For large-grained samples it is advantageous to perform pairs of neutron diffraction measurements at the same spatial location but rotated 180° around the geometric centre of the gauge volume as a means of minimizing the scatter coming from the random positioning of grains within the gauge volume

Joe Kelleher

Jon James

P. John Bouchard

Repper

Tom M. Holden

Traoré

Von Dreele

Wimpory

Yeli Traore

English

PubMed

For large-grained samples it is advantageous to perform pairs of neutron diffraction measurements at the same spatial location but rotated 180° around the geometric centre of the gauge volume as a means of minimizing the scatter coming from the random positioning of grains within the gauge volume.</jats:p

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short communications582 doi:10.1107/S1600576715002757 J. Appl. Cryst. (2015). 48, 582–584Journal ofAppliedCrystallographyISSN 1600-5767Received 5 January 2015Accepted 9 February 2015Determination and mitigation of the uncertainty ofneutron diffraction measurements of residual strainin large-grained polycrystalline materialTom M. Holden, Yeli Traore, Jon James, Joe Kelleher and P. John Bouchard*Engineering and Innovation, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK. Correspondencee-mail: john.bouchard@open.ac.ukFor large-grained samples it is advantageous to perform pairs of neutrondiffraction measurements at the same spatial location but rotated 180 aroundthe geometric centre of the gauge volume as a means of minimizing the scattercoming from the random positioning of grains within the gauge volume.1. IntroductionThe measurement of residual strains by neutron diffraction in large-grained polycrystalline material is inherently inaccurate. The reasonfor this, surmised for many years (Hutchings et al., 2005; Ohms, 2013),is the random positioning of the few diffracting grains in the gaugevolume, the region of overlap between the incident and diffractedbeams. Calibration of the neutron diffraction instrument makes useof a fine-grained standard powder whose centre of diffraction coin-cides with the geometric centre of the gauge volume in a perfectsetup. In large-grained polycrystalline materials used for engineeringapplications there is every reason to expect that large grains will bespatially offset from the geometric centre, but in a random way. Asystematic error is therefore introduced, analogous to a partly filledgauge volume, that shifts the diffraction pattern sometimes above,sometimes below and sometimes close to the correct result. Theconsequence is that the scatter in measured lattice parameter frompoint to point in the material can exceed the expected fitting preci-sion of the diffraction peaks, by a margin as much as an order ofmagnitude. In analysing neutron diffraction data from an interna-tional round robin for a weld bead-on-plate test specimen, Wimporyet al. (2009) suspected that underestimation of the uncertainty instress determination originated from grain size issues. Subsequently,Wimpory et al. (2010) developed a simple model quantifying the extrauncertainty that has to be added because of grain-size effects whenthere are an insufficient number of diffracting grains within the gaugevolume. Errors arising from large grains can be mitigated by selectinga relatively large gauge volume or by ‘rocking’ the specimen toincrease the number of diffracting grains sampled, but theseapproaches become less effective as the grain size increases (Ohms,2013).Recently, in the course of a neutron diffraction residual stressmeasurement on a thick-walled pipe, of outer diameter 352 mm andthickness 40 mm, containing a dissimilar metal girth weld, theopportunity arose to make multiple stress-free reference latticeparameter measurements in three materials of different grain sizes: afine-grained ferritic steel (16MND5), a large-grained austeniticstainless steel (Type 316L) with a grain size range up to 1000 mm andan average grain size of 313 mm, and nickel-based Alloy-52 weldmetal with a similar grain size and complex columnar structure. Theselattice parameter measurements allowed the expected standarddeviation to be determined for the large-grained samples as well asfor a control sample of ferritic steel with small grain size.2. MethodThe experiments were carried out on the ENGIN-X neutron time-of-flight diffractometer at the ISIS spallation neutron source at theRutherford Appleton Laboratory. The incident beam was defined bya cadmium mask 4 mm high and 4 mm wide. The diffracted beampassed through 4 mm radial collimators to two counter banks at90, which span 10 in the horizontal plane and 15 in thevertical plane. The time-of-flight spectra were analysed using theRietveld refinement method of Von Dreele et al. (1982), giving asingle lattice parameter result for each measurement.Reference lattice parameters were measured in small cylinders ofdiameter 6.2 mm and length 40 mm that had been extracted from thepipe weldment by wire electro-discharge machining (EDM). The axesof the reference cylinders sampling the stainless steel, ferritic steeland Alloy-52 materials were aligned with the pipe radial direction.Narrow circumferential grooves were cut by wire EDM at 6 mmintervals along each reference cylinder. The depth of the grooves wascontrolled to leave a 2 mm square cross section connecting ligament.This approach reduced the residual stress acting along the axis of thereference cylinder to an insignificant level. The magnitude of residualstresses remaining in the 6 mm reference cylinders was assessed to below on the basis of numerical studies of Repper et al. (2012) andapplication of the closed form analysis described by Traore´ et al.(2013), assuming an initial residual stress field with a wavelength ofthe order of the pipe thickness.Figure 1Schematic representation showing how the positions of grains change with respectto the centre of the gauge volume upon rotation from 0 orientation through 180about the geometric centre. The different colours represent families of grains wherethe normals to common crystallographic planes are aligned in the same direction(i.e. families of diffracting grains).The reference cylinders were mounted vertically in a three-jawchuck on the sample table, allowing measurements in the pipe axial-hoop plane at six positions midway between the cuts. In the case ofthe 16MND5 ferritic steel reference cylinder, five measurements weremade along the length and a single measurement in the centre of astainless steel cladding (7.5mm thick) adjacent to the inside of thepipe. Measurements were made at 0 and 180, corresponding to thepipe hoop direction, and at 90 and 270 for the pipe axial direction. Intwo measurements 180 apart, grains offset to the right of the centreof the gauge volume will move to the left of centre, as the cartoon inFig. 1 shows. For this reason, the systematic error in the diffractionincurred at 0 tends to reverse sign at 180. Averaging these pairs ofmeasurements will tend to cancel out the systematic errors, though itis unlikely to reduce them to zero owing, for example, to variations inintensity across the neutron beam. It is reasonable to expect thatthere will be no strong radial alloy concentration gradient in any ofthe materials and also that the two diffracted beam counter banks ofthe ENGIN-X instrument will give equally acceptable values oflattice parameter. This latter assumption can be tested for the fine-grained ferrite case. Thus, 48 equivalent measurements of latticeparameter were made at six radial locations, four angles and twocounters. These permitted estimates to be made of the standarddeviation resulting from large grains.3. ResultsFig. 2 shows the distribution of offsets about the average value of thelattice parameter, expressed in the form a/a, as a function ofposition along the reference cylinder for all 48 measurements for thelarge-grained 316L austenitic stainless steel and the 24 averages ofpairs of values. The average lattice parameter and standard deviationare noted. The standard deviation is reduced by 50% for the pairs.Fig. 3 presents similar results for the Alloy-52 weld metal, which had acolumnar grain structure. Fig. 4 illustrates the distribution of offsetsabout the average lattice parameter for the 40 measurements of strainfor the ferritic steel. In this case, the standard deviation onlydecreases by about 5%. A minor difference between the two counterbanks [24 (12)  106] can be discerned, but this is far less than theoffsets for the large-grained material. For the ferritic material there isshort communicationsJ. Appl. Cryst. (2015). 48, 582–584 Tom M. Holden et al.  Uncertainty of residual strain measurement 583Figure 3Deviations from the average lattice parameter, expressed in the form a/a, for 46measurements (top) and 23 pairs (bottom) for the Alloy-52 weld metal. Theaverage lattice parameter was 3.57947 A˚ and the standard deviations, expressed asa strain, were 103 and 55  106, respectively.Figure 4Deviations from the average lattice parameter, expressed in the form a/a, for 40measurements (top) and 20 pairs (bottom) for the 16MND5 ferritic steel. Theaverage lattice parameter was 2.86772 A˚ and the standard deviations, expressed asa strain, were 26 and 25  106, but included a slight difference between collectorbank 1 and collector bank 2 as well as a variation through wall of about40 106.Figure 2Deviations from the average lattice parameter, expressed in the form a/a, for 48measurements (top) and 24 pairs (bottom) for the Type 316L austenitic stainlesssteel. The average lattice parameter was 3.59500 A˚ and the standard deviations,expressed as a strain, were 84 and 42  106, respectively.a maximum variation in lattice parameter, expressed as a strainbetween the outside and inside surfaces of the pipe of 40  106.4. DiscussionIn the calculation of residual strain for the intact sample weldment(i.e. the pipe/dissimilar metal girth weld) there will be four contri-butions to the standard error: two from the fitting errors to thespectrum, fit,sample and fit,ref, one from the large grains (lg) for thereference lattice parameter, ref,lg, and one from the large grains in theintact sample, sample,lg, which can be added in quadrature. sample,lg inthis case would be the standard deviation determined from the 48measures of random grain offsets, since measurements cannot bemade at 0 and 180 because of the geometry of the bulky sample andexperimental time constraints. On the other hand ref,lg can be takenas the standard deviation of the 24 pairs, since measurements can bereadily made at 0 and 180 on the relatively small coupons. In general,fit,sample only makes a significant contribution to the error in the oneor two cases where the path length through the material is long andthe spectrum weak.For the large-grained samples, the 48 measurements gave a stan-dard deviation that was about eight times the fitting error. For thesmall-grained ferritic sample, the standard deviation of pairs ofmeasurements was on average only 10 (8) 106, that is, about 50%greater than the fitting error to the spectrum. Thus, the latter is seento be a reasonable estimate of the error in the absence of otherinformation, although it has always been recognized as being a lowerlimit on the standard deviation of a diffraction measurement.The same considerations apply to the errors in angular dispersiveneutron diffraction. Time-of-flight diffraction, however, does havethe advantage of a far larger counter area, thus collecting data frommore crystallites as well as averaging over the several peaks in thediffraction spectrum, in this case {111}, {002}, {220} and {113} foraustenitic material and {110}, {002}, {112} and {222} for the ferriticmaterial. Continual rotation of the reference sample in the axial hoopplane would have given a satisfactory reference lattice parameter, butthe information on the standard deviation coming from large grains ishidden in the line width. In the case of high-energy X-ray synchrotronmeasurements, it could be advantageous to defocus the beam to carryout the same kind of analysis.5. ConclusionsIn the case of a large-grained sample it is advantageous to performpairs of measurements at the same spatial location but rotated 180around the geometric centre of the gauge volume as a means ofminimizing the standard deviation and scatter coming from therandom positioning of grains within the gauge volume. If a sufficientnumber of equivalent measures of lattice parameter can be made inthe reference samples, the standard deviation associated with largegrains can be assessed for the sample. For small-grained samples, suchas the ferritic material in this case, the fitting error to the spectrummay be a reasonable estimate of the standard deviation in theabsence of other information.The work was funded by AREVA NP and supported by an STFCaward of neutron beamtime at the ISIS Facility (UK). The authorsacknowledge the support of Open University technical staff PeteLedgard and Stan Hiller for sample preparation.ReferencesHutchings, M. T., Withers, P. J., Holden, T. M. & Lorentzen, T. (2005).Introduction to the Characterization of Residual Stress by NeutronDiffraction. Boca Raton, London: CRC Press, Taylor and Francis.Ohms, C. (2013). PhD thesis, Delft University of Technology, The Netherlands.Repper, J., Hofmann, M., Krempaszky, C., Regener, B., Berhuber, E., Petry, W.& Werner, E. (2012). J. Appl. Phys. 112, 064906.Traore´, Y., Paddea, S., Bouchard, P. J. & Gharghouri, M. A. (2013). Exp. Mech.53, 605–618.Von Dreele, R. B., Jorgensen, J. D. & Windsor, C. G. (1982). J. Appl. Cryst. 15,581–589.Wimpory, R. C., Ohms, C., Hofmann, M., Schneider, R. & Youtsos, A. G.(2009). Int. J. Pres. Ves. Pip. 86, 48–62.Wimpory, R., Wasmuth, U., Rebelo-Kornmeier, J. & Hofmann, M. (2010).Mater. Sci. Forum, 638–642, 2405–2410.short communications584 Tom M. Holden et al.  Uncertainty of residual strain measurement J. Appl. Cryst. (2015). 48, 582–584

Journal of Applied Crystallography

Determination and mitigation of the uncertainty of neutron diffraction measurements of residual strain in large-grained polycrystalline material

Holden TM

Traore Y

James J

Kelleher J

Bouchard PJ

ePubs: the open archive for STFC research publications

Holden, Tom M.

Traore, Yeli

James, Jon

Kelleher, Joe

Bouchard, P. John

Open Research Online (The Open University)

Open Research OnlineThe Open University’s repository of research publicationsand other research outputsDetermination and mitigation of the uncertainty ofneutron diffraction measurements of residual strain inlarge-grained polycrystalline materialJournal ItemHow to cite:Holden, Tom M.; Traore, Yeli; James, Jon; Kelleher, Joe and Bouchard, P. John (2015). Determination andmitigation of the uncertainty of neutron diffraction measurements of residual strain in large-grained polycrystallinematerial. Journal of Applied Crystallography, 48(2) pp. 582–584.For guidance on citations see FAQs.c© 2015 The AuthorsVersion: Version of RecordLink(s) to article on publisher’s website:http://dx.doi.org/doi:10.1107/S1600576715002757Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyrightowners. For more information on Open Research Online’s data policy on reuse of materials please consult the policiespage.oro.open.ac.ukshort communications582 doi:10.1107/S1600576715002757 J. Appl. Cryst. (2015). 48, 582–584Journal ofAppliedCrystallographyISSN 1600-5767Received 5 January 2015Accepted 9 February 2015Determination and mitigation of the uncertainty ofneutron diffraction measurements of residual strainin large-grained polycrystalline materialTom M. Holden, Yeli Traore, Jon James, Joe Kelleher and P. John Bouchard*Engineering and Innovation, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK. Correspondencee-mail: john.bouchard@open.ac.ukFor large-grained samples it is advantageous to perform pairs of neutrondiffraction measurements at the same spatial location but rotated 180 aroundthe geometric centre of the gauge volume as a means of minimizing the scattercoming from the random positioning of grains within the gauge volume.1. IntroductionThe measurement of residual strains by neutron diffraction in large-grained polycrystalline material is inherently inaccurate. The reasonfor this, surmised for many years (Hutchings et al., 2005; Ohms, 2013),is the random positioning of the few diffracting grains in the gaugevolume, the region of overlap between the incident and diffractedbeams. Calibration of the neutron diffraction instrument makes useof a fine-grained standard powder whose centre of diffraction coin-cides with the geometric centre of the gauge volume in a perfectsetup. In large-grained polycrystalline materials used for engineeringapplications there is every reason to expect that large grains will bespatially offset from the geometric centre, but in a random way. Asystematic error is therefore introduced, analogous to a partly filledgauge volume, that shifts the diffraction pattern sometimes above,sometimes below and sometimes close to the correct result. Theconsequence is that the scatter in measured lattice parameter frompoint to point in the material can exceed the expected fitting preci-sion of the diffraction peaks, by a margin as much as an order ofmagnitude. In analysing neutron diffraction data from an interna-tional round robin for a weld bead-on-plate test specimen, Wimporyet al. (2009) suspected that underestimation of the uncertainty instress determination originated from grain size issues. Subsequently,Wimpory et al. (2010) developed a simple model quantifying the extrauncertainty that has to be added because of grain-size effects whenthere are an insufficient number of diffracting grains within the gaugevolume. Errors arising from large grains can be mitigated by selectinga relatively large gauge volume or by ‘rocking’ the specimen toincrease the number of diffracting grains sampled, but theseapproaches become less effective as the grain size increases (Ohms,2013).Recently, in the course of a neutron diffraction residual stressmeasurement on a thick-walled pipe, of outer diameter 352 mm andthickness 40 mm, containing a dissimilar metal girth weld, theopportunity arose to make multiple stress-free reference latticeparameter measurements in three materials of different grain sizes: afine-grained ferritic steel (16MND5), a large-grained austeniticstainless steel (Type 316L) with a grain size range up to 1000 mm andan average grain size of 313 mm, and nickel-based Alloy-52 weldmetal with a similar grain size and complex columnar structure. Theselattice parameter measurements allowed the expected standarddeviation to be determined for the large-grained samples as well asfor a control sample of ferritic steel with small grain size.2. MethodThe experiments were carried out on the ENGIN-X neutron time-of-flight diffractometer at the ISIS spallation neutron source at theRutherford Appleton Laboratory. The incident beam was defined bya cadmium mask 4 mm high and 4 mm wide. The diffracted beampassed through 4 mm radial collimators to two counter banks at90, which span 10 in the horizontal plane and 15 in thevertical plane. The time-of-flight spectra were analysed using theRietveld refinement method of Von Dreele et al. (1982), giving asingle lattice parameter result for each measurement.Reference lattice parameters were measured in small cylinders ofdiameter 6.2 mm and length 40 mm that had been extracted from thepipe weldment by wire electro-discharge machining (EDM). The axesof the reference cylinders sampling the stainless steel, ferritic steeland Alloy-52 materials were aligned with the pipe radial direction.Narrow circumferential grooves were cut by wire EDM at 6 mmintervals along each reference cylinder. The depth of the grooves wascontrolled to leave a 2 mm square cross section connecting ligament.This approach reduced the residual stress acting along the axis of thereference cylinder to an insignificant level. The magnitude of residualstresses remaining in the 6 mm reference cylinders was assessed to below on the basis of numerical studies of Repper et al. (2012) andapplication of the closed form analysis described by Traore´ et al.(2013), assuming an initial residual stress field with a wavelength ofthe order of the pipe thickness.Figure 1Schematic representation showing how the positions of grains change with respectto the centre of the gauge volume upon rotation from 0 orientation through 180about the geometric centre. The different colours represent families of grains wherethe normals to common crystallographic planes are aligned in the same direction(i.e. families of diffracting grains).The reference cylinders were mounted vertically in a three-jawchuck on the sample table, allowing measurements in the pipe axial-hoop plane at six positions midway between the cuts. In the case ofthe 16MND5 ferritic steel reference cylinder, five measurements weremade along the length and a single measurement in the centre of astainless steel cladding (7.5mm thick) adjacent to the inside of thepipe. Measurements were made at 0 and 180, corresponding to thepipe hoop direction, and at 90 and 270 for the pipe axial direction. Intwo measurements 180 apart, grains offset to the right of the centreof the gauge volume will move to the left of centre, as the cartoon inFig. 1 shows. For this reason, the systematic error in the diffractionincurred at 0 tends to reverse sign at 180. Averaging these pairs ofmeasurements will tend to cancel out the systematic errors, though itis unlikely to reduce them to zero owing, for example, to variations inintensity across the neutron beam. It is reasonable to expect thatthere will be no strong radial alloy concentration gradient in any ofthe materials and also that the two diffracted beam counter banks ofthe ENGIN-X instrument will give equally acceptable values oflattice parameter. This latter assumption can be tested for the fine-grained ferrite case. Thus, 48 equivalent measurements of latticeparameter were made at six radial locations, four angles and twocounters. These permitted estimates to be made of the standarddeviation resulting from large grains.3. ResultsFig. 2 shows the distribution of offsets about the average value of thelattice parameter, expressed in the form a/a, as a function ofposition along the reference cylinder for all 48 measurements for thelarge-grained 316L austenitic stainless steel and the 24 averages ofpairs of values. The average lattice parameter and standard deviationare noted. The standard deviation is reduced by 50% for the pairs.Fig. 3 presents similar results for the Alloy-52 weld metal, which had acolumnar grain structure. Fig. 4 illustrates the distribution of offsetsabout the average lattice parameter for the 40 measurements of strainfor the ferritic steel. In this case, the standard deviation onlydecreases by about 5%. A minor difference between the two counterbanks [24 (12)  106] can be discerned, but this is far less than theoffsets for the large-grained material. For the ferritic material there isshort communicationsJ. Appl. Cryst. (2015). 48, 582–584 Tom M. Holden et al.  Uncertainty of residual strain measurement 583Figure 3Deviations from the average lattice parameter, expressed in the form a/a, for 46measurements (top) and 23 pairs (bottom) for the Alloy-52 weld metal. Theaverage lattice parameter was 3.57947 A˚ and the standard deviations, expressed asa strain, were 103 and 55  106, respectively.Figure 4Deviations from the average lattice parameter, expressed in the form a/a, for 40measurements (top) and 20 pairs (bottom) for the 16MND5 ferritic steel. Theaverage lattice parameter was 2.86772 A˚ and the standard deviations, expressed asa strain, were 26 and 25  106, but included a slight difference between collectorbank 1 and collector bank 2 as well as a variation through wall of about40 106.Figure 2Deviations from the average lattice parameter, expressed in the form a/a, for 48measurements (top) and 24 pairs (bottom) for the Type 316L austenitic stainlesssteel. The average lattice parameter was 3.59500 A˚ and the standard deviations,expressed as a strain, were 84 and 42  106, respectively.a maximum variation in lattice parameter, expressed as a strainbetween the outside and inside surfaces of the pipe of 40  106.4. DiscussionIn the calculation of residual strain for the intact sample weldment(i.e. the pipe/dissimilar metal girth weld) there will be four contri-butions to the standard error: two from the fitting errors to thespectrum, fit,sample and fit,ref, one from the large grains (lg) for thereference lattice parameter, ref,lg, and one from the large grains in theintact sample, sample,lg, which can be added in quadrature. sample,lg inthis case would be the standard deviation determined from the 48measures of random grain offsets, since measurements cannot bemade at 0 and 180 because of the geometry of the bulky sample andexperimental time constraints. On the other hand ref,lg can be takenas the standard deviation of the 24 pairs, since measurements can bereadily made at 0 and 180 on the relatively small coupons. In general,fit,sample only makes a significant contribution to the error in the oneor two cases where the path length through the material is long andthe spectrum weak.For the large-grained samples, the 48 measurements gave a stan-dard deviation that was about eight times the fitting error. For thesmall-grained ferritic sample, the standard deviation of pairs ofmeasurements was on average only 10 (8) 106, that is, about 50%greater than the fitting error to the spectrum. Thus, the latter is seento be a reasonable estimate of the error in the absence of otherinformation, although it has always been recognized as being a lowerlimit on the standard deviation of a diffraction measurement.The same considerations apply to the errors in angular dispersiveneutron diffraction. Time-of-flight diffraction, however, does havethe advantage of a far larger counter area, thus collecting data frommore crystallites as well as averaging over the several peaks in thediffraction spectrum, in this case {111}, {002}, {220} and {113} foraustenitic material and {110}, {002}, {112} and {222} for the ferriticmaterial. Continual rotation of the reference sample in the axial hoopplane would have given a satisfactory reference lattice parameter, butthe information on the standard deviation coming from large grains ishidden in the line width. In the case of high-energy X-ray synchrotronmeasurements, it could be advantageous to defocus the beam to carryout the same kind of analysis.5. ConclusionsIn the case of a large-grained sample it is advantageous to performpairs of measurements at the same spatial location but rotated 180around the geometric centre of the gauge volume as a means ofminimizing the standard deviation and scatter coming from therandom positioning of grains within the gauge volume. If a sufficientnumber of equivalent measures of lattice parameter can be made inthe reference samples, the standard deviation associated with largegrains can be assessed for the sample. For small-grained samples, suchas the ferritic material in this case, the fitting error to the spectrummay be a reasonable estimate of the standard deviation in theabsence of other information.The work was funded by AREVA NP and supported by an STFCaward of neutron beamtime at the ISIS Facility (UK). The authorsacknowledge the support of Open University technical staff PeteLedgard and Stan Hiller for sample preparation.ReferencesHutchings, M. T., Withers, P. J., Holden, T. M. & Lorentzen, T. (2005).Introduction to the Characterization of Residual Stress by NeutronDiffraction. Boca Raton, London: CRC Press, Taylor and Francis.Ohms, C. (2013). PhD thesis, Delft University of Technology, The Netherlands.Repper, J., Hofmann, M., Krempaszky, C., Regener, B., Berhuber, E., Petry, W.& Werner, E. (2012). J. Appl. Phys. 112, 064906.Traore´, Y., Paddea, S., Bouchard, P. J. & Gharghouri, M. A. (2013). Exp. Mech.53, 605–618.Von Dreele, R. B., Jorgensen, J. D. & Windsor, C. G. (1982). J. Appl. Cryst. 15,581–589.Wimpory, R. C., Ohms, C., Hofmann, M., Schneider, R. & Youtsos, A. G.(2009). Int. J. Pres. Ves. Pip. 86, 48–62.Wimpory, R., Wasmuth, U., Rebelo-Kornmeier, J. & Hofmann, M. (2010).Mater. Sci. Forum, 638–642, 2405–2410.short communications584 Tom M. Holden et al.  Uncertainty of residual strain measurement J. Appl. Cryst. (2015). 48, 582–584

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Determination and mitigation of the uncertainty of neutron diffraction measurements of residual strain in large-grained polycrystalline material

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