ASTM E1426-98

Standard Test Method for Determining the Effective Elastic Parameter for X-Ray Diffraction Measurements of Residual Stress

SCOPE
1.1 This test method covers a procedure for experimentally determining the effective elastic parameter, Eeff , for the evaluation of residual and applied stresses by X-ray diffraction techniques. The effective elastic parameter relates macroscopic stress to the strain measured in a particular crystallographic direction in polycrystalline samples. Eeff should not be confused with E, the modulus of elasticity. Rather, it is nominally equivalent to E/(1 + [nu]) for the particular crystallographic direction, where [nu] is Poisson's ratio. The effective elastic parameter is influenced by elastic anisotropy and preferred orientation of the sample material.  
1.2 This test method is applicable to all X-ray diffraction instruments intended for measurements of macroscopic residual stress that use measurements of the positions of the diffraction peaks in the high back-reflection region to determine changes in lattice spacing.  
1.3 This test method is applicable to all X-ray diffraction techniques for residual stress measurement, including single, double, and multiple exposure techniques.  
1.4 The values stated in inch pound units are to be regarded as the standard. The SI units given in parentheses are for information only.  
1.5 This standard does not purport to address all of the safety problems, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 09-Oct-1998
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.13 - Residual Stress Measurement

Relations

• Replaced By: ASTM E1426-98(2003) - Standard Test Method for Determining the Effective Elastic Parameter for X-Ray Diffraction Measurements of Residual Stress
• Effective Date: 10-Apr-2003
• Referred By: ASTM E2860-20 - Standard Test Method for Residual Stress Measurement by X-Ray Diffraction for Bearing Steels
• Effective Date: 10-Oct-1998
• Referred By: ASTM E915-21 - Standard Practice for Verifying the Alignment of X-Ray Diffraction Instruments for Residual Stress Measurement
• Effective Date: 10-Oct-1998
• Referred By: ASTM A729/A729M-17(2022) - Standard Specification for Carbon and Alloy Steel Axles, Heat-Treated, for Mass Transit and Electric Railway Service
• Effective Date: 10-Oct-1998

Standards Content (Sample)

NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: E 1426 – 98
Standard Test Method for
Determining the Effective Elastic Parameter for X-Ray
Diffraction Measurements of Residual Stress
This standard is issued under the fixed designation E 1426; 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 (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
When a crystalline material is strained the spacings between parallel planes of atoms, ions, or
molecules in the lattice change. X-ray diffraction techniques can measure these changes and, therefore,
they constitute a powerful means for studying the residual stress state in a body. To calculate
macroscopic stresses from lattice strains requires a material constant, E , called the effective elastic
eff
parameter, that must be empirically determined by X-ray diffraction techniques as described in this test
method.
1. Scope 2. Referenced Documents
1.1 This test method covers a procedure for experimentally 2.1 ASTM Standards:
determining the effective elastic parameter, E , for the evalu- E 4 Practices for Force Verification of Testing Machines
eff
ation of residual and applied stresses by X-ray diffraction E 6 Terminology Relating to Methods of Mechanical Test-
techniques. The effective elastic parameter relates macroscopic ing
stress to the strain measured in a particular crystallographic E 7 Terminology Relating to Metallography
direction in polycrystalline samples. E should not be con- E 1237 Guide for Installing Bonded Resistance Strain
eff
fused with E, the modulus of elasticity. Rather, it is nominally Gages
equivalent to E/(1 + n) for the particular crystallographic
3. Terminology
direction, where n is Poisson’s ratio. The effective elastic
3.1 Definitions:
parameter is influenced by elastic anisotropy and preferred
orientation of the sample material. 3.1.1 Many of the terms used in this test method are defined
in Terminology E 6 and E 7.
1.2 This test method is applicable to all X-ray diffraction
instruments intended for measurements of macroscopic re- 3.2 Definitions of Terms Specific to This Standard:
3.2.1 interplanar spacing—the perpendicular distance be-
sidual stress that use measurements of the positions of the
diffraction peaks in the high back-reflection region to deter- tween adjacent parallel lattice planes.
3.2.2 macrostress—an average stress acting over a region of
mine changes in lattice spacing.
1.3 This test method is applicable to all X-ray diffraction the test specimen containing many crystals.
3.3 Symbols:
techniques for residual stress measurement, including single,
double, and multiple exposure techniques. 3.3.1 a = dummy parameter for Sum(a) and SD(a).
3.3.2 c = ordinate intercept of a graph of Dd versus stress.
1.4 The values stated in inch pound units are to be regarded
as the standard. The SI units given in parentheses are for 3.3.3 d = interplanar spacing between crystallographic
planes; also called d-spacing.
information only.
1.5 This standard does not purport to address all of the 3.3.4 d = interplanar spacing for unstressed material.
3.3.5 Dd = change in interplanar spacing caused by stress.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- 3.3.6 E = modulus of elasticity.
3.3.7 E = effective elastic parameter for X-ray measure-
priate safety and health practices and determine the applica-
eff
ments.
bility of regulatory limitations prior to use.
3.3.8 i = measurement index, 1 # i # n.
3.3.9 m = slope of a graph of Dd versus stress.
3.3.10 n = number of measurements used to determine
This test method is under the jurisdiction of ASTM Committee E-28 on
slope m.
Mechanical Testing and is the direct responsibility of Subcommittee E28.13 on
Residual Stress Measurement.
Current edition approved October 10, 1998. Published March 1999. Originally
published as E 1426 – 91. Last previous edition E 1426 – 94. Annual Book of ASTM Standards, Vol 03.01.
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NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 1426
3.3.11 SD(a) = standard deviation of a set of quantities “a”. instrument throughout the test with sufficient precision to
3.3.12 Sum(a) = sum of a set of quantities “a”. provide the desired levels of precision and bias in the mea-
3.3.13 T =X minus mean of all X values. surements to be made.
i i i
3.3.14 X = i-th value of applied stress. 6.2.3 The fixture may be designed to apply tensile or
i
3.3.15 Y = measurement of Dd corresponding to X . bending loads. A four-point bending technique such as that
i i
3.3.16 n = Poisson’s ratio. described by Prevey is most commonly used.
3.3.17 c = angle between the specimen surface normal and 6.3 Electrical resistance strain gages are mounted upon the
the normal to the diffracting crystallographic planes. test specimen to enable it to be accurately stressed to known
levels.
4. Summary of Test Method
7. Test Specimens
4.1 A test specimen is prepared from a material that is
7.1 Test specimens should be fabricated from material with
representative of that of the object in which residual stress
microstructure as nearly the same as possible as that in the
measurements are to be made.
material in which residual stresses are to be evaluated.
NOTE 1—If a sample of the same material is available it should be used.
7.2 For use in tensile or four-point bending fixtures, speci-
4.2 The test specimen is instrumented with an electrical
mens should be rectangular in shape.
resistance strain gage, mounted in a location that experiences
7.2.1 The length of tensile specimens, between grips, shall
the same stress as the region that will be subsequently
be not less than four times the width, and the width-to-
irradiated with X-rays.
thickness ratio shall not exceed eight.
4.3 The test specimen is calibrated by loading it in such a
7.2.2 For use in four-point bending fixtures, specimens
manner that the stress, where the strain gage is mounted, is
should have a length-to-width ratio of at least four. The
directly calculable, and a calibration curve relating the strain
specimen width should be sufficient to accommodate strain
gage reading to the stress is developed.
gages (see 7.5) and the width-to-thickness ratio should be
4.4 The test specimen is mounted in a loading fixture in an
greater than one and consistent with the method used to
X-ray diffraction apparatus, and sequentially loaded to several
calculate the applied stresses in 8.1.
load levels.
NOTE 2—Nominal dimensions often used for specimens for four-point
4.4.1 The change in interplanar spacing is measured for
bending fixtures are 4.0 3 0.75 3 0.06 in. (10.2 3 1.9 3 0.15 cm).
each load level and related to the corresponding stress that is
7.3 Tapered specimens for use in cantilever bending fix-
determined from the strain gage reading and the calibration
tures, and split-ring samples, are also acceptable.
curve.
7.4 Specimen surfaces may be electropolished or as-rolled
4.5 The effective elastic parameter and its standard devia-
sheet or plate.
tion are calculated from the test results.
7.5 One or more electrical resistance strain gages is affixed
5. Significance and Use
to the test specimen in accordance with Guide E 1237. The
5.1 This test method provides standard procedures for
gage(s) should be aligned parallel to the longitudinal axis of the
experimentally determining the effective elastic parameter for
specimen, and should be mounted on a region of the specimen
X-ray diffraction measurement of residual and applied stresses.
that experiences the same strain as the region that is to be
It also provides a standard means of reporting the precision of irradiated. The gage(s) should be applied to the irradiated
the parameter.
surface of the beam either adjacent to, or on either side of, the
5.2 This test method is applicable to any crystalline material irradiated area in order to minimize errors due to the absence
which exhibits a linear relationship between stress and strain in
of a pure tensile or bending load.
the elastic range.
NOTE 3—In the case of four-point bending fixtures the gage(s) should
5.3 This test method should be used whenever residual
be placed well inside the inner span of the specimen in order to minimize
stresses are to be evaluated by an X-ray diffraction technique
the stress concentration effects associated with the inner knife edges.
and the effective elastic parameter of the material is unknown.
8. Calibration
6. Apparatus
8.1 Calibrate the instrumented specimen using loads applied
6.1 Any X-ray diffraction instrument intended for measure-
by dead weights or by a testing machine that has been verified
ments of residual macrostress that employs measurements of
according to Practices E 4. The loading configuration is such
the diffraction peaks in the high back-reflection region may be
that the applied stresses, in the region where the strain gages
used, including film camera types, diffractometers, and por-
are mounted and where X-ray diffraction measurements will be
table systems.
made, are statically determinate (that is, may be calculated
6.2 A loading fixture is required to apply loads to the test
from the applied loads and the dimensions of the specimen and
specimen while it is being irradiated in the X-ray diffraction
the fixture).
instrument.
8.2 Prestress the specimen by loading to a level of approxi-
6.2.1 The fixture shall be designed such that the surface
mately 75 % of the load that is calculated to produce a
stress applied by the fixture shall be uniform over the irradiated
area of the specimen.
Prevey, P. S., “A Method of Determining the Elastic
...