The effect of mechanical properties on the wrinkling behaviour of sheet materials in the yoshida test

Journal of Mechanical Working Technology, 10 (1984) 87--102

87

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

THE EFFECT OF MECHANICAL PROPERTIES ON THE WRINKLING BEHAVIOUR OF SHEET MATERIALS IN THE YOSHIDA TEST

A.M. SZACINSKI and P.F. THOMSON

Department of Materials Engineering, Monash University, Clayton, 3168 (Australia) (Received October 17, 1983; accepted in revised form January 4, 1984)

Industrial Summary The effect of material properties on the initiation of wrinkling and on wrinkle height at 2% mean axial extension of a range of sheet metals was investigated using the Yoshida or 'handkerchief' test. It was found that the onset of wrinkling was accelerated by strain rate, normal plastic anisotropy and by yield strength, but was delayed by increase in Liiders strain (yield elongation) when present, by work hardening and by positive strainrate sensitivity. The growth of wrinkles was retarded by LiJders strain, work hardening, by high values of the ratio r*/YS and of the coefficient of strain-rate sensitivity, but was promoted by increasing yield strength. Initiation of wrinkling occurred later when the upper yield point had not been removed, but growth was more rapid. Growth was slower when Liidering had been removed: hence in industrial practice, the usual procedure of temper rolling before sheet forming might be disadvantageous in those applications in which Liiders bands (stretched strains) on the product could be tolerated. The close correlations obtainable for the same or similar materials in different conditions confirm the usefulness of the Yoshida test for comparing these materials with respect to the onset and growth of wrinkles, whereas the test appears less useful for rating the wrinkling behaviour of materials of different types because of unaccounted factors.

1. Introduction Wrinkling is one of the c o m m o n defects which occurs during press-forming, for example, in the automotive industry during the forming of car b o d y panels. A number of investigations of the wrinkling behaviour of sheet metal have been reported recently [1--6]. Yoshida and his co-workers proposed a buckling test [7] in which a square specimen was stretched diagonally to produce a wrinkle. The purpose of this simulative test was to determine the properties of the material relating to elastic recovery or springback, and the ease of control of defects such as wrinkles in press-forming. Previous work [7--10] has indicated correlation between wrinkle height at a given extension -- usually 2% or 4% -- and YS,~, ~/YS, n and n* (where n* is the value of the work-hardening exponent at low strains, usually in the range 1--5%). Published work has been restricted to steels. The aim of the present work was to investigate the material variables important in controlling wrinkling as measured in the Yoshida test, extending previous work on steel sheet to in-

0378-3804/84/$03.00

© 1984 Elsevier Science Publishers B.V.

88 clude other materials commonly used in sheet form, particularly copper, 70/30 brass, titanium and austenitic stainless steel, annealing to produce systematic changes in properties.

2. Experimental procedure 2.1 Equipment and materials Tests were performed using an Instron Universal Testing Machine. It was found that knurled grips tightened by screws independently of the test load minimised slip of the Yoshida specimens and tearing at the comers, which otherwise limited extension. Wrinkle height was measured with a digital transducer. Mechanical properties of the materials which were studied in the investigations are given in Table 1. Properties were determined using tensile specimens according to ASTM Standard E-8 with axes in the rolling direction: the cross-head speed was 5 ram/rain. The materials used in the experiments were: 1A, 2A, 4A cold-rolled mild steels 2AI, 2AII annealed mild steel 2A 3A galvanised mild steel 5A CA 2S~:~ Steels of forming grade. C -- cold-rolled, A -6A CA 3SY-G killed, S -- skin passed, G -- general purpose 7A CA 4 A ~ : ~ surface, Y -- yield strength modified b y rephosphorisation. Indices 2--4 rank the steels in order o f increasing formability. B cold-rolled austenitic stainless steel 409D 1B cold-rolled austenitic stainless steel 2B annealed austenitic stainless steel 404 C cold-roiled commercially-pure titanium CI, CII annealed titanium C D cold-rolled commerc'mlly-pure copper DI, DII annealed copper D E annealed 70/30 brass EI re-annealed 70/30 brass E F cold-rolled 70•30 brass FI, FII annealed 70/30 brass F Annealing t~eatments and results of the Yoshida test are shown in Table 1. An attempt was made to investigate wrLnkling of 1100 aluminium and alloys 3004 and 5005 using the Yoshida test. However, t h e material failed close to, or inside, the grips {whichever gripping technique was used) in every case before ~ occurred. 2.2 Yoshida test Specimens were 100 mm square, and extension was meas~vd on a :75ram gauge length: wrinkle height was measured as shown in Fig. 1. The rolling direction was again the direction of testing.

0.60

0.60 0.58 0.68 0.74 0.76 0.70 0.70 0.72 0.68 0.68

0.68

0.68 0.68

0.68

0.68 0.68

0.78 0.78

0.78

2AII

3A 4A 5A 6A 7A B 1B 2B C CI

CII

D DI

DII

E EI

F FI

FII

1 hour at 350°C 1 hour at 650°C

1 hour a t 3 50 ° C

1 hour a t 350°C 1 hour a t 650°C

1 hour a t 6 50°C 1 hour at 8 5 0 ° C

650°C

5 hrs at

350°C

5 hrs at

Annealing treatment

63

305 256

103 96

21

205 163

863

292 265 182 225 158 311 283 303 400 387

230

300 255 280

Yield Strength (MPa)

507

596 620

411 452

223

330 342

823

554 563 535 678 536 891 1033 1025 826 810

539

738 558 580

K (a) (MPa)

300

400 392

303 315

197

233 229

500

352 275 310 395 301 532 536 717 523 509

290

426 340 337

Tensile Strength (MPa)

S t a n d a r d tensile test

4.82 3.43 ~ --

--~ -0.74 0,51 0.13 ----

-~ ----

28.90 34,30 32.64 3 4 . 1 6

48.00 30.40 23.60 70.60 30.10 29.80 25.40 38.20 40.78 46.88 50.40 55.30 36.30 44.17 57.54

7,90

1.86 2.52 7.00

31.90 38.40 36.30 28.50

e y ~cJ'" (%)

e f ~bJ'" (%)

0,380

0,386

0.108 0.142 0.336

0,140 0,198 0.415

0,259 0,302

0,223 0,254

0.077 0.119

0.096 0,149

0,123

0.165 0.205 0.173 0.177 0.196 0,169 0.225 0.196 0.147 0.139

0.281

0.221 0.200 0.230

n *(d)

0.191

0.171 0.211 0.227 0.222 0.247 0,237 0,375 0.296 0.172 0.176

0.281

0.227 0.211 0,231

n

,r ,

0.93 0.90 0.69

0,78

0,87 0,85

0,79

0,47 0.69

2,27

0.81 1.25 2,04 2.10 2.80 1,09 0,68 0.93 3.09 2.54

0.47

1.53 1.32 1.27

r*(e)

0.93 0.93

0.94 0.38

0.87

0.53 0.62

1.88

0.78 1,26 1,60 2,29 2.32 0.98 0.86 0.92 3.26 3.66

1.07

1.67 1.41 1.14

r

0.59

0.34 0.37

0.54 0.72

0.60

0.46 0.48

2.25

0.72 1.05 0.89 0.67 0.97 1.16 1,48 1.55 1.92 2.18

1.14

1.29 0.98 1,06

m X l0 s

V a l u e o f K in p o w e r l a w e q u a t i o n o = K e n. T o t a l e x t e n s i o n to f r a c t u z e o n 50 m m g a u g e l e n g t h . Yield e l o n g a t i o n (L~/ders s t r a i n ) . O b t a i n e d f r o m t h e t r u e stresl---true s t r a i ~ c u r v e i m m e d i a t e l y a f t e r y i e l d or o n initial s t r a i n h a r d e n i n g a f t e r yield.

0.63 0.60 0.60

1A 2A 2AI

(a) (b) (c) (d)

Thickhess (mm)

Material

M a t e r i a l p r o p e r t i e s f r o m s t a n d a r d tensile t e s t a n d Y o s h i d a test . . . . . . . . . . . . . . . . . .

TABLE 1

1,42

2.55 2.30 0.60

0.15 0.45 0.65 0.32 0,10 0.20 0,28 0.36

2.29 4.21 37.57 8.45 8.85 3.05 3.53 11.08

2.92 2.58

0.15

1.96 1.90

2.24

2,12 2.20 2.25 2,52 2.25 2.51 2.32

1.80

6.25

2.84 2,74

1,82

2.37 2.58 2.30

Wrinkle H e i g h t at 2% E x t e n . (ram)

0.75 0,58 0.30 0.17 0.13 0.35 0,22 0.20 0.26 0.20

0.80

0.30 0.45 0.72

Extension at O n s e t of Wrinkling (%)

2.77 4,72 11.21 9.33 18.23 3.50 2.41 3.08 7.72 6,56

2.03

5.10 5.19 4.52

r*/YS X 103 (MPa -1)

Y o s h i d a test

O0

90

i I

SECTION

AA

h - ~RINKLE HEIGHI Fig. 1. S c h e m a t i c illustration o f the Yoshida buckling test and the m e t h o d of measuring wrinkle height.

2.3 Work-hardening exponent and coefficient o f normal plastic anisotropy The work-hardening e x p o n e n t was evaluated according to ASTM Standard E646, in which power-law hardening is assumed: thus o = K e n, where n is the work-hardening exponent and K is a constant. The work-hardening e x p o n e n t is then obtained as the slope of a straight line approximation to a logarithmic plot o f the stress--strain data. The value o f K is the stress ordinate on this straight line at a strain of 1,0. The value of n* was obtained from the true stress--true strain curve immediately after yield or on initial strain-hardening after yield in materials which displayed Liidering. The coefficient of normal plastic anisotropy at 20% extension (r) was evaluated in the rolling direction as r e c o m m e n d e d in ASTM Standard E517. The coefficient of normal plastic anisotropy at 5% extension (r*) was obtained according to the same procedure. 2.4 Coefficient o f strain-rate sensitivity The most c o m m o n l y used method -- the cross-head velocity change or " j u m p " m e t h o d -- was e m p l o y e d and was analyzed b y the extrapolation technique o f Backhofen, Turner and Avery as q u o t e d b y H e d w o r t h and StoweU [11] and shown in Fig. 2 to obtain m, the coefficient o f strain-rate sensitivity. The cross-head speed was changed from 0.5 m m / m i n to 5 m m / min at 10% extension. Hence,

91

log (PB/PA ) m-

log (V2/Vt)

where PB, PA correspond to the load at B, A respectively.

B

v,

7-{:D

v<

TIME

Fig. 2. S c h e m a t i c l o a d - - t i m e curve for strain-rate cycling.

3. Results and discussion

3.1 Relationship between wrinkle height and extension Examples of the plots of wrinkle height against extension on a 75 mm gauge length for galvanised steel (mat.3A) and titanium (mat.C) are shown in Figs. 3 and 4 respectively. 3.0

3.0 /

!

/ (ii) I. 5

~2 z ~

. . . .

i

. . . .

i

. . . .

i

. . . .

i

. . . .

i

. . . .

,

. . . .

2.0

L9 H

.+

i

2.5

2.0

~I

. . . .

(i~,i)

i.O

/

/

/

0.5

/

(D H

H

~.0

/

0.5

/

(i)/

0.5 ~.0 1.5 2.0 2.5 3.0 EXTENSION ON 75 MM GAUGE LENGTH [%]

./.".

0 0

0.5

,

,,

,i 1.0

. . . .

1.5

2.0

Illll 2.5

EXTENSION ON 75 MM. GAUGE LENGTH

3.0

[%]

Fig. 3. Wrinkle height versus e x t e n s i o n on a 75 m m gauge length for galvanised steel (mat. 3A). Fig. 4. Wrinkle height versus e x t e n s i o n on a 75 m m gauge length for titanium (mat. C).

92

The extension at the onset of wrinkling was taken as the point of intersection o f this curve -- extrapolated ff necessary -- and the extension axis. This may have contributed to error in the stated values of e x t e n s i o n at initiation, so that these values are regarded as less reliable than those of wrinkle height at a specified extension. Similar graphs were plotted for all materials but the straight-line relationship indicated by previous workers [7--10] was never found. These graphs can be divided into three parts: (i) initiation and slow growth o f the wrinkle; (ii) rapid growth o f the wrinkle (approximately linear); (iii) further slow growth (parabolic). The dependence o f wrinkle height on extension depended on the material tested: for example the initiation phase was more extended in some steels -- especially those with a substantial Liiders strain, as in the galvanised steel (Fig. 3) -- than it was in titanium or stainless steels, but later growth was m o r e rapid.

3.2 Yield stress and yield elongation The effect of yield stress (YS) on initiation of wrinkling and on wrinkle height at 2% mean axial extension (h2) is shown in Figs. 5(a) and (b) for all materials tested. In the present work the lower yield point was used as a measure of yield strength (in materials with both upper- and lower-yield point), because the latter is ~ i a l l y independent o f strain ~ and less affected by speed o f deformation and any imperfections in the specimen than is the upper yield point.

L~ Z

1.0

3.0

0.8

2.5

. . . .

i

. . . .

i

. . . .

i

. . . .

Z p~:

2.0

0.6

09 Z

0.4

~Z LU F-

0.2

t-

~.5

l.O Z

(a) o

,

o

,

,

,

,

i

'100 YIELD

,

L

,

J

. . . .

200 STRESS

,

300 [MPa]

,

(b)

0.5

. . . .

400

,~oo YIELD

200 STRESS

300

40(

[MPa]

Fig. 5. E f f e c t o f y i e l d stress on: (a) e x t e n s i o n at the o n s e t o f wrinkling; (b) w r i n k l e height at 2% e x t e n s i o n .

93 The linear correlation coefficient (-0.13) between yield stress and extension at the onset of wrinkling indicated a weak decreasing correlation, but the correlation coefficient (+0.64) between YS and h2 shows that yield stress is an important factor in development of wrinkles, confirming the results of Yoshida et al. [7], Satoh [9] and Gibson and Hobbs [10]. Materials with a smaller yield stress should provide better wrinkling resistance. Figures 6(a) and (b) show the substantial effect of yield elongation (Liiders strain), ey, on the onset of wrinkling and wrinkle height for steels (mats. 1A, 2A, 2AI, 2AII, 3A, 4A) and titanium (mats. C, CI, CII). There was a strong correlation, (coefficient +0.94), between extension at the onset of wrinkling and the Liiders strain, ey, but the correlation between h2 and ey was less strong (--0.31). It appears that the larger the Liiders strain, the later the initiation of wrinkles. ~..0

i

i

i

I

,

i

,

I

,

i

i

I

,I

,

,

I

I

i

i

3~0 ,

i

,

i

F

i

,

i

i

]

i

,

i

,

i

[

i

'

L

'

I

I

b

L

I

I

i

I

I

I

i

L

I

I

i

i

== z

0.8

o=

2.5

z~ w x w

0.6

o~ 2.0

o

0.4

W CO I

~ o

~Z 0.2 w b-

H

(a) I

I

I ~ I~

T

I

~

I 4 i~

t

b

i

I ~

I

I0

YIELD ELONGATION

d

I

I ~ I 0

[%]

I

I

I ~ 0 I 0

(b) ~ i 0

~ i0

4 i0

~ i0

YIELD ELONGATION

~ I0

I

I ~ 0 i0

[%]

Fig. 6. Effect of yield elongation on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension.

Generally, annealing for longer times or at higher temperature to increase the yield elongation decreases the yield stress, which in turn has been found to delay the onset of wrinkling and decrease wrinkle height at a given extension, so that the opposing increase in tendency to wrinkling with increasing Lfiders strain seems to be an independent effect. In fact the promotion of wrinkling by Liidering might be expected, because it permits large local deformation by progressive yield in adjacent zones before the strain is distributed uniformly and work hardening commences. These results again confirm those of Gibson and Hobbs [10]. However, the effect of temper rolling in removing the upper yield point (effectively decreasing the value of

94 the yield stress) and of yield elongation on initiation and growth of wrinkles are in fact independent. Referring again to the work of Gibson and Hobbs [!0], it is noteworthy that wrinkle growth was almost the same in their steels Co.s and C~.0 and in D0.s and Di.0 temper rolled respectively 0.5% and 1% (which removed the upper yield point in each without introducing work hardening}, whereas wrinkle growth was less in the steel which had not been temper rolled to remove the upper yield point. Close examination shows that the difference between the upper and lower yield points was substantially larger in steel D than in steel C (50 MPa compared with 30 MPa). Further temper rolling by 2% had clearly increased the yield point of steel C above its original upper yield point and wrinkle height was increased significantly, whereas after 2.3% reduction the yield point of steel D was still substantially below the level of its initial upper yield point and wrinkle height remained sensibly unchanged. Such a difference in the apparent effect of yield elongation is consistent with the differences in yield stress which Gibson and Hobbs imparted to the two steels by temper rolling, so that the effect of yield elongation may at least in part be only an apparent one. However, use of the lower yield point in the present experiments assists in separating the effect of yield stress and yield elongation. The effect was also observed in titanium, in which a yield elongation usually occurred without distinct upper- and lower-yield points. It is suggested that the effect of Liiders strain in promoting wrinkling should be studied further.

3.3 Work-hardening exponent The effect of the work-hardening exponent n, as usually determined from ASTM E646, and of n*, the value of the work-hardening exponent immediately after yield or at commencement of work,hardening after yield, on the initiation of wrinkling of all materials tested and on wrinkle height at 2% mean axial extension were compared (Figs, 7(a) and (b) and Figs. 8(a) and (b)). It was found that n* had more effect on the initiation of wrinkling than did n: the linear correlation coefficient between n* and extension at the onset of wrinkling was +0.43, higher in magnitude than for n (+0.13). This is to be expected, because initiation of plastic wrinkles depends on the properties at the instant of yield, whereas wrinkle growth depends on the properties subsequent to yield. Figures 7(b) and 8(b) show a strong decreasing relationship between wrinkle height and work-hardening exponent for all materials tested: the coefficient of correlation between n and wrinkle height at 2% axial exten, sion was - 0 . 7 5 , similar in magnitude to that between n* and h2 (--0.72). As previously suggested by Yoshida et al, [7], Satoh [9] and Gibson and Hobbs [10], materials which work harden rapidly should resist w r i n k ~ better than those with a low work-hardening exponent because rapid local workhardening would tend to distribute strain more widely. These workers [7, 9, 10] also suggested a closer relationship between h~ and a value of work,

95 3.0

~.0

,

,

.

|

w

,

,

.

.

,

w

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,

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,

,

i

,

,

,

m

,

.

.

i

,

,

I

=

,

w w

z Z H

0.8

2.5

,

a

Z

w,,

,~w

W FU~ 2 . 0

O.B

b U3 z 0

W

~

0.4

~ w

w

~.5

H

w w w

a

w

0.2 Ld p-

w

~

~w w w w

~.0

H

(a) 0

,

,

,

0

~

•

,

,

0.2

~

,

,

,

0.4

WORK

i

,

,

,

0.6

HARDENING

i

,

,

,

,

0.8

0.5 ~.0

EXPONENT

,

,

,

0

i

,

0.2

n

I

(b)

0.4

WORK

0.6

HARDENING

,

,

0.8

EXPONENT

~ .0 n

Fig. 7. Effect of work-hardening exponent n on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension. .0

3.0 ,

.

,

W

|

,

|

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,

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v

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O.B

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WW

~ Z~ H

,

W

o=

W

H

Z a

tiJ 0.6

w

X

2.0

~--

~.5

W

0

0.4 w

H

,#

~ T LU

0.2 LU

WW

Z H

W

Ld

W

0

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0.2

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(a) .

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WORK HARDENING EXPONENT

(b) 0.5

,

1.0

nw

, 0

,

,

, 0.2

WORK

,

,

,

0.4 HARDENING

0.6 EXPONENT

0.8

,

, ~.0

n*

Fig. 8. Effect o f work-hardening exponent n* on: (a) extension at the onset o f wrinkling; (b) wrinkle height at 2% extension.

hardening e x p o n e n t at low strain - - usually that in the range 1--5% - - than between h2 and the conventional work-hardening e x p o n e n t for strains between 10 and 20% as usually quoted. In the present work this result was n o t confirmed, because n and n* provided similar correlations with wrinkle height at 2% extension. The different conclusion may be a result of the

96

difference in the definition of n* adopted in the present work and in that of the previous workers [7, 9, 10] who assessed , * at 1--5% extension, whereas it was here assessed at the commencement of work hardening. The latter may be less relevant to wrinkle growth but more relevant to the initiation of wrinkles.

3.4 Strain rate and the coefficient o f strain.rate sensitivity The effect of strain rate on wrinkling of mild steel (mat. 2A), stainless steel (mat. 2B), titanium (mat. C) and 70/30 brass (mat. E) was investigated over a range of cross-head speeds -- 0.2 ram/rain, 0.5 ram/rain and 1.0 ram/ rain. The result of tests on stainless steel (mat. 2B) is shown as a typical example (Fig. 9). A higher test speed led to slightly earlier and higher wrinkles in each case. An increase in test speed promotes any temperature gradient arising from localised deformation, favouring the growth of ~ l e s . 3.0

• + I o mm/mlo 2.5

~ - 0.5 r o m / m l n + -

0,2 ram~rain

+ +

2.o +

H ~

+

~..5

~+ H

t.0 •

0.5

•

+

~+°~

i

Oi

.... ,

I1~.+. , . . . .

,

0.5

1.0

EXTENSION

ON

75

'I,5 MM.

....

, .... 2.0

GAUGE

, .... 2.5

LENGTH

3.0 [%]

Fig. 9. E f f e c t o f s t r a i n r a t e o n w r i n k l e height.

The effect of the coefficient o f strain-rate sensitivity on the onset of wrinkling and on wrinkle height at 2% mean axial extension was more evident for given materiRIA with different annealing ~ e m t s (Figs. 10(a) and (b)) than when materials of a different type were included (Figs. l t ( a ) and (b)). Generally, extension at the onset of w-~inkling of like msteriAI, increased with strain-rate sensitivity, except in the case of titani-m (Fig. 10(a)), but wrinkle height at 2% extension decreased with m in all cases (Fig. 10(b)): however, insufficient data were obtained to permit calculation of a corre]ation coefficient. No explanation was found for the exceptional behaviouxof titanium. ConskJering all mater~IA together, the linear coneJation coefficient

97 4.0

t.0

o-

o - MILD STEEL

~ Z H

• - 70/30

.4

,1(,- COPPER

W -COPPER

0

0.B

MILD STEEL

* - TITANIUM

3.5

* - TITANIUM

• -

BRASS

7 0 / 3 0 BRASS

H 3.0

e

z

W

:~

0.6

2.5

B

•

03 z o

W

0

+÷

2.0

0.4

~

°

g ~z

0

, 0.P

~

1.5

H

t.0

+

•

+

(a) 0

. . . .

i

. . . .

0.5 STRAIN

a .

I

i

t.0 RATE

i

i

i

i

d

1.5

SENSITIVITY

i

i

i

i

i

2.0 w

(b) 0.5

I

2.5

0.5

STRAIN

10"2

1.0 RATE

1.5

2.0

SENSITIVITY

~

2.5 ~0~2

Fig. 10. Effect of coefficient of strain-rate sensitivity on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension, for given materials after annealing.

1.0

3.0

.... ),,,

,

,

,

. . . .

,

. . . .

!

. . . .

!

. . . .

w

L90.B Z H

2.5 o=

H w

w w

Z H 0.6

C}

w

W W

0,4

2.0

1.5 (-b H

W W W

H

W

LU

W

0.2

1.0

~z W

3=

(a] ....

i ....

0.5 STRAIN

i ....

t.0 RATE

• ....

t.5

SENSITIVITY

I ....

2.0 ~

0.5

2.5 I0~2

0.5 STRAIN

1.0 RATE

t.5

SENSITIVITY

2.0 ~

2.5 10^2

Fig. 11. Effect of coefficient of strain-rate sensitivity on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension, for all materials tested.

between m and the extension o f the onset o f wrinkling was +0.03 and between m and h2 it was +0.16. Although little significance can be attached to correlation coefficients as small as these, the anomalous value o f that between m and h2 was caused by the very small value o f h2 for one o f the 70/

98

30 brasses tested (mat. FII). Again, no explanation was found for this result, although it is noted that the yield stress of the brass was very low, higher only than that o f annealed copper (mat. DID, and the effect o f strain-rate sensitivity may have been overshadowed by that o f yield strength. It appears that wrinkles initiated earlier and grew more rapidly in like materials with a lower coefficient o f strain-rate sensitivity. In such materials, the increased strain-rate associated with the strain locatisation would produce a smaller local increase in yield stress, allowing strain to continue locally, and strain would not be diffused as much as would be the case in materials o f higher strain-rate sensitivity. This tendency was observed in all materials tested (Figs. l l ( a ) and (b)).

3.5 Effect of the coefficient of normal plastic anisotropy and the ratio r* /YS Figures 12(a) and (b) show respectively the effect o f r -- the value o f normal plastic anisotropy at 20% -- on the extension at the initiation of wrinkling and on wrinkle height at 2% axial extension, whereas Figs. 13(a) and (b) show the correlation between r* -- the value of normal plastic anisotropy at 5% extension -- and the same wrinkling parameters. A fair correlation was f o u n d between both r and the initiation of wrinkling and between r* and the initiation o f wrinkling, for which the linear correlation coefficients were respectively--0.33 a n d - 0 . 2 3 (Figs. 1 2 ( a ) a n d 13(a)), but the correlation coefficients between r and h2 for all materials tested (+0.08) and between r* and h2 (+0.11) were very small (Figs. 12(b) and 13(5)). It appears, then, that neither the value of the normal anisotropy coefficient at 20% extension nor at 5% extension was a significant factor in l.O

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Fig. 12. Effect o f coefficient o f normal plastic anisotropy r on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% exterBion.

99 3.0

~.0

0.8

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Fig, 13. Effect o f the coefficient of normal plastic anisotropy r* on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension.

determining wrinkle height: this finding accords with that of Yoshida et al. [7], Satoh [9] and Gibson and Hobbs [10]. In the present work the coefficient of normal plastic anisotropy and wrinkling behaviour were assessed only in the rolling direction, whereas Yoshida et al. [7] related results of the Yoshida test to mean values of the material properties. Gibson and Hobbs [10] measured material properties in both the rolling and diagonal directions and showed that correlation of wrinkle height and normal plastic anisotropy was improved if the value in the direction of straining was used. The relation between r*/YS and extension at initiation of wrinkling and that between r*/YS and wrinkle height at 2% extension are shown in Figs. 14(a) and (b). The correlation (+0.08) of r*/YS with initiation of wrinkling was very weak, but the linear correlation coefficient o f - - 0 . 6 5 confirmed the conclusion of Yoshida et al. [7], Satoh [9] and Gibson and Hobbs [10], that r*/YS was an important parameter in determining the resistance of sheet metals to the growth of wrinkles.

3.6 Summary of results The effect of the material properties investigated -- namely yield stress, yield elongation (LEders strain), n and n*, r and r*, strain rate and.strainrate sensitivity -- on extension at initiation of wrinkling and on wrinkle height at 2% mean axial extension is summarized in Table 2. The linear correlation coefficients between wrinkling parameters and material and process variables in given materials after annealing were not evaluated, due to the limited number of test results for each material. Except in the case of the apparent effect of strain-rate sensitivity on wrinkle

100

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Fig. 14. Effect of ratio r*/YS on: (a) extension at the onset of wrinkling; (b) wrinkle height at 2% extension,

TABLE 2 The linear correlation coefficient between material variables and extension at the onset of wrinkling and wrinkle height at 2% mean axial extension Measured Variables

1 Yield stress 2 Yield elongation (Liiders Strain) 3 Work-hardening exponent (i) n (ii) n* 4 Coefficient of strain-rate sensitivity (all materials) 5 Coefficient of strain-rate sensitivity of given materials after heat treatment 6 Coefficient of normal plastic anisotropy (i) r (ii) r* 7 Ratio r*/YS 8 Testing speed

Linear Correlation Coefficient Extension at Onset of Wrinkling

Wrinkle Height at 2% Extension

--0.12 +0.94

+0.64 --0.31

+0.12 +0.43

--0.75 --0.72

+0.03 An increasing relationship

+0.16 A decreasing relationship

--0.23 --0.33 +0.08 A decreasing relationship

+0.08 +0.11 --0.64 An increasing relationship

101

height, which was influenced b y one seemingly anomalous result (that for a 70/30 brass -- FII), the behaviour of material variables for different materials and materials modified b y annealing were consistent. Generally, Table 2 shows that the wrinkling performance o f different materials was characterised more distinctly b y wrinkle height at 2% extension than b y the onset of wrinkling. This may be due less to inherent sensitivity than to the greater error in estimating the values of extension at initiation, which results from the dependence on extrapolation back to zerowrinkle height, so that values are regarded as less reliable than those of wrinkle height. 4. Conclusion The effect of mechanical properties on wrinkling behaviour of different materials and on that of given materials after different annealing treatments was examined at room temperature using the Yoshida test, with the following results: (1) strain rate, normal plastic anisotropy and yield strength p r o m o t e d the initiation of wrinkling, but an increase in yield elongation (Liiders strain), if present, and work hardening, delayed it. However, the effect of yield elongation requires further study. (2) wrinkling initiated earlier and grew more rapidly in like materials with a lower coefficient of strain-rate sensitivity, b u t it was found impossible to generalise this result to different materials. It was also found that a higher test speed p r o m o t e d the initiation and growth o f wrinkles slightly. (3) use of n*, the value of the work-hardening exponent immediately after yield or at c o m m e n c e m e n t of work hardening, and r*, the value of normal plastic anisotropy at 5% extension, correlated a little more strongly with the initiation of wrinkling than did the standard values, n and r. The exponent n* did not correlate more strongly with wrinkle height at 2% extension than did n: the use of r* rather than r did n o t improve correlation significantly in this case. This contradiction of the conclusions of Yoshida et al. [7], Satoh [9] and Gibson and Hobbs [10] may result from the difference in the definition o f n* and r* adopted here. (4) it was found that the wrinkling performance of different materials can be characterised more distinctly b y wrinkle height at 2% mean axial extension than b y the onset of wrinkling. (5) higher values of the work-hardening exponent n and ratio r*/YS retarded the growth of wrinkles, b u t a higher value of yield stress accelerated the growth, confirming the findings of Yoshida et al. [7], Satoh [9] and Gibson and H o b b s [10]. (6) it was found impossible to apply the Yoshida test to aluminium and its alloys, because rupture invariably occurred before wrinkling.

102

Acknowledgements The authors would like to thank Dr. R.M. Hobbs and Mr. T.J. Gibson of the BHP Co. Ltd., Melbourne Research Laboratories, for helpful discussions and supplying some materials. Thanks are also due to Messrs. John Lysaght (Aust.) Ltd. for the supply of materials.

References 1 K. Yoshida, H. Hayashi, K. Miyauchi, Y. Yamamoto, K. Abe, M. Ushda, R. Ishida and Y. Oike, Sci. Paper Inst. Phys. Chem. Res., 68 (1974) 85. 2 H. Hayashi, S. Kuriyama, K. Hirase, H. Takechi and K. Yoshida, Sci. Papers Inst. Phys. Chem. Res., 70 (3) (1976), 52. 3 J. Havranek, J. Mech. Work. Tech., 1 (1977) 115. 4 R.M. Hobbs, BHP Tech. Bull: 25 (2) (1961) 49. 5 H. Abe, K. Nakagawa, S. Sato, IDDRG/WGIII/81, International Congress, International Deep Drawing Research Group, May, 1981, Kyoto, Japan (preprint). 6 H. Abe, T. Hira, T. Sasaki and K. Nakagawa, 12th Biennial Congress International Deep Drawing Research Group, 24--28 May, 1982. St. Margherita Ligure, Genoa, Italy, 7 K. Yoshida, H. Hayashi, M. Hirata, T. Hira and S. Ujihara, IDDRG Paper DDR/WGIII/ 81, International Congress, International Deep Drawing Research Group, May, 1981, Kyoto, Japan (preprint). 8 JSFRG (IDDRG) Data Sheets IDDRG/WGIII/82, 12th Biennial Congress International Deep Drawing Research Group, 24--28 May, 1982. St. Margherita Ligure, Genoa, Italy. 9 T. Satoh, Personal communication to T.J. Gibson and R.M. Hobbs [reported in reference 10]. 10 T.J. Gibson and R.M. Hobbs, IDDRG/WGIII/82, 12th Biennial Congress International Deep Drawing Research Group, 24--28 May, 1982. St. Margherita Ligure, Genoa, Italy. 11 J. Hedworth and M.J. Stowell, J. Mat. Sci. 6 (1971) 1061.