0.60 D 1.30D 0.6 Max D Max D 0.024 D Min D Max D 0.012 D
0 0 0 0
⁄16 in. nominal 0.170 0.041 0.204 0.060 0.100 0.004 0.075 0.085 0.002
⁄16 in. nominal 0.170 0.102 0.221 0.060 0.100 0.004 0.076 0.084 0.002
(4.32) (1.04) (5.18) (1.52) (2.54) (0.10) (1.88) (2.12) (0.05)
(4.32) (2.59) (5.62) (1.52) (2.54) (0.10) (1.93) (2.13) (0.05)
A
Dimensions are in inches (mm).
B
See Note 6.
E837 − 20
8.2.12 Use the drilling procedure described in 8.3 when evaluating uniform stresses in a “thin” workpiece, in 8.4 for uniform
stresses in a “thick” workpiece, and in 8.5 for non-uniform stresses in a “thick” workpiece.
8.3 Drilling Procedure for a “Thin” Workpiece with Uniform Through-Thickness Stresses:
8.3.1 For a “thin” workpiece, as defined in 6.1.14.1.3, obtain an initial reading from each gage before starting the drilling
operation.
8.3.2 Start the cutter and slowly advance it until it cuts through the entire thickness of the workpiece. If using the orbiting
technique, also orbit the cutter. Stop and retract the cutter. Then measure one set of strain readings ε , ε and ε .
1 2 3
8.3.3 Measure the hole diameter and confirm that it lies within the target range specified in Table 2.
8.3.4 Check the hole concentricity and confirm that it lies within the tolerance specified in 8.2.1.
8.3.5 Compute uniform residual stresses as described in 9.2.
8.4 Drilling Procedure for a “Thick” or “Intermediate” Workpiece with Uniform Stresses:
8.4.1 For a “thick” or “intermediate” workpiece, as defined in 6.1.24.1.4, obtain an initial reading from each gage before starting
the drilling operation. Start the cutter and slowly advance it until it cuts through the rosette backing material and lightly scratches
the workpiece surface. This point corresponds to “zero” cutter depth.
NOTE 5—Some practitioners use a technique that identifies the “zero” point by the completion of an electrical connection between the cutter and the
workpiece.
8.4.2 Stop the cutter after reaching the “zero” point and confirm that all strain gage readings have not significantly changed. Use
the new readings as the zero points for the subsequent strain measurements.
1 1
8.4.3 Start the cutter and advance it by 0.004 in. (0.1 mm). If using a slowly by ⁄32 in. or ⁄8 in. size type A rosette, halve or double
the specified dimensions respectively. the Practical Depth Step listed in Table 2. If using the orbiting technique, also orbit the cutter.
Stop the cutter and record the readings from each strain gage, ε , ε and ε . Other similar depth increments are acceptable; however,
1 2 3
they are less convenient for calculations because they will require additional interpolations of the calibration constants listed
indepth increments of approximately similar size are also Table 3.acceptable.
NOTE 6—For practical measurements, the required cutter advance can be approximated in mm as specifed without significantly affecting the calculated
residual stress results.
8.4.4 Repeat the stepwise advance in hole depth followed by strain measurements to a total of 10 equal hole depth steps,
reachingin approximately similar hole depth steps until a final hole depth is reached approximately equal to 0.2D for a type A or
B rosette, or 0.24D for a type C rosette.
NOTE 6—The final hole depth is set at 0.2D or 0.24D because this limits the damage done to the workpiece and because it leaves by leaving intact some
material support below the hole to provide local reinforcement. This support reduces the local stress concentration effects and allows residual stress
measurements to be made to stresses up to 80%80 % of the material yield stress. Although Up to about 20%20 % larger strains could be measured using
deeper holes, but this practice is discouraged not specified here because it increases workpiece damage and stress concentration effects.
8.4.5 Measure the hole diameter and confirm that it lies within the target range specified in Table 2.
8.4.6 Check the hole concentricity and confirm that it lies within the tolerance specified in 8.2.1.
8.4.7 Compute uniform residual stresses as described in 9.3.
8.5 Drilling Procedure for a “Thick” Workpiece Workpieces with Non-Uniform Stresses:
E837 − 20
8.5.1 Obtain zero readings from each gage before starting the drilling operation. Start the cutter and carefully advance it until it
cuts through the rosette backing material and lightly scratches the workpiece surface. This point corresponds to “zero” cutter depth
(see Note 5).
8.5.2 Stop the cutter after reaching the “zero” point and confirm that all strain gage readings have not significantly changed. Use
the new readings as the zero points for the subsequent strain measurements.
8.5.3 Start the cutter and advance it by 0.001 in. (0.025 mm) for aslowly by the Practical Depth Step listed in ⁄32Table 2 in. Type
1 1
A Rosette, 0.002 in. (0.05 mm) for a . ⁄16 in. Type A, B or C Rosette, or 0.004 in. (0.10 mm) for a ⁄8 in. Type A Rosette. Stop
the cutter and record the readings from each strain gage.
8.5.4 When working with a Type A or B Rosette, repeat the stepwise advance in hole depth followed by strain measurements toin
a totalsequence of 20 equal hole depth steps.equal Practical Depth Steps until a final hole depth is reached, approximately equal
to the minimum of 0.2D or 0.6W.
8.5.5 When working with a Type C Rosette, repeat the stepwise advance in hole depth followed by strain measurements toin a
totalsequence of 25 equal hole depth steps.equal Practical Depth Steps until a final hole depth is reached approximately equal to
the minimum of 0.24D or 0.05W.
8.5.6 In circumstances where it may be desirable to concentrate hole depth steps within a particular depth range, it is permissible
to use unequal hole depth steps. In this case, the total number of steps used should be in the range of 75 %-200 % of the number
of steps that would be made if using equal Practical Depth Steps, as listed in Table 2. No step should be larger than three times
the listed Practical Depth Step.
8.5.7 Measure On completion of hole drilling, measure the hole diameter and confirm that it lies within the target range specified
in Table 2.
8.5.8 Check the hole concentricity and confirm that it lies within the tolerance specified in 8.2.1.
8.5.9 Compute non-uniform residual stresses as described in Section 10.
9. Computation of Uniform Stresses
9.1 Assumption of Uniform Stress:
9.1.1 A “uniform stress” calculation is appropriate when prior information is available, for example, based on workpiece geometry
or processing procedure, that indicates the likely presence of uniform residual stresses. This information should be recorded.
9.1.2 If there is doubt as to whether or not the residual stresses that are present are substantially uniform, then a non-uniform
residual stress measurement using the method described in Section 10 shouldshall be done.
9.1.3 Another purpose of doing a uniform stress calculation is to determine a representative size of the residual stresses that are
present. In this case, the “uniform stress” will be an average of the stresses that exist within the hole depth, weighted in favor of
the stresses near the measured surface.
9.2 “Thin” Workpiece:
9.2.1 Compute the following combination strains for the measured strains ε , ε , ε :
1 2 3
p 5 ε 1ε /2 (3)
~ !
3 1
q 5 ε 2ε /2 (4)
~ !
3 1
t 5 ~ε 1ε 2 2ε !/2 (5)
3 1 2
9.2.2 Compute the fractional hole diameter f using:
E837 − 20
f 5 D ⁄ D 2 0.40 ⁄0.10 ~for rosette types A or B! (6)
~ !
o
or
f 5 ~D ⁄ D 2 0.48!⁄0.12 ~for rosette type C!
o
9.2.3 Use Table 3 and the following interpolation equation to determine the numerical values of the calibration constants a¯ and
b¯ corresponding to the hole diameter and type of rosette used.
a¯ ~D ⁄ D! 5 0.5f~1 1 f! a¯ (7)
0 0.50
1~1 1 f!~1 2 f! a¯
0.40
20.5f 1 2 f a¯
~ !
0.30
~for rosette types A and B!
and analogously for b¯ and for rosette type C.
9.2.4 Compute the three combination stresses P, Q and T corresponding to the three combination strains p, q and t using (46):
σ 1σ E p
y x
P 5 52 (8)
2 a¯~11ν!
σ 2σ E q
y x
Q 5 52 (9)
2 ¯
b
E t
T 5τ 52 (10)
xy
¯
b
where:
P = isotropic (equi-biaxial) stress,
Q = 45° shear stress, and
T = xy shear stress.
9.2.5 Compute the in-plane Cartesian stresses σ , σ and τ using:
x y xy
σ 5 P 2 Q (11)
x
σ 5 P1Q (12)
y
τ 5 T (13)
xy
9.2.6 Compute the principal stresses σ and σ using:
max min
2 2
σ , σ 5 P6=Q 1T (14)
max min
9.2.7 The more tensile (or less compressive) principal stress σ is located at an angle β measured clockwise from the direction
max
of gage 1 in Fig. 23. Similarly, the less tensile (or more compressive) principal stress σ is located at an angle β measured
min
clockwise from the direction of gage 3.
TABLE 3 Through-Thickness Coefficients a¯ and b¯ for Various Rosette Types and Hole Diameters
Rosette Coefficient D/D = 0.30 D/D = 0.40 D/D = 0.50
0 0 0
a¯ -0.090 -0.160 -0.250
A
b¯ -0.289 -0.478 -0.664
Rosette Coefficient D/D = 0.30 D/D = 0.40 D/D = 0.50
0 0 0
a¯ 0/096 -0.170 -0.266
B
b¯ -0.331 -0.542 -0.743
Rosette Coefficient D/D = 0.36 D/D = 0.48 D/D = 0.60
0 0 0
a¯ -0.265 –0.471 -0.736
C
b¯ -0.554 -0.806 -0.877
E837 − 20
9.2.8 Compute the angle β using:
1 2T
β5 arctan (15)
S D
2 2Q
9.2.9 Calculation of the angle β using the common one-argument arctan function, such as is found on an ordinary calculator, can
give an ambiguity of 690°. The correct angle canmay be found by using the two-argument arctan function (function atan2 in some
computer languages), where the signs of the numerator and denominator are each taken into account. Alternatively, the result from
the one-argument calculation canmay be adjusted by adding or subtracting 90° as necessary to place β within the appropriate range
defined in Table 4.
9.2.10 A positive value of β, say β = 30°, indicates that σ lies 30° clockwise of the direction of gage 1. A negative value of
max
β, say β = –30°, indicates that σ lies 30° counter-clockwise of the direction of gage 1. In general, the direction of σ will
max max
closely correspond to the direction of the numerically most negative (compressive) relieved strain.
NOTE 7—The clockwise (CW) measurement direction for angle β defined in 9.2.10 applies only to a strain gage rosette with CW gage numbering, such
as that illustrated in Fig. 23. The opposite measurement direction for β applies to a counter-clockwise (CCW) strain gage rosette. In such a rosette, the
geometrical locations of gages 1 and 3 are interchanged relative to the CW case. The new gage 1 becomes the reference gage. For a CCW rosette, a
positive value of β, say β = 30°, indicates that σ lies 30° counter-clockwise of the direction of gage 1. All other aspects of the residual stress calculation
max
are identical for both CW and CCW rosettes.
9.2.11 If either of the computed principal stresses exceeds 50 % of the material yield stress, then some localized yielding has
possibly occurred in the material around the hole. In this case, the results are not quantitative, and mustshall be reported as
“indicative” only. In general, the computed stresses whose values exceed 50 % of the material yield stress tend to be overestimated.
Their actual values are usually smaller than indicated.
9.3 “Thick” Workpiece:
9.3.1 Plot graph
...