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Thermally-activated anelastic relaxation in a high-manganese Cu-Mn alloy studied by isothermal low-frequency internal friction
Materials Science & Engineering A 685 (2017) 139–144
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Thermally-activated anelastic relaxation in a high-manganese Cu-Mn alloy studied by isothermal low-frequency internal friction
MARK
⁎
S.A.E. Boyera,b, , M. Gerlanda, A. Rivièrea a PPRIME Institute, ISAE, ENSMA, UPR CNRS 3346, Department of Physics and Mechanics of Materials, 1 Av. Clément Ader, 86961 Futuroscope Chasseneuil Cedex, France1 b MINES ParisTech, PSL - Research University, Centre for Material Forming, UMR CNRS 7635, 1 Rue Claude Daunesse, 06904 Sophia Antipolis, France
A R T I C L E I N F O
A BS T RAC T
Keywords: Manganese-rich copper-manganese alloy Isothermal internal friction Point defects Dislocations
Low-frequency internal friction study has been conducted for a copper-manganese-rich alloy (Cu-60 at%, γ Mn). The study used a forced torsion pendulum working in low-frequency scans at constant temperatures, damping experiments ranging between 40 Hz and 10−4 Hz. The dependence on temperature was extended from room temperature to the spinodal curve frontier at 923 K. Phenomenological stages in anelastic relaxations of (Cu, γ Mn) were evidenced. Three thermally activated relaxation peaks were assigned respectively to point defects (Zener relaxation), dislocation segments and dislocation walls.
1. Introduction Interaction between copper and manganese has received an intense attention. Copper-manganese (Cu-Mn) alloys are regarded because of their multipurpose, as versatile magnetic feature, superior damping capacity, shape memory [1–8]. The magnetic properties study has had a very long history, as early as 1957 [9]. The multipurpose is connected to the microstructure, for instance antiferromagnetic ordering of the quenched face-centred tetragonal (fct) phase. Another attractive feature of Cu-Mn alloys is the existence of a mutual metastable miscibility interval of their γ-phase (Cu, γ Mn) [5,10,11], with the development of a two-phase microstructure in a spinodal decomposition mode [12]. The metastable transformation has been discussed in the literature [4,13,14]. However the mechanical behavior in the vicinity of the metastable separation has received not much attention and the literature concerning this point is almost indeed nonexistent. Most careful study that one can cite is the one of V′vunenko and Likhachev in 1985 [15], Tsuchiya et al. in 1999 [4], Markova et al. from 2004 [6,16]. It was reported by Tsuchiya et al. in 1999 the effect of γ-phase in aged (Cu-Mn) on the face-centred cubic (fcc) - face-centred tetragonal (fct) phase martensitic transformation behavior; the increase in the transformation temperature with the decrease in electrical resistivity was explained by the rule of mixture assuming a heterogeneous microstructure as a result of the spinodal decomposition [4]. Markova et al. in 2004 and later in 2013 have studied internal friction (IF) and elastic modulus for manganese-rich
⁎
1
(Mn-40 at%, Cu) and copper-rich (Mn-45 at%, Cu) alloys up to 573 K [6,16]. They observed a large damping maximum in the temperature gap of martensitic transformation [6], interpreted by a microstructure evolution (tweed structure - “parquet” structure - classical twinning martensite). Because the measurements were made during continuous heating or cooling, this transitory maximum was linked to the change of the microstructure during the damping measurement. The present work proposes to use the benefits of low-frequency forced torsion pendulum [17 Chap. 1.6]. For metals, it is generally preferred because it offers high sensitivity. The mechanical spectroscopy works at fine controlled-fixed temperatures, and at subresonant conditions in a continuous frequency range. The large transitory damping maximum linked to the phase transition cannot be observed but anelastic relaxation phenomena would be accurately evidenced. Isothermal low-frequency internal friction (IF) measurements are performed from room temperature to the vicinity of the spinodal curve of (Cu-60 at%, Mn) in a face-centred cubic (fcc) phase, referred to as γphase. To the best of our knowledge, the anelastic properties of (Cu60 at%, γ Mn) alloy in such isothermal way were not yet reported in the literature. Quantitative experimental data on some newly observed anelastic relaxations are provided.
Corresponding author at: MINES ParisTech, PSL - Resarch University, Centre for Material Forming, UMR CNRS 7635, 1 Rue Claude Daunesse, 06 904 Sophia Antipolis, France E-mail address: [email protected] (S.A.E. Boyer). Past address
http://dx.doi.org/10.1016/j.msea.2016.12.120 Received 13 September 2016; Received in revised form 26 November 2016; Accepted 30 December 2016 Available online 31 December 2016 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 685 (2017) 139–144
S.A.E. Boyer et al.
2.2. Material
2. Experimental procedure: damping evaluation statement and material
2.2.1. Manganese-rich Cu-Mn A Cu-60 at% Mn alloy, provided by Goodfellow (France), was used for investigation. According to the required internal friction set-up, CuMn alloy specimen was cut by spark machining in bar, with dimensions of 64 mm in length and 6×1 mm2 cross section. Specimen was previously heat-treated at 943 K under vacuum and water quenched. Initial structure after quench was face-centred cubic (fcc) phase, referred to as γ-phase (Cu, γ Mn) [25]. Several series of experiments were made for which the sample has been progressively heated step by step at desired temperatures, respectively 573, 673, 723, 773, 873, 903, 923 K (and even 963 K as an ultimate test).
2.1. Technique 2.1.1. Mechanical spectroscopy statement Anelasticty in materials was initially described by Zener [17 Chap. 2.2, 18]. A continue stress applied to a material with an anelastic behavior has two effects; the corresponding elastic strain but also a change of the equilibrium state of one (or more) internal variable(s). The return to the equilibrium state carries away a supplementary strain called the anelastic strain. When the applied stress is removed, the anelastic strain progressively vanishes. This anelastic strain can result from the motion of structural defects such as point defects, dislocations, sliding of polymeric chains, etc. Because this anelastic strain is generally very small, it can be more easily detected when submitting the anelastic material to a cyclic (the most often sinusoidal) stress. Then a phase lag φ appears between the applied stress and the resulting strain. This phase lag characterizes the so-called internal friction Q−1 as Q−1 = tan φ. Apparatus working in a large frequency range of 300−10−4 Hz [19 Chap. 9.1] allows the direct determination of tan φ. Plotting Q−1 versus the frequency, a mechanical loss peak appears described by a Debye equation (Eq.1) [18]:
⎛ ⎞ ϖτ Q−1 = Δ ⎜ ⎟ ⎝ 1 + (ωτ )2 ⎠
3. Results and discussion 3.1. Anelastic relaxations: analysis and annealing Fig. 1 shows the low frequency internal friction (IF) spectra in the first stages of annealing at low temperatures. The experiments described in Fig. 1(a) were performed during step temperature increase from 414 K to 599 K. A low frequency background increase with temperature is often linked to structural defects (dislocations) in solid induced by the rapid cooling. The experimental curve is corrected by subtracting an estimated exponential background. The technique of background subtraction has already been described, as explained on Cu-Al system [26]. The evidence of a relaxation peak, called here the P1 peak, is indicated in Fig. 1(b). Fig. 2(a) illustrates the low frequency internal friction (IF) spectra measured at 573 K after respective temperature annealing of 573, 673, 723, and 773 K. The background decreases when the temperature of annealing increases. It is linked to the dislocation density decreasing with annealing [27]. But, the relaxation peaks obtained after background removing are superimposable: same frequency close to 10−2 Hz and same height. The background decrease of the internal friction at low frequency in Fig. 2(a) is linked to the decrease of the dislocation density; in Fig. 2(b) is plotted the evolution of the square of free frequency with the annealing temperature on the as received sample (a – up triangles) and the sample after quenching (b – down triangles). The square of free frequency is directly proportional to the modulus of torsion. The modulus is influenced by several parameters and in particular by the dislocation density. As shown in Fig. 2(b) the rapid cooling (quenching) increased this dislocation density, then it decreases with annealing. In Fig. 3 is displayed the evolution of the low frequency internal friction peak P1, during cooling, after annealing at 673 K and in-situ measured at 662, 633, 603, 588, 573, and 562 K. Evidently, the IF peak P1 shifts towards low frequencies when temperature decreases. The evolution of the relaxation intensity stands out and presents the following particular aspect to first increases from 662 to 588 K then lowers. After annealing at 723 K, a second relaxation peak (P2) is evidenced with the increase of damping. Fig. 4(a) illustrates the experimental curve at 703 K during the first heating (see a) and after subtraction of an estimated exponential background (see b), resulting in the evidence of two maxima (see c). The maximum at high frequency corresponds to the P1 peak as previously described, and the maximum at about 0.1 Hz is assigned to the new P2 peak. This P2 peak was also observed for measurements at respectively 723 K and 673 K as pointed out in Fig. 4(b). The second peak, not present in the first temperature increase, grows progressively. Both the relaxation peaks, P1 and P2, shift towards lower frequencies for experiments at lower temperatures (Fig. 4(b)) corresponding to an Arrhenius behavior. For the P1 peak, the corresponding limit relaxation time τ0 is 3.6×10–15 s and the apparent activation energy HA is 1.76 eV. For the P2 peak, the
(1)
where τ is the relaxation time, Δ is the relaxation strength, ω=2πf with f the frequency of the mechanical vibrations. If the relaxation is thermally activated, the frequency of the maximum of the relaxation peak is shifted towards higher frequency if the temperature of the measurement is increased. This activation can be described by the Arrhenius equation as (Eq. (2)):
⎛ H⎞ τ −1 = τ0−1 exp ⎜ − ⎟ ⎝ kT ⎠
(2)
τ0−1
the limit of relaxation times. where H is the activation energy and When plotting the Napieran logarithm of the frequencies of the maxima of the relaxation peaks obtained at several temperatures versus the inverse of the measurement temperatures, the experimental points are aligned in a line (Arrhenius plot), allowing the determination of the relaxation parameters H and τ0−1 , and therefore the knowledge of the elementary mechanism leading to the internal friction. 2.1.2. Isothermal internal friction experiments Isothermal mechanical spectroscopy (IMS) experiments were carried out with an inverted forced torsion pendulum. Isothermal mechanical spectroscopy permits to measure materials in a state close to equilibrium and to avoid transient effects which accompany temperature dependent IF measurements. Torsional vibrations were excited by supplying to an oscillating electromagnet a sinusoidal signal from a generator. The equipment made it possible to control temperature in the range from room temperature to 1000 K which was measured accurate to within 1 K. The pendulum and its performance were described in [20–24]. Measurements were conducted under partial pressure of pure argon (0.1 bar) purchased from Air Liquid (France). Before each IF measurements, the alloy was aged in the temperature range from 523 K to the CuMn spinodal curve at around 923 K during 3–16 h and held constant during the measurement time (12–48 h). The vibration frequencies (f) ranged between 40 Hz and 10−4 Hz, and the measurements were made at 10 discrete frequencies per decade. The internal friction was also measured at the resonance frequency of the system (300 Hz) using the free-decay method. The maximum strain amplitude (εmax) applied on the sample was 5×10−6. 140
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Fig. 1. (a) Low frequency internal friction spectra after in-situ annealing at temperatures increasing from 414 K to 599 K. (b) P1 peak evidenced by exponential background subtraction.
corresponding limit relaxation time τ0 is 10–14 s and the apparent activation energy HA is 1.90 eV. When increasing the annealing temperature to 923 K, a third peak P3 appears, as illustrated in Fig. 5(a). By applying the same decay method as before, results give that for the P3 peak, the corresponding pre-exponential factor of limit relaxation time τ0 is 5×10−7 s and the apparent activation enthalpy HA is 1.70 eV (Fig. 5(b)). Note that our investigation stopped at 923 K, indeed higher temperature would most probably encourage a phase change in (Cu-60 at%, γ Mn) [11].
3.2. Discussion As measured by isothermal low-frequency internal friction, three relaxation peaks have been evidenced in the (Cu-60 at%, γ Mn) alloy. The IF response of (Cu-60 at%, γ Mn) is strongly dependent on the thermal treatment [28,29]. P1 peak is observed directly during the first heating at relatively low temperatures (T=562–703 K). P1 peak is stable and does not change after the high temperature annealing. This behavior and the relaxation
Fig. 2. (a) Low frequency internal friction spectra at the same temperature (573 K) after several in-situ annealings at 573, 673, 723, and 773 K. (b) Square of free frequency with the annealing temperature on a – as-received sample, and b – sample after quenching.
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of manganese (Mn) atoms in copper (Cu). It is closed to the value of Mn diffusion in copper alloys systems recently found for other compositions, i.e. 1.9 eV [30]. The tendency evolution of the relaxation intensity (increases then lowers, see part 3.1.-Fig. 3) has been observed in the anelastic Zener relaxation (as referred to in more general terms as ‘stress-induced ordering’) [31,32] of Cu-Al single crystals with solute content in the range from 7–19% Cu, as described in [33]. It has been explained by the short-range ordering as designated in the Le Claire-Lomer theory [34,35]. It is due to stress-induced changes of atomic order with respectively the influence of only neighboring atoms at lower temperature measurements (increasing relaxation) and more distant atoms at higher temperature measurements (decreasing relaxation). At intermediate temperatures and after annealing at 723 K, a second relaxation peak P2 is observed. Its relaxation parameters were deduced from the Arrhenius plot (Fig. 4(b)): limit relaxation time τ0 is 10–14 s and apparent activation energy HA(P2) is 1.9 eV. Relaxation peaks spreading out after annealing were very often observed in pure single or polycrystalline metals (as Ag, Al, Cu, Pd, and Ni; see [22,23,36,37]) or metallic alloys (as Cu-Al [38] or 2024 aluminum alloy [39]). The evolution of such a peak was studied in detailed way in pure Al sample during the recrystallization after cold-working [27]. The observed relaxation peak spreads out progressively after large decreases of the modulus and hardness corresponding to the end of the recovery stage. In parallel with the increase of the peak, an increase in mean grain size excludes a grain boundary relaxation and this peak in pure Al was explained by a relaxation linked to a dislocation mechanism according to the model proposed by Woirgard [40]. The similar evolution leads to associate P2 peak as a dislocation peak. At higher temperatures and at low frequency, after annealing at 923 K, a new P3 peak appears. Its relaxation parameters are a limit relaxation time τ0 of 5×10−7 s and an apparent activation energy HA(P3) of 1.7 eV. Such low frequency and very high temperature peaks have been already observed in pure metals and metallic alloys [23,41,42]. At frequencies close to 1 Hz with a classical apparatus, it cannot be observed because it would be at a temperature above the melting point or the liquidus. Such a peak was accurately studied in an
Fig. 3. Evolution of the low frequency internal friction peak P1 after annealing at 673 K and in-situ measurements at 662, 633, 603, 588, 573, and 562 K.
parameters (particularly the limit relaxation time τ0 of 3.6×10–15 s) allow attributing the P1 peak to a point defects relaxation mechanism. Zener [18] shows that a pair of substitutional atoms in fcc (as Cu, γ Mn) solid solution would reorient under stress and thereby display internal friction and a relaxation peak (Zener peak type). The apparent activation energy (HA(P1) =1.76 eV) would correspond to the diffusion
Fig. 4. (a) Internal friction spectrum at 703 K after in-situ annealing at 723 K. Peak background subtraction to evidence the P2 peak. (b) Napierian logarithm of peak frequencies vs. the inverse temperature for the relaxation peaks P1 and P2 obtained after annealing at 673 K (P1 – up-triangles) and annealing at 723 K (P2 – down-triangles).
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Fig. 5. (a) High temperature internal friction spectra at two temperatures (923 and 773 K) after in-situ annealing at 923 K. (b) Napierian logarithm of peak frequencies vs. the inverse temperature for the anelastic peak P3 obtained for low frequency-high temperature annealing.
References
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4. Conclusions A first attempt in the analysis of anelastic relaxations in a manganese-rich alloy (Cu-60 at%, γ Mn) is proposed by the use of isothermal low-frequency internal friction (IF) from room temperature to the vicinity of the spinodal curve of the alloy. Investigation is done in a large frequency range (40−10−4 Hz), at fixed temperatures (stable microstructural states), by continuously changing frequencies. The isothermal low-frequency IF is benefit. Three phenomenological stages in the anelastic relaxations are evidenced. At relatively low temperature (between 562 K and 662 K), Zener point defects relaxation mechanism is recognized in the anelastic relaxation peak P1. After annealing at 723 K, a new relaxation peak P2, evidenced between 673 K and 723 K, is explained by a reversible motion of dislocation segments. The P3 peak observed at very low frequency between 773 K and 923 K is associated with the motion of the generated dislocation walls. The internal friction peaks are thermally activated relaxation peaks; their activation parameters are calculated by plotting Arrhenius graph. In further work, interest would be to discuss the mechanisms of anelastic relaxations in reference to the phase transformations and/or heterogeneous microstructural evolutions formed as a result of the spinodal decomposition [7,10], which could be monitored by in-situ temperature-controlled transmission electron microscopy (TEM) and/ or in-situ temperature-controlled X-ray diffraction. Acknowledgements CNRS is acknowledged. Experimental works were done on pendulum setup at ISAE-ENSMA, UPR CNRS 3346, PPRIME institute. 143
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isothermal mechanical spectroscopy, J. De. Phys. IV 6 (C8) (1996) 81–84. [34] A.D. LeClaire, W.M. Lomer, Relaxation effects in solid solutions arising from changes in local order II - Theory of the relaxation strength, Acta Metall. 2 (6) (1954) 731–742. [35] C.M. Van Baal, Theory of the Zener relaxation strength -I, Physica 52 (1971) 410–421. [36] A. Rivière, J.P. Amirault, J. Woirgard, High temperature internal friction and dislocation motion in poly and single crystals of F.C.C. metals, J. De. Phys. 42 (C5) (1981) 439–444. [37] A. Rivière, J. Woirgard, Etude du frottement intérieur de haute température du palladium polycristallin ultra pur, J. De. Phys. Colloq. 44 (C9) (1983) 741–745. [38] S. Belhas, A. Rivière, J. Woirgard, J. Vergnol, J. de Fouquet, High temperature relaxation mechanisms in Cu-Al solid solutions, J. De. Phys. Colloq. 46 (C10) (1985) 367–370. [39] A. Rivière, V. Pelosin, Low frequency relaxation effect observed on 2024 aluminium alloy, J. Alloy. Compd. 310 (2000) 173–175. [40] J. Woirgard, A. Rivière, J. de Fouquet, Experimental and theoretical aspect of the high temperature damping of pure metals, J. De. Phys. 42 (C5) (1981) 407–419. [41] A. Rivière, Analysis of the low frequency damping observed at medium and high temperatures, Mater. Sci. Eng. A-Struct. Mater. 370 (2004) 204–208. [42] A. Rivière, V. Pelosin, M. Gerland, Eutectoid Al-51 at% Zn alloy studied by isothermal mechanical spectroscopy, Solid State Phenom. 184 (2012) 167–172. [43] M. Gerland, J. Woirgard, Mise en évidence de l′évolution de la microstructure d′un aluminium monocristallin par frottement intérieur isotherme, Scr. Metall. 16 (8) (1982) 923–927.
[23] A. Rivière, M. Gerland, V. Pelosin, Influence of dislocation networks on the relaxation peaks at intermediate temperature in pure metals and metallic alloys, Mater. Sci. Eng. A-Struct. Mater. 521–522 (2009) 94–97. [24] L.B. Magalas, Developement of high-resolution mechanical spectroscopy, HRMS: status and perspectives. HRMS coupled with a laser dilatometer, Arch. Metall. Mater. 60 (3) (2015) 2069–2076. [25] Zs Czigány, F. Misják, O. Geszti, G. Radnóczi, Structure and phase formation in Cu–Mn alloy thin films deposited at room temperature, Acta Mater. 60 (20) (2012) 7226–7231. [26] S. Belhas, C. Belamri, A. Rivière, Anelasticity in a Cu-Al single crystal at elevated temperatures, Mater. Sci. Eng. A-Struct. Mater. 521–522 (2009) 98–101. [27] A. Rivière, P. Gadaud, High temperature relaxations in aluminium studied by isothermal mechanical spectrometry, Metall. Mater. Trans. 28A (1997) 1661–1665. [28] I.S. Golovin, H. Neuhäuser, A. Rivière, A. Strahl, Anelasticity of FeAl alloys, revisited, Intermetallics 12 (2004) 125–150. [29] Z.C. Zhou, F.S. Han, Z.Y. Gao, The internal friction peaks correlated to the relaxation of Al atoms in Fe-Al alloys, Acta Mater. 52 (52) (2004) 4049–4054. [30] D.B. Butrymowicz, J.R. Manning, M.E. Read, J. Phys. Chem. Ref. Data 4 (1) (1975) 177–249. [31] A.S. Nowick, D.P. Seraphim, Magnitude of the Zener relaxation effect -I Survey of alloys systems, Acta Metall. 9 (1) (1961) 40–48. [32] F. Povolo, H.O. Mosca, Zener relaxation strength in bcc and fcc alloys under torsional and longitudinal excitation, Acta Metall. Et. Mater. 42 (1) (1994) 109–117. [33] A. Rivière, P. Gadaud, Zener relaxation in CuAl single crystals studied by
144
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Thermally-activated anelastic relaxation in a high-manganese Cu-Mn alloy studied by isothermal low-frequency internal friction
MARK
⁎
S.A.E. Boyera,b, , M. Gerlanda, A. Rivièrea a PPRIME Institute, ISAE, ENSMA, UPR CNRS 3346, Department of Physics and Mechanics of Materials, 1 Av. Clément Ader, 86961 Futuroscope Chasseneuil Cedex, France1 b MINES ParisTech, PSL - Research University, Centre for Material Forming, UMR CNRS 7635, 1 Rue Claude Daunesse, 06904 Sophia Antipolis, France
A R T I C L E I N F O
A BS T RAC T
Keywords: Manganese-rich copper-manganese alloy Isothermal internal friction Point defects Dislocations
Low-frequency internal friction study has been conducted for a copper-manganese-rich alloy (Cu-60 at%, γ Mn). The study used a forced torsion pendulum working in low-frequency scans at constant temperatures, damping experiments ranging between 40 Hz and 10−4 Hz. The dependence on temperature was extended from room temperature to the spinodal curve frontier at 923 K. Phenomenological stages in anelastic relaxations of (Cu, γ Mn) were evidenced. Three thermally activated relaxation peaks were assigned respectively to point defects (Zener relaxation), dislocation segments and dislocation walls.
1. Introduction Interaction between copper and manganese has received an intense attention. Copper-manganese (Cu-Mn) alloys are regarded because of their multipurpose, as versatile magnetic feature, superior damping capacity, shape memory [1–8]. The magnetic properties study has had a very long history, as early as 1957 [9]. The multipurpose is connected to the microstructure, for instance antiferromagnetic ordering of the quenched face-centred tetragonal (fct) phase. Another attractive feature of Cu-Mn alloys is the existence of a mutual metastable miscibility interval of their γ-phase (Cu, γ Mn) [5,10,11], with the development of a two-phase microstructure in a spinodal decomposition mode [12]. The metastable transformation has been discussed in the literature [4,13,14]. However the mechanical behavior in the vicinity of the metastable separation has received not much attention and the literature concerning this point is almost indeed nonexistent. Most careful study that one can cite is the one of V′vunenko and Likhachev in 1985 [15], Tsuchiya et al. in 1999 [4], Markova et al. from 2004 [6,16]. It was reported by Tsuchiya et al. in 1999 the effect of γ-phase in aged (Cu-Mn) on the face-centred cubic (fcc) - face-centred tetragonal (fct) phase martensitic transformation behavior; the increase in the transformation temperature with the decrease in electrical resistivity was explained by the rule of mixture assuming a heterogeneous microstructure as a result of the spinodal decomposition [4]. Markova et al. in 2004 and later in 2013 have studied internal friction (IF) and elastic modulus for manganese-rich
⁎
1
(Mn-40 at%, Cu) and copper-rich (Mn-45 at%, Cu) alloys up to 573 K [6,16]. They observed a large damping maximum in the temperature gap of martensitic transformation [6], interpreted by a microstructure evolution (tweed structure - “parquet” structure - classical twinning martensite). Because the measurements were made during continuous heating or cooling, this transitory maximum was linked to the change of the microstructure during the damping measurement. The present work proposes to use the benefits of low-frequency forced torsion pendulum [17 Chap. 1.6]. For metals, it is generally preferred because it offers high sensitivity. The mechanical spectroscopy works at fine controlled-fixed temperatures, and at subresonant conditions in a continuous frequency range. The large transitory damping maximum linked to the phase transition cannot be observed but anelastic relaxation phenomena would be accurately evidenced. Isothermal low-frequency internal friction (IF) measurements are performed from room temperature to the vicinity of the spinodal curve of (Cu-60 at%, Mn) in a face-centred cubic (fcc) phase, referred to as γphase. To the best of our knowledge, the anelastic properties of (Cu60 at%, γ Mn) alloy in such isothermal way were not yet reported in the literature. Quantitative experimental data on some newly observed anelastic relaxations are provided.
Corresponding author at: MINES ParisTech, PSL - Resarch University, Centre for Material Forming, UMR CNRS 7635, 1 Rue Claude Daunesse, 06 904 Sophia Antipolis, France E-mail address: [email protected] (S.A.E. Boyer). Past address
http://dx.doi.org/10.1016/j.msea.2016.12.120 Received 13 September 2016; Received in revised form 26 November 2016; Accepted 30 December 2016 Available online 31 December 2016 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 685 (2017) 139–144
S.A.E. Boyer et al.
2.2. Material
2. Experimental procedure: damping evaluation statement and material
2.2.1. Manganese-rich Cu-Mn A Cu-60 at% Mn alloy, provided by Goodfellow (France), was used for investigation. According to the required internal friction set-up, CuMn alloy specimen was cut by spark machining in bar, with dimensions of 64 mm in length and 6×1 mm2 cross section. Specimen was previously heat-treated at 943 K under vacuum and water quenched. Initial structure after quench was face-centred cubic (fcc) phase, referred to as γ-phase (Cu, γ Mn) [25]. Several series of experiments were made for which the sample has been progressively heated step by step at desired temperatures, respectively 573, 673, 723, 773, 873, 903, 923 K (and even 963 K as an ultimate test).
2.1. Technique 2.1.1. Mechanical spectroscopy statement Anelasticty in materials was initially described by Zener [17 Chap. 2.2, 18]. A continue stress applied to a material with an anelastic behavior has two effects; the corresponding elastic strain but also a change of the equilibrium state of one (or more) internal variable(s). The return to the equilibrium state carries away a supplementary strain called the anelastic strain. When the applied stress is removed, the anelastic strain progressively vanishes. This anelastic strain can result from the motion of structural defects such as point defects, dislocations, sliding of polymeric chains, etc. Because this anelastic strain is generally very small, it can be more easily detected when submitting the anelastic material to a cyclic (the most often sinusoidal) stress. Then a phase lag φ appears between the applied stress and the resulting strain. This phase lag characterizes the so-called internal friction Q−1 as Q−1 = tan φ. Apparatus working in a large frequency range of 300−10−4 Hz [19 Chap. 9.1] allows the direct determination of tan φ. Plotting Q−1 versus the frequency, a mechanical loss peak appears described by a Debye equation (Eq.1) [18]:
⎛ ⎞ ϖτ Q−1 = Δ ⎜ ⎟ ⎝ 1 + (ωτ )2 ⎠
3. Results and discussion 3.1. Anelastic relaxations: analysis and annealing Fig. 1 shows the low frequency internal friction (IF) spectra in the first stages of annealing at low temperatures. The experiments described in Fig. 1(a) were performed during step temperature increase from 414 K to 599 K. A low frequency background increase with temperature is often linked to structural defects (dislocations) in solid induced by the rapid cooling. The experimental curve is corrected by subtracting an estimated exponential background. The technique of background subtraction has already been described, as explained on Cu-Al system [26]. The evidence of a relaxation peak, called here the P1 peak, is indicated in Fig. 1(b). Fig. 2(a) illustrates the low frequency internal friction (IF) spectra measured at 573 K after respective temperature annealing of 573, 673, 723, and 773 K. The background decreases when the temperature of annealing increases. It is linked to the dislocation density decreasing with annealing [27]. But, the relaxation peaks obtained after background removing are superimposable: same frequency close to 10−2 Hz and same height. The background decrease of the internal friction at low frequency in Fig. 2(a) is linked to the decrease of the dislocation density; in Fig. 2(b) is plotted the evolution of the square of free frequency with the annealing temperature on the as received sample (a – up triangles) and the sample after quenching (b – down triangles). The square of free frequency is directly proportional to the modulus of torsion. The modulus is influenced by several parameters and in particular by the dislocation density. As shown in Fig. 2(b) the rapid cooling (quenching) increased this dislocation density, then it decreases with annealing. In Fig. 3 is displayed the evolution of the low frequency internal friction peak P1, during cooling, after annealing at 673 K and in-situ measured at 662, 633, 603, 588, 573, and 562 K. Evidently, the IF peak P1 shifts towards low frequencies when temperature decreases. The evolution of the relaxation intensity stands out and presents the following particular aspect to first increases from 662 to 588 K then lowers. After annealing at 723 K, a second relaxation peak (P2) is evidenced with the increase of damping. Fig. 4(a) illustrates the experimental curve at 703 K during the first heating (see a) and after subtraction of an estimated exponential background (see b), resulting in the evidence of two maxima (see c). The maximum at high frequency corresponds to the P1 peak as previously described, and the maximum at about 0.1 Hz is assigned to the new P2 peak. This P2 peak was also observed for measurements at respectively 723 K and 673 K as pointed out in Fig. 4(b). The second peak, not present in the first temperature increase, grows progressively. Both the relaxation peaks, P1 and P2, shift towards lower frequencies for experiments at lower temperatures (Fig. 4(b)) corresponding to an Arrhenius behavior. For the P1 peak, the corresponding limit relaxation time τ0 is 3.6×10–15 s and the apparent activation energy HA is 1.76 eV. For the P2 peak, the
(1)
where τ is the relaxation time, Δ is the relaxation strength, ω=2πf with f the frequency of the mechanical vibrations. If the relaxation is thermally activated, the frequency of the maximum of the relaxation peak is shifted towards higher frequency if the temperature of the measurement is increased. This activation can be described by the Arrhenius equation as (Eq. (2)):
⎛ H⎞ τ −1 = τ0−1 exp ⎜ − ⎟ ⎝ kT ⎠
(2)
τ0−1
the limit of relaxation times. where H is the activation energy and When plotting the Napieran logarithm of the frequencies of the maxima of the relaxation peaks obtained at several temperatures versus the inverse of the measurement temperatures, the experimental points are aligned in a line (Arrhenius plot), allowing the determination of the relaxation parameters H and τ0−1 , and therefore the knowledge of the elementary mechanism leading to the internal friction. 2.1.2. Isothermal internal friction experiments Isothermal mechanical spectroscopy (IMS) experiments were carried out with an inverted forced torsion pendulum. Isothermal mechanical spectroscopy permits to measure materials in a state close to equilibrium and to avoid transient effects which accompany temperature dependent IF measurements. Torsional vibrations were excited by supplying to an oscillating electromagnet a sinusoidal signal from a generator. The equipment made it possible to control temperature in the range from room temperature to 1000 K which was measured accurate to within 1 K. The pendulum and its performance were described in [20–24]. Measurements were conducted under partial pressure of pure argon (0.1 bar) purchased from Air Liquid (France). Before each IF measurements, the alloy was aged in the temperature range from 523 K to the CuMn spinodal curve at around 923 K during 3–16 h and held constant during the measurement time (12–48 h). The vibration frequencies (f) ranged between 40 Hz and 10−4 Hz, and the measurements were made at 10 discrete frequencies per decade. The internal friction was also measured at the resonance frequency of the system (300 Hz) using the free-decay method. The maximum strain amplitude (εmax) applied on the sample was 5×10−6. 140
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Fig. 1. (a) Low frequency internal friction spectra after in-situ annealing at temperatures increasing from 414 K to 599 K. (b) P1 peak evidenced by exponential background subtraction.
corresponding limit relaxation time τ0 is 10–14 s and the apparent activation energy HA is 1.90 eV. When increasing the annealing temperature to 923 K, a third peak P3 appears, as illustrated in Fig. 5(a). By applying the same decay method as before, results give that for the P3 peak, the corresponding pre-exponential factor of limit relaxation time τ0 is 5×10−7 s and the apparent activation enthalpy HA is 1.70 eV (Fig. 5(b)). Note that our investigation stopped at 923 K, indeed higher temperature would most probably encourage a phase change in (Cu-60 at%, γ Mn) [11].
3.2. Discussion As measured by isothermal low-frequency internal friction, three relaxation peaks have been evidenced in the (Cu-60 at%, γ Mn) alloy. The IF response of (Cu-60 at%, γ Mn) is strongly dependent on the thermal treatment [28,29]. P1 peak is observed directly during the first heating at relatively low temperatures (T=562–703 K). P1 peak is stable and does not change after the high temperature annealing. This behavior and the relaxation
Fig. 2. (a) Low frequency internal friction spectra at the same temperature (573 K) after several in-situ annealings at 573, 673, 723, and 773 K. (b) Square of free frequency with the annealing temperature on a – as-received sample, and b – sample after quenching.
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of manganese (Mn) atoms in copper (Cu). It is closed to the value of Mn diffusion in copper alloys systems recently found for other compositions, i.e. 1.9 eV [30]. The tendency evolution of the relaxation intensity (increases then lowers, see part 3.1.-Fig. 3) has been observed in the anelastic Zener relaxation (as referred to in more general terms as ‘stress-induced ordering’) [31,32] of Cu-Al single crystals with solute content in the range from 7–19% Cu, as described in [33]. It has been explained by the short-range ordering as designated in the Le Claire-Lomer theory [34,35]. It is due to stress-induced changes of atomic order with respectively the influence of only neighboring atoms at lower temperature measurements (increasing relaxation) and more distant atoms at higher temperature measurements (decreasing relaxation). At intermediate temperatures and after annealing at 723 K, a second relaxation peak P2 is observed. Its relaxation parameters were deduced from the Arrhenius plot (Fig. 4(b)): limit relaxation time τ0 is 10–14 s and apparent activation energy HA(P2) is 1.9 eV. Relaxation peaks spreading out after annealing were very often observed in pure single or polycrystalline metals (as Ag, Al, Cu, Pd, and Ni; see [22,23,36,37]) or metallic alloys (as Cu-Al [38] or 2024 aluminum alloy [39]). The evolution of such a peak was studied in detailed way in pure Al sample during the recrystallization after cold-working [27]. The observed relaxation peak spreads out progressively after large decreases of the modulus and hardness corresponding to the end of the recovery stage. In parallel with the increase of the peak, an increase in mean grain size excludes a grain boundary relaxation and this peak in pure Al was explained by a relaxation linked to a dislocation mechanism according to the model proposed by Woirgard [40]. The similar evolution leads to associate P2 peak as a dislocation peak. At higher temperatures and at low frequency, after annealing at 923 K, a new P3 peak appears. Its relaxation parameters are a limit relaxation time τ0 of 5×10−7 s and an apparent activation energy HA(P3) of 1.7 eV. Such low frequency and very high temperature peaks have been already observed in pure metals and metallic alloys [23,41,42]. At frequencies close to 1 Hz with a classical apparatus, it cannot be observed because it would be at a temperature above the melting point or the liquidus. Such a peak was accurately studied in an
Fig. 3. Evolution of the low frequency internal friction peak P1 after annealing at 673 K and in-situ measurements at 662, 633, 603, 588, 573, and 562 K.
parameters (particularly the limit relaxation time τ0 of 3.6×10–15 s) allow attributing the P1 peak to a point defects relaxation mechanism. Zener [18] shows that a pair of substitutional atoms in fcc (as Cu, γ Mn) solid solution would reorient under stress and thereby display internal friction and a relaxation peak (Zener peak type). The apparent activation energy (HA(P1) =1.76 eV) would correspond to the diffusion
Fig. 4. (a) Internal friction spectrum at 703 K after in-situ annealing at 723 K. Peak background subtraction to evidence the P2 peak. (b) Napierian logarithm of peak frequencies vs. the inverse temperature for the relaxation peaks P1 and P2 obtained after annealing at 673 K (P1 – up-triangles) and annealing at 723 K (P2 – down-triangles).
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Fig. 5. (a) High temperature internal friction spectra at two temperatures (923 and 773 K) after in-situ annealing at 923 K. (b) Napierian logarithm of peak frequencies vs. the inverse temperature for the anelastic peak P3 obtained for low frequency-high temperature annealing.
References
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4. Conclusions A first attempt in the analysis of anelastic relaxations in a manganese-rich alloy (Cu-60 at%, γ Mn) is proposed by the use of isothermal low-frequency internal friction (IF) from room temperature to the vicinity of the spinodal curve of the alloy. Investigation is done in a large frequency range (40−10−4 Hz), at fixed temperatures (stable microstructural states), by continuously changing frequencies. The isothermal low-frequency IF is benefit. Three phenomenological stages in the anelastic relaxations are evidenced. At relatively low temperature (between 562 K and 662 K), Zener point defects relaxation mechanism is recognized in the anelastic relaxation peak P1. After annealing at 723 K, a new relaxation peak P2, evidenced between 673 K and 723 K, is explained by a reversible motion of dislocation segments. The P3 peak observed at very low frequency between 773 K and 923 K is associated with the motion of the generated dislocation walls. The internal friction peaks are thermally activated relaxation peaks; their activation parameters are calculated by plotting Arrhenius graph. In further work, interest would be to discuss the mechanisms of anelastic relaxations in reference to the phase transformations and/or heterogeneous microstructural evolutions formed as a result of the spinodal decomposition [7,10], which could be monitored by in-situ temperature-controlled transmission electron microscopy (TEM) and/ or in-situ temperature-controlled X-ray diffraction. Acknowledgements CNRS is acknowledged. Experimental works were done on pendulum setup at ISAE-ENSMA, UPR CNRS 3346, PPRIME institute. 143
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