asbestos data

9
JOURNAL OF MATERIALS SCIENCE 4 (1969) 625-633 The Mechanical Properties of Asbestos d. AVESTON Nationa/ Physical Laboratory, Teddington, UK Received 4 Ja nuary 1969 Stereoscan electron microscope studies and measurements of tensile strength and Young's modulus have been made on chrysotile and five naturally-occurring fibrous amphiboles. The effect of heat on the modulus and fracture mechanism has also been examined. With the exception of tremolite which has a different microstructure from the remaining amphiboles, the moduli and strengths were similar. The loss of strength which occurs when the fibrous amphiboles, and to a lesser extent, chrysotile are heated below their decomposition temperature is shown to be due to an increase in interfibrillar bonding causing the material to become notch-sensitive 1. Introdu ction The commercially important fibrous silicates are chrysotile which accounts for 90~ of total asbestos production and the amphiboles crocido- lite and amosite which make up most of the remainder. Chrysotile, Mg3(Si~O~) (OH)4 has a complex tubular structure which has not been fully resolved whereas the amphiboles, although susceptible to extensive cation substitution, also occur in a non-fibrous form which enabled Warren to determine the structure of t remolite as early as 1930 [1]. It is based on infinite double chains of silicon oxygen tetrahedra, held together by five 6-co-ordinated and two 8-co-ordinated cations per unit cell. Two hydroxyl groups are attached to the central cation of each unit cell and there is a small amount of additional hydrogen, probably as SiOH groups on the peripheral silicate chains. The asbestiform varieties approximate to the following idealised formulae but with extensive interchange of Fe" and Mg": Crocidolite Na2Fea" F%'" SisO2z(OH)2 Amosite Mg2Fes" SisO22(OH)z Actinolite Ca2F%" SisO2~(OH)~ Tremolite Ca2Mg5 SisO~,2(OH)2 Anthophyllite Mg7 SisO~2(OH)2 They occur as extremely close packed lath-like crystals, which we shall call fibrils, aligned with their c-axes parallel. A bundle containing several hundred such fibrils will be called a fibre. The finest fibre which can be used for X-ray diffrac- tion (about 10 Fm thick) gives a photo graph with full rotational symm etry so that the fibrils cannot be much more than 0.1 Fm thick, nor can they be much less than this as quite sharp spots are obtained [2]. Electron micrographs of chrysotile fibres show them to average about 0.03 Fm diameter [2] and to be filled and surrounded by amorphous material of the same composition. The commo n structure and closely similar cell parameters of the amphiboles should give rise to fairly similar mechanical properties, but the published data, although conflicting, suggests otherwise. Thus Hodgson [3] reports tensile strengths of 35000 and 25000 kg/cm 2 for crocidolite and amosite but less than 5000 kg/cm 2 for the remaining amphiboles. Nadgornyi et al [4] however found that the strengths of crocido- lite and anthophyllite (and chrysotile) were similar but decreased inversely with fibre diameter, in a hyperbolic manner characteristic of whiskers, from 25 000 kg/cm 2 at a diameter d = 2/xm to 5000 kg/cm 2 at d = 25/zm. On the other hand Zukowski and Gaze [5] found a length/strength relationship but no diameter/ strength effect so that strengths up to 60 000 kg/cm ~ (depending on length) were maintained at least up to d = 30 Fm. Another puzzling feature is the drastic loss of strength which has been found [3] when the amphiboles are heated 6 2 5

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Page 1: Asbestos Data

8/3/2019 Asbestos Data

http://slidepdf.com/reader/full/asbestos-data 1/9

JO U R N A L O F MA T E R I A L S SC I E N C E 4 ( 1969) 625- 633

T h e M e c h a n i c a l P r o p e r tie s o f A s b e s to s

d . A V E S T O NNationa/ Physical Laboratory, Teddington, U K

Received 4 Ja nuary 1969

Ste reoscan e lec tron m ic roscope s tud ies and measuremen ts o f t ens i l e s t reng th and Yo ung 's

modu lus have been made on ch ryso t i l e and f i ve na tu ra l l y -occu r r i ng f i b rous amph ibo les .

The e f fec t o f hea t on the modu lus and f r ac tu re mechan ism has a l so been examined .

W i th the excep t ion o f t r emo l i t e w h ich has a d i f fe ren t m ic ros t ruc tu re f r om the rema in ing

amph ibo les , t he modu l i and s t reng ths were s im i la r . The loss o f s t reng th wh ich occu rs

when the f ib rou s amp h ibo les , and to a l esse r ex ten t, ch ryso t i l e a re hea ted be low th e i rdecompos i t i on tempera tu re i s shown to be due to an inc rease in i n te r f i b r i l l a r bond ing

caus ing the ma te r ia l t o become no tch -sens i t i ve

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

T he c om m e r c i a l l y i m po r t a n t f i b r ous s il ic a te s ar e

c h r y s o t il e w h i c h a c c o u n t s f o r 9 0 ~ o f t o t a l

a s b e st o s p r o d u c t i o n a n d t h e a m p h i b o l e s c r o c id o -

l it e a n d a m o s i t e w h i c h m a k e u p m o s t o f th e

rem a ind e r . Ch ryso t i l e , Mg3(Si~O~) (OH)4 has a

c o m p l e x t u b u l a r s t r u c t u r e w h i c h h a s n o t b e e nf u l l y r e s o lv e d w h e r e a s t h e a m p h i b o l e s , a l t h o u g h

s us c e p t ib l e t o e x t e ns ive c a t i on s ubs t i t u t i on , a l s o

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

W a r r e n t o d e t e r m i n e t h e s t r u c t u r e o f tr e m o l i t e a s

ea r ly a s 1930 [1] . I t i s base d o n inf in i t e do ub le

c ha i n s o f s i li c on oxyge n t e t r a he d r a , h e l d t oge t he r

by f i ve 6 - c o - o r d i na t e d a nd t w o 8 - c o - o r d i na t e d

c a t io n s p e r u n i t c el l. T w o h y d r o x y l g r o u p s a r e

a t t a c h e d t o t h e c e n t r a l c a t io n o f e a c h u n i t c e ll

a n d t h e re i s a s m a l l a m o u n t o f a d d i ti o n a l

h y d r o g e n , p r o b a b l y a s S i O H g r o u p s o n t h epe r i phe r a l s i l i c a t e c ha i n s . T he a s be s t i f o r m

va r i e ti e s a pp r ox i m a t e t o t he f o l l ow i ng i de a l is e d

f o r m u l a e b u t w i t h e x t e n s i v e i n t e r c h a n g e o f F e "

a n d M g " :

C r o c i d o l i t e N a 2 F e a " F%'" SisO2z(OH)2

Am os i te M g2F es" S isO22(OH)zAc t ino l i t e Ca2 F% " SisO2~(OH)~

Tr em ol i te Ca2Mg5 SisO~,2(OH)2

A n t hop hy l l i t e M g7 S is O ~2(O H )2

T h e y oc c u r a s e x t r e m e l y c lo s e pa c k e d l a t h - l i ke

c rys ta l s , which we sha l l ca l l f ib r i l s , a l igned wi th

t he i r c - a xes pa r al l e l. A bund l e c on t a i n i ng s e ve r al

hundred such f ibr i l s w i l l be ca l l ed a f ibre . The

f i ne st f i b re w h i c h c a n be u s e d f o r X - r a y d i f fr a c -

t i o n ( a b o u t 1 0 F m t h ic k ) g iv e s a p h o t o g r a p h w i t h

f u l l r o t a t i on a l s y m m e t r y so t ha t t he f i b ri ls c a nno t

b e m u c h m o r e t h a n 0 .1 F m t h ic k , n o r c a n t h e y be

m uc h l e s s t ha n t h i s a s qu i t e s ha r p s po t s a r eob t a i n e d [ 2] . E l e c t r on m i c r og r a ph s o f c h r ys o t i l e

f ib r e s s how t he m t o a ve r a ge a bou t 0 .03 F m

d i a m e t e r [2 ] a n d t o b e f il le d a n d s u r r o u n d e d b y

a m o r p h o u s m a t e r ia l o f t h e s a m e c o m p o s i t i o n .

T h e c o m m o n s t r u c tu r e a n d c l o se l y s i m i la r c el l

pa r a m e t e r s o f the a m ph i bo l e s s hou l d g i ve r is e t o

f a i r l y s i m i l a r m e c ha n i c a l p r ope r t i e s , bu t t he

pub l i s he d da t a , a l t hough c on f l i c t i ng , s ugge s t s

o t he r w i s e . T hus H odgs on [ 3 ] r e po r t s t e n s i l e

s t re n g t h s o f 3 5 0 0 0 a n d 2 5 0 0 0 k g / c m 2 f o r

c r oc i do l i t e a nd a m o s i t e bu t l e ss t ha n 5000 kg / c m 2f o r t h e r e m a i n i n g a m p h i b o l e s . N a d g o r n y i et al

[ 4] how e ve r f oun d t ha t t he s t r e ng t h s o f c r oc i do -

l i t e a nd a n t hophy l l i t e ( a nd c h r ys o t i l e ) w e r e

s i m i l a r bu t de c r e a s e d i nve r s e l y w i t h f i b r e

d i a m e t e r , i n a hype r bo l i c m a nne r c ha r a c t e r i s t i c

o f w h i s ke r s, f r om 25 000 k g / c m 2 a t a d i a m e t e r

d = 2 / x m t o 5000 kg / c m 2 a t d = 25 / z m . O n t he

o t h e r h a n d Z u k o w s k i a n d G a z e [5 ] f o u n d a

l e n g t h / s t r e n g t h re l a ti o n s h i p b u t n o d i a m e t e r /

s t r e ng t h e f fe c t s o t ha t s t r e ng t h s up t o 60 000

k g / c m ~ ( d e p e n d in g o n l e n g th ) w e r e m a i n t a i n e d

a t l e a st up t o d = 30 F m . A no t h e r puz z l i ngf e a t u r e i s t he d r a s t i c l o s s o f s t r e ng t h w h i c h ha s

b e e n f o u n d [3 ] w h e n t h e a m p h i b o l e s a r e h e a t e d

625

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J . A V E ST O N

t o a m o d e r a t e t e m p e r a t u r e w h i c h i s i n s u f f i c i e n t

t o c a u s e a n y c h a n g e i n c r y s t a l s t r u c t u r e .

T h e o b j e c t o f t h e p r e s e n t w o r k w a s t o m e a s u r e

t h e s t r e n g t h a n d m o d u l u s o f c hr y s o t il e , t h e

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

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

d e t e r m i n e w h e t h e r t h e r e i s a n y c o r r e l a t i o n

b e t w e e n s t r e n g t h a n d c o m p o s i t i o n , a n d a l s o t o

c o m p a r e t h e f r a c t u re m e c h a n i s m s o f th e

n a t u r a l a n d h e a t - t r e a t e d f i b r e s . T h e r e i s a l s o

n e e d f o r w o r k o n m o d e s o f fa i lu r e o f b u n d le s o f

i n t e rac t i n g f i b r i l s .

2 . E x p e r i m e n t a l

T h e a s b e s t o s f i b r e s , s u p p l i e d b y C a p e A s b e s t o s

F i b r e s L t d , w e r e a s f o l l o w s : c h r y s o t i l e , T h e t f o r d ,

C a n a d a ; c r o c i d o li t e , K o e g a s , C a p e P r o v i n c e ;a m o s i t e , P e n g e, T r a n s v a a l ; a n t h o p h y l l i te , F i n -

l a n d ; t r e m o l i t e , P a k i s t a n a n d a c t i n o l i t e , K o e g a s .

T h e y w e r e a s m i n e d , a n d c o n s i s te d o f b l o c k s o f

a d h e r e n t , c l o s e l y p a c k e d f i b r i l s v a r y i n g i n

l e n g t h f r o m 0 . 6 c m ( a c t i n o l it e ) t o 1 2 c m ( a m o s i t e )

S t a n d a rd T e m - P r e s h y d r o t h e r m a l e q u i p m e n t

w a s u s e d t o s y n t h e s i s e t h e s o d i u m m a g n e s i u m

a m p h i b o l e a c c o r d i n g to t h e m e t h o d o f G i e r e t a l

[6].

T e n s i l e s t r e n g t h s a n d Y o u n g ' s m o d u l i w e r e

m e a s u r e d w i t h a n " I n s t r o n " t e s ti n g m a c h i n e . T h e

s t r ai n r a t e w a s k e p t r o u g h l y c o n s t a n t b y v a r y -i n g th e c r o s s h e a d s p e e d b e t w e e n 0 . 01 a n d 0 . 1 c m /

m i n a c c o r d i n g to t h e l e n g t h o f f i br e , a l t h o u g h

p r e l i m i n a r y t e s t s w i t h 3 c m l o n g c r o c i d o l i t e a t

t h e s e t w o s p e e d s s h o w e d t h a t t h e s t r e n g t h w a s

i n d e p e n d e n t o f s t r a i n r a t e w i t h i n t h is r a n g e . E a c h

f ib r e w a s f i rs t w e i g h e d o n a " C a h n " e l e c tr o -

b a l a n c e [ 7 ] a n d i t s c r o s s - s e c t i o n o b t a i n e d f r o m

t h e m e a s u r e d d e n s i ty o f t h e m a t e r i a l i n th e c a s e

o f t h e A m p h i b o l e s , a n d t h e l i t e ra t u r e v a l u e o f

2 .5 5 [ 3] f o r c h r y s o t i l e . T h e f i b r e s w e r e t h e n g l u e d

w i t h A r a l d i t e to t h e c e n t r e s o f f la t s c u t i n t h ee n d s o f a p a i r o f 3/16 i n . d i a m e t e r b r a s s r o d s

w h i c h w e r e a l i g n e d i n a j i g a t t h e r e q u i r e d g a u g e

l e n g t h . W h e n t h e g l u e h a d s e t , t h e r o d s w e r e

i n s e r t e d i n t o s p ec ia l m o u n t i n g s o n t h e " I n s t r o n " ,

f i x e d i n p l a c e w i t h s e t s c r e w s a n d t h e j i g f i n a l l y

r e m o v e d . S p e c i m e n s f o r s h o r t t e r m s h e a r t e s t s

w e r e s e t i n c a s t i n g A r a l d i t e t o p r e v e n t s p l i t t i n g ,

c u t t o l e n g t h w i t h a d i a m o n d s a w a n d t h e n

c l e a v e d t o r e m o v e t h e A r a l d it e . T h e h e a t -

t r e a t e d c r o c i d o l i t e d i d n o t c l e a v e e a s i l y , s o

f u r t h e r m a c h i n i n g w i t h a d i a m o n d s u r f a ce

g r i n d e r w a s n e c e s s a r y .S t e r e o s c a n s a m p le s w e r e c o a t e d w i t h 5 0 0 A o f

g o l d - p a l l a d i u m a l l o y .

6 26

3 . R e s u l t s

3 .1 . T e n s i l e S t r e n g t h a n d M o d u l u s

T h e m e a n t e n s i l e s t r e n g t h s ( m a x i m u m l o a d

d i v i d e d b y t h e o r i g i n a l c r o s s - s e c t i o n ) a n d

m o d u l i a r e g i v e n i n th e t h i r d a n d s i xt h c o l u m n s

o f t a b le I . A p a r t f r o m t r e m o l i t e th e s t r en g t h s a r e

o f t h e s a m e o r d e r , a n d t h e m o d u l i t h e s a m e

w i t h i n t h e s c a t t e r o f t h e r e s u lt s , a g a i n w i t h th e

e x c e p t i o n o f t r e m o l i te . T h e m o d u l i o f a c t i n o li t e

a n d a n t h o p h y l l it e a ls o a p p e a r s o m e w h a t l ow e r ,

a l t h o u g h t h e s e a r e l e ss r e l i a b le d u e t o t h e s h o r t

s p e c i m e n l e n g t h a n d s m a l l n u m b e r ( a b o u t t e n

c o m p a r e d w i t h s i x ty t o s e v e n t y f o r t h e o t h e r s ) o f

s a m p l e s t e s t e d . C h r y s o t i l e l o s e s a b o u t o n e - t h i r d

o f i t s s t r e n g t h w h e n h e a t e d a t 5 0 0 ~ C ( 1 h , N ~

a t m o s p h e r e ) w h e r e a s c r o c i d o l i te u n d e r t h e s a m e

c o n d i t i o n s b e c o m e s s o b r i t t l e t h a t s a m p l e si n v a r i a b l y b r e a k a t t h e g l u e . E v e n a t 3 8 0 ~ C t h e y

r e t a i n o n l y a b o u t o n e - t h i r d o f t h e i r f o r m e r

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

F i b r e c r o s s - s e c t i o n a l a r e a s w e r e i n g e n e r a l

v a r i e d f r o m 5 t o 1 0 0 • 1 0 - 6 c m 2 ( d = 2 5 t o

1 14 / xm ) , b u t w e r e e x t e n d e d d o w n t o 5 • 1 0 7

c m z ( d ~ 7 / z m ) f o r c h r y s o t i l e a n d c r o c i d o l i t e ,

a n d u p t o 5 • 10 - ~ c m z ( d N 2 5 0 F m ) f o r

c h r y s o ti l e a n d t r e m o l i t e . T o t e s t f o r a n y d e p e n d -

e n c e o f s t r e n g th o r m o d u l u s o n c r o s s - s e c t i o n t h e

s l o p e o f t h e l i n e w h i c h g a v e t h e l e a s t s q u a r e s f i t

t o t h e d a t a , a n d i t s s t a n d a r d d e v i a t i o n w e r ec o m p u t e d . B r o a d l y s p e a k in g i f t h e r e s u l ts f o r a ll

l e n g t h s o f a g i v e n fi b r e a r e t a k e n t o g e t h e r t h e

o n ly ca ses w h ere t h e r e i s a s i g n i f i can t (b y t h e

c r i t e r i o n t h a t t h e s l o p e s h o u l d b e a t l e a s t t w i c e

i t s s t a n d a r d d e v i a t i o n ) s i z e d e p e n d e n c e a r e t h e

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

n a t u r a l c h r y s o t i l e . F o r a l l f i b r e s t h e s m a l l s i z e

d e p e n d e n c e c o u p l e d w i t h th e s c a t te r o f t h e

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

t o t h e d a t a d o w n t o 7 / z m .

T h e s t r e s s / s t r a i n c u r v e s f o r t h e a m p h i b o l e sw e r e e s s e n t i a l l y l i n e a r u p t o f r a c t u r e , w h i c h o n

s o m e o c c a s i o n s o c c u r r e d s u d d e n l y a n d o n o t h e r s

a s a se r i e s o f s t ep s a s i n f ig . 1 . As t h e r ed u c ed

s l o p e B C c o r r e s p o n d s t o t h e r e d u c e d c r o s s -

s e c t io n o f t h e f i br e r e m a i n i n g u n b r o k e n , t h e

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

p r o d u c t o f t h e s tr a i n a n d m o d u l u s . C o m p a r i s o n

w i t h t h e s t r e n g t h s a s o r i g i n a l l y d e f i n e d s h o w e d

t h a t t h e s c a t te r w a s r e d u c e d a n d o f c o u r s e t h e

m e a n s t r e n g th i n c r e a s ed .

Th e s t re s s / s t ra in cu rv e fo r ch ry so t i l e ( f i g . 2 ) i s

m o r e c o m p l e x : a f t e r a n i n i t i a l l i n e a r r e g i o n( w h i c h d e p e n d s o n t h e r a t i o o f f ib r e le n g t h t o

d i a m e t e r ) t h e c u r v e b e c o m e s c o n v e x , a l t h o u g h

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MECHANICAL PROPERTIES OF ASBESTOS

T A B L E I

Material Length Strength Youn g's modul us

cm

M ean :t : one Extrap olated Slope of s t rength M ean 4- one E xtrapolated Slope of

s tandard to zero cross- versus cross- s tandard to zero cross- mo dulusdeviation of sectional sectional area devia tion of sectional area versus cross-points fro m area ~ e* 4- ~* points from s ~* sectional area

me a n k g / c m ~ 10-4kg/cm~ 10 7 me an kg/cm 2x 10 ~ 4- ~*kg/cm 2 • 10 4 kg/cm ~ 10 6 kg/cm ~ 10-8

Croci dolit e 0.3 2.79 4- 0.66 3.03 t 0.14 6.02 4- 3.0 - - - - --

3.0 2.04 4- 0.46 2.10 • 0.08 - 2.04 • 2.0 1.69 4- 0.19 1.70 :k 0.03 - 1.0 i 1.5

5.0 1.68 4- 0.37 1.67 4- 0.07 0.49 4- 2.1 1.78 4- 0.09 1.81 • 0.02 - 73 ~_ 5 3

Crocidoli teaf ter 1 .0 1.104-0.25 1.294-0.07 -5. 1 • 1 .9 1.6 5• 1.69:t :0 .03 -11 .5 4- 9.7

3 h a t 380 ~ C 3.0 0.83 4- 0.21 0.94 4- 0.05 - 3.1 i 1.1 1.77 § 1.77 :k 0.02 - 2.3 i 5.9

5.0 0.65 4- 0.28 0.76 ~ 0.06 - 4.1 4- 1.9 1.76 • 0.13 1.77 :k 0.03 - 4.1 • 9.4

Am os it e 0.3 1.55 4- 0,50 1.59 • 0.18 - 0.55 4- 3.2

3.0 1.63 4- 0.40 1.74 4- 0.13 , - 2.2 ~ 2.4 1.71 4- 0.14 1.77 ~ 0.04 - 12.2 4- 7.8

5.0 1.714-0. 42 1.804-0.11 -2 .2 4- 2.3 1.72=k0.08 1.76=k0.02 - 10 .1 4- 4.1

9.0 1.16 4- 0.41 1.08 4- 0.10 1.9 4- 2.2 1.72 • 0.07 1.72 :k 0. 02 - 1.2 4- 4.1

Tr emo li te 3.0 0.31 4- 0.13 0.42 4- 0.04 - 0.36 4- 0.11 1.52 4- 0.15 1.49 :k 0.10 1.03 4- 3.8

Act ino lit e 0.6 1.89 4- 0.47 1.94 4- 0.31 - 1.58 4- 9.03 1.46 4- 0.20 1.59 :k 0.15 - 36.8 ~: 40.2

An th op hy ll it e 0.6 1.35 ~ 0.50 1.22 4- 0.46 3.15 ~: 4.55 1.54 :k 0.09 1.53 • 0.09 - 0.31 4- 10.8

Ch rys oti le 0.3 4.48 :k 1.02 4.59 4- 0.20 - 31.1 4- 24.7

3.0 3.06 ~ 0 . 8 3 3.13 4- 0.18 2.86 4- 5.7 1.60 =k 0.13 1,69 :k 0.04 - 20.5 ~: 8.1

Ch rys oti le aft er 3.0 2.31 :k 0.45 2.40 • 0.09 0.87 • 5.8 1.65 4- 0.06 1.64 4- 0.03 3.1 • 7.3

1 h a t 500 ~ C

e'is the standard deviation of the line or of its intercept on the strength or modulus axis.

t h e r e is n o a p p a r e n t b r e a k a g e o f t h e f ib r il s, a n do n r e m o v i n g t h e s tr e s s i t i s f o u n d t h a t a p e r m a n -

e n t s t r a in h a s d e v e l o p e d . O n f u r t h e r s t r e s s in g

o v e r t h e r a n g e A B , t h e o u t e r f i b r i l s w e r e s e e n t o

b e b r e a k i n g , a n d a t B t h e f i b r e e i t h e r b r o k e

c o m p l e t e l y o r a s i n t h e c a s e i l l u s t r a t e d i n f i g . 2 ,

t h e b u l k o f t h e f ib r e p u l l e d o u t f r o m a s h e a t h o f

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

s t a t i c f r i c t i o n e x c e e d s t h e s l i d i n g f r i c t i o n a p o i n t

C ( w h i c h i s a t s t r e s s z e r o f o r s o m e s p e c i m e n s ) i s

r e a c h e d , w h e r e t h e in t e r fi b r il l a r a d h e s i o n i s

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

s l op e f r o m C t o D . A t D p u l l - o u t o c c u r s a n d t h e

s t r e s s f a l l s t o z e r o a s t h i s i s c o m p l e t e d .

S p e c i m e n s w h i c h f a i l e d i n t h i s w a y w e r e n o t

i n c l u d e d i n th e d a t a o n w h i c h t a b l e I a n d f ig . l 3

a r e b a s e d b u t a r e p l o t t e d i n f i g . 3 a s a v e r s u s 1 / r .

W i t h t h e a s s u m p t i o n t h a t t h e r e m a i n i n g f i b r e

c r o s s - s e c t i o n i s c i r c u l a r , t h a t i t s c r o s s - s e c t i o n a l

a r e a is n o t s i g n i fi c a n t ly le s s t h a n t h e o r i g i n a l

f ib r e , a n d t h a t t h e l e n g t h b o n d e d t o t h e o u t s i d e

f ib r il s a t p u l l - o u t is e q u a l t o t h e l e n g t h l i m m e r s e d

i n th e g l u e ; t h e n a r o u g h e s t i m a t e o f t h e i n t e r -

f i b ri ll a r s h e a r s t r e n g t h r c a n b e m a d e f r o m t h ep u l l - o u t c o n d i t i o n :

2~rrlr ~ 7rr2~

2 r lor o- ~ -- "

r

T h e p u l l - o u t f a i lu r e s s h o u l d l ie o n a li n e o f s l o p e

2I t , a n d t h e t e n s i l e f a i l u r e s i n a r e g i o n b o u n d e d

b y t hi s li n e a n d t h e m a x i m u m t e n s il e s t re n g t h .

P u l l - o u t f a i l u re s t o t h e r i g h t o f t h e l in e w i ll o c c u r

w h e n t h e r e i s a s i g n i f i c a n t r e d u c t i o n i n c r o s s -

s e c t i o n a l a r e a o n p u l l - o u t .

T h e p o i n t s i n t h e r e g i o n s o f in t e r e st a r e r a t h e r

s p a r s e b u t i t d o e s a p p e a r t h a t t w o l i n e s t h r o u g h

t h e o r i g i n w i t h s i g n i f i c a n t l y d i f f e r e n t s l o p e s c a n

b e d r a w n f o r th e h e a t e d a n d u n h e a t e d f ib re s. T h e

l e n g t h o f f i b re e m b e d d e d i n t h e g l u e l, w a s 0 .8

c m i n e a c h c as e. T h e c o r r e s p o n d i n g v a l ue s o f r

a r e c a 1 7 0 a n d 1 00 k g / c m u r e s p e c ti v e ly .

3 .2 . S h o r t B e a m S h e a r T e s t s

W h e n a n i s o t r o p ic b r it t l e m a t e r i a l i n th e f o r m o f

a b e a m o f s p a n l, b r e a d t h b a n d d e p t h d i s

s u b j e c t e d t o a c e n t r a l l y a p p l i e d l o a d F , i t w i l l

f a i l w h e n t h e t e n s i l e s t r e s s a t t h e l o w e r s u r f a c e ( r ,

g i v e n a p p r o x i m a t e l y b y

3 F l

6 27

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J . A V E S T O N

7o

4Eo

b

2 .0

1 .0

D

A C

0 1 .0

~ strain

2 . 0

F i g u r e 7 S t r e s s / s t r a i n c u r v e fo r c r o c i d o li te f ib r e w i th I =

3 . 0 c m , d = 3 8 # m .

8 "0

4 " 0

3 . 0

1s

x

'Eo 2 . 0"a

b

1 . 0

/ l o o i x o

o~ Ix

J / . ~ , ~ , 9

A

A

A

lx

Ix

o

A A

A

A

&

0 1 0 1 I 0 [ 0 3 I 0 [ 0 5 I 0 " 0 7

~'r,u

F i g u r e 3 S t r e n g th o f c h r y s o ti le a s a fu n c t io n o f 1 / r . O p e n

s y mb o l s r e p r e s e n t u n h e a te d a n d s o l i d p o i n ts h e a te d

f ibres. Ci rc les corresp ond to pu l l -out and tr iangles to

tensi le fa i lure .

B

3 - 0 - v e r /R e

2 . 0 -

I E

o

1 " 0 I r

0 1 " O 2 " 0

~ s tra in

E

I8 . 0

F i g u r e 2 S t r e s s / s t r a i n c u r v e fo r c h r y s o t il e fi b r e w i th I = 3 . 0

c m, d = 4 1 F m .

e q u a l s t h e s t r e n g t h o f t h e m a t e r ia l . A t t h a t p o i n t

t h e s h e a r s t r e s s r i s a p p r o x i m a t e l y

3 F d e

r=~-d=~l"

H o w e v e r , i f t h e m a t e r i a l i s h i g h l y a n i s o t r o p i c

w i t h r ~ e , r m a y e x c e e d t h e s h e a r s t r e n g t h r F

6 2 8

b e f o r e e = e F a n d t h e m a t e r i a l w i l l t h e n f a i l

r e p e a t e d l y i n s h e a r a t c o n s t a n t F t o g i v e t w o

b e a m s o f d e p th d / 2 , a n d s o o n .

I n o r d e r t o e s t a b l i s h t h e e f fe c t o f h e a t o n t h e

s h e a r s t r e n g t h o f c r o c i d o l i t e , a s e r ie s o f s h o r t

b e a m s h e a r t e s t s o n t h e h e a t e d a n d n a t u r a l

m a t e r i a l w a s m a d e . T h e I n s t r o n l o a d t r a c es f o r

t y p ic a l u n h e a t e d a n d h e a t e d s p e c i m e n s a r e

i l lu s t r a t e d i n fi g s. 4 a n d 5 . T h e u n h e a t e d m a t e r i a l,

i n v a r i a b l y f a i l e d b y s h e a r w h e r e a s t h e s p e c i m e n s

h e a t - t r e a t e d a t 3 8 0 a n d 5 0 0 ~ C a l l f a i l e d i n

t e n s i o n , u s u a l l y a f t e r t h e s h e a r s t r e s s h a d

e x c e e d e d t h a t a t w h i c h t h e u n h e a t e d s p e c i m e n s

f a i le d . A l t h o u g h i n p r i n c i p le e a c h p e a k i n f ig . 4y i e l d s a s e p a r a t e v a l u e o f r F , in p r a c t i c e t h e

c o m p u t e d s tr es s a n d g e o m e t r y o f t h e sp e c im e n s

b e c o m e l e s s w e l l - d e f i n e d a s t h e d e f l e c t i o n a n d

n u m b e r o f c r a c k s i n c re a s e . A s i n g le v a l u e o f r F

w a s t h e r e f o r e c o m p u t e d f r o m e a c h s p e c i m e n

u s i n g t h e f i r s t m a x i m u m i n F a n d t h e o r i g i n a l

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

i n t a b l e I I w h e r e t h e f i g u r e s i n p a r e n t h e s e s a r e t h e

c o m p u t e d s tr es se s f o r t h e m o d e o t h e r th a n t h a t

i n w h i c h t h e s p e c i m e n f a i l e d .

3 .3 . S t e r e o s c a n M i c r o g r a p h sT h e S t e r e o sc a n e l e c t ro n m i c r o g r a p h o f c r o c i d o -

l i t e ( f ig . 6 ) is ty p i c a l o f a l l t h e s t r o n g a m p h i b o l e s

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M E C H A N I C A L P R O P E R T I E S O F A S B E S T O S

SO -

2C

o,

10

/I I ~ I I

0 0"01 0 "02 0"0 3 0"0 4 0"015

Flexure rnm

Figure 4 Thr ee po in t l oad ing t es t f o r na tu r a l c r oc i do l i t e

specimen 0.30 cm wide X 0.265 cm deep x 2.25 cm span.

Sam ple f a i l ed i n shear a t T = t 55 kg / cm 2.

40

30

:~ 20

o

1C

I I

0 0"01 0"02 0"03 0-04

F lexure mr&

Figure 5 T h r e e p o i n t l o a d i n g t e s t f o r c r o c i d o l it e a f t e r

hea t i ng f o r 4 .8 h a t 500 ~ cm i n a N 2 a tmo sphe r e . Spe c ime n

0.40 cm w ide = 0.35 cm deep X 2.0 cm span fa i led in

t ens i on a t cr = 2230 kg /em 2 a t wh i ch po in t t he shear s t r ess

wa s 195 kg/c m ~.

Figure 6 S t e r e o s c a n m i c r o g r a p h o f n a t u ra l c r o c i d o l it e .

Figure 7 S t e r e o s c a n m i c r o g r a p h o f t r e m o l it e .

T A B L E I I

Material Mode of failure Tensile stress at failure Shear stress at failure

kg/cm 2 kg/cm ~

Natur al crocidoli te shear (2600) 155

she ar (2860) 153

shear (2200) 176

Croc idol ite after 4 h at 280 ~ C shear (1850) 168

shear (1280) 168

Croc idol ite afte r 2 h at 380 ~ C tensile 2870 (193)

Croc idol ite after 5 h at 500 ~ C tensi le 2230 (195)

tensile 1840 (175)tensile 1330 (106)

tensile 1360 (221)

6 2 9

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J . A V E ST O N

to the principal tensile stress over large areas ofthe fractu re surface.

The surface o f chryso t i le which had been

carefully freed from fine materia l appeared

similar to crocidolite , except that the fibrils werefiner. However, some of the fine tangled ma teria l

which had been pee led f rom the main b lock and

bent through an acute angle in the process , or

any fibre which had been drawn over a sharp

edge such as a razor blade, assumed the curious

kinked or spira l configuration shown in fig . 10.

Figure 8 Stereoscan mic rograph o f f rac tured natura l

crocidol i te f ibre.

Figure 10 Stereoscan mic rograph o f "k i nked" chrysot i l e

f ibre.

Figure 9 Stereoscan mic rograph o f frac tured sur face o f

crocid ol i te f ibre which had been h eated for 1.5 h at 500 ~

in a N 2 atmosp here.

in revealing a c lose-packed bundle of well-

aligned fibrils 0.1 to 0.2 Fm across which

appeared to be con t inuous a long the whole

length of the specimen. The correspo nding

micro graphs of the h eated fibres are identical.

In contras t , tremolite (fig. 7) contains short , less

well-a ligned fibrils . Although the micrographs

of the s ides o f the na tura l and hea t- t rea ted

crocidolites are indis tinguishable from each

other, the fracture surfaces are s trikingly differ-

ent. The na tur al fibre (fig. 8) is alm ost com -

plete ly divided at the extreme ends into thecomponent fibrils , whereas in the heat-treatedmateria l (fig . 9) the crack has travelled normal

630

3 .4 . S y n th e t i c Amp h ib o le s

Gie r et al [6] have shown that under extreme

hyd roth erm al condi tions (3000 arm , 700 ~ C) i t is

possible to synthesise fibrous amphiboles of

con tro l led cat ion con ten t . We have been unab le

to do more than conf i rm the i r resu l ts : theprod uct a lways consis ted of a wadding-like mass

of den sely intertan gled fibres (fig. 11) whic h was

quite unsuitable for tensile measurements .

However, i t was c lear from the tes ts on the

na tura l f ib res repor ted above tha t the re was

unlikely to be any direct correla tion between

mechanic al properties and chem ical compo sition.

4. Discussions

According to Hodgson [3] asbestos fibres are

built up from a series of overlapping fibrils of

various lengths which are held together in thecrys ta l by hydrogen bonding . He showed tha tover the temp erature range (200 to 500 ~ C) in

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MECHANICAL PROPERTIES OF ASBESTOS

Figure 11 Stereoscan micrograph of sodium magnesium

amph ibole synthesised at 700 ~ C/3000 atm.

which virtually a ll the s trength is los t , the

amphibo le f ib res lose on ly a smal l amount o f

so-called physically combined water, which is not

associated with a ny crysta llographic change in the

fibrils , and suggested that the corresponding

decrease in hydrogen bonding so weakens the

adhesion between the fibrils that they are pulled

apar t on f rac ture .The Stereoscan microg raph of trem olite (fig. 7)

is consis tent with this mod el and the low s trength

of trernolite could well be du e to some of the

fibrils pulling out on fracture . Howeve r, the

micrographs o f a ll the s t rong amphibo les, o f

which crocidolite (fig. 6) is typical, show that the

fibrils are essentia lly continuous. I f this were not

so- for example if some fibrils were less than

1 mm - then the chance o f see ing the end of a

fibril in fig. 6 would be about 1/20, whereasapart from some surface debris a ll the 200 or so

fibrils appear continuous.Moreover , the shear s t reng ths repor ted in

sec t ion 3 .2 show tha t fa r f rom there be ing a

decrease in interfibril lar adhesion on heating

there is actually an increase. Admittedly if the

heat-tr eated (380 a nd 500 ~ C) specimens had

failed in shear a t the s tresses given in parenth eses

in table II then the increase in shear s trength

wou ld be ins ignificant, but i t must be em phasised

tha t a l l o f them fa i led in tens ion and th a t

judg ing f rom the difficulty experienced in c leav-ing these specimens the actual shear s trengths

were greatly in excess of these values . The shear

s trength of chrysotile on the oth er ha nd was so

low that i t was not possible to prepare three-

po in t load ing spec imens o f adequa te d imens ions

and with the ends free from splits .

We therefore propose a s tructure for asbestoswhich is based on bundles of continuous fibrils

in which the interfibril lar adhesion is low for

chrysotile , somewhat higher for the amphiboles ,

a n d much higher for the heat-treat ed amphiboles .

As the s trongest f ibres break at a s tress of ca E/30

compared to the theoretical value for a perfect

brit t le materia l of ca E/10 the component fibrils

are assumed to contain s tress-concentrating

flaws, such as growth s teps , dis tributed ran do ml y

throughout the fibrils . I t then follows that the

strength o f the bundle or fibre will be the average

of a la rge number o f un i ts a r ranged in pa ra l le land thus independent o f f ib re d iamete r . How-

ever, unless the fibre has completely uniform

properties a length-dependent s trength must

arise. In practice, fibres of length l/n with

strength dis tribution f(x) were cut from fibres of

leng th I . The combined probab i l i ty tha t any

one of the n fibres will have a s treng th between

x and (x ~- dx) and that the remaining (n -- 1)

will have a strength greater than x (i.e. that the

fibre of length l will fa il between x an d (x + dx)

is given byoo

n f ( x ) [ I f ( x ) d x l ( ~ - l ) d xx

and hence the s trength dis tribution for fibres of

leng th I i f they break a t the weakes t po in t i s

given by

oo

x

This func t ion , computed by assuming tha t the

under ly ing s t reng th d is t r ibu t ion of the shor tes t

(0.3 cm) fibres is normal , is draw n o n the s tr ength

his tograms of crocidolite and chrysotile in figs .

12 and 13. If the component fibrils were com-

plete ly indepe ndent over their entire length, then

each would b reak a t i t s weakes t po in t and the

strength of the fibres would be less tha n t hat

computed on the weakest l ink basis . Therefore

as the s trengths o f the chrysotile and crocidolite

fibres fi t the com pute d curves reasonably well i t

appears tha t the fibrils are coupled to the extentthat the fracture region is res tric ted to less than0.3 cm, a lthou gh over shor ter dis tances the fibre

6al

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J . A V E S T O N

m u s t e v e n t u a l l y b e h a v e m o r e a s a p a r a l le l b u n d l e

i n o r d e r t o a c c o u n t f o r t h e a p p e a r a n c e o f t h e

f r a c t u r e s u r f a c e i n f i g . 8 a n d t h e a b s e n c e o f a

s t r e n g t h d i a m e t e r e f f e c t .

2C ~ I= 5.0 cm16

12

4 I

o

1 1 ~ 3 ' 0 c m

i l 1= 0 . 3 c m

4 ;0 2 .0 3 " 0

(7 kgf cm-2x 10 4

Figure 12 H i s t o g r a m o f c r o c i d o l i t e s t r e n g t h . C u r v e f o r 3 m m

f i b re i s n o r m a l w i t h t h e v a l u e s o f th e m e a n a n d s t a n d a r d

d e v i a t i o n g i v e n i n ta b l e I . O t h e r c u r v e s a r e c o m p u t e d f r o m

t h is o n a " w e a k e s t l in k " h y p o t h e s i s .

16

14

12 1=3.0cm

10

8

l2k~

~6 0

0 i

1 2 3 4 "5 46 7 8o ' k g f c m - 2 x l 0 -

Figure 13 A s f i g . 1 2 b u t f o r e h r y s o t i l e .

O n h e a t i n g c r o c i d o l i t e fi b r e s it i s s u g g e s t e dt h a t t h e a d h e s i o n b e t w e e n t h e f ib r il s r e a c h e s th e

p o i n t w h e r e t h e s t r e s s c o n c e n t r a t i o n a t t h e t i p

6 3 2

o f a s u r f a c e c r a c k c a n n o l o n g e r b e r e l ie v e d b y a

s e c o n d a r y c r a c k p r o p a g a t i n g p e r p e n d i c u l a r l y i n

a p l a n e o f w e a k n e s s a c c o r d i n g t o t h e m e c h a n i s m

s u g g es t ed b y C o o k a n d G o r d o n [ 8] . T h e o n s e t o f

a s t r e n g t h / d i a m e t e r r e l a t i o n s h i p f o r c r o c i d o l i t e

w h i c h h a d b e e n h e a t e d a t 3 80 ~ C a n d t h e

f r a c t u r e s u r f a c e o f t h e h e a t - t r e a t e d ( 5 0 0 ~ C )

c ro c id o l i t e ( f i g . 9 ) a re co n s i s t en t wi th t h i s

i n c r e a s e i n n o t c h s e n s i t i v i t y a s t h e i n t e r f i b r i l l a r

a d h e s i o n i n c r e a s e s .

M a n y o f th e p r o p e r t i e s o f c h r y s o ti l e m a y b e

s i m i la r ly i n t e r p r e t e d i n t e r m s o f a d h e s i o n b e t w e e n

th e f i b r i l s . Th e p u l l -o u t d a t a i n f i g . 3 su g g es t a

m o d e r a t e i n c r e a s e i n i n t e r f i b r i l l a r a d h e s i o n o n

h e a t i n g w h i c h i s c o n s i s t e n t w i t h t h e l o w ( r e l a t i v e

t o c r o c i d o l i t e ) l o s s o f s t r e n g t h a n d a l s o w i t h t h e

d e c r e a s e d c u r v a t u r e o f th e s t r e s s / s tr a i n c u r v e sf o r t h e h e a t e d f i b r e s . T h e p e r m a n e n t s t r a i n

d ev e lo p ed i n t h e t h i ck e r ch ry so t i l e f i b re s ( f i g . 2 )

r e s u l t s f r o m t h e m o r e h i g h l y s t r e s s e d o u t e r

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

r e l a t i v e t o t h o s e a t t h e c e n t r e , s o t h a t t h e y

r e m a i n i n t e n s i o n w h e n t h e s t r a i n i s r e m o v e d .

S i m i l a r l y , w h e n a f i b r e i s b e n t t h r o u g h a n a c u t e

a n g l e t h e o u t e r f i br i ls a r e d i s p l a c e d , a n d i f t h e

a d h e s i o n c a n b e r e c o v e r e d - a n d t h e s t r e s s / s t r a in

c u r v e ( f i g . 2 ) p r o v i d e s s o m e e v i d e n c e f o r t h i s -

t h e n t h e f i b r e w i l l a s s u m e t h e s p i r a l c o n f i g u r a t i o n

sh o wn in f i g . 1 0 .T h e s t r e n g t h o f a s b e s to s , w h i c h i s i n f e r i o r o n l y

t o p r i s t i n e g l a s s f i b r e s a n d w h i s k e r s i s n o t

e x p l o i te d c o m m e r c i a l ly i n u n r e i n f o r c e d p r o d u c t s

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

f i b re s p u l l i n g a p a r t , o r i n r e i n f o r c e d p l a s t ic s

w h e r e t h e p r o b l e m is o n e o f a l ig n m e n t a n d

w h e r e t h e a b o v e r e s u l t s c o u l d b e s i g n i f i c a n t .

C u r r e n t a l i g n m e n t m e t h o d s i n v o lv e t h e e x t ru s i o n

o f a s u s p e n s i o n o f t h e d i s p e r s e d f ib r e t h r o u g h a

h o l e o r s l o t . W i t h t h e a m p h i b o l e s t h e p r o c e s s i s

s t r a i g h t f o r w a r d , b u t t h e y h a v e o t h e r d i s -a d v a n t a g e s a s a r e i n f o r c i n g m a t e r i a l . C h r y s o t i l e ,

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

f i n e f i b r e s a n d i t i s n e c e s s a r y t o p r e - t r e a t t h e

m a t e r i a l w i t h h o t p h o s p h o r i c a c i d [ 9 ] . I t w a s

f o u n d i n t h e p r e s e n t w o r k t h a t t h e i n c r e a s e i n

i n t e r f i b r i l l a r a d h e s i o n s i n t h e h e a t - t r e a t e d

m a t e r i a l w a s s u f f i c ie n t t o p r e v e n t c o m p l e t e

d i s p e r si o n a n d t h a t a p r o d u c t o f fi ne w h i s k e r-

l i k e f i b re s re su l t ed .

I n c o n c l u s i o n i t m u s t b e a d m i t t e d t h a t n o

s i n g l e p i e c e o f e v i d e n c e f o r t h e h y p o t h e s i s t h a t

t h e s t r e n g t h o f a s b e s t o s i s d e t e r m i n e d l a r g e l y b yth e i n t e r f i b r i l l a r ad h es io n i s su f f i c i en t i n i t s e l f .

T o p r o v e a d i r e c t c o r r e l a t i o n i t w o u l d b e

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MECHANICAL PROPERTIE S OF ASBESTOS

n e c e ss a r y t o m a k e m o r e a c c u r a t e m e a s u r e m e n t s

o f s h e a r s t r e n g t h e n c o m p a s s i n g s e v e r al v a ri e t ie s

o f a s b e s t o s b o t h b e f o r e a n d a f t e r h e a t i n g , b u t t h e

m a t e r i a l i s s u c h t h a t i t is d i f fi c u lt t o d e v i s e s u c h

e x p e r i m e n t s to g i ve a n u n a m b i g u o u s a n sw e r .

T h e d i s c r e p a n c i e s b e t w e e n t h e s t r e n g t h s o f th e

le ss c o m m o n a m p h i b o l e s r e p o r t e d h e re a n d t h o s e

i n th e l i te r a t u r e , f u r th e r e m p h a s i s e t h e p r o b l e m s

a s s o c i a t e d w i th o b t a i n i n g a r e p r e s e n t a t i v e s a m p l e

o f a n a t u r a l p r o d u c t . H o w e v e r , w h e n t a k e n

t o g e t h e r , t h e e v i d e n c e f r o m t h e s t e r e o s c a n m i c r o -

g r a p h s t h e s h e a r t e s t s, th e s h a p e o f t h e s t r e s s /

s t r a i n c u rv e s , th e s t r e n g t h / d i a m e t e r r e l a t i o n s h i p

f o r th e h e a t e d ( b u t n o t t h e u n h e a t e d ) c r o c i d o l i t e

f ib r e s a n d t h e p u l l - o u t d a t a f o r c h r y s o t i le , a r e

c o n s i d e r e d r e a s o n a b l y c o n v in c i ng .

R e f e r e n c e s

I . B . E . WARREN, Z . K r i s t . 72 (1930) 42.

2 . E . S . W . W H I TT A K E R " F i b r e S t r uc t u r e " , e d i t e d by

J . W . S . H e a r l e a nd R . H . P o t e n ( B u t t e r w or th s ,

L on don , 1963 ) p . 594 .

3 . a . A . H O D G S O N , R oy a l I n s t i t u t e o f C he mi s t r yLec tu re Ser ies (1965) No . 4 .

4. E. M. NADGOR NYI~ L. F. GRIGOREVA~ a nd A . P .

IVANOR, I z v e st A k a d . N a u k S S S R N e o r y . M a t h s .

1 (1965) 1117.

5 . R . ZUKOWSKI and R . GAZE, N a t u r e 183 (1959) 35.

6. T. E. GIER, N. L. COX, and H. S . YOUNG~ Inorg.

C h e m . 3 (1964) 100.

7 . L . CAHN and H . R . SCHULTZ, V a c u u m M i c r o b a la n c e

T e c h n i q u e s 3 (1963) 29.

8 . J . CO OK and s . E . GORDON, P r o c . R o y . S o c . A282

(1964) 508.

9. J . GOLDEN, N a t u r e 220 (1968) 64.

633