Materials Science & Engineering A 580 (2013) 133–141

Contents lists available at SciVerse ScienceDirect

Materials Science & Engineering A

0921-50http://d

n CorrE-m

journal homepage: www.elsevier.com/locate/msea

Importance of diffusional creep in fine grained Mg–3Al–1Zn alloys

T.J. Lee a, Y.B. Park b, W.J. Kim a,n

a Department of Materials Science and Engineering, Hongik University, Mapo-gu, Sangsu-dong 72-1, Seoul 121-791, Republic of Koreab Department of Materials Science and Engineering, Sunchon National University, 315 Maegok, Sunchon 540-742, Jeonnam, Republic of Korea

a r t i c l e i n f o

Article history:Received 25 March 2013Received in revised form15 April 2013Accepted 17 April 2013Available online 29 April 2013

Keywords:Mechanical characterizationMagnesium alloysGrain refinementThermomechanical processingSuperplasticity

93/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.msea.2013.04.061

esponding author. Tel.: +82 2 320 1468; fax: +ail address: kimwj@wow.hongik.ac.kr (W.J. Ki

a b s t r a c t

Deformation mechanisms of fine-grained Mg–3Al–Zn (AZ31) alloys that were prepared by using severeplastic deformation were identified at elevated temperatures between 473 K and 573 K by examiningtheir stress–strain rate relations at different grain sizes and temperatures. Unlike the previous reportswhere grain boundary sliding has been suggested to be the rate-controlling deformation mechanism inthe fine-grained AZ31 alloy, the current analysis indicated that Coble creep competes with grainboundary sliding and the contribution of Coble creep to overall strain rate increases as grain sizedecreases and temperature increases. Making the efforts to minimize grain growth during sampleheating and tensile deformation is, however, important for observing Coble creep. Texture variation tookplace during the tensile deformation and differed depending on the type of dominant deformationmechanism operating under the given testing condition.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

There have been many efforts towards reducing grain size ofMg alloys to improve their strength at ambient temperatures andtheir superplasticity at elevated temperatures. The most popular“top–down” approach used for effective grain refinement in Mgalloys is severe plastic deformation (SPD), which includes equalchannel angular pressing (ECAP) [1–3], accumulative roll bonding[4], multi-directional forging [5], friction stirring [6] and high-ratiodifferential speed rolling (HRDSR) [7,8]. According to the analysisof the relationship between strain rate and flow stress at differenttemperatures above 0.5 Tm (where Tm is the melting temperature)for a variety of Mg alloys with small grains a few micrometers insize, the typical value of strain rate sensitivity exponent (m) is∼0.5, and the activation energy for plastic flow is close to thatvalue for grain boundary diffusion at low flow stresses [2,9]. SomeMg alloys with high volume fractions of second phase of particlesor reinforcements exhibited m values considerably smaller than0.5, but after threshold-stress compensation, the m value became∼0.5 [10]. These results suggest that grain boundary sliding (GBS)is the rate-controlling deformation mechanism for fine-grainedMg alloys at low stresses and is responsible for superplasticity.

For Mg alloys with small grain sizes, however, diffusional creepsuch as Nabarro–Herring (N–H) creep and Coble creep can beimportant because, like GBS, these mechanisms are also grain-size

ll rights reserved.

82 2 325 6116.m).

sensitive.

_ε¼ 14DL

d2Eb3

kT

!sE

� �ð1Þ

_ε¼ 14πδDgb

d3Eb3

kT

!sE

� �ð2Þ

Eq. (1) [11] describes the strain rate (_ε) by Nabarro–Herringcreep, where s is the flow stress, T is the absolute temperature, DL

is the coefficient for lattice self-diffusion of Mg (¼1�10−4 exp(−135,000/RT) m2 s−1 [12], where R is the gas constant ), b is theBurger's vector (3.21�10−10 m [12]), k is the Boltzmann constant,E is the Young's modulus (¼4.3�104∙[1–5.3�10−4∙(T−300)] MPa[12]) and d is the grain size. Eq. (2) [11] depicts Coble creep, whereDgb is the coefficient for grain boundary diffusion (¼7.79�10−3

exp(−92,000/RT) m2 s−1 [12]) and δ is the grain boundary width(¼2b).

For SPD-processed Mg alloys with a typical grain size of 2 μm, thepredicted strain rates for N–H creep and Coble creep at 5–10MPa and523 K (DL¼3.29�10–18 m2 s−1 and Dgb¼5.05�10–12 m2 s−1) are2.63�10−7–5.27�10−7 s−1 and 2.32�10−4–4.64�10−4 s−1, respec-tively. This result indicates that Coble creep predicts a significantlyhigher strain rate than N–H creep (by a factor of ∼1000). Moreimportantly, the calculated strain rates for Coble creep are in thestrain rate range (1�10−5 s−1–1�10 s−1) that can be covered bytypical tensile test machines. For the same grain size and temperature,the calculated strain rates for Coble creep for aluminum andnickel (with Dgb¼3.57�10–13 m2 s−1 and 2.30�10–17 m2 s−1 [12],respectively) are 1.03�10−5–2.06�10−5 s−1 and 3.82�10−10

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141134

–7.65�10−10 s−1, respectively, indicating that the probability of obser-ving Coble creep in the typical strain rate range increases as Dgb

increases. Previously, however, Coble creep has rarely been observedin Mg alloys. Recently, Kim [13] showed that Coble creep can beimportant in ultrafine-grained AZ91 (Mg–9Al–1Zn) alloy.

Mg–3Al–1Zn (AZ31) is the most widely used wrought magne-sium alloy because of its good combination of strength, ductilityand corrosion resistance. Deformation mechanisms and super-plasticity of fine-grained AZ31 alloys have been extensively stu-died, typically in the temperature range between 573 K and 673 K[2,6,9]. Some studies were conducted at temperatures below 573 K[14,15], but the details of the associated deformation mechanismshave been scarcely analyzed.

In this paper, we studied the deformation mechanisms of fine-grained AZ31 alloys at temperatures between 473 and 573 K andexplored the possibility of and conditions for observing Coblecreep as the rate-controlling deformation mechanism.

2. Experimental procedures

Commercial AZ31 (Mg–3Al–1Zn) alloy sheets with a thicknessof 2 mm were used as the starting material. This material willhereafter be referred to as the as-received AZ31 alloy. HRDSR wasperformed on the as-received AZ31 alloy using a rolling mill with aroll diameter of 300 mm. The speed ratio of the upper to the lowerroll was set at 2 (6 rpm:3 rpm). A cold AZ31 sheet was fed to hotrolls (423 K or 473 K) for a total reduction of 70% in the thicknessthrough the two-step rolling process. The sheet was rolled to0.8 mm and then rolled again to a final thickness of 0.6 mm. Therewas no rotation of the samples between the two passes. The twomaterials obtained after the second passes at 473 and 423 K willhereafter be referred to as HRDSR-1 and HRDSR-2 AZ31 alloys,respectively.

For the microstructure study, the normal direction (ND) androlling direction (RD) planes of the samples were examined usingoptics after etching the samples in a solution of picric acid (4.2 g),water (10 ml), acetic acid (10 ml) and ethanol (70 ml). The grainsizes were measured by the linear intercept grain size method usingimage analysis software (Olympus analysis TS Materials). Electronback-scattering diffraction (EBSD) analyses were performed on theND-RD planes of the samples with a step size of 50 nm. TSL version5.31 was used as the analysis software, and data points withconfidence index (CI) values lower than 0.1 were removed fromthe EBSD data. The grain sizes of the samples were measured basedon the EBSD image maps for a tolerance angle of 151.

For tensile testing at high temperatures, tensile specimens witha dog-bone geometry and 5 mm gauge length were used. Tensileelongation-to-failure tests were performed (under constantcrosshead-speed condition) to evaluate the tensile ductility atseveral temperatures and strain rates. The strain rate change(SRC) tests were carried out in the crosshead speed range between0.05 (or 0.015) and 30 mm/min at 473, 523 and 573 K. A pre-strainof ∼0.15 was imposed at an initial strain rate of 4�10−3 s−1 before

Fig. 1. The optical microstructures of the (a) as-rece

the SRC was applied to stabilize the microstructure. A strain of∼0.03 was applied between the strain rates followed by the pre-straining. The SRC test at each temperature was repeated con-secutively, to confirm that the strain-rate–stress relation obtainedfrom the SRC test was reliable. That is, if the stress–strain ratecurves from the first and second (repeated) rounds overlap, thenlimited microstructural change can be assumed to have occurredduring the SRC test. In the case of HRDSR-2 AZ31, additional SRCtests were conducted in the crosshead speed range between 0.05and 0.3 mm/min to monitor the change in the local m value andflow-stress as a function of strain. A strain of ∼0.06 was appliedbetween the strain rates. During the SRC and elongation-to-failuretesting, the tensile jig was preheated to a testing temperature andthe sample was then mounted onto the sample holder in theheated jig. It took 5 min for the jig to reach the testing tempera-ture again. Then, the sample was allowed to equilibrate at thetesting temperature for an additional 5 min before initiatingstraining. This tensile jig preheating was performed to minimizegrain growth before the initiation of tensile loading. Microstruc-ture and microtexture of the as-received, HRDSR-1 and HRDSR-2AZ31 alloys were examined by EBSD just before the tensile loadingto evaluate the change in grain size during the sample heating andholding period. Microstructure and microtexture of some tensilesamples were also examined by EBSD in the gauge (at the center ofthe gauge or approximately 1 mm away from the fractured tip inthe case of fractured samples) and grip regions after the tensiledeformation.

3. Results and discussion

The optical images of the as-received, HRDSR-1 and HRDSR-2AZ31 alloys are shown in Fig. 1(a)–(c). The linear intercept grainsize (d) of the as-received material (6.1 μm) reduced significantlyafter deformation by HRDSR. The d values of HRDSR-1 AZ31 andHRDSR-2 AZ31 alloys were measured to be 2.7 and 2.1 μm,respectively.

Fig. 2(a)–(c) shows the EBSD images of the as-received, HRDSR-1and HRDSR-2 AZ31 alloys. Unlike the as-received AZ31 alloy, HRDSR-1and HRDSR-2 AZ31 alloys reveal large portions of dark regions in theirimages, indicating the presence of high dislocation density and highinternal stresses in their microstructure. The grain sizes of the threematerials measured by EBSD were 6.3, 2.0 and 1.9 μm, which arereasonably similar to those measured by optics. All three materialshave a strong basal texture with similar maximum basal textureintensities of 16.1–17.5.

Fig. 3 shows the true stress-true–strain curves for the as-received, HRDSR-1 and HRDSR-2 AZ31 alloys at different tempera-tures at a strain rate of 3.3�10−4 s−1. HRDSR-1 and HRDSR-2 AZ31alloys exhibit lower flow stresses and higher strain hardeningrates than the as-received AZ31 alloy. They also reveal largertensile elongations when compared at the same temperature.These results indicate that high temperature tensile deformationbehavior of AZ31 alloy depends on grain size.

ived, (b) HRDSR-1 and (c) HRDSR-2 AZ31 alloys.

Fig. 2. The EBSD images and (0001) pole figures of the (a) as-received, (b) HRDSR-1 and (c) HRDSR-2 AZ31 alloys.

Fig. 3. The true stress-true strain curves of the as-received, HRDSR-1 and HRDSR-2AZ31 alloys at different temperatures at an initial strain rate of 3.3�10−4 s−1. Fig. 4. The SRC test results for HRDSR-2 AZ31 alloy at 573 K in two different

crosshead speed ranges and two different sample heating periods. The numbers inthe parentheses next to the cross head speed (CHS) ranges indicates the sampleheating time prior to initiation of tensile loading.

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141 135

Fig. 4 shows the results of SRC tests (including the first and thesecond round) for HRDSR-2 AZ31 alloy conducted at 573 K, givenin plots of s against _ε on a log–log scale. On these plots, the slopeof the curves represents the m value. In the case when the lowestcrosshead speed is 0.05 mm/min, the curve obtained from thesecond round of the SRC test is to the right of the curve obtainedfrom the first round, but they are close to each other and theirslopes are very similar, implying that minimal microstructuralvariation (such as grain-size increase by grain growth) occurredduring the SRC test. In the case when an additional crossheadspeed (0.015 mm/min) is included in SRC test schedule, comparedto the case that excludes this speed, the curves from the first andthe second round are noticeably separated at low strain rates.Furthermore, there is a notable difference in the local m valuebetween the two curves. These results indicate that grain-sizeincrease occurs considerably during the SRC test when the cross-head speed of 0.015 mm/min is included. For this reason, theminimum strain rate for the SRC test was chosen to be higher than1�10−4 s−1. Fig. 4 also shows the SRC test result obtained withoutthe tensile-jig preheating technique. The tensile sample was

mounted onto the jig at room temperature and then held togetherin the furnace until temperature reached to 573 K. It took ∼1 hprior to the initiation of tensile loading. The obtained stress–strainrate curves exhibit markedly smaller m values (∼0.5) and higherflow stresses at low strain rates compared to the case that used thejig preheating technique. This result indicates that extensive graingrowth took place during the prolonged period of sample heating,when the tensile-jig preheating technique was not used.

Fig. 5(a)–(c) shows the SRC results for the as-received, HRDSR-1and HRDSR-2 AZ31 alloys at 473–573 K, which are presented inplots of flow stress normalized by the Young's modulus (s/E)against _ε on a log–log scale. Some m values measured in the curvesfrom the first rounds of the SRC tests are marked on the plots.On the same plots, the data of flow stresses read at ε¼0.1 in thetrue stress–true strain curves at different temperatures and strainrates (including the curves shown in Fig. 3) are also presented.In Fig. 5(d), the s/E−_ε curves of the as-received, HRDSR AZ-1 andHRDSR AZ-2 alloys are compared at a given temperature of 523 K.

Fig. 5. The SRC test results (including the first and the second rounds) for the (a) as-received, (b) HRDSR-1 and (c) HRDSR-2 AZ31 alloys at various temperatures.(d) Comparison of the SRC test results (first round) of the three materials at a given temperature of 523 K. The predictions based on Eq. (3) using the grain sizes listed inTable 1 are presented by dotted curves.

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141136

The following inferences are based on Fig. 5(a)–(d). First, at eachtesting temperature, the curve obtained from the second round ofthe SRC test is located close to the curve obtained from the firstround. This is true for all the three materials (Fig. 5(a)–(c)). Thisresult indicates that minimal grain growth occurred during theSRC testing for all the materials under the given testing conditions.Second, the data of flow stresses measured at ε¼0.1 from thestress–strain curves of the three materials coincide with their SRCcurves obtained from the first round (Fig. 5(a)–(c)). This furtherconfirms the validity of the stress–strain rate relationship obtainedby the current SRC tests. Third, for each material, the m valuemeasured at low strain rates tends to increase with temperature(Fig. 5(a)–(c)). As temperature increases from 473 to 573 K, the mvalue of the as-received AZ31 alloy increases from 0.28 to0.7 within the strain rate range between 1.5�10−4 and4.2�10−4 s−1, while the m value of HRDSR-1 and HRDSR-2 AZ31alloys increases from 0.47 to 0.72 and from 0.53 to 0.84, respec-tively, within the similar strain rate range. This result indicates apossibility that the contribution of diffusional creep to total strainrate increases as the grain size decreases and the testing tempera-ture increases. Fourth, when compared at a given temperature(Fig. 5(d)), HRDSR-1 and HRDSR-2 AZ31 alloys exhibit larger

m values and lower flow stresses than the as-received AZ31 alloyat strain rates below ∼10−3 s−1. At high strain rates, however, theflow stress levels and the m values of the three materials are verysimilar. This result indicates that the grain-size-sensitive deforma-tion mechanism is dominant at low strain rates, while the grain-size-insensitive deformation mechanism is dominant at highstrain rates.

When the contributions of diffusional creep, grain boundarysliding (GBS) and dislocation climb creep to the total plastic floware simultaneously considered, the strain rate of a material can beestimated by using the following equation:

_ε¼ 14Dn

ef f

d2Eb3

kT

!sE

� �þ A

Dn

ef f

d2sE

� �2þ B

Def f

b2sE

� �5ð3Þ

In this equation, Dneff is the effective diffusivity [16] (¼

DL+xfgbDgb where fgb is the fraction of atoms associated with grainboundaries (¼πδ/d). The term x is usually considered to be unity indiffusional creep mechanisms [12] and considered to be 1�10−2

for many superplastic materials [16]). Def f is another effectivediffusivity (¼DL þ α50ðs=EÞ2Dp [16], where Dp is the pipe diffusiv-ity for pure magnesium (¼Dgb) and α is a constant (0.016 [17])).

Fig. 6. The EBSD grain boundary maps for the (a) as-received, (b) HRDSR-1 and (c) HRDSR-2 AZ31 alloys obtained just after sample heating and holding at 473 K. (d) TheEBSD grain boundary map for HRDSR-2 AZ31 alloy obtained just after sample heating and holding at 573 K.

Table 1The grain sizes of the as-received, HRDSR-1 and HRDSR-2 AZ31 alloys, measuredjust before the tensile loading for SRC testing at various temperatures, and the grainsizes chosen for the best fit to the s/E vs. strain rate curves of the three materials atvarious temperatures.

Materials Initial grainsize (μm)

Grain size at473 K (μm)

Grain size at523 K (μm)

Grain size at573 K (μm)

As-receivedAZ31

6.08 6.22(6.22) 7.36(6.08) 7.61(6.7)

HRDSR-1AZ31

2.79 2.96(3.3) 5.62(4.8) 5.83(5.5)

HRDSR-2AZ31

2.1 2.57(3.1) 4.78(4.6) 5.15(5.0)

The numbers in parenthesis indicate the grain-size values used for the best fit tothe experimental curves shown in Fig. 5(a)–(c).

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141 137

The first term on the right side in Eq. (3) represents a combinationof N–H creep and Coble creep, the second term represents acombination of DL-controlled and Dgb-controlled GBS, and thethird term represents a combination of DL-controlled and Dp-controlled dislocation climb creep. It is worthwhile to note thatunlike diffusional creep and GBS mechanisms, dislocation climbcreep is not sensitive to grain size. The expressions for grainboundary sliding and dislocation climb creep given in Eq. (3) arethe phenomenological relations determined from a number of Mgalloys [16]. Kim et al. [17] reported that the typical values of A and

B for Mg alloys are 7.59�108 and 6.67�108, respectively. Thesevalues, however, can differ depending on the alloy compositionand texture. In this analysis, A and B were chosen as 1.55�108 and1.67�108, respectively, to obtain the best fit to the currentexperimental data. The current A value, which is smaller than itstypical value by a factor of five, may also represent the reduced Dgb

resulting from the presence of a high fraction of low-angleboundaries (will be discussed in Fig. 6) in the microstructures ofthe present AZ31 alloys. This is because Fujita et al. [18] showedexperimentally that grain boundary diffusion coefficients is lowerin fine-grained alloys having low fractions of high-angle bound-aries than in fine-grained alloys having high fractions of high-angle boundaries.

Unlike the Mg alloys with a high fraction of second phaseparticles, AZ31 alloy is a pseudo single-phase alloy that has a lowfraction of second phase (β-Mg17Al12). Therefore, rapid graincoarsening can occur in the AZ31 alloy during the sample heatingfor tensile tests. For this reason, it is important to have informationabout the grain sizes of the as-received, HRDSR-1 and HRDSR-2AZ31 alloys just before the initiation of tensile loading for the SRCtest for reliable evaluation of the grain-size effect on the stress–strain rate relationship. The grain sizes measured by optics justbefore the tensile loading are listed in Table 1. The result showsthat rapid grain growth starts above 523 K in all the threematerials. At 523 K, the grain sizes of HRDSR-1 and HRDSR-2AZ31 alloys almost doubled (5.6 and 4.8 μm, respectively), whilethe grain size of the as-received AZ31 alloy did not increased asmuch (by 18.3%). This result implies that grain growth rate ishigher in HRDSR-1 and HRDSR-2 AZ31 alloys. This finding isexpected because a finer-grained microstructure with a higher

Fig. 7. The s/E vs. strain rate plot for HRDSR-2 AZ31 alloy at 573 K and analysis ofdeformation behavior without considering Dgb-GBS or Coble creep.

Fig. 8. The deformation mechanism maps for AZ31 alloys at 473, 523 and 573 K,constructed based on the constitutive equations given in Eq. (3).

Fig. 9. (a) The repeated SRC results for HRDSR-2 AZ31 alloy performed at strain rates bemechanism map at 573 K.

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141138

fraction of grain boundaries naturally has a higher driving force forgrain growth. Fig. 6(a)–(c) shows the EBSD grain boundary maps ofthe as-received, HRDSR-1 and HRDSR-2 AZ31 alloy samples takenout of the furnace just prior to the tensile loading at the testingtemperature of 473 K. In the case of the as-received AZ31 alloy, themicrostructure change was small after the sample heating. On theother hand, a large portion of dark regions disappeared in HRDSR-1and HRDSR-2 AZ31 alloys. The HRDSR-2 AZ31 alloy, however, stillcontained non-fully recovered structure. These regions almost com-pletely vanished at a higher sample heating temperature of 573 K(Fig. 6(d)). The fractions of high angle boundaries (4151) in the threematerials measured from their EBSD images were in the similar rangebetween 0.52 and 0.58.

Using Eq. (3), the grain sizes for the best fit to the experimentaldata in Fig. 5(a)–(c) were determined at various temperatures. Thefitting results are presented by dotted curves in Fig. 5(a)–(c). Thegrain sizes used for the best fit, listed in Table 1, are reasonablyclose to those experimentally measured just before the tensileloading, indicating that Eq. (3) predicts the deformation behaviorof AZ31 alloy well. The virtually same quality of fitting could beobtained without considering contributions of N–H creep,DL-controlled GBS and DL-controlled dislocation climb creep inEq. (3), implying that grain boundary diffusion controls the plasticflow under the given testing conditions. Indeed, the measurementresults of activation energies for plastic flow (Qc) at some s/Evalues where similar m values are measured at different tempera-tures (Fig. 5(a)–(c)) indicate that the Qc values of the three AZ31alloys (72–88 kJ/ mole) are similar to the activation energy for Dgb.

Contributions of Coble creep and Dgb-controlled GBS to thestrain rate were separately analyzed for HRDSR-2 AZ31 alloy at523 K in Fig. 7. When Coble creep is not considered in calculationof the total strain rate, a large deviation from the experimentalresults occurs at low strain rates; when Dgb-controlled GBS is notconsidered, deviation occurs at intermediate strain rates. In bothcases, the strain rates are underestimated, indicating that thecontributions of Dgb-controlled GBS and Coble creep are equallyimportant at low flow stresses.

Fig. 8 shows the deformation mechanism maps (DMM) forAZ31 alloy at 473, 523 and 573 K constructed using the constitu-tive equations given in Eq. (3) assuming that six deformationmechanisms, namely, N–H creep, Coble creep, Dgb-controlled GBS,DL-controlled GBS, DL-controlled slip creep and Dp-controlleddislocation climb creep, compete with one another. For a given

low 1�10−3 s−1 at 573 K. (b) The presentation of the SRC data on the deformation

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141 139

set of operating conditions, strain rates predicted by the sixpossible deformation mechanisms are calculated and the defor-mation mechanism that exhibits the highest strain rate is markedas the dominant mechanism in the DMM. The s/E values for thethree materials in Fig. 5(a)–(c) were plotted on the DMMs withthe grain size values measured just before the tensile loading. Forthe as-received AZ31 alloy, Dp-controlled dislocation climb creep isthe dominant deformation mechanism at 473 K across the entirestrain rate range. At 523 K, Dgb-controlled GBS emerges as thedominant deformation mechanism at low flow stresses. ForHRDSR-1 and HRDSR-2 AZ31 alloys, Dgb-controlled GBS alreadyregulates the deformation at 473 K at low flow stresses. Coblecreep becomes important at low flow stresses at 573 K for all thethree materials. It is worthwhile to note that the location ofexperimental data in the Coble creep region in DMM does notmean that the experimental data exhibits m¼1. To illustrate thispoint, the m values measured from the curve (predicted by Eq. (3))of HRDSR AZ31-2 alloy at different s/E values at 573 K are markedon the map. The largest s/E value associated with m=1 is

Fig. 10. The s/E values from Fig. 5(a)–(c) plotted as a fu

Fig. 11. The tensile elongations (%) of the as-received, HRDSR-1 AZ31 and HRDSR-2 AZ31elongations (%) of the three materials presented as a function of _εexp(Qgb/RT).

2.66�10−6 (_ε¼1.7�10−6 s−1), which is considerably smaller thanthat for the boundary between Coble creep and Dgb-controlled GBS(5.4�10−4).

Fig. 9(a) shows the results of the SRC tests for HRDSR-2 AZ31 alloyat 573 K in the low strain rate range (below 1�10−3 s−1); the testswere repeated several times to monitor the variation of m value andflow stress as a function of strain. As shown, the flow stress levelgradually increased as the round was repeated, while m valuegradually decreased. After the fifth round (after an accumulated strainof 0.77), them value decreased from 0.85 to 0.64 in the low strain raterange, whereas it decreased from 0.68 to 0.46 in the high strain raterange. The grain size in the gauge region of the sample measured afterthe fifth round was 7.78 μm, indicating that grain coarsening occurredduring tensile straining. The data from the first and the fifth roundsare plotted on the DMM (Fig. 9(b)). The result indicates that thechange in m value and the flow stress level with tensile strainingresults from a gradual decrease in contribution of Coble creep and agradual increase in contribution of GBS to the total strain rate as theresult of grain-size increase by dynamic grain growth.

nction of (a) _εexp(Qgb/RT) and (b) _εexp(Qgb/RT)d3.

alloys as a function of testing temperatures at different strain rates. (b) The tensile

Fig. 12. The (0001) pole figures of HRDSR-2 AZ31 alloy measured in the gaugeregion after the tensile deformation at (a) 1�10−3 s−1–573 K, (b) 3.3�10−4 s−1–473 K, (c) 1�10−2 s−1–473 K, and (d) 3.3�10−4 s−1–573 K.

Fig. 13. Comparison of the s/E–strain rate relation between the current data withthe data provided by other investigators. The solid line curves represent theprediction by Eq. (3) with the grain sizes specified in Tables 1 and 2.

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141140

The s/E–strain rate curves in Fig. 5(a)–(c) are plotted as afunction of _εexp(Qgb/RT), and the result is presented in Fig. 10(a).Overall, all the curves tend to converge into a single curve.Excellent correlation is obtained at large values of _εexp(Qgb/RT)where Dp-controlled dislocation climb creep dominates the plasticflow. However, the correlation is poor at small values of _εexp(Qgb/RT), where Dgb-controlled GBS or/and Coble creep, both of whichare grain size sensitive, importantly influences the plastic flow.Fig. 10(b) shows the plot of s/E against _εexp(Qgb/RT)d3. After thegrain-size compensation, a good correlation is obtained at smallvalues of _εexp(Qgb/RT). This consideration of the grain-size effect,however, results in a poor correlation at large values of _εexp(Qgb/RT) because Dp-controlled dislocation climb creep is grain sizeinsensitive.

Fig. 11(a) shows the tensile elongation of the as-received,HRDSR-1 AZ31 and HRDSR-2 AZ31 alloys as a function of testingtemperatures at different strain rates. Fig. 11(b) shows the tensileelongation (%) in Fig. 11(a) plotted as a function of _εexp(Qgb/RT).The result shows that as temperature increases and strain ratedecreases (i.e., as _εexp(Qgb/RT) decreases), tensile elongationincreases. The HRDSR-1 and HRDSR-2 AZ31 alloys show greaterelongation than the as-received AZ31, especially at low _εexp(Qgb/RT) values. This result indicates that the tensile elongation beha-vior of three materials can be explained in terms of the variation oftheir m values as a function of strain rate and temperature.

Texture characteristics and maximum basal texture intensityvalues of the three materials examined by EBSD did not changenoticeably in the grip regions after tensile deformation at varioustemperatures and strain rates. The measured maximum basaltexture intensity values were typically in the range of 16–18. Thisobservation agrees with the previous report that during staticannealing in Mg alloys with fine grains, developed by continuousdynamic recrystallization, grain growth occurs with little changein texture [19]. In contrast, the variation of basal texture intensityin the gauge regions depended on which deformation mechan-ism was dominant during the tensile deformation. Fig. 12(a)–(d)shows the microtextures (measured by EBSD) of HRDSR-2 AZ31alloy after the tensile deformation at various temperatures andstrain rates. At 1�10−3 s−1–573 K, where the associated m valueis approximately 0.5, the basal texture intensity decreased con-siderably compared to the initial texture (Fig. 12(a)). This textureweakening also occurred at 3.3�10−4 s−1–473 K, where m≈0.5(Fig. 12(b)). These results agree with the report that GBS leads totexture weakening [20]. In contrast, the variation in texture wassmall at 1�10−2 s−1–473 K, where dislocation climb creep dic-tates deformation (Fig. 12(c)). Also at the strain rate of3.3�10−4 s−1–573 K, where contribution of Coble creep to plasticflow is significant (Fig. 12(d)), the texture intensity changewas small.

Finally, a question arises: why Coble creep has been previouslyrarely reported despite extensive studies on high temperaturedeformation behavior of AZ31 alloy? Fig. 13 shows comparison ofthe s/E–strain rate relation between the current data with the dataprovided by other investigators. The sources of the data used inFig. 13 as well as those not included in Fig. 13 are listed in Table 2.The AZ31 alloy with a relatively coarse grain size (d¼17 μm)shows m¼0.54 at low strain rates at 573 K [21]. Somekawa et al.[22] and Figueriredo et al. [2] reported that the AZ31 alloys withd¼4.9 μm and d¼5.9 μm show m≈0.5 at temperatures of 473–573 K and 623–723 K, respectively. However, careful examinationof their data at 573 or 623 K (Fig. 13) reveals that there are regionswhere m values are obviously larger than 0.5. The SRC test resultsof Somekawa et al. [22] show m¼0.72 at the strain rates between1�10−4 s−1 and 1�10−3 s−1 at 573 K and the tensile elongationdata (flow stresses read at ε¼0.1) of Figueriredo et al. [2] showm¼0.68 at the strain rates between 2�10−4 s−1 and 2�10−3 s−1 at

623 K. Furthermore, the deformation behavior of these two AZ31alloys can be reasonably well depicted by Eq. (3). These resultssupport the validity of our claim on the importance of Coble creepin fine-grained AZ31 alloy. The data of Figueriredo et al. [2],however, appreciably deviate from the prediction at low strainrates, showing m≈0.5 below 2�10−4 s−1. This may be attributed tolarge grain growth at strain rates lower than 10−4 s−1 as discussedearlier in Fig. 4. Lin and Huang [15] reported that the fine grainedAZ31 alloy showed m≈0.3, but their measurement of flow stresseswas made at ε¼0.5. Thus, it is quite possible that the low m value

Table 2The data of the fine-grained AZ31 alloys studied at high temperatures by other investigators.

References Linear intercept grain size(μm)

Processingmethod

Testing temp.(K)

Testing strain rate ranges(s−1)

m values at low strainrates

Measurement of flowstress

[2] 5.9b ECAP 623–723 10−5–10−2 ∼0.5(0.68) ε¼0.1

[15] 2.5a Extrusion 523–573 10−4–10−1 ∼0.3 ε¼0.5

[21] 17 Rolling 573–648 3�10−5–5�10−2 0.59 SRC

[22] 5.8c Rolling 473–573 9�10−5–2�10−2 ∼0.5(0.72) SRC

[23] 4.5a Extrusion 573–673 7�10−4–1.4�10−1 0.47 ε¼0.2

Numbers in parentheses ( ) indicate the maximum m values measured in this study.a Method of grain size measurement is not indicated in the literatures.b The grain size measured after annealing for 30 min at 673 K.c The grain size measured after sample holding for 15 min at 573 K.

T.J. Lee et al. / Materials Science & Engineering A 580 (2013) 133–141 141

is a result of extensive grain growth during large tensile deforma-tion. The fine grained AZ31 alloy studied by Yin et al. [23] showedm≈0.5 at 573 K, but the minimum strain rate in their investigatedstrain rate range was 7�10−4 s−1, which was somewhat too highto observe Coble creep according to our test results.

4. Conclusions

Deformation mechanisms in AZ31 alloys with initial grain sizesbetween 2 and 6 μm were examined in the temperature rangebetween 473 K and 573 K. The following observations were made:

(1)

Analysis of the stress–strain rate relations of AZ31 alloys withfine grains indicates that Coble creep, Dgb-controlled GBS andDp-controlled dislocation climb creep compete with oneanother. Unlike in the previous results on fine-grained AZ31alloys reported by many investigators, it was found that Coblecreep plays as an important role at low strain rates around10−4 s−1. Careful examination of the data of the fine-grainedAZ31 alloys reported by other investigators provided someevidence supporting this claim.

(2)

The probability of Coble creep becoming the dominant defor-mation mechanism increased as grain size decreased andtesting temperature increased. Rapid grain coarsening, how-ever, changed the rate-controlling deformation mechanismfrom Coble creep to grain boundary sliding during tensiletesting. When the sample heating time was long, Coble creepcould not be also observed. These results indicate that retarda-tion of grain growth during sample heating or/and tensiledeformation is important for observing Coble creep.

(3)

The tensile elongation behavior of three AZ31 alloys withdifferent grain sizes could be explained in terms of thevariation of their m values as a function of strain rate andtemperature.

(4)

The maximum basal texture intensity decreased when GBSdominated the plastic flow, whereas it changed insignificantlywhen Coble creep and dislocation climb creep dominated theplastic flow.

Acknowledgments

This work was financially supported by 'Research & Commer-cialization for Green-Components with High Specific HardnessMaterials Project (2010-H-004-00000000-2010)' funded by theMinistry of Knowledge Economy (MKE) of Korea. One of theauthors (Y.B. Park) acknowledges the financial assistance fromthe World Premium Material project through the Korean Ministryof Knowledge and Economy.

References

[1] F. Akbaripanah, F. Fereshteh-Saniee, R. Mahmudi, H.K. Kim, Mater. Sci. Eng. A565 (2013) 308.

[2] B. Roberto, R.B. Figueiredo, T.G. Langdon, J. Mater. Sci. 43 (2008) 7366.[3] W.J. Kim, S.I. Hong, Y.S. Kim, S.H. Min, H.T. Jeong, J.D. Lee, Acta Mater. 51 (2003)

3293.[4] J.A. del Valle, M.T. Pérez-Prado, O.A. Ruano, Mater. Sci. Eng. A 410–411 (2005)

353.[5] J. Xing, X. Yang, H. Miura, T. Sakai, Mater. Tran. 48 (2007) 1406.[6] Z. Da-tong, X. Feng, Z. Wei-wen, Q. Cheng, Z. Wen, Trans. Nonferrous Met. Soc.

China 21 (2011) 1911.[7] W.J. Kim, I.K. Moon, S.H. Han, Mater. Sci. Eng. A 538 (2012) 374.[8] W.J. Kim, B.H. Lee, Mater. Sci. Eng. A 527 (2010) 5984.[9] W.J. Kim, S.W. Chung, C.S. Chung, D. Kum, Acta Mater. 49 (2001) 3337.[10] H. Watanabe, T. Mukai, K.M. Mabuchi, K. Higashi, Acta Mater. 49 (2001) 2027.[11] O.D. Sherby, J. Wadsworth, Prog. Mater. Sci. 33 (1989) 169.[12] H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, Pergamon Press, Oxford,

1982.[13] W.J. Kim, Scr. Mater. 58 (2008) 659.[14] R. Lapovok, Y. Estrin, M.V. Popov, S. Rundell, T. Williams, J. Mater. Sci. 43

(2008) 7372.[15] H.K. Lin, J.C. Huang, Mater. Trans. 43 (2002) 2424.[16] O.D. Sherby, J. Wadsworth, Prog. Mater. Sci. 33 (1989) 169.[17] W.J. Kim, S.W. Chung, C.S. Chung, D. Kum, Acta Mater. 49 (2001) 3337.[18] T. Fujita, Z. Horita, T.G. Langdon, Mater. Sci. Eng A 371 (2004) 241.[19] X. Yang, H. Miura, T. Sakai, Trans. Nonferrous Met. Soc. China 17 (2007) 1139.[20] J. Pilling, N. Ridley, Superplasticity in Crystalline Solids, The Institute of Metals,

London, 1989, p. 4.[21] J.A. del Valle, M.T. Pérez-Prado, O.A. Ruano, Metall. Mater. Trans. A36 (2005)

1427.[22] H. Somekawa, H. Watanabe, T. Mukai, K. Higashi, Scr. Mater. 48 (2003) 1249.[23] D.L. Yin, K.F. Zhang, G.F. Wang, W.B. Han, Mater. Lett. 59 (2005) 1714.