# Hot Deformation Behavior of a New Al Mn Sc Alloy

## Transcript Of Hot Deformation Behavior of a New Al Mn Sc Alloy

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Article

Hot Deformation Behavior of a New Al–Mn–Sc Alloy

Weiqi Kang 1, Yi Yang 1,* , Sheng Cao 2,* , Lei Li 3, Shewei Xin 3, Hao Wang 4 , Zhiqiang Cao 1, Enquan Liang 5, Xi Zhang 5 and Aijun Huang 6

1 School of Materials Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China; [email protected] (W.K.); [email protected] (Z.C.)

2 School of Materials, University of Manchester, Oxford Road, Manchester M13 9PL, UK 3 Northwest Institute for Non-ferrous Metal Research, Xi’an 710016, China; [email protected] (L.L.);

[email protected] (S.X.) 4 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China; [email protected] 5 Shanghai Aircraft Design and Research Institute, Shanghai 201210, China; [email protected] (E.L.);

[email protected] (X.Z.) 6 Department of Materials Science and Engineering, Monash University, Clayton, VIC 3800, Australia;

[email protected] * Correspondence: [email protected] (Y.Y.); [email protected] (S.C.)

Received: 4 November 2019; Accepted: 13 December 2019; Published: 19 December 2019

Abstract: The hot deformation behavior of a new Al–Mn–Sc alloy was investigated by hot compression conducted at temperatures from 330 to 490 ◦C and strain rates from 0.01 to 10 s−1. The hot deformation behavior and microstructure of the alloy were signiﬁcantly aﬀected by the deformation temperatures and strain rates. The peak ﬂow stress decreased with increasing deformation temperatures and decreasing strain rates. According to the hot deformation behavior, the constitutive equation was established to describe the steady ﬂow stress, and a hot processing map at 0.4 strain was obtained based on the dynamic material model and the Prasad instability standard, which can be used to evaluate the hot workability of the alloy. The developed hot processing diagram showed that the instability was more likely to occur in the higher Zener–Hollomon parameter region, and the optimal processing range was determined as 420–475 ◦C and 0.01–0.022 s−1, in which a stable ﬂow and a higher power dissipation were achieved.

Keywords: Al–Mn–Sc alloy; hot deformation; ﬂow stress; processing map; dynamic recrystallization

1. Introduction

Casting and wrought aluminum (Al) alloys have been widely used as structural materials in aerospace industries owing to their high speciﬁc strength (strength to weight ratio), excellent fatigue resistance, and good formability [1–3]. The strength mainly arises from precipitation strengthening achieved from aging treatment [4–6]. Recently, a new high strength Al–Mn–Sc alloy has been developed by Jia et al. [7] using selective laser melting (SLM). The supersaturated Mn and Sc signiﬁcantly improve the mechanical property through solid solution strengthening of Mn and precipitation strengthening of nano-sized Al3Sc precipitates, which lead to a superior yield strength at 560 MPa and a good ductility at 18%. Such mechanical properties are attractive for aerospace industries. However, this Al–Mn–Sc alloy has only been studied in the additive manufactured condition, but has not been investigated in other forms like casting and wrought products.

After direct chill casting, Al ingots generally need various thermo-mechanical processing steps to obtain diﬀerent types of semi-ﬁnished products. The microstructure of the material depends on the thermo-mechanical processing parameters, which also determine the quality of the formed part. Thus, it is necessary to understand the inﬂuence of deformation parameters on hot deformation behavior

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and microstructure in this Al–Mn–Sc alloy. In general, the isothermal compression test is an appropriate method to study the hot deformation characteristics of materials [8,9]. The relationships among the ﬂow stress, strain, strain rate, and deformation temperature can be used to establish the hot deformation constitutive equation, and its hot activation energy can be calculated. The hot deformation behavior can be quantitatively described and applied to simulate the dynamic response of the material under speciﬁc loading conditions. In addition, the hot processing map is constructed to predict the plastic deformation mechanism and the unstable deformation domain in various deformation conditions, which provides insights into the optimization of thermo-mechanical processing. This method has been widely used in various alloys, such as Al alloys [8–10], Mg alloys [11–13], Ti alloys [14–16], and steel [17–19].

The present work aims to investigate the hot deformation behavior, to reveal the microstructure change, and to obtain the hot processing map of the casting Al–Mn–Sc alloy over wide temperature and strain rate ranges. The results will provide guides on its hot deformation processing and industrial applications.

2. Materials and Methods

The raw material (Table 1) used in this experiment was a casting ingot with a diameter of 150 mm. Cylindrical samples (ϕ10 × 15 mm) were sectioned by Electrical Discharge Machining (EDM) wire-cut from the ingot and then ground by SiC abrasive sandpaper before subjecting to isothermal hot deformation experiments conducted on a Gleeble-3800 system. According to the deformation conditions of aluminum alloy in normal industrial production, the test was carried out at temperatures from 330 to 490 ◦C and strain rates from 0.01 to 10 s−1. Graphite sheet was used as a lubricant between the compression plate and the sample to reduce friction. Before the compression test, the samples were solution treated at 500 ◦C for 5 min followed by gas quench in the Gleeble chamber. These samples were heated again to the testing target temperature at a ramping rate of 10 ◦C/s and held for 5 min to eliminate the thermal gradients before compression. Isothermal hot deformation experiments were conducted afterwards at various temperatures and strain rates. After a 60% deformation, the samples were gas-quenched to room temperature to freeze the microstructure after the hot deformation. The gas-quenched deformed samples were sectioned by EDM wire-cut along the axial direction, which is parallel to the compression direction. A standard metallographic sample preparation and etching by Keller’s solution (1 mL HF + 1.5 mL HCl + 2.5 mL HNO3 + 95 mL H2O) were carried out, and the microstructure characterization was conducted by using a Leica DMi8A light microscope (LM) and a FEI QUANTA 450 scanning electron microscope (SEM) equipped with an energy dispersive X-ray spectrometer (EDS) detector. The grain size was measured by ImageJ software.

Table 1. Composition of the studied Al–Mn–Sc alloy (wt.%).

Mn

Mg

Sc

Zr

Si

Fe

Al

4.3–4.7 1.4–1.6 0.65–0.85 0.7–0.8 <0.1 <0.1 Bal

3. Results and Discussion

3.1. Microstructure of As-Cast Al–Mn–Sc Alloy

Adding Mn element to aluminum alloy has a certain solid solution strengthening eﬀect. In addition, the Al6Mn phase can hinder the growth of recrystallized grains, reﬁne the grains, and improve the strength of the alloy. For Scandium (Sc) addition, the Al3Sc phase with an L12 structure can prevent recrystallization and promote ﬁne grain strengthening and ﬁne precipitation strengthening. Sc is considered to be the most eﬀective alloying element for aluminum alloys. Al3Sc precipitates show small lattice mismatches and low interfacial energy in aluminum matrix, and the low diﬀusivity of Sc also helps to improve thermal stability [20]. The addition of Zr can further reduce the lattice

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mismatch, because Zr has a lower diﬀusivity, and can replace some Sc atoms to form a protective

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3.2. Hot Deformation Behavior

In order to measure the validity of the thermal compression data, we veriﬁed the expansion coeﬃcient B of the material; Equation (1) is as follows [24]:

L0d20

B = L d2

(1)

ff

In Equation (1), L0 is the original height of the sample, d0 is the original diameter of the sample, Lf is the average height of the sample after compression (measured at the center axis of the cylinder and every 120◦ at the edge, and the average height is based on these four locations), and df is the average diameter of the sample after compression (taken the average diameter at top, middile, and bottom heights). When B ≥ 0.9, the results of the thermal compression experiment are valid. After measurement

and calculation, the thermal compression experimental data obtained by all samples are veriﬁed to

be valid. On the basis of the true stress–strain curves of Al–Mn–Sc alloy compressed at diﬀerent temperatures

and strain rates (Figure 3), the ﬂow behavior of the Al–Mn–Sc alloy was aﬀected by the deformation

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temperature and strain rate. Work hardening caused by dislocation generation and entanglement resulted in an increase in ﬂow stress at small strains. A further increase in strain led to a dynamic softening eﬀect, which gradually overweighed the work hardening eﬀect. As a result, the ﬂow stress ﬁrst increased to a peak and then slightly decreased with strains. In addition, the ﬂow stress decreased substantially with increasing temperatures and reducing strain rates. This indicates the dynamic softening is more suﬃcient at high temperatures and low strain rates, which is consistent with the previous observations in other hot compressed Al alloys [25,26]. Dynamic softening, including dynamic recovery (DRV) or dynamic recrystallization (DRX), reduces the dislocation density in contrast to work hardening. A lower strain rate allows a longer time to accumulate the activation energy, which reduces the stress in turn.

3.3. Constitutive Equations

Deformation temperature and strain rate are important factors controlling the hot deformation ﬂow stress. The hyperbolic sinusoidal constitutive equation in the Arrhenius model has been widely used to describe the complex relationships among ﬂow stress, heat distortion temperature, and strain rate [8–19,27]. Sellars and McTegart proposed the use of a hyperbolic sine function including the thermal deformation activation energy Q and temperature T to describe the thermal activation behavior of the material. The relation among the strain rate, ﬂow stress, and deformation temperature can be established by the following equation [28]:

ε. = AF(σ) exp(−Q/RT)

(2)

where ε. is the strain rate, A is the structural factor, F(σ) is a function of stress, σ is the ﬂow stress, Q is the activation energy, R is the gas constant, and T is the absolute temperature. At diﬀerent stress conditions, F(σ) has the following three expressions:

σn

(ασ ≤ 0.8)

F(σ) = exp(βσ) (ασ > 0.8)

(3)

[sin h(ασ)]n ( f or all σ)

where α is the stress level parameter and n is the strain hardening index, α = β/n. ασ ≤ 0.8 represents a low stress level, and ασ > 0.8 represents a high stress level. Substituting diﬀerent stress levels of Equation (3) into Equation (2) leads to Equations (4)–(6):

ε. = A1σn1

(4)

ε. = A2 exp(βσ)

(5)

ε. = A[sin h(ασ)]n exp(−Q/RT)

(6)

In order to determine the constant terms in Equations (4) and (5), the natural logarithm is applied on both sides of the equation, and the following equations can be obtained:

ln ε. = ln A1 + n1 ln σ

(7)

ln ε. = ln A2 + βσ

(8)

On the basis of Equations (7) and (8), the relationship between the stress and strain rate (Figure 4)

can be obtained by plotting using measured peak stress (Table 2). The curve ﬁtting was conducted by a linear least-squares regression. The average slopes of all the ﬁtted lines are the constant n1 and β, respectively (Figure 4a,b). The obtained n1 is 13.058, and β is 0.116. Hence, α is calculated at 0.009.

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3.2. Hot Deformation Behavior

In order to measure the validity of the thermal compression data, we verified the expansion coefficient B of the material; Equation (1) is as follows [24]:

=

(1)

In Equation (1), L0 is the original height of the sample, d0 is the original diameter of the sample, Lf is the average height of the sample after compression (measured at the center axis of the cylinder and every 120° at the edge, and the average height is based on these four locations), and df is the average diameter of the sample after compression (taken the average diameter at top, middile, and bottom heights). When B ≥ 0.9, the results of the thermal compression experiment are valid. After measurement and calculation, the thermal compression experimental data obtained by all samples are verified to be valid.

On the basis of the true stress–strain curves of Al–Mn–Sc alloy compressed at different temperatures and strain rates (Figure 3), the flow behavior of the Al–Mn–Sc alloy was affected by the deformation temperature and strain rate. Work hardening caused by dislocation generation and entanglement resulted in an increase in flow stress at small strains. A further increase in strain led to a dynamic softening effect, which gradually overweighed the work hardening effect. As a result, the flow stress first increased to a peak and then slightly decreased with strains. In addition, the flow stress decreased substantially with increasing temperatures and reducing strain rates. This indicates the dynamic softening is more sufficient at high temperatures and low strain rates, which is consistent with the previous observations in other hot compressed Al alloys [25,26]. Dynamic softening, including dynamic recovery (DRV) or dynamic recrystallization (DRX), reduces the dislocation

Figure 3. True stress–strain curves of the Al–Mn–Sc alloy deformed at various temperatures from 330 toF4i9g0u◦reC3w. Titrhudeisﬀtereresns–tssttrraaiinncruartvesesato(fat)h0e.0A1l–sM−1n, –(bS)c0a.l1losy−1d,e(fco)r1mse−d1,aatnvdar(dio)u1s0tse−m1p. eratures from 330

to 490 °C with different strain rates at (a) 0.01 s−1, (b) 0.1 s−1, (c) 1 s−1, and (d) 10 s−1.

3.3. Constitutive Equations

Deformation temperature and strain rate are important factors controlling the hot deformation flow stress. The hyperbolic sinusoidal constitutive equation in the Arrhenius model has been widely used to describe the complex relationships among flow stress, heat distortion temperature, and strain

Strain Rate/s−1

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0.01 0.1 1 10

Temperature/°C

330

370

410

450 490

116

110

92

68

59

153

129

108

90

73

170

143

132

115

92

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183

173

151

120 115

Figure 4. Linear curve ﬁttings of (a) lnε. vs. lnσ, (b) lnε. vs. σ, (c) lnε. vs. ln[sinh(ασ)], and (d) 1/T vs. Filgnu[srienh4(.αLσi)n].ear curve fittings of (a) ln vs. lnσ, (b) ln vs. σ, (c) ln vs. ln[sinh(ασ)], and (d) 1/T vs.

ln[sinh(ασ)]. Table 2. Peak stress (MPa) values of Al–Mn–Sc alloy samples deformed at diﬀerent conditions.

By applying Equation (6) to all stress levels, ETqeumapteiorantu(r8e)/◦cCan be obtained by taking the natural

logarithm:

Strain Rate/s−1

330

370

410

450

490

0.0l1n = 1ln16 sinh110 +92ln 68 / 59

(9)

0.1

153

129

108

90

73

1

170

143

132

115

92

10

183

173

151

120

115

By applying Equation (6) to all stress levels, Equation (8) can be obtained by taking the natural

logarithm:

ln ε. = n2 ln[sinh(ασ)] + ln A − Q/RT

(9)

The following equation of the hot activation energy Q can be obtained from Equation (9):

Q = R ln A − ln ε. + n2 ln[sinh(ασ)]

(10)

T

At a certain strain and strain rate, Equation (11) can be derived from Equation (10):

Q = ∂ ln[sinh(ασ)] (11)

Rn2

∂(1/T)

In Equation (9), n is the average slope of the linear relationship between ln ε. and ln[sinh(ασ)], and Q/Rn is the average slope of the linear relationship between ln[sinh(ασ)] and (1/T) in Equation (11). As shown in the Figure 4c,d, the mean values of these two slopes are 9.851 and 2449.059 respectively. As we know the value of n2 and R, the hot deformation activation energy Q of the Al–Mn–Sc alloy

elationship between strain rate and temperature can be expressed by the Z parameter, which is

emperature compensated strain rate factor. Hence, Equation (2) can be further derived to Equati

12):

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= exp = sinh (12

is determined at 200.581 kJ·mol−1. According to Zener and Hollomon [27,29], the strain rate of high

By applytbieenmtwgpeeterhnateustrrneaaipntlaursarttieac aldnledofogtremamrapitietorhnamtuisrecioncnatnErobqlelueedaxtpbiyroestnhsee(dh1be2ay)t,tahwcetiZevapctaiaornanmpoertobectre,aswsi,nhaicnthhdietshafeotrelemlloaptwieornaisntuhgirpeequation:

compensated strain rate factor. Hence, Equation (2) can be further derived to Equation (12):

ln = ln + . =Q ln sinh

Z = ε exp

= A[sin h(ασ)]n3

RT

+ ln

(13

(12)

By substitutBiny gappthlyeingvtahleuneatsuroalfloTgaarinthdm inlnEquiantioton (1E2q), uwae tciaonnob(ta1in3)th, etfhoellovwainlgueequoaftiotnh: e Zener–Hollom

parameter (lnZ) at different temperatures. anQd strain rates can be obtained. As shown in Figure 5 s worth noting that the value chanlgn Ze =trelnnεd+ oRfTl=nZn3 ilns[stihnhe(αsσa)m] +elnaAs the flow stress, an(d13)increases as t

deformation temBpyesruabtsutitruetindg ethcerevaalsueessofoTr atnhdelnsε. tirnatoinEqruaattieoni(n13c)r, ethaesveaslu. eTohf tehesZleonpere–Haotllo9m.9on78 is comput

between lnZ apanrdamlente[rs(ilnnZh)(aαt dσi)ﬀ]e,rewnthteimchperlaetaudressatnod stthraeinsrtarteuscctaun rbae lobftaacinteodr. AAs sahtow8n.1in71Fig×ur1e051,3it. iIsn summary,

worth noting that the value change trend of lnZ is the same as the ﬂow stress, and increases as the

onstant valudeesfoarmreatidonetteemrpmeriantuerde daecbreoavsees .orTthheestcraoinnrsatteitiunctrievaseese. Tqhueasltoipoenatf9o.9r78tihs ecomhoputtecdobmetwpereenssed Al–Mn–

alloy can thenlnbZeanpdrlens[seinnht(eαdσ)]i,nwhEicqhuleaatdisotno t(h1e4st)r.uctural factor A at 8.171 × 1013. In summary, all constant

values are determined above. The constitutive equation for the hot compressed Al–Mn–Sc alloy can

200581 then be presented in Equation (14).

.

= 8.171 10 sinh 0.009 exp ε. = 8.171 × 1013[sin h(0.009σ)]9.987 exp (− 200581 ) RT

(14

(14)

Figure 5. Linear relationship between ln[sinh(ασ)] and the Zener–Hollomon parameter, lnZ.

Figure 5. Linear relationship between ln[sinh(ασ)] and the Zener–Hollomon parameter, lnZ.

In general, the activation energy Q is closely related to the thermodynamic mechanism of dislocation movement and can reﬂect the processability of the material. It is thus meaningful to

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conditions are shown in Table 3.

understand the eAffseschtowofn pinrToacbeles3s,itnhge dpefaorrmamatieontearcstivoantioancetnievrgaytioofntheenAel–rMgny–.Sc alloy decreases with

increasing temperatures and strain rates. When the hot working conditions are changed in a wide range, the obtained deformation activation energy is also in a large range, which indicates that the alloy is sensitive to hot working deformation conditions.

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Table 3. The activation barriers Q (kJ·mol−1) at diﬀerent conditions in the isothermal deformation of Al–Mn–Sc alloy.

Strain Rate/s−1

0.01 0.1 1 10

330

210.439 231.688 197.168 190.941

Temperature/◦C

370

410

450

222.745 245.236 208.697 202.106

208.569 229.629 195.415 189.244

199.904 220.089 187.297 181.382

490

180.28 198.486 168.913 163.578

First, the activation energy decreases with increasing strain rates. This phenomenon should be related to dislocation movement. The external stress increases with increasing strain rates, and the shear stress applied in the dislocation sliding direction also increases [30]. Therefore, dislocation motion can be activated easily at a higher stress and lower activation barrier condition [31].

Second, the activation energy decreases with increasing deformation temperatures owing to the eﬀect of dislocation density. At higher temperatures, the rearrangement of dislocations during DRV and the formation and growth of recrystallized grains during DRX will be promoted, leading to a reduction in dislocation density. Therefore, as the deformation temperature increases, the resistance to dislocation movement decreases.

3.4. Processing Map

The thermo-mechanical processing maps (PMs) were extensively used to describe the microstructure evolution and establish the processing window, which provide guides for the industrial manufacturing such as rolling, extrusion, and forging [10,14,32,33]. PMs can be obtained by the dissipation power diagram and the processing instability diagram. On the basis of the principles of large plastic deformation continuum mechanics, physical system simulation, and irreversible thermodynamics theory, Prasad et al. established a dynamic material model (DMM), which regards the hot deformation process as a closed thermodynamic system [34].

During thermo-mechanical processing, the energy P obtained by the material per unit volume within a certain time can be divided into two parts according to the report by Prasad et al. [34]: (1) The energy consumed by plastic deformation is represented by G. Most of G is converted into heat, and a small portion is stored as crystal defect energy. (2) The energy consumed by the microstructure evolution during hot deformation is J, which represents the evolution of the microstructure during the deformation process, such as DRV, DRX, internal cracks (voids formation and wedge cracks), dislocations, growth of grains and precipitates under dynamic conditions, spheroidization of needle-like structures, phase transitions [35], and so on. Therefore, the total energy P can be expressed as follows:

ε.

σ

P = G + J = σdε. + ε. dσ = σε.

(15)

0

0

For most pure metal or low alloy materials, the energy distribution relationship between G and J satisﬁes Equation (16) when the temperature and strain rate are constant:

∂J ε. ∂σ ∂ ln σ

m = ∂G = σ∂ε. = ∂ ln ε.

(16)

where m is the strain rate sensitivity factor and is independent to strain. For the condition of the ideal linear dissipation (m = 1), J has the maximum value at Jmax = P/2. The ratio between J and Jmax was determined by the dissipation eﬃciency factor (η) [34]:

η = J = P − G = 2m

(17)

Jmax P/2 1 + m

linear dissipation (m = 1), J has the maximum value at Jmax = P/2. The ratio between J and Jmax was determined by the dissipation efficiency factor (ƞ) [34]:

= = /2 = 12+ (17)

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where ƞ represents a dimensionless parameter that describes the ratio between the energy consumed

by the microstructure evolution and the total energy consumed by a linear hot deformation. ƞ is also

wtheermreeηdraeps rtehseenmtsicarodsitmruecntsuiroentlerasscep.aDraommeatienrsthwaitthdehsicgrhibdesistshipeartaitoino befeftiwcieeenncythfeacetnoerrsgiyncPoMnssuimndedicate

bythtehfeormmicartoiosntruocftsupreeceiavloslturtuioctnuraensdotrhoectcoutrarleennceerogfyscooftnesnuimngedbebhyavaiolirnse, asruchhotasdeDfRorXmaantidonD.RηV,isand

alpsoostseirbmleedloacsalthdeemfoircmroasttirounctuinrestatrbaicliet.y.DTohmearienfsorwe,iththheiguhndstiassbilpeatrieognioenﬃcoief ntchyefamctaotresriianl PiMn shot

inddeifcoartme tahtieofnormmuasttiobne oidf esnpteicfiieadl sitnruocrtduererstoordoectecrumrriennecea osuf istoafbtelenipnrgocbeeshsainvgiowrsi,nsduocwh a[s34D,3R5X]. aOnndthe

DbRaVs,isanodf pthosesipbrlienlcoicpalledoeffoirrmreavteiorsnibinlestathbeilrimty.odThyneraemfoirces, tohfeluarngsetabplleasrteigciodnefoofrtmheatmioantepriraolpinosheodt by

dPefroarsmada,titohne minustsatbbileitiydecnrittieﬁreiodninisoersdtearbltioshdeedtearsmfionleloawssu:itable processing window [34,35]. On the

basis of the principle of irreversible thermodynamics of large plastic deformation proposed by Prasad,

the instability criterion is established as follows:

(18)

dJ

.

<

J

.

(18)

. = ∂ lldnnε mml+n1ε+ 1 + 0 (19)

ξε =

. +m<0

(19)

∂ ln ε

ThTehevavlauleuseosfomf ,mη,,ηa,nadnξd

ξ were calculated by cubic spline interpolation. The equivalent maps were calculated by cubic spline interpolation. The equivalent maps of

of

the dissipate the dissipated

dpopwowereηr

aηnadntdhtehiensintasbtailbitiylitfyacftaocrtoξraξreaprelopttleodtteind

in Figure 6a,b, respectivel Figure 6a,b, respectively.

y

.

Figure 6. Power dissipation eﬃciency map (a), instability map (b), and processing map (c) of Al–Mn–Sc

alFloiyguatreε =6.0P.4o.wer dissipation efficiency map (a), instability map (b), and processing map (c) of Al– Mn–Sc alloy at ɛ = 0.4.

A domain with a higher dissipation eﬃciency factor indicates that more energy is dissipated in microsAtrudcotumraeienvwoliuthtioanh, iwghhiecrhdisispsirpeafetriorendeafsficthieenpcryofcaecstsoinrginwdiincdatoews tfhoarthmotodreefeonrmeragtyioins.dFiisgsuipreat6ead in shmoiwcrsoastrcuocnttuorueremvoalputoiof nη, awt hεic=h 0is.4p. rWefeitrhretdheastetmhepperraotcuersessinagt w42i0n–d4o7w5 ◦fCorahnodt dtheefosrtmraaintiorna.teFiagture 0.01–0.022 s−1, the dissipated power increases to the maximum value of 26%. Figure 6b shows the instability map of the Al–Mn–Sc alloy at ε = 0.4, and the shaded domains (the negative instability

factor) represents the unstable windows. When the deformation temperature is low and the strain rate

is large (i.e., a higher Z parameter), the instable deformation is more likely to occur. Hot processing in

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these parameters is prone to introduce defects and is not eﬀective in facilitating the recrystallization.

A suitable processing window should be the rest region outside the regions mentioned above.

Figure 6c is the PM generated by superimposing the dissipated power and the ﬂow instability

diagrams when the strain is ﬁxed at 0.4. Comparing the samples under the two deformation conditions of 370 ◦C/1 s−1 (stable region) and 490 ◦C/10 s−1 (unstable region) in Figure 6c, it is apparent that severe cracking happened in 490 ◦C/10 s−1.

The peak domain (26%) with deformation temperatures and strain rates at 420–475 ◦C and 0.01–0.022 s−1 is the most suitable processing window. The strain rate is low, but the deformation

temperature is high, and there should be enough driving force to promote the dynamic recovery or

dynamic recrystallization to optimize the microstructure. Although the dissipated power value is low at 370 ◦C, regions A and B in Figure 6c are also interesting by considering that most conventional forming processes operate with forming rates signiﬁcantly above 1s−1.

3.5. Microstructure Analysis

Many studies have shown that the microstructure after hot deformation is closely related to the Zener–Hollomon (Z) parameter [8,36–39]. The Z parameter was used to evaluate the hot deformation behaviours, and a larger lnZ corresponds to a higher strain rate or a lower deformation temperature. In order to further verify the feasibility of the hot processing map and understand the deformation mechanism, the deformed microstructures processed at the ﬁve regions (A) to (E) in Figure 6c are presented in Figure 7, and the corresponding lnZ are listed in Table 4. Figure 7 shows that grains are aligned in the transverse direction and intermetallic compounds are distributed in the matrix. As shown in Table 4, the lnZ value decreases with reducing deformation rates when the deformation temperature is 370 ◦C. Most of the grain boundaries remain straight, and DRV is the main softening mechanism in Figure 7a–c. The dislocations in this process change from the mixed arrangement of high-energy states to the regular arrangement of low-energy states, forming vertically arranged dislocation walls [8,33]. The strain rates of Figure 7a,d, and e are ﬁxed at 0.01 s−1, and the value of lnZ decreases with an increasing deformation temperature, as shown in Table 4. The grain boundary is no longer straight and becomes relatively curved at high deformation temperatures. Moreover, some small grains appear at grain boundaries in sample deformed at 490 ◦C (Figure 7e), which are preferred locations for recrystallization [40]. Therefore, in these cases, DRX is the main mechanism for the hot deformation. In Figure 7e, the value of lnZ is the smallest with the deformation temperature at 490 ◦C and strain rate at 0.01 s−1, which leads to a substantially increased DRX and is consistent with the ﬁndings in previous studies [39–41]. DRX is beneﬁcial for the hot deformation process, which provides a stable ﬂow and results in a good processability. A high temperature accelerates the diﬀusion of atoms and promotes the microstructure change of materials. A reduced dislocation density achieved by either DRV or DRX is able to compensate the work hardening eﬀect, which leads to a steady ﬂow in thermo-mechanical processing. In addition, a low strain rate provides suﬃcient time for microstructural evolution during plastic deformation. Thus, high deformation temperature and low strain rates are favorable to achieve a steady-state deformation, and a processing window is proposed at 420–475 ◦C/0.01–0.022 s−1 for the new Al–Mn–Sc alloy.

Table 4. lnZ values of Al–Mn–Sc alloy samples deformed at diﬀerent regions in the PM in Figure 6c.

Regions in PM

A B C D E

Temperature/◦C

370 370 370 410 490

Strain Rate/s−1

10 1 0.1 0.01 0.01

LnZ

39.823 37.520 35.217 30.718 26.317

Article

Hot Deformation Behavior of a New Al–Mn–Sc Alloy

Weiqi Kang 1, Yi Yang 1,* , Sheng Cao 2,* , Lei Li 3, Shewei Xin 3, Hao Wang 4 , Zhiqiang Cao 1, Enquan Liang 5, Xi Zhang 5 and Aijun Huang 6

1 School of Materials Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China; [email protected] (W.K.); [email protected] (Z.C.)

2 School of Materials, University of Manchester, Oxford Road, Manchester M13 9PL, UK 3 Northwest Institute for Non-ferrous Metal Research, Xi’an 710016, China; [email protected] (L.L.);

[email protected] (S.X.) 4 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China; [email protected] 5 Shanghai Aircraft Design and Research Institute, Shanghai 201210, China; [email protected] (E.L.);

[email protected] (X.Z.) 6 Department of Materials Science and Engineering, Monash University, Clayton, VIC 3800, Australia;

[email protected] * Correspondence: [email protected] (Y.Y.); [email protected] (S.C.)

Received: 4 November 2019; Accepted: 13 December 2019; Published: 19 December 2019

Abstract: The hot deformation behavior of a new Al–Mn–Sc alloy was investigated by hot compression conducted at temperatures from 330 to 490 ◦C and strain rates from 0.01 to 10 s−1. The hot deformation behavior and microstructure of the alloy were signiﬁcantly aﬀected by the deformation temperatures and strain rates. The peak ﬂow stress decreased with increasing deformation temperatures and decreasing strain rates. According to the hot deformation behavior, the constitutive equation was established to describe the steady ﬂow stress, and a hot processing map at 0.4 strain was obtained based on the dynamic material model and the Prasad instability standard, which can be used to evaluate the hot workability of the alloy. The developed hot processing diagram showed that the instability was more likely to occur in the higher Zener–Hollomon parameter region, and the optimal processing range was determined as 420–475 ◦C and 0.01–0.022 s−1, in which a stable ﬂow and a higher power dissipation were achieved.

Keywords: Al–Mn–Sc alloy; hot deformation; ﬂow stress; processing map; dynamic recrystallization

1. Introduction

Casting and wrought aluminum (Al) alloys have been widely used as structural materials in aerospace industries owing to their high speciﬁc strength (strength to weight ratio), excellent fatigue resistance, and good formability [1–3]. The strength mainly arises from precipitation strengthening achieved from aging treatment [4–6]. Recently, a new high strength Al–Mn–Sc alloy has been developed by Jia et al. [7] using selective laser melting (SLM). The supersaturated Mn and Sc signiﬁcantly improve the mechanical property through solid solution strengthening of Mn and precipitation strengthening of nano-sized Al3Sc precipitates, which lead to a superior yield strength at 560 MPa and a good ductility at 18%. Such mechanical properties are attractive for aerospace industries. However, this Al–Mn–Sc alloy has only been studied in the additive manufactured condition, but has not been investigated in other forms like casting and wrought products.

After direct chill casting, Al ingots generally need various thermo-mechanical processing steps to obtain diﬀerent types of semi-ﬁnished products. The microstructure of the material depends on the thermo-mechanical processing parameters, which also determine the quality of the formed part. Thus, it is necessary to understand the inﬂuence of deformation parameters on hot deformation behavior

Materials 2020, 13, 22; doi:10.3390/ma13010022

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and microstructure in this Al–Mn–Sc alloy. In general, the isothermal compression test is an appropriate method to study the hot deformation characteristics of materials [8,9]. The relationships among the ﬂow stress, strain, strain rate, and deformation temperature can be used to establish the hot deformation constitutive equation, and its hot activation energy can be calculated. The hot deformation behavior can be quantitatively described and applied to simulate the dynamic response of the material under speciﬁc loading conditions. In addition, the hot processing map is constructed to predict the plastic deformation mechanism and the unstable deformation domain in various deformation conditions, which provides insights into the optimization of thermo-mechanical processing. This method has been widely used in various alloys, such as Al alloys [8–10], Mg alloys [11–13], Ti alloys [14–16], and steel [17–19].

The present work aims to investigate the hot deformation behavior, to reveal the microstructure change, and to obtain the hot processing map of the casting Al–Mn–Sc alloy over wide temperature and strain rate ranges. The results will provide guides on its hot deformation processing and industrial applications.

2. Materials and Methods

The raw material (Table 1) used in this experiment was a casting ingot with a diameter of 150 mm. Cylindrical samples (ϕ10 × 15 mm) were sectioned by Electrical Discharge Machining (EDM) wire-cut from the ingot and then ground by SiC abrasive sandpaper before subjecting to isothermal hot deformation experiments conducted on a Gleeble-3800 system. According to the deformation conditions of aluminum alloy in normal industrial production, the test was carried out at temperatures from 330 to 490 ◦C and strain rates from 0.01 to 10 s−1. Graphite sheet was used as a lubricant between the compression plate and the sample to reduce friction. Before the compression test, the samples were solution treated at 500 ◦C for 5 min followed by gas quench in the Gleeble chamber. These samples were heated again to the testing target temperature at a ramping rate of 10 ◦C/s and held for 5 min to eliminate the thermal gradients before compression. Isothermal hot deformation experiments were conducted afterwards at various temperatures and strain rates. After a 60% deformation, the samples were gas-quenched to room temperature to freeze the microstructure after the hot deformation. The gas-quenched deformed samples were sectioned by EDM wire-cut along the axial direction, which is parallel to the compression direction. A standard metallographic sample preparation and etching by Keller’s solution (1 mL HF + 1.5 mL HCl + 2.5 mL HNO3 + 95 mL H2O) were carried out, and the microstructure characterization was conducted by using a Leica DMi8A light microscope (LM) and a FEI QUANTA 450 scanning electron microscope (SEM) equipped with an energy dispersive X-ray spectrometer (EDS) detector. The grain size was measured by ImageJ software.

Table 1. Composition of the studied Al–Mn–Sc alloy (wt.%).

Mn

Mg

Sc

Zr

Si

Fe

Al

4.3–4.7 1.4–1.6 0.65–0.85 0.7–0.8 <0.1 <0.1 Bal

3. Results and Discussion

3.1. Microstructure of As-Cast Al–Mn–Sc Alloy

Adding Mn element to aluminum alloy has a certain solid solution strengthening eﬀect. In addition, the Al6Mn phase can hinder the growth of recrystallized grains, reﬁne the grains, and improve the strength of the alloy. For Scandium (Sc) addition, the Al3Sc phase with an L12 structure can prevent recrystallization and promote ﬁne grain strengthening and ﬁne precipitation strengthening. Sc is considered to be the most eﬀective alloying element for aluminum alloys. Al3Sc precipitates show small lattice mismatches and low interfacial energy in aluminum matrix, and the low diﬀusivity of Sc also helps to improve thermal stability [20]. The addition of Zr can further reduce the lattice

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mismatch, because Zr has a lower diﬀusivity, and can replace some Sc atoms to form a protective

psrhoetlelcbtiyvseesghrelgl abtyinsgeagroeguantdintghearporuencidpitthaetep, rtehceirpeibtaytef,utrhthereerbeynhfuarnthcienrgetnhheasntcriennggthensitnregnegﬀthecetnainngd

etfhfercmt anl dstatbhielritmya[l21s]t.abTihliteyas[2-c1a].stTmheicraoss-ctraustctmuriecroofstrhuecAtulr–eMonf–tShceaAllol–yM(Fni–gSucreal1l)oyis (cFoimguproese1d) iosf

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lpohnagsleast,ha-nlidkesmphalals-seisz,eadnhdesxmagaolln-sailzaenddhseqxuaagroenpahl aasneds,sdqiustarriebuptheadsiens,thdeisAtrlibmuatetrdixi.nTthe eAtcl hmeadtrsiaxm. Tphlees

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wsiizteh oafnaapvperroaxgiemsaizteelyof3a0pµpmroaxcimcoardteilnyg3t0oµimmaagcecoanrdailnygsisto. image analysis.

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IInn oorrddeerr ttoo identiiffyy these intermetallliicc phasess,, EDS analyses were applied. TThhee llaarrggeerr ssiizzeedd ppoollyyggoonnaallaannddlaltaht-hli-kliekephpahsaesews ewreereenreicnhriecdheindAinl wAitlhwaitshmallsammaolluanmt oofuMntno(fFiMgunre(F2aig,bu)r,ew2hai,cbh), swuhggicehstseudgtgheesytewdetrheeAylw6Menre. TAhle6Mprni.mTahrye Aprl6iMmnarwy aAsli6nManpwolaysgoinnalpsholaypgeoannadl shhaadpsehaanrpd ehdagdeshaanrdp ceodrgneesrsa,nsdhocowrinnegrsa, nshoobwvinogusanfaocbetvigoruoswftahcebteghraovwiothr.bAehftaevriionrt.eArmftertailnlitcergmroetwaltlhic, tghreowprthim, tahreypprhimasaersy gprheawsepsregfreerwenptiraelfleyraetnthiaellpyoalyt gthoenpcorlyngerosn, acnodrnaercso,natninduaoucos nsltainbusohuaps esdlaTbis6MhanpwedasTfi6inManllywoabstaﬁinaeldly. TohbetaEinDeSd.reTshueltsErDeSveraelseudlttshreevheaxlaegdonthael phhexaasegson(Failgpuhreas2ecs) (hFaigvuinrge 2acs)lhigahvtilnyghaigshleigrhMtlyn hcoigmhperarMedn wcoitmhpoatrheedr winittehrmotehtearllinctpehrmaseetsal(lFicigpuhraes2eas,(bF)i,gwuhreic2ha,ibs)s,iwmhiliacrhtios tshime iλla-Ar tl4oMthnerλep-Aolr4tMedninreapoprrteevdioinusa spturedvyio[u22s]s.tTuhdey s[m22a].lleTrh-seizsmedal(l~e1r0-sµizmed) s(~q1u0arµemp)hsaqsuesar(eFipghuarsee2sd(F) iwguere 2edn)riwcheerde einnrAiclh, eSdc,inanAdl,ZSrc,, wanhdicZhrs,hwohuilcdhbsehoAull3d(Sbc,eZAr)l,3a(SscZ,Zrrc)a, nasrZeprlcaacne rseopmlaecoefstohmeeScofathoemSscinatothmesAinl3Sthc.eTAhle3Srce.pTlahceedreSpclaccaend sSecgcreagnasteegtroegthaeteetdogtehoefetdhgeeporfecthipeitparteecsipanitdatfeosramnda fporromteactpivreotsehcetilvl e[2s3h].ell [23].

3.2. Hot Deformation Behavior

In order to measure the validity of the thermal compression data, we veriﬁed the expansion coeﬃcient B of the material; Equation (1) is as follows [24]:

L0d20

B = L d2

(1)

ff

In Equation (1), L0 is the original height of the sample, d0 is the original diameter of the sample, Lf is the average height of the sample after compression (measured at the center axis of the cylinder and every 120◦ at the edge, and the average height is based on these four locations), and df is the average diameter of the sample after compression (taken the average diameter at top, middile, and bottom heights). When B ≥ 0.9, the results of the thermal compression experiment are valid. After measurement

and calculation, the thermal compression experimental data obtained by all samples are veriﬁed to

be valid. On the basis of the true stress–strain curves of Al–Mn–Sc alloy compressed at diﬀerent temperatures

and strain rates (Figure 3), the ﬂow behavior of the Al–Mn–Sc alloy was aﬀected by the deformation

Materials 2020, 13, 22

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temperature and strain rate. Work hardening caused by dislocation generation and entanglement resulted in an increase in ﬂow stress at small strains. A further increase in strain led to a dynamic softening eﬀect, which gradually overweighed the work hardening eﬀect. As a result, the ﬂow stress ﬁrst increased to a peak and then slightly decreased with strains. In addition, the ﬂow stress decreased substantially with increasing temperatures and reducing strain rates. This indicates the dynamic softening is more suﬃcient at high temperatures and low strain rates, which is consistent with the previous observations in other hot compressed Al alloys [25,26]. Dynamic softening, including dynamic recovery (DRV) or dynamic recrystallization (DRX), reduces the dislocation density in contrast to work hardening. A lower strain rate allows a longer time to accumulate the activation energy, which reduces the stress in turn.

3.3. Constitutive Equations

Deformation temperature and strain rate are important factors controlling the hot deformation ﬂow stress. The hyperbolic sinusoidal constitutive equation in the Arrhenius model has been widely used to describe the complex relationships among ﬂow stress, heat distortion temperature, and strain rate [8–19,27]. Sellars and McTegart proposed the use of a hyperbolic sine function including the thermal deformation activation energy Q and temperature T to describe the thermal activation behavior of the material. The relation among the strain rate, ﬂow stress, and deformation temperature can be established by the following equation [28]:

ε. = AF(σ) exp(−Q/RT)

(2)

where ε. is the strain rate, A is the structural factor, F(σ) is a function of stress, σ is the ﬂow stress, Q is the activation energy, R is the gas constant, and T is the absolute temperature. At diﬀerent stress conditions, F(σ) has the following three expressions:

σn

(ασ ≤ 0.8)

F(σ) = exp(βσ) (ασ > 0.8)

(3)

[sin h(ασ)]n ( f or all σ)

where α is the stress level parameter and n is the strain hardening index, α = β/n. ασ ≤ 0.8 represents a low stress level, and ασ > 0.8 represents a high stress level. Substituting diﬀerent stress levels of Equation (3) into Equation (2) leads to Equations (4)–(6):

ε. = A1σn1

(4)

ε. = A2 exp(βσ)

(5)

ε. = A[sin h(ασ)]n exp(−Q/RT)

(6)

In order to determine the constant terms in Equations (4) and (5), the natural logarithm is applied on both sides of the equation, and the following equations can be obtained:

ln ε. = ln A1 + n1 ln σ

(7)

ln ε. = ln A2 + βσ

(8)

On the basis of Equations (7) and (8), the relationship between the stress and strain rate (Figure 4)

can be obtained by plotting using measured peak stress (Table 2). The curve ﬁtting was conducted by a linear least-squares regression. The average slopes of all the ﬁtted lines are the constant n1 and β, respectively (Figure 4a,b). The obtained n1 is 13.058, and β is 0.116. Hence, α is calculated at 0.009.

Materials 2020, 13, 22 Materials 2018, 11, x FOR PEER REVIEW

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localoticoantisonosf EofDESDaSnaanlyalsyesseisnineaecahchimimaaggee..

3.2. Hot Deformation Behavior

In order to measure the validity of the thermal compression data, we verified the expansion coefficient B of the material; Equation (1) is as follows [24]:

=

(1)

In Equation (1), L0 is the original height of the sample, d0 is the original diameter of the sample, Lf is the average height of the sample after compression (measured at the center axis of the cylinder and every 120° at the edge, and the average height is based on these four locations), and df is the average diameter of the sample after compression (taken the average diameter at top, middile, and bottom heights). When B ≥ 0.9, the results of the thermal compression experiment are valid. After measurement and calculation, the thermal compression experimental data obtained by all samples are verified to be valid.

On the basis of the true stress–strain curves of Al–Mn–Sc alloy compressed at different temperatures and strain rates (Figure 3), the flow behavior of the Al–Mn–Sc alloy was affected by the deformation temperature and strain rate. Work hardening caused by dislocation generation and entanglement resulted in an increase in flow stress at small strains. A further increase in strain led to a dynamic softening effect, which gradually overweighed the work hardening effect. As a result, the flow stress first increased to a peak and then slightly decreased with strains. In addition, the flow stress decreased substantially with increasing temperatures and reducing strain rates. This indicates the dynamic softening is more sufficient at high temperatures and low strain rates, which is consistent with the previous observations in other hot compressed Al alloys [25,26]. Dynamic softening, including dynamic recovery (DRV) or dynamic recrystallization (DRX), reduces the dislocation

Figure 3. True stress–strain curves of the Al–Mn–Sc alloy deformed at various temperatures from 330 toF4i9g0u◦reC3w. Titrhudeisﬀtereresns–tssttrraaiinncruartvesesato(fat)h0e.0A1l–sM−1n, –(bS)c0a.l1losy−1d,e(fco)r1mse−d1,aatnvdar(dio)u1s0tse−m1p. eratures from 330

to 490 °C with different strain rates at (a) 0.01 s−1, (b) 0.1 s−1, (c) 1 s−1, and (d) 10 s−1.

3.3. Constitutive Equations

Deformation temperature and strain rate are important factors controlling the hot deformation flow stress. The hyperbolic sinusoidal constitutive equation in the Arrhenius model has been widely used to describe the complex relationships among flow stress, heat distortion temperature, and strain

Strain Rate/s−1

Materials 2020, 13, 22

0.01 0.1 1 10

Temperature/°C

330

370

410

450 490

116

110

92

68

59

153

129

108

90

73

170

143

132

115

92

6 of 14

183

173

151

120 115

Figure 4. Linear curve ﬁttings of (a) lnε. vs. lnσ, (b) lnε. vs. σ, (c) lnε. vs. ln[sinh(ασ)], and (d) 1/T vs. Filgnu[srienh4(.αLσi)n].ear curve fittings of (a) ln vs. lnσ, (b) ln vs. σ, (c) ln vs. ln[sinh(ασ)], and (d) 1/T vs.

ln[sinh(ασ)]. Table 2. Peak stress (MPa) values of Al–Mn–Sc alloy samples deformed at diﬀerent conditions.

By applying Equation (6) to all stress levels, ETqeumapteiorantu(r8e)/◦cCan be obtained by taking the natural

logarithm:

Strain Rate/s−1

330

370

410

450

490

0.0l1n = 1ln16 sinh110 +92ln 68 / 59

(9)

0.1

153

129

108

90

73

1

170

143

132

115

92

10

183

173

151

120

115

By applying Equation (6) to all stress levels, Equation (8) can be obtained by taking the natural

logarithm:

ln ε. = n2 ln[sinh(ασ)] + ln A − Q/RT

(9)

The following equation of the hot activation energy Q can be obtained from Equation (9):

Q = R ln A − ln ε. + n2 ln[sinh(ασ)]

(10)

T

At a certain strain and strain rate, Equation (11) can be derived from Equation (10):

Q = ∂ ln[sinh(ασ)] (11)

Rn2

∂(1/T)

In Equation (9), n is the average slope of the linear relationship between ln ε. and ln[sinh(ασ)], and Q/Rn is the average slope of the linear relationship between ln[sinh(ασ)] and (1/T) in Equation (11). As shown in the Figure 4c,d, the mean values of these two slopes are 9.851 and 2449.059 respectively. As we know the value of n2 and R, the hot deformation activation energy Q of the Al–Mn–Sc alloy

elationship between strain rate and temperature can be expressed by the Z parameter, which is

emperature compensated strain rate factor. Hence, Equation (2) can be further derived to Equati

12):

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= exp = sinh (12

is determined at 200.581 kJ·mol−1. According to Zener and Hollomon [27,29], the strain rate of high

By applytbieenmtwgpeeterhnateustrrneaaipntlaursarttieac aldnledofogtremamrapitietorhnamtuisrecioncnatnErobqlelueedaxtpbiyroestnhsee(dh1be2ay)t,tahwcetiZevapctaiaornanmpoertobectre,aswsi,nhaicnthhdietshafeotrelemlloaptwieornaisntuhgirpeequation:

compensated strain rate factor. Hence, Equation (2) can be further derived to Equation (12):

ln = ln + . =Q ln sinh

Z = ε exp

= A[sin h(ασ)]n3

RT

+ ln

(13

(12)

By substitutBiny gappthlyeingvtahleuneatsuroalfloTgaarinthdm inlnEquiantioton (1E2q), uwae tciaonnob(ta1in3)th, etfhoellovwainlgueequoaftiotnh: e Zener–Hollom

parameter (lnZ) at different temperatures. anQd strain rates can be obtained. As shown in Figure 5 s worth noting that the value chanlgn Ze =trelnnεd+ oRfTl=nZn3 ilns[stihnhe(αsσa)m] +elnaAs the flow stress, an(d13)increases as t

deformation temBpyesruabtsutitruetindg ethcerevaalsueessofoTr atnhdelnsε. tirnatoinEqruaattieoni(n13c)r, ethaesveaslu. eTohf tehesZleonpere–Haotllo9m.9on78 is comput

between lnZ apanrdamlente[rs(ilnnZh)(aαt dσi)ﬀ]e,rewnthteimchperlaetaudressatnod stthraeinsrtarteuscctaun rbae lobftaacinteodr. AAs sahtow8n.1in71Fig×ur1e051,3it. iIsn summary,

worth noting that the value change trend of lnZ is the same as the ﬂow stress, and increases as the

onstant valudeesfoarmreatidonetteemrpmeriantuerde daecbreoavsees .orTthheestcraoinnrsatteitiunctrievaseese. Tqhueasltoipoenatf9o.9r78tihs ecomhoputtecdobmetwpereenssed Al–Mn–

alloy can thenlnbZeanpdrlens[seinnht(eαdσ)]i,nwhEicqhuleaatdisotno t(h1e4st)r.uctural factor A at 8.171 × 1013. In summary, all constant

values are determined above. The constitutive equation for the hot compressed Al–Mn–Sc alloy can

200581 then be presented in Equation (14).

.

= 8.171 10 sinh 0.009 exp ε. = 8.171 × 1013[sin h(0.009σ)]9.987 exp (− 200581 ) RT

(14

(14)

Figure 5. Linear relationship between ln[sinh(ασ)] and the Zener–Hollomon parameter, lnZ.

Figure 5. Linear relationship between ln[sinh(ασ)] and the Zener–Hollomon parameter, lnZ.

In general, the activation energy Q is closely related to the thermodynamic mechanism of dislocation movement and can reﬂect the processability of the material. It is thus meaningful to

In generuanld, etrhstaendatchteiveﬀaetcitoonf preocneessrigngypaQramiestercsloonseacltyivartieolnaetneedrgyt. o the thermodynamic mechanism dislocation moveAmcceorndtingatnodEqcuaatnionrse(9f)leancdt (t1h1)e, thpe raoctciveastisoanbenileirtgyiesoofbtatihneed munadetrevrairaiol.usIdt eifosrmthatuiosn meaningful

conditions are shown in Table 3.

understand the eAffseschtowofn pinrToacbeles3s,itnhge dpefaorrmamatieontearcstivoantioancetnievrgaytioofntheenAel–rMgny–.Sc alloy decreases with

increasing temperatures and strain rates. When the hot working conditions are changed in a wide range, the obtained deformation activation energy is also in a large range, which indicates that the alloy is sensitive to hot working deformation conditions.

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Table 3. The activation barriers Q (kJ·mol−1) at diﬀerent conditions in the isothermal deformation of Al–Mn–Sc alloy.

Strain Rate/s−1

0.01 0.1 1 10

330

210.439 231.688 197.168 190.941

Temperature/◦C

370

410

450

222.745 245.236 208.697 202.106

208.569 229.629 195.415 189.244

199.904 220.089 187.297 181.382

490

180.28 198.486 168.913 163.578

First, the activation energy decreases with increasing strain rates. This phenomenon should be related to dislocation movement. The external stress increases with increasing strain rates, and the shear stress applied in the dislocation sliding direction also increases [30]. Therefore, dislocation motion can be activated easily at a higher stress and lower activation barrier condition [31].

Second, the activation energy decreases with increasing deformation temperatures owing to the eﬀect of dislocation density. At higher temperatures, the rearrangement of dislocations during DRV and the formation and growth of recrystallized grains during DRX will be promoted, leading to a reduction in dislocation density. Therefore, as the deformation temperature increases, the resistance to dislocation movement decreases.

3.4. Processing Map

The thermo-mechanical processing maps (PMs) were extensively used to describe the microstructure evolution and establish the processing window, which provide guides for the industrial manufacturing such as rolling, extrusion, and forging [10,14,32,33]. PMs can be obtained by the dissipation power diagram and the processing instability diagram. On the basis of the principles of large plastic deformation continuum mechanics, physical system simulation, and irreversible thermodynamics theory, Prasad et al. established a dynamic material model (DMM), which regards the hot deformation process as a closed thermodynamic system [34].

During thermo-mechanical processing, the energy P obtained by the material per unit volume within a certain time can be divided into two parts according to the report by Prasad et al. [34]: (1) The energy consumed by plastic deformation is represented by G. Most of G is converted into heat, and a small portion is stored as crystal defect energy. (2) The energy consumed by the microstructure evolution during hot deformation is J, which represents the evolution of the microstructure during the deformation process, such as DRV, DRX, internal cracks (voids formation and wedge cracks), dislocations, growth of grains and precipitates under dynamic conditions, spheroidization of needle-like structures, phase transitions [35], and so on. Therefore, the total energy P can be expressed as follows:

ε.

σ

P = G + J = σdε. + ε. dσ = σε.

(15)

0

0

For most pure metal or low alloy materials, the energy distribution relationship between G and J satisﬁes Equation (16) when the temperature and strain rate are constant:

∂J ε. ∂σ ∂ ln σ

m = ∂G = σ∂ε. = ∂ ln ε.

(16)

where m is the strain rate sensitivity factor and is independent to strain. For the condition of the ideal linear dissipation (m = 1), J has the maximum value at Jmax = P/2. The ratio between J and Jmax was determined by the dissipation eﬃciency factor (η) [34]:

η = J = P − G = 2m

(17)

Jmax P/2 1 + m

linear dissipation (m = 1), J has the maximum value at Jmax = P/2. The ratio between J and Jmax was determined by the dissipation efficiency factor (ƞ) [34]:

= = /2 = 12+ (17)

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where ƞ represents a dimensionless parameter that describes the ratio between the energy consumed

by the microstructure evolution and the total energy consumed by a linear hot deformation. ƞ is also

wtheermreeηdraeps rtehseenmtsicarodsitmruecntsuiroentlerasscep.aDraommeatienrsthwaitthdehsicgrhibdesistshipeartaitoino befeftiwcieeenncythfeacetnoerrsgiyncPoMnssuimndedicate

bythtehfeormmicartoiosntruocftsupreeceiavloslturtuioctnuraensdotrhoectcoutrarleennceerogfyscooftnesnuimngedbebhyavaiolirnse, asruchhotasdeDfRorXmaantidonD.RηV,isand

alpsoostseirbmleedloacsalthdeemfoircmroasttirounctuinrestatrbaicliet.y.DTohmearienfsorwe,iththheiguhndstiassbilpeatrieognioenﬃcoief ntchyefamctaotresriianl PiMn shot

inddeifcoartme tahtieofnormmuasttiobne oidf esnpteicfiieadl sitnruocrtduererstoordoectecrumrriennecea osuf istoafbtelenipnrgocbeeshsainvgiowrsi,nsduocwh a[s34D,3R5X]. aOnndthe

DbRaVs,isanodf pthosesipbrlienlcoicpalledoeffoirrmreavteiorsnibinlestathbeilrimty.odThyneraemfoirces, tohfeluarngsetabplleasrteigciodnefoofrtmheatmioantepriraolpinosheodt by

dPefroarsmada,titohne minustsatbbileitiydecnrittieﬁreiodninisoersdtearbltioshdeedtearsmfionleloawssu:itable processing window [34,35]. On the

basis of the principle of irreversible thermodynamics of large plastic deformation proposed by Prasad,

the instability criterion is established as follows:

(18)

dJ

.

<

J

.

(18)

. = ∂ lldnnε mml+n1ε+ 1 + 0 (19)

ξε =

. +m<0

(19)

∂ ln ε

ThTehevavlauleuseosfomf ,mη,,ηa,nadnξd

ξ were calculated by cubic spline interpolation. The equivalent maps were calculated by cubic spline interpolation. The equivalent maps of

of

the dissipate the dissipated

dpopwowereηr

aηnadntdhtehiensintasbtailbitiylitfyacftaocrtoξraξreaprelopttleodtteind

in Figure 6a,b, respectivel Figure 6a,b, respectively.

y

.

Figure 6. Power dissipation eﬃciency map (a), instability map (b), and processing map (c) of Al–Mn–Sc

alFloiyguatreε =6.0P.4o.wer dissipation efficiency map (a), instability map (b), and processing map (c) of Al– Mn–Sc alloy at ɛ = 0.4.

A domain with a higher dissipation eﬃciency factor indicates that more energy is dissipated in microsAtrudcotumraeienvwoliuthtioanh, iwghhiecrhdisispsirpeafetriorendeafsficthieenpcryofcaecstsoinrginwdiincdatoews tfhoarthmotodreefeonrmeragtyioins.dFiisgsuipreat6ead in shmoiwcrsoastrcuocnttuorueremvoalputoiof nη, awt hεic=h 0is.4p. rWefeitrhretdheastetmhepperraotcuersessinagt w42i0n–d4o7w5 ◦fCorahnodt dtheefosrtmraaintiorna.teFiagture 0.01–0.022 s−1, the dissipated power increases to the maximum value of 26%. Figure 6b shows the instability map of the Al–Mn–Sc alloy at ε = 0.4, and the shaded domains (the negative instability

factor) represents the unstable windows. When the deformation temperature is low and the strain rate

is large (i.e., a higher Z parameter), the instable deformation is more likely to occur. Hot processing in

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these parameters is prone to introduce defects and is not eﬀective in facilitating the recrystallization.

A suitable processing window should be the rest region outside the regions mentioned above.

Figure 6c is the PM generated by superimposing the dissipated power and the ﬂow instability

diagrams when the strain is ﬁxed at 0.4. Comparing the samples under the two deformation conditions of 370 ◦C/1 s−1 (stable region) and 490 ◦C/10 s−1 (unstable region) in Figure 6c, it is apparent that severe cracking happened in 490 ◦C/10 s−1.

The peak domain (26%) with deformation temperatures and strain rates at 420–475 ◦C and 0.01–0.022 s−1 is the most suitable processing window. The strain rate is low, but the deformation

temperature is high, and there should be enough driving force to promote the dynamic recovery or

dynamic recrystallization to optimize the microstructure. Although the dissipated power value is low at 370 ◦C, regions A and B in Figure 6c are also interesting by considering that most conventional forming processes operate with forming rates signiﬁcantly above 1s−1.

3.5. Microstructure Analysis

Many studies have shown that the microstructure after hot deformation is closely related to the Zener–Hollomon (Z) parameter [8,36–39]. The Z parameter was used to evaluate the hot deformation behaviours, and a larger lnZ corresponds to a higher strain rate or a lower deformation temperature. In order to further verify the feasibility of the hot processing map and understand the deformation mechanism, the deformed microstructures processed at the ﬁve regions (A) to (E) in Figure 6c are presented in Figure 7, and the corresponding lnZ are listed in Table 4. Figure 7 shows that grains are aligned in the transverse direction and intermetallic compounds are distributed in the matrix. As shown in Table 4, the lnZ value decreases with reducing deformation rates when the deformation temperature is 370 ◦C. Most of the grain boundaries remain straight, and DRV is the main softening mechanism in Figure 7a–c. The dislocations in this process change from the mixed arrangement of high-energy states to the regular arrangement of low-energy states, forming vertically arranged dislocation walls [8,33]. The strain rates of Figure 7a,d, and e are ﬁxed at 0.01 s−1, and the value of lnZ decreases with an increasing deformation temperature, as shown in Table 4. The grain boundary is no longer straight and becomes relatively curved at high deformation temperatures. Moreover, some small grains appear at grain boundaries in sample deformed at 490 ◦C (Figure 7e), which are preferred locations for recrystallization [40]. Therefore, in these cases, DRX is the main mechanism for the hot deformation. In Figure 7e, the value of lnZ is the smallest with the deformation temperature at 490 ◦C and strain rate at 0.01 s−1, which leads to a substantially increased DRX and is consistent with the ﬁndings in previous studies [39–41]. DRX is beneﬁcial for the hot deformation process, which provides a stable ﬂow and results in a good processability. A high temperature accelerates the diﬀusion of atoms and promotes the microstructure change of materials. A reduced dislocation density achieved by either DRV or DRX is able to compensate the work hardening eﬀect, which leads to a steady ﬂow in thermo-mechanical processing. In addition, a low strain rate provides suﬃcient time for microstructural evolution during plastic deformation. Thus, high deformation temperature and low strain rates are favorable to achieve a steady-state deformation, and a processing window is proposed at 420–475 ◦C/0.01–0.022 s−1 for the new Al–Mn–Sc alloy.

Table 4. lnZ values of Al–Mn–Sc alloy samples deformed at diﬀerent regions in the PM in Figure 6c.

Regions in PM

A B C D E

Temperature/◦C

370 370 370 410 490

Strain Rate/s−1

10 1 0.1 0.01 0.01

LnZ

39.823 37.520 35.217 30.718 26.317