Materials Science & Engineering A 650 (2016) 382–388

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Effect of cooling rate on damping capacity of Fe–Cr basedferromagnetic metal alloy

Hui Wang a,b, Fu Wang c, Jun Xiao a,b, Yuan Wang d, Ce Ma a, Zuoyong Dou a, Min Wang a,Pengcheng Zhang a,n

a Science and Technology on Surface Physics and Chemistry Laboratory, P.O. Box No. 9-35, Huafengxincun, Jiangyou City, Sichuan Province 621908, Chinab National Key Laboratory for Nuclear Fuel and Materials, Nuclear Power Institute of China, Chengdu 610041, Chinac School of Material Science and Engineering, Southwest University of Science and Technology, Mianyang 621010, Sichuan, Chinad Institute of France-China Nuclear Engineering and Technology, Sun-Yat Sen University, Zhuhai 519000, China

a r t i c l e i n f o

Article history:Received 9 October 2015Received in revised form22 October 2015Accepted 23 October 2015Available online 24 October 2015

Keywords:Fe–Cr–Mo based alloyDamping capacityCooling ratesCoercive force

x.doi.org/10.1016/j.msea.2015.10.08693/& 2015 Elsevier B.V. All rights reserved.

esponding author. Fax: þ86 2885903294.ail address: zoucongpei5525@163.com (P. Zha

a b s t r a c t

The Fe–15Cr–3Mo–0.5Si alloy was treated by furnace cooling, air cooling or water cooling after annealingat 1100 °C for 1 h in vacuum atmosphere. The damping performance of the as-treated alloys was testedwith dynamic mechanical thermal analyzer and the effects of different cooling rates on phase, micro-structure, coercive force and damping capacity were investigated. The results show that the cooling rateshave no influence on the crystalline phase and grain sizes of the Fe–15Cr–3Mo–0.5Si alloy. The phase ofthe as-treated alloys is a single α-Fe. Moreover, Cr- and Mo-containing carbide precipitation is detectedon alloy grain boundary of the furnace-cooled alloy, while no precipitated phase on the alloy grainboundary of the air-cooled and water-cooled alloy. In addition, the furnace-cooled alloy shows thesmallest coercive force comparing with the air-cooled alloy, and the water-cooled alloy shows the biggestcoercive force. The peak values of logarithmic decrement δ of furnace-cooled, air-cooled and water-cooled alloy are 0.209, 0.188 and 0.175 respectively. The gradual decrease of the damping capacity withincreasing cooling rate for the alloy mainly lies in the discrepancy of their micro internal stress.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

With the ever-accelerated industry, the problems of vibrationand noise become increasingly worse, which not only affect thesafety and service life of mechanical and military equipment, butalso are of great harm to people's health. Therefore, the reductionof vibrations and noises is an urgent task. The current solution,which is regarded as the most important and effective means atpresent, to this problem is to use high damping alloys. As is knownto all, Fe-based alloys with α phase, such as Fe–Cr based ferro-magnetic metal alloys, have attracted much attention to manyresearchers due to their excellent mechanical properties, corrosionresistance and high damping capacity [1–7].

The damping mechanism of the Fe–Cr based ferromagneticdamping alloy is that the vibration energy is transferred to heatenergy through the irreversible movement of magnetic domainwalls, and then the resultant heat energy is dissipated by heatconduction [1–3]. Many factors affect the damping capacity offerromagnetic Fe–Cr based damping alloy. Studies [3–8] suggest

ng).

that, in order to achieve better damping capacity, the alloy shouldmeet the following requirements. Firstly, the content of impurityelements, such as C and N, should be strictly controlled. Usuallythese impurities should be strictly limited to lower than 0.01 wt%,which is the only way to significantly reduce the micro internalstress of alloy structure. Secondly, heat treatment process must bereasonable. Current research on heat treatment process mainlyfocuses on the effects of temperature and holding time on thedamping capacity of ferromagnetic alloy. Most studies [6–10]concluded that, in the process of annealing below 1100 °C and heatpreservation for 1 h, the internal friction of Fe–Cr based ferro-magnetic damping alloy increases and its damping capacity im-proves with the increase of heat treatment temperature. This isattributed to the fact that the internal stress of the alloy caused bydislocation, grain boundary and interstitial atoms hinders the ir-reversible movement of the magnetic domain wall and reduces thedamping capacity of the alloy [11,12]. If an alloy anneals at hightemperature, its internal stress, dislocation and other defects willeliminate and thus the damping capacity is improved. The im-provement of the damping capacity through heat treatment athigher temperature is mainly due to the change of the distributionof the micro internal stress.

In addition to the heat treatment temperature and holding

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388 383

time, the cooling rate also has a significant effect on micro-structure, magnetic domain structure and the distribution of microinternal stress of an alloy, which in turn affect the damping ca-pacity of Fe–Cr based damping alloy. However, when it comes tothe effect of heat treatment process on the microstructure anddamping capacity of an alloy, the factor of the cooling rates isseldom taken into consideration. However, in order to furtherimprove the damping capacity of Fe–Cr based damping alloy, it isnecessary to carry out systematic research on the effect of coolingrates on the microstructure and damping capacity of the alloy.Based on the quaternary iron-based damping alloy, Fe–15Cr–3Mo–0.5Si, which was obtained by our previous research and wasproved to be with good damping capacity [9,10], this paper furtherstudies the effect of different cooling rates (furnace cooling, aircooling and water cooling) on the damping capacity, the micro-structure and the internal stress of the alloy.

2. Experimental method

2.1. Alloy melting

In order to reduce the influences of interstitial impurity atomssuch as C and N on the damping capacity of the alloy, highly pureFe (the content of C and N is lower than 0.02%), 99.9% highly puremetal Cr, Mo and Si were chosen as raw materials for the experi-ment. ZG-50 vacuum induction furnace with capacity of 25 kg wasused for melting the alloys, the compositions of which is shown inTable 1. It can be seen that the real compositions of the two alloyswas very close to its nominal composition and the content ofimpurities is within good control.

2.2. Sample preparation

The obtained alloy ingots were first annealed at 1200 °C for 2 h.Then, the annealed ingots were forged. The initial forging tem-perature was about 1100 °C and the final forging temperature washigher than 900 °C. Remelting was set to be less than three timesand the ingots would be forged into 15 mm thick plates. Based onthe requirements of different experiments, samples were chosenfrom the forged plates and then processed. The samples for thedamping capacity testing were sheet samples with the size of55 mm�10 mm�1 mm. The samples for microstructure ob-servation were block samples with the size of10 mm�10 mm�10 mm. Three group samples were annealed at1100 °C for 1 h, and then treated by furnace cooling (FC), aircooling (AC) and water cooling (WC) respectively to roomtemperature.

2.3. Performance test and microstructure observation of the samples

Damping capacity test was conducted with TAQ800 dynamicmechanical analyzer (DMA) and the damping capacity was re-presented by logarithmic decrement. Three point bending vibra-tion mode was adopted to measure alloy damping capacity δchanging along with strain amplitude γ. Vibration frequency was1 Hz, the measuring temperature was 30 °C and the variationrange of γ was 2�10�6–6�10�4.

Table 1Chemical compositions of Fe–15Cr–3Mo alloy (wt%).

No. Si Mo Cr N C Fe

No-1 0.48 2.96 14.96 0.003 0.012 MarginNo-2 0.53 3.02 14.07 0.004 0.015 Margin

Metallographic structure observation samples were corroded inhydrochloric acid alcohol solution (10 mL HCIþ90 mL CH3CH2OH)under the voltage of 3–4 V for 20 s. Metallographic structure wasobserved by means of Optical Microscope (OM). Device name:optical microscope (OLYMPUS), specification and model: BX51. Theaverage grain size was measured by cutting line method.

Cutting line method:

(1) On the grain images, the measuring grid was comprised byone or several lines. Appropriate length and magnification ofthe measuring grid were necessary to ensure a minimum of 50points.

(2) The terminal point of the measuring line was not included inthe total of the points. When the terminal point just touchedthe grain boundary, 0.5 point was recorded. When the mea-suring line and the grain boundary were tangent, 1 point wasrecorded. When the three grains intersected, 1.5 points wererecorded.

(3) Actual line length (total length/magnification/the number ofpoints) was the average grain size.

The characteristics of alloy grain boundary were observed bySEM and the compositions of precipitates on the grain boundarywere analyzed with SEM-EDS. Device name: scanning electronmicroscope, specification and model: S4800. XRD was used tomeasure the alloy structure change. The coercive force of the alloywas measured with vibration magnetometer.

3. Results and analysis

3.1. Effect of cooling modes on the microstructure

Fig. 1 shows the microstructures of the Fe–15Cr–3Mo–0.5Sialloy annealing at 1100 °C for 1 h and treating by different coolingmodes. From Fig. 1(a), the forged alloy shows isometric crystalwith unevenly distributed sizes. The grains are fine and arelengthened in the deformation direction. Therefore, they showobvious directivity, because the final forging temperature (900 °C)is higher than the recrystallization temperature of the alloy anddynamic recrystallization occurs in the process of forging. FromFig. 1(b)–(d), all the grains grow up after annealing and coolingtreating. The experimental results show that the influence ofcooling rates on the grain sizes of the alloy is insignificant. Theaverage grain sizes of the alloys cooling by FC, AC and WC are244 μm, 256 μm and 225 μm respectively.

Fig. 2 shows the precipitated phase of the Fe–15Cr–3Mo–0.5Sialloy on the grain boundary under the condition of differentcooling rates. The SEM shows that the second phase was pre-cipitated for the Fe–15Cr–3Mo–0.5Si alloy treating by FC. Asshown in Fig. 2(a), the content of C, Cr and Mo elements in theprecipitated phase are significantly higher than those of the matrixcomposition (as shown in Table 2). From the content of the ele-ments and the morphology of the precipitated phase, the secondphase is cementite M23C6 precipitated from ferrites in the processof slow cooling. While the precipitated phase is not detected in thealloys treating by both AC and WC, which are mainly due to thefact that there is not enough time for C and the alloy elements toform the phase when high cooling rate are adopted.

Fig. 3 shows the equilibrium phase diagram of Fe–15Cr–3Mobased alloy at different temperature, where the content of carbonin the alloy is 0.15 wt%. As can be seen from the figure, metalcarbides M23C6 phase (generally a Cr-rich carbide phase, Cr23C6)easily forms in the structure of the Fe–15Cr–3Mo based alloy whileannealing at 1100 °C, and no M7C3 phase presents. This furtherconfirms that the formed second phase is cementite M23C6

Fig. 1. Microstructures of (a) the forged alloy and the Fe–15Cr–3Mo–0.5Si alloy annealing at 1100 °C for 1 h and cooling by (b) FC, (c) AC and (d) WC.

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388384

(generally a Cr-rich carbide phase, Cr23C6).Although the cooling rate has little effect on the grain sizes of

the alloy, there is a small amount of C in the alloy. When the an-nealing temperature is above 1000 °C, Cr23C6 rich phase easilyprecipitates from Fe–Cr based alloys. While annealing at 1100 °C,different cooling rates have influence on the precipitation of theCr23C6 rich phase. There is more amount of Cr23C6 rich phase in theslowly cooled alloy, while there is less or even no precipitation ofCr23C6 rich phase in the rapidly cooled alloy. Moreover, for a givenchemical composition of the alloy, higher cooling rates lead tohigher supersaturated vacancy concentration. There were a lot ofvacancies due to the intense thermal motion of the atoms at hightemperature. If the alloys are cooled slowly from the high tem-perature, a large number of vacancies will transfer to the freesurface or grain boundary of the crystal in the cooling process.When the temperature decreases to room temperature, the lowlyinternal supersaturated vacancy concentration is obtained. On thecontrary, if the alloys are cooled quickly, the vacancies will retainin the crystal of the alloy and the highly supersaturated vacancyconcentration still exists. This also confirms the reason for theformation of precipitated phase on the grain boundary of the alloytreating by FC while the failure of formation of precipitated phases

for the alloy treating by AC and WC method.

3.2. Effect analysis of cooling rates on the internal stress and yieldstrength of the alloys

Fig. 4 shows the magnetostriction coefficient curves of the al-loys treating by different cooling rates. The figure shows that thedifferent cooling rates have insignificantly effect on the saturatedmagnetostriction coefficient λs of the Fe–15Cr–3Mo–0.5Si alloy.

Based on the principle of ferromagnetics [1], the physical re-lationship between internal stress and coercive force is expressedby formula (1).

HM L

32 1c

s

S

π λ σμ

δ=( )

where sλ is saturated magnetostrictive coefficient, μ is perme-ability in vacuum, MS refers to saturation magnetization, δ is thethickness of the magnetic domain wall, and L is the magneticdomain size. For an alloy with complete recrystallization, thecoercive force only depends on its internal stress.

From Fig. 5 and Table 3, the alloy treating by FC shows the leastcoercive force compared with the other two alloys, while the alloy

Fig. 2. Precipitated phases of the samples on the grain boundary cooling by (a) furnace cooling (FC), (b) air cooling (AC) and (c) water cooling (WC).

Table 2Compositions of the precipitated phases of the alloy in Fig. 2(a).

No. C/wt% Cr/wt% Mo/wt% Fe/wt%

No.1 0.59 21.76 3.26 MarginNo.2 0.011 14.58 2.89 Margin

Fig. 3. Equilibrium phase diagram of Fe–15Cr–3Mo based alloy at different tem-perature (C¼0.015%).

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388 385

treating by WC shows the largest coercive force. This suggests thatthe internal stress of the alloy obviously decreases with the de-crease of the cooling rates, which is consistent with the researchresults from literatures [13,14]. Firstly, lower cooling rate gives riseto larger average grain sizes and lower grain boundary con-centration. The energy on grain boundaries is higher, so the de-crease of the grain boundary concentrate is beneficial to the de-crease of the internal stress. Secondly, for the alloy treating by FC,the segregation of C, N and other interstitial atoms on the grainboundary cause the decreasing degree of internal lattice distortion,and the internal stress inside the grains is loosen. While for thealloys treating by AC and WC, the C, N and other interstitial atomswhich lead to lattice distortion and the increase of internal stressstill exist in the matrix.

Fig. 6 shows the yield strength curves of furnace-cooled, air-cooled and water-cooled Fe–15Cr–3Mo–0.5Si alloys annealing at1100 °C for 1 h. It can be seen from the figure that the water-

cooled alloy shows the maximum strength and the furnace-cooledalloy shows the minimum strength. The content of C and N is verylow and the content of elements such as Nb, Ti and V which can

Fig. 4. Magnetostriction curves of the prepared alloys after treating by differentcooling modes.

Fig. 5. Hysteresis curves of the coercive force of the alloys treating by (a) FC, (b) ACand (c) WC.

Table 3Coercive force values of the alloys treating by different cooling modes.

Cooling rates FC AC WC

Coercive force 369.44 374.14 382.85

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388386

intensely react with C and N, is zero. Therefore, the formation ofcarbonitride MX to disperse in the alloy matrix is difficult duringhigh temperature annealing, and the strength of the alloy is in-significantly change. The high content of Mo which has strongsolution strengthening effect in the Fe–15Cr–3Mo alloy sig-nificantly improves the high-temperature strength of the alloy.The Fe–15Cr–3Mo–0.5Si alloy is in a complete solid solution stateat the temperature of 1100 °C, the water-cooling leads to theconcentration of thermal stress due to fast cooling rate. However,there is no stress concentration because of the lower cooling ratefor the furnace-cooled alloy, thus the yield strength of the water-cooled alloy is slightly higher than that of the air-cooled alloy andthe furnace-cooled alloy.

3.3. Effect of cooling modes on the damping capacity of the alloys

Fig. 7 shows the variation of the logarithmic decrement δ withthe varying of strain amplitude γ for the alloys cooling by differentrate. It can be seen from Fig. 7 that, in the rising part of the curves,the values of logarithmic decrement δ increase fast with the in-crease of the strain amplitude γ, and all these values begin todecline after achieving a peak values. The peak values of δ are0.209, 0.188 and 0.175 for the alloys cooling by FC, AC and WCrespectively. The rate of the changing of logarithmic decrement δwith strain amplitude and the strain corresponding to the peakvalue are different for the alloys treating by different coolingmodes. The lower the cooling rate is, the faster the logarithmicdecrement δ reaches the peak value. This means that, at lowercooling rate, the logarithmic decrement δ reaches maximum valueat lower strain amplitude. The strain amplitudes corresponding toits maximum logarithmic decrements for the alloys treating by FC,AC and WC are 1.72�10�4, 1.87�10�4 and 2.0�10�4. Moreover,for an alloy treating by a lower cooling rate, the strain amplitudecorresponding to the maximum logarithmic decrement δ value issmall. And after the alloy reaches its δmax, the decrease rate of thecurve also is lower and the damping curve is broader, making apossibly wider strain range in high damping value region. Fig. 7also shows that the variation trend of the damping capacity ofdifferent cooled alloys are opposite to that of the strength varia-tion trend. Therefore, the further study should be focused on howto reasonably balance the relationship between the damping ca-pacity and the mechanical strength.

In the rising stage of δ–γ curve, the damping capacity of fer-romagnetic alloy improves with the increasingly irreversible

movement of magnetic domain wall. The δmax reaches when theirreversible movement of the magnetic domain wall reaches itssaturation state. Studies [9–11] showed that grain boundary and

Fig. 6. Yield strength curves of different cooled alloys after annealing at 1100 °C/1 h.

Fig. 7. Damping-strain amplitude curves of the alloys treating by different coolingmodes.

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388 387

interstitial atoms have a pinning effect on the irreversible move-ment of magnetic domain wall. The irreversible movement ofmagnetic domain wall requires overcoming the barriers of theinternal stress arisen from grain boundary, interstitial atoms, va-cancies, etc. For the alloy treating by FC, the movement of mag-netic domain wall is more ease and starts under smaller strainamplitude due to the segregation of C, N and other interstitialatoms on the grain boundary and lower internal supersaturatedvacancy concentration. Therefore, the strain amplitude corre-sponding to δmax is smaller and the logarithmic decrement δ ishigher under the same strain amplitude for the alloy.

It is widely recognized that the magnetic elastic coupling is themain damping source for a ferromagnetic alloy, and so thedamping is called magnetic-mechanical hysteresis damping. Thedamping mechanism mainly comes from macro eddy-currentdamping, micro eddy-current damping and magnetic-mechanicalhysteresis damping. In these three mechanisms, the magnetic-mechanical hysteresis damping, which is dependent on strainamplitude, is one order of magnitude higher than the sum ofmacro eddy-current damping and micro eddy-current damping.So, the magnetic-mechanical hysteresis damping is the mainsource of the ferromagnetic damping material at low frequency.The magnetic-mechanical hysteresis damping can also be ex-plained by the S–B theory which was put forward by Smith andBirchak [15]. The theory gives the formulas (formula (2)) for

ferromagnetic damping and the slope of damping curve at lowstrain amplitude.

QkE kE43

43 2

s

i

s

i

12 2

δ πλ γ

πσπ

λ γσ

= = =( )

−

where k is dimensionless constant, sλ is the saturated magne-tostriction coefficient, E is the Young's modulus, γ is the strainamplitude and si is the internal stress. From formula (2), the in-ternal friction of the damping alloy is proportional to the strainamplitude and they show a linear relationship. Rayleigh slope SRcan be obtained after differential of γ by formula (2):

dd

kES

43 3

s

iR

2δγ

λσ

= =( )

From formula (2) and formula (3), for a given alloy, SR is in-versely proportional to iσ at small strain amplitude, which is alsoreflected in Fig. 7. For water-cooled alloy, the biggest internalstress exists in the alloy due to the interstitial C atoms withincrystals and high supersaturation vacancy concentration. There-fore, the minimum SR and the smallest logarithmic decrement δ atlow strain amplitude are obtained. After reaching δmax, δ–γ curvebegins to decline, because the irreversible movement of magneticdomain wall, which attains its saturated state at δmax, can notconvert mechanical energy into heat energy. It means that theferromagnetic damping disappears. It has been revealed that thedamping is caused by dislocation glide after reaching the max-imum δ value [16]. Energy dissipation caused by dislocations isanother important damping source for the ferromagnetic dampingalloy. In this paper, for the alloy annealing at 1100 °C for 1 h, thehigh annealing temperature and low cooling rate greatly elim-inates their dislocations. Therefore, the δ–γ curves after reachingδmax at high strain amplitude begin to decline rapidly.

4. Conclusions

The Fe–15Cr–3Mo–0.5Si alloy was prepared and the effect ofcooling modes on the phase structure, microstructure, coerciveforce and damping capacity of the as-prepared alloys was studied.The following conclusions are drawn:

(1) For the Fe–15Cr–3Mo–0.5Si alloy annealing at 1100 °C for 1 h,the cooling rates insignificantly affect its grain sizes. Cr- andMo-containing carbide precipitation is detected on the grainboundaries of the alloy when furnace cooling is adopted,while no precipitated phase is found on the grain boundariesof the alloys treating by air cooling and water cooling.

(2) The furnace-cooled Fe–15Cr–3Mo–0.5Si alloy shows theminimum coercive force, and the water-cooled alloy showsthe biggest coercive force, which demonstrates that the in-ternal stress of the alloy reduces with the decreasing coolingrate.

(3) The damping capacity of the Fe–15Cr–3Mo–0.5Si alloy in-creases first with the increase of strain amplitude and thendecreases after reaching the maximum logarithmic decrementδ. The values of the logarithmic decrement δ are 0.209, 0.188and 0.175 for the alloys treating by furnace cooling, air coolingand water cooling respectively. The reason why the dampingcapacity of the three cooled alloys gradually decreases is thatthe internal stress of the alloys gradually increases.

(4) The variation trend of the damping capacity of different cooledalloys is opposite to the variation trend of the strength.Therefore, the further study should be focused on how toreasonably balance the relationship between the dampingcapacity and the mechanical strength, on the basis of

H. Wang et al. / Materials Science & Engineering A 650 (2016) 382–388388

improving the mechanical properties of the alloy withoutlowering the damping capacity.

Acknowledgments

Great thanks to China Academy of Engineering Physics andNuclear Power Institute of China for help in terms of experimentalconditions.

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