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Internal friction study of AISI 410 stainless steel
Scripta
METALLURGICA
Vol. 17, pp. 5 2 1 - 3 2 5 , 1983 P r i n t e d in the U.S.A.
P e r g a m o n P r e s s Ltd. All r i g h t s r e s e r v e d
INTERNAL FRICTION STUDY OF AISI 410 STAINLESS STEEL Alan Wolfenden Texas A&M University Mechanical Engineering Department College Station, Texas 77843 (Received (Revised
N o v e m b e r 22, 1982) J a n u a r y i0, 1983)
Introduction It is remarkable that, in spite of the recent great advances in the development of turbine technology, there appear to be no reports in the open literature on the relationship between internal friction properties of turbine blade alloys and microstructure. In 1968, Lazan (i) summarized the available information on turbine blade materials but this was limited strictly to damplng/stress or damplng/stress/magnetlc field (for ferromagnetic materials) relations. Since then several authors (2-5) have published results of studies on the magnetoelastic damping properties of ferromagnetic turbine blade alloys such as AISI 403 steel. Recently the author (6) reported internal friction (Q-z) and Young's modulus (E) results for a variety of turbine blade alloys measured with the piezoelectric ultrasonic composite oscillator technique (PUCOT) at 40 or 80 kHz and stress levels (o) in the range 70 kPa to 37 MPa. From a plot of unit damping energy D (= Q-Zo2/E) versus stress amplitude it was shown that the PUCOT data for AISI 410 stainless steel had a slope of 2, indicative of anelastlc dislocation damping behavior (i). The slope for the case where magnetoelastic damping is dominant (at stresses higher than about I00 MPa) would be 3. In this paper the results of an internal friction study done at low stress (< 37 MPa) on AISI 410 stainless steel in four different conditions of heat treatment are reported. Young's modulus values are given and the strain amplitude dependence of Q-Z is analyzed in terms of the Granato-L~cke theory (7) to provide an interpretation of the internal friction in terms of mlcrostructural features. Finally, a comparison of the results of this interpretation with metallographlc observations on similar turbine blade alloys is made. Experimental Procedure The PUCOT incorporated piezoelectric quartz drive D and gauge G crystals to excite longitudinal ultrasonic resonant stress waves in the cylindrical specimen S of appropriate resonant length for 80 kHz. The three component oscillator system has been reported elsewhere (8,9). During the experiments, which were conducted at room temperature, the values of the drive voltage Vd, the gauge voltage Vg, and the resonant period T (DGS) of the three component oscillator were measured. The specimen and crystals were under vacuum (I mPa) for the tests. From these values the following could be calculated: Q-Z; the maximum stress and strain amplitudes, o and e, respectively, and Young's modulus E. Specimen details are listed in Table I. The heat treatments given to Specimens i, 2, 3, and 4 of AISI 410 stainless steel were designed to yield microstructures ranging from fully martensltlc to spheroldized or coalesced carbides. TABLE I Details of the AISI 410 Stainless Steel Specimens Used in the PUCOT Experiments Specimen
Heat Treatment A A A A
960°C, 960°C, 960°C, 960°C,
OQ; OQ; OQ; OQ;
tempered tempered tempered tempered
Length/--,
250°C/ih 650°C/1.5h 650°C/3h; FC 780°C/Ih
32.12 32.48 32.00 32.22
A - austenitlzed, OQ - oll quenched, FC - furnace cooled
321 0036-9748/83/030321-0553.00/0 C o p y r i g h t (c) 1983 P e r g a m o n Press
Ltd.
322
INTERNAL FRICTION OF STAINLESS
STEEL
Vol.
17, No. 3
Results and Discussion The measured values of Young's modulus E for the four specimens are shown in Figure i. These values were calculated from the measured values of specimen length 1 and T(S), the value of the resonant period of the specimen (in turn calculated from T(DGS)), taking the density 0 of the steel as 7800 kg/m 3. Since T(DGS) can be measured to an accuracy of i0 ps on the electronic counter, the major error in the calculated value of E comes from the error in measuring I (±0.01 mm). With E = 4012/T(S) 2 the error in Young's modulus is about 0.2 GPa (or ± 0.1%).
218
10
i
i
i
216
A ..Q
Q,.
6
214
T
UJ
o 0 T-
4 212
0 10 -7
I
I
I
10 -e
lO-S
10-4
10-s
210= Specimen
FIG. 1 Measured values of Young's modulus E and break away strain amplitude c(b) for specimens of AlSl 410 stainless steel in four conditions of heat treatment.
FIG. 2 Strain amplitude dependence of internal friction Q-z in four differently heat treated specimens of AISI 410 stainless steel.
Thus the differences in Young's modulus shown in Figure 1 are real and result from the differences in mlcrostructure of the specimens caused by the various heat treatments. The martensitlc mlcrostructure (Specimen i) has a modulus of 2 1 1 G P a . The modulus increases to 218 GPa for the specimens with tempered martensite or partially spheroidized carbides, and drops back again to 215 GPa for the specimen with fully spheroldized or coalesced carbides. Such small changes in modulus (about 3%) may be difficult to detect using more conventional Young's modulus measuring apparatus such as tensile machines. Figure 2 shows the strain amplitude dependence of the internal friction in the four specimens. Clearly the effects of heat treatment on the damping properties are significant. At low strain amplitudes the Q-z values are near 2 x 10 -4 , while at high strain amplitudes the Q-I values for Specimens 2 and 3 reach 8 x 10 -4 . The break away strain amplitude E(b) varies from i0 -e to 3 x 10-5 as shown in Figure I. The trend in the change of E(b) is the inverse of that for E, with Specimen 3 having the highest Young's modulus but the lowest break away strain amplitude. Thus the results also show that heat treatment has a significant effect on the break away
Vol.
17, No. 3
strain amplitude,
INTERNAL FRICTION OF STAINLESS
namely on the dlslocatlon-plnning
STEEL
525
point interaction
(7).
The form of the damping curves In Figure 2 lends itself to analysis in terms of the GranatoL~cke (GL) theory (7) of dislocation damping and break away at hlgh strain amplitudes. According to the GL theory, the internal friction has two components -- an amplitude independent part QI -I and an amplitude dependent part QH -I. Thus Q-I = Q -i + Q -I. With the curves in Figure 2 we have found values of Q -i for the specimens and made ~L plot~ of EQ~ -I versus E -I as shown in Figure 3. For the GL model of dislocation damping to hold the curves In Figure 3 should be linear, while thls seems to be the case only at low values of E-I. We shall use the data at 10-sE -I < I and assume that the GL model Is valid in thls region. From the slope of the GL plot one
50
[LJK]~ 2 4
40
10-'
30
10-1
//p/
E
o 2O 10-9. 10 10-"
i
i
1
i
/
25
i
2
lO-S~-',
0 0.1
0
0.2
0.3
0.4
0.5
K
FIG. 3
FIG. 4
Granato-L~cke plot of the internal friction data for four specimens of AISI 410 stainless steel,
Values of the minor dislocation loop length L derived from the Granato-L~cke c analysis plotted as a function of the variable K for four specimens of stainless steel.
obtains a value for L , the minor loop length of the vibrating dislocation line, and from the intercept of the plotCat g-l = 0 one obtains a value for the mobile dislocation density A. All the pertinent equations and terms are given in the reference (7). As discussed in the original GL theory, the determination of L involves a variable K which c would vary wlth crystallographic orientation (of the grains wlth respect to the stress axis) and material and which would be limited to the range of values 0.02 to 0.5. Hence in the present determination of L the data are shown in Figure 4 as a function of K in thls range. The ratio L^/K is in any cas~ constant for a particular specimen and has values in the range 25 to 93 nm f~r the four specimens. The various values of L are listed in Table 2. Likewise, the deterc TABLE 2 Summary of Results of the Granato-L~cke Analysis of Internal Friction Data for AISI 410 Stainless Steel Specimen
Minor Pinning Length Lc/nm
1 2
0.5 1.6
-
12.6 39.7
3 4
1.0 - 25.4 1.9 - 46.4
Mobile Dislocation Density A/m -2 8.7 3.0
x x
105 107 -
2.2 7.6
x x
(Lc/K)/nm
101° 1011
25 79
I.I x l0 T - 2.7 x I0 II 5.3 x IO s - 1.7 x 101°
51 93
324
INTERNAL
FRICTION
OF STAINLESS
STEEL
Vol.
17, No.
5
mination of t~e mobile dislocation density depends on the variable K (A ~ K-Z), but also on the major dislocation loop length Lw determined by the dislocation network (A = LN-3). In Figure 5 values of A are plotted as a fuHction of K for each specimen, using two different value@ of the 10 TM
10"
1 0 '0
109
) 10 8
1 10 •
10 e
10s
0
0.'1
012
i ,0.3
014
i 0.5
0.6
K
FIG. 5 Derived values of the mobile dislocation density A plotted as a function of the variable K for four specimens of AISI 410 stainless steel. The parameter L N is the major dislocation loop length in terms of the Granato-L~cke theory. parameter LN (10-6 and lO-Tm). For a given specimen and L N value, the mobile dislocation density increases by about an order of magnitude as K goes from 0.02 to 0.5. These dislocation densities for the steel specimens are listed in Table 2. It is obviously desirable to be able to pin down the range of some of the variables (such as K) used in the GL analysis. This can be done to some extent by bringing into the analysis available results of metallographic observations on turbine blade materials. Unfortunately, a literature search has revealed only one report of transmission electron microscopy (TEM) observations on AISI 410 stainless steel. This report by Dulls et el. (i0) dealt with TEM observations of the alloy fatigued at 260°C. While these experimental conditions are not directly applicable to the present work, we shall use their observation of u' precipitation in the form of a sheaf-like structure to calculate a possible value for the concentration of pinned dislocations. Their finest network of precipitates had a spacing of about 80 nm, which would correspond to a dislocation density of i0 I~ m -z. For some ocher turbine blade materials (i Cr - 0.5 Ho steel and AlSl 316 stainless steel) there are some pertinent TEM observations available and we shall use these also to aid the GL analysis. Etienne et al.(ll) have studied the microstructure of AIS~ 316 stainless steel after extensive creep rupture tests at 600°C. A micrograph of the carbides in their steel indicates that the particle spacing is in the approximate range 0.I to 0.5 ~m. If these carbides define the network of pinned dislocations, the dislocation density would be approximately 1012 to I0 I~ m -2. Another micrograph of the steel in the as-delivered condition indicates a dislocation density of roughly 1012 m -2. Carruthers and Collins (121 studied the microstructure of I Cr - 0.5 Mo steel after creep rupture tests at temperatures up to 575°C. They showed that creep data indicated a transition from "grain boundary damage" to "matrix damage" reflecting difficulties encountered in causing dislocations to propagate
Vol.
17,
No.
3
INTERNAL
FRICTION
OF
STAINLESS
STEEL
325
across sessile dislocation networks inherited from the transformation product and anchored by carbide particles. These carbide particles have spacings around 4 to 400 nm which could correspond, for our purpose, to a dislocation density of roughly i0 IS to 1017 m -2. Thus the TEM observations on turbine blade materials seem to indicate a dislocation density of at least 1012 m - 2 a n d the presence of dislocation-partlcle interactions. Referring now to Table 2 and Figures 4 and 5, we shall assess the values of L , A and particularly K in terms of the metallographic information. Clearly the lower boun~ values (iO s to 106 m -2) of A are too low. Better agreement is obtained by taking values of K near the 0.5 upper limit, and values of L. such as 10 -7 m rather than 10 -6 m. Then we obtain A = i0 I° N to i012 m -2. In any case, it should be recalled that the total dislocation density will be greater than the mobile dislocation density A (7). Thus the present values of A are quite acceptable. With K taking the value of 0.5, L ranges from 13 to 46 nm for the four specimens. These values of L overlap the carbide particl~ spacings mentioned earlier (12) and are thereC fore acceptable. Summary From this study of the internal friction at low stresses of AISI 410 stainless four different conditions of heat treatment the following conclusions are made: i. 2. 3.
4.
5.
6. 7.
steel in
Young's modulus of the material is influenced by heat treatment and varies in the range 211 to 218 GPa. The internal friction is amplitude dependent and varies in the range 2 to 8 x I0 -~ for the different heat treatments and range of strain amplitudes investigated. The break away strain amplitude of the internal friction depends on the heat treatment of the specimen and varies in the range 10-6 to 3 x i0 -s. Moreover, the trend of the break away strain amplitude with heat treatment is the inverse of that for the trend of Young's modulus. When the internal friction data for lO-Sg -I < i are analyzed in terms of the Granato-Lbcke (GL) theory of dislocation damping, values of the minor loop length L^ of the vibrating dislocation line and of the mobile dislocation density A could be extracted for the specimens. The values of L (13 to 46 nm) and of A (10 I° to 1012 m -2) obtained from the analysis are acceptable when interpreted in terms of TEM observations on carbide precipitates and dislocations in turbine blade materials similar to the material used in this study. The mobile dislocation density under conditions of amplitude dependent internal friction is less than the estimated total dislocation density. The internal friction results suggest that the value of K (the variable in the GL theory which depends oncrystallographlc orientation and specimen material) for the specimens used should be near 0.5, and that the value of L N (the major dislocation loop length) should be near 10-Tm. References
i.
B. J. Lazan, Damping of Materials
and Members
in Structural Mechanics,
Pergamon Press,
New York (1968). 2. M. Nakamura, H. Kawakaml, and Y. Takano, Technical Review. Mitsubishi Heavy Industries, Ltd. ii, 95-101 (1974). 3. T. Oda, M. Nakamura, K. Uehara, and K. Kawakami, Technical Review. Mitsubishi Heavy Industries, Ltd. 7, 198-206 (1970). 4. L. E. Willertz, Journal of Testing and Evaluation 2, 478-482 (1974). 5. B. Dubois, S. A. Rizkallah, G. Brun, G. Flamant, and G. Bouquet, Ii Nuovo Cimento 33B, 354-367 (1976). 6. A. Wolfenden, Journal of Testing and Evaluation i0, 17-20 (1982). 7. A. Granato and K. Lucke, Journal of Applied Physics 27, 583-593 and 789-805 (1956). 8. J. Marx, Review of Scientific Instruments 22, 503-509 (1951). 9. W. H. Robinson and A. Edgar, Institute of Electrical and Electronics Engineers. Transactions on Sonics and Ultrasonics SU-21, No. 2, 98-105 (1974). i0. E. J. Dulls, V. K. Chandhok and J. P. Hirth, Trans. Quart. ASM, 54, 456-465 (1961). ii. C. F. Etienne, O. van Rossum and F. Roode, "Creep of Welded Joints in AISI 316," I. Mech. E/ASME/ASTM/JSME International Conference "Engineering Aspects of Creep," Sheffield, U.K., Sept. 15-19, 1980. Paper C328/80, Vol. 2, 113-121. 12. R. B. Carruthers and M. J. Collins, '~icrostructural Aspects of Creep in Low Alloy Ferritic Steels," Ibld. Paper C204/80, Vol. 2, 223-231.
METALLURGICA
Vol. 17, pp. 5 2 1 - 3 2 5 , 1983 P r i n t e d in the U.S.A.
P e r g a m o n P r e s s Ltd. All r i g h t s r e s e r v e d
INTERNAL FRICTION STUDY OF AISI 410 STAINLESS STEEL Alan Wolfenden Texas A&M University Mechanical Engineering Department College Station, Texas 77843 (Received (Revised
N o v e m b e r 22, 1982) J a n u a r y i0, 1983)
Introduction It is remarkable that, in spite of the recent great advances in the development of turbine technology, there appear to be no reports in the open literature on the relationship between internal friction properties of turbine blade alloys and microstructure. In 1968, Lazan (i) summarized the available information on turbine blade materials but this was limited strictly to damplng/stress or damplng/stress/magnetlc field (for ferromagnetic materials) relations. Since then several authors (2-5) have published results of studies on the magnetoelastic damping properties of ferromagnetic turbine blade alloys such as AISI 403 steel. Recently the author (6) reported internal friction (Q-z) and Young's modulus (E) results for a variety of turbine blade alloys measured with the piezoelectric ultrasonic composite oscillator technique (PUCOT) at 40 or 80 kHz and stress levels (o) in the range 70 kPa to 37 MPa. From a plot of unit damping energy D (= Q-Zo2/E) versus stress amplitude it was shown that the PUCOT data for AISI 410 stainless steel had a slope of 2, indicative of anelastlc dislocation damping behavior (i). The slope for the case where magnetoelastic damping is dominant (at stresses higher than about I00 MPa) would be 3. In this paper the results of an internal friction study done at low stress (< 37 MPa) on AISI 410 stainless steel in four different conditions of heat treatment are reported. Young's modulus values are given and the strain amplitude dependence of Q-Z is analyzed in terms of the Granato-L~cke theory (7) to provide an interpretation of the internal friction in terms of mlcrostructural features. Finally, a comparison of the results of this interpretation with metallographlc observations on similar turbine blade alloys is made. Experimental Procedure The PUCOT incorporated piezoelectric quartz drive D and gauge G crystals to excite longitudinal ultrasonic resonant stress waves in the cylindrical specimen S of appropriate resonant length for 80 kHz. The three component oscillator system has been reported elsewhere (8,9). During the experiments, which were conducted at room temperature, the values of the drive voltage Vd, the gauge voltage Vg, and the resonant period T (DGS) of the three component oscillator were measured. The specimen and crystals were under vacuum (I mPa) for the tests. From these values the following could be calculated: Q-Z; the maximum stress and strain amplitudes, o and e, respectively, and Young's modulus E. Specimen details are listed in Table I. The heat treatments given to Specimens i, 2, 3, and 4 of AISI 410 stainless steel were designed to yield microstructures ranging from fully martensltlc to spheroldized or coalesced carbides. TABLE I Details of the AISI 410 Stainless Steel Specimens Used in the PUCOT Experiments Specimen
Heat Treatment A A A A
960°C, 960°C, 960°C, 960°C,
OQ; OQ; OQ; OQ;
tempered tempered tempered tempered
Length/--,
250°C/ih 650°C/1.5h 650°C/3h; FC 780°C/Ih
32.12 32.48 32.00 32.22
A - austenitlzed, OQ - oll quenched, FC - furnace cooled
321 0036-9748/83/030321-0553.00/0 C o p y r i g h t (c) 1983 P e r g a m o n Press
Ltd.
322
INTERNAL FRICTION OF STAINLESS
STEEL
Vol.
17, No. 3
Results and Discussion The measured values of Young's modulus E for the four specimens are shown in Figure i. These values were calculated from the measured values of specimen length 1 and T(S), the value of the resonant period of the specimen (in turn calculated from T(DGS)), taking the density 0 of the steel as 7800 kg/m 3. Since T(DGS) can be measured to an accuracy of i0 ps on the electronic counter, the major error in the calculated value of E comes from the error in measuring I (±0.01 mm). With E = 4012/T(S) 2 the error in Young's modulus is about 0.2 GPa (or ± 0.1%).
218
10
i
i
i
216
A ..Q
Q,.
6
214
T
UJ
o 0 T-
4 212
0 10 -7
I
I
I
10 -e
lO-S
10-4
10-s
210= Specimen
FIG. 1 Measured values of Young's modulus E and break away strain amplitude c(b) for specimens of AlSl 410 stainless steel in four conditions of heat treatment.
FIG. 2 Strain amplitude dependence of internal friction Q-z in four differently heat treated specimens of AISI 410 stainless steel.
Thus the differences in Young's modulus shown in Figure 1 are real and result from the differences in mlcrostructure of the specimens caused by the various heat treatments. The martensitlc mlcrostructure (Specimen i) has a modulus of 2 1 1 G P a . The modulus increases to 218 GPa for the specimens with tempered martensite or partially spheroidized carbides, and drops back again to 215 GPa for the specimen with fully spheroldized or coalesced carbides. Such small changes in modulus (about 3%) may be difficult to detect using more conventional Young's modulus measuring apparatus such as tensile machines. Figure 2 shows the strain amplitude dependence of the internal friction in the four specimens. Clearly the effects of heat treatment on the damping properties are significant. At low strain amplitudes the Q-z values are near 2 x 10 -4 , while at high strain amplitudes the Q-I values for Specimens 2 and 3 reach 8 x 10 -4 . The break away strain amplitude E(b) varies from i0 -e to 3 x 10-5 as shown in Figure I. The trend in the change of E(b) is the inverse of that for E, with Specimen 3 having the highest Young's modulus but the lowest break away strain amplitude. Thus the results also show that heat treatment has a significant effect on the break away
Vol.
17, No. 3
strain amplitude,
INTERNAL FRICTION OF STAINLESS
namely on the dlslocatlon-plnning
STEEL
525
point interaction
(7).
The form of the damping curves In Figure 2 lends itself to analysis in terms of the GranatoL~cke (GL) theory (7) of dislocation damping and break away at hlgh strain amplitudes. According to the GL theory, the internal friction has two components -- an amplitude independent part QI -I and an amplitude dependent part QH -I. Thus Q-I = Q -i + Q -I. With the curves in Figure 2 we have found values of Q -i for the specimens and made ~L plot~ of EQ~ -I versus E -I as shown in Figure 3. For the GL model of dislocation damping to hold the curves In Figure 3 should be linear, while thls seems to be the case only at low values of E-I. We shall use the data at 10-sE -I < I and assume that the GL model Is valid in thls region. From the slope of the GL plot one
50
[LJK]~ 2 4
40
10-'
30
10-1
//p/
E
o 2O 10-9. 10 10-"
i
i
1
i
/
25
i
2
lO-S~-',
0 0.1
0
0.2
0.3
0.4
0.5
K
FIG. 3
FIG. 4
Granato-L~cke plot of the internal friction data for four specimens of AISI 410 stainless steel,
Values of the minor dislocation loop length L derived from the Granato-L~cke c analysis plotted as a function of the variable K for four specimens of stainless steel.
obtains a value for L , the minor loop length of the vibrating dislocation line, and from the intercept of the plotCat g-l = 0 one obtains a value for the mobile dislocation density A. All the pertinent equations and terms are given in the reference (7). As discussed in the original GL theory, the determination of L involves a variable K which c would vary wlth crystallographic orientation (of the grains wlth respect to the stress axis) and material and which would be limited to the range of values 0.02 to 0.5. Hence in the present determination of L the data are shown in Figure 4 as a function of K in thls range. The ratio L^/K is in any cas~ constant for a particular specimen and has values in the range 25 to 93 nm f~r the four specimens. The various values of L are listed in Table 2. Likewise, the deterc TABLE 2 Summary of Results of the Granato-L~cke Analysis of Internal Friction Data for AISI 410 Stainless Steel Specimen
Minor Pinning Length Lc/nm
1 2
0.5 1.6
-
12.6 39.7
3 4
1.0 - 25.4 1.9 - 46.4
Mobile Dislocation Density A/m -2 8.7 3.0
x x
105 107 -
2.2 7.6
x x
(Lc/K)/nm
101° 1011
25 79
I.I x l0 T - 2.7 x I0 II 5.3 x IO s - 1.7 x 101°
51 93
324
INTERNAL
FRICTION
OF STAINLESS
STEEL
Vol.
17, No.
5
mination of t~e mobile dislocation density depends on the variable K (A ~ K-Z), but also on the major dislocation loop length Lw determined by the dislocation network (A = LN-3). In Figure 5 values of A are plotted as a fuHction of K for each specimen, using two different value@ of the 10 TM
10"
1 0 '0
109
) 10 8
1 10 •
10 e
10s
0
0.'1
012
i ,0.3
014
i 0.5
0.6
K
FIG. 5 Derived values of the mobile dislocation density A plotted as a function of the variable K for four specimens of AISI 410 stainless steel. The parameter L N is the major dislocation loop length in terms of the Granato-L~cke theory. parameter LN (10-6 and lO-Tm). For a given specimen and L N value, the mobile dislocation density increases by about an order of magnitude as K goes from 0.02 to 0.5. These dislocation densities for the steel specimens are listed in Table 2. It is obviously desirable to be able to pin down the range of some of the variables (such as K) used in the GL analysis. This can be done to some extent by bringing into the analysis available results of metallographic observations on turbine blade materials. Unfortunately, a literature search has revealed only one report of transmission electron microscopy (TEM) observations on AISI 410 stainless steel. This report by Dulls et el. (i0) dealt with TEM observations of the alloy fatigued at 260°C. While these experimental conditions are not directly applicable to the present work, we shall use their observation of u' precipitation in the form of a sheaf-like structure to calculate a possible value for the concentration of pinned dislocations. Their finest network of precipitates had a spacing of about 80 nm, which would correspond to a dislocation density of i0 I~ m -z. For some ocher turbine blade materials (i Cr - 0.5 Ho steel and AlSl 316 stainless steel) there are some pertinent TEM observations available and we shall use these also to aid the GL analysis. Etienne et al.(ll) have studied the microstructure of AIS~ 316 stainless steel after extensive creep rupture tests at 600°C. A micrograph of the carbides in their steel indicates that the particle spacing is in the approximate range 0.I to 0.5 ~m. If these carbides define the network of pinned dislocations, the dislocation density would be approximately 1012 to I0 I~ m -2. Another micrograph of the steel in the as-delivered condition indicates a dislocation density of roughly 1012 m -2. Carruthers and Collins (121 studied the microstructure of I Cr - 0.5 Mo steel after creep rupture tests at temperatures up to 575°C. They showed that creep data indicated a transition from "grain boundary damage" to "matrix damage" reflecting difficulties encountered in causing dislocations to propagate
Vol.
17,
No.
3
INTERNAL
FRICTION
OF
STAINLESS
STEEL
325
across sessile dislocation networks inherited from the transformation product and anchored by carbide particles. These carbide particles have spacings around 4 to 400 nm which could correspond, for our purpose, to a dislocation density of roughly i0 IS to 1017 m -2. Thus the TEM observations on turbine blade materials seem to indicate a dislocation density of at least 1012 m - 2 a n d the presence of dislocation-partlcle interactions. Referring now to Table 2 and Figures 4 and 5, we shall assess the values of L , A and particularly K in terms of the metallographic information. Clearly the lower boun~ values (iO s to 106 m -2) of A are too low. Better agreement is obtained by taking values of K near the 0.5 upper limit, and values of L. such as 10 -7 m rather than 10 -6 m. Then we obtain A = i0 I° N to i012 m -2. In any case, it should be recalled that the total dislocation density will be greater than the mobile dislocation density A (7). Thus the present values of A are quite acceptable. With K taking the value of 0.5, L ranges from 13 to 46 nm for the four specimens. These values of L overlap the carbide particl~ spacings mentioned earlier (12) and are thereC fore acceptable. Summary From this study of the internal friction at low stresses of AISI 410 stainless four different conditions of heat treatment the following conclusions are made: i. 2. 3.
4.
5.
6. 7.
steel in
Young's modulus of the material is influenced by heat treatment and varies in the range 211 to 218 GPa. The internal friction is amplitude dependent and varies in the range 2 to 8 x I0 -~ for the different heat treatments and range of strain amplitudes investigated. The break away strain amplitude of the internal friction depends on the heat treatment of the specimen and varies in the range 10-6 to 3 x i0 -s. Moreover, the trend of the break away strain amplitude with heat treatment is the inverse of that for the trend of Young's modulus. When the internal friction data for lO-Sg -I < i are analyzed in terms of the Granato-Lbcke (GL) theory of dislocation damping, values of the minor loop length L^ of the vibrating dislocation line and of the mobile dislocation density A could be extracted for the specimens. The values of L (13 to 46 nm) and of A (10 I° to 1012 m -2) obtained from the analysis are acceptable when interpreted in terms of TEM observations on carbide precipitates and dislocations in turbine blade materials similar to the material used in this study. The mobile dislocation density under conditions of amplitude dependent internal friction is less than the estimated total dislocation density. The internal friction results suggest that the value of K (the variable in the GL theory which depends oncrystallographlc orientation and specimen material) for the specimens used should be near 0.5, and that the value of L N (the major dislocation loop length) should be near 10-Tm. References
i.
B. J. Lazan, Damping of Materials
and Members
in Structural Mechanics,
Pergamon Press,
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