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Internal friction behavior of twin boundaries in tensile-deformed Mn–15 at.% Cu alloy
Materials Science and Engineering A 442 (2006) 433–438
Internal friction behavior of twin boundaries in tensile-deformed Mn–15 at.% Cu alloy Qingchao Tian a,b , Fuxing Yin a,∗ , Takuya Sakaguchi c , Kotobu Nagai a a
Steel Research Center, National Research Institute for Materials Science, Tsukuba 305-0047, Japan b Technology Center, Baoshan Iron and Steel Co. Ltd., Shanghai 201900, PR China c Materials Engineering Div. III, Toyota Motors Co., Shizuoka 410-1193, Japan Received 29 July 2005; received in revised form 10 April 2006; accepted 12 April 2006
Abstract An orientation image microscope was used to characterize the orientation features in a deformed Mn–15 at.% Cu alloy. It was found that twinning and subsequent de-twinning prevailed during the deformation process of the twin bands, which were separately identified as massive and twinning type bands. The 111 and 100 fibers steadily developed along the tensile direction as the prestrain increased. The internal friction due to the movement of the twin boundary was investigated using a dynamic mechanical analyzer. It was deduced that the twin-boundary internal friction greatly depended on the arrangement of the twin variants, which can be changed by deformation or a thermal treatment. © 2006 Elsevier B.V. All rights reserved. Keywords: Manganese–copper alloy; Internal friction; Twin boundary; Twinning–de-twining
1. Introduction Mn–Cu alloys are well-known materials with a high internal friction capacity, which has been attributed to the movement of the {0 1 1} twin boundaries [1–4]. These alloys show a martensitic transformation from a face-centered cubic (fcc) structure to a tetragonal (fct) structure at a temperature that depends on the alloy composition [5]. The thermal martensitic microstructure with a fct lattice has been extensively investigated [6]. According to the double shear theory [7], Basinski and Christian concluded that each cubic crystal in the parent orientation might produce 36 fct variants, of which 24 are twin variants [8]. Thus, the fct martensite microstructure has the characteristics of {0 1 1} twins. The thermally activated relaxation of those twin boundaries causes an internal friction peak profile around 220 K, which is called the twin-boundary internal friction peak [9]. The mechanism of the relaxation process is regarded as an elementary process that involves twin boundary motion [10]. Bacon et al. found that applied stress caused the c axis of the fct phase to rotate in a favorable direction [11]. Meanwhile, the deformation of shape memory alloys at the martensitic state
∗
Corresponding author. Fax: +81 298 59 2101. E-mail address: [email protected] (F. Yin).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.04.135
has been reported to cause the reconfiguration of the martensite variants [12]. However, few reports have examined the deformed martensite structure of Mn–Cu alloys or the twin-boundary internal friction under a preferentially orientated state. In the present work, tensile deformation was applied to a Mn–15 at.% Cu alloy, which shows a martensitic transformation at 353 K and is in a martensitic state at room temperature [2–4]. It is characterized that the evolution of the twinning microstructure as well as the twin-boundary internal friction behavior exhibits an unique twostage behavior with the increased prestrains. 2. Experimental A Mn–15 at.% Cu alloy was induction melted in an argon atmosphere from manganese (99.99%) and copper (99.999%). The ingots were forged at 1173 K and cold-rolled to thin strips of 1 mm thick. Specimens, which had dimension of 1 mm × 10 mm × 60 mm, were cut out and held in a solid solution at 1123 K for 3.6 × 103 s in an argon-filled vacuum furnace and were subsequently quenched into ice water. Tensile deformations were applied to the specimens at a strain rate of 0.01 s−1 to induce different prestrains. A retransformation treatment (RTT) was performed as follows: first the as-tensioned specimens were heated to 473 K for 600 s to induce a phase transformation, and then cooled to room temperature. For con-
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Fig. 1. Internal friction of the specimens with different prestrains: (a) as-tensioned; (b) after RTT.
venience, 1st refers to the as-tensioned specimens and 2nd refers to specimens that have undergone a RTT. The orientation image observation was carried out by a SEM/EBSD technique using a LEO 1550 scanning electron microscope (SEM) equipped with an electron back-scattered diffraction (EBSD) system. For the EBSD measurements, the specimens were electrochemically polished with a solution of H3 PO4 saturated with Cr2 O3 . The electron beam was scanned with a step size of 0.4 m in a selected area of 250 m × 250 m. A dynamic mechanical analyzer of model 2980 (TA Instrument Co. Ltd.) was used to measure the internal friction under the dual-cantilever mode. The specimens were cooled from room temperature to 170 K at a cooling rate of 0.083 K s−1 and a strain amplitude of 1 × 10−4 . The applied vibrating frequencies varied from 0.1 Hz to 10 Hz. The internal friction (Q−1 ) was measured as a function of temperature. A RIGAKU RINT-2200 X-ray diffractometer was used at 40 kV and 40 mA with Cu K␣ radiation. It was found that the c/a ratio of the Mn–15 at.% Cu alloy remained near 0.97 before and after RTT. 3. Results and discussion 3.1. Twin-boundary internal friction The internal friction profile of the prestrained specimens cooled from 300 K to 180 K shows the relaxation process of the twin boundaries, as illustrated in Fig. 1(a). The internal friction value for the undeformed specimen is very high near room temperature and drops significantly after deformation. Meanwhile, the peak magnitude of the twin-boundary internal friction (Q−1 ) significantly decreases as the prestrain increases. After the RTT, the internal friction values recover to certain degree compared to those of the as-tensioned specimens, as shown in Fig. 1(b). It is noted that the temperature change of the internal friction peaks before and after the RTT is negligible. Q−1 represented in Fig. 2 shows a two-stage behavior. Within the prestrain region of 2%, Q−1 drastically decreases to a low level (stage I) and then remains nearly constant (stage II) for the as-tensioned specimens. After the RTT, Q−1 at stage I completely recovers, but Q−1 at stage II does not; that is, Q−1 decreases as the prestrain increases. After all, the internal friction dependence on deformation and thermal history is similar to that observed in the cold-rolled specimens [13].
Fig. 2. Comparison of internal friction at the peak temperature before and after RTT.
Fig. 3 shows the activation energy of the twin-boundary internal friction, determined using the peak shift method with the frequencies of 10 Hz, 1 Hz, and 0.1 Hz. An activation energy of Hact = 6.1 × 104 J mol−1 is obtained for the undeformed specimen, which is consistent with that reported in [14]. As the prestrain increases, Hact decreases, but Hact is nearly constant regardless of the prestrain increase after the RTT.
Fig. 3. Variation of activation energy with prestrain for the twin-boundary internal friction behavior obtained with the peak shift method.
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Fig. 4. Microstructure evolution of the as-tensioned specimens, before RTT: (a) undeformed; (b) 4%; and (c) 20%; and after RTT: (d) 4%; and (e) 20%. Arrows show the trace of misorientation and coarse arrow with TD indicates the tensile direction.
3.2. Microstructure changes caused by prestrain Fig. 4(a)–(c) show the image quality maps of the as-tensioned specimens with various prestrains. Because the transformation shear strain is very small [6] in the specimen without prestrain (Fig. 2(a)), the self-accommodation of the twin bands within grains is a characteristic of the Mn–Cu alloy. The bands are usually 1–5 m wide, and both the twin boundaries and grain
boundaries are basically smooth or straight. In the specimen with a 4% prestrain (Fig. 4(b)), the band boundaries get fairly snicked and, to some extent, loose the original straightness. The bands seem to align with the deformation direction, indicating a diminution of some twin variants with the unfavorable orientations. In the specimen with a 20% prestrain (Fig. 4(c)), the microstructure drastically changes, and a slip deformation between grains obviously occurs. The bands aligned with the
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Fig. 5. Misorientation histogram of selected traces in Fig. 4(a), dark lines indicate the point-to-point misorientation, while the gray lines indicate the point-to-origin misorientation.
deformation direction form kinks and look like flowing streamlines. Since kink deformation is associated with dislocation multiplication and the dislocation density increases as the prestrain increases, it is concluded that the dislocation density is substantially multiplied in the 20% specimen. After the RTT, the martensite variants are rearranged according to the residual elastic stress field of the dislocations. Accordingly, we find that the snick character shown in the specimens with a prestrain less than 4% disappears, but the streamline character in more extensively prestrained specimens remains, as shown in Fig. 4(d)–(e), respectively. Fig. 4(d) shows a full recovery of the twin bands in the 4% specimen, except the band boundaries become blurred. In the 20% specimen (Fig. 2(e)), the characteristics of the microstructure are the same as those in the as-tensioned specimen, but the recovery of the twin bands can still be discerned.
for Hedley’s prediction on twin movement under applied stress [2]. Another feature for the as-tensioned specimens is that the fraction of low angle misorientation (<5◦ ) apparently increases in stage II, which must correlate to the large deformation of the microstructure at this stage. After the RTT, the location of the curve for the quantity of the 90◦ twin boundary is lower, but the location of the curve for the number fraction of the low angle misorientation is much higher compared to that of the as-tensioned specimens. Thus, the increase in the 90◦ twin boundaries in stage I recovers to its undeformed level after the RTT. However, the number fraction cannot recover in stage II. Two reasons can be raised to explain the larger quantity of low angle misorientation. Because the end temperature of the RTT is higher, less of the twin boundary is produced to accommodate the transformation strain. The other
3.3. Prestrain induced reorientation of twin variants Fig. 5 shows the misorientation histogram of selected traces in Fig. 4(a). It is found that the misorientations within the twin bands along different traces (T1-4) are generally either about 90◦ or less than 2◦ , and the profiles of the point-to-origin misorientation indicate that the misorientations between the bands are approximately 1.5◦ . Fig. 6 represents the change in the fraction of the 90◦ twin boundary along with the change in the fraction of the boundaries with a misorientation less than 5◦ . According to the variation characteristics for the as-tensioned specimens (1st curve), two stages can be identified, which is consistent with the results determined from the internal friction characteristics. In stage I, the twin boundaries per unit volume in the prestrain region, which is less than 2%, increase. However, in stage II, the prestrain region greater than 2% decreases as the prestrain increases. The results provide direct evidence
Fig. 6. Fraction of the low-angle misorientation boundaries and 90◦ twin boundaries in the different specimens before and after RTT. Dotted lines and solid lines indicate the results before and after RTT, respectively. Filled symbol and open symbol indicate the misorientation of 90◦ and <5◦ , respectively.
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Fig. 7. Microtexture evolution: (a) inverse pole figures correspond to the position at the stress–strain curve; and (b) orientation preference variation with prestrain shown by the number fraction of 1 1 1//TD orientation within 10◦ tolerance.
reason is the residual stress field, which can accommodate the martensite variants formed. Thus, fewer twins are needed to release the transformation strain during the cooling process. The different slopes in the stress–strain curve provide additional evidence of two stages and indicate that the deformation is macroscopically uniform due to the absence of L¨uders-type deformation behavior (Fig. 7(a)). The inverse pole figures, which correspond to different prestrains, show an obvious process for microtexture evolution. As the prestrain increases, the 1 1 1 and 1 0 0 fibers along the tensile direction steadily develop, similar to the common phenomenon where the 1 1 1 and 1 0 0 fibers exist in the fcc metals deformed in tension [15]. The intensity of 1 1 1 within 10◦ tolerance is integrated into the prestrain plot of Fig. 7(b). The 1 1 1 fiber develops during stage I within a 2% prestrain and remains stable. However, after the RTT, the reorientation completely disappears in stage I, and partially recovers in stage II. These changes are consistent with the recovery phenomenon of the 90◦ -twin fractions. Since the twinning mode of the fct lattice is mechanical twinning [16,17], new twins with an orientation favorable to the stress would nucleate while the existing twins, that do not have the favorable orientations to the stress, may de-twin. When the twin density becomes so high that the distance between adjacent boundaries approaches a certain dimension, the density becomes saturated. Upon further deformation, the number of twin boundaries is drastically reduced as the twins coalesce (de-twinning). That is, although de-twinning might occur in both stages of pre-straining, twinning prevails in stage I and de-twinning or twin coalescence prevails in stage II. In this process, dislocation multiplication may play an important role. Although the exact developing mechanism of the fibers is unclear, the results of the RTT specimens support that the 1 1 1 and 100 fibers are formed through such a twinning-de-twinning process. 3.4. Effects of twinning microstructure on internal friction According to the double shear theory [7], the successive shears of (1 1 0) [1 1 0] leads to neighboring fct lattices, which have c-axes that are about 90◦ apart, resulting in a (1 0 1) twin boundary between neighboring lattices [2,18,19]. This is the reason why numerous fractions of the boundaries are occupied by 90◦ misorientation. On the other hand, according to 3ε = 90◦ − 2 tan−1 (c·a−1 ), where c and a are lattice parameters,
the misorientation angles between the two martensite variants may also be 2ε = 1.2◦ [16,17]. The twinning mechanism in the Mn–Cu alloy can be characterized by the appearance of four {1 0 1} twin boundaries [20]. For one set of twins, the orientation relationship can be expressed by transformation matrix (T) shown in Eq. (1). T =
1 + q2 + r 2 ⎡ 2 p − q2 − r 2 ⎢ ×⎣ 2qp p2
2rp
2pq
2pr
q 2 − p2 − r 2
2qr
2rq
r 2 − p2 − q 2
⎤ ⎥ ⎦ , (1)
where p, q, and r are the plane indices of the twin boundary. Obviously, the misorientations between the twin variants are either low angle or 90◦ apart from each other, and the secondary twinning of an existing twin is regarded as a de-twinning process of the 90◦ twin. Secondary twinning can produce the repeated symmetry of the martensite matrix, which decreases the fraction of 90◦ twin boundaries and increases the <5◦ misorientation boundaries in specimens with large prestrains. Therefore, the rotation of the c-axis under the applied prestrain [11] is a secondary twinning for Mn–Cu alloys. On the other hand, motion of the surface dislocations on the twin boundaries can cause the de-twinning processes [10]. The low angle (<5◦ ) or 90◦ misorientation boundaries are differentiated into two kinds of twin bands, as shown in Fig. 4(a). Accordingly, these two kinds of bands are described as a massive band with a nearly unified orientation and as a twinning band of microtwins. During deformation, twinning in the massive band prevails in stage I, but de-twinning of the twinning band prevails in stage II. During this process the 1 1 1 and 1 0 0 fibers are developed by exhausting the unfavorable twin variants, which accompanies the dislocation multiplication. After the RTT, reorientation due to twinning in stage I is fully recovered. However, the microtexture develops due to de-twinning in stage II and is only partially recovered because dislocations with a high density are introduced. The residual stress dependence of the plastic prestrain (εp ) is determined from the following experimental equation σ r = Bεp [21], where B is a constant. Twinning and de-twinning, as well as dislocation multiplication can introduce an internal stress field during the deformation processes. From the fact that the internal
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friction significantly decreases in the deformed specimens, it is deduced that introducing a residual stress field effectively pins the interface dislocations in the twin boundaries, which suppresses the movement of twin boundaries. After the RTT, the residual stress field introduced by twinning in stage I may be completely eliminated, so that the internal friction completely recovers. However, many dislocations remain after the RTT because the treatment temperature is much lower than the dislocation recovery temperature. Consequently, the change in the residual stress is negligible. Thus, stage II only partially recovers. Obviously, the twin-boundary internal friction behavior of both the deformed and treated specimens is consistent with the analyses of the microstructure changes. If the relaxation process of the twin boundaries is considered as a motion of the surface dislocation [10], then the internal friction peak profile has the form:
1 1 −1 −1 −1 Hact Q = Qmax cos h , (2) − k T TP where Tp is the peak temperature for relaxation-type internal friction profile. The activation energy can be expressed as Hact = H0 − Aσ * , in which H0 is the enthalpy change, and σ * is the work done by the stress to promote the jump over the barrier [22]. The effective stress σ * = σ − σ i is the difference between the applied oscillating stress (σ) and the mean field of the internal stress (σ i ) for a given microstructure. During internal friction measurements, an oscillating stress is applied and the mechanical wave is propagated along the tensile direction of the specimens. The residual stress may contribute to the effective stress to do the additional work, which decreases Hact . After the RTT, the residual stress should relax due to the rearrangement of the twin variants. Thus, the change in Hact is negligible. 4. Conclusion The twin-boundary internal friction of Mn-15 at.% Cu alloy shows a two-stage behavior for the as-tensioned specimens. In stage I when the prestrain region is less than 2%, Q−1 drastically decreases to a low level and then remains nearly constant in stage II as the prestrain increases. After the RTT, Q−1 is almost completely recovered in stage I, but the recovery in stage II decreases as the prestrain increases. It is deduced that a thermal treatment relaxes the residual stress and that the thermal treatment is responsible for both the recovery of the internal friction and the activation energy.
At the prestrains less than 2%, the fraction of 90◦ twin boundaries increases with the increased prestrains, while at the larger prestrain range, the fraction decreases with the increased prestrain. During this process, the 1 1 1 and 1 0 0 fibers steadily form along the tensile direction as the prestrain increases. After the RTT, the increased twin-boundaries fraction fully recovers and the twin-variant reorientation disappears in stage I, but both the fraction and reorientation do not recover in stage II due to the introduction of a residual internal stress field. The low angle (<5◦ ) or 90◦ misorientation boundaries differentiate the two kinds of twin bands. The massive band has a nearly unified orientation, while the other band is composed of microtwins. During deformation, twinning in the massive band prevails in stage I, but de-twinning of the twinning band prevails in stage II, which is accompanied by the generation of dislocations with a high density. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
D. Birchon, D.E. Bromley, D. Healey, Met. Sci. J. 2 (1968) 41–46. J.A. Hedley, Met. Sci. J. 2 (1968) 129–137. J.M. Vitek, H. Warlimont, Met. Sci. J. 10 (1976) 7–13. O. Nittono, T. Satoh, Y. Koyama, Trans. JIM 22 (1981) 225–236. F. Yin, K. Nagai, K. Watanabe, K. Kawahara, Mater. Trans. 44 (2003) 1671–1674. B.A. Bilby, J.W. Christian, The Mechanism of Phase Transformations in Metals, Institute of Metals, London, 1956, pp. 121–172. J.S. Bowles, C.S. Barrett, L. Guttmann, Trans. AIME 188 (1950) 1478–1484. Z.S. Basinski, J.W. Christian, Acta Met. 1 (1953) 759–761. K. Sugimoto, T. Mori, S. Shiode, Met. Sci. J. 7 (1973) 103–108. K. Sumino, Acta Mater. 14 (1966) 1607–1615. G.E. Bacon, I.W. Dunmur, J.H. Smith, R. Street, Proc. Roy. Soc. Lond. A241 (1957) 223–238. Y. Liu, Z.L. Xie, J.V. Humbeeck, L. Delaey, Mater. Sci. Eng. A273–A275 (1999) 679–684. E.P. Butler, P.M. Kelly, Trans. AIME 242 (1968) 2099–2109. T. Aoyagi, K. Sumino, Physica Status Solidi 33 (1969) 317. U.F. Kocks, C.N. Tome, H.R. Wenk, Texture and Anisotropy, Cambridge University Press, 1998, pp. 192. Z.S. Basinski, J.W. Christian, J. Inst. Met. 80 (1951-52) 659–666. Z.S. Basinski, J.W. Christian, Acta Met. 2 (1954) 149–165. F. Yin, Y. Ohsawa, A. Sato, K. Kawahara, Z. Metallkd. 89 (1998) 481– 486. K. Adachi, T. Yamashita, Y. Taneda, D.M. Farkas, J. Perkins, Philosophical Mag. A73 (1996) 1009–1034. X.Y. Huang, Transmission Electron Micrology, Shanghai Sci. Tech. Press, Shanghai, 1987, pp. 164. D. Feng, Metal physics, Science Press, Beijing, 1999, pp. 364. R. Schaller, G. Fantozzi, G. Gremaud, Mechanical Spectroscopy Q−1 2001, Trans Tech Publications, Switzerland, 2001, pp. 49.
Internal friction behavior of twin boundaries in tensile-deformed Mn–15 at.% Cu alloy Qingchao Tian a,b , Fuxing Yin a,∗ , Takuya Sakaguchi c , Kotobu Nagai a a
Steel Research Center, National Research Institute for Materials Science, Tsukuba 305-0047, Japan b Technology Center, Baoshan Iron and Steel Co. Ltd., Shanghai 201900, PR China c Materials Engineering Div. III, Toyota Motors Co., Shizuoka 410-1193, Japan Received 29 July 2005; received in revised form 10 April 2006; accepted 12 April 2006
Abstract An orientation image microscope was used to characterize the orientation features in a deformed Mn–15 at.% Cu alloy. It was found that twinning and subsequent de-twinning prevailed during the deformation process of the twin bands, which were separately identified as massive and twinning type bands. The 111 and 100 fibers steadily developed along the tensile direction as the prestrain increased. The internal friction due to the movement of the twin boundary was investigated using a dynamic mechanical analyzer. It was deduced that the twin-boundary internal friction greatly depended on the arrangement of the twin variants, which can be changed by deformation or a thermal treatment. © 2006 Elsevier B.V. All rights reserved. Keywords: Manganese–copper alloy; Internal friction; Twin boundary; Twinning–de-twining
1. Introduction Mn–Cu alloys are well-known materials with a high internal friction capacity, which has been attributed to the movement of the {0 1 1} twin boundaries [1–4]. These alloys show a martensitic transformation from a face-centered cubic (fcc) structure to a tetragonal (fct) structure at a temperature that depends on the alloy composition [5]. The thermal martensitic microstructure with a fct lattice has been extensively investigated [6]. According to the double shear theory [7], Basinski and Christian concluded that each cubic crystal in the parent orientation might produce 36 fct variants, of which 24 are twin variants [8]. Thus, the fct martensite microstructure has the characteristics of {0 1 1} twins. The thermally activated relaxation of those twin boundaries causes an internal friction peak profile around 220 K, which is called the twin-boundary internal friction peak [9]. The mechanism of the relaxation process is regarded as an elementary process that involves twin boundary motion [10]. Bacon et al. found that applied stress caused the c axis of the fct phase to rotate in a favorable direction [11]. Meanwhile, the deformation of shape memory alloys at the martensitic state
∗
Corresponding author. Fax: +81 298 59 2101. E-mail address: [email protected] (F. Yin).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.04.135
has been reported to cause the reconfiguration of the martensite variants [12]. However, few reports have examined the deformed martensite structure of Mn–Cu alloys or the twin-boundary internal friction under a preferentially orientated state. In the present work, tensile deformation was applied to a Mn–15 at.% Cu alloy, which shows a martensitic transformation at 353 K and is in a martensitic state at room temperature [2–4]. It is characterized that the evolution of the twinning microstructure as well as the twin-boundary internal friction behavior exhibits an unique twostage behavior with the increased prestrains. 2. Experimental A Mn–15 at.% Cu alloy was induction melted in an argon atmosphere from manganese (99.99%) and copper (99.999%). The ingots were forged at 1173 K and cold-rolled to thin strips of 1 mm thick. Specimens, which had dimension of 1 mm × 10 mm × 60 mm, were cut out and held in a solid solution at 1123 K for 3.6 × 103 s in an argon-filled vacuum furnace and were subsequently quenched into ice water. Tensile deformations were applied to the specimens at a strain rate of 0.01 s−1 to induce different prestrains. A retransformation treatment (RTT) was performed as follows: first the as-tensioned specimens were heated to 473 K for 600 s to induce a phase transformation, and then cooled to room temperature. For con-
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Fig. 1. Internal friction of the specimens with different prestrains: (a) as-tensioned; (b) after RTT.
venience, 1st refers to the as-tensioned specimens and 2nd refers to specimens that have undergone a RTT. The orientation image observation was carried out by a SEM/EBSD technique using a LEO 1550 scanning electron microscope (SEM) equipped with an electron back-scattered diffraction (EBSD) system. For the EBSD measurements, the specimens were electrochemically polished with a solution of H3 PO4 saturated with Cr2 O3 . The electron beam was scanned with a step size of 0.4 m in a selected area of 250 m × 250 m. A dynamic mechanical analyzer of model 2980 (TA Instrument Co. Ltd.) was used to measure the internal friction under the dual-cantilever mode. The specimens were cooled from room temperature to 170 K at a cooling rate of 0.083 K s−1 and a strain amplitude of 1 × 10−4 . The applied vibrating frequencies varied from 0.1 Hz to 10 Hz. The internal friction (Q−1 ) was measured as a function of temperature. A RIGAKU RINT-2200 X-ray diffractometer was used at 40 kV and 40 mA with Cu K␣ radiation. It was found that the c/a ratio of the Mn–15 at.% Cu alloy remained near 0.97 before and after RTT. 3. Results and discussion 3.1. Twin-boundary internal friction The internal friction profile of the prestrained specimens cooled from 300 K to 180 K shows the relaxation process of the twin boundaries, as illustrated in Fig. 1(a). The internal friction value for the undeformed specimen is very high near room temperature and drops significantly after deformation. Meanwhile, the peak magnitude of the twin-boundary internal friction (Q−1 ) significantly decreases as the prestrain increases. After the RTT, the internal friction values recover to certain degree compared to those of the as-tensioned specimens, as shown in Fig. 1(b). It is noted that the temperature change of the internal friction peaks before and after the RTT is negligible. Q−1 represented in Fig. 2 shows a two-stage behavior. Within the prestrain region of 2%, Q−1 drastically decreases to a low level (stage I) and then remains nearly constant (stage II) for the as-tensioned specimens. After the RTT, Q−1 at stage I completely recovers, but Q−1 at stage II does not; that is, Q−1 decreases as the prestrain increases. After all, the internal friction dependence on deformation and thermal history is similar to that observed in the cold-rolled specimens [13].
Fig. 2. Comparison of internal friction at the peak temperature before and after RTT.
Fig. 3 shows the activation energy of the twin-boundary internal friction, determined using the peak shift method with the frequencies of 10 Hz, 1 Hz, and 0.1 Hz. An activation energy of Hact = 6.1 × 104 J mol−1 is obtained for the undeformed specimen, which is consistent with that reported in [14]. As the prestrain increases, Hact decreases, but Hact is nearly constant regardless of the prestrain increase after the RTT.
Fig. 3. Variation of activation energy with prestrain for the twin-boundary internal friction behavior obtained with the peak shift method.
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Fig. 4. Microstructure evolution of the as-tensioned specimens, before RTT: (a) undeformed; (b) 4%; and (c) 20%; and after RTT: (d) 4%; and (e) 20%. Arrows show the trace of misorientation and coarse arrow with TD indicates the tensile direction.
3.2. Microstructure changes caused by prestrain Fig. 4(a)–(c) show the image quality maps of the as-tensioned specimens with various prestrains. Because the transformation shear strain is very small [6] in the specimen without prestrain (Fig. 2(a)), the self-accommodation of the twin bands within grains is a characteristic of the Mn–Cu alloy. The bands are usually 1–5 m wide, and both the twin boundaries and grain
boundaries are basically smooth or straight. In the specimen with a 4% prestrain (Fig. 4(b)), the band boundaries get fairly snicked and, to some extent, loose the original straightness. The bands seem to align with the deformation direction, indicating a diminution of some twin variants with the unfavorable orientations. In the specimen with a 20% prestrain (Fig. 4(c)), the microstructure drastically changes, and a slip deformation between grains obviously occurs. The bands aligned with the
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Fig. 5. Misorientation histogram of selected traces in Fig. 4(a), dark lines indicate the point-to-point misorientation, while the gray lines indicate the point-to-origin misorientation.
deformation direction form kinks and look like flowing streamlines. Since kink deformation is associated with dislocation multiplication and the dislocation density increases as the prestrain increases, it is concluded that the dislocation density is substantially multiplied in the 20% specimen. After the RTT, the martensite variants are rearranged according to the residual elastic stress field of the dislocations. Accordingly, we find that the snick character shown in the specimens with a prestrain less than 4% disappears, but the streamline character in more extensively prestrained specimens remains, as shown in Fig. 4(d)–(e), respectively. Fig. 4(d) shows a full recovery of the twin bands in the 4% specimen, except the band boundaries become blurred. In the 20% specimen (Fig. 2(e)), the characteristics of the microstructure are the same as those in the as-tensioned specimen, but the recovery of the twin bands can still be discerned.
for Hedley’s prediction on twin movement under applied stress [2]. Another feature for the as-tensioned specimens is that the fraction of low angle misorientation (<5◦ ) apparently increases in stage II, which must correlate to the large deformation of the microstructure at this stage. After the RTT, the location of the curve for the quantity of the 90◦ twin boundary is lower, but the location of the curve for the number fraction of the low angle misorientation is much higher compared to that of the as-tensioned specimens. Thus, the increase in the 90◦ twin boundaries in stage I recovers to its undeformed level after the RTT. However, the number fraction cannot recover in stage II. Two reasons can be raised to explain the larger quantity of low angle misorientation. Because the end temperature of the RTT is higher, less of the twin boundary is produced to accommodate the transformation strain. The other
3.3. Prestrain induced reorientation of twin variants Fig. 5 shows the misorientation histogram of selected traces in Fig. 4(a). It is found that the misorientations within the twin bands along different traces (T1-4) are generally either about 90◦ or less than 2◦ , and the profiles of the point-to-origin misorientation indicate that the misorientations between the bands are approximately 1.5◦ . Fig. 6 represents the change in the fraction of the 90◦ twin boundary along with the change in the fraction of the boundaries with a misorientation less than 5◦ . According to the variation characteristics for the as-tensioned specimens (1st curve), two stages can be identified, which is consistent with the results determined from the internal friction characteristics. In stage I, the twin boundaries per unit volume in the prestrain region, which is less than 2%, increase. However, in stage II, the prestrain region greater than 2% decreases as the prestrain increases. The results provide direct evidence
Fig. 6. Fraction of the low-angle misorientation boundaries and 90◦ twin boundaries in the different specimens before and after RTT. Dotted lines and solid lines indicate the results before and after RTT, respectively. Filled symbol and open symbol indicate the misorientation of 90◦ and <5◦ , respectively.
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Fig. 7. Microtexture evolution: (a) inverse pole figures correspond to the position at the stress–strain curve; and (b) orientation preference variation with prestrain shown by the number fraction of 1 1 1//TD orientation within 10◦ tolerance.
reason is the residual stress field, which can accommodate the martensite variants formed. Thus, fewer twins are needed to release the transformation strain during the cooling process. The different slopes in the stress–strain curve provide additional evidence of two stages and indicate that the deformation is macroscopically uniform due to the absence of L¨uders-type deformation behavior (Fig. 7(a)). The inverse pole figures, which correspond to different prestrains, show an obvious process for microtexture evolution. As the prestrain increases, the 1 1 1 and 1 0 0 fibers along the tensile direction steadily develop, similar to the common phenomenon where the 1 1 1 and 1 0 0 fibers exist in the fcc metals deformed in tension [15]. The intensity of 1 1 1 within 10◦ tolerance is integrated into the prestrain plot of Fig. 7(b). The 1 1 1 fiber develops during stage I within a 2% prestrain and remains stable. However, after the RTT, the reorientation completely disappears in stage I, and partially recovers in stage II. These changes are consistent with the recovery phenomenon of the 90◦ -twin fractions. Since the twinning mode of the fct lattice is mechanical twinning [16,17], new twins with an orientation favorable to the stress would nucleate while the existing twins, that do not have the favorable orientations to the stress, may de-twin. When the twin density becomes so high that the distance between adjacent boundaries approaches a certain dimension, the density becomes saturated. Upon further deformation, the number of twin boundaries is drastically reduced as the twins coalesce (de-twinning). That is, although de-twinning might occur in both stages of pre-straining, twinning prevails in stage I and de-twinning or twin coalescence prevails in stage II. In this process, dislocation multiplication may play an important role. Although the exact developing mechanism of the fibers is unclear, the results of the RTT specimens support that the 1 1 1 and 100 fibers are formed through such a twinning-de-twinning process. 3.4. Effects of twinning microstructure on internal friction According to the double shear theory [7], the successive shears of (1 1 0) [1 1 0] leads to neighboring fct lattices, which have c-axes that are about 90◦ apart, resulting in a (1 0 1) twin boundary between neighboring lattices [2,18,19]. This is the reason why numerous fractions of the boundaries are occupied by 90◦ misorientation. On the other hand, according to 3ε = 90◦ − 2 tan−1 (c·a−1 ), where c and a are lattice parameters,
the misorientation angles between the two martensite variants may also be 2ε = 1.2◦ [16,17]. The twinning mechanism in the Mn–Cu alloy can be characterized by the appearance of four {1 0 1} twin boundaries [20]. For one set of twins, the orientation relationship can be expressed by transformation matrix (T) shown in Eq. (1). T =
1 + q2 + r 2 ⎡ 2 p − q2 − r 2 ⎢ ×⎣ 2qp p2
2rp
2pq
2pr
q 2 − p2 − r 2
2qr
2rq
r 2 − p2 − q 2
⎤ ⎥ ⎦ , (1)
where p, q, and r are the plane indices of the twin boundary. Obviously, the misorientations between the twin variants are either low angle or 90◦ apart from each other, and the secondary twinning of an existing twin is regarded as a de-twinning process of the 90◦ twin. Secondary twinning can produce the repeated symmetry of the martensite matrix, which decreases the fraction of 90◦ twin boundaries and increases the <5◦ misorientation boundaries in specimens with large prestrains. Therefore, the rotation of the c-axis under the applied prestrain [11] is a secondary twinning for Mn–Cu alloys. On the other hand, motion of the surface dislocations on the twin boundaries can cause the de-twinning processes [10]. The low angle (<5◦ ) or 90◦ misorientation boundaries are differentiated into two kinds of twin bands, as shown in Fig. 4(a). Accordingly, these two kinds of bands are described as a massive band with a nearly unified orientation and as a twinning band of microtwins. During deformation, twinning in the massive band prevails in stage I, but de-twinning of the twinning band prevails in stage II. During this process the 1 1 1 and 1 0 0 fibers are developed by exhausting the unfavorable twin variants, which accompanies the dislocation multiplication. After the RTT, reorientation due to twinning in stage I is fully recovered. However, the microtexture develops due to de-twinning in stage II and is only partially recovered because dislocations with a high density are introduced. The residual stress dependence of the plastic prestrain (εp ) is determined from the following experimental equation σ r = Bεp [21], where B is a constant. Twinning and de-twinning, as well as dislocation multiplication can introduce an internal stress field during the deformation processes. From the fact that the internal
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friction significantly decreases in the deformed specimens, it is deduced that introducing a residual stress field effectively pins the interface dislocations in the twin boundaries, which suppresses the movement of twin boundaries. After the RTT, the residual stress field introduced by twinning in stage I may be completely eliminated, so that the internal friction completely recovers. However, many dislocations remain after the RTT because the treatment temperature is much lower than the dislocation recovery temperature. Consequently, the change in the residual stress is negligible. Thus, stage II only partially recovers. Obviously, the twin-boundary internal friction behavior of both the deformed and treated specimens is consistent with the analyses of the microstructure changes. If the relaxation process of the twin boundaries is considered as a motion of the surface dislocation [10], then the internal friction peak profile has the form:
1 1 −1 −1 −1 Hact Q = Qmax cos h , (2) − k T TP where Tp is the peak temperature for relaxation-type internal friction profile. The activation energy can be expressed as Hact = H0 − Aσ * , in which H0 is the enthalpy change, and σ * is the work done by the stress to promote the jump over the barrier [22]. The effective stress σ * = σ − σ i is the difference between the applied oscillating stress (σ) and the mean field of the internal stress (σ i ) for a given microstructure. During internal friction measurements, an oscillating stress is applied and the mechanical wave is propagated along the tensile direction of the specimens. The residual stress may contribute to the effective stress to do the additional work, which decreases Hact . After the RTT, the residual stress should relax due to the rearrangement of the twin variants. Thus, the change in Hact is negligible. 4. Conclusion The twin-boundary internal friction of Mn-15 at.% Cu alloy shows a two-stage behavior for the as-tensioned specimens. In stage I when the prestrain region is less than 2%, Q−1 drastically decreases to a low level and then remains nearly constant in stage II as the prestrain increases. After the RTT, Q−1 is almost completely recovered in stage I, but the recovery in stage II decreases as the prestrain increases. It is deduced that a thermal treatment relaxes the residual stress and that the thermal treatment is responsible for both the recovery of the internal friction and the activation energy.
At the prestrains less than 2%, the fraction of 90◦ twin boundaries increases with the increased prestrains, while at the larger prestrain range, the fraction decreases with the increased prestrain. During this process, the 1 1 1 and 1 0 0 fibers steadily form along the tensile direction as the prestrain increases. After the RTT, the increased twin-boundaries fraction fully recovers and the twin-variant reorientation disappears in stage I, but both the fraction and reorientation do not recover in stage II due to the introduction of a residual internal stress field. The low angle (<5◦ ) or 90◦ misorientation boundaries differentiate the two kinds of twin bands. The massive band has a nearly unified orientation, while the other band is composed of microtwins. During deformation, twinning in the massive band prevails in stage I, but de-twinning of the twinning band prevails in stage II, which is accompanied by the generation of dislocations with a high density. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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