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Journal of Materials Processing Technology 210 (2010) 37–47

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

ormability of a more randomly textured magnesium alloy sheet:pplication of an improved warm sheet formability test

.E. Dreyera, W.V. Chiua, R.H. Wagonerb, S.R. Agnewa,∗

Department of Materials Science and Engineering, University of Virginia, 395 McCormick Rd, Charlottesville, VA 22904-4745, USADepartment of Materials Science and Engineering, The Ohio State University, 477 Watts Hall, 2041 College Rd, Columbus, OH 43210-1178, USA

r t i c l e i n f o

rticle history:eceived 11 June 2008eceived in revised form 16 July 2009ccepted 18 August 2009

a b s t r a c t

The warm formability of three sheet magnesium alloys was measured using the OSU formability testadapted for testing at elevated temperatures under isothermal conditions. The adapted test is shown toreliably enforce plane strain tension over a significant fraction of the sample, thus providing an assessmentof FLD(0), typically the minimum major strain value on a forming limit diagram. By mathematicallymodeling the strain as a function of punch displacement, a case is made that the punch displacementitself provides an expedient approach to ranking the relative formability of sheet metals. Combined

eywords:lasticitynstabilityractureormabilityhear

with knowledge of the constitutive behavior of the material, the punch displacement–strain relationshipprovides an explanation for the observed shape of the punch load versus displacement curves. OSUformability test results show that a new magnesium sheet alloy, yttrium-containing ZW41, is significantlymore formable than traditional magnesium alloys AZ31 and ZK10. The improvement is linked to a morerandom texture in the new alloy, which diminishes the tendency for gross, catastrophic shear instability

tured

ttriumare earth

typical of the strongly tex

. Introduction

The forming limit diagram (FLD) provides a rather completessessment of sheet metal formability under various strain paths.he concept of FLD was originally proposed by Keeler (1965), whooncluded, from tests of various metals biaxially stretched overunches, that there was a critical ratio of major to minor strain thatroduced fracture. Goodwin (1968) combined Keeler’s data withracture strains gathered on materials stretched under conditionsf negative minor strain to produce the first rudimentary FLD. Cur-ently, the standard approach to experimentally probe the FLD iso test strips of various widths, which enforce various strain paths,sing the limiting dome height (LDH) apparatus (Hecker, 1975).he limit strains are generally measured post-mortem using gridsrinted or etched on the sheet surface prior to forming. It is almostniversally observed that the minimum in the FLD is observedlose to the plane strain tension condition (Wagoner et al., 1989),enoted FLD(0).

In fact, it has been shown that the majority of press-shop fail-

res occur under conditions of plane strain tension (Wagoner etl., 1989). Traditional sheet formability tests, such as the Erick-on/Olsen ball punch tests (ASTM E 643-84, 2000) primarily enforceiaxial stretching, rather than plane strain; hence, the results

∗ Corresponding author. Tel.: +1 434 924 0605; fax: +1 434 982 5660.E-mail address: agnew@virginia.edu (S.R. Agnew).

924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2009.08.022

traditional alloys.© 2009 Elsevier B.V. All rights reserved.

obtained often do not correlate well with practical formability. Inaddition, the results from these tests suffer from large uncertainties.The OSU formability test (OSUFT) was introduced by Miles (1991)and developed by Narasimhan et al. (1995) to enforce plane straintension, while also simulating the typical die-sheet metal inter-action. The test has been demonstrated to be highly reproduciblein several studies, such as those conducted by Narasimhan et al.(1995) and Karthik et al. (2002), when compared to previously con-ceived plane strain formability testing procedures, including theuse of the LDH apparatus (Ayers et al., 1984).

The objective of the present research is to determine thepotential of the OSUFT for characterizing the formability of sheetmaterials at elevated temperatures, since a number of high specificstrength materials exhibit poor room temperature formability, thusrequiring warm forming. Post-mortem measurements of FLD(0)are compared with the data gathered during the test, in the formof load versus punch displacement curves. Establishing a relation-ship between the two would eliminate the need for time intensivemeasurement of strains of circle grids.

The formabilities of three magnesium alloys, including arecently developed alloy denoted ZW41, are assessed at temper-atures in the range of T = 160–350 ◦C using the OSUFT apparatus

modified to test at elevated temperatures under isothermal con-ditions. Therefore, the results gathered can be used to determinethe effect of temperature alone for validating constitutive modelsused in simulations. Notably, it has been claimed that alloy ZW41has improved warm formability over traditional magnesium alloys

38 C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47

Table 1Nominal compositions (in wt%, balance Mg), grain sizes (�m), and texture strength(root mean squared value of the orientation distribution) of the three alloys.

Alloy Al Zn Y Zr Grain size Texture strength

(taadf

2

2

Aptfiatttcf0

appEtra

mitt(rtPpttawtsetb

2

twk

AZ31 3 1 – – 6.5 2.59ZK10 – 1 – 0.3 20 2.03ZW41 – 4 0.7 – 11 1.39

Kim et al., 2006). A recent report of Chino et al. (2009) confirmshat Mg–Zn–Y alloys can have exceptional stretch formability, event room temperature. Explanations for the improved formabilityre sought in an attempt to develop insight required to inspire theesign of new magnesium alloys with even further improved warmorming properties.

. Experimental procedures

.1. Materials and microstructure characterization

Formability testing was conducted on three magnesium alloys:Z31, ZK10, and ZW41. The nominal compositions of the alloys arerovided in Table 1. AZ31 and ZK10 are tradition magnesium alloyshat were produced by DC casting, hot rolling, and warm-rolling to anal gage of 1.03 ± 0.02 mm. Alloy ZW41 was DC cast, extruded intothin plate, and warm-rolled to a final gage of 1.02 ± 0.02 mm. All of

he sheets were sheared into smaller 127 mm wide blanks. For theraditional alloys, the blanks were 127 mm in length. ZW41 tendedo draw over the lock beads of the test apparatus so the blanks wereut with a length of 178 mm to increase the effect of the clampingorce. Blanks were then electro-etched with a square grid of circles.254 mm in diameter for post-mortem strain measurements.

Metallographic samples were prepared by grinding with SiCbrasive paper and then polishing with 3 and 1 �m diamond sus-ensions. The polished samples were chemically etched with aceticicral (5 mL acetic acid, 6 g picric acid, 10 mL H2O, 100 mL ethanol).ach of the alloys exhibited roughly equiaxed grain structuresypical of warm-worked Mg alloys that have undergone dynamicecrystallization during primary sheet processing (Fig. 1). The aver-ge lineal intercept grain sizes of the sheets are presented in Table 1.

Texture measurements were performed on samples ground toid-plane using SiC abrasive paper, and then chemically etched

n 20% Nital (20 mL HNO3, 80 mL methanol). A Scintag X1 diffrac-ometer with Cu K� sealed tube source (40 kV, 35 mA) was usedo measure the basal (0 0 0 2), prismatic (1 0 1 0), and pyramidal1 0 1 1) pole figures on a 5◦ × 5◦ grid of tilt and azimuth. Theesulting pole data were corrected for defocusing using experimen-al data from a randomly texture powder and analyzed using thereferred Orientation Package-Los Alamos (popLA) software. Com-lete basal and prismatic pole figures are presented in Fig. 2, andhe texture strengths (the root mean squared value of the orien-ation distribution function) are listed in Table 1. Alloy AZ31 hasstrong basal texture, with the basal poles preferentially alignedith the sheet normal direction (ND). ZK10 has a similarly strong

exture, but with basal poles of the peak texture component tiltedlightly away from the ND toward the rolling direction (RD). ZW41xhibits a much weaker texture which will figure prominently inhe understanding of the improved formability that this alloy wille shown to possess.

.2. Formability testing apparatus

The geometry of the OSUFT apparatus (Fig. 3) was based onhat optimized by Narasimhan et al. (1995). The punch and dieere machined from D2 tool steel (ASTM A 681-08, 2007), which is

nown for its wear and oxidation resistance at the moderate form-

Fig. 1. Optical micrographs reveal the essentially equiaxed grain structure in theas-rolled condition of all three alloys, (a) AZ31, (b) ZK10, and (c) ZW41.

ing temperatures of interest. The binding plate was secured to thedie by 8 (1/2 in.-20, grade 8 Zn-plated hex cap) bolts, as opposed tothe hydraulic clamp normally implemented (Sriram and Wagoner,1994). This allows the apparatus to entirely fit within a standardATS Series 3620 convection furnace that, in turn, fits within stan-dard computer controlled universal testing system (MTS Sintech10/GL). Notably, there was no specific seasoning (Karthik et al.,2002) of the punch or binding plates, or lubrication of the sam-

ple, punch, or die. Rather, all contact surfaces were cleaned withacetone and polished daily.

The whole apparatus was heated to temperature prior to secur-ing the blank. The furnace was then opened and the sample was

C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47 39

Fig. 2. Distinct texture types are revealed by the basal (0 0 0 2) and prismatic (1 0 1 0)pole figures (top and bottom, respectively) of alloys, (a) AZ31, (b) ZK10, and (c) ZW41.

Fd

it(att

3((mwtTapmmtf(meota

cwtaga

ig. 3. Schematic diagram of the OSU formability testing apparatus including theie, punch, blank holder, and deformed sheet.

nserted. The clamping force provided by increasing the torque onhe 8 bolts (to 22.5 Nm) was sufficient to prevent any significant<1 mm) draw-in over the lock beads. The furnace was then closed,nd once the temperature of the gauge region of the blank reachedemperature, the test was conducted. This practice resulted in aemperature uncertainty of ±2 ◦C.1

Tests were conducted at temperatures ranging from 150 to50 ◦C and at a punch velocity of 1 mm/s. Analytical calculationssee Appendix) show that this correlates with an maximum Hosford1979) effective strain rate of ∼0.045 s−1. Because of the afore-

entioned texture and the likelihood of anisotropic behavior, testsere conducted both on blanks with the major straining direc-

ion aligned with the rolling (RD) and transverse (TD) directions.he punch load was recorded as a function of punch displacement,nd it will be shown that the relative formability of the alloys isrovided by these simple data alone. On-sample strain measure-ents were also made by comparing the length of the major andinor axes of etched circles immediately surrounding the frac-

ure to the diameter of undeformed circles. Digital images of theractured region (Fig. 4) were uploaded into Image Tool softwareUTHSCSA, 2002), which was calibrated by measuring a line seg-

ent on the physical sample (with uncertainty of less than or

qual to ±0.03 mm) using an optical microscope. Several methodsf fully automatic image analysis were tested, and it was foundhat manually highlighting the ellipsoidal-grids on the digital imagellowed data to be gathered accurately even when the etching was

1 In some of the earlier tests, the temperature was measured on the materiallamped by the die lock bead (see “original thermocouple position” in Fig. 3); itas later shown in tests where the temperature was measured on the middle of

he gauge section (see “revised thermocouple position” in Fig. 3), that there wastemperature difference between the die and the sheet of ∼15 ◦C (higher in the

age region). Therefore, greater uncertainty in the revised temperatures (±5 ◦C) isdmitted for these earlier tests, as reflected by the error bars in Figs. 7, 8, and 9.

Fig. 4. Digital photograph of etched circle grid on a deformed alloy ZW41 sample.

not of the highest quality or there was damage to the surface ofthe material.

3. Experimental results

On-sample strain measurements show that a large region ofthe sample indeed undergoes plane strain tension, including thelocation where failure initiates. Figs. 5(a)–(c) present the minorstrain versus position for each of the alloys tested along the trans-verse direction (TD) at 275 ◦C. We observe a region in each wherethe minor strains are approximately zero, within a range of about±0.05. There is a significant amount of minor strain close to theedges of the sample due to the lack of constraint, approachinguniaxial straining at the edge itself. We find that an average of36 ± 3 mm or 28%, of the sample is under plane strain. Finally,using the technique illustrated by Ghosh et al. (1984), we deter-mine the limit strains (the FLC) close to the plane strain conditionon a forming limit diagram and extrapolate to obtain FLD(0) (seeFig. 5(d)–(f)).

3.1. Punch load and displacement versus temperature

The punch load versus displacement curves from the three alloyscollected at different temperatures and strain rates all show similartrends. There was a concave up region during initial contact (labeled(1) in Fig. 6(a)), followed by a nearly linear region labeled (2), and adeparture from near linearity labeled (3). The samples tested at thelowest temperatures (T = 160–175 ◦C) failed abruptly within thisnon-linear region (3), and close inspection of these samples showedvery little plastic localization prior to fracture. At higher tempera-tures, a fourth region (4) was observed in which the load reached amaximum, followed by failure (5). See Fig. 6 for an illustration of thetrends in the load versus displacement curves at different temper-atures. Two critical points in the load versus displacement curveswere compared: the maximum load and the displacement at thepoint of fracture. Notably, all of the materials demonstrated a sim-ilar trend of monotonically decreasing punch load with increasingtemperature (Fig. 7). The two curves (with the range denoting thescatter in the data points) superposed in Fig. 7 are scaled versionsof the viscoplastic model of Sellars and Tegart (1967),(

Q)

˙ε expRT

= A · [sinh(��)]n, (1)

which, Neil and Agnew (2009) have shown well-describes theflow stress of Mg alloy, AZ31 over the warm forming tempera-ture regime (T ∼ 200–300 ◦C). This relationship will later be used

40 C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47

F ) showi d) AZ

talh

scaippda2at

ig. 5. Minor strains in the free region of the sample (and in the vicinity of fracturen a forming limit diagram illustrates how the values of FLD(0) are obtained, (a and

o model the punch load versus displacement. The samples testedt T = 160–175 ◦C that fractured prior to reaching the decreasingoad region (4) in load versus displacement curve were observed toave peak loads that fall below the curves presented in Fig. 7.

In contrast with the simple trend observed for punch load ver-us temperature, the punch displacements at fracture show a ratheromplex trend for all three alloys (Fig. 8). Firstly, all the materialsnd test directions had local maxima at ∼215 ◦C and local min-ma at 250 ◦C; at temperatures above 250 ◦C and below 215 ◦C, theunch displacement at fracture increases monotonically with tem-erature. Notably, alloy ZW41 showed significantly higher punch

isplacements at all temperatures of 215 ◦C and above. Taking anverage value of 19 mm for the conventional alloys and a value of6 mm for ZW41 (the average of the responses measured along RDnd TD) suggests that ZW41 performs ∼35% better than the conven-ional alloys at 215 ◦C. None of the alloys exhibit strong anisotropy

a significant region of plane strain tension, and plotting major and minor strains31, (b and e) ZK10, and (c and f) ZW41.

in the punch displacement at failure. Though the data is scant, itappears that alloy ZW41 may be anisotropic, since the RD samplesshow higher punch displacements at failure in comparison to TD.

3.2. FLD(0) versus temperature

The results of FLD(0) measurements re-emphasizes that magne-sium alloys exhibit acceptable formability at only mildly elevatedtemperatures. For example, the most common magnesium sheetalloy, AZ31, yielded a FLD(0) value of 0.32 at 215 ◦C, which is com-parable to automotive mild steel sheet tested at room temperature

(Wagoner et al., 1989). Fig. 9 illustrates that FLD(0) values show thesame complex trend with temperature that was observed for thepunch displacement at fracture; in fact, the same “curves to guidethe eye” that were developed for the punch displacement plot werescaled and superimposed on these data. Considering the FLD(0) val-

C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47 41

FA

uZt

4

4

tint

2007), including the AZ31 and ZK10 alloy sheets examined in thisstudy (Fig. 2). This naturally calls attention to the plastic anisotropyof the alloys. Curiously, the room temperature strength anisotropyof alloy ZW41 is greater than the other two alloys (Agnew et al.,2008). This has to do with a detail of the texture of the alloys, namely

ig. 6. Punch load vs. displacement as a function of temperature for three alloys, (a)Z31, (b) ZK10, and (c) ZW41.

es as a quantitative measure of formability, it is shown that alloyW41 performs ∼37% better than the conventional alloy AZ31 at aemperature of 215 ◦C (FLD(0) ∼ 0.44 vs. ∼ 0.32).

. Discussion

.1. Relative warm formability of Mg alloy sheets

In an attempt to explain the enhanced formability of ZW41,he constitutive behaviors of the alloys were compared. Accord-ng to Agnew et al. (2008), the alloys examined in this study doot exhibit appreciable strain hardening within the warm formingemperature regime (T ∼ 175–350 ◦C). The strain rate sensitivities

Fig. 7. Peak punch load vs. temperature for all three alloys tested along the rolling(RD) and transverse (TD). Curves provided to guide the eye are based upon anempirical relationship described in the text.

of the three alloys are also quite similar; at 200 ◦C, for example,all three alloys exhibited rate sensitivities of m = 0.12 ± 0.02, eventhough the formability of alloy ZW41 is most exceptional at thattemperature (Agnew et al., 2008). Finally, the tensile flow stressesof the three alloys were similar to one another over the tempera-ture regime of interest. In fact, the RD samples of alloy ZW41 wereamong the stronger samples tested in the study (Fig. 7). Thus, it doesnot appear that alloy ZW41 avoids a stress-based fracture criterionby simply flowing at a lower stress.

The grain size of the exceptional alloy, ZW41, is intermediate tothe two conventional alloys, AZ31 and ZK10 (Table 1). On the otherhand, the crystallographic texture of alloy ZW41 sheet is excep-tionally weak, as compared to other Mg alloy sheets (Bohlen et al.,

Fig. 8. Punch displacement at fracture vs. temperature for all three alloys testedalong the rolling (RD) and transverse (TD) directions. Curves provided to guide theeye.

42 C.E. Dreyer et al. / Journal of Materials Proc

Fc

tpwonl

mrrpcddraoflairmbdiafa

amcvE

decreases as the temperature is increased in a number of metal

Tr

ig. 9. FLD(0) vs. temperature for the three alloys. Curves are based upon moreomplete data in this figure.

he non-trivial volume fraction of grains with basal poles nearlyarallel to the TD in comparison to the very few grains orientedith basal poles parallel to the RD. This causes the soft mechanism

f {1 0 1 2} extension twinning to be active during TD tension, butot RD tension (Bohlen et al., 2007). This strength anisotropy is

argely absent in the warm forming regime (Agnew et al., 2008).The strain anisotropy of the three alloys was characterized by

easurements of the r-values (Table 2) within the temperatureange of interest. The tensile testing practice and procedure of-value measurement applied to these alloys has been reportedreviously (Agnew et al., 2008). At room temperature, the twoonventional alloys exhibit marked anisotropy with the transverseirection having an r-value much greater than 1, and the rollingirection having a lower r-value, rRD < rTD. On the other hand, the-values of alloy ZW41 are lower than 1 at room temperaturend a reversal in the sense of the in-plane anisotropy, rRD > rTD, isbserved. The sense of the in-plane anisotropy remains constantor all three alloys at all temperatures examined; however, theevel of in-plane anisotropy is significantly diminished for all threelloys within the temperature range, T = 200–300 ◦C, where signif-cant formability is obtained. ZW41-TD samples have the lowest-values and best formability, at all temperatures. However, thisay be coincidental since a collective comparison of all the forma-

ility testing results (Figs. 8 and 9) with the r-value data in Table 2oes not reveal any other obvious trends. This latter observation

s consistent with previous understanding that the forming limitst plane strain condition (FLD(0)), and on the stretching side of theorming limit diagram are relatively insensitive to r-value (Hosfordnd Caddell, 1993).

Finally, the nature of the sample failures themselves, as char-cterized by fractographic examination using a scanning electron

icroscope (JEOL 840, with LaB6 filament operated at 30 kV), are

ompared. It has already been mentioned that the failures wereery abrupt at the lowest testing temperatures (T ∼ 160–175 ◦C).ven at higher temperatures, macroscopic examination of the frac-

able 2-Values measured along the rolling and transverse directions (RD, TD) for the three alloy

Alloy RT (Agnew et al., 2008) 100 150

AZ31 2.2, 4.0 0.93,2.6a 0.67ZK10 0.69, 1.6 –,– –,–ZW41 0.95, 0.71 1.02, 0.80 0.94

a The quantities in italics were measured on a sheet of the same alloy and H24 temper,

essing Technology 210 (2010) 37–47

tures gives the appearance of interconnected, catastrophic shearfailures, particularly in the case of the conventional alloys AZ31 andZK10; appreciable local thinning (necking) is not observed macro-scopically until 250 ◦C or higher. Scanning electron microscopyrevealed that facture occurred by a transgranular, ductile tearingmechanisms in all cases, rather than cleavage or intergran-ular cracking (Fig. 10(a)–(d)). SEM images of ZK10 tested at200 ◦C (Fig. 10(a)) show a fracture surface highly inclined to themajor stress axis, characteristic of shear failure. Alloy ZW41 alsoshows elongated dimples and inclined fracture surfaces at 200 ◦C(Fig. 10(c)). However, the fracture surface frequently switched fromone inclined plane (e.g., ∼45◦) to another (e.g., ∼135◦) and theregion where the different inclined surfaces meet one another con-tains more equiaxed, ductile dimples characteristic of pure tensilefailure. At higher temperatures, alloy ZK10 continued to fail byshear localization (Fig. 10(b)), while alloy ZW41 necked down toa virtual knife’s edge (Fig. 10(d)).

The differences observed in the fracture surfaces give insightregarding the improved formability of alloy ZW41, relative to tra-ditional magnesium alloys, AZ31 and ZK10. The macroscopic strainpath (plane strain tension) promotes failure by simple shear on aplane inclined ∼45◦ from the plane of the sheet. Magnesium alloys,in general, seem prone to shear failure and this is likely connectedwith the plastic anisotropy of the single crystal. Only hard defor-mation mechanisms, such as mechanical twinning, non-basal 〈c + a〉slip, and/or kink banding, can accommodate strain along the hexag-onal close packed crystal c-axis (e.g., Agnew and Duygulu, 2005).As mentioned earlier, the conventional alloy sheets tend to bestrongly textured; thus, it is hypothesized that once a shear insta-bility develops in one grain, it may have little difficulty propagatinginto adjacent grains because they are similarly oriented (in particu-lar concerning the orientation of the c-axis). Ando and Koike (2007)and Barnett (2007) have recently noted that compression twins andso-called “double twins” may be important shear-based crack ini-tiation mechanisms. For weakly textured alloys, like ZW41, suchshear instabilities may not propagate from one grain to the nextwith such ease; this would cause it to resist the shear failure thatcauses fracture in the other alloys at temperatures under 250 ◦C,improving formability.

4.2. The formability plateau or decrease with temperature

An explanation for the anomalous formability decrease withincreasing temperature that occurred for each of the alloys atapproximately 250 ◦C was sought. In a previous publication (Agnewet al., 2008), it was shown that an observed plateau in tensile elon-gation between 200 and 300 ◦C can be explained in terms of changesin constitutive behaviors, namely the strain hardening exponentand strain rate hardening exponent. However, this does not read-ily provide an explanation for the observed dramatic decrease informability in-plane strain tension.

Dynamic strain aging (DSA) has been used to explain ductility

alloys, ranging from the well-known “blue brittleness” of steelsto the poor room temperature formability of Al–Mg alloys. Thisis an attractive explanation since there have been a number ofrecent reports of DSA in rare earth-containing Mg alloys tested at

s at different temperatures (◦C).

200 250 300

, 1.7* 0.70, 1.5* 0.67, 1.2 0.88, 1.0–,– 1.2, 1.4 0.83, 1.2

,0.84 0.76,0.66 0.66,0.59 –,–

but of different thickness, originally reported by Agnew and Duygulu (2005).

C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47 43

F 00 ◦C,Z

msbsoisaorham

rohsdbsss

soaoitof

ig. 10. SEM fractographs of alloys (a and b) ZK10 and (c and d) ZW41 at 200 and 3W41.

oderately elevated temperatures. Zhu and Nie (2004) observederrated flow of a Mg–Y–Nd alloy tensile tested at temperaturesetween 150 and 215 ◦C, along with a yield strength plateau andome evidence of a negative strain rate sensitivity, all indicationsf DSA. Curiously, they noted the absence of a loss in ductility, whichs often associated with DSA. Zhongjun et al. (2007) observed theame effects at temperatures between 200 and 300 ◦C in an Mg–Erlloy. Trojanová et al. (2005) present similar results for a numberf rare earth alloys, including alloy ZE41 (where E denotes an Nd-ich rare earth mischmetal). Finally, Wang et al. (2007) present aistorical overview of DSA observations in magnesium, along withpresentation centered on alloy ZE43 (where E denote Ce-richischmetal).None of the characteristics of DSA, such as serrated flow,

educed strain rate sensitivity or yield strength anomaly, have beenbserved for the present ZW41 alloy sheet (Agnew et al., 2008). Per-aps a reason for the distinction is that all of the aforementionedtudies of DSA in Mg–rare earth alloys appear to have been con-ucted on cast alloys, where yielding is known to be controlledy basal slip and/or tensile twinning. Bohlen et al. (2007) havehown that even weakly textured Mg alloy sheets, such as ZW41,till exhibit a significant non-basal slip activity at relatively lowtrains.

DSA has also been observed for non-rare earth-containing alloys,uch as AZ91, close to room temperature (Corby et al., 2007); thisbservation is consistent with the expectation that the diffusivity oflloy elements like Al and Zn in Mg are higher than the diffusivities

f rare earth elements. Curiously, alloys AZ31 and ZK10 examinedn this study show a formability minimum at a similar elevatedemperature to alloy ZW41 (Fig. 7). It is concluded that DSA mayccur in magnesium alloys, but it does not appear to be responsibleor the observed ductility minimum.

respectively, show reduced propensity for catastrophic shear failure in the case of

Most likely candidate explanations for the formability minimumare associated with the aforementioned transition in failure mech-anism from one of localized shear instability (Fig. 10(a) and (c))to necking (Fig. 10(b) and (d)). A connection with a transition inthe dynamic recrystallization (DRX) mechanism, as observed byGaliyev et al. (2001), from localized shear band-related mecha-nisms at low temperatures to more uniform discontinuous dynamicrecrystallization at the highest temperatures, is also likely. Jiang(2007) observed similar anomalous ductility trends in her uniax-ial test data collected on extruded alloys, AZ31 and AM30, with alocal minimum at 250 ◦C at a strain rate of 0.001 s−1. In that study,incomplete DRX was illustrated to have led to local softening andpremature failure; it is likely that the same phenomenon is respon-sible for the formability minimum observed in the present study,and none of the alloys examined are immune from the effect. Fur-thermore, Semiatin et al. (1998) have shown a relationship betweenthe nucleation and growth kinetics of cavities and anomalous duc-tility trends in titanium alloy Ti–6Al–4V.

Careful metallographic examination of alloy AZ31 after test-ing in the OSUFT apparatus has revealed an expected trend withrespect to DRX. A sample tested at 215 ◦C (Fig. 11a) shows evidenceof DRX localized to the grain boundaries, a mechanism which hasbeen associated with shear band formation in prior work of Ionet al. (1982). The AZ31 sample tested at 250 ◦C (Fig. 11b) has amicrostructure that suggests more uniform DRX, yet there is stillevidence that the material is susceptible to shear banding associ-ated with cavity link up at that temperature. A note of caution is

expressed regarding these micrographs; since the present imple-mentation of the OSUFT apparatus prevents immediate quenchingof the sample after deformation, it is very likely that some of the evi-dence provided for DRX is, instead, evidence of post-deformationstatic recrystallization.

44 C.E. Dreyer et al. / Journal of Materials Processing Technology 210 (2010) 37–47

F2

bceaAtaT(tt

Table 3Comparison of elongation to failure of samples tested at 275 ◦C with punch velocitiesof 1 and 10 mm/s.

Alloy Test direction Punch Stroke at failure (mm)

v = 1 mm/s v = 10 mm/s

AZ31 RD 19.2 17.1TD 17.7 17.4

ZK10 RD 20.4 18.0TD 19.0 16.7

ig. 11. Optical micrographs of AZ31 (transverse sections near the fracture) at (a)15 ◦C, (b) 250 ◦C with cavity link up on highlighted shear band, and (c) 300 ◦C.

Finally, at 300 ◦C, within the temperature range where forma-ility is increasing normally, there is the most obvious evidence ofomplete DRX and grain growth (Fig. 11c). At this temperature, allvidence of shear banding is absent but there is some cavitationssociated with the Mn-rich dispersoid particles contained in alloyZ31. All of the alloys examined contain some dispersed phases

hat are expected to initiate such cavitation; see work of Bohlen et

l. (2007) concerning the phase content of alloys ZK10 and ZW41.he intersection of the changes in the fundamental mechanismsDRX, cavitation, and shear banding) are no doubt responsible forhe observed trends in fracture and formability. However, a quan-itative description is presently elusive.

ZW41 RD 24.0 24.2TD 22.3 22.9

Admittedly, the prior observations of a ductility anomaly inthe vicinity of 250 ◦C by Jiang (2007) and Agnew et al. (2008)were at slightly lower strain rates than the present tests (1 mm/spunch speed correlates with a strain rate generally less than 0.05/s,Appendix) However, the temperature compensated strain rate (orZener–Holloman parameter given by the left hand side of Eq. (1)) ismuch more strongly affected by temperature than by rate. Increas-ing from 200 to 250 ◦C will lower this parameter by a factor ofgreater than 25, given the typical activation energy of magnesiumalloy hot deformation of about 135 kJ/mol, which is also an acceptedvalue for the self-diffusion of Mg (Vagarali and Langdon, 1982).Even so, we do not suggest that the precise temperatures of theductility transitions are the same for the various alloys and strainrates; rather, we observe that the basic trends are similar.

Future work should examine the effect of strain rate on forma-bility, since Mg alloys have been shown to exhibit a monotonicincrease in formability with decreasing strain rate at elevated tem-peratures (e.g., Abu-Farha and Khraisheh, 2007). Preliminary testsconducted at 275 ◦C at a higher punch velocity of 10 mm/s revealanother interesting aspect of the behavior of alloy ZW41. Whilethe conventional alloys experienced a decrease in formability atthe higher rate, ZW41 had a similar or even increased formability(Table 3).

4.3. OSUFT punch displacement as a measure of formability

The correlation between the punch displacement and FLD(0)datasets (Figs. 8 and 9), and the desire to develop a simple meansof ranking sheet metal formability based upon the punch dis-placement data encouraged the development of a mathematicalrelationship between strain and punch stroke. We assume that thestrain is uniform plane strain within the metal spanning betweenthe die and punch, enabling a two-dimensional analysis based uponthe schematic in Fig. 3. The free section of the half blank has anoriginal length of x0 when the punch displacement, d, is zero. Weexamine two limiting cases to compute the strain: frictionless andcomplete sticking interactions between the sheet and the punchand die. The length, x, of the half blank once the punch has traveledto a depth, d, is the sum of the lengths of the arcs FG and BE and thesegment EG (Fig. 3). It can be rewritten as AI − (IG + AE) + (FG + BE)or

x = x0

cos(�)− 2r tan(�) + 2r�, (2)

since the arc lengths are both r�, where r is the radius of the dieand punch (r = 12.7 mm, in the present case). From similar triangles,we observe that the angle GHC and EGJ are equal to the angle �.

Recognize, further, that the triangle HCA is similar to GEJ. Therefore,

tan(�) = d − 2(r − rcos(�))x0 − 2rsin(�)

. (3)

C.E. Dreyer et al. / Journal of Materials Proc

Fco

Sd

�

Ut

ε

Ut

z

ws

ε

Fatabsopebptsbitwr

Suitable selection of parameters in Eq. (8) allows degeneracy ofHosford’s (1979) yield locus to Hill’s (1950) quadratic, or von Misesisotropic yield locus.

The predictions also show that the maximum in the punch loadversus displacement is not a signature of plastic instability, as it is in

ig. 12. Computed strain as a function of punch depth assuming frictionless andomplete sticking interactions between the punch/die and workpiece. Superposedn these calculations are the experimental measures of FLD(0).

olving for � with appropriate boundary conditions (e.g., � = 0 at= 0; � → �/2 as d → ∞) gives:

(d) = −2 tan−1

(x0 −

√d2 − 4rd + x0

2

d − 4r

). (4)

nder the assumption of no friction, the strain in the major direc-ion is simply

1,no friction(d) =∫ x(d)

x0

dx′

x′ = ln(

x(d)x0

)

= ln

((x0/cos(�)) − 2rtan(�) + 2r�

x0

). (5)

nder conditions of complete sticking, the portion of the samplehat is involved in the straining, z, is also evolving:

= x0

cos(�)− 2rtan(�) = x − 2r�, (6)

hich leads to an expression similar to Eq. (5), though not withuch a simple analytical solution:

1,friction(d) =∫ x(d)

x0

dx′

z. (7)

ig. 12 presents these two bounding solutions (Eqs. (5) and (7))s a function of punch displacement. Superposed on the curve arehe measured values of FLD(0) versus d at failure, irrespective oflloy, test direction, or test temperature. Quantitative comparisonetween the FLD(0) data and the analytical curves is not intendedince the Eqs. (5) and (7) were developed under the assumptionf uniform elongation, and the FLD(0) values include at least someost-uniform strain. However both the predicted curves and thexperimental FLD(0) data demonstrate a monotonic relationshipetween strain and punch displacement, signifying that punch dis-lacement is a valid metric to rank formability. It is worth notinghat the FLD(0) values from alloy ZW41 appear to fall on a line oflightly lower slope than those from AZ31 and ZK10. This may beecause, as was mentioned earlier, ZW41 had a slick surface finish

n comparison to the other alloys, reducing the friction betweenhe punch and die and the material. Further tests with lubricantsould be necessary to determine if that is the case and how to

educe those effects.

essing Technology 210 (2010) 37–47 45

4.4. Analysis of the punch load versus displacement

Calculations of the punch load versus displacement wereperformed to better understand the different regimes (1–5) high-lighted in the experimental data (Fig. 6). Complete sticking (Eqs. (6)and (7)) was assumed, as well as steady state flow with no strainhardening, which is a reasonable assumption for these alloys in thetemperature and strain regime of interest (Agnew et al., 2008).

As mentioned above, magnesium alloy sheets typically havestrong crystallographic texture and attendant anisotropy. Thus,Hosford’s (1979) higher order anisotropic yield surface is usedalong with Eq. (1) to describe the major stress as

�1(d) = 1�

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

× sinh−1

((1A

ε1(d)

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

eQ/RT

)n)

(8)

where r and r90 are the r-values in the direction of major and minorstrain rates, ε1 and ε2, respectively; ˛ is the ratio between the majorand minor stress, �1 and �2; and a is the higher order exponent usedto alter the shape of the yield locus (see Appendix for a completederivation). Combining the material constitutive rule, Eq. (8) withthe geometry of Eq. (7), the punch load may be computed as

P(d) = �1(d)2 sin(�(d))(w · t0)e−ε1(d), (9)

where w is the sheet width and t0 is the original thickness of thesheet.

Punch load versus displacement curves predicted at275 ◦C (Fig. 13) are plotted, again, using an activation energyQ = 135 kJ/mol, n = 6, � = 0.0107 MPa−1, A = 2 × 1011, similar to thoseused to fit tensile data by Neil and Agnew (2009). The shape ofthe modeled curves compare very well with the shape of theexperimental curves (Fig. 6); the fact that the peak loads predictedat 275 ◦C do not precisely match the experimental (they are underpredicted) is most likely connected to the assumption of zero strainhardening. Notably, different a values do not have a gross impactupon this predicted flow stresses, which was expected sinceat 275 ◦C, neither rRD ∼ 0.78 nor rTD ∼ 1.1 are far from isotropy.

Fig. 13. Computed punch load vs. displacement at 275 ◦C for different Hosford expo-nents using empirical constitutive data obtained for alloy AZ31.

46 C.E. Dreyer et al. / Journal of Materials Proc

Fi

aoitt

5

beipidowfpwksvf(fsllAiaim

A

DMLoLPsuN

ig. 14. Computed major and effective strain rates vs. punch displacement, assum-ng complete sticking conditions.

constant strain rate tensile test. Rather, it appears to be the resultf the simultaneous decrease in sheet thickness and a slowing in thencrease in strain rate (Fig. 14). The precise displacement at whichhis peak in the load occurs will vary with the temperature, due tohe varying dependence of the effective stress on the strain rate.

. Conclusions

Magnesium alloy sheets do not typically exhibit useful forma-ility at room temperature. In order to probe the formability atlevated temperatures, the OSU formability test was modified forsothermal testing up to 350 ◦C. It is shown that the test enforceslane strain over an appreciable portion of the sample, includ-

ng the site of fracture initiation, and therefore can be used toetermine FLD(0). Analysis shows that the major strain enforcedn the sample can be simply correlated with punch displacement,hich allows the relative formability of different sheet metals or

orming conditions to be readily assessed. Punch load versus dis-lacement behavior, including the observed peak in punch load,as qualitatively explained in terms of the test geometry and

nown constitutive behavior of magnesium alloy AZ31. Test resultshow good formability at mildly elevated temperatures for the con-entional magnesium alloys, AZ31 and ZK10, as well as superiorormability of alloy ZW41, with an FLD(0) value of ∼0.44 at 215 ◦C∼37% improvement over the conventional). Microstructure andracture surface examination, as well as r-value measurements,uggest that the reason for the improvement is a weaker crystal-ographic texture relative to the traditional alloys studied, whicheads to a reduced susceptibility to catastrophic shear instability.n anomalous formability decrease lead to a formability minimum

n all three alloys in the range of T = 250 ◦C. Most likely explanationsre associated with a transition in failure mechanism from local-zed shear band-related plastic instability at low temperatures to

ore uniform necking at the highest temperatures.

cknowledgements

This research was supported by the NSF Grant NumbersMI-0322917 and DMR-0603066. The material was provided byagnesium Elektron North America (MENA) and Primometal Co.,

TD., Korea. Our thanks are extended to Mr. Ryan Neuhart for devel-ping the specific die design employed and Oak Ridge National

aboratory for funding that initial development work; to Mr. Johnolesak for performing some of the metallography and r-value mea-urements; to Drs. Richard Gangloff and Yunjo Ro for encouragings to think more about fracture and fractography; and to Mr. C. Johneil for helpful discussions of the results.

essing Technology 210 (2010) 37–47

Appendix. Derivation of major strain

In what follows, the major strain versus displacement at a giventemperature is modeled using the Sellars–Tegart constitutive rela-tion from Eq. (1). Using the chain rule, the strain rate of the materialduring the test is given by

∂ε

∂t= ∂ε

∂d

∂d

∂t= ∂ε

∂d· v, (10)

where v is the punch velocity, held constant during the test. It isshown that the strain rate within the sheet steadily increases dur-ing the test to a maximum and then decreases (Fig. 14). However,the maximum do not occur until a punch depth of approximately30 mm, whereas all the samples in this study failed at values of26 mm or less. For the critical range of punch displacement in whichall the samples in this study failed (d = 15–30 mm), the strain rateincreased a nominal amount from 0.032 to 0.058 s−1 (Fig. 14).

Given a measure of ‘effective stress’ based upon a yield criterion,an associated ‘effective strain’ measure can be derived (Hosfordand Caddell, 1993). Because strain anisotropy was measured, Hos-ford’s higher order anisotropic yield surface (Hosford, 1979) whichwas based on Hill (1950) quadratic surface, was employed. Hosford(1979) gives the effective stress, assuming conditions of planestress (�3 = 0), as

� =[

r90|�1|a + r|�2|a + r90r|�1 − �2|ar90(r + 1)

]1/a

, (11)

where r is the r-value of the material in the direction of major strainand r90 is the r-value in the direction of minor strain. Eq. (11) repre-sents the Hill’s model when a = 2, though it has been shown that ther-value effects on flow stress are better captured by higher expo-nents (Hosford, 1979). In order to find the relationship between theminor and major strain, the enforced ratio of strain increments isused, again given by Hosford (1979) as

� = dε2

dε1=(

r

r90

)(˛a−1 − r90(1 − ˛)a−1

1 + r90(1 − ˛)a−1

), (12)

where ˛ is the ratio of minor to major stress (�2/�1), and dε1 anddε2 are major and minor strain increments, respectively. Assumingplane strain (dε2 = 0), Eq. (12) can be solved for ˛, yielding

˛ = r901/a−1

1 + r901/a−1

. (13)

Therefore, we can solve Eq. (11) for �1, giving

�1 = �

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

. (14)

The effective strain given by Hosford (1979) is

ε = ε1 (1 + ˛�)�1

�. (15)

For plane strain (� = 0), this combined with Eq. (14) gives

ε = ε1

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

. (16)

Combining Eqs. (14) and (16) with Eq. (1), and solving for the majorstress, gives:

�1(d) = 1�

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

× sinh−1

((1A

ε1(d)

[r90(r + 1)

r90 + r˛a + r90r(1 − ˛)a

]1/a

eQ/RT

)n).

(17)

s Proc

R

A

A

A

A

A

A

A

B

B

C

C

G

G

G

H

H

H

C.E. Dreyer et al. / Journal of Material

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