strength of sapphire as a function of temperature and crystal orientation

8/10/2019 Strength of Sapphire as a Function of Temperature and Crystal Orientation

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S t r e n g t h o f s a p p h i r e a s a f u n c t i o n o f t e m pJ o h n W . F i s c h e r , * W . R . C o m p t o n , N a n c y A . J a

* C h e m i s t r yD i v i s i o n ,R e s e a r c hD e p a r t m e n t

t M i s s i l e A i r f r a m e D i v i s i o n , A t t a c k W e a p oN a v a l W e a p o n s C e n t e r , C h i n a L a k e C A , 9 3

A B S T R A C T

T h e s t r e n g t h s o f s a p p h i r e d i s k s o f t w o d i f f e r e nb a r s o f t h r e e d i f f e r e n t o r i e n t a t i o n s w e r e m e a s u r e d o n - r i n g f l e x u r e o r 4 - p o i n t b e n d i n g . O n e s e t o f d i s k sC - a x i sn o r m a l t o t h e f l a t s u r f a c e w h i c h c o n t a i n e d t h e c rT h ea v e r a g e s t r e n g t h o f t h e s e d i s k s d r o p p e d f r o m 1 5 4 k ss e t o f d i s k s ( 9 0 0c u t ) ,t h e c r y s t a l l o g r a p h i c c - a n d m - a x e s w e rT h e a v e r a g e s t r e n g t h o f t h e s e d i s k s d r o p p e d f r o m 8 4

s t r e n g t h o f s a p p h i r e b a r s w h o s e t e n s i l e a x i s w a s t h e1 0 3 k s i a t 2 0 C t o 8 6 k s i a t 1 4 0 0 C . T h e s t r e n g t h o f c r y s t a l l o g r a p h i c a - a x i s d r o p p e d f r o m 1 1 3 k s i a t 2 0 Cs a p p h i r e b a r s w h o s e t e n s i l e a x i s w a s t h e c r y s t a l l o g r2 0 C t o 3 5 k s i a t 1 4 0 0 C .

1 . I N T R O D U C T I O N

S i n g l e - c r y s t a l s a p p h i r e i s a s t r o n g , h a r d o p t i c a l r e s i s t a n c e , l o w o p t i c a l s c a t t e r , a n d e x c e l l e n t t r a n s m i5 - r i m . 1 - 3R e c e n t a d v a n c e s i n m a n u f a c t u r i n g t e c h n o l o g yq u a l i t y m a t e r i a l . 4 ' 5T h e s t r e n g t h s o f s a p p h i r e f i b e r s , 6 1 1s i n g l ec r y s t a l s o f v a r i ot a t i o n s , ' 2 1 6 a n d p o l y c r y s t a l l i n e m a t e r i a l 1 4 h a v e b e

o f t e m p e r a t u r e , b u t a d e q u a t e d a t a f o r e n g i n e e r i n g i s l a c k i n g . T w o s t u d i e s o f s a p p h i r e f i l a m e n t s w h o s et e n s i l e s t r e n g t h s o f a p p r o x i m a t e l y 2 8 0 1 1 a n d 3 8 0 6 k1 0 0 0l b s / i n 2 ) a t 2 0 Ca n i n i t i a l s h a r p d r o p i n s t r e n g t h t o a m i n i m u m i n t hs t r e n g t h u p t o 9 0 0 - 1 0 0 0 C a n d t h e n a n o t h e r d e c r e aa - A x i ss a p p h i r e f i l a m e n t s h a d s i m i l a r s t r e n g t h a n d t e mc - a x i s f i b e r s . 7F o u r m e a s u r e m e n t s 1 2 1 6 o f t h e f l e x u r e s t rs a p p h i r e o f v a r i o u s o r i e n t a t i o n s g a v e s t r e n g t h s a t 2 0o f t h e t e m , p e r a t u r e d e p e n d e n c e o f t h i s s t r e n g t h s h o wr a n g e , 1 4 , 1A t h i r d s t u d y s h o w e d d e c r e a s i n g s t r e n g t h f r o m6 f o r o n ec r y s t a l o r i e n t a t i o n , w h i l e a f o u r t h s t u d y n o t e d d e c r ef o r t w o d i f f e r e n t c r y s t a l1 2 T h e s t r e n g t h o f p o l y c r y s t a l l ic o n s t a n t f r o m 2 0 - 8 0 0 C b e f o r e g r a d u a l l y d e c r e a s i n

m i n i m u m t e n s i l e s t r e n g t h o f C z o c h r a l s k i - g r o w n s a5 8 k s i a t 2 0 C , 4 0 k s i a t 5 0 0 C , a n d 5 2 k s i a t 1 0 0 0 Cp r o v i d e f l e x u r e s t r e n g t h d a t a a s a f u n c t i o n o f t e m ps i n g l e - c r y s t a l s a p p h i r e w i t h a r e p r e s e n t a t i v e o p t i c a6 0 / 4 0 .

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

S P I EV o l . 1 3 2 6 W i n d o w a n d D o m e T e c h n o l o g

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2 . S P E C I M E N S

S a p p h i r e o b t a i n e d f r o m C r y s t a l S y s t e m s ( S a l e m ,V i e c h n i c k i m e t h o d a n d p o l i s h e d t o a n o m i n a l s c r a t cr a n d o m c i r c u l a r m o t i o n .F l e x u r e t e s t i n g w a s c a r r i e d o u t a t t h e

R e s e a r c h I n s t i t u t e , W r i g h t - P a t t e r s o n A i r F o r c e B a s e ,U n i v e r s a l T e s t i n g M a c h i n e a t a c r o s s h e a d s p e e d o f 0t u r e s . B e n d b a r s w i t h d i m e n s i o n s 4 5 x 4 x 3 m m w e ru s i n g l o a d s s e p a r a t e d b y 1 0 m m a n d s u p p o r t s s e p a r a tT h e l o n g e d g e s o f t h e b a r s w e r e r o u n d e d t o a r a d i u s r a n d o m c i r c u l a r m o t i o n .R i n g - o n - r i n g b i a x i a l f l e x u r e t e s t i n g od i a m e t e r o f 3 8 m m w a s p e r f o r m e d w i t h a l o a d r i n g rr a d i u s o f 1 5 . 8 7 5 m m .

F i g u r e l a d e s i g n a t e s v a r i o u s f a c e s o f a s a p p h i r e d o w n t h e 3 - f o l d s y m m e t r y c - a x i s o f t h e c r y s t a l .T h e c r y s t a l l o g r a p h i c a - a x2 - f o l d s y m m e t r y a x i s . T h e m - a n d c - a x e s i n F i g . l at y p e s o f s p e c i m e n s w e r e p r e p a r e d f o r f l e x u r e t e s t i n g .F i g u r e 2 s h o w s a b e nt e n s i o n w i l l b e d i r e c t e d a l o n g t h e r n - a x i s , w i t h t h e cI n F i g s . 3 a n d 4 t h e t e n s i l e a x e s a r e t h e c r y s t a l l o g r a pF i g u r5 a n d 6 s h o w t w o o r i e n t a t i o n s o f d i s k s u s e d f o r r i n g -I n o nc a s e ( c a l l e d a O c u t ) t h e c - a x i s i s p e r p e n d i c u l a r t o t( c a l l e d a 9 0 0 c u t ) t h e d i s k f a c e i s t h e a - p l a n e c o n t a i

3 . S T R E S S A N A L Y S I S

S t r e s s l e v e l s a t f r a c t u r e f o r t h e 4 - p o i n t f l e x u r e bs i m p l e b e a m t h e o r y a s

9 P Ly U = 28 w t ( 1 )

w h e r e u i s t h e m a x i m u m s t r e s s o n t h e t e n s i l e s u r f a ct h e w i d t h o f t h e b a r , t i s t h e t h i c k n e s s o f t h e b a r , a ns u p p o r t s . T h e s t r e s s o n t h e t e n s i l e s u r f a c e s o f t h e bv a l u e t o z e r o a t t h e s u p p o r t s i n t h e l o n g i t u d i n a l d i rn e u t r a l a x i s i n t h e b a r t h i c k n e s s d i r e c t i o n ( s i d e s o f

F l e x u r e s t r e n g t h m e a s u r e m e n t s r e p o r t e d l a t e r is t r e n g t h o f s a p p h i r e i n t h e c r y s t a l l o g r a p h i c a d i r e cd i r e c t i o n .T h e r e f o r e , s t r e s s l e v e l s a t f r a c t u r e f o r d i s k s ws u r f a c e w e r e c o m p u t e d f r o m E q u a t i o n 2 , w h i c h a p p l

U = 2{ [ 2 1 + v I f l ( ) ] + [ 1 v ) ( ) ] [ 1 ( ) 2 ] }4 i r t ( 2 )

w h e r e c 7 u i s t h e m a x i m u m e q u i b i a x i a l s t r e s s o n t h e i n s i d e o f t h e l o a d r i n g r a d i u s ( b ) w h e r e t h e a p p l i e d d i s k h a s o u t s i d e r a d i u s ( R ) a n d i s s u p p o r t e d o n a r is t r e s s l e v e l s f o r a p o i n t o n t h e t e n s i l e s u r f a c e o u t s i de q u a t i o n s

1 2 / S P I E V o l . 1 3 2 6 W i n d o w a n d D o m e T e c h n o l o g i e s a n d M a t e r i a l s I I ( 1 9 9 0 )



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a n d U B a U { 1 [ 1 K 8 1 c 0 s ( 3 } ( 9 )w h e r eu m i s t h e a v e r a g e f l e x u r e s t r e n g t h w i t h t h e t e n sa v e r a g e f l e x u r a l s t r e n g t h w i t h t h e t e n s i l e a x i s a l o n gi s t h e a v e r a gf l e x u r a l s t r e n g t h w i t h t h e t e n s i l e a x i s a l o n g t h e c - a xF i n a l l y , t h e t w o t e r ms i d e o f E q u a t i o n 7 a r e d e f i n e d b y t h e r e l a t i o n s2 r 2 2 " 2 2 1c o s+ K s i n i n 9 + c o s O i +a 1 L H U I J

{ a 2 [ ( K c o s 2 +K s i n 2 i n 2 O + c o s 2 O ] 2 + 0 3 [ 1 _ K c o s 2 K S( 1 0 )a n d

c , j c o s 2 o + K 2s i n 2 Oz b ( 1 1 )w h e r ea i =0 ,a ( 1 . 1 2 1 5 ) 2 , a n d a =( 1 / ( 1 - 0 . 5 v ) 2a r e c o n s t a n t s d e r i v e d f r or e l e a s e r a t e r e l a t i o n s f o r a p e n n y - s h a p e d s u r f a c e c r

T h e p r o b a b i l i t y o f s u r v i v a l o f a p a r t i c u l a r f l e x us u b d i v i d i n g t h e t e n s i l e s u r f a c e o f t h e f l e x u r e s p e c i mc o m p u t i n g t h e p r o b a b i l i t y o f s u r v i v a l f o r e a c h o f t hi n d i v i d u a l a r e a e l e m e n t p r o b a b i l i t i e s o f s u r v i v a l w as u r v i v a l o f t h e f l e x u r e s p e c i m e n . T h e W e i b u l l p a r a ma n d m , w e r e t h e n b y m i n i m i z i n g t h e a b s o l u t e e r r o r b e t w e e n t h e p r e d if a i l u r e ( P 1 =1 - P )f o r t h e f l e x u r e s p e c i m e n t e n s i l e s u r f a c e s m e t h o d . 2

5 . R E S U L T S

A l t h o u g h 4 0 b a r s w e r e t e s t e d a t e a c h t e m p e r a t u ra b o v e 2 0 C w e r e d i s c a r d e d b e c a u s e f r a c t u r e a p p e a rp o s i t i o n s . A l l o f t h e b a r d a t a c o l l e c t e d a t 2 0 C w e r e ac o l l e c t e d a t 2 0 a n d 8 0 0 C w e r e c o n s i d e r e d v a l i d .F i g u r e s 9 - 1 3 p r e s e n t t h e f l e x u r e s t r e n g t h w i t h t e m p e r a t u r e f o r t h e s p e c i m e n sT h e v e r t i c a l b as t a n d a r d d e v i a t i o n s .T a b l e 3 p r e s e n t s a s u m m a r y o f t h e a v e rW e i b u l l s t a t i s t i c s ( m a n d )a n ds t r e n g t h r a t i o s ( K a a n d K b i n E q uu n i a x i a l b a r a n d t h e b i a x i a l d i s k s p e c i m e n s . T h e f i r sh a s o n l y 3 4 r e s u l t s b e c a u s e s i x s p e c i m e n s w e r e t e s t er e s t . F i g u r e s 1 4 - 1 6 p r e s e n t a c o m p a r i s o n o f t h e e x p e rt h e b e s t f i t o b t a i n e d f r o m B a t d o r f s t h e o r y f o r t h e 4 -

T h e f i l l e d s q u a r e s i n F i g . 1 7 a r e e x p e r i m e n t a l r e2 0 C . T h e o p e n s q u a r e s ( a n d s o l i d l i n e ) a r e f r o m t hi n F i g . 1 7 s h o w t h e e x p e c t e d b e h a v i o r o f t h e s e d i s ka - a x i s a n d r n - a x i s 4 - p o i n t b e n d s p e c i m e n s a r e u s e d tT h eu n i a x i a l r e s u l t s p r e d i c t a h i g h e r p r o b a b i l i t y o f f a i l ut h e b i a x i a l c a s e .T h e b a r s , t h e r e f o r e , g i v e a c o n s e r v a t i v e p r eF i g u r eg i v e s t h e c o r r e s p o n d i n g r e s u l t s f o r t h e d i s k s i n F i g .

1 4 / S P I E V o l . 1 3 2 6 W i n d o w a n d D o m e T e c h n o l o g i e s a n d M a t e r i a l s 1 1 ( 1 9 9 0 )

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u n i a x i a l r e s u l t s p r e d i c t a s l i g h t l y l o w e r p r o b a b i l i t y t h e d i s k s .

6 . D I S C U S S I O N

T h e b i a x i a l f l e x u r e s t r e n g t h s r e p o r t e d i n T a b l e 3 c o n s i s t e n t w i t h a p r e v i o u sr t 2 i n w h i c h t h e s t r e n g t h o f 5 0 . 8 - mt h i c k n e s s o f 2 . 5 4 m m d r o p p e d f r o m 1 0 2 k s i a t 2 0 C t o o b s e r v e a d e c r e a s e i n s t r e n g t h f r o m 1 5 4 k s i a t 2 0 C to f t h e a - a n d m - c r y s t a l l o g r a p h i c a x e s .I n c o n t r a s t , t h e d i s k s i n F i g . 6 ,s t r e s s i s a p p l i e d i n t h e p l a n e o f t h e c - a n d r n - a x e s , d e c8 0 0 C . T a k e n t o g e t h e r , t h e s e t w o s e t s o f r e s u l t s i m pr n - a x i s s t r e n g t h a t 2 0 C , b u t t h a t c - a x i s s t r e n g t h d o e sa x i ss t r e n g t h w h e n t h e t e m p e r a t u r e i s r a i s e d t o 8 0 0 C .

T h e 4 - p o i n t b e n d i n g r e s u l t s i n T a b l e 3 s h o w t h aa - a x i s i s e s s e n t i a l l y e q u a l t o t h e s t r e n g t h a l o n g t h e r nT h e 4 - p o i n t u n i a x ir e s u l t s a r e n o t c o n s i s t e n t w i t h t h e b i a x i a l f l e x u r e s ti s t h e s t r o n g e s t a t 2 0 C , w h e r e a s t h e d i s k s i m p l y t h as h o w t h a t t h e s t r e n g t h d r o p s t h e m o s t a l o n g t h e c - a xt h e d i s k s s h o w t h e l e a s t d r o p f o r c - a x i s s t r e n g t h .

W h e n t h e W e i b u l l c o n s t a n t s d e r i v e d f r o m 2 0 C ut h e 2 0 C b i a x i a l f l e x u r e t e s t d a t a ( c - a x i s n o r m a l t o tt i v e l y p r e d i c t s a h i g h e r p r o b a b i l i t y o f f a i l u r e a t a pe x p e r i m e n t a l l y ( F i g . 1 7 ) .T h e t h e o r y s i g n i f i c a n t l y u n d e r p r e d i cw h e n t h e W e i b u l l c o n s t a n t s d e r i v e d f r o m 5 0 0 - 1 0 0 0 8 0 0 C b i a x i a l f l e x u r e t e s t d a t a f o r t h e s a m e c r y s t a l o

A p p l i c a t i o n o f W e i b u l l c o n s t a n t s d e r i v e d f r o m 2 0b i a x i a l f l e x u r e t e s t s w h i c h h a d t h e c r y s t a l r n - a x i s as l i g h t l y u n d e r p r e d i c t t h e o b s e r v e d p r o b a b i l i t y o f f a i lI n t h i s i n s t a n ct h e o r y a g a i n u n d e r p r e d i c t s t h e p r o b a b i l i t y o f f a i l u rf r o m 5 0 0 - 1 0 0 0 C u n i a x i a l f l e x u r e t e s t s a r e a p p l i e d t ot h e s a m e c r y s t a l o r i e n t a t i o n .

S a p p h i r e w i n d o w a n d d o m e t e m p e r a t u r e s i n t y pn o r m a l l y l e s s t h a n 5 0 0 C .F o r t h e s e a p p l i c a t i o n s , i t i s r e c o m m eb i a x i a l f r a c t u r e s t a t i s t i c s s h o w n i n T a b l e 3 f o r 2 0 C a n a l y s i s t o p r e d i c t t h e p r o b a b i l i t y o f f a i l u r e f o r t h eb i a x i a l r e s u l t s a t e l e v a t e d t e m p e r a t u r e s i n T a b l e 3 a rc a u t i o n i n t h e a b s e n c e o f f u r t h e r e x p e r i m e n t s .

7 . R E F E R E N C E S

1 . R . L . G e n t i l m a n , C u r r e n t a n d E m e r g i n g M a t e r i aP r o c . S P I E , 6 8 , 2 - 1 1 ( 1 9 8 6 ) .2 . S . M u s i k a n t , O p t i c a l M a t e r i a l s , M a r c e l D e k k e r , N3 . J . A . S a v a g e , I n f r a r e d O p t i c a l M a t e r i a l s a n d t h e i r

H i l g e r , B r i s t o l , 1 9 8 5 .4 . F . S c h m i d a n d C . P . K h a t t a k , C u r r e n t S t a t u s o f

D o m e A p p l i c a t i o n s , P r o c . S P I E , 1 1 1 2 , 2 5 - 3 0 ( 1 9 8 9 ) .5 . H . E . L a B e l l e , J . S e r a f i n o a n d J . J . F i t z g i b b o n , R

S h a p e d S a p p h i r e C r y s t a l s , P r o c . S P I E , 6 8 3 , 3 6 - 4 0 ( 1 9 8

S P I E V o l . 1 3 2 6 W i n d o w a n d D o m e T e c h n o l o g



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6 . H . E . L a B e l l e , J r . a n d G . F . H u r l e y , S t r e n g t h a nS a p p h i r e F i l a m e n t s , S A M P E J . , 6 , 1 7 - 3 5 ( 1 9 7 0 ) .

7 . G . F . H u r l e y , M e c h a n i c a l B e h a v i o r o f M e l t - G rT e m p e r a t u r e , A p p l i e d P o l y m e r S y m p o s i u m , 2 1 , 1 2 1

8 . R . L . C r a n e , A n I n v e s t i g a t i o n o f t h e M e c h a n i

S a p p h i r e F i l a m e n t s , A i r F o r c e M a t e r i a l s L a b o r a t o r yR e p o r t N o . A F M L - T R - 7 2 - 1 8 0 , 1 9 7 2 .9 . J . T . A . P o l l o c k a n d G . F . H u r l e y , D e p e n d e n c e o

S t r e n g t h o n S t r a i n - R a t e i n S a p p h i r e , J . M a t e r . S c i . , 81 0 . D . M . K o t c h i c k a n d R . E . T r e s s l e r , S u r f a c e D a

S t r a i n - R a t e S e n s i t i v i t y o f t h e S t r e n g t h o f S a p p h i r e aS c i . , 1 0 , 6 0 8 - 6 1 2 ( 1 9 7 5 ) .

1 1 .R .L . C r a n e a n d R . E . T r e s s l e r , E f f e c t o f S u r f a c e DS a p p h i r e F i l a m e n t s , J . C o m p o s i t e M a t e r . , 5 , 5 3 7 - 5 4 1

1 2 . R . L . G e n t i l m a n , E . A . M a g u i r e , H . S . S t a r r e t t , S t r e n g t h a n d T r a n s m i t t a n c e o f S a p p h i r e a n d S t r e n gS o c . ,C 1 1 6 - C 1 1 7 1 9 8 1 ) .

1 3 . P . F . B e c h e r , F r a c t u r e - S t r e n g t h A n i s o t r o p y o f S

( 1 9 7 6 ) .1 4 . E . A . J a c k m a n a n d J . P . R o b e r t s , T h e S t r e n g t hC o r u n d u m , P h i l . M a g . , 4 6 , 8 0 9 - 8 1 1 ( 1 9 5 5 ) .

1 5 . J . B . W a c h t m a n , J r . a n d L . H . M a x w e l l , S t r e na n d R u b y a s a F u n c t i o n o f T e m p e r a t u r e a n d O r i e n t a t

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