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Internal friction in martensitic, ferritic and bainitic carbon steel; cold work effects
Materials Science and Engineering A 370 (2004) 213–217
Internal friction in martensitic, ferritic and bainitic carbon steel; cold work effects I. Tkalcec∗ , D. Mari Institut de Physique de la Matière Complexe, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland Received 12 July 2002
Abstract We present the comparative analysis of the temperature dependent internal friction (IF) spectra for 1.23 wt.% carbon steel with martensitic, bainitic or ferritic structure as well as cold-work effects. Samples that have a martensitic structure at room temperature show a characteristic spectrum consisting of five peaks and an exponential background. Tempering at 800 K transforms the sample structure to a completely ferritic one. All peaks are erased upon tempering, except the peak P5 identified as a Snoek–Köster (S-K) relaxation, the amplitude of which is however drastically reduced. The Snoek–Köster peak is also present in the bainitic structure as well as in initial ferrite, but with an amplitude much lower than in martensitic samples. Cold work performed on tempered samples at room temperature either by bending or roll milling is followed by the formation of a very broad double peak between 200 and 300 K. A similar peak is also found in initial ferrite, which has been subjected to heavy machining. A local minimum in the IF spectrum is found at the temperature of cold work and post-aging. This minimum is the effect of dislocation pinning by carbon precipitates. © 2003 Elsevier B.V. All rights reserved. Keywords: Mechanical spectroscopy; Martensite; Ferrite; Snoek–Köster; Dislocations
1. Introduction Thermal treatments of steels with the same chemical composition may produce a broad variety of structures with very different mechanical properties. In particular, a ferritic, bainitic or martensitic structure along with iron carbides can be obtained in carbon steels. Mechanical spectroscopy is a particularly useful technique to investigate such structure changes in the material. Pure body centered cubic (BCC) materials such as Ta, Nb, W, Mo and Fe exhibit relaxations associated with internal friction (IF) peaks identified as kink pair formation on non-screw dislocations (␣-peak) [1] and on screw dislocations (␥-peak) [2]. The presence of light interstitial atoms shifts the peaks observed in pure materials to higher temperatures [3], as their movement influences the thermal activation. The interaction of interstitials with kink pairs formed on dislocations is generally called Snoek–Köster ∗ Corresponding author. Tel.: +41-21-693-3393; fax: +41-21-693-4470. E-mail address: [email protected] (I. Tkalcec).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.04.004
(S-K) relaxation [4]. Thus, the presence of hydrogen transforms the ␣-peak occurring in ␣-iron at 30 K for 1 Hz to S-K(H) observed around 100 K [5]. Correspondingly, the ␥-peak is transformed to a S-K peak that appears around 500 K at 1 Hz [6]. The mechanical spectroscopy investigations available for martensitic steels are much less extended. Three thermally activated IF peaks have been observed in Fe–Ni–C virgin martensite at about 185, 215 and 255 K for 1 Hz measurements [7,8]. The peaks observed at 185 and 255 K are attributed to the kink pair formation on non-screw dislocations. The 215 K peak is attributed to the interaction between non-screw dislocations and carbon interstitials. Klems et al. [9] report the presence of a S-K peak in martensite. The relaxation phenomena in martensitic carbon steel have been recently described by Bagramov et al. [10]. This paper presents a comparative analysis of the internal friction spectra of a high carbon steel thermally treated in order to obtain most basic structures: the ferritic, bainitic and martensitic ones. The effects of cold work are studied in order to shed light on the relaxations that could be attributed to dislocations.
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I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
Table 1 Chemical composition of base material (wt.%) Element
Fe
C
Cr
Mn
Si
S
P
Ni
Mo
Cu
Al
Content
Bal.
1.23
0.64
0.34
0.22
0.006
0.006
0.07
0.02
0.10
0.018
2. Materials and experimental methods The material studied here is a high carbon tool steel used for the production of files. The chemical composition is presented in Table 1. As a part of the heat treatment, the material is normalized by annealing for 15 min at 1150 K and subsequent air-cooling, in order to obtain a ferritic structure with embedded spheroidized carbide particles. The material is then machined in file shape (bars 2.2 mm thick), and then thermally treated. Rapid quenching after 15 min of austenitization at 1100 K produces a fully martensitic ferrous phase. The structure of martensitic samples (Fig. 1) consists of a matrix, made of plate and lath martensite and less than 1% residual austenite at the former grain boundaries, and of (Fe, Cr)3 C carbides (0.2–2 m in diameter). Quenching to intermediate temperature (720 K) after the austenitization and subsequent air-cooling results in the formation of bainite, a structure composed of fine aggregates of ferrite and cementite. Measurements of internal friction as a function of temperature were made in the temperature range 80–800 K in a vibrating reed setup (free–free). The sample is excited to oscillate at the resonant frequency (∼1.5 kHz) and then the number n of oscillations in free decay between two fixed
amplitudes is recorded. IF is calculated according to: 1 Ai IF = ln nπ Ai+n
(1)
Heating and cooling rates used were 1 K min−1 and maximal oscillation amplitude 2 × 10−7 .
3. Results IF spectra for the martensitic, ferritic and bainitic structure are shown in Fig. 2. The IF spectrum that characterizes the martensitic structure has been discussed in detail previously [10,11]. It consists of four relaxation peaks (P1 at 130 K, P2 at 260 K, P4 at 510 K and P5 at 600 K for 2 kHz) and an IF maximum (P3 at 380 K). Tempering at 800 K transforms the sample structure into a ferritic one (Fig. 3). It consists of ferritic grains and carbide particles of comparable size (0.5–2 m). The increased mobility of dislocations causes a strong recrystallization producing polygonized cells. The length of dislocations increases and the dislocation density is reduced. All peaks are erased upon tempering except for 4
P2 x10-4
8x10
3
-3
2
P5
Internal Friction
P1 6
1 100 150 200 250 300 350
4
P4 martensitic tempered martensitic bainitic P3
2
P2
P1 0 100
Fig. 1. TEM image of martensitic structure with embedded (Fe, Cr)3 C carbide (on the left end of the image). Matrix is composed of plate and lath martensite and residual austenite visible as the dark lines between the laths.
200
300
400 500 Temperature [K]
600
700
800
Fig. 2. IF spectra for martensitic, tempered martensitic and bainitic structure. Five peaks (full lines) and an exponential background (dashed line) are visible in IF spectrum of martensite. P1 and P2 are magnified in the inset.
I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
215
450x10-6
1.3
cold worked by roll milling (right scale) cold worked by bending (left scale) ferritic (left scale) 400
1.2
1.1
300
250
0.9
200
0.8
150 150
Fig. 3. TEM image of tempered martensite. The structure is composed of carbides and ferritic recristallized grains of comparable size.
the peak P5. After tempering, the peak is found at a temperature 20 K higher, with an amplitude reduced by 90%. The same peak is present in the bainitic structure as well as in the primary ferrite (Fig. 4), and it is further decreased by tempering of these materials. Samples tempered at 800 K are cold worked at room temperature either by bending (ε = 0.2%) or roll milling (ε = 11%). The effects of cold work are most clearly visible in
-3
1.0
x10
Internal Friction
350
200
250 300 350 Temperature [K]
400
0.7 450
Fig. 5. Effects of cold work on tempered martensite and ferrite. A broad IF peak distribution ranging from 100 to 400 K is obtained. A local dip with minimum at room temperature (arrow) is observed.
the internal friction spectra below 400 K (Fig. 5). Spectra recorded in first heating after cooling to 100 K show the formation of a very broad peak between 100 and 400 K. The same feature is seen in initial ferritic samples which can be considered as heavily cold worked during the pro-
500x10
-6
A
1.4x10-3
tempered martensitic ferritic bainitic
B
400 Internal Friction
Internal Friction
1.2
1.0
C 300 D
0.8 200 E
0.6 100
0.4 100
0.2 450
500
550 600 650 Temperature [K]
700
750
Fig. 4. IF peak found in tempered martensite, bainite and ferrite, corresponding to peak P5 in martensite. The amplitude of these peaks is about 10 times smaller than P5.
150
200
250 300 350 Temperature [K]
400
450
Fig. 6. Time and temperature effects of cold work and post-aging on the IF minimum. (A) cold worked and post-aged for 30 min at room temperature; (B) cold worked and post-aged for 15 h at 273 K; (C) cold worked and post-aged for 20 h at 320 K; (D) cold worked and post-aged for 8 h at room temperature; (E) cold worked and post-aged for 3.5 days at 325 K. Arrows mark the positions of IF minima.
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I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
duction process. The common feature in all three spectra is a local minimum of IF at room temperature, separating the broad lower temperature part from a sharper peak above room temperature. Measurements performed at low frequency (1.5 Hz) in a torsion pendulum show that the position of the minimum does not depend on the oscillation frequency. To clarify the origin of the local minimum appearing after cold work, experiments were performed changing the cold work temperature and the time of aging at that temperature (post-aging). The results are shown at Fig. 6. Without a sufficiently long post-aging after cold work (curve A in Fig. 6), no minimum is observed. On the other hand, too long post-aging leads to an important reduction of the IF and the double peak is no longer visible (curve E). A further decrease of IF is observed in heating above 390 K (which coincides with P3 in the martensitic structure). The clear shift of the local minimum to the temperature of post-aging is observed for the sample cold worked and post-aged at 273 K (curve B). For the sample cold worked and post-aged for 20 h at 320 K (curve C), the minimum is shifted to 320 K, but is much less pronounced.
4. Discussion The peak present around 600 K in all IF measurements is identified [10,11] as a Snoek–Köster peak, and is strikingly high for the martensite. The amplitude of the peak (∆/2 = 4.5 × 10−3 ) is related to the density of dislocations Λ and ¯ according to [12]: their average free length L ∆=
¯ b2 L 12γJ
2
(2)
where b is the Burgers vector, γ the line tension of a dislocation, and J the elastic compliance of the material (inverse of its Young modulus E = 214 GPa). Taking γ = 0.5µb2 , ¯ = µ being a shear modulus of the material (83 GPa), and L 20 nm as an estimation from TEM images, Eq. (2) gives the dislocation density in martensite = 5 × 1013 m−2 . This dislocation density is close to that of a cold worked metal. The reduction of the peak after tempering is likely to be as¯ = 100 nm sociated with the dislocation recovery. Taking L and the amplitude of the peak measured in tempered martensite, ∆/2 = 4.5 × 10−4 , the calculated value for the dislocation density is Λ = 2 × 1011 m−2 , which seems reasonable looking at the TEM images. The peak P2 observed in the IF spectrum of the martensitic sample, and the broad increase of IF between 100 and 400 K created by cold work performed on the ferritic samples, probably have the same origin. Being sensitive to cold work, the peak is clearly related to the dislocation movement. Screw dislocations should become mobile at much higher temperatures, when P5 is activated. Therefore, a possible interpretation of this peak is a relaxation of Snoek–Köster type [8], involving non-screw dislocations
and interstitial carbon, which is present in a material in large quantities and is already very mobile around room temperature. Upon cold work, dislocations break away from the pinning points issued from aging and simultaneously new ones are created. The result is the formation of a very broad peak due to the wide distribution of free dislocation lengths. For the formation of a minimum in the peak we suggest a mechanism of dislocations–point defects interaction. Post-aging after cold work leads to the pinning of dislocations, reducing again their mobility. Presuming that the post-aging has not been too long, the dislocations can break away from pinning points, probably carbon, upon cooling, due to the internal stresses that change with temperature. As they pass back through their initial positions during heating, their mobility is first reduced by the carbon atmosphere creating a local minimum. Increasing the temperature they can break away from carbon atoms and/or drag them causing the abrupt increase of the IF. The pinning effect is similar to that observed by Vincent [13] in ultrasonic attenuation in aluminium submitted to an external stress. The effect is smaller for the sample cold worked and post aged at 320 K. In this case weaker pinning points like carbon interstitials or clusters are already very mobile at the temperature where the dip should appear and the effect is decreased.
5. Conclusions The IF spectrum of the martensite is very rich, showing four relaxation peaks and an IF maximum. The peak located at 600 K for 1.5 kHz is interpreted as the Snoek–Köster peak involving screw dislocations and interstitial carbon. It is present also in a bainitic and ferritic structure, but with the amplitude 10 times smaller, due to the lower dislocation density. Cold work performed on a ferritic structure results in the formation of a very broad peak between 100 and 400 K, with a local minimum at the temperature of aging after cold-work. The peak can be explained as a Snoek–Köster relaxation involving non-screw dislocations and carbon interstitials, and the local minimum as the effect of dislocation pinning by carbon precipitates. The shift of the dislocation position due to changes of internal stress with temperature produces a sort of memory effect of the aging temperature.
Acknowledgements The authors would like to thank C. Azcoitia and S. Crevoiserat for TEM images, and G. Gremaud for helpful discussions. They furthermore acknowledge the company UMV SA, Vallorbe (Switzerland) for support and sample supply and the Swiss “Commission pour la Technologie et l’Innovation” (project 4743.1) for financial support.
I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
References [1] [2] [3] [4] [5]
A. Seeger, C. Wüthrich, Nuovo Cim. 33B (1976) 39. H. Schultz, Mater. Sci. Eng. A141 (1991) 149. A. Seeger, Phys. Stat. Sol. (a) 55 (1979) 457. M. Weller, J. Phys. 44 (1983) C9. J. San Juan, G. Fantozzi, M.L. No, C. Esnouf, J. Phys. F 17 (1987) 837. [6] L.B. Magalas, J.F. Dufresne, P. Moser, J. Phys. C5-42 (1981) 127. [7] Y. Liu, Acta Metal. Mater. 41 (1993) 3277. [8] Y. Liu, Acta Metal. Mater. 42 (1994) 621.
217
[9] G.J. Klems, R.E. Miner, F.A. Hultgren, R. Gibala, Metal. Trans. A 7 (1976) 839. [10] R. Bagramov, D. Mari, W. Benoit, Phil. Mag. A 81 (2001) 2797. [11] I. Tkalcec, D. Mari, Defect Diffusion Forum 203–205 (2002) 253. [12] G. Gremaud, Dislocation—Point Defect Interactions, in: R. Schaller, G. Fantozzi, G. Gremaud (Eds.), Mechanical Spectroscopy Q-1 2001 with Applications to Materials Science, Trans Tech Publications, Uetikon-Zuerich, Switzerland, 2001, p. 178. [13] A. Vincent, Réalisation d’un ensamble de mesures ultrasonores; Application à l’étude des défauts cristallins dans l’aluminium, Ph.D. Thesis Universite Claude Bernard de Lyon, Lyon, 1973, pp. 112–124.
Internal friction in martensitic, ferritic and bainitic carbon steel; cold work effects I. Tkalcec∗ , D. Mari Institut de Physique de la Matière Complexe, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland Received 12 July 2002
Abstract We present the comparative analysis of the temperature dependent internal friction (IF) spectra for 1.23 wt.% carbon steel with martensitic, bainitic or ferritic structure as well as cold-work effects. Samples that have a martensitic structure at room temperature show a characteristic spectrum consisting of five peaks and an exponential background. Tempering at 800 K transforms the sample structure to a completely ferritic one. All peaks are erased upon tempering, except the peak P5 identified as a Snoek–Köster (S-K) relaxation, the amplitude of which is however drastically reduced. The Snoek–Köster peak is also present in the bainitic structure as well as in initial ferrite, but with an amplitude much lower than in martensitic samples. Cold work performed on tempered samples at room temperature either by bending or roll milling is followed by the formation of a very broad double peak between 200 and 300 K. A similar peak is also found in initial ferrite, which has been subjected to heavy machining. A local minimum in the IF spectrum is found at the temperature of cold work and post-aging. This minimum is the effect of dislocation pinning by carbon precipitates. © 2003 Elsevier B.V. All rights reserved. Keywords: Mechanical spectroscopy; Martensite; Ferrite; Snoek–Köster; Dislocations
1. Introduction Thermal treatments of steels with the same chemical composition may produce a broad variety of structures with very different mechanical properties. In particular, a ferritic, bainitic or martensitic structure along with iron carbides can be obtained in carbon steels. Mechanical spectroscopy is a particularly useful technique to investigate such structure changes in the material. Pure body centered cubic (BCC) materials such as Ta, Nb, W, Mo and Fe exhibit relaxations associated with internal friction (IF) peaks identified as kink pair formation on non-screw dislocations (␣-peak) [1] and on screw dislocations (␥-peak) [2]. The presence of light interstitial atoms shifts the peaks observed in pure materials to higher temperatures [3], as their movement influences the thermal activation. The interaction of interstitials with kink pairs formed on dislocations is generally called Snoek–Köster ∗ Corresponding author. Tel.: +41-21-693-3393; fax: +41-21-693-4470. E-mail address: [email protected] (I. Tkalcec).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.04.004
(S-K) relaxation [4]. Thus, the presence of hydrogen transforms the ␣-peak occurring in ␣-iron at 30 K for 1 Hz to S-K(H) observed around 100 K [5]. Correspondingly, the ␥-peak is transformed to a S-K peak that appears around 500 K at 1 Hz [6]. The mechanical spectroscopy investigations available for martensitic steels are much less extended. Three thermally activated IF peaks have been observed in Fe–Ni–C virgin martensite at about 185, 215 and 255 K for 1 Hz measurements [7,8]. The peaks observed at 185 and 255 K are attributed to the kink pair formation on non-screw dislocations. The 215 K peak is attributed to the interaction between non-screw dislocations and carbon interstitials. Klems et al. [9] report the presence of a S-K peak in martensite. The relaxation phenomena in martensitic carbon steel have been recently described by Bagramov et al. [10]. This paper presents a comparative analysis of the internal friction spectra of a high carbon steel thermally treated in order to obtain most basic structures: the ferritic, bainitic and martensitic ones. The effects of cold work are studied in order to shed light on the relaxations that could be attributed to dislocations.
214
I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
Table 1 Chemical composition of base material (wt.%) Element
Fe
C
Cr
Mn
Si
S
P
Ni
Mo
Cu
Al
Content
Bal.
1.23
0.64
0.34
0.22
0.006
0.006
0.07
0.02
0.10
0.018
2. Materials and experimental methods The material studied here is a high carbon tool steel used for the production of files. The chemical composition is presented in Table 1. As a part of the heat treatment, the material is normalized by annealing for 15 min at 1150 K and subsequent air-cooling, in order to obtain a ferritic structure with embedded spheroidized carbide particles. The material is then machined in file shape (bars 2.2 mm thick), and then thermally treated. Rapid quenching after 15 min of austenitization at 1100 K produces a fully martensitic ferrous phase. The structure of martensitic samples (Fig. 1) consists of a matrix, made of plate and lath martensite and less than 1% residual austenite at the former grain boundaries, and of (Fe, Cr)3 C carbides (0.2–2 m in diameter). Quenching to intermediate temperature (720 K) after the austenitization and subsequent air-cooling results in the formation of bainite, a structure composed of fine aggregates of ferrite and cementite. Measurements of internal friction as a function of temperature were made in the temperature range 80–800 K in a vibrating reed setup (free–free). The sample is excited to oscillate at the resonant frequency (∼1.5 kHz) and then the number n of oscillations in free decay between two fixed
amplitudes is recorded. IF is calculated according to: 1 Ai IF = ln nπ Ai+n
(1)
Heating and cooling rates used were 1 K min−1 and maximal oscillation amplitude 2 × 10−7 .
3. Results IF spectra for the martensitic, ferritic and bainitic structure are shown in Fig. 2. The IF spectrum that characterizes the martensitic structure has been discussed in detail previously [10,11]. It consists of four relaxation peaks (P1 at 130 K, P2 at 260 K, P4 at 510 K and P5 at 600 K for 2 kHz) and an IF maximum (P3 at 380 K). Tempering at 800 K transforms the sample structure into a ferritic one (Fig. 3). It consists of ferritic grains and carbide particles of comparable size (0.5–2 m). The increased mobility of dislocations causes a strong recrystallization producing polygonized cells. The length of dislocations increases and the dislocation density is reduced. All peaks are erased upon tempering except for 4
P2 x10-4
8x10
3
-3
2
P5
Internal Friction
P1 6
1 100 150 200 250 300 350
4
P4 martensitic tempered martensitic bainitic P3
2
P2
P1 0 100
Fig. 1. TEM image of martensitic structure with embedded (Fe, Cr)3 C carbide (on the left end of the image). Matrix is composed of plate and lath martensite and residual austenite visible as the dark lines between the laths.
200
300
400 500 Temperature [K]
600
700
800
Fig. 2. IF spectra for martensitic, tempered martensitic and bainitic structure. Five peaks (full lines) and an exponential background (dashed line) are visible in IF spectrum of martensite. P1 and P2 are magnified in the inset.
I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
215
450x10-6
1.3
cold worked by roll milling (right scale) cold worked by bending (left scale) ferritic (left scale) 400
1.2
1.1
300
250
0.9
200
0.8
150 150
Fig. 3. TEM image of tempered martensite. The structure is composed of carbides and ferritic recristallized grains of comparable size.
the peak P5. After tempering, the peak is found at a temperature 20 K higher, with an amplitude reduced by 90%. The same peak is present in the bainitic structure as well as in the primary ferrite (Fig. 4), and it is further decreased by tempering of these materials. Samples tempered at 800 K are cold worked at room temperature either by bending (ε = 0.2%) or roll milling (ε = 11%). The effects of cold work are most clearly visible in
-3
1.0
x10
Internal Friction
350
200
250 300 350 Temperature [K]
400
0.7 450
Fig. 5. Effects of cold work on tempered martensite and ferrite. A broad IF peak distribution ranging from 100 to 400 K is obtained. A local dip with minimum at room temperature (arrow) is observed.
the internal friction spectra below 400 K (Fig. 5). Spectra recorded in first heating after cooling to 100 K show the formation of a very broad peak between 100 and 400 K. The same feature is seen in initial ferritic samples which can be considered as heavily cold worked during the pro-
500x10
-6
A
1.4x10-3
tempered martensitic ferritic bainitic
B
400 Internal Friction
Internal Friction
1.2
1.0
C 300 D
0.8 200 E
0.6 100
0.4 100
0.2 450
500
550 600 650 Temperature [K]
700
750
Fig. 4. IF peak found in tempered martensite, bainite and ferrite, corresponding to peak P5 in martensite. The amplitude of these peaks is about 10 times smaller than P5.
150
200
250 300 350 Temperature [K]
400
450
Fig. 6. Time and temperature effects of cold work and post-aging on the IF minimum. (A) cold worked and post-aged for 30 min at room temperature; (B) cold worked and post-aged for 15 h at 273 K; (C) cold worked and post-aged for 20 h at 320 K; (D) cold worked and post-aged for 8 h at room temperature; (E) cold worked and post-aged for 3.5 days at 325 K. Arrows mark the positions of IF minima.
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I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
duction process. The common feature in all three spectra is a local minimum of IF at room temperature, separating the broad lower temperature part from a sharper peak above room temperature. Measurements performed at low frequency (1.5 Hz) in a torsion pendulum show that the position of the minimum does not depend on the oscillation frequency. To clarify the origin of the local minimum appearing after cold work, experiments were performed changing the cold work temperature and the time of aging at that temperature (post-aging). The results are shown at Fig. 6. Without a sufficiently long post-aging after cold work (curve A in Fig. 6), no minimum is observed. On the other hand, too long post-aging leads to an important reduction of the IF and the double peak is no longer visible (curve E). A further decrease of IF is observed in heating above 390 K (which coincides with P3 in the martensitic structure). The clear shift of the local minimum to the temperature of post-aging is observed for the sample cold worked and post-aged at 273 K (curve B). For the sample cold worked and post-aged for 20 h at 320 K (curve C), the minimum is shifted to 320 K, but is much less pronounced.
4. Discussion The peak present around 600 K in all IF measurements is identified [10,11] as a Snoek–Köster peak, and is strikingly high for the martensite. The amplitude of the peak (∆/2 = 4.5 × 10−3 ) is related to the density of dislocations Λ and ¯ according to [12]: their average free length L ∆=
¯ b2 L 12γJ
2
(2)
where b is the Burgers vector, γ the line tension of a dislocation, and J the elastic compliance of the material (inverse of its Young modulus E = 214 GPa). Taking γ = 0.5µb2 , ¯ = µ being a shear modulus of the material (83 GPa), and L 20 nm as an estimation from TEM images, Eq. (2) gives the dislocation density in martensite = 5 × 1013 m−2 . This dislocation density is close to that of a cold worked metal. The reduction of the peak after tempering is likely to be as¯ = 100 nm sociated with the dislocation recovery. Taking L and the amplitude of the peak measured in tempered martensite, ∆/2 = 4.5 × 10−4 , the calculated value for the dislocation density is Λ = 2 × 1011 m−2 , which seems reasonable looking at the TEM images. The peak P2 observed in the IF spectrum of the martensitic sample, and the broad increase of IF between 100 and 400 K created by cold work performed on the ferritic samples, probably have the same origin. Being sensitive to cold work, the peak is clearly related to the dislocation movement. Screw dislocations should become mobile at much higher temperatures, when P5 is activated. Therefore, a possible interpretation of this peak is a relaxation of Snoek–Köster type [8], involving non-screw dislocations
and interstitial carbon, which is present in a material in large quantities and is already very mobile around room temperature. Upon cold work, dislocations break away from the pinning points issued from aging and simultaneously new ones are created. The result is the formation of a very broad peak due to the wide distribution of free dislocation lengths. For the formation of a minimum in the peak we suggest a mechanism of dislocations–point defects interaction. Post-aging after cold work leads to the pinning of dislocations, reducing again their mobility. Presuming that the post-aging has not been too long, the dislocations can break away from pinning points, probably carbon, upon cooling, due to the internal stresses that change with temperature. As they pass back through their initial positions during heating, their mobility is first reduced by the carbon atmosphere creating a local minimum. Increasing the temperature they can break away from carbon atoms and/or drag them causing the abrupt increase of the IF. The pinning effect is similar to that observed by Vincent [13] in ultrasonic attenuation in aluminium submitted to an external stress. The effect is smaller for the sample cold worked and post aged at 320 K. In this case weaker pinning points like carbon interstitials or clusters are already very mobile at the temperature where the dip should appear and the effect is decreased.
5. Conclusions The IF spectrum of the martensite is very rich, showing four relaxation peaks and an IF maximum. The peak located at 600 K for 1.5 kHz is interpreted as the Snoek–Köster peak involving screw dislocations and interstitial carbon. It is present also in a bainitic and ferritic structure, but with the amplitude 10 times smaller, due to the lower dislocation density. Cold work performed on a ferritic structure results in the formation of a very broad peak between 100 and 400 K, with a local minimum at the temperature of aging after cold-work. The peak can be explained as a Snoek–Köster relaxation involving non-screw dislocations and carbon interstitials, and the local minimum as the effect of dislocation pinning by carbon precipitates. The shift of the dislocation position due to changes of internal stress with temperature produces a sort of memory effect of the aging temperature.
Acknowledgements The authors would like to thank C. Azcoitia and S. Crevoiserat for TEM images, and G. Gremaud for helpful discussions. They furthermore acknowledge the company UMV SA, Vallorbe (Switzerland) for support and sample supply and the Swiss “Commission pour la Technologie et l’Innovation” (project 4743.1) for financial support.
I. Tkalcec, D. Mari / Materials Science and Engineering A 370 (2004) 213–217
References [1] [2] [3] [4] [5]
A. Seeger, C. Wüthrich, Nuovo Cim. 33B (1976) 39. H. Schultz, Mater. Sci. Eng. A141 (1991) 149. A. Seeger, Phys. Stat. Sol. (a) 55 (1979) 457. M. Weller, J. Phys. 44 (1983) C9. J. San Juan, G. Fantozzi, M.L. No, C. Esnouf, J. Phys. F 17 (1987) 837. [6] L.B. Magalas, J.F. Dufresne, P. Moser, J. Phys. C5-42 (1981) 127. [7] Y. Liu, Acta Metal. Mater. 41 (1993) 3277. [8] Y. Liu, Acta Metal. Mater. 42 (1994) 621.
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