ASTM E1426-14(2019)e1

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.
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Designation: E1426 − 14 (Reapproved 2019)
Standard Test Method for
Determining the X-Ray Elastic Constants for Use in the
Measurement of Residual Stress Using X-Ray Diffraction
Techniques
This standard is issued under the fixed designation E1426; 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.
ε NOTE—Section 11.3 and the caption of Fig. 4 were editorially corrected in October 2019.
INTRODUCTION
When a crystalline material is strained, the spacing between parallel planes of atoms, ions, or
molecules in the lattice changes. X-Ray diffraction techniques can measure these changes and,
therefore, they constitute a powerful means for studying the residual stress state in a body. The
calculation of macroscopic stresses using lattice strains requires the use of x-ray elastic constants
(XEC) which must be empirically determined by x-ray diffraction techniques as described in this test
method.
1. Scope responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.1 This test method covers a procedure for experimentally
mine the applicability of regulatory limitations prior to use.
determining the x-ray elastic constants (XEC) for the evalua-
1.6 This international standard was developed in accor-
tion of residual and applied stresses by x-ray diffraction
dance with internationally recognized principles on standard-
techniques. The XEC relate macroscopic stress to the strain
ization established in the Decision on Principles for the
measuredinaparticularcrystallographicdirectioninpolycrys-
Development of International Standards, Guides and Recom-
tallinesamples.The XECareafunctionoftheelasticmodulus,
mendations issued by the World Trade Organization Technical
Poisson’sratioofthematerialandthe hklplaneselectedforthe
hkl Barriers to Trade (TBT) Committee.
measurement.Therearetwo XECthatarereferredtoas ⁄2 S
hkl
and S .
2. Referenced Documents
1.2 This test method is applicable to all x-ray diffraction 2
2.1 ASTM Standards:
instruments intended for measurements of macroscopic re-
E4Practices for Force Verification of Testing Machines
sidual stress that use measurements of the positions of the
E6Terminology Relating to Methods of Mechanical Testing
diffraction peaks in the high back-reflection region to deter-
E7Terminology Relating to Metallography
mine changes in lattice spacing.
E1237Guide for Installing Bonded Resistance Strain Gages
1.3 This test method is applicable to all x-ray diffraction
3. Terminology
techniques for residual stress measurement, including single,
double, and multiple exposure techniques. 3.1 Definitions:
3.1.1 Manyofthetermsusedinthistestmethodaredefined
1.4 The values stated in SI units are to be regarded as
in Terminology E6 and Terminology E7.
standard. The values given in parentheses after SI units are
3.2 Definitions of Terms Specific to This Standard:
providedforinformationonlyandarenotconsideredstandard.
3.2.1 interplanar spacing—the perpendicular distance be-
1.5 This standard does not purport to address all of the
tween adjacent parallel lattice planes.
safety concerns, if any, associated with its use. It is the
3.2.2 macrostress—anaveragestressactingoveraregionof
the test specimen containing many crystals.
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
Currenteditionapproved.PublishedOctober2019.Originallyapprovedin1991. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Last previous edition approved in 2014 as E1426–14. DOI: 10.1520/E1426- Standards volume information, refer to the standard’s Document Summary page on
14R19E01. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E1426 − 14 (2019)
hkl hkl
3.3 Symbols: 1
⁄2 S and S = are the XEC.
2 1
3.3.1 x = dummy parameter for Sum(x) and SD(x).
For a body that is elastically isotropic on the microscopic
3.3.2 c = ordinate intercept of a graph of ∆d versus stress.
hkl hkl
scale, ⁄2 S = (1+ v)/E and S =–(v/E) where E and v are
2 1
3.3.3 d = interplanar spacing between crystallographic
the modulus of elasticity and Poisson’s ratio respectively for
planes; also called d-spacing.
the material for all hkl.
3.3.4 d = interplanar spacing for unstressed material.
4.2 When a uniaxial force is applied along e.g. ϕ=0, Eq 1
3.3.5 ∆d = change in interplanar spacing caused by stress.
becomes:
3.3.6 E = modulus of elasticity.
3.3.7 ν = Poisson’s ratio.
hkl hkl A 2 hkl A
ε 5 S σ sin ψ1S σ (2)
3.3.8 XEC = x-ray elastic constants for residual stress ϕψ 2 1
measurements using x-ray diffraction.
where:
3.3.9 hkl = Miller indices.
A
hkl
1 σ = the applied stress due to the uniaxial force.
3.3.10 ⁄2 S = (1+v)/E for an elastically isotropic body.
hkl
3.3.11 S =–v/E for an elastically isotropic body.
Therefore:
3.3.12 i = measurement index, 1 ≤ i ≤ n.
2 hkl
1 ] ε
ϕψ
hkl
3.3.13 m = slope of a plot of ∆d versus stress.
S 5 (3)
2 2 A
2 ] ~sin ψ!·]σ
hkl
3.3.14 n=numberofmeasurementsusedtodetermineslope
S is embedded in the intersection term for each applied
m.
force increment and is necessary when performing triaxial
3.3.15 SD(x) = standard deviation of a set of quantities “x”.
measurements.
3.3.16 Sum(x) = sum of a set of quantities “x”.
3.3.17 T = X minus mean of all X values.
5. Summary of Test Method
i i i
3.3.18 X = i-th value of applied stress.
i
5.1 A test specimen is prepared from a material that is
3.3.19 Y = measurement of ∆d corresponding to X.
i i
representative of the object in which residual stress measure-
3.3.20 ψ = angle between the specimen surface normal and
ments are to be performed.
the normal to the diffracting crystallographic planes.
3.3.21 ϕ = the in-plane direction of stress measurement. NOTE1—Ifasampleofthesamematerialisavailableitshouldbeused.
3.3.22 ij = in-plane directions of the sample reference
5.2 The test specimen is instrumented with an electrical
frame.
resistance strain gauge, mounted in a location that experiences
3.3.23 σ = calculated stress tensor terms.
ij
the same stress as the region that will be subsequently
hkl
3.3.24 ε = measured lattice strain tensor terms at a
ϕψ
irradiated with x-rays.
given ϕψ tilt angle.
A
5.3 The test specimen is calibrated by loading it in such a
3.3.25 σ = applied stress.
manner that the stress, where the strain gauge is mounted, is
3.3.26 ε = maximum strain.
max
directly calculable, and a calibration curve relating the strain
3.3.27 δ = maximum deflection.
max
gauge reading to the applied stress is developed.
3.3.28 h = specimen thickness.
3.3.29 b = width of specimen.
5.4 The test specimen is mounted in a loading fixture in an
3.3.30 A = cross sectional area of specimen.
x-ray diffraction instrument and sequentially loaded to several
X
3.3.31 L=distancebetweenouterrollersonfour-pointbend
force levels.
fixture.
5.4.1 The change in interplanar spacing is measured for
3.3.32 a = distance between inner and outer rollers on
each force level and related to the corresponding stress that is
four-point bend fixture.
determined from the strain gauge reading and the calibration
3.3.33 F = known force applied to specimen.
curve.
3.3.34 ε = the intercept value for each applied force
ϕψ0
5.5 The XECanditsstandarddeviationsarecalculatedfrom
necessary for S calculation.
the test results.
4. Theory
6. Significance and Use
4.1 The sin ψ method is widely used to measure stresses in
materials using x-ray diffraction techniques. The governing
6.1 This test method provides standard procedures for
3,4
equation can be written as follows:
experimentally determining the XEC for use in the measure-
ment of residual and applied stresses using x-ray diffraction
hkl hkl 2 2 2
ε 5 S σ cos ϕ 1 σ sin 2 ϕ 1 σ sin ϕ 2 σ sin ψ1
~ !
ϕψ 2 11 12 22 33 techniques. It also provides a standard means of reporting the
precision of the XEC.
(1)
6.2 Thistestmethodisapplicabletoanycrystallinematerial
1 1
hkl hkl hkl that exhibits a linear relationship between stress and strain in
S σ 1S σ 1σ 1 σ 1 S σ cos ϕ 1 σ sin ϕ sin2ψ
~ ! ~ !
2 33 1 11 22 33 2 13 23
2 2
the elastic range, that is, only applicable to elastic loading.
where:
6.3 This test method should be used whenever residual
stresses are to be evaluated by x-ray diffraction techniques and
Evenschor P.D., Hauk V. Z., Metallkunde, 1975, 66 pp. 167–168.
Dölle H., J. Appl. Cryst, 1979, 12, pp. 489-501. the XEC of the material are unknown.
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E1426 − 14 (2019)
7. Apparatus specimen that experiences the same strain as the region that is
to be irradiated. The gauge(s) should be applied to the
7.1 Any x-ray diffraction instrument intended for the mea-
irradiated surface of the beam either adjacent to, or on either
surement of residual macrostress that employs measurements
side of, the irradiated area in order to minimize errors due to
of the diffraction peaks that are, ideally and for best accuracy,
the absence of a pure tensile or bending force.
in the high back-reflection region may be used, including film
camera types, diffractometers, and portable systems.
NOTE 3—In the case of four-point bending fixtures the gauge(s) should
be placed well inside the inner span of the specimen in order to minimize
7.2 Aloading fixture is required to apply a force to the test
thestressconcentrationeffectsassociatedwiththeinnerknifeedgesofthe
specimen while it is being irradiated in the x-ray diffraction
fixture.
instrument.
9. Calibration
7.2.1 The fixture shall be designed such that the surface
stressappliedbythefixtureshallbeuniformovertheirradiated
9.1 Calibrate the instrumented specimen using forces ap-
area of the specimen.
plied by dead weights or by a testing machine that has been
7.2.2 The fixture shall maintain the irradiated surface of the
verified according to Practices E4. Use a loading configuration
specimen at the exact center of rotation of the x-ray diffraction
that produces statistically determinate applied stresses in the
instrument throughout the test with sufficient precision to
region where the strain gauges are mounted and where x-ray
provide the desired levels of precision and bias in the mea-
diffraction measurements will be performed (that is, such that
surements to be performed.
stresses may be calculated from the applied forces and the
7.2.3 The fixture may be designed to apply tensile or
dimensionsofthespecimenandthefixture).Inthecaseofpure
bending forces. A four-point bending technique such as that
bending using a four-point bending apparatus, the strain gauge
described by Prevey is most commonly used.
may be calibrated by measurement of applied strains via
deflection of the specimen and calculated using the following
7.3 Electricalresistancestraingaugesaremounteduponthe
equation:
test specimen to enable it to be accurately stressed to known
levels.
δ 12h
max
ε 5 (4)
max 2 2
3L 24a
8. Test Specimens
where:
8.1 Test specimens should be fabricated from material with
ε = maximum applied strain to the strain gauge
max
microstructure as nearly the same as possible as that in the
δ = maximum applied deflection
max
material in which residual stresses are to be evaluated. It is
h = specimen thickness
preferred for superior results to use the same material with a
L = distance between outer rollers on four-point bend
fine grain structure and minimum cold work on the surface to
fixture
minimize measurement errors.
a = distance between inner and outer rollers on each side
8.2 For use in tensile or four-point bending fixtures, speci- of the four-point bend fixture
mens should be rectangular in shape.
If the modulus of elasticity E for the material being tested is
8.2.1 The length of tensile specimens, between grips, shall
known, the applied stress on the specimen may then be
be not less than four times the width, and the width-to-
calculated using Hooke’s law.
thickness ratio shall not exceed eight.
A
σ 5 Eε (5)
max
8.2.2 For use in four-point bending fixtures, specimens
should have a length-to-width ratio of at least four. The
If the modulus of elasticity E for the material being tested is
specimen width should
...