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Comments on “bulk or surface control of cyclic hardening?”
153
Materials Science and Engineering, 24 ( 1 9 7 6 ) 153 - 155 © Elsevier Sequoia S.A., L a u s a n n e - - P r i n t e d in the N e t h e r l a n d s
Letter to the Editor
Comments on "Bulk or surface control of cyclic h a r d e n i n g ? "
I. R. K R A M E R and D A V I D T A Y L O R
Naval Ship Research and Development Center, Annapolis, Maryland (U.S.A.) (Received D e c e m b e r 5, 1975)
In their article [1] the authors have raised a question regarding the contribution of the surface and the interior to cyclic hardening. Previously, one of these authors (Laird [2] ) raised the same question and in a published c o m m e n t [3] it was pointed out t h a t while the evidence available showed that for a relatively small number of cycles the hardening could be explained in terms of the surface layer there were no measurements of the surface layer stress of specimens that had been cyeled a large number of times. On the basis of the data sent to me by Dr. Laird, I also stated that it appeared possible that when specimens were cycled for a large number of times the hardening of both the interior and surface layer could account for the cyclic work hardening. Unfortunately, data are still n o t available to determine the respective roles of the surface layer and the interior when copper specimens are subjected to a large number of cycles. There are data available for titanium (6A1-4V), 4130 steel, 7075-T6 and 2014-T6 aluminum. It was shown [4, 5] that when these materials were cycled at a constant stress amplitud e, the proportional limit increased. But, it returned to the same value as that of the virgin specimen after the surface layer was removed after cycling. Accordingly, these data show that, under the test conditions employed, cycling did n o t work harden the interior of these materials. Note, however, that the stress amplitude was always less than the proportional limit. Finney e t al. (F.L.V.) state that their loadstrain curves are n o t linear. However, this, p e r se, does n o t prove that other investigators could n o t produce linear curves. It is very difficult to know why the F.L.V. curves are not
linear, but it should be noted, however, that in their work the surface layer was removed from only two sides of the specimen. This condition would create an unsymmetrical distribution of residual stresses and an unsymmetrical distribution of the excess dislocations in the surface layer. This type of imbalance could cause early departure from linearity. There is also an obvious experimental inconsistency in the load-strain curves reported in their Fig. 7. The slope of the curve {modulus) obtained from the bonded strain gages is about 15% higher than that obtained from specimens with a clip-on-gage. F.L.V. reported that the measurements were taken at the same time on the same specimen. It would have been supposed that the gages would have been properly calibrated for a paper of the type presented by F.L.V. An untouched X-Y recorder chart of the load-strain relationship is shown in Fig. 1 for a specimen of 2014-T6 aluminum t h a t had been cycled 30 × 103 times at -+25 k.s.i, and the surface layer was removed. Note that the curve is linear up to the point marked 1000 lb. and is the same as that of the virgin specimen. Other curves after cycling but n o t polished are given in reference 5 and are shown to be linear. In their statements with respect to the activation volume F.L.V. argue that one should properly compare the behavior of the cyclic condition with that of the cycled-andpolished condition. Actually the data presented in the paper [6] compared all three cases. For clarity then let us reexamine the data. According to Fig. 5, reference 6, one set of specimens were cycled at Aec = 0.008, or in terms of 7 using the conversion factor used in the paper, ~/p = 0.009. The first point recorded for the as-cycled specimen was at a strain, 7 = 0.01, a difference of 0.001 from the terminal strain amplitude, +~p. A corresponding point for the cycled and polished specimens was also located at 7 = 0.01. However, the activation volume of the cycled and polished specimen was larger by a factor of 2 than that of the cycled specimen. At some-
154
what high strains 7 = 0.014, the activation volume for the cycled and polished specimen was still larger than that of the cycled specimen. An examination of the data in Fig. 5(a), for Aec = 0.004, (Tp = 0.0045) shows again that the activation volumes for the cycled and polished specimens are larger than those for the cycled specimen for strains of less than about 7 = 0.03. In both cases, 7 = 0.009 and 0.0045, the activation volume at the corresponding terminal strain, ~,p, was equal to that of the uncycled specimens. Clearly all the conditions (virgin, cycled, and cycled and polished) are required to analyze the data properly. When the specimens are cycled they work harden and the activation volume at the same strain is expected to be smaller than that of the uncycled specimen. Figure 5, reference 6, shows that the curve for the cycled specimen does indeed lie below that of the uncycled specimen. Now, if the work hardening of a cycled specimen is assumed to be uniform throughout the crosssection of the specimen then polishing would not have any effect and the curve would maintain its same position. Certainly, none of the activation volume points would coincide with any of the data points of the uncycled specimen. If it is assumed that both the surface layer and the interior play a role in cyclic hardening it would be expected that polishing would increase the activation volume. But, because the interior was assumed to have been work hardened, the volume would still be smaller than that of the uncycled specimen. Only if it is assumed that the cyclic work hardening is due entirely to the hardening of the surface layer would the polishing increase the activation volume to the same value as that of the uncycled specimen at and near the 1/4 cycle as reported in Fig. 5, reference 6. Accordingly, it is apparent that data are n o t required for the cycled specimens over the very small strain range of strain at +% as argued by F.L.V. The F.L.V. explanation for the improvement in fatigue resistance when specimens are prestressed and polished in terms of the removal of an adverse slip step profile does not agree with.known data. If was found during various investigations that elimination of the surface layer of strained specimens b y relaxation at room temperature improves the fatigue life by the same amount as that
achieved by polishing [7]. (Relaxation of the surface layer occurs in copper and titanium (6A1/4V) b u t n o t in age hardening alloys as 2014-T6, 7075-T6, etc.) Under this condition the slip step profile is unchanged and the improvement can be attributed only to the elimination of the surface layer. Further evidence that it is not the slip steps, p e r se, that play a dominate role in fatigue may be found in experiments on aluminum 2014-T6, 4130 steel and titanium (6A1/4V). It was reported [5] that only a b o u t a 30% increase in the number of cycles to failure was obtained when the specimens were polished to remove the slip bands. It is estimated that roughly 30% of the surface layer was also removed. By periodically eliminating the surface layer completely the fatigue life was greatly extended and limited only by the size of the specimen remaining. Further, when the surface layer was completely removed after cycling for over five times its normal life, the cycles required to cause failure was a b o u t the same or greater than that of the virgin specimen. These observations show very convincingly that the interior of the specimen was n o t damaged by the cyclic process. Similar observations were made b y Grosskreutz [8] with the same conclusions. It should be emphasized that F.L.V. experimental work on cyclic hardening and softening differs considerably from those reported in refs. 6, 9, 10 and 11. In the F.L.V. work the specimens were swaged to reduce the area by 80% while in our work the specimens were strained uniaxially only a few percent. It does not seem reasonable w i t h o u t sufficient data to expect these specimens to behave in the same manner as the swaged specimens. It is n o t the intention to answer the F.L.V. points one-by-one. It should be fairly obvious that many of their points are speculative and data are n o t available to reinforce their arguments. In some, data are available b u t are n o t in agreement with the F.L.V. statements. For example, data are available for the relaxation of unidirectional strained aluminum, copper and titanium; some of these were obtained by noting the change in strain at zero load and not by the proportional limit method. These two methods gave the same relaxation rates [ 10]. Concerning their statement regarding relaxation it should be clear that an apparent activation energy [6] of only 3340 cal/mole
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for unidirectionally strained copper cannot be associated with bulk relaxation. Therefore, the suggestion of F.L.V. to measure the surface layer stress in terms of the 1/4 cycle curve at zero strain rather than at +% would be unsatisfactory. Actually it is required t h a t the work hardening of the surface layer and the interior be known at the strain ep under the applied stress. Unfortunately this has n o t been done. However, data are available t h a t show that the cyclic work hardening of aluminum is decreased when specimens are cycled in vacuum. The surface layer stress was also lower. If cyclic hardening were purely a bulk effect the change in an environment would not be expected to change the cyclic work hardening characteristics. If as suggested by F.L.V. the measurements are taken by unloading at ep = 0, difficulty is to be expected in interpreting the data for ep ¢ 0. Obviously the state of work hardening will differ at e = 0 and ep #= 0. But most important it is n o t known quantitatively how the surface layer changes along the entire hysteresis loop during cyclic loading. A correction is required for the F.L.V. calculation regarding the stress supported by the surface layer. For the cyclic hardening/softening work in references 6 and 10, the specimens were 1/8-inch in diameter and not 1/2-inch. The increase in stress was by a factor of 2.6 and n o t 10. The depth of the surface layer of 0.0025-inch is for aluminum crystals of 1/8inch-diameter and not copper of 1/2-inchdiameter. Using these data [10] the resistive stress "to plastic flow due to the surface layer is 16 times that of the interior for the copper specimens and n o t 500 as claimed by F.L.V.
A similar analysis cannot be made on the F.L.V. data because the depth of the surface layer is n o t known and as mentioned above we do not know the extent of the work hardening in the interior for large numbers of cycles on copper. We would like to call attention to some additional evidence that for a steel the work hardening during cycling is predominantly in the surface layer. Using micro beam X-ray techniques Taira and Tanaka [ 12] determined the rocking curve width as a function of distance from the fractured surface. They reported that the excess dislocation density decreased as a function of depth from the surface. For an annealed 0.03% C steel the dislocation density at the crack surface was about 20 times greater than that in the interior. REFERENCES 1 J. M. Finney, C. Laird and R. de |a Veaux, Mater. Sci. Eng., 24 (1976) 19. 2 C. Calebrese and C. Laird, Mater. Sci. Eng., 13 (1974) 141. 3 I. R. Kramer, Mater. Sci. Eng., 15 (1974) 95. 4 I. R. Kramer, Proc. Air Force Conf. on Fatigue and Fracture, AFFDL-TR-70-144, 1969. 5 I. R. Kramer, Met. Trans., 5 (1974) 1735. 6 I. R. Kramer and A. Kumar, Met. Trans., 3 (1972) 1223. 7 I. R. Kramer and A. Kumar, Air Force Rept., MRC 72-64, F44620-69-C-0065. 8 J. C. Grosskreutz, ASTM Spec. Tech. Publ. 495, 1972, p. 5. 9 I. R. Kramer, Am. Soc. Metals, 62 (1969) 521. 10 I. R. Kramer, Am. Soc. Metals, 60 (1967) 310. 11 I. R. Kramer and A. Kumar, Corrosion Fatigue, NACE 2, 1972, p. 146. 12 S. Talra and K. Tanaka, Eng. Frac. Mech., 4 (1972)925.
Materials Science and Engineering, 24 ( 1 9 7 6 ) 153 - 155 © Elsevier Sequoia S.A., L a u s a n n e - - P r i n t e d in the N e t h e r l a n d s
Letter to the Editor
Comments on "Bulk or surface control of cyclic h a r d e n i n g ? "
I. R. K R A M E R and D A V I D T A Y L O R
Naval Ship Research and Development Center, Annapolis, Maryland (U.S.A.) (Received D e c e m b e r 5, 1975)
In their article [1] the authors have raised a question regarding the contribution of the surface and the interior to cyclic hardening. Previously, one of these authors (Laird [2] ) raised the same question and in a published c o m m e n t [3] it was pointed out t h a t while the evidence available showed that for a relatively small number of cycles the hardening could be explained in terms of the surface layer there were no measurements of the surface layer stress of specimens that had been cyeled a large number of times. On the basis of the data sent to me by Dr. Laird, I also stated that it appeared possible that when specimens were cycled for a large number of times the hardening of both the interior and surface layer could account for the cyclic work hardening. Unfortunately, data are still n o t available to determine the respective roles of the surface layer and the interior when copper specimens are subjected to a large number of cycles. There are data available for titanium (6A1-4V), 4130 steel, 7075-T6 and 2014-T6 aluminum. It was shown [4, 5] that when these materials were cycled at a constant stress amplitud e, the proportional limit increased. But, it returned to the same value as that of the virgin specimen after the surface layer was removed after cycling. Accordingly, these data show that, under the test conditions employed, cycling did n o t work harden the interior of these materials. Note, however, that the stress amplitude was always less than the proportional limit. Finney e t al. (F.L.V.) state that their loadstrain curves are n o t linear. However, this, p e r se, does n o t prove that other investigators could n o t produce linear curves. It is very difficult to know why the F.L.V. curves are not
linear, but it should be noted, however, that in their work the surface layer was removed from only two sides of the specimen. This condition would create an unsymmetrical distribution of residual stresses and an unsymmetrical distribution of the excess dislocations in the surface layer. This type of imbalance could cause early departure from linearity. There is also an obvious experimental inconsistency in the load-strain curves reported in their Fig. 7. The slope of the curve {modulus) obtained from the bonded strain gages is about 15% higher than that obtained from specimens with a clip-on-gage. F.L.V. reported that the measurements were taken at the same time on the same specimen. It would have been supposed that the gages would have been properly calibrated for a paper of the type presented by F.L.V. An untouched X-Y recorder chart of the load-strain relationship is shown in Fig. 1 for a specimen of 2014-T6 aluminum t h a t had been cycled 30 × 103 times at -+25 k.s.i, and the surface layer was removed. Note that the curve is linear up to the point marked 1000 lb. and is the same as that of the virgin specimen. Other curves after cycling but n o t polished are given in reference 5 and are shown to be linear. In their statements with respect to the activation volume F.L.V. argue that one should properly compare the behavior of the cyclic condition with that of the cycled-andpolished condition. Actually the data presented in the paper [6] compared all three cases. For clarity then let us reexamine the data. According to Fig. 5, reference 6, one set of specimens were cycled at Aec = 0.008, or in terms of 7 using the conversion factor used in the paper, ~/p = 0.009. The first point recorded for the as-cycled specimen was at a strain, 7 = 0.01, a difference of 0.001 from the terminal strain amplitude, +~p. A corresponding point for the cycled and polished specimens was also located at 7 = 0.01. However, the activation volume of the cycled and polished specimen was larger by a factor of 2 than that of the cycled specimen. At some-
154
what high strains 7 = 0.014, the activation volume for the cycled and polished specimen was still larger than that of the cycled specimen. An examination of the data in Fig. 5(a), for Aec = 0.004, (Tp = 0.0045) shows again that the activation volumes for the cycled and polished specimens are larger than those for the cycled specimen for strains of less than about 7 = 0.03. In both cases, 7 = 0.009 and 0.0045, the activation volume at the corresponding terminal strain, ~,p, was equal to that of the uncycled specimens. Clearly all the conditions (virgin, cycled, and cycled and polished) are required to analyze the data properly. When the specimens are cycled they work harden and the activation volume at the same strain is expected to be smaller than that of the uncycled specimen. Figure 5, reference 6, shows that the curve for the cycled specimen does indeed lie below that of the uncycled specimen. Now, if the work hardening of a cycled specimen is assumed to be uniform throughout the crosssection of the specimen then polishing would not have any effect and the curve would maintain its same position. Certainly, none of the activation volume points would coincide with any of the data points of the uncycled specimen. If it is assumed that both the surface layer and the interior play a role in cyclic hardening it would be expected that polishing would increase the activation volume. But, because the interior was assumed to have been work hardened, the volume would still be smaller than that of the uncycled specimen. Only if it is assumed that the cyclic work hardening is due entirely to the hardening of the surface layer would the polishing increase the activation volume to the same value as that of the uncycled specimen at and near the 1/4 cycle as reported in Fig. 5, reference 6. Accordingly, it is apparent that data are n o t required for the cycled specimens over the very small strain range of strain at +% as argued by F.L.V. The F.L.V. explanation for the improvement in fatigue resistance when specimens are prestressed and polished in terms of the removal of an adverse slip step profile does not agree with.known data. If was found during various investigations that elimination of the surface layer of strained specimens b y relaxation at room temperature improves the fatigue life by the same amount as that
achieved by polishing [7]. (Relaxation of the surface layer occurs in copper and titanium (6A1/4V) b u t n o t in age hardening alloys as 2014-T6, 7075-T6, etc.) Under this condition the slip step profile is unchanged and the improvement can be attributed only to the elimination of the surface layer. Further evidence that it is not the slip steps, p e r se, that play a dominate role in fatigue may be found in experiments on aluminum 2014-T6, 4130 steel and titanium (6A1/4V). It was reported [5] that only a b o u t a 30% increase in the number of cycles to failure was obtained when the specimens were polished to remove the slip bands. It is estimated that roughly 30% of the surface layer was also removed. By periodically eliminating the surface layer completely the fatigue life was greatly extended and limited only by the size of the specimen remaining. Further, when the surface layer was completely removed after cycling for over five times its normal life, the cycles required to cause failure was a b o u t the same or greater than that of the virgin specimen. These observations show very convincingly that the interior of the specimen was n o t damaged by the cyclic process. Similar observations were made b y Grosskreutz [8] with the same conclusions. It should be emphasized that F.L.V. experimental work on cyclic hardening and softening differs considerably from those reported in refs. 6, 9, 10 and 11. In the F.L.V. work the specimens were swaged to reduce the area by 80% while in our work the specimens were strained uniaxially only a few percent. It does not seem reasonable w i t h o u t sufficient data to expect these specimens to behave in the same manner as the swaged specimens. It is n o t the intention to answer the F.L.V. points one-by-one. It should be fairly obvious that many of their points are speculative and data are n o t available to reinforce their arguments. In some, data are available b u t are n o t in agreement with the F.L.V. statements. For example, data are available for the relaxation of unidirectional strained aluminum, copper and titanium; some of these were obtained by noting the change in strain at zero load and not by the proportional limit method. These two methods gave the same relaxation rates [ 10]. Concerning their statement regarding relaxation it should be clear that an apparent activation energy [6] of only 3340 cal/mole
155
for unidirectionally strained copper cannot be associated with bulk relaxation. Therefore, the suggestion of F.L.V. to measure the surface layer stress in terms of the 1/4 cycle curve at zero strain rather than at +% would be unsatisfactory. Actually it is required t h a t the work hardening of the surface layer and the interior be known at the strain ep under the applied stress. Unfortunately this has n o t been done. However, data are available t h a t show that the cyclic work hardening of aluminum is decreased when specimens are cycled in vacuum. The surface layer stress was also lower. If cyclic hardening were purely a bulk effect the change in an environment would not be expected to change the cyclic work hardening characteristics. If as suggested by F.L.V. the measurements are taken by unloading at ep = 0, difficulty is to be expected in interpreting the data for ep ¢ 0. Obviously the state of work hardening will differ at e = 0 and ep #= 0. But most important it is n o t known quantitatively how the surface layer changes along the entire hysteresis loop during cyclic loading. A correction is required for the F.L.V. calculation regarding the stress supported by the surface layer. For the cyclic hardening/softening work in references 6 and 10, the specimens were 1/8-inch in diameter and not 1/2-inch. The increase in stress was by a factor of 2.6 and n o t 10. The depth of the surface layer of 0.0025-inch is for aluminum crystals of 1/8inch-diameter and not copper of 1/2-inchdiameter. Using these data [10] the resistive stress "to plastic flow due to the surface layer is 16 times that of the interior for the copper specimens and n o t 500 as claimed by F.L.V.
A similar analysis cannot be made on the F.L.V. data because the depth of the surface layer is n o t known and as mentioned above we do not know the extent of the work hardening in the interior for large numbers of cycles on copper. We would like to call attention to some additional evidence that for a steel the work hardening during cycling is predominantly in the surface layer. Using micro beam X-ray techniques Taira and Tanaka [ 12] determined the rocking curve width as a function of distance from the fractured surface. They reported that the excess dislocation density decreased as a function of depth from the surface. For an annealed 0.03% C steel the dislocation density at the crack surface was about 20 times greater than that in the interior. REFERENCES 1 J. M. Finney, C. Laird and R. de |a Veaux, Mater. Sci. Eng., 24 (1976) 19. 2 C. Calebrese and C. Laird, Mater. Sci. Eng., 13 (1974) 141. 3 I. R. Kramer, Mater. Sci. Eng., 15 (1974) 95. 4 I. R. Kramer, Proc. Air Force Conf. on Fatigue and Fracture, AFFDL-TR-70-144, 1969. 5 I. R. Kramer, Met. Trans., 5 (1974) 1735. 6 I. R. Kramer and A. Kumar, Met. Trans., 3 (1972) 1223. 7 I. R. Kramer and A. Kumar, Air Force Rept., MRC 72-64, F44620-69-C-0065. 8 J. C. Grosskreutz, ASTM Spec. Tech. Publ. 495, 1972, p. 5. 9 I. R. Kramer, Am. Soc. Metals, 62 (1969) 521. 10 I. R. Kramer, Am. Soc. Metals, 60 (1967) 310. 11 I. R. Kramer and A. Kumar, Corrosion Fatigue, NACE 2, 1972, p. 146. 12 S. Talra and K. Tanaka, Eng. Frac. Mech., 4 (1972)925.