10-A New Direct Biaxial Testing Machine for Ani So Tropic Materials

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A N e w D i r e c t B ia x ia l Te s t ing M a c h ine

for A n is o t r op ic M a te ria ls

by J .P . Boehler , S . D em m er le and S . Koss

Abs t rac t - -A sc rew-d r i ven new b i ax ia l tes t i ng m ach i ne f o rthe rea l i za t ion o f exper ime nta l invest igat ions on an iso-t rop ic shee t materia ls , such a s com posi te p la tes or ro l ledsheet meta ls , i s presented. The descr ibed mechanica l

concept and servocont ro l system a l low cruc i form spec i -mens to be sub jected to la rge s t ra in b iax ia l tens i le andcom press i ve t es t s w i t hou t k i nem at i c i ncom pa t i b i l i t i es .Moreover , for the pro per implem entat ion o f b iax ia l tens i letests , the sp ec i f i c prob lems l inked to the an iso t rop ic prop-er t ies o f the inve st igated mater ia ls are taken in to accou nt ;therefore , for the f i rs t time, the b iax ia l ma chine i s sup pl iedwi th the or ig ina l 'o f f -axes test ing dev ice, ' cons is t ing o fh inged f i x tures w i th kn i fe-edg es a t each arm of the cruc i -form spec imen. A recen t l y deve loped opt im izat ion methodfor the opt imal des ign o f fl a t tens i le cruc iform spec imen s i sshor t l y rev iewed. N um er ica l s imula t ions i l lus t ra te the deci-

sive supe r i o r i ty o f t he op t i m i zed spec i m en com pared w i thspec im en de s igns prop osed in the l ite ra ture , as w el l as thenece ss i ty to us e the 'o f f -axes ' tes t ing techn ique in b iax ia l

tests on an isot rop ic mater ia ls .

I n t r o d u c t i o n

W i t h t he i nc r eas i ng i mpor t ance o f l igh t e r - w e i gh t s t r uc -

t u r e s i n any i ndus t r i a l b r anch ( e .g . ae r onau t i c o r au t omo-

t i ve i ndus t r i e s ) , b i ax i a l t e s t i ng o f shee t ma t e r i a l s has

beco me o f g r ea t p r ac t i ce i n t e re s t . T he c l a s s i ca l t e s ts und e r

un i ax i a l s t re s s have t u r ned ou t t o be i n su f f i c i en t t o p r ov i de

a r e l i ab l e mechan i ca l cha r ac t e r i za t i on w hi ch i s e s sen t ia l t o

t he e f f i c i en t u se o f t he m a t e r ia l s . T he b i ax i a l t e s ti ng en -

ab l e s be t t e r p r ed i c t i ons t o be ma de on t he mechan i ca l

p r ope r t i e s o f new ma t e r i a l s ( e .g . comp os i t e s ) , a s w e l l a s

on t he mech an i ca l behav i o r o f , f o r exampl e , r o l l ed shee tme t a l s du r i ng f u r t he r manu f ac t u r i ng p r oces ses . P r i o r t o t he

r ea l i za ti on o f a b i ax i a l t e s t i ng f ac i l i ty , t h r ee ma j o r p r ob-

l ems have t o be so l ved :

J.P. Boehler is Professor, and S. Demmerle and S. Koss are Engineers,

Equipe Mdcanique d es Milieu x Anisotropes, U niversiM Joseph F ourier,

L3S-MMA , Dom aine U niversitaire, B.P. 53X, F-38041 Grenoble, France.

Orig ina l m anuscrip t submit ted Novem ber 25 , 1992 . Final manuscrip t

received: May 1 0 ,1993 .

- - t h e a p p l ie d t e c h n i q u e s h o u l d a l lo w t h e e x i s t e n c e o f a n

a r ea i n t he spec i men sub j ec t ed t o w e l l - de f i ned b i ax i a l

s ta tes of s t ress and s t ra in;

- -- -especia lly for the tes t ing o f rol led sheet me ta l s , in ord er

t o op t i mi ze me t a l f o r mi ng p r oces ses f o r exampl e , t he

mach i ne shou l d enab l e l a r ge de f o r ma t i ons t o be sub-

j ec t ed t o t he spec i men ;

t he t e s t i ng sys t em has t o t ake i n t o accoun t t he an i so -

t ropic proper t ies of the mater ia l s ; th i s i s val id for both

comp os i t e s and r o l l ed shee t me t a l s .

I n o r de r t o d i s cus s t he f i r s t r equ i r emen t , t he f ou r mos t

i mpor t an t t echn i ques , w i t h d i f f e r en t t e s t i ng sys t ems and

spec i mens used t o p r oduce s t a t e s o f b i ax i a l s t r e s s and

s t ra i n , a r e r ev i ew ed i n t he f o l l ow i ng .

B e n d i n g o f b e a m s a n d t h i n p l a t e s c a n b e u s e d t o c re a t e

a b i a x i a l s t r es s s t a t e a s r e p o r t e d , f o r e x a m p l e , b y H a z e l l

a n d M a r i n ' w h o t e s t e d a n a l u m i n iu m a l lo y b y e m p l o y i n g

r h o m b o i d a l s h a p e d c o m p o s i t e p l a t e s c o n s i st i n g o f af i be r g la s s h o n e y c o m b e d s t ru c t u re s a n d w i c h e d b e t w e e n

t w o t h i n s h e e t s o f a l u m i n i u m . T h i s t e s t a ll o w s t h e m a -

t e r ia l t o b e a n a l y z e d i n t h e s e c o n d a n d f o u r t h q u a d r a n t s

o f t he t w o- d i mens i ona l s t re s s space , how ev e r , each p r in -

c ipal s t ress ra t io requi res a speci f ic shape of the pla tes .

A no t he r d i s advan t age o f t h i s t echn i que cons i s t s i n t he

nonu n i f o r m s t re s s d i s t r ibu t i on ( i n t he p l ane o f t he spec i -

men , a s w e l l a s ove r t he spec i men t h i cknes s ) , e spec i a l l y

a f t e r the occur r en ce o f t he f i r s t p la s t i c de f o r ma t i ons , so

t ha t t he r ea l st r e sse s canno t be de t e r mi ned f r om t he meas -

u r ed f o r ces .

A no t he r t echn i que t o be men t i oned i s t he hydr au l i c

bu l ge t e s t , a s r epor t ed by B i r d an d D uncan , 2 o r L uk yano v

e t a l . , 3 w her e a p r e s su r e i s app l i ed to t he su r f ace o f a r ound

or e l l i p t i ca l f l a t shee t spec i men . O n t he one hand , i t i s

ev i den t t ha t t he r e appea r s a s t r e s s g r ad i en t i n t he t h i cknes s

o f t he spec i men . O n t he o t he r hand , D udde r a r e t a l . 4 p r o v e d

t h e n o n h o m o g e n e o u s c h a r a c te r o f t h e d e v e l o p i n g s t r e ss

f i e lds , due t o t he g r i pp i ng o f the spec i m en edges . L i ke t he

bend i ng me t hod , t h i s t echn i que r equ i r e s a d i f f e r en t spec i -

me n ' s shape f o r each r a t io o f t he p r i nc ipa l s t r e s se s ( ' l eng t h

of t he ma j o r ax i s ' / ' l eng t h o f t he mi nor ax i s ' ) , and t h i s does

no t a l l ow a va r i ab l e l oad i ng r a t i o to be app l i ed dur i ng t he

test .

E x p e r i m e n t a l M e c h a n i c s * 1



T h e m o s t p o p u l a r t e c hn i q u e e m p l o y e d b y , f o r e x a m p l e ,

H a v a r d a n d T o p p e r ,5 A n d re w s a n d E l li so n 6 o r L e fe b v re e t

a l . , 7 u s e th in -w a l l e d tu b e s s u b je c t e d to t e n s i l e o r c o m p re s -

s iv e lo a d s c o m b in e d w i th to r s io n a l l o a d s o r i n t e rn a l - e x te r -

na l p ressure , in o r de r to c rea te b iax ia l s ta te s o f s t res s . Th is

t e c h n iq u e s e e m s to b e v e ry v e r s a t i l e , b e c a u s e i t a l l o w s t e s t s

w i th a n y c o n s t a n t s t r e s s o r s t r ain r a t io to b e p e r fo rm e d ; b u t

i t p re s e n t s s o m e in c o n v e n ie n c e s :

- - -due to the rad ia l s t re s s g rad ien t the s t re s s s ta te is no t

e x a c t ly b i a x ia l;

- - fo r a g iv e n o r i e n ta t io n 0 o f t h e p r in c ip a l - s t r e s s d i r e c -

t ions , the s t re s s ra t io is no t va r iab le , i . e . i t is no t poss ib le

to rea l ize any s t re s s o r s t ra in pa th ;

- - th e a n i s o t ro p ic p ro p e r t i e s o f t u b e s a n d s h e e t m a te r i a l s

a re n o t c o m p a ra b le .

T h e m o s t r e a l i st i c e x p e r im e n ta l t e c h n iq u e to c re a t e a b i a x -

i a l s t r e s s s t a t e i n s h e e t m a te r i a l s c o n s i s t s o f a p p ly in g

in -p la n e lo a d s a lo n g tw o p e rp e n d ic u la r d i r e c t io n s to th e

a rm s o f a c ru c i fo rm s p e c im e n . D i f f e re n t t y p e s o f l o a d

a p p l i c a t io n s y s t e m s h a v e b e e n p ro p o s e d in th e l i t e r a tu re .

H a y h u r s t 8 d e v e lo p e d a b i a x ia l c re e p - ru p tu re t e n s i l e t e s t -

in g m a c h in e , w h e re a d e a d w e ig h t l e v e r s y s t e m i s u se d , a n d

th e lo a d s a re a p p l i e d b y m e a n s o f w i re ro p e s w h ic h p a s s

o v e r p u l l e y s . D u e to a r e l a t iv e ly h ig h l e v e l o f f r i c t io n inth e b e a r in g s , t h e t e s t in g w a s l im i t e d to a s m a l l l e v e r

m o v e m e n t , i .e . , s m a l l s t ra in s. A s im i l a r t e c h n iq u e w a s

p r o p o s e d b y B r e m a n d a n d L a g a r d e , 9 w h e r e i n e a c h d i r e c -

t io n d e a d w e ig h t l o a d s a re a p p l i e d to th e c ru c i fo rm s p e c i -

m e n ( m a d e o f u r e t h an e ) b y m e a n s o f n y l o n t h r e a ds a n d

p u l l e y s o n ro l l e r b e a r in g s . In o rd e r t o a v o id d i f f i c u l t ie s d u e

to th e f r i c t io n in th e b e a r in g s , i n th e c re e p t e s t in g m a c h in e1 0 1 1

o f Mo r r i s o n a n d K e l ly , t h e c ro s s - s h a p e d s p e c im e n i s

s u b je c t e d to d e a d w e ig h t l o a d s b y a k n i f e -e d g e l e v e r s y s -

t e m ( ra t io 2 0 :1 ) w i th p u l l - ro d s . T h i s t e c h n iq u e p re s e n t s a

v e ry g o o d s u i t a b i l i t y fo r c re e p t e s t s , b e c a u s e i t e n a b le s

s t e a d y lo a d s to b e m a in ta in e d fo r l o n g p e r io d s o f t im e .

A n i n e x p e n s i v e t e c h n iq u e w a s p r o p o s e d b y F e n ' o n a n d1 2M a k i n d e . I t c o n s i s t s o f a s y m m e t r i c a l j o i n t e d - a r m

m e c h a n i s m to a p p ly b i a x ia l, b u t c o u p le d , i n -p l a n e lo a d s to

a f i a t c ru c i fo rm s p e c im e n b y u s in g a c o n v e n t io n a l u n ia x ia l

t e s t in g m a c h in e . T h e v a lu e o f t h e s t r ain r a t io c a n v a ry

b e tw e e n 0 a n d l , b u t i t d e p e n d s o n th e g e o m e t r i c a l c o n -

f ig u ra t io n o f t h e d e v ic e , a n d i t is t h e re fo re c o n s t a n t d u r in g

a tes t.

T h e u s e o f h y d ra u l i c a c tu a to r s r e p re s e n t s a v e ry v e r s a t i l e

t e c h n iq u e fo r t h e a p p l i c a t io n o f l o a d s. B e s id e s th e d e v ic e

o f S h i ra to r i a n d Ik e g a m i , t3 o n e o f t h e f i r s t m a c h in e s u s in g

th i s m e th o d w a s d e v i s e d b y P a s c o e a n d d e V i l l i e r s 14 w h e re

th e f i a t c ru c i fo rm s p e c im e n i s l o a d e d d i r e c t ly b y fo u r

d o u b le -a c t in g j a c k s , w i th a c a p a c i ty o f 2 0 0 k N in t e n s io n

a n d c o m p re s s io n . In o rd e r t o r e a l i z e te s t s a t a n y r a t io o f t h eprinc ip a l s t ra ins , Pa rs ons and P ascoe ~5 equ ip ped th e o r ig i -

n a l d e v ic e w i th a c lo s e d - lo o p s e rv o c o n t ro l u s in g th e m e a s -

u r e d s t r a i n s o r l o a d s a s f e e d b a c k s i g n a l s . A s i m i l a r

s e r v o h y dr a n l ic t e s t in g m a c h i n e w a s d e v e l o p e d b y M a k -

in d e e t a t . I6 w i th fo u r p u l l -p u s h a c tu a to r s p ro v id e d w i th

h y d ra u l i c w e d g e g r ip s a n d a h o r i z o n ta l lo a d f r a m e w h ic h

i s s i t u at e d o u t o f t h e s p e c im e n p la n e ; t h i s m a k e s i t n e c e s -

s a ry to p ro v id e a v e ry s t i f f c o n s t ru c t io n , i n o rd e r t o m in i -

m i z e t h e d e f l e ct i o n d u e t o h i g h b e n d i n g m o m e n t s u n d e r

lo a d . A n o th e r e l e c t ro h y d ra u l i c c lo s e d - lo o p c o n t ro l l e d m a -

c h i n e , p r o p o s e d b y C h a u d o n n e r e t e t a l . , 17 h a s th e s a m e

ty p e o f l o a d f r a m e , b u t o n ly o n e a c tu a to r p e r l o a d in g

d i re c t io n . D u e to th i s f a c t , t h e c e n te r o f t h e s p e c im e n

m o v e s d u r in g a t es t . T h u s , in c a s e o f l a rg e d e fo rm a t io n s ,

k in e m a t i c i n c o m p a t ib i l i t i e s c a u s e a s id e b e n d in g o f t h e

s p e c im e n , e v e n w h e n u s in g f l e x ib l e l i n k s b e tw e e n th e

s p e c im e n ' s g r ip h e a d s a n d th e p i sto n s . A d d i t io n a l ly , s u c h

a s y s t e m c a n n o t b e u s e d fo r c o m p re s s iv e t e st s . In o rd e r t o

e n s u re th e in d e p e n d e n c e o f t h e lo a d in g in th e tw o m u tu a l l~

p e rp e n d ic u la r p r in c ip a l d i r e c t io n s , F e s s l e r a n d Mu s s o n

d e v e lo p e d a 3 0 0 -k N b ia x ia l h y d ra u l i c t e s t in g m a c h in e ,

w h e re th e h o r i z o n ta l a n n o f t h e v e r t i c a l l o a d f r a m e i s

s u s p e n d e d a n d b a la n c e d in d e p e n d e n t ly .

In th i s p a p e r , a s c re w -d r iv e n e l e c t ro m e c h a n ic a l b i a x ia l

t e s t in g m a c h in e i s p re s e n te d ; t h e m a c h in e i s c o n c e iv e d to

t e s t c ro s s s h a p e d s p e c im e n s m a d e o f a n i s o t ro p ic m a te r i a l s

s u c h a s f l a t c o m p o s i t e p l a t e s o r ro l l e d s h e e t m e ta l s . T h e

u s e d s p e c im e n d e s ig n fo l lo w s f ro m a s h a p e o p t im iz a t io n

p ro p o s e d b y D e m m e r le a n d B o e h le r 19 w h ic h i s b r i e f ly

d e s c ri b e d i n ' T h e C r u c i f o r m S p e c i m e n ' b e l o w .

Mechanical Concept

C o m p a re d to th e s e rv o h y d ra u l i c t e s t in g f a c i l i t i e s , t h i s

e l e c t ro m e c h a n ic a l m a c h in e r e p re s e n t s a l o w -c o s t s o lu t io nfo r t h e r e a l i z a t io n o f b i a x ia l t e s t s o n s h e e t m a te r i a l s . I t c a n

a p p ly e i th e r t e n s i l e o r c o m p re s s iv e q u a s i - s t a t i c l o a d s to

c ru c i fo rm f l a t s p e c im e n s . F o r th e f i r s t t im e , t h is m a c h in e

i s s u p p l i e d w i th th e o f f - a x e s t es t in g d e v ic e ( s e e ' C o n n e c -

t io n Ma c h in e S p e c im e n ' b e lo w ) ; t h i s e n a b le s a n e a r ly

p e r fe c t im p le m e n ta t io n o f o f f a x e s t en s i l e t e s ts o n a n i s o t -

ro p ic m a te r i a l s . A t p re s e n t , t h e d e v e lo p m e n t o f a s p e c im e n

d e s ig n to g e th e r w i th a s u i t a b le g r ip p in g s y s t e m to c a r ry o u t

c o m p re s s iv e t e s t s i s i n p re p a ra t io n .

General Features

T h e p re s e n te d m a c h in e , F ig . 1 , c o n s i s t s o f fo u r d o u b le -

a c t in g s c re w -d r iv e n p i s to n s , tw o in e i th e r d i r e c t io n , r i g id lys u p p o r t e d o n a n o c ta g o n a l v e r t i c a l f r a m e . In e a c h d i r e c -

t io n , t h e m a x im u m lo a d i s a b o u t 1 0 0 k N in t e n s io n a n d

c o m p re s s io n . T h e u n o b s t ru c te d w o rk in g a re a o f 9 0 0 • 9 0 0

m m 2 e n a b le s t e s t s o n s p e c im e n s w i th a s i z e u p to 5 0 0 •

5 0 0 m m . 2 T h e v e r t i c a l i n s t al l a t io n o f t h e o c t a g o n a l f r a m e

w h ic h s u r ro u n d s th e s p e c im e n e n s u re s a n e x c e l l e n t a c c e s -

s ib i li t y f ro m b o th s id e s to th e w o rk in g a re a ; t h is f a c i l i t at e s

th e m o u n t in g a s w e l l a s th e o b s e rv a t io n th ro u g h o u t a t es t ,

e . g . t o t a k e p h o to s , i n o rd e r t o a n a ly z e th e s t r a in f i e ld b y

a p p ly in g th e s t e re o p h o to g ra m m e t r i c m e th o d . 2~ F u r th er -

m o re , a s t h e p l a n e o f t h e s p e c im e n c o in c id e s w i th th e s y m -

m e t ry p l a n e o f t h e f r a m e , t h e l a t t e r i s n o t s u b je c t e d to h ig h

b e n d in g m o m e n t s c a u s in g d e f l e c t io n s w h ic h in tu rn l e a dto a n in -p la n e b e n d in g o f t h e s p e c im e n . O n th e o th e r h a n d ,

d u e to th e v e r t i c a l i n s ta l l a tio n , i t i s n e c e s s a ry to c o m p e n -

s a t e th e d e a d w e ig h t o f e a c h h o r i z o n ta l a rm o f th e s p e c im e n

to g e th e r w i th th e g r ip p in g s y s t e m f ix e d to i t s e n d , i n o rd e r

to a v o id a s id e b e n d in g o f a t h in s p e c im e n , s e e (1 0 ) in F ig .

2 . N o te th a t i t is n o t n e c e s s a ry to e m p lo y th e s a m e p ro c e -

d u re fo r t h e lo w e r v e r t i c a l s p e c im e n a rm , s in c e th e d e a d -

w e ig h t o f t h e g r ip p in g s y s t e m c a u s e s o n ly a n e g l ig ib l e

p re s t r e s s i n th e c ro s s - s e c t io n a l a re a o f t h e s p e c im e n .

T h e fo u r a c t in g p i s to n s e n a b le l a rg e d e fo rm a t io n t e s t s t o

b e p e r f o r m e d w i t h o u t k i n e m a t i c i n c o m p a t i b i l i t i e s , b e -

2 9 March 1994



gear (4), r = 309, the rotation of the shaft is transformed

into a t rans lat ion of the pis ton (5) by mea ns of an endless

screw (lead = 2 ram) situated inside the piston itself . A high

precis ion screw is used, in order to minimize the clearance

when revers ing the load. In the mode ' tes t , ' the displace-

ment speed of each pis ton is inf ini te ly var iable between

0.003 mm/min and 0.3 mm/min, and control led by rect i-

f ier -governors (type TMD, Leroy-Som er) . The synchroni-

zat ion between the m otors is real ized by means of s ignals

der ived f rom optical incremental encoders (6) whichmeasure the present motor speed (see 'Servocontrol Sys-

tem ' below) . The four ac-motors work independently f rom

each other and al low the pis tons to be moved with 20

mm/min without speed control .

The ful l s troke of each pis ton is l imited to about 245 ram.

In order to prevent dam age to the screw-d r iven pis tons , the

two extreme posi t ions are detected by microswitches (7)

which are connected d irect ly to the control c ircuit.

Fig. 1--Genera l view of the testing machine: 1-frame, 2-power unit, 3-analog/logic unit, 4-control panel, 5-servo-control unit

cause the machine ensures that the center of the specimen

remains s ta t ionary dur ing the tes t ( see 'Servocon trol Sys-

tem ' below); this feature is a lso impor tant when ap plying

the s tereophotogrammetr ic method. S ince the load is ap-

plied independently in each of the two pr incipal direct ions ,

the loading ratio (Fz/F~) can be var ied inf ini te ly, even

during a test.

The machine provides two operat ion modes: the mode

' tes t ' to car ry out the tes ts and the mode ' fas t feed' to

posi t ion the pis tons . In the ' te s t ' mode, the actuators can

operate under two control mod es , that is, the manual and

the numer ical control . In the case of the manual control ,

the des ired value s ignals are obtained f rom the control

panel . In the case of the numer ical control , they are ob-

tained f rom calculat ions by a microcomputer taking into

account the feedback s ignals of dif ferent measurement

facilities (e.g. load cells or strain gages); this allows any

stress or strain path to be realized. Additionally, three

synchronizat ion mode s can be chosen: a l l four pistons can

work independently, or the two op posite pis tons of each

direct ion are synchronized, or there is a total synchroniza-

t ion of a l l four pis tons. The mod e ' fas t feed' provides jus t

a manual control without synchronizat ion which is suf f i-

cient for the mounting and the dismantl ing o f the speci-

mens.

The Drive U n i t

As shown in Fig. 2, each of the four actuators is supplied

with two motors : a geared var iable-speed dc-motor (1)

with a gear rat io of 61.4 wh ich is act ive in the ' te s t ' mode ,

and a ac-motor (2) used to real ize the high displacement

speeds in the ' fas t feed' mode. For each pair , a manual

clutch (3) enables one of the two motors to be chosen, and

a coupled safety device prevents the s imultaneous opera-

t ion of both mo tors . Af ter another reduction in the two-s tep

Connection Machine Specimen(The Off-axes Testing Device)

One of the most impor tant or iginal i t ies of the presented

machine consis ts in the real izat ion of the fir s t ' of f axes '

tes t ing dev ice for biaxial tens i le tes ts on anisotropic mate-

rials, cf . Dem me rle and B oehler. ~9 In the so called 'off-

axes ' tes t, the pr incipal direct ions o f the applied loads do

not coincide with the pr ivi leged axes o f the mater ial sym -

metries; it results that in the doma in o f elastic behavio r, as

well as in the domain of plas t ic behavior , the pr incipal

directions of the stress state, in general, do not coincide

with that o f the strain state, Boehler, 21 Boe hler et al. 2z

showed that in of f -axes tes ts on anisotropic mater ials this

noncoincidence ini t ia tes the developmen t of s trongly non-

homo geneou s s tress and s train f ie lds in the specimen w hen

using the class ical tes t ing method consis t ing of r igidly

clamped heads . Moreo ver , s ince the s tress and s train s ta tesdo no t cor r espond to the in tended ones , e r r oneous ex-

per imenta l da ta a r e ob ta ined which cann ot be used f or a

pr oper iden t i f i ca t ion of cons t i tu t ive laws f or an i so t r op ic

mate r ia l s. The so lu t ion to these pr oblems was f ound by

5 4

Fig. 2--Co mpon ents of the direct biaxial testing m achine

ExperimentalMechanics 9 3



~ Knife-restie

[ " ~ Shrrup i e c e

I I . . .. I

- Loadcell

Fig. 3- -Of f -a xes test ing device for b iax ia l tensi le cruc i -f or m spec imen s

B o e h l e r2~' ~3, 24 an d B oe hl er e t a l . 2 5 ' 2 2 wh o d ev i sed a sp ec i f i co f f - ax es t e s t in g d e v i ce fo r u n i ax i a l t en s i l e sp ec imen s , c o n -

s is t ing of h inged f ix tures wi th kn i fe edges . This technique

a l l o ws t h e d ev e lo p men t o f an a lmo s t n o n co n s t r a in ed s t r a in

state in the tes t reg ion , and i t has p roved i t s ef f ic ienc y to

p ro d u ce h o m o g en eo u s s t r e ss an d s t r ain f i e ld s i n v a r i o u s

t es t s o n u n i ax i a l t en s i l e sp ec imen s mad e o f o r t h o t ro p i c

ro l led sheet s teel , cf . Boehler . z3

Th e ab o v e d e sc r i b ed t ech n iq u e co n s t it u t es t he b as i s o f

t h e h e re in d ev e lo p ed co n n ec t i o n b e tween t h e m ach in e an d

th e a rms o f t h e c ru c i fo rm f la t sp ec imen , F ig. 3 . On each o f

the four jacks o f the b iax ial tes t ing mac hine, two s t i r rup-

p i eces a r e f i x ed . Th e k n i f e - r es t t i es o f each co u p l e su p p o r t

o n e k n i f e - ed g e p ass in g t h ro u g h t h e g r i p h ead an d t h e

sp ec imen i t s e l f a t t h e en d s o f t h e sp ec imen a rms . Th e g r i phead consis t s o f two r ig id s teel p lates wi th a cen t ral ho le

( a l lo win g t h e k n i f e ed g e t o p ass t h ro u g h ) f i x ed o n b o th

s id es t o t h e en d o f each sp ec imen a rm b y mean s o f fo u r

screws. Th us, the load i s app l ied th rough the s t i r rup-p ieces

and the kn i fe- res t t ies to the kn i fe-edge, which al lows a

n o n co n s t r a in ed ro t a t io n o f t h e g r i p h ead f i x ed t o t h e sp ec i -

men . A s sh o wn in t h e case o f u n iax i a l t en s il e sp ec imen s ,

th is ro tat ion i s ind ispensab le , in o rder to ob tain homoge-

neous s t ress and s t rain f ie lds in the cen t ral tes t reg ion .

Nev er th e l es s , d u e t o t h e co m p lex i t y o f t h e b i ax ia l sp ec i -

men g eo met ry , t h is t e s t i n g d ev i ce wi l l n o t b e ab l e t o e f f ec t

an ab so lu t e ly p e r f ec t h o mo g en e i t y o f t h e s t r es s an d s t ra in

states compa red to i t s fo rm er app l icat ion to un iax ial tensi le

sp ec imen s , b u t t h e r esu l t s p r esen t ed i n 'Th e Cru c i fo rm

S p ec ime n ' m ak e c l ea r t h e ab so lu t e n ecess i t y o f t h e p ro -

p o sed b i ax i a l o f f - ax es t e st i n g d ev i ce fo r an i so t ro p i c mate -

rials.

M e a s u r e m e n t a n d C o n t r o l

Th e o p era t i o n o f t h e mach in e r eq u i r es two p e r so n a l

co mp u te r s . Th e f i r s t o n e (CP U In t e l 8 0 38 6 S X, 1 6 M H z,

1 M B RA M ) i s i n t eg ra ted i n a 4 0 -ch an n e l d ig i ta l d a t a -ac -

q u i s i t i o n sy s t em Vi sh ay (M icro M easu remen t s ) S y s t em

4 0 0 0 , w h ich p ro cesses a l l d a t a co n cern in g th e me asu re -

ments o f loads , s t rains o r d isp lacements and , i f requ i red ,

t h a t o f t emp era tu re . Th e seco n d o n e (CP U In t e1 8 0 3 8 6 DX ,

1 6 M H z, 4 M B RA M ) r ep resen ts , t o g e th e r wi th t h e d ev e l -

o p ed p a r t i cu la r so f tware ( i n BAS IC) , t h e co re o f t h e se r -

v o co n t ro l sy s t em.

Load and Strain-measurement Equipment

In con t ras t to mo st b iax ial tes t ing machine s , each p is ton

is suppl ied wi th a load cel l , see (8 ) in F ig . 2 , i.e . , two cel l s

i n e i t h e r l o ad in g d i r ec ti o n . A l th o u g h t h e seco n d l o ad ce l l

p e r ax i s i s n o t ab so lu t e ly n ecessa ry fo r t h e p ro p er o p era t i o n

o f t h e m ach in e , i t i s v e ry h e lp fu l , f o r i n st an ce , t o ch eck t h e

sy m met ry o f t h e t e s t in g d ev i ce , an d t o su p erv i se t h e sy m-

me try of the load ing condi t ions dur ing the tes t , in o rder to

av o id t h e ap p l i ca ti o n o f sh ea r l o ad s t o t h e sp e c imen ' s t e s t

r e g i o n . T h e u s e d l o a d c e l l s o f t h e t y p e S t r a i n S e r t

FL2 5UM (C) ha ve a capa ci ty o f 25 000 lb (- -- 111 kN) and

en su re a p r ec i s i o n o f 0 .1 p e rcen t b y emp lo y in g a fu l l

s t rain -gage-br idge conf igurat ion .

In o rd e r t o ca r ry o u t s t r a in m easu rem en t o n t h e sp ec i -

men , two d i f f e r en t me th o d s a r e ap p l i ed , a s r ep o r t ed b y

Koss.26 n t h e d o m ain o f sm al l d e fo rmat io n s , s t ra i n g ag es ,M icro M easu remen t t y p e EA, a r e u sed . Wi th t h e so -o b -

tained data the elas t ic coeff ic ien ts o f the mater ial are

d e t e rmin ed . S in ce t h e measu rem en t o f l a rg e d e fo rmat io n s

on th in s t ructures by mean s o f s t rain gages i s d is tu rbed by

a s t r en g th en in g o f t h e as sem b ly ' s t ru c tu re + g lu e + g ag e , '

c f . Ko ss an d Bo eh l e rY h ig h - s t r a in ex t en so mete r s S ch en ck

( ty p es DS A2 5 /2 0 an d DS A1 0 /2 0 ) a r e u sed fo r t h i s p u r -

p o se . Th ey h av e a g ag e l en g th o f 2 5 mm an d 1 0 mm,

resp ec t i v e ly ; s t r a i n s u p t o 4 0 p e rcen t can b e measu red

accu ra t e ly . Th e o r i g in a l s t r a i g h t k n i fe - ed g es w ere r ep l aced

b y o n e-p o in t co n t ac t k n i f e - ed g es , wh ich mu s t b e u sed

wh en p e r fo rmin g o f f - ax es t e st s o n an i so t ro p ic m ate r ia l s ,

becau se in such tes ts the p r incipal d i rect ions o f the s t rain

t en so r a r e u n k n o wn a p r i o r i , so t h a t t h e ex t en so mete r s

can n o t b e p l aced i n t h ese d i r ec ti o n s ; t h u s t h e k n i f e - ed g es

mo u n ted o n t h e ex t en so m ete r a rms m u s t b e ab l e t o ro ta t e

wi thou t s l id ing .

Ad d i t i o n a l l y , each ac tu a to r i s su p p l i ed wi th two d i s -

p l aceme n t t r an sd u cer s (LV DT) , c f . ( 9 ) i n F ig . 2 . Th e f i r s t

o n e (S ch aev i t z 1 2 F 1 0 0 ) , w i th a s tro k e o f +1 0 0 m m an d a

p rec i s i o n b e t t e r th an 0 .2 5 p e rcen t , i s u sed t o mo n i to r t h e

d i sp l acemen t o f t h e p i s to n i n t h e o p era t i o n mo d e ' f a s t f eed '

wh i l e m o u n t in g t h e sp ec imen ; t h i s i s v e ry im p o r t an t, i n

o rd er t o p l ace t h e sp ec imen ex ac t l y i n t h e cen t e r o f t h e

t es ti n g d ev i ce . Th e o th e r o n e (S ch aev i t z 1 2 F 2 0 ), w i th a

s t ro k e o f +2 0 mm an d a p rec i s i o n b e t te r t h an 0 .1 0 p e rcen t ,

p ro v id es t h e measu remen t o f t h e g lo b a l d i sp l acemen t o fthe p is ton dur ing the tes t .

No te t h a t th e s i g n a l s o f each m easu rem en t f ac i l i ty d e -

sc r i b ed ab o v e can b e u sed as f ee d b ack s i g n a ls i n o rd e r t o

co n t ro l t he m ach in e .

Servocontrol System

Th e se rv o co n t ro l sy s t em co n s i s t s o f t h e co n t ro l p an e l ,

the serv ocontro l un i t and the analog / log ic un i t , F ig . 4 . In

th e fo l l o win g , t h ese t h r ee co mp o n en t s a r e d esc r i b ed t o -

g e th e r wi th a mo re d e t a i led su rv ey o f t h e o p era t i o n mo d es .

4 9 Marc h 1994



THE CONTROL PANEL

T og e t he r w i t h t he s e r vo con t r o l un i t, t he con t r o l pane l i s

r e s pons i b l e f o r t he communi ca t i on be t w een t he us e r and

t he s ys t em. I t i s equ i pped w i t h s eve r a l s w i t ches t o s e l ec t

t he ope r a t i on mode unde r manua l o r numer i ca l con t r o l ,

w i t h o r w i t hou t s ynchr on i za t i on . Fu r t he r mor e , i t p r ov i des

f o r each o f t he f ou r dc - mot o r s t w o s w i t ches ( s t a r t/ s t op and

f o r w ar d / backw ar d ) and a po t en t i ome t e r , w h i ch s upp l i e s

t h e T M D - g o v e r n o r o f t h e r e s p e c ti v e m o t o r w i t h t h e d e -

s i r ed va l ue inpu t f o r t he mot o r s peed . E ach o f the ac - mo -t o r s can be man i pu l a t ed by t w o f u r t he r s w i t ches ( s t a r t

f w d / s t op f w d and s t a r t bw d/ s t op bw d) . T he p r e s en t con-

f i gu r a t i on o f a l l s w i t ches i s on l y t r ans mi t t ed t o t he ana -

l og / l og i c un it , and t hus t o t he com put e r , w hen p r e s s i ng t he

' va l i da t i on ' pus h - bu t t on on t he pane l ; t h is a l l ow s t he op -

e r a t i on o f t he mot o r s t o be ch anged s i mul t aneous l y , e . g . to

s t a r t o r s t op t he m ot o r s , and t o r eve r s e t he i r d i r ec t i on o f

r o t a t ion . N o t e t ha t t he ou t pu t s o f t he f ou r po t en t i ome t e r s

a r e t r ans mi t t ed i mm edi a t e l y t o t he ana l og / l og i c un i t , i . e. ,

no va l i da t i on i s neces s a r y , s o tha t an ' on l i ne ' va r i a t i on o f

t h e m o t o r s p e e d c a n b e p e r f o r m e d .

THE SERVOCONTROL UN IT

T he s e r voco n t r o l un i t i s l inked b y an i n t e r f ace ca r d t o

t he ana l og / l og i c un i t ; t hus i t ha s acces s t o a l l in f o r m a t i on

w hi ch i s neces s a r y t o con t r o l the mach i ne . A t t he co r e o f

t he s e r vocon t r o l s ys t em, i t ha s t o accompl i s h t h r ee ma i n

tasks .

( 1 ) Syn chr on i za t i on o f t he p i s t ons . A s s t a ted ea r l i e r, i n

o r de r t o ca r r y o u t r ea l i st i c t e st s unde r l a r ge de f o r ma t i ons ,

i t i s i nd i s pens ab l e f o r t he homogene i t y o f t he k i nema t i c

f i e l ds i n t he s pec i men t e s t a r ea t ha t t he cen t e r o f t he

s pec i men does no t move du r i ng t he t e s t , i . e . , i n e i t he r

d i r ec t i on a pe r f ec t s ynchr on i za t i on o f oppos i t e p i s t ons has

t o be gua r an teed . Fo r t h is pu r pos e , a l t hough t he T M D - g ov-

e r nor s enab l e cons t an t s peeds o f t he dc - mo t o r s t o be ma i n -

t a i ned , a c l os ed - l oop con t r o l s ys t em w as r ea l i zed by t he

us e o f op t i ca l i nc r emen t a l encode r s . T he enco de r s p r ov i de

a T T L quadr a t u r e ou t pu t , and us i ng t he h i ghes t p r ec i s i on

one pu l s e co r r e s pond s , t heo r e t i ca l l y , t o a l i nea r d i s p l ace -

men t o f t he p i s t on o f abou t 1 .6 .1 0 6 mm , w h i ch cons t i t u te s

an exc e l l en t ba si s f o r t he r equ i r ed s ynch r on i za t i on qua l it y .

I n t he f o l l ow i ng , t he s ynchr on i za t i on p r oces s i s b r i e f l y

d e s c r i b e d . A c c o r d i n g t o t h e c h o s e n m o d e , o n e o r t w o

p i s t ons a r e cons i de r ed a s ' i ndep ende n t ' , t he o the r s p l ay the

r o l e o f t he ' depend en t ' p i s t ons . N ow , i n o r de r t o ca r r y ou t

t he s ynchr on i za t i on , t he mi c r oco mp ut e r coun t s i n pe r ma-

nence t he pu l s e s f r om t he f ou r op t i ca l i nc r emen t a l encod -

e r s a n d c o m p u t e s , b y m e a n s o f a p r o g r a m r e a l i z i n g a

PI D - con t r o l l e r , t he r e s pec t i ve co r r ec t ed s i gna l t o be s en tt o th e T M D - g o v e r n o r o f e a c h ' d e p e n d e n t ' p i s to n . T h e

s peeds o f t he ' i ndepend en t ' p i s t ons a r e s upp l i ed by t he

r e s pec t i ve po t en t i ome t e r s , and a r e a l w ays cons i de r ed a s

r e f e r ences ; t hey a r e no t man i pu l a t ed by t he s ynchr on i za -

t i on a l go r i thm. I n gene r a l , t he s ynch r on i za t i on s i gna ls a r e

upda t ed ev e r y 0 .3 s - 0 .4 s .

( 2 ) N umer i ca l con t r o l o f t he mach i ne . B es i des t he man-

ua l con t r o l f r om t he con t r o l pane l , t he mach i ne i s a l s o

p r ov i ded w i t h a numer i ca l con t r o l by t he mi c r ocom put e r .

I n con t r a s t t o t he manua l con t r o l , t he de s i r ed va l ue i npu t s

f o r t he d i s p l acemen t s peeds o f t he p i s tons a r e no t s upp l i ed

. . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . .F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T I . . . . . . . . . . . . . . . . . . . . . . q

F ig . 4 - - S c h e m a t i c s t ru c t u r e o f t h e m e a s u r e m e n t a n dcont ro l f ac i l i ti es

by t he po t en t i ome t e r s on t he con t r o l pane l , bu t by t he

comput e r i t s e l f . I n o r de r t o ca l cu l a t e t he des i r ed va l ue

i npu t s, s pec i f i c s o f t w a r e can be w r i tt en t ak i ng i n t o accoun t

t he da t a f r om any meas u r i ng dev i ce on t he t e s t ed s pec i -

men , a s w e l l a s s i gna l s f r om o t he r ex t e r na l f ac i l i t i e s .

T he r e f o r e , the mi c r oc om put e r ha s a pe r man en t acces s to

t he ana l og s i gna ls o f t he me as u r em en t f ac i li t ie s and t o

o t he r ex t e r na l ana l og i npu t s by mean s o f t he 1 6 - channe lad - conve r t e r o f t he ana l og / l og i c un i t . T he ana l og s i gna l s

ma y cha r ac t e r i ze the me as u r ed f o r ce s app l i ed t o t he s pec i -

men a r ms , t he s t r a i ns a t t he s pec i men cen t e r , t he d i s p l ace -

m e n t s o f t h e p i s to n s , o r s i g n a l s d e r i v e d f r o m o t h e r

meas u r emen t o r con t r o l dev i ce s . T he ca l cu l a t i on o f t he

upda t ed des i r ed va l ue i npu t s i s c a r r i ed ou t be t w een t he

s ynchr on i za t i on cyc l e s .

( 3 ) C ommuni ca t i on w i t h t he us e r . A t t he beg i nn i ng o f

t he t e s t , t he comput e r r eads t he p r e s en t conf i gu r a t i on o f

t he con t r o l pane l ( a f t e r va l i da t i on ) and checks pos s i b l e

i ncompa t i b i l it i e s i n t he chos en op t i ons . I f t he mod e ' t e s t '

i s s e l ec t ed , s upp l emen t a r y i n f o r ma t i ons on t he con t r o l

cha r ac t e r is t i cs a r e dem anded ( e .g . max i m um m ot o r s peed ,p r ec i s i on o f t he op t i ca l i nc r emen t a l encode r s , de f i n i t i on o f

channe l s f o r ex t e r na l - o r f eedback - i npu t s , de s i r ed f o r ce - ,

s t ra i n - o r d i s p l acemen t - r a t io s ) ; i f the ' f a s t f eed ' mo de i s

chos en , no f u r t he r i npu t i s r equ i r ed and t he ac - mot o r s can

be ac t i va t ed f r om t he con t r o l pane l . D ur i ng t he t e s t , i n

o r de r t o mon i t o r t he cour s e o f t he t e s t i ng p r ocedur e and

t he qua l i t y o f t he s ynchr on i za t i on , t he coun t ed pu l s e s o f

t he op t i ca l i nc r emen t a l encode r s a r e u s ed t o com put e t he

mo t o r s peeds , a s w e l l a s t he s peeds and t he d i s p l acemen t s

o f t he p i s t ons ; a l l o f t h i s i n f o r ma t i on i s d i s p l ayed on t he

s c r een . Fu r t he r mor e , t he i npu t s i gna l s o f eve r y ex t e r na l

Experimental Mechanics 9 5



ch an n e l can b e d i sp lay ed . Th u s , t h e co m p u te r en ab l es t h e

user to act immediately upon the con t ro l character i s t ics .

THE ANALOG /LOGICUNIT

Th e t h i rd co mp o n en t o f t h e se rv o co n t ro l sy s t em, t h e

analog / log ic un i t , const i tu tes the in ter face between the

se rv o co n t ro l u n i t, t h e co n t ro l p an e l, an d t h e p o wer su p p ly

of the eigh t motors . I t i s equ ipp ed wi th a 16-channel

ad -co n v er t e r th a t en ab l es a p e rm an en t access t o an y an a lo g

feed b ack s i g na l .

Beside s the descr ibed in ter fac e funct ion , th is un i t super-

v i ses two sa fe ty d ev i ces : ( 1) t h e ' en d o f s t ro k e ' d ev i ce ,

wh ich p rev en t s d amag e t o t h e sc r ew sy s t em b y d e t ec t i n g

th e two ex t r eme p o s i t i o n s o f each p i s t o n ; an d (2 ) t h e

seco n d d ev i ce , wh ich p rev en t s s imu l t an eo u s o p era t i o n o f

b o th mo to r ty p es ( ac - an d d c -mo to r s ) , wh ich co u ld d ama g e

th e o p t i ca l i n c remen ta l en co d er s an d d c -m o to r s .

OPERATION MODES

In t h e ' t e s t ' m o d e , wh ere t h e v a r i ab l e sp eed mo to r s a r e

act ive, the fo l lowing op t ions are avai lab le .

(1 ) Al l f o u r p i s t o n s wo rk i n d ep en d en t ly . Co n t ro l l ed b yth e TM D -g o v em o r , each mo to r fo l l o ws t he d es i r ed v a lu e

in p u t o f i t s o w n p o t en t i o mete r . Th u s , i t i s eas i l y p o ss ib le

to vary the speed , eve n dur ing the tes t.

( 2 ) S y n ch ro n i za t i o n o f t h e two p i s t on s i n e i t h e r d ir ec -

t i o n . In each d i r ec t i o n X an d Y, o n ly o n e p o t en t i o mete r i s

act ive (X1 and Y1) , i .e . , X1 an d Y1 are the ' indepe nden t '

p i s to n s , X2 an d Y2 t h e ' d ep en d en t ' o n es .

(3 ) Synch roniza t ion of a l l four p is tons . This op t ion

enables equ ib iax ial tes ts to be real ized . Only the po ten t i -

o me te r X1 i s ac t i v e imp o s in g t h e sp eed t o th e t h r ee ' d e -

pendent ' p is tons .

(4 ) C lo sed - lo o p n u mer i ca l co n t ro l b y mean s o f t h e se r -

voco ntro l un it . In th is case, a l l po ten t iom eters are inact ive

an d t h e d es i r ed v a lu e i np u t s a r e co mp u ted b y t h e mic ro -co mp u te r , t ak in g i n to acco u n t t h e f eed b a ck s i g na l s . Th e

mach in e can o p era t e u n d er d i sp l acemen t , f o r ce o r s t r a in

cont ro l . Note that th is op t ion includes the sync hronizat ion

o f o p p o s i t e p i s t o n s . T h ese f ea tu res o f f e r a l o t o f p o ss ib il i -

t i e s t o p e r fo rm t es t s an d t o r ea l i ze an y l o ad in g p a th o r t o

au to mate cy c l i c t e s t s.

In t h e mo d e ' f a s t f eed ' , t h e ac -mo to r s wo rk i n d e-

p en d en t l y .

The Cruciform Specimen

As a l r ead y d i scu ssed i n t h e i n t ro d u c t io n , t h e mach in e i s

co n ce iv ed t o p e r fo rm t es t s o n f i a t c ru c i fo rm sp ec imen s o fi so t ro p ic an d an i so t ro p ic mate r i a l s. T h e p ro b l em a r i si n g

n o w i s t o f in d a sp ec imen d es ig n t h a t en ab les t h e p ro p er

real izat ion of b iax ial tes ts under large deform at ions , tak ing

in to acco u n t t h e p h en o men a l i n k ed t o t h e i n i t i a l ( e .g .

co mp o s i t e ma t e r i a ls , r o l l ed meta l s ) an d s t r a in - i n d u ced an -

iso t ropy . In the l i teratu re , a l l the used specimen designs

h av e b een o b t a in ed em p i r ica l l y , f o r ex amp le b y m ean s o f

p h o to e l as t ic o r n u m er i ca l an a ly s i s o n g iv en p ro to ty p es . I n

o rd er t o o b t a in ad eq u a t e sp ec imen d es ig n s i n a r a t i o n a lm a n n e r , D e m m e r l e a n d B o e h l e r19 deve loped a new design

cr i t e ri o n an d ap p l i ed en g in ee r in g -o p t imiza t i o n t ech n iq u es

F ig. 5wG eom et r i ca l pa r amet e r s o f the nu mer i ca l model

t o o p t imize t h e g eo m et ry o f an y b i ax i a l f l a t sp ec imen . T h e

p resen t p a rag rap h g iv es a sh o r t su rv ey o f t h i s wo rk .

C r i t e ri o n f o r S p e c i m e n O p t i m i z a t i o n

Gen era l l y , wh en em p lo y in g an o p t imiza t i o n meth o d t o

so lv e a p ro b l em, i t is n ecessa ry t o h av e a t o u r d i sp o sa l a

we l l -d e f i n ed c r i te r i o n . In t h e case o f c ru c i fo rm sp ec imen s '

o p t imiza t io n , t h e c r i t e r i o n fo r t h e as ses smen t o f t h e sp ec i -men d es ig n mu s t t ak e i n to co n s id e ra t i o n t h e fo l l o win g

th ree r eq u i r emen t s :

- - t h e r e ex i s t s h o mo g en eo u s s t r e ss an d s t r a in d is t r ib u t i on s

in the tes t sect ion ;

- - the s t ress values in the tes t reg ion are iden t ical to the

n o min a l s t re s s v a lu es , wh ich a r e o b t a in ed b y d iv id in g

each o f t h e two ap p l i ed l oad s t h ro u g h t h e co r r esp o n d in g

cross- sect ional areaA , F ig . 5. Th is i s very impo rtan t fo r

the iden t i f icat ion of const i tu t ive laws;

the h ighest s t ress level can be obs erved in the tes t sect ion

and i t i s there , where in i t ia l y ield ing occurs ; no s t ress

concent rat ion appears ou ts ide th is area.

S in ce t h e o p t imiza t i o n sh o u ld b e p e r fo rme d o n a co m-

p u t e r b y mean s o f a f i n i t e - e l emen t so f tware , t h e c r i t e r io n

mu s t r ep resen t an o b j ec t i v e an d math emat i ca l l y we l l -d e -

f i n ed measu re t o ev a lu a t e t o wh ich ex t en t t h e t h r ee r eq u i r e -

men t s a r e sa t i sf i ed . Th e emp i r i ca l me th o d s co n s i s ti n g o f

' l o o k in g ' a t i so s tr es s o r i so d i sp l acemen t l i nes d o n o t co n -

s t i tu te an adequate w ay to so lve th is p rob lem.

Th e b as i c i d ea o f t h e p ro p o sed c r i t e r i o n co n si s t s i n t h e

stat i st ical descr ip t ion of the s t ress f ie lds in the tes t reg ion

o f t h e sp ec imen . F o r t h e v a lu es o f t h e s t r e s ses i n t h i s a r ea ,

the s tandard dev iat ions , as we l l as the dev iat ions f ro m the

co r r esp o n d in g n o min a l v a lu es , a r e co mp u ted . T h ese d e -

v i a t io n s r ep resen t m a th emat i ca l l y we l l -d e f i n ed measu resto ev a lu a t e t h e h o m o g en e i t y o f t h e co n s id e red s t re s ses, a s

we l l a s t h e co mp at ib i l i t y b e tween ac tu a l an d n o min a l

s t re s ses , c f . Dem mer l e an d Bo eh l e r )9

For ea ch considered load case, the cr i terion is com posed o f

th ree parts. The f i rst par t evaluates the hom ogenei ty o f the

stress distribution in the test section. In the sec ond one, the

com patibil i ty of the actual stresses in the ce ntral test region

with the correspo nding nomina l stresses is investigated. Th e

las t par t considers the locat ion and the imp ortance of s t ress

concent rat ions in the en t i re specimen . The weigh ted sum ofthe three parts consti tutes the ' load-ca se specific cri terion. '

6 9 M a rc h 1994



Acco rd in g t o t h e ap p l i ca t i o n o f t h e i n v es t i g a t ed sp ec i -

men to b iax ial tensi le tes ts in the en t i re f i rs t quadran t o f

the two -d ime nsional s t ress spac e (ox, Or), the to tal cr i ter ion

t ak es i n to acco u n t t h e fo l l o win g t h r ee l o ad cases , i n wh ich

th e d i sp l acemen t s o f t h e sp ec ime n ' s g r i p h ead s a r e im-

p o sed :

equib iax ial load , A y / , S x = 1 ;

biax ial load , A y / A x = 0.4;

un iax ial load , Ay = ' f r ee. '

F inal ly , the to tal cr i ter ion consis t s o f the sum ov er thesethree load-ca se speci f ic cr i ter ia ; i t enab les a general evalu-

a t i on o f an y b i ax i a l p l an e sp ec imen t o b e p e r fo rm ed . Th e

o p t imiza t i o n o f t h e sp ec imen d es ig n i s ca r r i ed o u t b y

min imiz in g t h e v a lu e o f t h e p ro p o sed c r i t e r i on , w i th t h e

h e lp o f s t an d ard n u mer i ca l me th o d s .

T h e O p t im i z e d S p e c im e n D e s ig n

Th e o p t imiza t i o n p ro cess is ca rd ed o u t i n two s t eps . I n

the f i rs t s tep , the cr i ter ion i s used to assess d i f feren t basic

co n cep t s fo r t h e sh ap e o f a b i ax i a l f l a t sp ec imen . In t h e

seco nd s tep , the best basic design , i .e . , that wi th the low est

c r i t e r io n v a lu e i s e mp lo y ed t o c r ea t e a f i n i te - e l emen t

mo d e l , w h ere 1 2 p a ramete r s r ea l i ze t h e co mp le t e d esc r i p -

t i o n o f t h e sp ec im en ' s g eo m et ry , Fig . 5 . Th e v a lu e o f t h e

c r i t e r i o n i s t h en min imized b y v a ry in g t h ese g eo met r i c

p a ramete r s .

Concern ing the basic specimen design , the best resu l t s

have be en ob tained for that p roposed by several invest igators

l ike Hayhurst8 o r Kel ly .11 The design i s based on a concep t

o f M rn c h an d Ga l st e r,28 and presents a series of l imbs,

separated by s lo ts, ex tend ing f rom eac h edge of a un i form ly

th inned square-shaped cen t ral region . This geo me try enab les

the deformat ions to be co ncent rated on the th inned gage area,

whereas the slotted arms reduce the lateral st iffness of the

specim en; this is essential for the prop er realization of biaxial

tes ts on f ia t cruci form specimens. The num erical model basedon this specimen design is presented in Fig. 5, in order to

il lustrate the 12 geome trical param eters. The m odel consists

of on ly a one-eigh th par t o f the specimen , i .e ., x < 0 , y < 0 , z

_< 0. A s m ost im portant originalit ies, the num erical m odel

takes in to considerat ion the o ff -axes tes ting technique de-

scr ibed in 'Co nnect ion Ma chine Specim en ' above, and i t

allows non unifo rm slot- and l imb-w idth distributions within

each sp ec imen an n .

Th e 1 2 p a ramete r s d esc r i b in g en t i r e l y t h e sp ec imen

g eo m et ry a re :

the hal f - leng th a o f the th inned ce n t ral tes t sect ion ;

- - t h e h a l f - t h ick n ess b o f th e t h in n ed cen t r a l te s t s ec t io n ;

- - - -~e transi t ion rad ius c betw een the in i tia l th ickness 2 t o ft h e a rms an d t h e t h in n ed r eg io n ;

- - t h e l e n gt h d o f th e a r m s ;

t h e r ad iu s e o f t h e co m er f i l l e t b e tween two ad j acen t

a r m s ;

- - t h e r a t i o f b e twee n t h e c ro ss sec t i o n a l a rea o f t h e s l o ts

an d t h a t o f t h e l imb s ;

- - - -~e parameter g descr ib ing the d is t r ibu t ion of the s lo t

wid th s wi th in t h e a rms ;

- - t h e p a rame te r h d esc r i b in g t h e d i s t ri b u t io n o f t h e l imb

wid th s wi th in t h e a rms ;

- - - -~e n u mb er n o f s l o ts wi th in t h e a rm wid th ;

TABLE 1--ORT HOTROPIC ELASTIC COEFFICIENTS

OF A COLD-ROLLED CU-ZN ALLOY WITH 12 WT PCT

ZN, BASED ON INVESTIGATIONS BY LIU ANDALERS29

Young's modulus Poisson's ratio

E~ = 109.9 GPa vlz = 0.330

E2 = 142.1 GPa v23 = 0.280

E3 = 155.0 GPa v31 = 0.353

Shear modulus

G12 = 51.80 GPa

G23 = 55.51 GPa

G31 = 57.28 GPa

- - t h e l en g th r o f th e g r i p h ead s ;

- - t h e h a l f - th i ck n ess s o f t h e g ri p h ead s ;

- - t h e h a l f - th i ck n ess t o f th e p l a t e , o f wh ich t h e sp ec imen

i s mad e .

F o r t h e au to mat i c sh ap e o p t imiza t i o n , two g eo met r i ca l

param eters are main taine d constan t ( in it ia l p late th ickness

2 t , n u mb er o f s l o ts p e r ed g e n ) . Th e t en o th e r s a r e v a r i ab l e

wh i l e m in imiz in g t h e c r i t e r i o n v a lu e .

F o r b o th s t ep s o f t h e o p t imiza t i o n p ro ced u re , th e m ate -

r i a l o f t h e sp ec imen was co n s id e red t o b e i so t ro p i c e l ast i c .

I t i s character ized by elas t ic mater ial coeff ic ien ts corre-sp o n d in g t o t h e Yo u n g ' s m o d u lu s i n t h e ro ll i n g d i rec t i o n

an d t h e P o i s so n ' s r a t i o i n t h e ro l l i n g p l an e o f a ro l l ed

o r th o t ro p ic Cu -Zn a l l o y , (Tab l e 1 ):

Yo u n g ' s m o d u lu s : E = 1 09 .9 GP a ,

Poisson 's ra t io : v = 0 .33 .

La t e r o n , t h e an i so t ro p i c b eh av io r o f t h e so -o p t imized

sp ec imen i s i n v es t i g a t ed fo r ro l l ed Cu -Zn a l l o y .

Th e o p t imized g e o me t ry o f th e sp ec imen wi th an i n it i a l

p late th ickness o f 7 nun and 7 s lo ts wi th in each arm is

show n in F ig . 6 . I t i s impor tan t to po in t ou t that the second

step , the au tomat ic op t imizat ion , has to be repeated , i f a

sp ec imen w i th d i f f e r en t ma t e r i a l p ro p er t ie s o r wi th a d i f -

feren t in i t ia l p late th ickness should be invest igated . The

n u mb er o f s l o ts wi th in each a rm d ep e n d s o n t h e d es i r ed

sp ec imen s i ze.

In t h e fo l l o win g , t h e p e r fo rman ce o f t h e o p t imized

specimen for an iso t rop ic elas t ic mater ials i s d iscussed by

th e s imu la t i o n o f o f f ax es t e s t s o n an o r t h o t ro p i c co ld -

Y xJ

F i g. 6 - - G e o m e t r y o f t h e o p ti m iz e d s p e c i m e n in thec a s e o f i s o tr o p i c material

Experimental Mechan ics 9 7



U , k

O-

- U . k

--121,

E

/ 2

r ,

i

v = O { ~m

- - ' X O -

V 7

V 2) 2

f /

0

~ X

--0.

- - ( / , ( / ,

V t / 2

- a 1 3

- " X

" ~ " V #

(a ) Spec imen by Ke l ly (b ) Opt imized spec imen (c ) Opt imized spec imen(13mm ) r ig id ly c lamped (7mm ) r ig id ly c lamped (7mm ) o f f -axes tes t ing

techn ique

F ig . 7~ lsod isp la cem ent l ines ins ide the tes t sec t ion o f the spec imens; an iso trop ic e las t ic mater ia l , o ff axes equ ib iax ia lload; s tep between two iso l ines fo r (a ) : 3 ~m ; fo r (b ) , (c ) : 2 I~m

ro l l ed Cu-Z n a l loy . T he n ine independen t o r tho t rop ic e la s -

t i c cons tan t s wi th re s pec t to the m a te r ia l s ym met ry axes(vb v~, v3) are given in Table 1. The initial orientation 0

betw een the principal direct ions (x, y) of the appl ied load s

and the p rivi leged axes (v, , v~) of the m ateria l orthotropy

i s f ixed to 30 deg . T hree d i f fe ren t f in i t e -e lement ana lyses

have been c a rded ou t . F ir s t , in o rde r to s how the s upe -

r io r i ty o f the op t imized s pec imen des ign compared wi th

thos e p ropos ed in the l i te ra tu re , the s pec imen des igned by

K e l l yH wi th r ig id ly c lamped g r ip heads i s com pared wi th

the op t imized s pec imen , mounted w i th the s ame g r ipp ing

s ys tem. T hen , thes e re su l t s a re compared wi th thos e ob-

ta ined by employ ing the o f f -axes t e s t ing t echn ique to -

ge the r wi th the op t imized s pec imen , in o rde r to po in t ou t

the g rea t impo r tance o f th i s t echn ique .

T he d i s t inc t d i f fe rences be tween thes e th ree mode l s a revisual ized by isol ine plots of the displaceme nts (u = cons t ,

v = cons t , in the x and y direct ion, respect ively) and o f the

shea r stresses (O~y= cons t) in the centra l tes t region of the

s pec imen in the ca s e o f equ ib iax ia l load ing cond i t ions ,F igs . 7 and 8 . We can obs e rve a quas i -pe rfec t hom ogene i ty

of the s t ra in s ta te in the ent i re tes t sect ion of the opt im ized

specime n us ing the off-ax es tes t ing techniqu e [Fig. 7(c)].

This is expressed by the isodisplacement l ines cons is t ing

of tw o fam i l i e s o f equ id i st an t s t raigh t l ines . T hey a re no t

paral le l to the specimen ax es (x, y) , which, in turn, do no t

co inc ide wi th the p r inc ipa l d i rec tions o f the de fo rma t ions .

T he i s od i s p lacement p lo t s fo r the two s pec imens moun ted

wi th r ig id ly c lamped heads s ho w he te rogeneous nes s in the

s tra in f ie lds ins ide the tes t sect ion [Figs. 7(a) and (b)] . This

is expressed by the isodisplacement l ines , which are nei-

ther s t ra ight nor equidis tant . Nevertheless , the resul ts are

bet ter in plot 7(b); this underl ines the superiori ty of the

op t imized s pec imen even w i th r ig id ly c lamped heads .T he mos t d i s t inc t d i f fe rence be tween the two te s t ing

methods i s ob s e rved fo r the s hea r s t res s f i e ld ~ y (F ig . 8 ).

Y ,v

t /

" ~ ' : ' : ' : " ' : . . . . . . . . . . . i ' " . " ' 6 ~ . . . . . . . . ' " ~

- - r " ' ~ i ( " " . . . . . " -

/ i

_ : h ' k !A c "Ir I

~ X

" s , ~ U r

o c~

V 112

t /t ) - - , ,,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ---~Xy l /

t i ,~ , / , "N LlJ. . ; : , . - . . , , ( ;" " -

- -r 'J '

- ~ o

Yt / 2 ,

~ i ......................... .......................... x

- a 0

(a ) Spec imen by Ke l ly (b ) Opt imized spec imen (7mm ) (c ) Opt imized spec imen(13mm ) r ig id ly c lamped r ig id ly c lamped (7mm ) o f f -axes tes t ing

techn ique

F ig . 8 - - Is os tre ss l ines fo r ~ ins ide the tes t sec t ion o f the spec imens; an iso trop ic e las t ic mater ia l , o f f axes equ ib iax ia lload; s tep between two iso l ines : 1 MP a

8 9 Mar ch 1994



In the plo t sh ow n in Fig . 8 (c ) , G~y= 0 i s va l id in a lmo s t the

ent ire t es t s ec t ion. D ue to thi s fac t , the pr inc ipa l direc t ions

o f the s t re s s s ta te are we l l de termined, s ince they co inc ide

w i t h t he pr i nc i pa l d ir e c t io ns o f t he a pp l i e d l o a d , w h i c h a r e

a l s o t he a x e s o f t he s pe c i m e n . I n F i g . 7 , w e h a v e s e e n t ha t

the pr inc ipa l direc t ions o f the de format ions are di f f erent

f r o m t he s pe c i m e n a x e s ; t hus , t he y do no t c o i nc i de w i t h

the pr inc ipa l direc t ions o f the a ppl ied load. In fac t , gener -

a l ly , in o f f -axe s t e s t s on an i so tropic mater ial s , th e pr inc ipa l

direc t ions o f the de format ions and tha t o f the s t re s se s dono t c o i nc i de . T he s he a r s t r e s s f i e l ds c o nc e r n i ng t he t w o

s pe c i m e ns w i t h r i g i d l y c la m p e d g r ip he a ds [ F i g s . 8 ( a) a nd

(b) ] exhibi t s t rong gradients for the spec im en (a ) and mu ch

wea ker gradients for the opt imized spec im en (b) ; for bo th

spec imens the va lue in the center o f the t e s t s ec t ion i s G~y

= 5 . 8 M P a . C o m pa r e d t o t he d i f f e r e nc e (a yy - ~ = ) = 2 2 . 7

M P a , t h i s le a ds t o a n a ng l e o f a bo ut 1 3 . 6 de g b e t w e e n t he

pr inc ipa l direc t ions o f the s t re s se s and the axe s (x , y ) o f the

a pp l i e d l o a d . T hus , w he n e m pl o y i ng t he r i g i d l y c l a m pe d

heads d ev ice in t e s ts on an i so tropic mater ial s, the obta ined

da ta c a nno t be us e f u l t o i de nt i f y c o ns t i t u t iv e l a w s , be c a u s e

the pr inc ipa l axes o f the obta ined biax ia l s tre s s f i e ld cann ot

be de t e r m i ne d .

C o n c l u s i o n s

T he de s c r i be d s c r e w - dr i v e n ne w b i a x i a l te s t ing m a c h i ne

t o g e the r w i t h t he us e o f t he s pe c i f i c o f f - a x e s t e s ti ng d e v i c e

a nd s pe c i m e n s w i t h o pt i m i z e d de s i g n a l l o w a nea r ly pe r -

f e c t i m pl e m e nt a t i o n o f o f f - a x e s t e ns i l e t es t s o n a n i s o t r o p i c

shee t materia ls . Th e four dou ble -ac t ing pi s tons and the

contro l ensur ing a very accurate synchroniza t ion o f each

c o up l e o f o p po s i t e p i s t o ns , e na b l e l a r g e de f o r m a t i o n t es t s

to be rea l i zed wi thou t kinemat ic incom pat ibi l i t i e s or intro -

duc t i o n o f pa r a si ti c m o m e n t s i n t o t he s pe c i m e n .

T he m a c h i ne i s pr o v i de d w i t h t w o c o nt r o l m o de s : t he

m a nua l c o nt r o l a nd t he c l o s e d- l o o p num e r i ca l c o nt ro l . T hefeedb ack s igna l s may charac ter ize the appl ied forces to the

spec imen's arms , the s t ra ins in the centra l t e s t reg ion, or

the di splacem ents o f the pi s tons . Thu s , any s t res s or s tra in

path can b e rea l i zed throughout the t e s t.

T he o pt i m i z a t i o n o f t he f la t c r uc i f o rm s pe c i m e n g e o m e -

try was per formed on i so tropic mater ia l , but the re sul t s

show that even for ani so tropic mater ia l s the opt imized

s pe c i m e n de s i g n r e s u lt s i n c o ns i de r a b l y m o r e r e l i a b le e x -

per imenta l da ta than the des igns a lready proposed in the

l it era ture. B es ide s the fac t tha t the opt im ized sp ec im en w as

used for the nu mer ica l s imu la t ion, thi s superiori ty i s a l so

due t o t he a pp l i c a t i o n o f t he s pe c i f i c o f f - a x e s t e s t i ng

techniqu e to the biax ia l t ens i l e t e s t.

A d i r e ct o p t im i z a t i o n o f a s pe c i m e n m a de o f a n i s o t r o p icmater ia l requires an ex tens ion o f the proposed des ign

cr it erion; thi s inves t iga t ion i s present ly in pro gress .

References

1 . Hazel l, C .R. and Marin, J . , "A Possib le Specimen fo r the S tudy o f

Biax ial Yielding o f Ma teria ls," Int. J. Mech. Sci. , 9, 57-63 (1967).

2. Bird, J.E. and Duncan, J.L. , "Strain Harde ning at Hig h Strain in

Alumin ium A l loys and I ts Ef fec ts on S tra in Lo ca l isa t ion ," Met . Trans.

12A, 235-241 (1981).

3. Lukyanov, V.F., Lyudmirskii, Y.G . and Naprasnikov, V. V., "Testing

Components o f Shel l S tructures in the Biaxia l S tressed S ta te ," Ind . Lab .

- USSR, 52(7 ), 661-664 (1986).

4. Dudderar, T.D., Koch, F.B. and Doerries, E.M., " 'Measurement of

t h e S h a p e s o f F o i l B u lg e T e s t S a mp le s ," EXPERIMENTALMECHANICS r/ ,

133-140 (1977).

5. Havard, D . G. and Topper, T.N., "Biaxial Fatigue of O18 M ild Steel

at Lo w Endurance, " 'Proc. 1st Int. Conf. on Pressur e Vessels Tech.,

ASME, 1267-1277 (1969) .

6. Andrews, ZM .H. and Ellison, E.G., " 'A Testing Rig fo r Cycling at

Hig h Bia xial Strains, '" J. Strain Analysis, 8 (3), 168-175 (1973).

Z Lefebvre, D., Chebl, C., Thibodeau, L. and Khazzari, E., "A High-

S train Biaxia l Testing Rig or Th in-Walled Tubes Under Axia l Loud and

P re ssu re , " E~NT AL MECHANICS, 23, 384-392 (1983).

8. Hayhurst, D.R., "A Biaxial-Tension Creep-Rupture Testing M a-

chine, " J. Strain Ana lysis, 8 (2), 119-123 (1973).

9 . Bremand F. and Lagarde , A . , "Sur une form e simp le d 'dprouvet te

de traction biaxiale po ur un dlastomOre, " Comptes R endu s de l 'Acaddmie

des Sciences - Sdrie I1, 305 (11), 929-934 (1987).

10. Morrison, C.J. , "Development of a Hig h Temperature Bia xial

Creep Testing Mac hine ," U niv. of Leicester, Dept. o f Eng., Repor t 71-13

(1974).

11. Kelly, D.A., "P roble ms in Creep Testing Under Biaxia l Stress

Systems, " J. Strain Analysis, 11 (1), 1-6 (1976).

12. Ferron, G. and Makinde, A., "Design and Development o f a Biaxial

S t r e n g t h Testing Device," J. Test. and Eval., 16 (3), 253-256 (1988).

13. Shiratori, E. an d Ikegami, K., "A New Bia xial Tensile Testing

Mac hine wi th Fla t Specimen , " BuL Tokyo Inst . o f Tech . (82) , 105-1 i 8

(1967).14. Pascoe, K.J. and de Villiers, J. W.R., "Low Cycle Fatig ue of Steels

Under B iaxial Straining, '" J. Strain Analysis, 2, 117-126 (1967).

15 . Parsons, M .W. and Pascoe , K J. , "Development o f a Biaxia l

Fatigue Testing Rig," J. Strain Analysis, 10 (1), 1-9 (1975).

16. Makinde, A., Thibodeau, L. and Neale, K. W., "D evelopment of an

Appara tus or Biaxia l Testing Using Cruci form Specim ens," EXPERtMEN-

TAL MECHANICS, 32 (2), 138-144 (1992).

17. Chaudonneret, M ., Gilles, P., Labourdette, R . and Policella, H.,

"M achin e d'essais de traction biaxiale pour essais statiques et dy-

namiques ," La Recherche A~rospat ia le , (5 ) , 299-305 (1977).

18. Fessler, H. an d Musson, J.K., "A 30 Ton Biaxial Testing Ma-

chine, " ' J. Strain Analysis, 4 (1s 22-2 6 (1969).

19. Demmerle, S. and Boehler, J.P., "Optimal D esign o f Biaxial

Tensile Cruci form Specime ns," J . Mech . and Physics o f So l ids , 41 (1),

143-181 (1993).

20. Benefice, P . and Boehler, J.P., "The Applica tion of Stereophoto-

gramm etry to the Analysis o f Disp lacement Fie lds in So l id Mec hanics ,"

Opt ica l Me thods in M echanics o f Sol ids , Proc . IU TAM Syrup. , ed . A .

Lagarde, S ijtho ff and Noordhoff, 657-668 (1981).

21. Boehler, J.P., "Anisotropie e t Comportement Rh~ologique des

Ma tdriaux ," Rhdologie des matdriaux anisotropes, 19e Colloque GFR,

ed. C. Hu et et al. , Editions CEP ADU ES, Toulouse, 19-50 (1984).

22. Boehler, J.P., E1Aoufi, L. and Raclin, J. , "On Experimental Testing

Methods for Anisotropic Materials," Res Mech., 21, 73-95 (1987).

23. Boehler, J.P., Chapters I to 7, Application of Tens or Fun ctions in

Solid Mechanics, CISM Courses an d Lecture s - No. 292, ed. J.P. Boehler,

Springer- Verlag, W ien, New York, 3-139 (1987).

24. Boehler, J.P., " 'On Experimental Investigations of Anisotropic Sol-

ids," 17th Int. Cong. on Theo. and AppL Mech., Grenoble, (Aug. 1988).

25. Boehler, J.P., Raclin, J. and Benefice, P., " 'Etude des Cham ps

Cin~matiques Non-Homog~nes, de l 'Ecrou issage et de la Fissuration des

Mil ieux Anisotropes, ' " Rappor t con tra t ATP du C NRS, Grenoble (1981) .

26. Koss, S. , Ecrouissage isotrope et anisotrope d es aciers lamindssoum is g~ de gran des ddformations, P hD Thesis, U niv. Jose ph Fourier,

Grenoble 1 (1992).

2Z Koss, S. and Boehler, J.P., "Les jau ge s grandes dlongations, " J.

d'Etude "Extensomgtrie, " Editions Ampdre, Paris (1990).

28 . M6nch , E . and Galster , D. , "A Method or Producing a Def ined

Uniform Biax ial Tensile Stress Field, "Br it. J. AppL Physics, 14, 810-812

(1963).

29 , Liu , Y. C . and Alers , G.A. , "The Aniso tropy o f Yo ung 's Mod ulus in

Coid-Rol led Sheets o f Binary Cu-Zn Al loys ," Trans. Meta lL Soc . o f

AIME, 236, 489-495 (1966).

E x p e r i m e n t a l M e c h a n i c s 9 9

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10-A New Direct Biaxial Testing Machine for Ani So Tropic Materials