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Microhardness : fracture studies : high alumina cement systems
Beaudoin, J. J.
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!MICROHARDNESS-FRACTURE STUDIES:
HIGH ALUMINA CEMENT S Y S T E M
by J. J. Beaudoin
ANALYZED
Reprinted f r o m
Cement and Concrete R e s e a r c h
Vol. 12, 1982
P O289-299
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L I B R A R Y
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P7
B I B L I O T ~ ~ ~ Q U E
Rech. BS.irn.
CDBR P a p e r No. 1040
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CEMENT and CONCRETE RESEARCH. Vol. 1 2 , p p . 289-299, 1982. P r i n t e d i n t h e USA.
0 0 0 8 - 8 8 4 6 / 8 2 / 0 3 0 2 8 9 - 1 1 $ 0 3 . 0 0 / 0 Copyright ( c ) 1982 Pergamon P r e s s , L t d .
MICROHARDNESS-FRACTURE STUDIES: H I G H ALUMINA CEMENT SYSTEMS
J
.
J. BeaudoinD i v i s i o n of B u i l d i n g Research, Na t i o n a l Research Council of Canada, Ottawa Canada K1A OR6
(Cormunicated by F.H. Wittmann) (Recevied Oct. 20, 1981)
? i ~ r o h a r d n e s s and f r a c t u r e parameters of s e v e r a l high alumina cement p a s t e systems c o n t a i n i n g v a r y i n g p r o p o r t i o n s of hexagonal and c u b i c
y L - 3 2 3 have been determined u s i n g s i n g l e edge-notched f l e x u r a l foecimens from each system. Specimens were c o n d i t i o n e d and t e s t e d a t
lib p H i n a s p e c i a l l y c o n s t r u c t e d e n v i r o n m e n t a l chamber. Data
demonstrated dependence of the f r a c t u r e p a r a m e t e r s on microhardness
.
E f f e c t of morphology and o t h e r micros t r u c t u r a l f e a t u r e s on f r a c t u r e i nHAC p a s t e is a l s o d i s c u s s e d . Some e v i d e n c e s u p p o r t i n g argument f o r t h e v a l i d i t y of a p p l y i n g l i n e a r - e l a s t i c f r a c t u r e mechanics i n s t u d y i n g f r a c t u r e i n b r i t t l e c e m e n t i t i o u s systems i s p r e s e n t e d .
RESUME
p a r t i r d q C p r o u v e t t e s h encoche pCriphCrique s i m p l e pour e s s a i s de f l e x i o n , on a determind l e s parametres de m i c r o d u r e t g e t de r u p t u r e d e p l u s i e u r s s y s t3mes de p h t e de ciment alumineux c o n t e n a n t d i f f e r e n t e s p r o p o r t i o n s de phases hexagonales e t cubiques. Les Cprouve t t e s o n t Ct6 conditionnCes e t m i s e s h l ' e s s a i 2 11% d ' h u m i d i t g r e l a t i v e dans un c o n t e n a n t s p g c i a l e m e n t c o n s t r u i t
2
c e t ef f e t . Les donnCes o n t montrg que l e s p a r a m e t r e s d e r u p t u r e C t a i e n t f o n c t i o n de l a m i c r o d u r e t e . Onexamine a u s s i l ' e f f e t de l a morphologie e t a u t r e s c a r a c t C r i s t i q u e s de l a m i c r o s t r u c t u r e s u r l a r u p t u r e dans l a p a t e de ciment alumineux. On
prCsente d e s f a i t s venant c o r r o b o r e r l ' a r g u m e n t s e l o n l e q u e l il e s t
v a l a b l e d'employer l a mgcanique de r u p t u r e l i n C a i r e - C l a s t i q u e pour C t u d i e r l a r u p t u r e dans l e s s y s tPmes de l i a n t s f r a g i l e s .
I n t r o d u c t i o n
High alumina cement (HAC) c o n s i s t s of approximately e q u a l p a r t s of alumina and lime, a b o u t 40% each, w i t h f e r r o u s and f e r r i c o x i d e s and up t o 5% s i l i c a . I t comprises s e v e r a l phases, v i z . , CA, C % , C I 2 A 7 , C2AS, C2S, C2F and C,+AF, b u t the main c e m e n t i t i o u s compounds a r e CA and C12A7
.*
The h y d r a t i o n*In cement chemistry nomenclature: C = CaO, A = A1203, S = S i 0 2 , F = Fe20g, H = H20.
J . J . Beaudoin
Vol. 1 2 , No. 3
p r o d u c t s of CA c o n s i s t of CAH1
,,
,
C2A%, C 3 q and AH3 ( g e l o r c r y s t a l l i n e ) , t h e r e l a t i v e p r o p o r t i o n s depending on t h e hydra t i o n c o n d i t i o n s and c u r i n g p e r i o d . A t lower t e m p e r a t u r e s CAHIO and C 2 q ( b o t h hexagonal p h a s e s ) and AH3 g e l a r e p r e f e r e n t i a l l y formed, and a t h i g h e r t e m p e r a t u r e s a r e c o n v e r t e dt o C3AH6 and g i b b s i t e . Most a t t e m p t s t o e x p l a i n s t r e n g t h g a i n o r l o s s have r e l a t e d t o t h e r e l a t i v e amounts of calcium a l u m i n a t e h y d r a t e i n t h e h y d r a t e d p r o d u c t s . Formation of C 3 q has been a s s o c i a t e d w i t h s t r e n g t h d e c r e a s e , a l t h o u g h under c e r t a i n c o n d i t i o n s i n c r e a s e d s t r e n g t h has been o b t a i n e d ( 1 )
A p p l i c a t i o n s of HAC i n c l u d e s u l p h a t e - r e s i s t a n t cements, b o r e h o l e p l u g g i n g cements
,
f a s t-se t t i n g p a t c h i n g compounds, rock a n c h o r s , g r o u t i n g , c o l d t e m p e r a t u r e c o n c r e t i n g , and r e f r a c t o r i e s . R e c e n t l y , HAC has been used i n s t e a d of CaC12 a s a n a c c e l e r a t o r .I n t h e p a s t decade f i b r e - r e i n f o r c e d cement composites having a v a r i e t y of cement-based m a t r i c e s and o r g a n i c and i n o r g a n i c f i b r e s have proved p a r t i c u - l a r l y u s e f u l i n some r e p a i r a p p l i c a t i o n s . W i t h i n 24 h HAC d e v e l o p s high compressive s t r e n g t h and a p p e a r s t o be a good c a n d i d a t e f o r s u c h a p p l i c a - t i o n s . F i b r e - r e i n f o r c e d cement composites, when compared t o u n r e i n f o r c e d s y s tems, g e n e r a l l y have i n c r e a s e d f l e x u r a l s t r e n g t h and f r a c t u r e toughness, i . e . , r e s i s t a n c e t o c r a c k i n i t i a t i o n and p r o p a g a t i o n . As t h e m a t r i x p l a y s an i m p o r t a n t r o l e i n composite behaviour, knowledge of i t s f r a c t u r e p r o p e r t i e s is n e c e s s a r y f o r u n d e r s t a n d i n g t h a t behaviour. There i s , however, a d e a r t h of i n f o r m a t i o n on f r a c t u r e of non-portland cements and f o r HAC systems t h e r e a p p e a r t o be few p u b l i s h e d d a t a .
The p o s s i b i l i t y of u s i n g m i c r o h a r d n e s s measurements t o p r e d i c t f r a c t u r e mechanics parameters i n non-porous s o l i d s , e.g., soda-lime g l a s s , has been e x p l o r e d w i t h some s u c c e s s (2,3). The o b j e c t i v e of t h e p r e s e n t s t u d y was t o o b t a i n e x p e r i m e n t a l d a t a on t h e f r a c t u r e behaviour of HAC and t o i n v e s t i g a t e t h e p o s s i b l e dependence of s e v e r a l f r a c t u r e mechanics e x p r e s s i o n s ( c r i t i c a l v a l u e s of s t r e s s i n t e n s i t y f a c t o r , s t r a i n energy r e l e a s e r a t e , J - i n t e g r a l , work of f r a c t u r e ) on microhardness.
I n d e n t a t i o n F r a c t u r e
T h i s s e c t i o n i s i n c l u d e d t o p r o v i d e a b a s i s f o r t h e e x p e c t a t i o n of a dependence of f r a c t u r e p r o p e r t i e s on microhardness. The p r i n c i p l e s and a p p l i c a t i o n s of i n d e n t a t i o n f r a c t u r e have been reviewed, p r i n c i p a l l y by Lawn and Wilshaw ( 4 ) and o n l y a few s a l i e n t p o i n t s w i l l be d i s c u s s e d . The c a r d i n a l f e a t u r e s of Lawn and Wilshaw's approach, upon which f r a c t u r e mechan- ics a n a l y s i s was based, a r e :
(1) t h e s h a r p p o i n t of t h e i n d e n t o r produces a n i n e l a s t i c d e f o r m a t i o n zone; ( 2 ) a deformation-induced f l a w suddenly d e v e l o p s i n t o a s m a l l c r a c k ( c a l l e d median v e n t ) on a p l a n e of symmetry c o n t a i n i n g t h e c o n t a c t a x i s ; ( 3 ) i n c r e a s e d l o a d c a u s e s f u r t h e r s t a b l e growth of t h e median v e n t ;
(4)
on u n l o a d i n g t h e median v e n t d o e s n o t c o m p l e t e l y c l o s e and l a t e r a l v e n t s begin t o develop. F i g u r e 1 i l l u s t r a t e s v e n t c r a c k f o r m a t i o n under a s h a r p i n d e n t o r ( 4 ) . C a l c u l a t i o n s approximating t h e s t r e s s f i e l d b e n e a t h t h e i n d e n t o r by a Boussinesq e l a s t i c f i e l d ( e x c l u d i n g t h e small d i s t u r b e d zone b e n e a t h t h e i n d e n t o r ) where t h e d e p t h of t h e median v e n t , c , i s much g r e a t e r t h a n t h e d e p t h of t h e d i s t u r b e d zone r e s u l t i n t h e f o l l o w i n g e x p r e s s i o n f o r s t r a i n energy r e l e a s e r a t e :G = (1-v2) [ ( ~ - ~ v ) ~ / u T ~ ] ( a / f i 2 ) (HIE) P/c
Vol. 1 2 , No. 3
MICROHARDNESS, FRACTURE, ALUMINATE CEMENT
FIG. 1
Schematic of Lawn's model of v e n t c r a c k f o r m a t i o n under p o i n t i n d e n t a t i o n . Dark r e g i o n is i n e l a s t i c d e f o r m a t i o n zone ( 2 )
of e l a s t i c i t y , H is m i c r o h a r d n e s s , P i s a p p l i e d l o a d and a and 0 a r e
d i m e n s i o n l e s s g e o m e t r i c a l f a c t o r s .
The r a t i o P / c h a s been found t o be c o n s t a n t . For many porous c e m e n t i t i o u s m a t e r i a l s E and H a r e e m p i r i c a l l y r e l a t e d by a n e x p r e s s i o n of t h e form E = kHn (k and n a r e c o n s t a n t s ) ( 5 ) . Thus, i t might be e x p e c t e d from e q . (1) t h a t G would b e r e l a t e d t o m i c r o h a r d n e s s through a power law r e l a t i o n . I t i s assumed t h a t t h e c r a c k is i d e a l l y Hookean and t h a t l i n e a r e l a s t i c i t y t h e o r y a p p l i e s , and, t h e r e f o r e , l i n e a r e l a s t i c f r a c t u r e mechanics (LEFM)
.
A p p l i c a t i o n of F r a c t u r e Mechanics t o Cement P a s t e Sys tems The m a j o r i t y of f r a c t u r e mechanics s t u d i e s of cement p a s t e s y s t e m s , u s u a l l y p o r t l a n d cement p a s t e , have been conducted i n t h e l a s t decade (6). D a t a a r e o f t e n c o n f l i c t i n g , and t h e r e i s d i s a g r e e m e n t c o n c e r n i n g t h e a p p l i c a - b i l i t y of LEFM and t h e r e l a t i v e m e r i t s of e x p r e s s i o n s d e s c r i b i n g f r a c t u r e behaviour. There
i s
a l s o d i s a g r e e m e n t c o n c e r n i n g t h e c r a c k p r o p a g a t i n g mechanism i n c e m e n t i t i o u s m a t e r i a l s . The b a s i c i s s u e is one of b r i t t l e n e s s v e r s u s d u c t i l i t y i n t h e c r a c k t i p zone. There a r e two major s c h o o l s of thought. One assumes a n i d e a l l y s h a r p c r a c k i n which f r a c t u r e p r o c e e d s by p r o g r e s s i v e r u p t u r e of c o h e s i v e bonds a c r o s s a s e p a r a t i o n p l a n e , c r e a t i n g new s u r f a c e a r e a i n a r e v e r s i b l e manner. The o t h e r s c h o o l p o s t u l a t e s t h a t t h e macroscopic " p l a s t i c - z o n e " c o n c e p t d e s c r i b i n g t h e c r a c k t i p r e g i o n of some metals and polymersis
a p p l i c a b l e t o ceramic m a t e r i a l s on a m i c r o s c a l e . The c o n t r o v e r s y remains u n r e s o l v e d . There a p p e a r s t o be, however, a u n i v e r s a l concensus t h a t , whatever t h e e x t e n t of t h e v a l i d i t y of LEFM t o b r i t t l e f r a c - t u r e , t h e i n f o r m a t i o n g a t h e r e d h a s been v a l u a b l e i n b o t h c h a r a c t e r i z i n g m a t e r i a l s and p r o v i d i n g i n p u t t o t h e d e s i g n p r o c e s s .Some c r i t i c s have s u g g e s t e d t h a t f r a c t u r e terms c a l c u l a t e d u s i n g maximum l o a d v a l u e s ( o b t a i n e d from l o a d - d e f l e c t i o n c u r v e s ) a r e e s s e n t i a l l y i n d i c a t o r s of r e s i s t a n c e t o c r a c k " i n i t i a t i o n " and d o n o t n e c e s s a r i l y a s s e s s r e s i s t a n c e t o c r a c k "propagation." The t o t a l work of f r a c t u r e , however, determined by i n t e g r a t i o n of b o t h a s c e n d i n g and d e s c e n d i n g b r a n c h e s of l o a d - d e f l e c t i o n t r a c e , r e f l e c t s r e s i s t a n c e t o b o t h c r a c k i n i t i a t i o n and p r o p a g a t i o n . I n t e g r a t i o n of a r e a s u n d e r t h e a s c e n d i n g b r a n c h only r e f l e c t s r e s i s t a n c e t o c r a c k i n i t i a t i o n . E x p e r i m e n t a l M a t e r i a l s
The c o m p o s i t i o n of t h e HAC was a s f o l l o w s : A1203 = 40.02%; Fe203 = 17.71%; CaO = 37.26%; Si02 = 3.46%; MgO = 0.91%; SO3 = 0.08%; Na20 = 0.08%; K20 = 0.08%. B l a i n e f i n e n e s s was 394 &/kg.
V o l . 1 2 , No. 3
J
.
J.
BeaudoinE i g h t s e r i e s of samples were prepared. Each c o n s i s t e d of a s e t of samples f o r t h e f o l l o w i n g waterlcement r a t i o s : 0.25, 0.30, 0.35, 0.40, 0.45 and 0.50. Mixes were c a s t i n moulds 1.2 x 7.5 x 20 cm t h a t were f i t t e d w i t h m e t a l shims 0.6 x 0.025 cm t h i c k ( r u n n i n g t h e l e n g t h of t h e mould) t o p r o v i d e a p r e c a s t c r a c k i n t h e specimen. The samples were removed a f t e r 3 d a y s a t 100% RH and sawn a t 0.127 cm i n t e r v a l s a l o n g t h e i r l e n g t h t o produce t h e f i n a l t e s t specimens. Thus, t h e t e s t p i e c e was a beam 1.2 cm deep x 0.127 cm t h i c k x 7.5 cm long w i t h a mid-span n o t c h 0.025 cm wide x 0.6 cm deep. A l l
beam samples were s t o r e d a t 11% RH f o r a minimum of 14 d a y s p r i o r t o t e s t i n g o r p r e t r e a t m e n t . * Various t r e a t m e n t s a r e summarized i n Table I. T h e i r o b j e c t i v e was t o produce systems having v a r i e d amounts of hexagonal and c u b i c phases.
The systems were c h a r a c t e r i z e d u s i n g a d i f f e r e n t i a l s c a n n i n g c a l o r i m e t e r (DSC). Within e a c h s e r i e s t h e r a t i o of peak h e i g h t s a t approximately 300 and 140 t o 155OC was k e p t constant.** Endothermic peaks a t 300 and 140 t o 155OC r e p r e s e n t t h e thermal decomposition of c u b i c and hexagonal p h a s e s ,
r e s p e c t i v e l y . I n s e r i e s 1 t o 5 t h e peak a t 140 t o 155'C d e c r e a s e d w i t h l e n g t h of h e a t t r e a t m e n t a t 80°C due t o d e h y d r a t i o n of CAHL0.
Technique DSC
D i f f e r e n t i a l thermograms of t h e samples were o b t a i n e d by DSC s u p p l i e d a s a module t o Du Pont 900 thermal a n a l y s i s system. T h i s u n i t u t i l i z e s chromel- cons t a n t a n thermocouples f o r d i f f e r e n t i a l t e m p e r a t u r e measurement. The r e f e r e n c e m a t e r i a l was i g n i t e d cr-A1203 and t h e h e a t i n g r a t e 20°C
min-l .
The d i f f e r e n t i a l temperature was r e g i s t e r e d a t a s e n s i t i v i t y of 0.02 mV in.'l. Thermograms were o b t a i n e d i n a i r , and i n e a c h e x p e r i m e n t 20 mg of t h e sample was s u b j e c t e d t o a n a l y s i s .Microhardness
Hardness was measured w i t h a L e i t z m i n i l o a d t e s t e r i n a c o n d i t i o n e d box (11% RH) f r e e of C02 u s i n g t h e Vickers pyramid i n d e n t o r . F i v e d e t e r m i n a t i o n s were performed on t h e s u r f a c e of e a c h sample.
F r a c t u r e T e s t i n g
An e n v i r o n m e n t a l chamber (Fig. 2) was mounted on t h e cross-head of an I n s t r o n t e s t i n g machine (10,000 kg c a p a c i t y ) . Notched beam specimens c o n d i t i o n e d t o 11% RH were simply supported i n i t and loaded a t t h e mid- p o i n t . The mid-span d e f l e c t i o n was measured u s i n g an LVDT w i t h a r e a d o u t a c c u r a t e t o 0.0001 mm. The cross-head s p e e d was 0.005 mm/min. Load- d e f l e c t i o n c u r v e s were o b t a i n e d from t h e I n s t r o n c h a r t r e c o r d s ; t h e maximum l o a d s were g e n e r a l l y l e s s t h a n 1 kg ( t h e s t i f f n e s s of t h e I n s t r o n machine is extremely l a r g e r e l a t i v e t o t h e f l e x u r a l s t i f f n e s s of t h e t e s t p i e c e s ) .
* S t r e n g t h and f r a c t u r e of hydrated cements a r e humidity dependent. The 11% RH c o n d i t i o n minimizes t h e r i s k of c a r b o n a t i o n , f u r t h e r h y d r a t i o n , e x c e s s volume change and i s a c o n v e n i e n t r e f e r e n c e s t a t e .
**This was achieved by p r e - s e l e c t i n g t r e a t m e n t times from t h e r e s u l t s of time s e q u e n t i a l DSC r u n s , i . e . , t r e a t m e n t times f o r samples were i n c r e a s e d i n c r e m e n t a l l y u n t i l t h e d e s i r e d DSC peak r a t i o was a t t a i n e d .
Vol. 1 2 , No. 3 293 MICROHARDNESS, FRACTURE, ALUMINATE CEMENT
TABLE I D e s c r i p t i o n of Sample Treatments f o r F r a c t u r e S t u d i e s S e r i e s Treatment 100% RH, 3 d; 11% RH, 21°C 100% RH, 3 d; 11% RH, 21°C; vacuum 3 h, 80°C; 11% RH 100% RH, 3 d; 11% RH, 21°C; vacuum 6 h, 80°C; 11%
RH
100% RH, 3 d ; 11% RH, 21°C; vacuum 24 h, 80°C; 11% RH 100% RH, 3 d ; 11% RH, 21°C; vacuum 21 d, 80°C; 11% RH 100% RH, 3 d; 11% RH, 21°C; 100% RH, 80°C; 11%RH
100% RH, 3 d; 11%RH,
21°C; 100% RH, 80°C; 11%RH
100% RH, 3 d; 11% RH, 2 1 ' ~ ; a u t o c l a v e d , 216OC; 11% RH Very l i t t l e c u b i c phase Mostly hexagonal i n o r d e r 1 2 3 4 5Cubic and hexagonal approximately e q u a l Approx. 80% c u b i c 20% hexagonal Mostly c u b i c
*For s e r i e s 6 and 7 t h e times a t 100% RH, 80°C, v a r i e d w i t h water/cement r a t i o from a b o u t 1 0 t o 25 min. S e r i e s 7 was
t r e a t e d f o r l o n g e r p e r i o d s .
**Approximations made by e s t i m a t i n g DSC peak h e i g h t s a t 300°C
'allowing i s a d e s c r i p t i o n of the e x p r e s s i o n s d e f i n i n g t h e c o n d i t i o n s of i r a c t u r e and t h e i r method of d e t e r m i n a t i o n from l o a d - d e f l e c t i o n curves: 1 Kc: S t r e s s i n t e n s i t y f a c t o r , K, has been d e s c r i b e d a s a s i n g l e -
parameter d e s c r i p t i o n of t h e s t r e s s and d i s p l a c e m e n t f i e l d s i n t h e r e g i o n of t h e c r a c k t i p . The c r i t i o a l s t r e s s i n t e n s i t y f a c t o r , Kc, i s t h e v a l u e of K f o r u n s t a b l e f r a c t u r e .
For mid-point l o a d i n g of s i n g l e e d g e n o t c h e d f l e x u r a l specimens ( 7 ) Kc = Y 312 (pmaxt%/(b.d2)
where
Y = 1.93
-
3.07 a / d+
14.53 (a/d12-
25.11 ( a ~ d ) ~+
25.8 ( a / d ) 4 Pmax = maximum l o a d ; t = l e n g t h of beam; a = l e n g t h of notch;2 9 4 J . J . Beaudoin Vol. 1 2 , No. 3 FIG. 2 F r a c t u r e - t e s t i n g a r r a n g e m e n t showing e n v i r o n m e n t a l chamber mounted on cross-head of I n s t r o n machine ( 2 ) Gc: S t r a i n e n e r g y r e l e a s e r a t e , G , i s a m a t e r i a l c o n s t a n t d e p e n d i n g on t h e p h y s i c a l p r o c e s s e s o c c u r r i n g a t t h e c r a c k t i p and i s e q u a l t o t w i c e t h e f r a c t u r e s u r f a c e e n e r g y p e r u n i t a r e a . C r i t i c a l s t r a i n e n e r g y r e l e a s e r a t e i s d e s i g n a t e d Gc. The dependence of c o m p l i a n c e ( r a t i o of c e n t r e - s p a n d e f l e c t i o n t o l o a d ) on c r a c k l e n g t h was d e t e r m i n e d a t e a c h w a t e r l c e m e n t r a t i o f o r e v e r y s e r i e s . For a g i v e n c r a c k l e n g t h s a m p l e s w e r e l o a d e d t o a b o u t 70% of t h e maximum d u r i n g e a c h l o a d i n g c y c l e . A f t e r a compliance d e t e r m i n a t i o n t h e c r a c k was e x t e n d e d u s i n g a saw and t h e c o m p l i a n c e f o r t h e new c r a c k was d e t e r m i n e d . Gc was c a l c u l a t e d a c c o r d i n g t o t h e f o l l o w i n g e x p r e s s i o n :
Gc =
PL,
( d ~ / d a ) 12b wherePmax = maximum l o a d ; C = compliance; a = c r a c k l e n g t h ;
b = beam w i d t h .
(3) Jc: J i s a p a t h i n d e p e n d e n t l i n e i n t e g r a l d e s c r i b i n g t h e c r a c k t i p s t r e s s - s t r a i n f i e l d i n t e n s i t y u n d e r e l a s t i c - p l a s t i c c o n d i t i o n s . For e l a s t i c b o d i e s t h e c r i t i c a l v a l u e of J - i n t e g r a l e q u a l s Gc, i . e . ,
Jc = Gc.
T h i s c a l c u l a t i o n r e q u i r e s load-def lec t i o n c u r v e s f o r b o t h n o t c h e d and u n n o t c h e d samples.
where
An = a r e a u n d e r l o a d - d e f l e c t i o n c u r v e u p t o maximum l o a d , P,, f o r n o t c h e d sample;
Vol.
12,
No. 3MICROHARDNESS, FRACTURE, ALUMINATE CEMENT
Au = a r e a u n d e r l o a d - d e f l e c t i o n c u r v e of t h e unnotched sample up
t o t h e maximum l o a d , P,,, which was determined f o r t h e
n o t c h e d sample;
b = specimen width.
( 4 ) Work of f r a c t u r e , yT: T h i s term i s d e t e r m i n e d by d i v i d i n g t h e a r e a u n d e r t h e t o t a l l o a d - d e f l e c t i o n c u r v e by t h e a r e a of t h e uncracked beam l i g a m e n t ( b . { d - a ) ) . y~ r e p r e s e n t s t h e work of f r a c t u r e f o r c r a c k i n i t i a t i o n and p r o p a g a t i o n . The a r e a u n d e r t h e a s c e n d i n g p o r t i o n of t h e l o a d - d e f l e c t i o n c u r v e c a n a l s o be d e t e r m i n e d , and when t h i s a r e a i s d i v i d e d by t h e uncracked l i g a m e n t a r e a a n e s t i m a t e of t h e work of f r a c t u r e f o r c r a c k i n i t i a t i o n , y
i,
i s o b t a i n e d . FIG. 3 P l o t of s t r e s s i n t e n s i t y f a c t o r ,E
Kc v e r s u s microhardness f o r2
20 v a r i o u s HAC p r e p a r a t i o n s + 5 V) V) u, E VI 20 30 40 50 60 70 80 90 !OOMICROHARDNESS. H x lo-', MPa
O b s e r v a t i o n s Dependence of F r a c t u r e Terms on Microhardness
F r a c t u r e t e r m s , K c , G c , J C a n d y T , a r e p l o t t e d a g a i n s t
m i c r o h a r d n e s s , H, f o r s e r i e s 1-8 p r e p a r a t i o n s ( F i g s . 3-6). There is a l i n e a r dependence of l o g a r i t h a s on m i c r o h a r d n e s s f o r many of t h e terms; some depen- dences a r e non-linear. R e g r e s s i o n a n a l y s i s f o r t h e l i n e a r c u r v e s i s presen- t e d i n T a b l e 11, and c a n g e n e r a l l y be d e s c r i b e d a s f o l l o w s : semi-log p l o t s of Kc, Gc and Jc v e r s u s H f o r s e r i e s 1 t o 4 a r e l i n e a r , and v a l u e s of
t h e s e terms i n c r e a s e w i t h microhardness. One c u r v e f o r e a c h f r a c t u r e term
f i t s t h e d a t a f o r s e r i e s 1 t o 4. A semi-log p l o t of y, v e r s u s H f o r s e r i e s 1 i s a l s o l i n e a r . A l l o t h e r l o g y v e r s u s H c u r v e s ( s e g i e s 2 t o 8 ) a r e non- l i n e a r and i n c r e a s e t o a maximum v a l u e , t h e n d e c r e a s e a s H i n c r e a s e s . The l o g
(
K c,
J c,
Gc, yT) v e r s u s H c u r v e s f o r s e r i e s 5 a r e n o n - l i n e a r andg e n e r a l l y i n c r e a s e t o a maximum v a l u e a s H i n c r e a s e s ; f o r yT and Gc they
s u b s e q u e n t l y d e c r e a s e w i t h i n c r e a s i n g H. The c u r v e , l o g K, v e r s u s H f o r
s e r i e s 8, i s l i n e a r and l o g
K,
i n c r e a s e s w i t h H. Log ( J c , Gc, Y ~ )f o r system 8 i n c r e a s e s , however, t o a maximum and t h e n d e c r e a s e s a s h a r d n e s s
i n c r e a s e s . Log ( K ~ , Gc, Jc) v e r s u s H c u r v e s f o r s e r i e s 6 and 7 a r e
a l s o l i n e a r and e a c h c u r v e has a g r e a t e r s l o p e t h a n t h e c u r v e f o r s e r i e s 1 t o 4.
J . J . Beaudoin Vol. 1 2 , No. 3 I I I t r J . . I I 1 1 -1 : ; i'd
-
7 . . N E 30-
U C ) - 2 0 - C 4 (LHIGH ALUMINA CEMENT
.
I m 2 A 3 v 4 1 . 1 ~ [ I I I I I 0 10 20 30 40 5 0 60 70 80 90 100 FIG.4
P l o t of s t r a i n energy r e l e a s e r a t e v e r s u s microhardness f o r v a r i o u s KAC p r e p a r a t i o n s MICROHARONESS. H x l o - ' , MPa D i s c u s s i o nI n t h i s s t u d y f r a c t u r e terms ( K c Gc, J,) f o r HAC systems a r e dependent: on microhardness, i n agreement w i t h measurement of i n d e n t a t i o n f r a c t u r e of non-porous ceramic bodies. Hydrated
HAC
s y s tems c o n t a i n i n g m i x t u r e s of hexagonal p h a s e s and c u b i c p h a s e s had l a r g e r i n c r e a s e s i n t h e s e f r a c t u r e terms f o r an e q u i v a l e n t microhardness change than t h e s y s tems c o n s i s t i n g mainly of hexagonal p h a s e s alone.A p o s s i b l e e x p l a n a t i o n of t h i s behaviour i s t h a t t h e d e n s e r c u b i c phase ( d e n s i t y of C AH6 = 2.52; CAH = 1.75) o c c u r s a s f i n e l y d i s p e r s e d i n c l u s i o n s t h a t modify t i e s t r e s s f i e l d i n t h e m a t e r i a l and a c t a s c r a c k a r r e s t o r s . The ( K c G,, J,) v e r s u s microhardness c u r v e s f o r t h e mixed morphology p r e p a r a t i o n s c r o s s t h e c u r v e s f o r p r e p a r a t i o n s c o n s i s t i n g mainly of hexagonal phases. A t lower m i c r o h a r d n e s s v a l u e s mixed morphology systems have lower f r a c t u r e v a l u e s , p o s s i b l y owing t o t h e r e l a t i v e e a s e of c r a c k i n i t i a t i o n and p r o p a g a t i o n through weak a r e a s a t p o i n t s of i n t e r p a r t i c l e c o n t a c t .
The r a t e of change of Kc w i t h h a r d n e s s f o r t h e p r e p a r a t i o n c o n t a i n i n g mainly c u b i c phase i s a l s o g r e a t e r t h a n t h e mainly hexagonal systems. Gc and Jc f o r t h e c u b i c m a t e r i a l i n c r e a s e w i t h h a r d n e s s i n t h e same manner a s do the mixed morphology systems, b u t d e c r e a s e a t h i g h e r microhardness v a l u e s . The d e c r e a s e may be due t o pore-crack, i n t e r a c t i o n . F r a c t u r e toughness may be dependent on c r a c k - a r r e s t i n g p r o p e r t i e s of p o r e s a s w e l l a s on t o t a l p o r o s i t y (8). Values of Kc f o r some porous c e r a m i c s , e.g., b e r y l l i u m , i n c r e a s e t o a maximum and t h e n d e c r e a s e a s s t r e n g t h i n c r e a s e s ( 9 ) .
Vol. 1 2 , No. 3 297 MICROHARDNESS, FRACTURE, ALUMINATE CEMENT
TABLE I1 R e g r e s s i o n A n a l y s i s of Fracture-Microhardness Data S e r i e s R e g r e s s i o n C o r r e l a t i o n E q u a t i o n C o e f f i c i e n t ( r ) 1-4 K, = 16.86 exp (0.019) H G, = 1.88 exp (0.041)
H
J, = 4.29 exp (0.027) H 1 y~ = 6.12 exp (0.026)H
6 K, =9.33
exp (0.060)H
7 K, = 2.08 exp (0.101)H
8K,
= 14.45 exp (0.046)H
6 Gc = 0.51 exp (0.104) H 7 Gc = 0.71 exp (0.099)H
6,7 J, = 0.19 exp (0.124) H 100 9 0 - I II
'
I I' -
80-
70-
60-
50-
00-
7 ! I . U-
20-
i i 1. I i a a C3 Y,-
Z-
.
NUMBERS REFER TO H l G H ALUMINA CEMENT ' t I 2 4-
a 3-
. 4 3 1 I f l I I I I I 0 10 20 30 40 50 60 70 80 90 100 VARIOUS PREPARATIONS OF HlGH ALUMINA CEMENTM I C R O H A R D N E S S , H x lo-', M P a M I C R O H A R D N E S S , H x lo-', MPa
FIG. 5 FIG. 6
P l o t of J - i n t e g r a l v e r s u s P l o t of work of f r a c t u r e v e r s u s microhardness f o r v a r i o u s m i c r o h a r d n e s s f o r v a r i o u s HAC
Vol. 1 2 , No. 3 3.5. Beaudoin
1 -1
HIGH ALUMINA CEMENT PREPARATIONS
-
-
SERIES-
1 m 2-
A 3 v 4 0 5-
0 6 A 7 V 8-
-
REGRESSION LINE Jc= 5.07 + 0.70 G, FIG. 7 P l o t of J - i n t e g r a l v e r s u s s t r a i n energy r e l e a s e r a t e f o r v a r i o u s HAC p r e p a r a t i o n s S T R A I N E N E R G Y R E L E A S E R A T E , G c . J l m 2I t i s a p p a r e n t t h a t i n cement s y s terns micros t r u c t u r a l f e a t u r e s , e.g., p o r o s i t y , pore s t r u c t u r e , d e n s i t y , c r y s t a l l i n i t y and morphology, may a f f e c t
t h e dependence of t h e f r a c t u r e terms on microhardness. Two p i e c e s of e v i d e n c e s u p p o r t t h e a p p l i c a t i o n of l i n e a r f r a c t u r e mechanics and t h e bond r u p t u r e p r o c e s s f o r t h e m a t e r i a l s s t u d i e d .
(1) Measured v a l u e s of G, f o r c e r a m i c m a t e r i a l s and f o r t h e HAC systems s t u d i e d approach v a l u e s of 2-y w i t h i n a f a c t o r of two o r t h r e e ( s e e T a b l e 111). Gc is s e v e r a l o r d e r s of magnitude i n e x c e s s of 2y f o r m e t a l l i c and polymeric m a t e r i a l s , which f r a c t u r e a c c o r d i n g t o a p l a s t i c c r a c k - t i p s e p a r a t i o n p r o c e s s . ( 2 ) I d e a l l y , i f l i n e a r e l a s t i c p r o c e s s e s a r e i n v o l v e d i n f r a c t u r e , Jc = Gc. F i g u r e 7 i s a p l o t of Jc v e r s u s Gc f o r t h e HAC s y s t e m s . The d a t a p o i n t s a r e p o s i t i o n e d a b o u t t h e " l i n e of e q u a l i t y . " R e g r e s s i o n a n a l y s i s g i v e s a l i n e , Jc = 5.07
+
0.700 Gc w i t h c o r r e l a t i o n c o e f f i c i e n t = 79.3%. TABLE 111 R a t i o of ~ , / y f o r V a r i o u s M a t e r i a l s Reference M a t e r i a l s HAC S e r i e s * - - - - *Values f o r e a c h s e r i e s a r e a v e r a g e v a l u e s f o r v a r i o u s w/c p r e p a r a t i o n sVol. 12, No. 3
MICROHARDNESS, FRACTURE, ALUMINATE CEMENT
Conclusions
1. There i s a r e l a t i o n between f r a c t u r e b e h a v i o u r of high alumina cement systems and microhardness. T h i s means t h a t i t may be p o s s i b l e t o e s t i m a t e t h e v a l u e s of t h e f r a c t u r e terms from microhardness measurements.
2. The r e l a t i o n between t h e f r a c t u r e terms and microhardness i s dependent on t h e morphology of t h e h y d r a t i o n p r o d u c t s .
3. Mixed morphology (hexagonal and c u b i c p h a s e s ) systems have g r e a t e r
f r a c t u r e toughness than systems c o n t a i n i n g mainly hexagonal phases e x c e p t a t low v a l u e s of microhardness.
4. Non-linear r e l a t i o n s between l o g a r i t h n s of work of f r a c t u r e and micro- hardness a r e o b t a i n e d f o r most systems. N o n - l i n e a r i t y may r e s u l t from energy d i s s i p a t i o n p r o c e s s e s due t o pore-crack i n t e r a c t i o n .
5. Approximate e q u i v a l e n c e of J - i n t e g r a l and s t r a i n energy r e l e a s e r a t e s u p p o r t s t h e assump t i o n t h a t l i n e a r e l a s t i c f r a c t u r e mechanics i s a p p l i c - a b l e high alumina cement p a s t e s y s terns.
References
1. V.S. Ramachandran and R.F. Feldman. Cem. Concr. Res.
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729 (1973)- 2.B.
Lawn and E.R. F u l l e r . J. Mats. Sci.,10,
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B.
Lawn and M. Swain. J. Mats. Sci.,10,
113 (1975). 4.B.
Lawn and R. Wilshaw. J. Mats. S c i . , 1 0 , 1 0 4 9 (1975).5.
J.J. Beaudoin and R.F. Feldman. Cem. Concr. Res.5,
103 (1975).6. S. Mindess. Mats. Res. Ser. ( 2 ) , U n i v e r s i t y of B r i t i s h Columbia, p. 95 (1981).
7.
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Gross and J. Srawley. ASTM STP 410, 1 3 (1966).8. R.W. Rich. I n T r e a t i s e on M a t e r i a l s S c i e n c e and Technology, Vol. 11, Acad. P r e s s , Chapt. 4, 1977, p. 200, (ed. by R.K. MacCrone).
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Acknowledgement
The a u t h o r a c k n w l e d g e s t h e s k i l f u l a s s i s t a n c e of J. Wood i n c o n d u c t i n g t h e e x p e r i m e n t a l work.
T h i s paper is a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research Council of Canada, and i s p u b l i s h e d w i t h t h e a p p r o v a l of
