1

Twinning-Slip Transitions in Mg AZ31B

K. Piao1, K. Chung2, M. G. Lee3, R. H. Wagoner1*

1Department of Materials Science and Engineering, 2041 College Road Ohio State University, Columbus, OH 43210, USA

2Department of Materials Science and Engineering, Research Institute of Advanced Materials, Seoul National University, 599 Gwanak-ro, Gwanak-gu Seoul 151-742,

Republic of Korea

3Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

Many metals, particularly ones with HCP crystal structures, undergo deformation by

combinations of twinning and slip, the proportion of which depends on variables such as

temperature and strain rate. Typical techniques to reveal such mechanisms rely on

metallography, x-ray diffraction, or electron optics. Simpler, faster, less expensive

mechanical tests were developed in the current work and applied to Mg AZ31B. The

curvature of compressive stress-strain plots over a fixed strain range was found to be a

consistent indicator of twinning magnitude, independent of temperature and strain rate.

The relationship between curvature and areal fraction of twins was determined.

Transition temperatures determined based on stress-strain curvature were consistent with

ones determined by metallographic analysis and flow stresses, and depended on strain

rate by the Zener-Hollomon parameter, a critical value for which was measured. The

transition temperature was found to depend significantly on grain size, a relationship for

which was established. Finally, it was shown that the transition temperature can be

determined consistently, and much faster, using a single novel “Step-Temperature” test.

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Keywords: Deformation mechanisms; Magnesium AZ31 alloy sheet; Deformation twin;

Dislocation slip; Transition temperature, Mechanical testing, Compression test, Cyclic

test, Grain size, Strain rate.

*Corresponding Author: R. H. Wagoner; Tel.: +1-614-292-2079, Fax: +1-614-292-6530,

E-mail address: wagoner.2@osu.edu

Manuscript date: August 30th, 2011

Submitted to Metallurgical and Materials Transactions A

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1. INTRODUCTION

As the lightest structural metal[1], magnesium with low density (1.74 g/cm3) and

moderate ductility [2] is attractive to the automobile industry, among others, because of

its light weight, high tensile strength (vs. Al) [1, 3] and high fatigue resistance (vs. Al) [2,

4, 5]. Most magnesium products are made by die casting [6] because of its poor

formability at room temperature, which is attributed to the low symmetry of the

hexagonal close packed (HCP) crystalline structure and thus the limited slip systems [3].

Magnesium wrought alloys have strong plastic anisotropy, especially in the strongly

textured sheet alloys [2]. At room temperature, the yield stress in compression in the

sheet plane is approximately half of that in tension [7, 8]; and the stress-strain curve in

compression shows an unusual inflected shape, distinct from the normal concave-down

aspect in tension. These phenomena are attributed to 1) the strong texture with the basal

plane parallel to the plane of sheet resulting from the manufacture process (c-axis

perpendicular to the sheet plane); and 2) the activation of { }2110 twinning in in-plane compression (with c-axis elongated) [9]. Un-twinning (or “detwinning”) also occurs in

the subsequent reverse loading after compression and shows a similarly inflected stress-

strain curve [8, 10].

According to the Von Mises criterion [11, 12], an arbitrary homogeneous deformation of

polycrystalline metals requires five independent slip systems [13]. In magnesium alloys,

basal slip, prismatic slip and pyramidal slip provide four independent slip

systems, facilitating deformation only in the basal plane. At room temperature,

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{ }2110 twinning, as the most common twinning mode in magnesium, can provide an independent deformation mechanism (in the c-direction) to satisfy the Von Mises

criterion [14].

Pyramidal slip, with high critical resolved shear stress (CRSS, ~90MPa), is

difficult to activate at room temperature in magnesium [15, 16]. Twinning has a polar

nature, which means that the { }2110 twin in magnesium can only be activated when the c-axis is elongated [17, 18]. The maximum strain along the c-axis is 0.064 [14, 19], with

the basal planes in the twinned region rotated 86.3o about the intersection line with the

twinning plane [20].

At elevated temperatures, as the only two systems that provide for deformation in the c-

axis direction, twinning and pyramidal slip are in competition with each other. The

critical resolved shear stress (CRSS) for ac + slip decreases to ~35MPa at 200oC and

to ~25MPa at 300oC [21-23], whereas that for twinning is expected to be relatively

temperature insensitive [24]. Thus, as the testing temperature is increased, the difference

between the activation stresses of these two mechanisms is reduced until a critical

temperature, Tt, is reached where the two stresses are equal [25]. At temperatures higher

than this, slip dominates the flow. Similar behavior has been identified for other twinning

metals [24, 26]

The activation of deformation twinning is correlated to the shape of stress-strain curves.

For example, the slope of the normalized strain hardening rate ((dσ/dε)/G with respect to

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deformation strain) changed from negative to positive, in various metals: brasses [27-29],

stainless steels [27], Co-Ni alloys [27-30], Ti [31-34], Zr [35], and Mg [36]. The

curvature of the stress-strain curve has been proposed to represent differences between

slip-dominant flow (d2σ/dε20) [37], and was used

to discern the grain-size effect in Mg alloys [38].

Deformation twinning has been more directly revealed by various experimental methods:

optical metallurgraphy [8, 39, 40], in-situ acoustic emission to detect twin activation [8,

41], X-ray diffraction to measure texture changes [8, 42, 43], EBSD for similar results

[44-48], and in-situ neutron diffraction to measure residual stress and local relaxed strain

[41, 49-52]. Each of these methods has specific disadvantages for testing transition

temperatures because of special equipment, specimen preparation, numerous samples,

and high times and costs.

The polar nature of { }2110 twinning in rolled, basal-textured Mg AZ31B sheet requires large in-plane compressive strains (corresponding to large through-thickness extensile

strains) in order to reveal the shape of the stress-strain curve under conditions where

twinning is possible. Large compressive strains are not readily obtained in sheet alloys

because of buckling, but several schemes for avoiding buckling at room temperature have

been introduced [53-56]. At least one of these methods [53] has been shown to permit

continuous compressive and tensile testing, including cycling between the two, thus

permitting the development of detailed constitutive equations [57-60], and the calibration

of acoustic emission signatures [8], and anelasticity results after strain reversal [53]. In a

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recent development by the co-authors, the Boger technique has been extended [61, 62] to

allow elevated-temperature tension/compression testing, potentially allowing the

possibility of determining transition temperatures mechanically.

A schematic of the new device and specimen are presented in Figure 1, and will be

described in more detail in the Experimental Procedures of this paper. Tension-

Compression-Tension (T-C-T) tests were carried out from room temperature to 250oC at

a strain rate of 10-3/s [62], with results summarized as shown in Figures 2. Figure 2(a)

shows the stress-strain curve; and Figures 2(b)-(c) are the enlarged portions for

compressive and tensile legs at 125oC and 150oC, revealing the distinctive features of

slip-dominant (always concave-down) and twin-dominant (concave-down transitioning to

concave-up) curves. A transition temperature Tt between these two deformation

mechanisms (or at least between curve shapes) is clearly seen within the temperature

range of 125oC to 150oC. This range of values of Tt was preliminarily verified by

quantitative metallography showing that the areal fraction of twins after compression

were 4.5% at 150oC and 43% at 125oC [62].

It should also be noted that other evidence for twinning during the first compressive leg

at temperatures below 150oC can be seen in the jerky flow during twinning [8] and the

almost-athermal aspect of compressive flow stress with temperatures associated with

twinning domination, particularly as compared with compressive curves at higher, slip-

dominated temperatures. Finally, it is worth noting that these distinguishing aspects

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largely disappear in the final tension cyclic, presumably because of the much lower

nucleation stress of untwining [8].

The new elevated-temperature, tension-compression test introduces the possibility of

revealing the transitions among deformation mechanisms (twinning vs. slip)

mechanically. The hypothesis underlying the approach is that the curvature of the stress-

strain curve is related in an identifiable, consistent way to the predominant slip

mechanism. In order to test this hypothesis and the mechanically-based approach that is

suggested, a series of compression tests were conducted over a range of temperatures and

strain rates, then analyzed both mechanically and metallographically. An even

faster/simpler/cheaper “Step-Temperature” (“ST”) test was developed subsequently and

results from it compared with the monotonic compression tests to evaluate its potential

utility.

2. EXPERIMENTAL PROCEDURES

Mg AZ31B sheet alloy was mechanically tested at a temperature range of 110oC-250oC

and strain rates of 0.0005/s-0.1/s using monotonic compression [62] and a novel “ST”

test. The deformation mechanisms were revealed by standard optical metallography.

2.1 Materials

Six batches of Mg AZ31B alloy sheet from various suppliers were used. The chemical

compositions, thicknesses, and grain sizes are shown in Table 1. The additions of Al and

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Zn to Mg act as solid-solution strengthening agents [1]. Alloy AU was the primary

material for the work in this paper; the other alloys were used primarily to estimate the

role of grain size on deformation mechanism.

2.2 Mechanical tests

A test device, presented elsewhere in detail [61, 62] and shown schematically in Figure 1,

uses side loading through heated plates to stabilize in-plane compressive deformation of

an exaggerated dog-bone shape specimen. For all the tests presented here, a constant side

force of 2.5kN was used and was found sufficient to prevent buckling. An automatic

feedback system controls the temperature of the specimen in range of 100oC-250oC, with

a temperature fluctuation with time within 1oC and a temperature difference throughout

the gage length (38mm) less than 5oC at 250oC [62]. Heating times from room

temperature range from 2 to 5 minutes depending on the target temperature. Tests were

carried out using an MTS 810 testing machine with a 200kN load cell.

For monotonic compression testing, a maximum strain of -0.08 was obtained at strain

rates of 0.001/s, 0.01/s, and 0.1/s. Following deformation, samples were quenched into

water. A non-contact EIRTM LE-05 laser extensometer was used to measure the specimen

deformation over a gage length of 25.4mm. The friction and biaxial effects introduced by

the side force were corrected for after testing [8, 53, 63]. To obtain a uniaxial-equivalent

stress without friction, friction coefficients of 0.03 and 0.08 were determined by a series

of tensile and compressive tests, respectively, with various side forces at room

temperature using procedures described elsewhere [8, 53, 63].

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A novel Step-Temperature test (“ST test”) was conceived of as a way to efficiently

determine the transition temperature, Tt, between deformation twin and dislocation slip

using a single sample. The concept started with a tension-compression cycle of

deformation at a temperature T where T>Tt. The temperature would then be reduced by

some decrement, say -10oC, and the deformation cycle repeated at progressively lower

temperatures until the stress-strain curves indicated a twinning-dominated mechanism.

The underlying assumption was that cyclic deformation by slip (i.e. at T>Tt) would not

change the microstructure sufficiently to alter Tt.

For the implementation attempted here, the cyclic deformation range was tension (to a

strain of 0.04)-compression (to a strain of -0.04) for 5 cycles, each at a constant strain rate

with the temperature for each compression-tension cycle decreased by 10oC from the

previous cycle. Each cycle was preceded by a hold time to reach the new target

temperature, typically 40s. The total testing strain range of 0.08 (absolute accumulated)

was accomplished in strain control mode, with holding between deformation cycles in

stroke control. A total strain range of 0.08 was chosen to be large enough to reveal stress-

strain patterns characteristic of deformation twinning and to allow 5-cycle tests without

fracture. Instead of standard true strain, the absolute value of each strain increment is

summed to produce an accumulated absolute strain εΔ=ε 2 , where Δ ε is the true

strain increment over a monotonic interval. Strain rates of 0.0005, 0.001, 0.005, 0.01,

0.05, and 0.1/s were used. A few examples of an alternate form of ST test with

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temperature increased for each cycle were done for comparison. The analysis of

mechanical tests is presented in the “Results and Analysis” section of this paper.

2.3 Metallography measurement

Samples for optical metallography were cut from the gauge regions where the material

was deformed and heated uniformly. Specimens were mounted using epoxy, then

successively ground and polished, finishing with 1 μm diamond paste. Acetic picral

solution (4.2 g picric acid, 10 ml acetic acid, 70 ml ethanol and 10 ml water) was used to

etch for 5-10 seconds. Specimens were examined immediately after etching to avoid

oxidation.

In order to assess the scatter and reproducibility of twin fractions and grain sizes, analysis

was conducted for 5 observation areas of 130μm × 108μm from a single specimen

compressively deformed to a strain of -0.08 at 150oC and at 0.01/s. The areal fraction of

deformation twins was determined by a point counting method according to ASTM

standard E562-08 [64]. 320 points were uniformly distributed over each microstructural

image. The grain size was calculated using a linear intercept method following [65]. At

least 200 grains were imaged in each field of view. The standard deviations for the five

images were 0.04 for areal fraction of twin, i.e., 0.266 ± 0.04, and 0.3μm for grain size,

i.e., 4.8μm ± 0.3μm.

3. RESULTS AND ANALYSIS

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Monotonic compression tests at various temperatures and strain rates for the AU material

(Figure 3) were first used to ascertain the estimated transition temperatures based on

stress-strain curvature. These results were then compared with measured twin areal

fractions to check for consistency. With that correlation established, the faster ST test

was carried out to compare its ability to reproduce distinctions among dominant

deformation mechanisms. Finally, the fast ST test was used to correlate the mechanical

behaviors of 6 Mg31AZ alloys in terms of transition temperature and grain size.

3.1 Monotonic compression testing and analysis

Isothermal monotonic compression tests were carried out at strain rates of 10-1/s, 10-2/s,

and 10-3/s, Figures 3 (a)-(c), respectively. Results at lower temperatures exhibit an

inflected aspect (concave up) associated with twinning while higher temperatures exhibit

the “normal” concave down curvature typical of slipping-only materials. To enable

quantification of the shape of the stress-strain curve, a quadratic equation

( CBA 2 +ε+ε=σ ) was fit to the data for the effective strain range 0.03-0.08. The sign of

the first coefficient, A, is equal to the second derivative, one measure of curvature:

A=(d2σ/dε2). A positive value of A over this strain range corresponds to a concave-up

(twinning-dominant) appearance while a negative value of A over this strain range

corresponds to a concave down (slip dominant) appearance.

A simple examination of Figures 3 reinforces the impressions gained from the tension-

compression test results in Figures 2. The shape (curvature sign and magnitude) of

compressive stress-strain curves over the strain range 0.03-0.08 are affected markedly by

the temperature and strain rate of the deformation. Based on the hypothesis that the value

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of A is directly related to the ratio of twinning strain to dislocation slipping strain, Figures

3 show that higher temperatures favor slip while higher strain rates favor twinning. The

hypothesized transition temperatures (from visual inspection of the curves) are presented

on each plot. They are significantly affected by strain rate, with an increase of 65oC

corresponding to a strain rate change of 2 orders of magnitude.

Figure 4 quantifies the visual interpretation of Figure 3 using the least-square values of A

(curvature). The lines shown in the figure are themselves best-fit quadratic

representations of A vs. test temperature, and the intersection with the A=0 axis

represents a hypothetical dividing line between twin dominated deformation (A greater

than 0) and slip dominated deformation (A less than 0). The condition A=0 represents an

estimate, based on mechanical behavior, of the transition temperature, Tt, between the

two regimes. As shown in the figure, the values of Tt obtained in this way are 138oC,

165oC, and 204oC, respectively, consistent with the visual estimates from Figure 3 of

145oC, 170oC, and 210oC.

In order to assess whether the mechanically-indicated transition temperatures correlate

with other indications, optical metallography was carried out to measure the areal fraction

of twins after deformation. Examples of such micrographs are shown in Figures 5 for

temperatures below, at, and above the estimated transition temperature of 138oC as

determined by mechanical analysis for a strain rate of 10-3/s. At 160oC, the areal fraction

of twins, Af, is 0.02. This value is consistent with minimum values of approximately

0.06 observed by Lou et. al. [8] after cyclic testing causing twinning and untwining. This

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range of values presumably represents the minimum fractions of twins attainable by

removal by mechanical means. At 140oC, near the transition temperature determined by

mechanical means, Af is 0.09. At 120oC, Af is 0.27. These results are consistent with the

transition temperatures from Figure 4, and furthermore are consistent with the hypothesis

that curvature A is an indirect measure of twin fraction Af after a fixed amount of

compressive deformation.

Additional metallography was done to test and quantify the postulated relationship

between A and Af. Figure 6 presents measured twin areal fractions, Af , and compressive

stress-strain curvatures, A, for a range of temperatures and strain rates. Note that the data

do not reveal a systematic variation with respect to temperature or strain rate. The best-

fit line is represented by the following relationship:

03.010.0)MPa(A)MPa(00005.0A 1Monof ±+=− (1)

where the standard error of fit of 0.03.

The A-intercept of Eq. (1) (Af=0.1 at A=0) represents the area fraction of twins observed

after a monotonic compressive strain of -0.08 where the stress-strain curve is essentially

linear (A=0). This value serves to calibrate phenomenologically the definition of

transition between twin-dominated and slip-dominated deformation, as interpreted by the

shape of the mechanical stress-strain curve.

The fact that for a given test and strain range the areal fraction of twins is related to the

curvature, but independent otherwise of both temperature and strain rate suggests that

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temperature and strain rate might be representable by a single variable. The obvious

choice to try is the Zener-Hollomon parameter [66], Z, which is represented by the

following:

=

RTQZ expε (2)

where Q is the activation energy for self diffusion, R is the ideal gas constant

(8.31J/molK) and T is the absolute temperature in K. A value of Q equal to

135,000J/mol has been found to correlate temperature and flow stress of magnesium

alloys [47].

In order to first test the usefulness of Equation 2, the compressive test data from Figures

3 were rearranged and plotted in terms of the yield stress and Z, Figure 7(a). Note that

the data represents a range of temperatures from 120oC to 250oC and strain rates from 10-

3/s to 10-1/s correlating to a range of Z of 4 orders of magnitude. The data fall onto two

straight lines which intersect at a transition value of 2.28.31Z

Zln

0

trans ±=

. The best-

fit lines can be represented as follows, with the standard errors of fits shown:

)MPa(5)MPa(55ZZln)MPa(5.5)MPa(

0

twiny ±−

=σ (3)

)MPa(4)MPa(187ZZln)MPa(6.9)MPa(

0

slipy ±−

=σ (4)

where Z0=1/s, and the two lines and corresponding yield stresses have tentatively been

divided into twin-dominated deformation ( twinyσ ) and slip-dominated deformation (slipyσ )

based on the intersection point of the two lines.

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The existence of two lines suggest a mechanistic interpretation that is consistent with the

literature, i.e., slip-dominated deformation at higher temperatures/lower strain rates, and

twin-dominated deformation at lower temperatures/higher strain rates. In a simplistic

interpretation, the lines represent the lower activation stress of the two deformation

mechanisms, but of course in reality a combination of mechanisms can be, and usually is,

required in order to satisfy the von Mises rule [11]. The slopes of the two lines in Figure

7(a) are consistent with the observation that the flow stress for slip is more rate-

dependent (or, equivalently, by Equation 2, temperature-dependent) than that for

twinning [24]. The slope of the slip line is approximately 1.7 times that of twin line.

This is qualitatively consistent with many reports of twinning occurring athermally when

taking into account the combined nature of slip and twinning required at lower

temperatures, where non-basal slip requires a much higher stress to activate [67]. If, in

fact, twinning is completely athermal, the ratio of slopes suggests that the initial ratio of

strain from twinning to slip would likely be in the range of 2/3 near the transition

temperature. This can be compared with Lou’s results [8] at room temperature where the

initial ratio of twinning strain to total strain was approximately 0.85. The sign of the

difference is consistent with slip being favored at higher temperatures, thus

reducing the initial fraction of deformation accomplished by twinning.

While Figure 7(a) is conceptually appealing because it emphasizes the cross-over of

activation stresses for the two combinations of deformation mechanisms (i.e. slip only

and slip+twinning), a more direct and hopefully more sensitive measure is related to the

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emerging concept in the current work of characterizing the combination of deformation

mechanisms using the stress-strain curvature, A. Figure 7(b) is similar to Figure 7(a), but

is based on the curvature rather than the yield stress. Again, two lines fit the data, with a

transition determined from their intersection near the same value of ln(Ztrans/Z0) as for

yield stress ( ( ) 2.28.31.vs,9.07.31Z/Zln 0trans ±±= ). The reduced scatter reflects the

better consistency of curvature data as compared with yield stress data. This ln(Ztrans/Z0)

value is also indistinguishable from the one for A=0, established earlier in this paper

( ) 4.02.32Z/Zln 0trans ±= . The best-fit straight lines are as follows, with the standard

errors of fits shown:

)MPa(586)MPa(51715ZZln)MPa(1604)MPa(A

0

twin ±−

= (5)

)MPa(480)MPa(14388ZZln)MPa(427)MPa(A

0

slip ±−

= (6)

Figure 7(c) is a plot similar to Figures 7(a) and (b) except using measured areal fractions

of twins. The transition values, respectively from the intersection of the two lines

( ( ) 8.03.31Z/Zln 0trans ±= ) and from the Af=0.10 calibrated criterion

( ( ) 4.02.32Z/Zln 0trans ±= ) are identical within the scatter, and are consistent with the

ones determined from Figures 7a and b. The best-fit equations are as follows, with the

standard errors of fits shown:

03.04.2ZZln079.0A

0

twinf ±−

= (7)

01.07.0ZZln023.0A

0

slipf ±−

= (8)

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Note that standard deviation from twin-fraction measurement is 0.04, which is consistent

with the above fit errors. Using each of the various criteria obtains an average critical

Zener-Hollomon parameter in a logarithm format as follows: ( ) 3.18.31Z/Zln 0trans ±= .

If the yield stress criterion is eliminated because of its higher inherent scatter, the scatter

is reduced but the average is unchanged: ( ) 8.08.31Z/Zln 0trans ±= . The scatter of these

numbers is approximately the same as combined uncertainty of the experiments and

fitting to obtain the lines and their intersections. Thus, it is concluded an identical value

of Ztrans is obtained by all of the techniques used to reveal it, both mechanical and

metallographic.

3.2 ST testing and analysis

Easily conducted and interpreted, the monotonic compressive test usually requires at least

5 samples to determine a transition temperature, Tt, between slip and twin for one strain

rate, excluding the trial samples to provide on estimate of Tt within approximately 10oC.

Optical metallography is even more cumbersome, and requires a similar number of

destructively-tested specimens. Based on the validity of the curvature of the stress-strain

curve on determining Tt, a step-temperature (ST) cyclic T/C test was conceived and

designed to potentially shorten the experimental time, and to reduce the required

specimen number. Detailed experimental procedures have been described in the

Experimental Procedures section of this paper.

Figure 8 presents a typical ST test result for Mg (AU) alloy at a strain rate of 10-3/s. Both

T and C legs show the expected transition from concave-down (slip) at higher

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temperatures and inflected shapes (twinning or untwinning) at lower temperatures. A

quadratic equation ( CBA 2 +ε+ε=σ ) was again fit to the true stress-strain curves for an

incremental strain range of 0.03-0.08 following each stress reversal, Figures 9. The first

tension leg is excluded in the plots because of its different strain range, 0.04 vs. 0.08.

Figures 9a and b compare the various legs and the best-fit curvature values (and the

visual goodness of fit).

Figure 9c illustrates the variation of curvature with temperature obtained from an ST test

in compressive legs ( CtT ) and tension legs (TtT ), respectively, and compares with a series

of isothermal monotonic compression tests presented earlier. The transition temperatures

from the ST test are 140oC from both tension and compression legs, as compared with

145oC from the series of monotonic tests. Analysis of the expected combined uncertainty

of Ztrans from all monotonic tests excluding yield stress characterizations (i.e.

( ) 8.08.31Z/Zln 0trans ±= ) gives the equivalent untertainty for Ttrans of C9C147 oo ±

for this case. Therefore, the ST test offers a faster, more economical, material-conserving

and equally-accurate alternative to performing a series of compression tests, with or

without metallographic analysis.

ST tests were performed over a range of strain rates and using temperature decrements of

5oC and 10oC, with results shown in Table 2. The transition temperatures, Tt (defined as

the average values of CtT and TtT from compression and tension legs of the ST test,

respectively) are identical for the two decrements within the overall scatter of the

technique (standard deviation of 3.6oC). For all subsequent results, the transition

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temperatures are determined by the average results from tension and compression legs for

ST testing.

In Figure 10, the ST test results (points) are compared with the corresponding monotonic

compression results presented previously (solid line, with dashed lines representing the

scatter):

( )( ) ( )( ) ( ) ( ) ( )CCKCLnmolKJ

molJCT oooot 9273//8.08.31/31.8/000,135)(

0

±−−±×

=εε

(9)

where s/10 =ε and the standard error of Tt is 9oC. Except at the highest strain rate of

0.1/s (corresponding to a transition temperature of 231oC for ST tests), the ST tests and

monotonic tests give identical results within the experimental scatter for each technique.

The difference of transition temperature from the two techniques at 0.1/s will be

discussed below.

The time-efficient and specimen-efficient ST test, being now been confirmed as giving

transition temperatures consistent with monotonic compression testing and

metallographic methods (except at the highest strain rate, 0.1/s), allows the rapid testing

of a range of material to look at other relationships. As a test of this capability, and to

assist with understanding the discrepancy of testing at 0.1/s-230oC, five other batches of

Mg AZ31B with varying grain sizes in the as-received (annealed) condition were

subjected to ST testing, with results shown in Figure 11. The equation for the best-fit line

shown in Figure 11 is as follows:

( ) ( ) ( ) ( )C8.6mdm/C5.6C6.118)C(T oooot ±μ×μ+= (10)

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where d is the average grain size and the standard error of fit is 6.8oC. This dependence

is consistent with similar reports in the literature [38]. Equation (10) can be converted to

a Zener-Hollomon basis using the known strain rate of 0.001/s used in the tests

represented in Figure 11:

( ) ( ) 6.0/546.01.34)/( 0 ±×−= mdmZZLn trans μμ (11)

where Z0=1/s, and the standard error of Eq. (11) is 0.6, corresponding to the standard

deviation of Tt, 6.8oC, for Eq. (10).

With known relationships for transition temperatures or critical Zener-Hollmon

parameters in terms of grain size (Eqs. 10 and 11), the question of the discrepancy of

results between ST and monotonic tests at the highest tested strain rate can be addressed.

Given the high transition temperature for ST testing at 0.1/s (231oC) an obvious

possibility is grain growth occurring during the test, thus increasing the measured Tt. To

test this hypothesis, the grain sizes for Mg AZ31B (AU) were measured after the

monotonic tests on either side of the transition temperature, 200oC and 210oC, and for the

single ST test which started at 250oC and ended at 210oC. The monotonic tests showed no

grain growth, with measured values of 4.0μm and 4.1μm, respectively, for the two

temperatures. (Recall that the initial grain size for Mg AZ31B (AU) was 4.0μm +/- 0.3

μm.) Conversely, the grain size of the ST specimen after testing had increased to 7.6μm 1.

Using Equation 11 to predict the role of a grain size change from 4.05μm to 7.6μm shows 1 In order to see if the grain growth rates during testing were consistent with regular grain growth kinetics, undeformed specimens of Mg AZ31B (AU) were heat-treated for 5 minutes at 150oC, 200oC, and 250oC. The specimens heat treated at 150oC and 200oC showed no grain growth (3.8μm and 4.0μm finally, compared with 4.0 +/- 0.3 initially) whereas the specimen heat treated at 250oC showed a grain size increased to 6.8μm. The grain growth behavior under deformation conditions at similar temperatures is similar.

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an expected change of transition temperature from 202oC to 231oC, a difference of 29oC.

That corresponds closely with the measured differences of Tt between the two tests of

27oC (204oC vs. 231oC). Thus, the principal source of discrepancy between ST and

monotonic tests at the highest strain rate (and thus highest tested temperatures) is caused

by grain growth.

In order to determine whether a similar one-to-one relationship between A and Af can be

established for ST tests, metallographic analysis was conducted for ST tests stopped after

1, 3 and 5 cycles. The results, Figure 12, are similar to those for monotonic compression

tests conducted isothermally, Figure 6, in terms of exhibiting a one-to-one

correspondence between A and Af, unaffected by temperature or strain rate. The actual

relationship is not identical to the one observed for monotonic, isothermal tensile tests.

Except at very small values of A and Af, the relationships are the same except for a fixed

offset (of either A or Af). Differences such as are shown in Figure 12 are to be expected

when considering the complex effects of cyclic deformation, time-at-temperature changes,

and the different accumulated strain magnitudes between the two tests, and the possible

effects on slip resistance and twin nucleation.

In order to clarify the origins of the different relationship between A and Af for the two

kinds of tests, modified ST tests starting a low temperature were conducted. The

transition temperatures obtained from these “ST-up” tests were significantly higher than

measured by the standard ST test, monotonic tests, or metallographic examination (all of

which are consistent). The ST-up tests give Tt of 156oC, versus 141oC obtained from the

22

standard ST test (Table 2). This difference is likely attributable to long-lasting changes of

microstructure based on the twinning at the initial, lower-temperature cycles. In a

simplified view, twinning and untwining during cycling at temperatures below Tt make

subsequent twinning easier by reducing the twin nucleation stress. This is consistent with

acoustic emission and mechanical testing results presented by Lou (2007).

Metallographic examination after an ST-up test at 0.001/s starting at 120oC and finishing

at 160oC exhibited an areal twin fraction of 0.1. That is, twinning continued at

temperatures above the value of Tt for the virgin material.

As a final probe to discern the role of mechanical cycling separate from the thermal

complexities of the ST test, isothermal “ST-no” tests were done. The observed curvatures

of the ST-no tests are compared with the ST and ST-up tests in Figure13. The isothermal

tests show that cycling alone increases the curvature of the stress-strain curve, with

results intermediate between St-up and ST tests. This is consistent with the expectation

that cycling reduces the activation stress for twinning (and untwining) [8], thus making

twin-dominant deformation possible at higher temperatures than for monotonic tests. This

tends to confirm the origin of the differences seen in the ST-up and standard ST tests.

The conclusion is that the ST-up test is unlikely to give Tt values consistent with other

measures because of the reduction of twinning activation stress by low-temperature

mechanical cycling.

4. CONCLUSIONS

23

The following conclusions were reached by mechanical testing in monotonic

compression, cyclic tension/compression, and metallographic analysis of Mg AZ 31B:

1. It is possible to measure transition temperature for dominant deformation

mechanisms (slip vs. slip-plus-twinning) purely mechanically based on the

curvature of the stress-strain relationship over fixed strain intervals. Procedures

for carrying out such tests have been presented. Mechanical tests based on

compressive yield stress are simpler to interpret and yield similar results, but are

less accurate.

2. Mechanical measurement of transition temperatures are consistent with, and have

similar scatter to, metallographic determinations.

3. Transition temperature depending on strain rate according to a critical Zener-

Hollomon parameter, the value of which has been measured consistently using

several kinds of tests. The activation energy is consistent with presentations in

the literature [38].

4. Transition temperatures are linearly related to grain size, in agreement with the

literature [38].

5. There is a one-to-one relationship between stress-strain curvature over a fixed

strain interval and the area fraction of twins measured after such deformation.

This relationship is independent of temperature and strain rate over the ranges

used here. An explicit form has been presented.

6. The deformation mechanism transition can defined mechanically by a zero-

curvature stress strain response over a strain range 0.03-0.8 corresponding to a

24

final areal fraction of twins equal to 0.1 for monotonic compression tests and 0.04

for “ST” (step temperature, cyclic tension/compression) tests.

7. Cyclic deformation at temperatures above the transition temperature (i.e.slip-

dominated) has little effect on the subsequent transition temperature. Conversely,

cyclic deformation below the transition temperature (twin-dominated) increases

the subsequent transition temperature, likely by a reduction of twin nucleation

stress at proposed by Lou [8].

8. Care must be taken with ST tests to avoid times-at-temperatures sufficient to

induce grain growth. Grain growth raises the transition temperature relative to that

for the virgin material.

9. Mechanical tests are faster, simpler, less expensive, and consume less material

than traditional techniques used for determining transition temperatures. They

introduce the possibility of rapidly testing in a range of material using small

quantities of each.

ACKNOWLEDGMENTS

This work was supported by the National Research Foundation of Korea (Grant NRF-

2010-220-D00037). Many thanks to AUSTEM Co. for providing materials, to Dr. Lou

Hector, Jr. (GM R&D Center) for providing materials, to Mr. Steve Bright for assistance

with sample preparation for optical metallography, and to Professors Sean Agnew and

Frederic Barlat for always-helpful discussions.

25

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List of Tables Table 1: Summary properties of Mg AZ31B alloys; compositions in weight percent.

Table 2: Transition temperatures Tt for alloy AU obtained from ST tests.

Table 1: Summary properties of Mg AZ31B alloys; compositions in weight percent.

Sheet* Al (%) Zn (%)

Mn (%)

Mg (%)

Thickness (mm) gs (μm)

AU 2.8 0.90 0.46 Balance** 2.02 4.0

GM-A N/A N/A N/A Balance 1.05 6.0-10.0

GM-M 2.6 0.71 0.32 Balance 1.01 11.0

GM-N 3.0 0.74 0.35 Balance 0.99 8.2

GM-O 3.0 0.74 0.32 Balance 1.00 5.8

GM-X 2.9 0.95 0.53 Balance 0.98 8.3

* Materials except for AU were provided by Dr. Lou Hector at General Motors, US. More information on the GM-designated alloys appear in the literature [68]. The AU material was provided by the AUSTUM company, Korea [69]. ** The AU alloy also contained 0.02% Ca, 0.005% Fe, and 0.0007% Cu. The remaining alloys were not tested for such trace quantities.

Table 2: Transition temperatures Tt for alloy AU obtained from ST tests.

Strain Rate (/s) ΔT (

oC) ttT (oC) ctT (

oC) 2

TTT

ct

tt

t+

= (oC)

0.0005 10 129 137 133 0.0005 5 129 134 132 0.001 10 141 140 141 0.001 5 143 142 143 0.005 10 161 169 165 0.005 5 167 170 169 0.01 10 171 180 176 0.01 5 169 174 172 0.05 10 195 205 200 0.05 5 196 201 199 0.1 10 230 231 231 0.1 5 231 229 230

List of Figures

Figure 1. Schematic of elevated-temperature T/C test and sample dimensions [53, 62] Figure 2. Isothermal cyclic T-C-T test results for Mg AZ31B(AU) at 0.001/s: (a) full results for testing at 25oC to 250oC [62]; (b) expanded compressive results after tension to a strain of 0.04 (not shown), and (c) expanded tension results after T( 04.0=ε ) and C( 08.0=ε ) intervals (not shown). Figure 3. Isothermal, monotonic compressive test results for Mg AZ31B (AU) at strain rates of (a) 0.001/s, (b) 0.01/s, and (c) 0.1/s. Figure 4. Determination of transition temperatures, Tt, of Mg AZ31B (AU) for isothermal monotonic compression tests at strain rates of 10-3, 10-2, 10-1/s. Figure 5. Optical micrographs of Mg AZ31B (AU) samples with deformation of ε=-0.08 at (a) 120oC, (b) 140oC, and (c) 160oC at a strain rate of 0.001/s. Figure 6. Experimental and best-fit linear correlation between the areal fraction of deformation twins and the stress-strain curvature, A=(d2σ/dε2), obtained from monotonic compressive hardening tests for the strain range -0.03 to -0.08 at various temperatures and strain rates.

Figure 7. Correlation of quantitative indicators of deformation mechanism with Zener-Hollomon parameter Z at various temperatures and strain rates as shown: a) compressive yield stress (-0.002 offset), b) stress-strain curvature, A, strain range -0.03- -0.08, c) measured areal twin fraction, Af, after a compressive strain of -0.08. Figure 8. Step-temperature cyclic T/C test at temperature from 150oC to 110oC, at a strain rate of 0.001/s using Mg AZ31B (AU) material. Figure 9. Determination of transition temperature, Tt, of Mg AZ31B (AU) using an ST cyclic test at a strain rate of 0.001/s: a) fitting of curvatures in compression portions; b) fitting of curvatures in tension portions; and c) transition temperatures determined from compression and tension portions compared with the one from isothermal monotonic compression tests. Figure 10. Evolution of transition temperature with strain rate. The solid line is the best-fit representation of the combined monotonic compression data corresponding to

( ) 8.08.31Z/ZLn 0trans ±= , Eq. 9. The dashed lines represent the scatter of Eq. 9, i.e., C9o .

Figure 11. Dependence of transition temperature with grain size determined from ST tests for six Mg AZ31B alloys.

Figure 12. Correlation between the areal fraction of deformation twin and the curvature, A (d2σ/dε2), obtained from ST cyclic T/C tests. Figure 13. Development of stress-strain curvature with mechanical tension-compression cycling in ST, ST-up, and ST-no tests.

Figure 1. Schematic of elevated-temperature T/C test and sample dimensions [53, 62].

0

100

200

300

400

0 0.05 0.1 0.15 0.2 0.25

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Accumulated Absolute True Strain

Mg AZ31B (AU), RD, TCT testThickness = 2.02 mmStrain rate = 0.001/s, μ = 0.03Side force = 2.5kN

25oC50oC

75oC

100oC

125oC

150oC

175oC

200oC225oC

250oCTension TensionCompression

25oC 50oC

75oC

100oC

125oC

150oC175oC

200oC225oC250oC

(a)

120

130

140

150

160

170

180

0.05 0.06 0.07 0.08 0.09 0.1 0.11

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Accumulated Absolute True Strain

Mg AZ31B (AU), RD, TCT testThickness = 2.02 mmStrain rate = 0.001/s, μ = 0.03Side force = 2.5kN

125oC

150oC

C after T

(b)

100

125

150

175

200

0.12 0.14 0.16 0.18 0.2

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Accumulated Absolute True Strain

Mg AZ31B (AU), RD, TCT testThickness = 2.02 mmStrain rate = 0.001/s, μ = 0.03Side force = 2.5kN 125oC

150oC

T after T-C

(c)

Figure 2. Isothermal cyclic T-C-T test results for Mg AZ31B(AU) at 0.001/s: (a) full results for testing at 25oC to 250oC [62]; (b) expanded compressive results after tension to a strain of 0.04 (not shown), and (c) expanded tension results after T( 04.0=ε ) and C( 08.0=ε ) intervals (not shown).

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Absolute True Strain

120oC

130oC

140oC

150oC

160oC

Mg AZ31B (AU), Ct=2.02mm, gs=4.0μm, strain rate = 0.001/s

(a)

100

120

140

160

180

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Absolute True Strain

Mg AZ31B (AU), Ct=2.02mm, gs=4.0μm, strain rate = 0.01/s

150oC

160oC

170oC

180oC

190oC

(b)

C145T ot ≅

C170T ot ≅

100

110

120

130

140

150

160

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Absolute True Strain

Mg AZ31B (AU), Ct=2.02mm, gs=4.0μm, strain rate = 0.1/s 190oC

200oC

210oC

220oC

230oC

(c)

Figure 3. Isothermal, monotonic compressive test results for Mg AZ31B (AU) at strain rates of (a) 0.001/s, (b) 0.01/s, and (c) 0.1/s.

C210T ot ≅

-2x103

-1x103

0

1x103

2x103

3x103

4x103

5x103

100 120 140 160 180 200 220 240

Cur

vatu

re A

(MPa

)

Test Temperature (oC)

Mg AZ31B(AU), Monotonic Ct=2mm, gs=4.0μm

0.001/s0.01/s0.1/s

0.001/s

0.01/s

0.1/s

Tt=138oC 165oC 204oC

Concave-up

Concavedown

Figure 4. Determination of transition temperatures, Tt, of Mg AZ31B (AU) for isothermal monotonic compression tests at strain rates of 10-3, 10-2, 10-1/s.

(a) 10-3/s, 120oC. Af=0.27

(b) 10-3/s, 140oC. Af=0.09

(c) 10-3/s, 160oC. Af=0.02

Figure 5. Optical micrographs of Mg AZ31B (AU) samples with deformation of ε=-0.08 at (a) 120oC, (b) 140oC, and (c) 160oC at a strain rate of 0.001/s.

0

0.05

0.1

0.15

0.2

0.25

0.3

-4000 -2000 0 2000 4000 6000

Are

al fr

actio

n of

twin

Curvature A (MPa)

Mg AZ31B, RD, Monotonic Ct=2mm, gs=4.0mm

0.001/s0.01/s0.1/s

Fig. 5(a)

120oC

Fig. 5(b), 140oC

Fig. 5(c)

160oCTwin dominated

Slip dominated

150oC

160oC

170oC

130oC

150oC

190oC

200oC

210oC220oC

230oC

180oC190oC

Figure 6. Experimental and best-fit linear correlation between the areal fraction of deformation twins and the stress-strain curvature, A=(d2σ/dε2), obtained from monotonic compressive hardening tests for the strain range -0.03 to -0.08 at various temperatures and strain rates.

80

90

100

110

120

130

140

28 30 32 34 36

Abs

olut

e Yi

eld

Stre

ss, |

σ y| (

MPa

)

Ln(Z/Z0)

0.001/s0.01/s0.1/s

Twin dominant (A>0)Slip dominant (A0)

0.1/s

Twin dominated

Slip dominated

120oC

130oC

140oC

150oC160oC

150oC

160oC

170oC180oC

190oC

190oC

200oC

210oC

240oC230oC

220oC

Slip dominant (A

0

0.05

0.1

0.15

0.2

0.25

0.3

28 30 32 34 36

Are

al F

ract

ion

of T

win

Ln(Z/Z0)

Mg AZ31B (AU), RD, Monotonic Ct=2.02mm, gs=4.0μm

0.001/s0.01/s

Twin dominant (A>0)

0.1/s

Twin dominated

Slip dominated

120oC

130oC

140oC

150oC

160oC

150oC

160oC

170oC180oC

190oC

190oC200oC

210oC220oC

240oC230oC

Slip dominant (A

-200

-100

0

100

200

300

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

Accumulated Absolute True Strain

Mg AZ31B (AU) ST cyclic T/C test t=2.02mm, gs=4.0μm, strain rate=0.001/s

150oC 140oC 130oC 120oC 110oC

Figure 8. Step-temperature cyclic T/C test at temperature from 150oC to 110oC, at a strain rate of 0.001/s using Mg AZ31B (AU) material.

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Absolute True Strain after Revesal

110oC (A=4219MPa)

120oC (A=2223MPa)

130oC (A=1078MPa)

140oC (A=-164MPa)

150oC (A=-1956MPa)

Mg AZ31B (AU) compressive cycles,t=2.02mm, gs =4.0μm, strain rate = 0.001/s

Fit curve: Aε2+Bε+C=σ

(a)

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Absolute True Strain after Reversal

110oC (A=16465MPa)

120oC (A=10143MPa)

130oC (A=3946MPa)

140oC (A=27MPa)

150oC (A=-2591MPa)

Mg AZ31B (AU), Tensile cycles,t=2.02mm, gs=4.0μm, strain rate = 0.001/s

Fit curve: Aε2+Bε+C=σ

(b)

-5x103

0

5x103

1x104

1.5x104

2x104

100110120130140150160

Cur

vatu

re A

(MPa

)

Temperature (oC)

Mg AZ31B (AU), strain rate=0.001/sT

down, t=2.02mm, gs=4.0μm

ST, Tension

ST,Compression

Monotonic,Compression

Tt, Mono

Tt, ST

(c)

Figure 9. Determination of transition temperature, Tt, of Mg AZ31B (AU) using an ST cyclic test at a strain rate of 0.001/s: a) fitting of curvatures in compression portions; b) fitting of curvatures in tension portions; and c) transition temperatures determined from compression and tension portions compared with the one from isothermal monotonic compression tests.

120

140

160

180

200

220

240

0.0001 0.001 0.01 0.1

Tran

sitio

n te

mpe

ratu

re (o

C)

Strain rate (/s)

Mg AZ31B (AU), RD,t=2.02mm, gs=4.0μm

ST Cyclic Data, ΔT=10oCST Cyclic Data, ΔT=5oCEq. 9 (Monotonic Tests)

Figure 10. Evolution of transition temperature with strain rate. The solid line is the best-fit representation of the combined monotonic compression data corresponding to

( ) 8.08.31Z/ZLn 0trans ±= , Eq. 9. The dashed lines represent the scatter of Eq. 9, i.e., C9o .

120

140

160

180

200

2 4 6 8 10 12

Tran

sitio

n te

mpe

ratu

re (o

C)

Grain size (μm)

Mg AZ31B, RD,Strain rate = 0.001/s

Cyclic, ΔT=10oC

Cyclic, ΔT=5oC

Best-fit line

AU

GM-O

GM-A

GM-N

GM-XGM-M

Figure 11. Dependence of transition temperature with grain size determined from ST tests for six Mg AZ31B alloys.

0

0.04

0.08

0.12

0.16

-2000 -1000 0 1000 2000 3000

Are

al fr

actio

n of

twin

Curvature A (MPa)

Mg AZ31B, RD, Cyclic Ct=2.02mm, gs=4.0mm

0.001/s0.01/s0.1/s

Twin dominated

Slip dominated

160oC-120oC

160oC-140oC

160oC

190oC

190oC-170oC

190oC-150oC

250oC

250oC-230oC

250oC-210oC

ST testMonotonic test

Figure 12. Correlation between the areal fraction of deformation twin and the curvature, A (d2σ/dε2), obtained from ST cyclic T/C tests.

-3x103

-2x103

-1x103

0

1x103

2x103

3x103

0 1 2 3 4 5 6

A (M

Pa)

Cycle

Mg AZ31B (AU), strain rate=0.01/st=2.02mm, gs=4.0μm

ST-up

ST

ST-no

190oC

180oC

170oC

170oC

170oC

170oC170oC

170oC

170oC160oC

150oC

150oC 190oC

160oC180oC

Figure 13. Development of stress-strain curvature with mechanical tension-compression cycling in ST, ST-up, and ST-no tests.

Article FileTable 1-2Figure 1-13