ON THE MECHANICS OF FAILURE IN
CERAMIC/METAL BONDED SYSTEMS
A. Evans, M. Rühle, M. Turwitt
To cite this version:
A. Evans, M. Rühle, M. Turwitt.
ON THE MECHANICS OF FAILURE IN CERAMIC/METAL BONDED SYSTEMS. Journal de Physique Colloques, 1985, 46 (C4), pp.C4613-C4-626. <10.1051/jphyscol:1985466>. <jpa-00224719>
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Submitted on 1 Jan 1985
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JOURNAL DE PHYSIQUE
Colloque C4, suppl6ment a u n04, Tome 46, avril 1985
A.G.
page C4-613
Evans, M. ~ i i h l e ' and M. ~ u r w i t t '
Department of Materials Science and Mineral Engineering, University of
California, Berkeley, CA 94720, U.S.A.
' ~ m - ~ Z a n c k - l n s t i t ufiir
t
Metallforschung, I n s t i t u t fiir
Werkstoffwissenschaften, 0-7000 S t u t t g a r t I , F.R. G.
-
Abstract
S t r e s s c o n c e n t r a t i o n s t h a t d e v e l o p i n m e t a l / c e r a m i c bonded
systems h a v e been e v a l u a t e d and shown t o encourage c r a c k p r o p a g a t i o n a t , o r
n e a r , t h e edge o f bonded i n t e r f a c e s . Experiments 1 i n d e n t a t i o n o b s e r v a t i o n s
on Nb/A1203 c o n f i r m t h e e x i s t e n c e o f t h e p r e d i c t e d s t r e s s c o n c e n t r a t i o n s .
I n t h i s system, f a i l u r e was i n v a r i a b l y o b s e r v e d t o i n i t i a t e i n t h e ceramic,
such t h a t q u a s i - s t a t i c c r a c k s l o c a t e d a t t h e i n t e r f a c e e x h i b i t e d c r a c k
b l u n t i n g . However, s u b s t a n t i a l d y n a m i c r e d u c t i o n s i n t h e c r a c k g r o w t h
r e s i s t a n c e o f t h e i n t e r f a c e a r e i n f e r r e d from f r a c t u r e s u r f a c e
observations. I m p l i c a t i o n s f o r t h e optimal s t r e n g t h s o f ceramic/metal
bonded systems a r e presented.
1.
INTRODUCTION
The mechanical r e s p o n s e o f a system is governed by t h e s t r e s s d i s t r i b u t i o n and by
t h e f r a c t u r e c h a r a c t e r i s t i c s o f each m a t e r i a l c o n s t i t u e n t . Both a s p e c t s must be
s e p a r a t e l y i n v e s t i g a t e d b e f o r e d e v i s i n g an a p p r o a c h f o r o p t i m i z i n g m e c h a n i c a l
s t r e n g t h . Consequently, i n v e s t i g a t i o n o f t h e mechanical b e h a v i o r o f c e r a m i c / m e t a l
bonded s y s t e m s r e q u i r e s c o n s i d e r a t i o n o f t h e stress s t a t e , a s d i c t a t e d by t h e
a p p l i e d l o a d s a n d t h e e l a s t i c a n d t h e r m a l e x p a n s i o n mismatch, a s w e l l as t h e
i n d i v i d u a 1 f r a c t u r e c h a r a c t e r i s t i c s o f t h e c e r a m i c , meta 1 a n d i n t e r f a c e . The
l i m i t e d a v a i l a b l e r e s e a r c h on c e r a m i c / m e t a l bonded systems i n d i c a t e s t h a t f r a c t u r e
i n t h e c e r a m i c , a d j a c e n t t o t h e i n t e r f a c e , is a f r e q u e n t f a i l u r e mode (1,2).
I n t e r f a c e s with a g r e a t e r f r a c t u r e r e s i s t a n c e than t h e ceramic thus appear t o be
attainable.
Consequently, an i s s u e o f g r e a t e r p r e s e n t c o n c e r n is t h e s t a t e of
s t r e s s a s s o c i a t e d w i t h bonded s y s t e m s . The i n t e n t o f t h i s a r t i c l e i s t o e x a m i n e
v a r i o u s problems a s s o c i a t e d with t h e growth o f c r a c k s a t , o r n e a r , t h e i n t e r f a c e in
c e r a m i c / m e t a l bonded systems, a s a b a s i s f o r u n d e r s t a n d i n g mechanical s t r e n g t h .
The s t r e n g t h i s s u e s a r e i l l u s t r a t e d by experiments conducted i n t h e A1203/Nb system.
T h i s system h a s t h e a t t r a c t i v e f e a t u r e s t h a t t h e r m a l expansion mismatch is minimized
a n d t h a t d i s c r e t e i n t e r f a c e s c a n b e a c h i e v e d (3). However, m i s m a t c h i n e l a s t i c
modulus p r o v i d e s unique f a i l u r e modes, t y p i c a l o f c e r a m i c / m e t a l bonded systems. I n
p a r t i c u l a r , f a i l u r e f r e q u e n t l y i n i t i a t e s a t e d g e s , d u e t o s u b s t a n t i a 1 stress
c o n c e n t r a t i o n s (4).
Edge e f f e c t s a r e t h u s a f f o r d e d s p e c i a l emphasis.
The mechanical r e s p o n s e o f t h e system is probed u s i n g i n d e n t a t i o n s p l a c e d a t v a r i o u s
s i t e s a d j a c e n t t o , and remote from, t h e i n t e r f a c e . The i n d e n t a t i o n method h a s been
s e l e c t e d because it s i m u l a t e s t h e f r a c t u r e b e h a v i o r induced by machining damage (5)
and by i n c l u s i o n s (6) two o f t h e most d e l e t e r i o u s d e f e c t t y p e s i n h i g h s t r e n g t h
m a t e r i a l systems (6).
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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985466
JOURNAL DE PHYSIQUE
2. EDGE EFFECTS
2.1
S t r e s s Concentrations
When a mismatch e x i s t s i n e i t h e r t h e r m a l e x p a n s i o n o r e l a s t i c m o d u l u s , e d g e s a n d
The b a s i c n a t u r e o f t h e e d g e p r o b l e m i s
c o r n e r s a r e major s o u r c e s o f f a i l u r e .
i l l u s t r a t e d f o r t h e c o n f i g u r a t i o n d e p i c t e d i n f i g . 1. When t h e m e t a l s t r i p h a s
e i t h e r a l a r g e r t h e r m a l expansion c o e f f i c i e n t o r a lower modulus than t h e m a t r i x ;
t h e unconstrained m e t a l d e v e l o p s a s m a l l e r l a t e r a l dimension than t h e ceramic ( f i g .
l b ) . Hence, t o s i m u l a t e t h e s t r e s s s t a t e i n t h e bonded s y s t e m , t h e u n c o n s t r a i n e d
m e t a l must b e u n i f o r m l y e x t e n d e d by t h e a p p l i c a t i o n o f e d g e t r a c t i o n s ( f i g . 1c).
Then, s u r f a c e f o r c e s ( e q u a l i n m a g n i t u d e b u t o p p o s i t e i n s i g n ) must b e a p p l i e d t o
t h e m e t a l , i n t h e bonded s t a t e , t o a c h i e v e s t r e s s f r e e c o n d i t i o n s a t t h e s u r f a c e
( f i g . Id). This l a t t e r s t e p induces l a r g e normal and s h e a r s t r e s s e s n e a r t h e edge,
which t y p i c a l l y a c t o v e r a d i s t a n c e similar t o t h e t h i c k n e s s , h, o f t h e m e t a l .
Furthermore, t h e s t r e s s e s a r e f r e q u e n t l y s i n g u l a r (4).
I n t h e p r e s e n c e o f e l a s t i c mismatch, t h e s t r e s s e s n e a r t h e e d g e , i n d u c e d by a n
a p p l i e d s t r e s s a,, e x h i b i t a s i n g u l a r f o r m (4). F o r p l a n e s t r a i n c o n d i t i o n s , t h e
edge s t r e s s e s can b e expressed a s
where
CERAMIC
ERAMlC
t
o) INITIAL STATE
-
b) STRESSED: UNCONSTRAINED
+
c) UNCONSTRAINED:
DISPLACEMENT
CONTINUITY AT
INTERFACE
SURFACE FORCES APPLIED.
FOR STRESS FREE SLRFACE
REQUIREMENTS
Fig. 1
A schematic i l l u s t r a t i n g t h e development o f i n t e r f a c i a l s t r e s s
c o n c e n t r a t i o n s due t o e l a s t i c ( o r t h e r m a l expansion) mismatch.
p is t h e s h e a r modulus, v is Poisson's r a t i o , f is a f u n c t i o n , Y is a c o e f f i c i e n t
( < I ) and r is t h e d i s t a n c e from t h e edge, a l o n g t h e i n t e r f a c e . Some t y p i c a l r e s u l t s
( 4 ) a r e p l o t t e d i n f i g . 2. Very l a r g e t e n s i l e a n d s h e a r s t r e s s e s t h u s e x i s t o v e r
sma 11 r e g i o n s ad jaoent t o t h e edge.
CERAMIC
I~~ERFACE
METAL
Qzz/=m
0.8
-
Fig. 2
S t r e s s e s n e a r a f r e e s u r f a c e a t t h e i n t e r f a c e between a bonded system f o r
t h e c o n d i t i o n p l / u 2 = 0.11, vl
1 / 2 ( a = -0.8, B = 0 ) (4).
The maximum s h e a r
stress o c c u r s j u s t beneath t h e s=u v?=
r ace.
T h e r m a l e x p a n s i o n mismatch h a s a s i m i l a r e f f e c t , by v i r t u e o f l a r g e r e s i d u a l
s t r e s s e s c r e a t e d n e a r t h e edge. S p e c i f i c a l l y , i f t h e e l a s t i c p r o p e r t i e s a r e t h e
same f o r t h e m e t a l a n d c e r a m i c , t h e i n t e r f a c e s t r e s s e s a r e g i v e n f o r a bonded
c y l i n d e r by (7);
where
d
is t h e diameter o f t h e c y l i n d e r and t h e a n c t i o n 51 is p l o t t e d i n fig. 3.
A mismatch i n m o d u l u s g e n e r a t e s i n t e r f a c i a l t e n s i l e s t r e s s e s o
,
a t t h e edge,
i r r e s p e c t i v e o f t h e s i g n o f t h e mismatch and t h u s , i n v a r i a b l y , e n h a n c e s t h e
p r o p e n s i t y t o f r a c t u r e . T h e r m a l e x p a n s i o n mismatch i n d u c e s ,a, t e n s i l e s t r e s s e s
j u s t o u t s i d e t h e i n t e r f a c e , w i t h i n e i t h e r t h e m e t a l o r t h e ceramic, depending upon
t h e s i g n o f t h e t h e r m a l expansion and t h e e l a s t i c mismatch.
Generally, the metal
h a s the l a r g e r thermal expansion c o e f f i c i e n t and t h e expansion mismatch t h e n induces
,a,
t e n s i l e s t r e s s e s i n t h e c e r a m i c , a d j a c e n t t o t h e i n t e r f a c e , and e n c o u r a g e s
f a i l u r e i n t h e ceramic. Large s h e a r s t r e s s e s always e x i s t a l o n g t h e i n t e r f a c e , near
t h e e d g e , i n t h e p r e s e n c e o f e l a s t i c o r t h e r m a l mismatch. A s u b s t a n t i a l mode I1
c o n t r i b u t i o n t o edge f a i l u r e s h o u l d t h u s be a n t i c i p a t e d in a l l s i t u a t i o n s .
JOURNAL DE PHYSIQUE
-
Fig. 3
S t r e s s e s induced by a t h e r m a l expansion mismatch i n a bonded c y l i n d e r .
The s h e a r s t r e s s e s a r e a t t h e i n t e r f a c e , whereas t h e t e n s i l e s t r e s s e s are i n t h e
ceramic c l o s e t o t h e i n t e r f a c e (z/d = 0.05).
The normal s t r e s s e s immediately a t t h e
i n t e r f a c e a r e zero. The maximum s h e a r s t r e s s o c c u r s j u s t beneath t h e surface.
2.2
Crack
Propagation
The p r o p a g a t i o n o f c r a c k s from a n e d g e a l o n g , o r a d j a c e n t t o , t h e i n t e r f a c e i s
g o v e r n e d by t h e a p p r o p r i a t e s t r a i n e n e r g y r e l e a s e r a t e (8,g).
For example, t h e
t o t a l s t r a i n energy r e l e a s e 9 f o r an i n t e r f a c e crack i n t h e absence o f thermal
mismatch has t h e g e n e r a l form (10,11,12)
where Ec is t h e composite modulus (121,
r
such t h a t , f o r p l a n e s t r a i n , X = 3-4v,
and
$,
-4
the variable
g is t h e f u n c t i o n p l o t t e d in f i g . 4.
deduced from f i g . 4, is (101,
r; is g i v e n by,
An approximate a n a l y t i c e x p r e s s i o n f o r
BONDED
HOMOGENEOUS
MATERIAL
Fig. 4
crack.
-
-
The v a r i a t i o n i n t h e n o r m a l i z e d s t r a i n e n e r g y r e l e a s e f o r an i n t e r f a c e
Trends in t h e i n t e r f a c e crack growth s t r e s s w i t h i n crack l e n g t h f o r v a l u e s
Fig. 5
o f t h e s i n g u l a r i t y y e i t h e r s m a l l e r o r l a r g e r than u n i t y .
JOURNAL DE PHYSIQUE
C4-6 18
where X1,2 a r e c o e f f i c i e n t s and 4 is an exponent. When (e d i c t a t e s crack growth a t
some c r i t i c a l l e v e l , (ec ( d i c t a t e d by the lower v a l u e f o r e i t h e r the i n t e r f a c e or t h e
ceramic), t h e equilibrium crack growth s t r e s s h a s t h e dimensionless form
where A is t h e function p l o t t e d iri fig. 5. It is o f i n t e r e s t t o note t h a t when4.1,
t h e c r a c k grows s t a b l y under i n c r e a s i n g l o a d and r e a c h e s an i n s t a b i l i t y a t a
c r i t i c a l s t r e s s , o- , given by
-
-
The observed f a i l u r e s t r e s s associated with edge flaws is d i c t a t e d i n t h i s instance
by t h e metal l a y e r thickness, r a t h e r than t h e i n i t i a l crack s i z e (analagous to t h e
behavior observed a t indentations (5)). The metal l a y e r thickness t h u s emerges a s a
preeminent f r a c t u r e c o n t r o l l i n g parameter, c o n s i s t e n t with p r a c t i c a l experience (2).
-
Fig. 6
O p t i c a l m i c r o g r a p h s o f i n d e n t a t i o n c r a c k s b e f o r e and a f t e r l o a d i n g t o a
nominal s t r e s s o f 80 MPa. ( a ) an i n d e n t a t i o n remote from t h e i n t e r f a c e , (b) an
indentation remote from t h e i n t e r f a c e but c l o s e to t h e edge, (c) an indentation near
t h e center, c l o s e t o the interface
An important l i m i t a t i o n o f t h e preceding a n a l y s i s is t h e i m p l i c i t assumption t h a t
a l l of t h e s t r a i n energy is a v a i l a b l e f o r c r a c k propagation. Experience with
d e l a m i n a t i o n i n polymer m a t r i x composites (9) r e v e a l s t h a t , f r e q u e n t l y , t h e opening
mode component, gL,is more important than t h e t o t a l 9 . Such b e h a v i o r is i n d i c a t i v e
o f minimal c o u p l i n g o f t h e s h e a r component o f t h e s t r a i n energy r e l e a s e r a t e (e t o
t h e f r a c t u r e mechanism. Consequently, s i n c e a s u b s t a n t i a l c o n t r i b u t i o n t o 9 , y o r
i n t e r f a c i a l edge c r a c k s , d e r i v e s from t h e s h e a r s t r e s s ( s e c t i o n 2.11,
it is deemed
improper t o presume t h a t t h e t o t a l 9 is t h e p e r t i n e n t c r a c k d r i v i n g force.
Careful
experimental s t u d i e s o f the r e s p e c t i v e influence o f
a n d 911 on t h e g r o w t h o f
i n t e r f a c e cracks a r e required before f u l l y specifying an acceptable f r a c t u r e
criterion.
Thermal expansion mismatch imposes a d d i t i o n a l edge s t r e s s e s t h a t a l s o c o n t r i b u t e t o
B (13). C o m p u t a t i o n s o f 9 c r a c k s h a v e n o t y e t b e e n c o n d u c t e d . The r e l a t i v e
i n f l u e n c e o f t h e e l a s t i c m o d u l u s and t h e r m a l e x p a n s i o n mismatch on t h e n e t c r a c k
d r i v i n g f o r c e t h u s a w a i t s f u r t h e r i n v e s t i g a t i o n . I n t h i s c o n t e x t it s h o u l d a l s o be
r e c a l l e d t h a t s t r a i n energy r e l e a s e r a t e s a r e n o t a d d i t i v e . I n t e r a c t i o n terms must
a l s o be i n c l u d e d , based on computations o f 9 and (e f o r each problem.
I
3.
I1
EXPERIMENTAL OBSERVATIONS
3.1
Test Procedures
F o u r p o i n t f l e x u r e s p e c i m e n s c o n s i s t i n g o f t h i n (2.1 mm) s t r i p s o f Nb, d i f f u s i o n
bonded t o p o l y c r y s t a l l i n e a l u m i n a , were p r e p a r e d and c a r e f u l l y p o l i s h e d on t h e
t e n s i l e surface.
V i c k e r s i n d e n t a t i o n s were then p l a c e d a t v a r i o u s l o c a t i o n s with
r e s p e c t t o t h e i n t e r f a c e , b u t w i t h i n t h e uniformly s t r e s s e d r e g i o n s o f t h e f l e x u r e
s p e c i m e n ( v i z . , between t h e i n n e r l o a d i n g r o d s ) and t h e i n d e n t a t i o n c r a c k s
c h a r a c t e r i z e d by o p t i c a l microscopy ( f i g . 6).
T h e r e a f t e r , t h e specimens w e r e loaded
Changes i n t h e i n d e n t a t i o n crack l e n g t h s induced by t h e
t o % 80 MPa and unloaded.
l o a d were determined and r e l a t e d to l o c a l stress c o n c e n t r a t i o n s . Subsequently, t h e
specimens were loaded t o f a i l u r e . F r a c t u r e o r i g i n s were t h e n i d e n t i f i e d and used t o
assess crack configurations a t the f a i l u r e i n s t a b i l i t y .
3.2
Observations
I n d e n t a t i o n c r a c k s remote from t h e i n t e r f a c e ( f i g . 6a) e x h i b i t e d l i t t l e extension,
e x c e p t a t i n d e n t a t i o n s c l o s e t o a n e d g e ( f i g . 6b). However, on t h e same s p e c i m e n ,
i n d e n t a t i o n c r a c k s p l a c e d a d j a c e n t t o t h e i n t e r f a c e experienced s u b s t a n t i a 1 growth
( f i g . 6c). The c o m p a r a t i v e e x t e n s i o n p r o v i d e s a d i r e c t m e a s u r e o f t h e s t r e s s
c o n c e n t r a t i o n f a c t o r s , a s d e s c r i b e d i n t h e subsequent s e c t i o n . Maxima 1 c r a c k growth
occurred a t i n d e n t a t i o n s p l a c e d near t h e i n t e r f a c e , a t t h e specimen edge.
Observations o f c r a c k s t h a t t e r m i n a t e a t t h e i n t e r f a c e r e v e a l s l i p band formation i n
t h e Nb and c r a c k b l u n t i n g ( f i g . 7a,b), i n d i c a t i v e o f a p p r e c i a b l e d u c t i l i t y i n t h e Nb
a d j a c e n t t o t h e i n t e r f a c e . The l a r g e p l a s t i c s t r e t c h observed a t o t h e r c r a c k t i p s
( f i g . 7 c ) s u b s t a n t i a t e s t h a t t h e Nb c a n s u s t a i n e x t e n s i v e p l a s t i c s t r a i n . Y e t ,
o b s e r v a t i o n s o f t h e f r a c t u r e s u r f a c e , away from t h e i n i t i a t i o n s i t e , i n d i c a t e t h a t
r a p i d c r a c k propagation t o f a i l u r e has occurred a t t h e i n t e r f a c e , with no e v i d e n c e
o f p l a s t i c deformation i n t h e Nb ( f i g . 7c). T h i s paradox a p p e a r s t o b e e x p l i c a b l e
b a s e d on more d e t a i l e d o b s e r v a t i o n s o f f r a c t u r e i n i t i a t i o n s i t e s . I n d e n t a t i o n
c r a c k s t h a t e i t h e r t e r m i n a t e a t t h e i n t e r f a c e , o r grow s t a b l y t o t h e i n t e r f a c e
d u r i n g l o a d i n g , i n v a r i a b l y e x h i b i t c r a c k t i p b l u n t i n g and n e v e r i n i t i a t e t h e f i n a l
f a i l u r e ( f i g . 8). F a i l u r e always i n i t i a t e s from c r a c k s i n t h e A1203 which becomes
u n s t a b l e w h i l e s t i l l c o n t a i n e d w i t h i n t h e c e r a m i c ( f i g . 8). F u r t h e r , u n s t a b l e ,
growth o f t h e crack t h e n e n t a i l s a t t r a c t i o n o f t h e c r a c k t o t h e i n t e r f a c e , whereupon
i n t e r f a c e p r o p a g a t i o n o c c u r s i n a n o m i n a l l y b r i t t l e mode.
These f r a c t u r e
c h a r a c t e r i s t i c s a r e deemed t o b e c o n s i s t e n t w i t h a v e l o c i t y s e n s i t i v e 9, f o r t h e
i n t e r f a c e crack, a s d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n .
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metal
interface
--
-
Fig. 7
Crack t i p s a t t h e i n t e r f a c e showing s h e a r bands and c r a c k t i p b l u n t i n g (a)
c r a c k n o r m 1 t o t h e i n t e r f a c e (b) a crack i n c l i n e d t o t h e i n t e r f a c e (c) t h e p l a s t i c
s t r e t c h z o n e a f t e r r e m o v a l o f t h e c e r a m i c by r a p i d f r a c t u r e . The r a p i d f r a c t u r e
s u r f a c e on fig. 7c i n d i c a t e s l i n e s where t h e A1203 g r a i n boundaries i n t e r s e c t t h e
i n t e r f a c e , b u t t h e r e i s no e v i d e n c e o f p l a s t i c d e f o r m a t i o n a t t h e i n t e r f a c e away
from t h e s t r e t c h zone.
One f i n a l f e a t u r e o f t h e f a i l u r e t h a t m e r i t s c o n s i d e r a t i o n is t h e o b s e r v a t i o n t h a t
i n d e n t a t i o n s e m p l a c e d v e r y c l o s e t o t h e i n t e r f a c e ( f i g . 9) r e s u l t i n l o w f a i l u r e
loads.
An accompanying o b s e r v a t i o n is t h e s u b s t a n t i a l r e s i d u a l openings e x h i b i t e d
by t h e i n d e n t a t i o n c r a c k , and t h e e x t e n s i v e d e f o r m a t i o n o f t h e Nb a d j a c e n t t o t h e
i n t e r f a c e ( f i g . 9).
T h e s e o b s e r v a t i o n s are shown t o b e c o n s i s t e n t w i t h t h e
development o f r e s i d u a l s t r e s s , due t o t h e l o c a l i z e d p l a s t i c deformation o f t h e Nb,
and t h e e f f e c t s o f t h e r e s i d u a l s t r e s s e s on c r a c k propagation i n t h e Al2O3.
3.3
Analysis
The r e l a t i v e e x t e n s i o n s o f i n d e n t a t i o n c r a c k s a t v a r i o u s l o c a t i o n s throughout t h e
test specimens may be used t o e s t i m a t e s t r e s s d i s t r i b u t i o n s (Appendix I ) u s i n g ;
T h i s formula is o n l y
minimal u t i l i t y f o r
estimates of stress
t h e i n t e r f a c e exceed
Bogy (4).
s t r i c t l y v a l i d f o r c r a c k s i n i s o t r o p i c m a t e r i a l and t h u s , h a s
c r a c k s v e r y c l o s e t o t h e i n t e r f a c e . With t h i s r e s t r i c t i o n ,
r a t i o s from f i g . 6 r e v e a l t h a t e d g e s t r e s s e s w i t h i n ~ 1 0 0 p r no f
t h e a p p l i e d stress byQ1.6, c o n s i s t e n t u i t h t h e c a l c u l a t i o n s by
-
Fig. 8
Two i n d e n t a t i o n s on t h e same s p e c i m e n b u t on o p p o s i t e s i d e s o f t h e Nb
l a y e r . The i n d e n t which becomes u n s t a b l e i n t h e A1203 i s t h e f a i l u r e o r i g i n : ( a )
a n d (b). The i n d e n t w i t h an i n i t i a l c r a c k t i p a t t h e i n t e r f a c e d o e s n o t c a u s e
f a i l u r e : ( c ) a n d (d).
-
Fig. 9
An i n d e n t a t i o n c l o s e t o t h e i n t e r f a c e c a u s e s premature f a i l u r e . Note t h e
s u b s t a n t i a l r e s i d u a l opening o f t h e c r a c k in t h e A1203 and t h e deformation o f t h e
Nb
.
JOURNAL DE PHYSIQUE
4.
DISCUSSION
Various experiments 1 (14) and t h e o r e t i c a 1 s t u d i e s ( 15) o f r a p i d c r a c k propagation i n
b.c.c. m e t a l s h a v e i n d i c a t e d t h a t g c d e c r e a s e s r a p i d l y w i t h i n c r e a s e i n c r a c k
v e l o c i t y , due t o t h e s t r o n g s t r e s s dependence o f t h e d i s l o c a t i o n v e l o c i t y . Such
b e h a v i o r e x p l a i n s , f o r example, t h e e x i s t e n c e o f u n s t a b l e b r i t t l e f a i l u r e i n s t e e l s ,
a f t e r i n i t i a l c r a c k t i p p l a s t i c b l u n t i n g ( v i z . i n t h e upper t r a n s i t i o n range). A
c o m p a r a b l e r a t e d e p e n d e n c e Ee, s h o u l d b e e x p e c t e d i n t h e Nb, e s p e c i a l l y i f
a p p r e c i a b l e amounts o f oxygen a r e i n s o l u t i o n n e a r t h e i n t e r f a c e . F u r t h e r m o r e
s i m i l a r r a t e d e p e n d e n t p l a s t i c i t y e f f e c t s s h o u l d b e e x p e r i e n c e d by a c r a c k t i p
l o c a t e d a t t h e Nb/A1203 i n t e r f a c e ( a l b e i t t o a r e d u c e d e x t e n t , b e c a u s e o f t h e
c o n s t r a i n t e x e r t e d by t h e non-deformable Al2O3).
It is t h u s proposed t h a t (e, f o r
t h e i n t e r f a c e e x h i b i t s t h e c r a c k v e l o c i t y dependence d e p i c t e d in fig. 10. A t high
c r a c k v e l o c i t i e s , . p l a s t i c deformation o f t h e Nb is e s s e n t i a l l y i n h i b i t e d and gc f o r
t h e i n t e r f a c e , (91) , is s m a l l e r than t h a t f o r t h e p o l y c r y s t a l l i n e A ~ ~ o ~ ( @ )I n
t h i s s i t u a t i o n , 'g; is l a r g e l y d i c t a t e d by t h e i n t e r f a c i a l energy a s s o c i a f e d w i t h
the interface structure, viz;
.
where t h e y a r e s u r f a c e e n e r g i e s and y i n t i s t h e i n t e r f a c e e n e r g y .
A t lower
v e l o c i t i e s , p l a s t i c z o n e s c a n b e a c t i v a t e d by t h e c r a c k t i p stress f i e l d and t h e
A l a r g e increase i n g t h u s ensues,
a s s o c i a t e d p l a s t i c work c o n t r i b u t e s t o 9:.
s u c h t h a t g l s u b s t a n t i a 1l y e x c e e d s g E ( w h i c h is known t o b e i n s e n s i t i v e t o c r a c k
v e l o c i t y (56)).
SUBSTANTIAL
PLASTICITY IN Nb
I
I
I
A1203,
I
J-INTERFACE,
5;
I
Fig. 10
-
P o s t u l a t e d t r e n d s i n gc with crack v e l o c i t y .
The p r e c e d i n g t r e n d s i n @ = f o r t h e c o m p o s i t e s y s t e m a r e f u l l y c o n s i s t e n t w i t h t h e
experimental observations.
S p e c i f i c a 1l y , s t a t i o n a r y . c r a c k s a t t h e i n t e r f a c e
i n v a r i a b l y b l u n t ( f i g . 7) d u e t o t h e l a r g e a s s o c i a t e d 9; and h a v e , c o n s e q u e n t l y ,
n e v e r been o b s e r v e d a s f a i l u r e i n i t i a t i o n s i t e s ( f i g . 8). F a i l u r e a l w a y s o c c u r s
from c r a c k s which become u n s t a b l e i n t h e Al203. The r a p i d l y moving c r a c k , t h u s
formed i n t h e A1203, s u b s e q u e n t l y extends p r e f e r e n t i a l l y a l o n g t h e i n t e r f a c e , where
9, now e x h i b i t s i t s minimal v a l u e , due t o t h e absence o f p l a s t i c i t y i n t h e Nb (fig.
8 ) . V a l i d a t i o n o f t h i s h y p o t h e s i s , o f c o u r s e , r e q u i r e s c r a c k g r o w t h s t u d i e s as a
f u n c t i o n o f v e l o c i t y . However, t h e a s s o c i a t e d i m p l i c a t i o n f o r t h e m e c h a n i c a l
s t r e n g t h o f t h e bonded system is t h a t , f o r most s i t u a t i o n s , t h e i n t e r f a c e f r a c t u r e
r e s i s t a n c e 9 f is e n t i r e l y adequate, viz., f r a c t u r e is not l i m i t e d by t h e i n t e r f a c e .
( P r o b l e m s may a r i s e a t h i g h l o a d i n g r a t e s , b u t s u c h c o n d i t i o n s a r e i n f r e q u e n t l y
encountered).
Another important i n f l u e n c e o f p l a s i t i c i t y i n t h e m e t a l concerns t h e d e v e l o ment o f
r e s i d u a l s t r e s s . The presence e i t h e r o f machining damage o r o f i n c l u s i o n s P in t h e
ceramic immediately a d j a c e n t t o t h e i n t e r f a c e is l i k e l y to induce p l a s t i c i t y i n t h e
m e t a l , c o m p a r a b l e t o t h a t o b s e r v e d a r o u n d t h e i n d e n t a t i o n d e p i c t e d i n f i g . 9.
R e s i d u a l s t r e s s e s o f o r d e r , 4Y/3, a r e t h u s t o b e a n t i c i p a t e d (Appendix 1 1 ) i n t h e
c e r a m i c , where Y i s t h e y i e l d s t r e n g t h . The r e s i d u a l s t r e s s e s s u p e r p o s e on t h e
Such h i g h l y
c o n c e n t r a t e d a p p l i e d l o a d s a t t h e edges and cause premature f a i l u r e .
d e l e t e r i o u s f a i l u r e c h a r a c t e r i s t i c s c a n be a v e r t e d by a v o i d i n g n e a r - i n t e r f a c e
d e f e c t s o f t h i s t y p e and/or by s e l e c t i n g a m e t a l w i t h a low y i e l d s t r e n g t h .
5.
CONCLUDING REMARKS
The i n d e n t a t i o n experiments r e v e a l t h e s e n s i t i v i t y o f t h e i n t e r f a c i a l zone t o t h e
presence o f d e f e c t s i n t h e a d j a c e n t ceramic by v i r t u e o f t h e l a r g e a s s o c i a t e d s t r e s s
c o n c e n t r a t i o n s . The p r o c e s s i n g o f h i g h q u a l i t y bonded s y t e m s t h u s r e q u i r e s t h a t
g r e a t c a r e be e x c e r c i s e d in t h e avoidance o f d e f e c t s i n t h e i n t e r f a c i a l zone, n e a r
t h e surface. S p e c i f i c a l l y , e x c e s s i v e i n c l u s i o n s o r v o i d s i n t h i s zone would be most
damaging.
F u r t h e r m o r e and p e r h a p s , most i m p o r t a n t l y , m a c h i n i n g damage i n t h e
ceramic n e a r t h e i n t e r f a c e ( a phenomenon c l o s e l y s i m u l a t e d by t h e i n d e n t a t i o n c r a c k s
(5)) would b e e x t r e m e l y d e l e t e r i o u s . M a c h i n i n g c o n d i t i o n s t h u s demand c a r e f u l
control.
Severa 1 remarks concerning t h e i n f l u e n c e o f p l a s i t i c i t y on t h e mechanica 1 p r o p e r t i e s
a r e a l s o deemed w o r t h y o f c o n s i d e r a t i o n . P l a s t i c i t y i n t h e m e t a l a t low l o a d i n g
r a t e s i m p l i e s t h a t i n t e r f a c i a l c r a c k s a r e l i k e l y t o be s u s c e p t i b l e t o f a t i g u e .
Fatigue c r a c k growth r a t e s (da/dN v s . 9 ) should t h u s be measured, a s w e l l a s f a t i g u e
c r a c k i n i t i a t i o n e f f e c t s . P l a s t i c d e f o r m a t i o n i n t h e m e t a l is a l s o e x p e c t e d t o
i n d u c e c o m p l e x b e h a v i o r i n n o t c h e d s p e c i m e n s . I n t h i s c o n t e x t , it s h o u l d b e
r e c a l l e d t h a t n o t c h e d beam t e s t s (e.g. Charpy t e s t s ) and JIG t e s t s i n s t e e l s c a n
y i e l d o p p o s i t e t r e n d s in f a i l u r e l o a d with m i c r o s t r u c t u r e , due t o t h e d i f f e r e n c e i n
t h e s c a l e o f t h e p l a s t i c z o n e r e l a t i v e t o t h e m i c r o s t r u c t u r a l s c a l e a t which t h e
f r a c t u r e mechanisms o p e r a t e (17).
APPENDIX
I
Growth C h a r a c t e r i s t i c s
of
I n d e n t a t i o n Cracks
An i n d e n t a t i o n c r a c k o f r a d i u s , a, contained i n an i s o t r o p i c body e x h i b i t s a s t r e s s
i n t e n s i t y f a c t o r , K, given by (18) ;
her ma 1 e x p a n s i o n mismatch between t h e i n c l u s i o n and t h e m a t r i x i n d u c e m a t r i x
d e f o r m a t i o n t h a t may e x c e e d t h e y i e l d s t r e n g t h o f t h e metal; t h e r e b y c a u s i n g
residual stress.
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where C1 a n d C2 a r e c o n s t a n t s f o r a g i v e n i n d e n t a t i o n l o a d a n d
stress. Hence, t h e s t r e s s and c r a c k l e n g t h a r e r e l a t e d by;
0
is t h e a p p l i e d
However, Kc is a l s o r e l a t e d t o t h e i n i t i a l c r a c k r a d i u s , ao, a t z e r o a p p l i e d s t r e s s
Consequently, from eqn (A2), t h e s t r e s s is g i v e n by;
by, Kc = c2aO-3/2.
Furthermore, i f s i m i l a r i n d e n t a t i o n s are p l a c e d a t two d i f f e r e n t l o c a t i o n s w i t h i n an
i s o t r o p i c b r i t t l e s o l i d t h e r a t i o o f s t r e s s e s d e v e l o p e d a t t h o s e s i t e s is
where R i s t h e c r a c k l e n g t h r a t i o , ao/a. S t r e s s v a r i a t i o n s w i t h i n a bcdy may t h u s
be e s t i m a t e d from i n d e n t a t i o n c r a c k l e n g t h r a t i o s , w i t h o u t r e q u i r i n g knowledge o f
e i t h e r m a t e r i a l p a r a m e t e r s o r geometric c o n s t a n t s .
APPENDIX
Residual S t r e s s E f f e c t s
R e s i d u a l s t r e s s e f f e c t s and t h e i r i n f l u e n c e on crack e x t e n s i o n can be i l l u s t r a t e d
u s i n g t h e p r e s s u r i z e d s p h e r i c a l c a v i t y a s a n e x a m p l e (19). When two c o n n e c t e d
m a t e r i a l s w i t h d i f f e r e n t e l a s t i c and p l a s t i c p r o p e r t i e s a r e s u b j e c t t o i n t e r n a l
p r e s s u r e , s u c h t h a t t h e i n n e r m a t e r i a l i s immune t o p l a s t i c y i e l d i n g , t h e o u t e r
m a t e r i a l f i r s t e x p e r i e n c e s p l a s t i c deformation when t h e normal compression a t t h e
i n t e r f a c e e x c e e d s , p = 2Y/3,
where Y i s t h e y i e l d s t r e n g t h . F u r t h e r p l a s t i c
d e f o r m a t i o n r e s u l t s i n t h e r a d i a l s t r e s s d i s t r i b u t i o n d e p i c t e d i n f i g . 11, w i t h a
minimum o c c u r r i n g a t t h e i n t e r f a c e and a maximum a t t h e e l a s t i c / p l a s t i c boundary i n
t h e o u t e r m a t e r i a l . Unloading r e q u i r e s t h a t t h e e l a s t i c s t r e s s d i s t r i b u t i o n be
s u b t r a c t e d from t h e s t r e s s a t p e a k p r e s s u r e ( f i g . 11 ), r e s u l t i n g i n t h e r e s i d u a l
f i e l d d e p i c t e d i n f i g . 11. The r e s i d u a l r a d i a l s t r e s s e x h i b i t s a peak t e n s i o n a t
the i n t e r face.
However, f o r r e l a t i v e l y low y i e l d s c r e n g t h m a t e r i a l , r e v e r s e y i e l d i n g o c c u r s and t h e
peak r e s i d u a l t e n s i o n is t h e n (191, 0~ = 4Y/3.
REFERENCES
1.
C. C. Berndt and R. McPherson, S u r f a c e s and I n t e r f a c e s in Ceramic and
C e r a m i c / M e t a l S y s t e m s (Ed. J. A . P a s k and A. G. E v a n s ) Plenum, N.Y. (1981) p. 619.
2.
M. E. Twentyman and P. Hancock, S u r f a c e s and I n t e r f a c e s i n Ceramic and
Ceramic/Metal Systems, ibid., p. 535.
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M. F l o r j a n i c , W. Fader, M. & h l e and M. T u r w i t t , t h i s volume.
4.
D. G. Bogy, J. Appl. Mech.
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D. B. M a r s h a l l , A. G. E v a n s , B. T. Khuri-Yakub,
Proc. Roy. Soc.
(1983) 461.
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A. G. Evans, J. Am. Ceram. S o c .
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(1975) 93.
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(1982) 127.
J. W. T i e n a n d G. S. Kino,
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S. Timoshenko and J . N. Goodier, Theory of E l a s t i c i t y , McGraw H i l l (1951).
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F. Erdogan a n d G. D. Gupta, I n t . J. S o l i d s and S t r u c t u r e s ,
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T. K. O'Brien ASTM STP
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S. Schmauder, M. ~ i h l eand A. G. Evans, t o be published.
T. Suga, Ph.D.
(1984).
775
(1982) p.
1, (1971)
36.
140.
Thesis, Max Planck I n s t i t u t f u r Metallforschung, S t u t t g a r t
13 (1980)
A . Piva and E. Viola, Engng. Frac. Mech.
F. Erdogan, J. Appl. Mech.
2
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H. Vehoff and P. Neumann, Acta Met.
L. B. Freund and J. W.
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265.
Hutchinson, t o be published.
R . L. B e r t o l o t t i , J. Am.
Ceram. Soc.
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R. 0. R i t c h i e , B. F r a n c i s and W. L. Server, Met. Trans.
D. B. P a r s h a l l and B. R. Lawn, J. Am.
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63 (1980)
(1976) 831.
532.
R. H i l l , Theory o f P l a s t i c i t y , Oxford Univ. P r e s s (1950).
-
Fig. 11
Residual s t r e s s e s c r e a t e d by expansion o f an e l a s t i c s p h e r i c a l s h e l l i n t o
an e l a s t i c / p l a s t i c uatrix.