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Materials Transactions, JIM, Vol. 40, No. 8 (1999), pp. 825 to 829

Special Issue on Towards ZnnovatL'on in SuperplastT'city

Simple Evaluation of Superplasticity Using a Tensile Test

wi仙R-type Specimens

Mitsuji Hirohashi, Yun Lu and Masanori Nishizawa†

Department of Electronics and Mechanical Engineering, Chiba University, Chiba 26318522, Japan

Superplastic elongation depends heavily on a value of strain-rate sensitivityindex m. The value of m is obtained by

variOus methods, using specimens of various shapes for uniaxial tensile tests. A specialtechmique is required to measure

the m-value･ In this study, R-type specimens having no smoothed region were employed instead of ordinary smoothed

specimens. A series of tests for variousaluminum alloy sheetsand titanium alloy bars were carried out at elevated

temperatures to evaluate superplasticity. It was di銃cult to measure the m-value using a single R-type specimen.

However, the obtained value uslng more thanthree specimens was in fairly good agreement with the value of smoothed

specimen･ Furthermore, the totalelongation of the gauge length of 6 mm at the bottom of the RIPart could replace that

of the smoothed test-pieces. The obtained value was less scatteredinComparisonwith the value of the smoothed

specimens. Consequently, R-type specimen can be useful for simple evaluation of superplasticity.

(Received February 24, 1999; ln FhalFon June 14, 1999)

Keywords: supeT'Plasticity, tensile test, aluminum alloy, strain rate sensitivity, R-type specimen, total elonga-

lion

I. Introduction

Superplastic behavior is associated with a large

amount of neck-free elongation. Generally, the total

elongation is correlated positively with the strain rate

sensitivityindex of m. Specialtechniques and many test

pleCeSーaLre required to measure the m-Value(1)(2)･ Further-

more, a specialized long furnace should be prepared for

tensile tests of the superplastic materials. The tempera-

ture of the atmosphere in the furnace should be kept at a

constant value for a long time over the elongated speci-

men d也g deformation. The constant strain rate is hard

for the conventional smoothed specimens to handle be-

cause of its large elongation.

}　By contrast, the R-type specimen was developed to

ev血ate the superplastic characteristics(1). The ex-

perinentalmethod using the R-type specimen is useful to

deternine the m-Value, theflOw stress and the total

elongation to fracture. These values agree with the results

obt血ed by usmg conventional smoothed specimens.

hl this report, different materials, such as two kinds of

al血umalloys, a zinc alloy and a titanium alloy, are

considered. Furthermore, different shapes of sheet and

bar for tensile specimens are prepared to clarify the su-

perplastic characteristic of the various materials. The

method to obtain the m-value is developed and simplified

using R-type specimens. The freshly induced constitutive

equation for superplasticity is examined for practical

application.

千 Graduate Student, Cbiba University･

II. Experimental Details

1. Materials and specimens

Commercial alloys in the shape of either sheets or bars

were received as shown in Table 1. In this table, Zn1

220/oAl (SPZ) alloy shows remarkable diffusional neck-

ing by comparison with the other alloys. The 良-type

specimens without smoothed reglOnS Were prepared to

evaluate the superplastic characteristics of both the

sheets and bars as shown in Figs. 1(a)-(d). The radius R

of the R-part was constant of 25 mm. A good correla-

tion(1) between the results uslng the ordinary smoothed

specimen and the 良-type specimens for A7475 aluminum

alloy was reported at the condition of R-25 mm. Gauge

marks 3 mm in length as shown in Fig. 1(a) were scribed

in the 良-part of the 良-type specimen.

2. Experimental procedure

The tensile tests uslng an instron type machine were

carried out in air for two kinds aluminum alloys of

A7475 and A5083, and a zinc alloy of SPZ at 803, 803

and 523 Ⅹ, respectively. A titanium alloy of Ti-6Aト4V

was tested in argon at 1173 K. The testing temperature

was kept over the elongated sample usmg three divided

Nichrome wire heaters during deformation. Each speci一

men was suspended by the grlpper in the heated furnace.

An attempt was made to estimate the load on the speci-

men resulting from thermal expansion was balanced ap-

proximately with this hanglng method before the pulling

test was carried out.

826 M. Hirohashi, Y. Luand M･ Nishizawa

Table 1 Chemical composition or the alloys･

Alloymarks Zn Cu Si Fe Mg Mn Cr Ti Al

A7475　　　5.74 I.50　0.04　0･07　2･57　1　0120

A5083　　　-　　-　0.03　0.04　4･70　0･65　0･10

spz　　　77.9　0.05　-　-　0.01　-　-

Til6Al14V　(6.38 - 6.51)Al-(4.07 - 4･21)V-(0･ 15 - 0･18)Fe-Ti

(a) R-type specimen (sheet)

t

L 唯�

SPZ ��"�1

A5083 ����1.6

(b) smoothed specimen (sheet)

(C) R-type specimen (bar)

for Ti16A1-4V and SPZ

(d) smoothed specimen (bar)

for Ti16A1-4V

Fig. I Shape and dimensions of the R-typeand smoothed specimens

for the tensile test.

IⅡ. Results atLd Discussion

1. Strain rate sensitivity index m

The values of stress are diqerent according to the loI

cation of the R-part in the 良-type specimen･ Of course,

the maximum stress is given in the bottom of the R-part

where strain is concentrated. Therefore, the change in the

stress corresponding to the cross-sectional area of the

R-part follows the strain rate･ The strain rate sensitivity

index m is obtained by assuming that each crossISeCtion

is supported as a uniaxial stress q against the strain rate

台in the whole R-part.

FigtLre 2 shows the relationship between both the

above described values obtained from the R-type speci-

I 0-5　　　　10-4

T,ue St,aim Rate,き/S-1

Fig. 2　Relationship between the true stress assuming uniaxialtensile

stress at each slab of the R-part and the strain rate obtained from the

R-type specimens.

机ens. Generally, plural smoothed specimens were ten-

siled at the different pulling speeds to obtain the m-value･

The procedure uslng a Slngle 良-type specimen was as

follows: the specimen was pulled up to 6 mm, the cross-

head was stopped, the specimen was un fastened, and

then each gauge mark shown in Fig･ 1(a) was carefully

measured by a measurement machine･ The stress, as-

suming uniaxial tension, and the strain rate were calcu-

lated by measurlng each strain･ As the plotted data were

widely scattered, it was dincult to obtain the m-value of

thealloy. It was also technically dincult to measure the

strain of each small slab. Fllrthermore, the condition of

uniaxial tension ceases to be reliable in the reg10n at a

distance from the bottom of the R-part.

Figure 3(b) shows the relation between the nominal

stress instead of the true stress and the pulling speed for

the 良-type specimen･ The stress was calculated by as-

sumlng the stress was uniaxial･ The plot of a nominal

stress on the verticalaxis was calculated simply from the

original cross-sectionalarea, and the horizontal axis was

simply showed the pumng speed or the cross-head speed･

The obtained m-Value of 0.59 wasalmost the same as

the va血e obtained by uslng the conventional smoothed

specimen. Therefore, the gradient of the line in Fig･ 3(a)

was transfered in parallel to theline shown in Fig･ 3(b)･

2. Effects of materials atLd specitnetL Shape on the

m-vane

lt was found that the m-value of thealloy could be

decided easily even if R-type speclmens were used instead

of the smoothed specimens･ Then the various aluminum

alloysand the titaniumalloy were tested to obtain their

m_values. The results for the three kinds of alloys were

shown in Figs･ 4, 5 and 6･ The stresses at the bottom in

the R-part obtained by the 良-type specimens were shown

in order to decide the m-Value more easily. The values of

each alloy were distributed as a straight line, and the m-value was obtained easily as the slope of the line de丘ned

＼ヽ_　ヽ-

'a al d

B B B

o･｡2竺

OIt!dMJP'SSaJtS9nJト

Simple Evaluation of Superplasticity Using a Tensile Test with R-type Specimens

10~4 1 0-3

True Strain Rate, i /S~1

(a) smoothed specimen

10~1　　　　100　　　　　101

. -1

pulling Speed, ; /mm ･ mln

P) R-type specimen

Fig. 3　Comparison of the m-Value with the results for the ordinary

smoothed specimen.

by in these figures.Although the horizontal axes in these

Agures for R-type specimen were simply shown as pulling

speed, the values obtained by boththe R-type and the

smoothed specimens were in approximate agreement.

These m-values were summarized in Table 2. It is

worthy note that the agreement is obtained despite the

differences in shape between sheets and bars.

3. Constitutive equation between stress and strain-

rate

As it well known, the constitutive equation(3) of su-

perplastic materials is

q-K台m　　　　　　　　　(1)

where α is the true stress of the material corresponding to

the strain rateと, m is the strain rate sensitivity indexand

Kis the strength coe缶cient. The value ofKis in eqect the

flow stress at the strain rate of I s-I practically. It was

inpracticalto apply the K-value of the strength coe瓜cient

to the plastic working, because the strain rate showing

the superplasticity of commercial alloys, apart from the

10-3

True Strain Rate, i /S-I

(a)smoothed

827

100● . -1

Pulling Speed, C /mm ･ mln

(b) R-type

Fig. 4　Comparison of the m-values with the results of the smoothed

specimens in A5083 aluminum alloy sheets.

special materials(4)(5) showing superplasticity at a high

strain rate, was different from the strain rate of 1 s-I.

In this paper, the new modified equation proposal to

glVe a more accurate expression is

q-Ksp(訂or Ksp-q(Cfjm　(2,

where Ksp is the flow stress at the strain rate of台sp

showing superplasticity of the material. The strain rate of

esp IS expressed in round terms to digit decimalnumbers,

such as a 10-3S-I. The analytical data for the various

specimens werelisted with the other data in Table 2. The

value of Ksp is usefully expressed as the flow stress

showing superplasticity of the material. The difference of

the Ksp-Value obtained uslng the different shapes of

specimen (sheets and bars) became very small in com-

parison with the K-Value. The K-Value changes remarka-

bly in accordance with the change of J乃-Value, because

the value is obtained from the intersection of the exten-

sion of the slope and the strain rate of 1 s~1.

ハUO1

dd∑＼j?.SSaとStt!u!uON

tZdMJL)'SSaJTSanJL

828 M. Ilirohashi, Y. Luand M. Nishizawa

■■l■l 綿�"�

SPZ ��

△

△ 盲ﾓ��3��

.I.‥l 呈ﾂ粐粐�

10-3　　　　　　　10-2

T,ue Strain Rate, i/S~l

(a) smoothed (sheet)

l■l 白�

SPZ ��

m=0.36

.I....l 停貭粳?｢�

100　　　‥1 101

pulling Speed, ; /mm ･ mln

P) R-type (sheet)

ll 敦ﾈ��ﾄ����

SPZ ��･■■■■■

･■-

m=0.39

I 鳴��?｢貭�

10-1　　　　100　　　　　101

. -1

puuing Speed, ;/mm ･ mln

(C) 良-type (bar)

Fig. 5　The m-Value obtained by two shapes of specimen for SPZ zinc

alloys.

4. Total elotLgation to fracture

Formability of superplastic materials depends on the

m-value(3),and the totalelongation in tensile tests is im-

portant, because the elongation depends on the m-value･

On the other hand, it is difRcult to obtain the value of

total elongation llSlng a COnVentional smoothed specimen

having a uniform cross sectioninarea, because of its

huge ductility. And the values are generally dispersed

depending on the breaking part of the specimen.

So a new 氏-type specimen has been proposed to ob-

tained the superplastic characteristics(2). In the results,

101 0-4　　　　　　1 0-3

True Strain Rate, I /S-1

(a) smoothed (bar)

10110-1　　　　　100

. -1

pulling Speed, ; /mm ･ mln

O)) R-type (bar)

Fig. 6　Comparison of the m-Values for the ordinary smoothed and

the R-type specimens in the titaniumalloy.

Table 2　Superplastic characteristic obtained by tensile tests on vari-

ous specimens.

Specimen m-Value KIValue Ks,/MPa

A7475　　　　R-type O･59　1 57　　　2･7

(sheet)　　　sm.othed 0.58　168　　　3. I

A5083　　　　R-type O･ 54　　206　　　5 ･08

(sheet)　　　sm｡｡thed 0. 5 5　　225　　　4. 92

R-type 0.36　　　47.9　　　3.99

smootlled 0.39　　　　52. 1　　　　3.59

bar R-type 0.39　　　58. 3　　　3.94

R-type 0.37　　　41 8　　　　32.4

smoothed 0. 42　　　798　　　　　43. 9

m-Value, the flow stress at the strain rate ofとsp and the

constitutive equation of these parameters were ob-

tained easily uslng 良-type specimen. In general, the

tZdMJL)'SSaJ1S9ruL

0ll

tZdMJb nSSaJtSt昌!uJON

HHO1

ddWD'SS9JIStTZtt!uON

t!dMJL)'SSaJtSaruLL

tZd言＼D'SS917Slt!u!uON

simple Evaluation of Superplasticity Using a Tensile Testwith R-type Specimens

I.Al川Il. 免ﾄ売��

● ��

A7475 ��ﾂ�

●∂6:R-type ��

△∂12:Smoothed ��

..tlHHl. 呈ﾉ?ｩ?｢�

10-1　　　　10(1　　　　10l

.一1

pullingspeed, ;･/mm ･ mln

(a) A7475 aluminum alloy sheets

■■■●HHl 白�■l

△全会 ��●

A5083 仞��

+66:R-type ��

.△.6.i:.sP.o禦ed 免ﾂ�.l

101l■

Pullingspeed, C /mm ･ min

(b) A5083 aluminum alloy sheets

10-1　　　　100　　　　　10l● . -1

Pulling speed, C/mm ● mln

(C) sheets and bars of SPZ

Fig. 7　Comparison of the total elongation of R-type specimens with

one of tile Smoothed specimens for various alloys.

fracture in R-type specimenalways occurs near the bot-

tom of the minimum cross sectional area in the RIPart.

Figures 7(a)-(C) shows the elongation of the various

materialSand the different shape of specimen against the

pulling speed. The elongation ∂6 is the total elongation in

829

6 mm gauge length of the bottom of the R-type speci-

men. And the elongation ∂12 is the total elongation

obtained by the ordinary smoothed specimen with a

uniform gauge length of 12 mm. Although the plotted

data were scattered over a narrow range, the value of 66

obtained by R-type specimen was approximately equlVal

lent to the ∂12 Obtained by the smoothed specimen. Espe-

cially, the agreement was shown in Fig. 7(C) whether the

shape of specimen was a sheet or a bar in zinc alloy of

SPZ. The alloy of SPZ shows remarkable dimISional

necking in comparison with the other materials.

Consequently, the 良-type specimen was useful to

evaluate superplasticity in the same manner as using a

smootIled specimen, because the experimental method

was very easy and simple with good reproductive pos-

sibilities.

IV.　ConclusioTLS

The R-type specimens in tensile tests both sheets and

bars were useful to evaluate superplastic behaviorin

comparison with ordinary smoothed specimens.

(1) The m-Value can be obtained easily from the log-

log graph paper between the nominal stress in the bottom

of R-partand the pulling speed of the R-type specimens.

(2) The modified constitutional equation is proposed

aS

q-Ksp(訂or Ksp-相m

where esp IS a Strain rate showing the superplasticity of

thealloy, and Ksp is theflOw stress at台sp, respectively.

(3) The total elongation of the 6 mm gauge length in

the bottom of the R-part agrees with the results ob-

tained from the smoothed gauge length for the conven-

tional smoothed specimens.

A ckn o wledgemen ts

The work was supported in p∬t by a Grant-in-Aid for

Scienti丘C Research from the Ministry of Education,

Science, Sports and Culture of Japan, and in part by

Osaka New Materials Center. The authors wish to

acknowledge for the helpful suggestions of Prof.

Y. Takayama of Utsunomiya University in Japan.

REFERENCES

(1) Y. Takayama, N. Furushiro, T. Ozawaand H. Kato: Mater. Sci.

Forun, 170-172 (1994), 561-570.

(2) Y. Takayama, T. Tozawa, H. Kato and N. Furushiro: Mater. Sci.Forum, 2331234 (1997), 1 171122.

(3) A. W. Backofen, I. R. Turnerand D. H. Avery: Trams. ASM, 57

(1964), 980-990.

(4) K. Higashi: Mater. Sci. Eng., A166 (1993), 1091118.

(5) M. Mabuchiand K. Higashi: J. Mater. Res., 10 (1995), 2494-2502,

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