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The use of neutrons to measure stresses
Scripta
METALLURGICA
V o l _ 18, pp. Pr i n t e d in
627-628, 1984 the U.S.A.
Pergamon P r e s s Ltd. All r i g h t s r e s e r v e d
THE USE OF NEUTRONS TO MEASURE STRESSES
I. C. Noyan and Jo B. Cohen Department of Materials Science and Engineering The Technological Institute, Northwestern University Evanston, Illinois 60201 USA (Received September 29, 1 9 8 3 ) (Revised December 7, 1 9 8 5 ) (Addendum received February 24, 1 9 8 4 ) In the overview "The Use of Time-of-Flight Neutron Diffraction to Study Grain Interaction Stresses" by S° R. MacEwen, J. Faber, Jr. and A. P. L. Turner (i), there are a number of points that must be clarified in order to justify the conclusions arrived at by the authors that "time-of-flight" neutron diffraction, can be a sensitive and powerful tool for measuring residual stresses in bulk materials .... ° There are basically three types of residual stresses. Macro stresses are those stresses that arise because of differences in plastic flow of different parts of a body. It is these stresses that are often of interest to engineers in practical situations, and these components average to zero over the volume of the part (2,3)° Because neutrons penetrate an appreciable depth, these stresses will, in general, make no contribution to the positions of neutron diffraction peaks (although they will cause a broadening). Conversely, because of the low x-ray penetration, this component can be sampled, and its variation with depth can be examined by etching, with well-known corrections for depth of penetration and layer removal (4). (Some information can even be obtained without etching (5).) The other two types of stresses arise because of the interactions between "hard" and "soft" regions (see refo 6)° Balance occurs between such regionSo One kind of interaction stress varies rapidly between such regions, and averages to zero for a random sample, with x-rays or neutrons (see refs. 2 and 7 for further discussion of this). Thus there is no peak shift but only peak broadening. If the sample has preferred orientation (as in ref. i) some portion of this stress component will affect peak position, although there is as yet no formalism to ascertain the amount; it will depend on the degree of orientation and the volume fraction sampled for each reflection. Because of this, the meaning of the results in (i) is not clear. Furthermore, the strains measured from peak shifts in such a case cannot be converted to stress, because the required elastic constants are different from the single crystal values and depend on the interaction° They have the symmetry of the texture, not that of the crystal, and have not been measured. Finally, unless a strong orientation occurs, there will be considerable variation in this stress determined from different peaks in a pattern, since different grains with different surroundings contribute to each peak. The third kind of stress is also due to grain interactions, the slowly varying component between the "hard" and "soft" regions. For a random sample, peak shifts due to this component can be converted to stresses with the usual elastic constants and would be measured directly by peak shifts in a neutron diffraction pattern, because the macrostresses average to zero. However, in such a case, the two components can be separated by using x-rays (3). Thus, the measurement of stress with neutrons (when a large volume is sampled) has a readily interpreted meaning only in the absence of preferred orientation° However, in such a case, xrays actually provide more information. Neutrons can be particularly useful in this field for sampling the stresses below the surface, by restricting the volume sampled, as in ref. 7. The authors acknowledge support by ONR under contract No. N0014-80-C-0116. References i. 2. 3. 4.
S° R. MacEwen, J. Faber, Jr. and Ao P. L. Turner, Acta Met., 31, 657 (1983). T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague I. C° Noyan, Met. Trans., 14A, 1907 (1983). Soc. of Automotive Engineers, Inc. Information Report J784a, New York (1971).
0036-9748/84 Copyright (c) 1 9 8 4
627 $ 3 . 0 0 + .00 Pergamon Press
Ltd.
(1982)o
628
5. 6. 7.
THE
USE
OF
NEUTRONS
TO
MEASURE
STRESSES
Vol.
18,
J . B . Cohen, H. D~lle and M. R. James, Symposium on Accuracy in Powder Diffraction, Special Pub. 567, 453 (1980). K° Hashimoto and H. Margolin, Acta. Met., 31, 773; 787 (1983). M . J . Schmank and A. D. Krawitz, Met° Trans=, 13A, 1069 (1982). Addendum
(Received
February
22,
No.
6
NBS
1984)
I) In reply to our letter, MacEwen et al (i) review the common procedures for stress analysis via diffraction (their first three paragraphs). In their third paragraph, they state that "The crux of the analysis is that diffraction at each ~ angle samples a different depth..." This is erroneous. Certainly, there must be gradients~ in =i~' for they vanish at the surface, but the usual analysis (their Eq. I) assumes that the value is constant over the sampled volume. Also we are pleased that they agree with our conclusions concerning the effect of grain interaction stresses. However, the stresses that arise from second-phase particles ca___~nbe measured (see ref. 3 above)° 2) We do not disagree with their fifth paragraph; broadening of peaks will occur° In fact this is mentioned in our letter above. (However, only the variance in strains can be obtained from such broadening, not the strains themselves.) 3) Their sixth paragraph (concerning measuring stresses with neutrons and averaging the entire sample) can be stated succinctly as follows: ~=ij d V
0
[amean + ~ ]
d V +
[=mean " ~ ]
d V
d V
over
(I)
Clearly, if the volume where =he mean stress exists is large, those (f~ and ~ ) where the dev.iations ~ exist must be small; to obtain a balance, ~ must be large. There seems to be little value in knowing the mean stress in such a case! 4) Concerning their ninth and tenth paragraphs: If the grains in a sample are so well oriented that the sample is essentially a single crystal, we agree that measured strains can be readily converted to stresses. The point in our letter was that such ideal orientations are rare~ and in other cases they seem to agree that the conversion is extremely questionable. Thus, the measurement of stress with neutrons when a large volume is sampled (and especially when any texture is present) is not yet in a satisfactory state, as we pointed out in our letter. Even if the sample has no preferred orientation, the stress measured is not the macrostress. I)
S. R° MacEwen,
References J° Faber, Jr°, and A. P. Lo Turner,
this issue°
METALLURGICA
V o l _ 18, pp. Pr i n t e d in
627-628, 1984 the U.S.A.
Pergamon P r e s s Ltd. All r i g h t s r e s e r v e d
THE USE OF NEUTRONS TO MEASURE STRESSES
I. C. Noyan and Jo B. Cohen Department of Materials Science and Engineering The Technological Institute, Northwestern University Evanston, Illinois 60201 USA (Received September 29, 1 9 8 3 ) (Revised December 7, 1 9 8 5 ) (Addendum received February 24, 1 9 8 4 ) In the overview "The Use of Time-of-Flight Neutron Diffraction to Study Grain Interaction Stresses" by S° R. MacEwen, J. Faber, Jr. and A. P. L. Turner (i), there are a number of points that must be clarified in order to justify the conclusions arrived at by the authors that "time-of-flight" neutron diffraction, can be a sensitive and powerful tool for measuring residual stresses in bulk materials .... ° There are basically three types of residual stresses. Macro stresses are those stresses that arise because of differences in plastic flow of different parts of a body. It is these stresses that are often of interest to engineers in practical situations, and these components average to zero over the volume of the part (2,3)° Because neutrons penetrate an appreciable depth, these stresses will, in general, make no contribution to the positions of neutron diffraction peaks (although they will cause a broadening). Conversely, because of the low x-ray penetration, this component can be sampled, and its variation with depth can be examined by etching, with well-known corrections for depth of penetration and layer removal (4). (Some information can even be obtained without etching (5).) The other two types of stresses arise because of the interactions between "hard" and "soft" regions (see refo 6)° Balance occurs between such regionSo One kind of interaction stress varies rapidly between such regions, and averages to zero for a random sample, with x-rays or neutrons (see refs. 2 and 7 for further discussion of this). Thus there is no peak shift but only peak broadening. If the sample has preferred orientation (as in ref. i) some portion of this stress component will affect peak position, although there is as yet no formalism to ascertain the amount; it will depend on the degree of orientation and the volume fraction sampled for each reflection. Because of this, the meaning of the results in (i) is not clear. Furthermore, the strains measured from peak shifts in such a case cannot be converted to stress, because the required elastic constants are different from the single crystal values and depend on the interaction° They have the symmetry of the texture, not that of the crystal, and have not been measured. Finally, unless a strong orientation occurs, there will be considerable variation in this stress determined from different peaks in a pattern, since different grains with different surroundings contribute to each peak. The third kind of stress is also due to grain interactions, the slowly varying component between the "hard" and "soft" regions. For a random sample, peak shifts due to this component can be converted to stresses with the usual elastic constants and would be measured directly by peak shifts in a neutron diffraction pattern, because the macrostresses average to zero. However, in such a case, the two components can be separated by using x-rays (3). Thus, the measurement of stress with neutrons (when a large volume is sampled) has a readily interpreted meaning only in the absence of preferred orientation° However, in such a case, xrays actually provide more information. Neutrons can be particularly useful in this field for sampling the stresses below the surface, by restricting the volume sampled, as in ref. 7. The authors acknowledge support by ONR under contract No. N0014-80-C-0116. References i. 2. 3. 4.
S° R. MacEwen, J. Faber, Jr. and Ao P. L. Turner, Acta Met., 31, 657 (1983). T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague I. C° Noyan, Met. Trans., 14A, 1907 (1983). Soc. of Automotive Engineers, Inc. Information Report J784a, New York (1971).
0036-9748/84 Copyright (c) 1 9 8 4
627 $ 3 . 0 0 + .00 Pergamon Press
Ltd.
(1982)o
628
5. 6. 7.
THE
USE
OF
NEUTRONS
TO
MEASURE
STRESSES
Vol.
18,
J . B . Cohen, H. D~lle and M. R. James, Symposium on Accuracy in Powder Diffraction, Special Pub. 567, 453 (1980). K° Hashimoto and H. Margolin, Acta. Met., 31, 773; 787 (1983). M . J . Schmank and A. D. Krawitz, Met° Trans=, 13A, 1069 (1982). Addendum
(Received
February
22,
No.
6
NBS
1984)
I) In reply to our letter, MacEwen et al (i) review the common procedures for stress analysis via diffraction (their first three paragraphs). In their third paragraph, they state that "The crux of the analysis is that diffraction at each ~ angle samples a different depth..." This is erroneous. Certainly, there must be gradients~ in =i~' for they vanish at the surface, but the usual analysis (their Eq. I) assumes that the value is constant over the sampled volume. Also we are pleased that they agree with our conclusions concerning the effect of grain interaction stresses. However, the stresses that arise from second-phase particles ca___~nbe measured (see ref. 3 above)° 2) We do not disagree with their fifth paragraph; broadening of peaks will occur° In fact this is mentioned in our letter above. (However, only the variance in strains can be obtained from such broadening, not the strains themselves.) 3) Their sixth paragraph (concerning measuring stresses with neutrons and averaging the entire sample) can be stated succinctly as follows: ~=ij d V
0
[amean + ~ ]
d V +
[=mean " ~ ]
d V
d V
over
(I)
Clearly, if the volume where =he mean stress exists is large, those (f~ and ~ ) where the dev.iations ~ exist must be small; to obtain a balance, ~ must be large. There seems to be little value in knowing the mean stress in such a case! 4) Concerning their ninth and tenth paragraphs: If the grains in a sample are so well oriented that the sample is essentially a single crystal, we agree that measured strains can be readily converted to stresses. The point in our letter was that such ideal orientations are rare~ and in other cases they seem to agree that the conversion is extremely questionable. Thus, the measurement of stress with neutrons when a large volume is sampled (and especially when any texture is present) is not yet in a satisfactory state, as we pointed out in our letter. Even if the sample has no preferred orientation, the stress measured is not the macrostress. I)
S. R° MacEwen,
References J° Faber, Jr°, and A. P. Lo Turner,
this issue°