ASTM E915-21

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Designation: E915 − 19 E915 − 21
Standard Test Method Practice for
Verifying the Alignment of X-Ray Diffraction
InstrumentationInstruments for Residual Stress
Measurement
This standard is issued under the fixed designation E915; 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.
1. Scope
1.1 This test method covers the procedure for preparation and usage of a stress-free test specimen for the purpose of verifying the
systematic error caused by instrument misalignment and/or sample positioning during X-ray diffraction residual stress
measurement.
1.2 This test method is applicable to all X-ray diffraction instruments that measure diffracted X-rays from the crystal structure
of a polycrystalline specimen and is applicable to single, double, and multiple exposure techniques. Through measurement of a
high-angle back-reflection, these techniques are used to derive the interatomic spacing (d-spacing) and the macroscopic strain and
to then calculate residual stress in which the θ, 2θ, and ψ rotation axes can be made to coincide (see Fig. 1).
1.3 This test method describes the use of iron powder for fabrication of the stress-free test specimen that is used to verify the
systematic error for residual stress measurement of ferritic or martensitic steels. This test method is easily adapted to other alloys
and ceramics through use of powder having a similar diffraction angle as the material to be measured.
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.
2. Referenced Documents
2.1 ASTM Standards:
E6 Terminology Relating to Methods of Mechanical Testing
3. Terminology
3.1 The definitions of mechanical testing terms that appear in Terminology E6 apply to this test method.
This test method practice 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 Oct. 15, 2019Nov. 1, 2021. Published December 2019January 2022. Originally approved in 1983. Last previous edition approved in 2016 as
E915 – 16. DOI: 10.1520/E0915-19.10.1520/E0915-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E915 − 21
FIG. 1 X-Ray Diffraction Residual Stress Measurement Geometry and Angles Defined
3.1.1 In addition, the following common term from Terminology E6 is defined:
-2
3.1.2 residual stress [FL ], n—stress in a body that is at rest and in equilibrium and at uniform temperature in the absence of
external and mass forces.
4. Significance and Use
4.1 This test method provides a means of verifying the alignment of an X-ray diffraction instrument in order to quantify and
minimize systematic experimental error in residual stress measurement. This method is suitable for application to conventional
diffractometers or to X-ray diffraction instrumentation designed for residual stress measurement of either the diverging or parallel
3,4
beam types.
4.2 Application of this test method requires the use of a flat stress-free specimen that diffracts X-rays within the angular range of
the diffraction peak to be used for residual stress measurement. The specimen shall be sufficiently fine-grained, homogeneous,
isotropic, and of sufficient depth such that incident X-rays interact with and diffract from an adequate number of individual
coherent domains and or grains such that a near random grain orientation distribution is sampled. The crystals shall provide intense
diffraction at all angles of tilt, ψ, which will be employed (see Note 1).
NOTE 1—Complete freedom from preferred orientation in the stress free specimen is, however, not critical in the application of the technique.
5. Procedure
5.1 Instrument Alignment:
5.1.1 The X-ray diffraction instrument shall be aligned in accordance with the instructions supplied by the instrument
manufacturer. In general, this alignment shall achieve the following, whether the θ, 2θ, and ψ axes are variable or fixed (see Fig.
1):
Ahmad, A., Prevéy, P, Ruud, C.O., , eds., Residual Stress Measurement by X-ray Diffraction, SAE HS-784, Society of Automotive Engrs., Inc., Warrendale, PA (2003).
“Standard Method for X-Ray Stress Measurement,” Committee on Mechanical Behavior of Materials, The Society of Materials Science, Japan, (20 April 1973).
E915 − 21
5.1.1.1 The θ, 2θ, and ψ axes shall coincide.
5.1.1.2 The incident X-ray beam shall be centered on the ψ and 2θ axes, within a focusing range, which will conform to the desired
error and precision tolerances (see Sections 6 and 7).
5.1.1.3 The X-ray tube focal spot, the ψ and 2θ axes, and the receiving slit positioned at 2θ equals zero degrees shall be on a line
in the plane of diffraction. Alternatively, for instrumentation limited to the back reflection region, the diffraction angle 2θ shall be
calibrated.
5.1.1.4 The proper sample position shall be established, such that the surface of the sample is positioned at the θ and ψ axes, within
the focal distance range which will conform to the desired error and precision tolerances (see Sections 6 and 7).
5.1.1.5 The angle ψ shall be determined accurately. Values for accuracy and precision of the various angles and displacements are
not specified herein. These may be considered to be met collectively when overall measurement errors and tolerances are within
those specified in Sections 6 and 7.
5.2 X-Ray Optics:
5.2.1 Selection of the appropriate X-ray peak should be made at the highest diffraction angle possible, consistent with peak
intensity, and the X-ray wavelength used.
5.2.2 For the purpose of verifying systematic errors, residual stress measurements on the stress-free specimen shall employ the
Kα diffraction peak at all ψ angles of interest. This is in contrast to actual stress measurements where the Kα characteristic
radiation doublet is used to improve accuracy. Kβ peaks may also be used; although they are generally less intense than Kα lines
they are not doublet peaks, so subsequent analysis on test articles is simplified.
5.2.3 It is desirable to select incident and receiving X-ray beam optics that will produce maximum separation of the Kα – Kα
1 2
doublet. Because resolution of the Kα doublet may vary with the angle ψ, and because some instrumentation may be incapable
(due to fixed X-ray optics) of obtaining resolution of the doublet, care shall be taken not to resolve the doublet at some ψ angles
while blending the doublet into a single peak at other ψ angles.
5.3 Selection of Powder for a Stress-Free Iron Specimen:
− 5
5.3.1 Use iron powder with a particle size greater than 1 μm (4 × 10 in.) (See Note 2.)
NOTE 2—Annealed iron powder of <45 μm (325 mesh) has been found suitable when using Cr Kα X-radiation.
5.3.2 This standard may be applied to other metallic alloys and ceramics (see 1.3).
5.3.3 The reporting of crystallographic strain instead of stress circumvents the necessity of establishing applicable elastic constants
and serves to eliminate a source of uncertainty. It should be noted that crystallographic strains differ from macroscopic strains in
most materials since the single crystal elastic properties in most materials are anisotropic.
5.3.4 The iron (or other) powder under vacuum may be annealed so as to reduce the diffraction peak width, and thereby increase
the diffracted intensity and subsequently, the peak position resolution. This is generally desirable (see Note 3). Powders in the form
of filings may be used, but may produce broader diffraction peaks due to plastic deformation; the broadening can persist even after
annealing.
NOTE 3—It can be advantageous to anneal an oxide-forming powder in a reducing atmosphere rather than in vacuum to avoid problems from surface
contamination. I may not be necessary to anneal ceramic powders since these materials do not tend to exhibit line broadening due to plastic deformation.
5.3.5 In the event that an instrument is incapable of resolving the Kα – Kα doublet being employed, it may be desirable to
1 2
deliberately obtain plastically deformed powders which ensure that partial resolution of the Kα doublet does not occur.
5.3.6 Extremely fine powders have also been shown to produce line broadening, sufficient to suppress resolution of the Kα doublet.
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5.3.7 The need for broader peaks or full resolution may be eliminated by fitting the observed, either fully resolved or partially
resolved or unresolved, doublet to a single equation defined by the sum of the Kα and Kα contributions; then the peak position
1 2
is given by that of the fitted Kα position.
5.4 Stress-Free Specimen Preparation—Preparation methods other than those described below may be used providing that no
residual stress (strain) is sustained in the binder that may be used to hold the crystalline particles together.
5.4.1 A permanent stress-free (strain-free) specimen may be prepared by mounting the powder on the face of a microscope slide
or in a shallow powder tray (of the type used for powder diffraction work on a diffractometer) using a 10 % solution of
nitrocellulose cement diluted with acetone. The binder should not diffract in the high-angle back-reflection region and interfere
with the diffraction peaks of interest. Place several drops of the solution on a clean microscope slide or in a sample tray, and
sprinkle the powder into the binder. The powder may be spread and leveled with a second microscope slide. When a uniform flat
surface has been produced by alternately wetting with the binder solution and wiping with a second slide, set the specimen aside
and allow it to dry for several hours. Excess amounts of the binder may cause it to peel away from the surface of the microscope
slide. Rewetting of the surface with acetone and redrying may eliminate this difficulty. Make the surface of the specimen as flat
as possible so that the specimen surface is clearly defined and consistent across the surface.
5.4.2 A temporary specimen may be rapidly prepared using petroleum jelly as an amorphous binder. Place a small quantity of
petroleum jelly on the face of one microscope slide and press it against a second slide to extrude the petroleum jelly into a uniform
flat film. Remove the second microscope slide with a wiping action taking care to keep the surface layer of petroleum jelly thin
and flat. Holding the petroleum jelly-coated slide at a steep angle to a vertical line, sprinkle the iron powder from a sufficient height
above the slide so that the powder strikes the coated surface and either adheres or is deflected away. Do not allow the powder to
pack and build up on the surface. For instruments that do not tilt or rapidly rotate the sample during the measurement of residual
stress, a binder may not be necessary.
5.4.3 The surface area of the powder shall be of sufficient size to intersect the entire incident X-ray beam at all ψ angles to be used
during the measurement of residual stress.
5.5 X-ray Diffraction Instrument Alignment Verification:
5.5.1 The X-ray diffraction instrument shall be aligned in accordance with the instructions supplied by the instrument
manufacturer. Position the stress-free (strain-free) specimen in line with the X-ray aperture of the X-ray diffraction instrument (see
5.1.1.4). (See Note 4.)
NOTE 4—Failure to place the powder surface on the center of rotation of the ψ and 2θ axes induces a systematic specimen displacement error.
5.5.2 In the event that a mechanical gage which contacts the surface of the specimen is used for specimen positioning, a thin metal
shim may be placed in front of the powder surface to protect it. Place this gage against the face of the metal shim, and adjust the
positioning to account for the inclusion of the shim in front of the gage such that the surface of the powder is at the correct distance
from the reference point of the gage for residual stress measurement.
5.5.3 Without adjusting the specimen position, perform five successive residual stress measurements using the method and
correction procedures normally employed for the instrument, including positive and negative ψ tilts when applicable, where ψ is
the angle between the specimen surface normal and the diffracting plane normal. ψ splitting is a symptom of misalignment.
5.5.4 The differential between the split portions of the least squares fit d-spacing versus sin (ψ) data shall result in a shear stress
equivalent to or less than 614 MPa (62.0 ksi). To avoid systematic error in the verification process when Kα radiation is being
used, care shall be taken to either completely split or blend the Kα – Kα doublet (see 5.2), or consistently define the peak position
1 2
by fitting to a single equation summing the Kα and Kα contributions.
1 2
6. Calculations and Interpretation of Results
6.1 Systematic Error—All methods leading to the calculation of both in-plane and shear stresses may be employed. These methods
are based on the calculation of the slope and the opening of the d-spacing versus sin (ψ) values or fitting to an ellipse.
6.1.1 Reduce the X-ray diffraction data obtained from the five measurements in whatever manner is normally employed for the
E915 − 21
X-ray diffraction instrument in use, and include all corrections normally applied to raw X-ray diffraction data. Application of the
X-ray elastic constants appropriate for the stressed material to be measured is important. It can be advantageous to report strain
values, rather than stress, to avoid the uncertainty of specifying elastic constants. Calculate the simple arithmetic mean and
standard deviation about the mean for the five measurements. If the mean value is within 614 MPa (62.0 ksi) of zero, the
instrument is properly aligned. In the event that the mean differs from zero by more than 614 MPa (62.0 ksi), repeat 5.1 and 5.5.
6.1.2 Alternatively, strain values may be used. This avoids error due to selection of inappropriate elastic constants. The acceptable
mean normal strain 6100 ppm and the acceptable mean shear strain is 650 ppm with respect to the stress-free (strain-free)
d-spacing.
6.2 Random Error:
6.2.1 Experience has shown that the standard deviation of the five measurements using a well aligned goniometer is ≤ 7MPa (61.0
ksi). In the event that the standard deviation of the five measurements exceeds 614 MPa (62.0 ksi), the stress-measurement
technique employed and the instrumentation shall be investigated for other sources of error affecting the measurement precision.
Error due to counting statistics can result from a failure to take sufficient time during the measurement to obtain precise intensity
information, and to subsequently determine the precise diffraction peak positions
6.2.2 Methods are available for estimating the standard deviation of the measured stress that is related to counting statistics, and
fitted peak positions. Mechanical sources of error such as loose bearings and ways within the X-ray diffraction instrument can
result in significant random error
6.2.3 When strain values are reported, the standard deviation of the five measurements shall be ≤100 ppm and ≤50 ppm for shear
stress.
7. Precision and Bias
7.1 The precision of this method will be dependent upon the type of X-ray diffraction instrumentation employed and the methods
of data reduction used in residual stress measurement. The preliminary results of round-robin investigations using this method
indicate that instrument alignment resulting in measured stress of stress-free powders of zero 614 MPa (62.0 ksi) (see 6.1) was
achieved for both standard diffractometers and X-ray diffraction instrumentation designed for residual stress measurement in the
back reflection region only. Instrumental precision measured by this method (see 6.2) has been found to be less than 67 MPa (61.0
ksi).
7.2 The accuracy of this method is considered to be absolute because the specimen is stress-free. Deviation of results obtained
when using this method, provided the specimen has been properly prepared and maintained, are attributed to the instrumentation
under investigation.
7.3 Additional sources of error may be related to other factors, including the quality of the diffracted X-ray peaks (background
and noise). They may be classified as either instrumental/equipment or specimen-related factors. If other errors are suspected, the
use of a high-strain standard is recommended.
7.4 In some cases, depending on the material being used, the specified average stress (strain) precision may not be achievable.
Thus, users should investigate the issue or choose a different stress-free (strain-free) material.
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8. Keywords
8.1 alignment; residual stress; stress-free specimen; systematic error; x-ray diffraction
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1. Scope
1.1 This practice describes the procedure for verifying the alignment of X-ray diffraction instruments used for residual stress
measurements.
1.2 This practice further describes the use of iron powder for fabrication of a stress-free test specimen to be used to quantify the
systematic error that can occur in residual stress measurement of ferritic or martensitic steels. This practice is easily adapted to
other alloys and ceramics by
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