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The fracture behaviour of fibre reinforced concrete
CEMENT and CONCRETE RESEARCH. V o l . 2, pp. 447-461, 1972. Pergamon Press, Inc. Printed in the United States.
THE F R A C T U R E B E H A V I O U R OF F I B R E R E I N F O R C E D C O N C R E T E
B. H a r r i s , J. V a r l o w and C. D. E l l i s S c h o o l of A p p l i e d S c i e n c e s , U n i v e r s i t y of S u s s e x , B r i g h t o n ,
U. K.
(Communicated by A. M. Neville)
ABSTRACT T h e w o r k of f r a c t u r e , YF, and the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r Kc, have b e e n d e t e r m i n e d f o r the f a i l u r e in b e n d i n g of n o t c h e d s a m p l e s of s a n d / c e m e n t m o r t a r r e i n f o r c e d with s h o r t , r a n d o m l y d i s t r i b u t e d f i b r e s of g l a s s , h i g h c a r b o n s t e e l , and m i l d s t e e l . R e s u l t s w e r e o b t a i n e d on wet and d r y s t o r e d m a t e r i a l a f t e r 7 w e e k s and a g a i n a f t e r 6 m o n t h s c u r i n g . T h e r e is c l e a r e v i d e n c e that the h i g h e s t f r a c t u r e r e s i s t a n c e is o b t a i n e d in the long t e r m by r e i n f o r c e m e n t with m i l d s t e e l . H o w e v e r , w h e r e a s the w o r k of f r a c t u r e of plain c o n c r e t e c a n be i n c r e a s e d by two o r d e r s of m a g n i tude by a d d i n g a s little a s 2 vol. % of s t e e l w i r e s , the m o r e c r i t i cal p a r a m e t e r K c is i n c r e a s e d at m o s t by a f a c t o r of 2. G l a s s f i b r e r a i s e s YF by a f a c t o r of only 40. T h e e x p e r i m e n t a l v a l u e s of "(F f o r w i r e r e i n f o r c e d c o n c r e t e a r e c o m p a r e d with t h e o r e t i c a l e s t i m a t e s b a s e d on c o n s i d e r a t i o n s of f i b r e p u l l - o u t and f i b r e d e formation.
Die B r u c h a r b e i t ~(F und d e r K e r b s p a n n u n g s f a c t o r Kc ftir B i e g e b e l a s t u n g w u r d e ftlr a n g e k e r b t e W e r k s t t i c k e a u s m i t statistisch verteilten Glas-und Stahlfasern verst~irktem Beton b e s t i m m t . M e s s u n g e n w u r d e n n a c h 7 W o c h e n sowie n a c h 6 M o n a t e n T r o c k e n - u n d F e u c h t l a g e r u n g d u r c h geftlhrt. Ganz o f f e n s i c h t l i c h w i r d d i e h~Schste B r u c h f e s t i g k e i t auf lange Sicht bei Verst~irkung m i t W e i c h s t a h l e r z i e l t . W~lhrend j e d o c h die B r u c h a r b e i t von g e w b h n l i c h e m B e t o n d u t c h g e r i n g e Zus/ttze yon 2 V o l u m e n p r o z e n t S t a h l d r a h t u m zwei G r S s s e n o r d n u n g e n e r h S h t w e r d e n kann, w i r d d e r n o c h w i c h t i g e r e K e r b s p a n n u n g s f a k t o r h S c h s t e n s v e r d o p p e l t . D u r c h G l a s f a s e r n w i r d ~(F n u r auf d a s v i e r z i g f a c h e e r h S h t . Die f[ir d r a h t v e r s t ~ i r k t e n B e t o n g e m e s s e n e n W e r t e yon YF w e r d e n m i t t h e o r e t i s c h e n Absch~ttzungen in d e n e n d a s H e r a u s z i e h e n und d i e D e f o r m a t i o n d e r F a s e r n b e r [ i c k s i c h t i g t ist, v e r g l i c h e n . 447
448
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE Introduction If c o n c r e t e is to r e m a i n a cheap s t r u c t u r a l m a t e r i a l , r e i n f o r c e m e n t with strong
f i b r e s may only be feasible if s m al l volume f r a c t i o n s of fibre a r e used and if the addition of the f i br es does not entail s e r i o u s modifications to o n - s i t e p r e p a r a t i o n methods.
Two or t h r e e p e r c e n t by volume of chopped glass or s t e e l w i r e s is about
all that can be s a t i s f a c t o r i l y i n c o r p o r a t e d into c o n c r e t e by o r d i n a r y mixing methods, and the r e s u l t i n g m a t e r i a l may contain e i t h e r a r a n d o m or a pl anar random d i s t r i b ution.
T h e r e is also a limit to the lengths of fibre that can be so i n c o r p o r a t e d ,
since f o r a given d i a m e t e r the w i r e s or f i b r e s must not b e c o m e so flexible that they a r e e a s i l y tangled.
Depending upon the f i b r e / c o n c r e t e bond strength, then, the only
additions that can e a s i l y be made in p r a c t i c e may well t u r n out to be ineffective as fibre s t r e n g t h e n e r s .
F r o m the f r a c t u r e toughness point of view, however, even
f i b r e s that a r e too short to s t r engt hen the c o n c r e t e can, by c r a c k a r r e s t and fibre pull-out, contribute significantly to the m e a s u r e d w ork of f r a c t u r e .
We r e p o r t h e r e
s o me e x p e r i m e n t s in which f r a c t u r e m e c h a n i c s methods have been used to study the toughening of sand/cement= m o r t a r by additions of chopped s t e e l w i r e s and glass f i b r e s , and we c o m p a r e the r e s u l t s with some r e c e n t t h e o r e t i c a l studies of fibre reinforcement.
E x p e r i m e n t a l Work
The mix u s e d throughout this w or k was of fine sand and P o r t l a n d c e m e n t in the weight r a t i o 3 : 1 with a c e m e n t : w a t e r r a t i o of 3 : 2.
T hi s composition was the
d r i e s t m o r t a r that could subsequently be mixed without difficulty with 2% by volume of g las s o r s t e e l f i b r e s .
The c u r e conditions for the basi c m o r t a r w e r e studied by
c o m p r e s s i o n testing c y l i n d r i c a l s a m p l e s 2. 5 c m in d i a m e t e r by 2.5 c m high which had been cas t to shape f r o m s m a l l batch m i x e s in wooden moulds.
These were
r e m o v e d f r o m the moulds a f t e r 24 hours: some w e r e then left to c u r e in a i r , some w e r e s t o r e d in w a t e r , and some w e r e o v e n - c u r e d at 50°C.
Samples c u r e d up to
70 days w e r e c o m p r e s s i o n - t e s t e d between l ubri cat ed s t e e l platens at a s t r a i n - r a t e of 10-3 s e c - 1 The r e s u l t s of t hes e t e s t s , shown in figure 1, suggested that a f t e r 45 days the r a t e of change of s t r engt h of the w a t e r - c u r e d m a t e r i a l was s m a l l enough to be ignored.
Vol. 2, No. 4
449 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE I
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FIG. 1 Compression strength of plain concrete as a function of curing t i m e . AI! toughness testing was t h e r e f o r e c a r r i e d out on samples aged for 7 weeks in the f i r s t instance.
It is commonly accepted that o r d i n a r y glass and steel fibres are
strongly attacked by a highly alkaline cement matrix, p a r t i c u l a r l y if free m o i s t u r e is present.
In o r d e r to study the deleterious effect of m o i s t u r e , t h e r e f o r e , samples of
all m a t e r i a l s were stored, in w a t e r and in a i r , for a total of 6 months and subjected to a second s e r i e s of f r a c t u r e t e s t s identical with that c a r r i e d out on samples t e s t e d a f t e r 7 weeks. P r e p a r a t i o n of Materials A large batch of m o r t a r was p r e p a r e d in a r o t a r y m i x e r (10 minute mix) and then divided into parts.
One part was poured into a r e c t a n g u l a r ingot mould without any
fibre addition, and each of the remaining parts was s e p a r a t e l y r e t u r n e d to the m i x e r
450
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
f o r a f u r t h e r 5 m i n u t e s d u r i n g which t i m e a p r e - w e i g h e d b a t c h of f i b r e s of the r e q u i r e d kind w e r e s p r i n k l e d into the m o r t a r .
It was found a s long as the f i b r e s
w e r e w e l l s e p a r a t e d b e f o r e s p r i n k l i n g t h e y did not b a l l - u p o r s t i c k t o g e t h e r in the mixer.
A f t e r m i x i n g in the f i b r e s , t h e s e m i x e s w e r e a l s o c a s t into b a r m o u l d s .
A f t e r c a s t i n g the m o u l d s w e r e t a m p e d and t h e n v i b r a t e d f o r about 2 m i n u t e s . A c o n s e q u e n c e of this m e t h o d of p r e p a r a t i o n was that the f i b r e s t e n d e d to s e t t l e into a r a n d o m , p l a n a r d i s t r i b u t i o n r a t h e r t h a n r e m a i n in a genuine 3 - d i m e n s i o n a l a r r a y . When the c o n c r e t e was h a r d e n e d , the ingots w e r e r e m o v e d f r o m t h e i r m o u l d s and cut into two: half of e a c h was then s t o r e d in w a t e r and half in a i r f o r the p r e d e t e r mined cure period. T h r e e t y p e s of f i b r e have b e e n u s e d .
C o l d - d r a w n m i l d s t e e l w i r e s , 2 . 5 c m long
and 0.25 m m in d i a m e t e r , and c o l d - d r a w n high c a r b o n s t e e l w i r e s , 1 . 9 c m long and 0.38 m m in d i a m e t e r , both m a n u f a c t u r e d by National S t a n d a r d L t d . , w e r e u s e d in this work.
The l a t t e r w e r e b r a s s - p l a t e d but the f o r m e r w e r e u n c o a t e d .
f i b r e w a s obtained f r o m F i b r e g l a s s Ltd. 1 . 3 e m long. manufacture
E-glass
It w a s in the f o r m of chopped, s i z e d tows
The s i z e was the c o n v e n t i o n a l PVA s i z e t h a t is put on the f i b r e s d u r i n g to p r o t e c t t h e m f r o m handling d a m a g e .
w a s i n c o r p o r a t e d into one o r two b a t c h e s of m o r t a r .
E a c h of t h e s e t y p e s of f i b r e The s l a b s of m a t e r i a l w e r e
s l i c e d on a w a t e r - c o o l e d d i a m o n d saw and e a c h s l i c e was cut into two t e s t s a m p l e s , a s shown in f i g u r e 2.
T h e s a m p l e s w e r e t h e n n o t c h e d , u s u a l l y t o one t h i r d of t h e i r
depth a s d e s c r i b e d in the next s e c t i o n , a l s o with the d i a m o n d saw. Toughness Testing Most s a m p l e s w e r e t e s t e d in slow t h r e e - p o i n t bending at an I n s t r o n c r o s s - h e a d s p e e d of 1.25 c m min -1.
F r o m the l o a d / d e f l e x i o n t r a c e s the c r i t i c a l s t r e s s
i n t e n s i t y f a c t o r , Kc, and the t o t a l w o r k of f r a c t u r e , ~ F ' w e r e o b t a i n e d a s follows. At the point of r a p i d p r o p a g a t i o n of a c r a c k f r o m the tip of the notch, the load P and the s p e c i m e n d i m e n s i o n s d e t e r m i n e the v a l u e of K c a s : 6Pl 1.93(C/d) ~1 - 3.07(C/d) 3/2 + 1 4 . 5 3 ( C / d ) 5/2 - 25. K =m c bd~
ll(C/d) 7/2 + 2 5 . 8 ( e / d ) 9 / 2 . .
(1)
f o r a s p e c i m e n w h e r e the span L = 4d, w h e r e the p o l y n o m i a l in notch depth r a t i o , C/d, is the f a c t o r that c o r r e c t s the s t r e s s f i e l d solution f o r the e f f e c t s of finite s a m p l e s i z e (1).
The r a w data w e r e a n a l y s e d by c o m p u t e r to obtain K v a l u e s . c
These K
c
Vol. 2, No. 4
45 FRACTURE, MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
I-
FIG. 2 Manner of cutting s a m p l e s f r o m c o n c r e t e slabs, and 3 point bend t e s t g e o m e t r y . must be r e g a r d e d as " a p p a r e n t " o r " e f f e c t i v e " values b e c a u s e of the fact that f r a c t u r e m e c h a n i c s c o n c e p t s apply s t r i c t l y to homogeneous m a t e r i a l s only.
The
i n t e g r a t e d f o r c e / d e f l e x i o n c u r v e gives the total work of f r a c t u r e of the s a m p l e .
If
the a r e a under the c u r v e is U, then the work of f r a c t u r e is U v F
-
. .......
2 ( d - c) b
(2)
w h e r e the f a c t o r 2 is included to give a d i r e c t c o m p a r i s o n with Grfffith e n e r g i e s for f a i l u r e of brittle solids.
Under ideal conditions f o r a b r i t t l e solid KC
2
= 2E%,F =
EG C
w h e r e Gc is the 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 .
........
(3)
F o r m a t e r i a l s such as those
c o n s i d e r e d h e r e , however, it is usually found that 2 "/F >> Gc"
F o r plain c o n c r e t e
452
Vol. 2, No. 4
FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
FIG. 3 O r i e n t a t i o n s of s a m p l e s u s e d to c h e c k a n i s o t r o p y of fracture behaviour. t h e v a r i a t i o n of ~ F w i t h notch depth w a s s t u d i e d .
At l e a s t s i x a n d s o m e t i m e s up to
20 s p e c i m e n s w e r e t e s t e d t o give a m e a n r e s u l t f o r a n y p a r t i c u l a r m a t e r i a l .
For
t h e f i b r e - r e i n f o r c e d c o n c r e t e t h i s w a s e s s e n t i a l b e c a u s e of a t e n d e n c y f o r n o n u n i f o r m f i b r e d i s t r i b u t i o n w h i c h in e x t r e m e c a s e s m e a n t t h a t the r a n g e of m e a s u r e d ~'F o r K c w a s s o m e t i m e s a s w i d e a s + 50%, but the s c a t t e r in t e s t r e s u l t s on p l a i n concrete was much smaller.
B e c a u s e of the m a n n e r in w h i c h the s t e e l w i r e s
s e t t l e d during c a s t i n g of the s l a b s , w h e r e w a s a c o n s i d e r a b l e a n i s o t r o p y in the reinforced concrete.
T h i s w a s i n v e s t i g a t e d by t e s t i n g s a m p l e s cut in the o r i e n t a t i o n s
shown in f i g u r e 3, f r o m one of the d r y - c u r e d ,
mild steel wire reinforced blocks.
T h e s e t e s t s w e r e c a r r i e d out in a H o u n s f i e l d m i n i a t u r e C h a r p y i m p a c t t e s t e r , s a m p l e s s l i g h t l y s m a l l e r t h a n t h o s e u s e d f o r the s l o w b e n d t e s t s : were 1 cmx
1 cmx
5 cm.
using
their dimensions
T h e s e s a m p l e s w e r e a l s o n o t c h e d t o C/d N ½.
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453 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
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FIG. 4 Work of fracture of plain c o n c r e t e as a function of notch depth (material d r y - c u r e d for 7 weeks). Results Plain Concrete The total work of fracture, YF' for plain c o n c r e t e is, like that of most other m a t e r i a l s , dependent on the depth of notch.
This e m p h a s i s e s that only under c l o s e l y
specified conditions does the equality 2 ~F = Gc apply.
Figure 4 shows that for w e t -
c u r e d concrete YF fails from about 80 J m -2 in unnotched s a m p l e s to about 10 J m -2 at C/d ~ 0.6, but the variation of YF with C/d is probably well within experimental s c a t t e r as long as C/d > ½.
Kaplan (2) has determined the c r i t i c a l strain energy
r e l e a s e rate, Gc, for large c o n c r e t e b e a m s containing c o a r s e aggregate using a v a r i e t y of t e s t p r o c e d u r e s and mixes.
His r e s u l t s , which a r e independent of C/d,
range between 14 and 28 J m -2, and his mean value of about 20 J m -2 is t h e r e f o r e in excellent a g r e e m e n t with our values of YF % 10 J m -2 for deep notches.
Kaplan
pointed out that on the b a s i s of the known s u r f a c e e n e r g i e s of t o b e r m o r i t e gel and quartz, the true s u r f a c e energy for his concrete should be about 0. 8 J m -2, assuming no bond failure: this is about an o r d e r of magnitude lower than the m e a s u r e d work of f r a c t u r e .
In our e x p e r i m e n t s t h e assumption of no bond failure would not be
454
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE TABLE F r a c t u r e Toughness P a r a m e t e r s for Plain and Reinfcr ced Concrete
Reinforcement
~'F kJm-2
6 month cure ~ F (6 months) t-test significance* level for difference in YF Kc Kc MNm-3/2 YF (7 weeks) MNm-3/2 kJm-2 Kc v a l u e s a f t e r 7 weeks and 6 months
7 week c u r e
Condition
Plain c o n c r e t e
Dry
0.02 (6)
0.40
0.023 (5)
0.29
0.8
<0.1%
(no r e i n f o r c e ment)
Wet
0.025(6)
0.41
0.04
(4)
0.44
1.6
> 10~%
> 40%
Mild steel**
High c a r b o n steel*** {brass-plated) E-glass; chopped tows
Dry
2.97 (ll)
0,61
3.20 (23)
0.63
1.1
Wet
3.80(12)
0,74
4.05 (27)
0.83
1.1
1.5%
Dry
3.15 (12)
0,43
2.65 (16)
0.46
0.9
~ 4.5%
Wet
4.56 (10)
0.57
3.60 (14)
0.56
0.8
> 20%
Dry Wet
0.88 (5)
0.47
0.32 (5)
0.35
0.4
0.70 (5)
0.76
0.83 (5)
0.42
1.2
* Figures in brackets indicate n u m b e r s of r e s u l t s used in significance t e s t s . 5% is probably significant, while 0.1% is highly significant. ** Cold drawn mild steel w i r e s , 2 . 5 c m long x 0.24 m m dia;
A [eve[ of
tensile strength 0.9 GNm -2.
*** Cold drawn high c a r b o n steel w i r e s , 1.9 c m long x 0.38 m m dia;
tensile s t r e n g t h 2.1 GNm -2.
valid; in addition to new fracture surfaces created in the gel and in the aggregate particles there was ample m i c r o s c o p i c evidence of interface failure.
But the
tortuous crack path alone could probably account for a single order of magnitude increase in ~F over the true surface energy. A mean notch depth C/d ~ ½ was used for all experiments other than this study of the effect of notch depth.
The table therefore lists fracture properties of plain
concrete for various cure conditions m e a s u r e d at this C/d ratio.
There is little
difference between either the work of fracture or the K values of concrete cured C -2 for 7 weeks in the wet or dry state. ~ F in both c a s e s is about 30 Jm and Kc is 0.4 MNm_3Z2t .
The latter compares with a value of~bout 0. 6 MNm - 3 /~2 reported by
Welch and Haisman (3).
On ageing for a further 17 weeks the w e t - c u r e d concrete
i n c r e a s e s its fracture energy considerably and its K value by a small amount, c w h e r e a s the toughness of the d r y - c u r e d material, as determined by either parameter, decreases.
The increase in K with wet storage is not significant, as the table C
indicates, but the decrease for the d r y - s t o r e d concrete is w e l l outside the range of experimental variation.
This s u g g e s t s that continued curing in the absence of
external water results in f i n e - s c a l e porosity or cracking from shrinkage as the
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455 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
hydration process continues: this can c l e a r l y be avoided if an e x t e r n a l source of m o i s t u r e is available, as in wet curing. Wire Reinforced Concrete The most significant r e s u l t is that for so small a fibre volume fraction as 2%, the f r a c t u r e energy of the composite is at least 2 o r d e r s of magnitude g r e a t e r than that of u n r e i n f o r c e d concrete.
F u r t h e r m o r e , in each case the f r a c t u r e e n e r g y of
w e t - c u r e d m a t e r i a l is higher than that of the d r y - c u r e d , and the ratio 7F(wet)/TF(dry) is slightly higher (about 1.5) for the high carbon steel m a t e r i a l than for the mild steel m a t e r i a l (about 1.3).
T h e r e appears to be no v e r y m a r k e d effect of continued curing
in w a t e r or in air, although t h e r e is a slight indication that the toughness of concrete r e i n f o r c e d with mild steel is i n c r e a s e d very slightly as curing continues, w h e r e a s that of the concrete containing b r a s s - p l a t e d wire falls slightly.
It t h e r e f o r e appears
that in the long t e r m r e i n f o r c e m e n t with mild steel wire is likely to give the more s a t i s f a c t o r y r e s u l t s , f r o m a f r a c t u r e e n e r g y point of view. wire has the higher strength and is b r a s s - p l a t e d .
The high-carbon steel
It is t h e r e f o r e more expensive.
But since the short lengths used were below the c r i t i c a l t r a n s f e r length, Lc, for both types of w i r e , the strength advantage of the high carbon steel is partly wasted since no fibres as short as 2.5 cm can be broken during f r a c t u r e .
The b r a s s plating might
be supposed to inhibit attack on the wire by the alkaline m a t r i x and the unplated mild steel ought, in t h e o r y , to be s e r i o u s l y attacked especially in wet concrete.
A small
degree of c h e m i c a l attack could of course account for an i n c r e a s e d f i b r e / m a t r i x bond strength and this, for fibres s h o r t e r than Lc, should i n c r e a s e the work of fracture. Although 7 F is i n c r e a s e d by at least 2 o r d e r s of magnitude by the incorporation of 2 vol. % of w i r e s , K concrete.
C
is only marginally i n c r e a s e d above its value for plain
The effect of continued ageing is again not very significant except for
the w e t - c u r e d mild s t e e l / c e m e n t .
There does, however, appear to be reasonable
evidence that the use of the mild steel r e i n f o r c e m e n t confers g r e a t e r r e s i s t a n c e to c r a c k initiation, as indicated by Kc, than the high carbon steel.
However, it is
c l e a r l y the concrete r a t h e r than the w i r e s that controls this phase of f r a c t u r e . In o r d e r to t e s t the effect of fibre settling during casting, samples cut in the t h r e e orientations shown in figure 3 were impact t e s t e d a f t e r 7 weeks curing.
The
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m a t e r i a l was d r y - c u r e d c o n c r e t e r e i n f o r c e d with 0.25 m m dia. m i l d st eel w i r e s . The ef f ect of f i br e settling is to r e d u c e the n u m b e r of f i b r e s lying in or cl ose to the x 3 direction. cut f a c e s .
In v e r t i c a l cut s l i c e s t h e r e w e r e r a r e l y any of t h e s e visible on the Breaking s a m p l e s of or i e nt a ti on C should r e q u i r e m a x i m u m e n e r g y since
this mode of f r a c t u r e would involve the l a r g e s t num ber of w i r e s , while those in orientations A and B should r e q u i r e roughly s i m i l a r e n e r g i e s , but c o n s i d e r a b l y less than s amp les C.
The means of six Charpy t e s t s f o r ori ent at i ons A, B and C w e r e :
7 F (A) = 3. 8 k J m 7F (B) - 5 . 9 k J m ~F (C) = 9.5 k J m
-2 -2
-2
F r o m these r e s u l t s it can be s e e n that the w o r k of f r a c t u r e of B s a m p l e s is in fact higher than that of A s a m pl es , possibly b e c a u s e in the slicing of A -t ype s a m p l e s , f i b r e s that will ul t i m a t e l y sp~m the c r a c k a r e cut s h o r t e r than t h o s e in B s a m p l e s . A is also the o r i e nt a t i on of all s a m p l e s f o r which t e s t r e s u l t s a r e given in the table. Samples cut f r o m the s a m e b a r as that used for the o r i e n t a t i o n e x p e r i m e n t s and t e s t e d in slow bending gave a m ean value of ~ F = 3 . 4 k J m -2.
This suggests, f i r s t ,
that the v a r i a t i o n f r o m b a r to b a r was not g r e a t (see table) and, second, that the simple and r a p i d Charpy impact t e s t may give a l m o s t the s a m e r e s u l t as the slow bend tes t, a m a t t e r of some i m p o r t a n c e to any d e s i g n e r i n t e r e s t e d in s e r i o u s a p p l i c ation of f r a c t u r e m echani cs to o n - s i t e testing of m a t e r i a l s .
However this is a
hypothesis that r e q u i r e s much f u r t h e r testing. Glass F i b r e R e i n f o r c e d Concrete T h e r e is an i n c r e a s e in ~ F of only 20 or so t i m e s in wet and d r y c u r e d c o n c r e t e r e i n f o r c e d with E - g l a s s , and although a continued w e t - c u r e a p p e a r s to r a i s e this still f u r t h e r , continued dry curing br i ngs about a d e t e r i o r a t i o n in toughness.
T h i s is by
no m e a n s the c a t a s t r o p h i c d e t e r i o r a t i o n that might have been e x p e c t e d f r o m the known e f f e c t s of the alkaline m a t r i x on f i br e strength.
However Kc, which r e f l e c t s the
a c tu al f r a c t u r e s t r engt h instead of the w o rk of f r a c t u r e , is c o n s i d e r a b l y r e d u c e d on prolonged e x p o s u r e even though in the f i r s t instance the w e t - c u r e d gl ass r e i n f o r c e d c o n c r e t e has a higher K value than plain c o n c r e t e . This m a t e r i a l is t h e r e f o r e c i n f e r i o r on mo s t counts to the w i r e r e i n f o r c e d s y s t e m , and even the substitution of
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457 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
a l k a l i - r e s i s t a n t g l a s s could not make it a s e r i o u s c o m p e t i t o r f r o m the point of view of f r a c t u r e toughness.
Discussion F r a c t u r e of Plain Concrete The values of YF and Kc are in reasonable a g r e e m e n t with those c i ~ d by others, viz Welch and Haisman (3) and Kaplan (2) for example.
An indication of the applic-
ability of f r a c t u r e mechanics ideas to a nonhomogeneous s y s t e m such as concrete can be obtained f r o m the equality K
2 c
= EG
C
if independent m e a s u r e m e n t s of K and G can be obtained. C
c
Since for deep notches
our YF for plain concrete a g r e e s almost exactly with Kaplan's value of Gc m e a s u r e d by the compliance method, we have f o r dry and wet c u r e d concrete K = 0. 4 MNm - 3 / 2 , c G = 20 J m -2. If we a s s u m e that E for a s a n d / c e m e n t m o r t a r is about 20 GNm -2, e
then K2 ~ 1 6 x 1010 N2m -3,
and
EG ~ 4 0 x 1 0 1 0 N 2 m -3
c
C
The discrepancy is not too g r e a t considering the complexity of the concrete s t r u c t u r e . F r o m another point of view, given the flexural f r a c t u r e s t r e s s , af, for un-notched samples, and the m e a s u r e d values of YF' we can e s t i m a t e the inherent flaw size in the plain concrete as given by the Grfffith equation 2EY F c = ~
........
(4)
M e a s u r e d values of ~f were as follows: Cured 7 weeks:
~f (wet) = 11.1 MNm -2 ; ~f (dry) = 4.7 MNm -2
Cured 6 months:
~f (wet) = 11.3 MNm-2; vf (dry) = 7.3 MNm -2
With these values and those of YF in the table we find that the inherent c r a c k size is 7 to 10 m m in dry c u r e d concrete and 2 to 3 m m in the w e t - c u r e d .
The implication
is that cracking in w e t - c u r e d concrete occurs at the a g g r e g a t e / c e m e n t interface, since the size of the largest sand particles is of the o r d e r of 2ram, whereas in d r y c u r e d m a t e r i a l much l a r g e r shrinkage c r a c k s a r e p r e s e n t . new - they m e r e l y confirm r e s u l t s of other work.
These ideas are not
458
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F r a c t u r e of R e i n f o r c e d C oncr e t e The s o u r c e of the high f r a c t u r e e n e r g y of c o n c r e t e r e i n f o r c e d with 2 vol. % of s t eel wire is la r gel y the work of pulling f i b r e s out of the m a t r i x a f t e r the latter has cracked.
Cottrell (4} has pr opos e d a simple model which gives the f r a c t u r e e n e r g y
of a composite that r e s u l t s f r o m w or k done in pulling out the fi bre ends against the f i b r e / m a t r i x friction: Wf =
Vf • £2 12d
. ........
~ < ~ c
(5) ........
w her e Vf is the fibre volume fraction, • is the f i b r e / m a t r i x i n t e r f a c i a l friction, ~ is the fibre length and d its d i a m e t e r .
The fri ct i on s t r e s s was d e t e r m i n e d independently
by pulling out lengths of w i r e e m b e d d e d in the c o n c r e t e a f t e r 7 weeks curing. Approximate values w e r e : f o r low carbon s t eel w i r e in w e t - c u r e d c o n c r e t e , ~ ~
1.5 MNm -2, -2 in d r y - c u r e d c o n c r e t e , ~ ~. 0.7 MNm ;
f o r high c a r b o n s t eel w i r e (brass-plated} wet cured, • ~ 0.5 MNm -2, and dry cured, ~ Z 0.5 MNm -2. T hes e r e s u l t s suggest that t h e r e is a c h e m i c a l r e a c t i o n between the c o n c r e t e and s t eel that is intensified by the p r e s e n c e of e x c e s s m o i s t u r e .
The b r a s s plating, as
might be expected, pr e ve nt s any such i nt eract i on however.
The highest value found
in this w o r k was much lower than the range of about 2.5 - 4 . 0 MNm -2 usually quoted f o r bond s t r e n g t h s .
It should be noted however that t hese a r e the dynamic f r i c t i o n
s t r e s s e s and not the much higher static f r i c t i o n s t r e s s e s that a r e usually r e a c h e d only m o m e n t a r i l y until the initial c h e m i c a l bond is b r o k e n and b e f o r e the p r o c e s s of pull-out p r o p e r begins.
Substitution of values of v, £ and d then gives for the
f r i c t i o n a l f r a c t u r e w or k of w e t - c u r e d c o n c r e t e , Wf = 6.5 k J m -2 (mild s t e e l wires} and 0. 8 k J m -2 (high c a r b o n s t eel wires}.
C o t t r e l i ' s model is f o r c o m p o s i t e s
containing aligned f i b r e s , and the effective volume f r a c t i o n of r e i n f o r c e m e n t will be less than the nominal Vf in r a ndom fibre c o m p o s i t e s .
By inspection of a large
n u mb er of f r a c t u r e s u r f a c e s it was possible to e s t i m a t e that an a v e r a g e of 30 f i b r e s 2 i n t e r s e c t e d the c r a c k plane. This is equivalent to about 105 f i b r e s p e r m of f r a c t u r e s u r f a c e , o r about 55% of the nominal fibre content which, f o r Vf = 0.02, is 4 V f / ~ d 2 = 1.8 x 105 f i b r e s m -2.
This is a much higher p r o p o r t i o n than the 41%
e s t i m a t e d by Romualdi and Mandel (5) for a p e r f e c t l y random com posi t e, and this
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459 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
probably r e f l e c t s the fact that the fibre distribution in our m a t e r i a l s was not fully r a n d o m in t h r e e dimensions.
This c o r r e c t i o n f a c t o r for Vf (effective) then gives f o r
the f r i c t i o n a l f r a c t u r e work: Wf = 3.6 k J m -2 f o r mild st eel w i r e s ; Wf = 0.44 kJ m -2 f or high carbon st eel w i r e s . T h e s e r e s u l t s suggest that o v e r t h r e e - q u a r t e r s of the total f r a c t u r e e n e r g y of mild s t e e l r e i n f o r c e d c o n c r e t e is d e r i v e d f r o m the w ork of fibre pull-out, p a r t i c u l a r l y if t h e r e has been s om e s u r f a c e attack of the w i re by the cem ent , butthe pull-out of b r a s s - p l a t e d high car bon s t e e l f i b r e s a p p a r e n t l y c o n t r i b u t e s less than a fifth of the total. Helfet and H a r r i s (6) have shown that an important contribution to the f r a c t u r e e n e r g y of c o m p o s i t e s containing r a n d o m l y - o r i e n t e d f i b r e s is the w ork of plastic s h e a r i n g of any f i b r e s that a r e not lying n o r m a l or p a r a l l e l to the c r a c k plane.
A
m e t a l f ib r e of s h e a r s t r e n g t h ~y, lying at an angle 0 to the c r a c k plane, will be pulled out of one c r a c k face and at the s a me t i m e will be s h e a r e d along the complete pull-out length through the angle 0.
If the pulled out length is ~' and the fibre c r o s s
s ectio n al a r e a is A, the work of plastic sheari ng a non-work hardening wire is • 0 Y p e r unit volume, or v 0 $ ' A Joules p e r fibre. If N f i b r e s p e r square m e t r e of c r a c k Y face a r e involved and t h e i r mean d i s p e r s i o n about the n o r m a l to the c r a c k plane is e , the plastic d ef o r m a t i on w or k is
or
Ws = NVy~ ~' A
J m -2
p e r f r a c t u r e face,
W
Jm -2
if both f r a c t u r e faces a r e
s
= ½N ~ e ~' A y
c o n s i d e r e d by analogy with Wf and ~F"
N is, as we have seen, about 105 f i b r e s m
and ~ ' was found, by inspection, to be always of the o r d e r of 7 m m .
-2
The t ensi l e
s t r e n g t h of the high c a r b o n s t e e l w i r e s is 2.1 GNm -2 and that of the mild st eel is 0.9 GNm -2
"Cy = ay/2
If we make the additional crude assum pt i on that ~ is ~/6, and take , we obtain: W W
s s
= 3.4 k J m
-2
f o r w e t - c u r e d high c a r b o n st eel f i b r e s ,
= 0.8 k J m -2 f o r w e t - c u r e d mild s t e e l f i b r e s .
The total wo r k o f f r a c t u r e , (Wf +W ), is thus some 4 . 4 kJm -2 f o r the mild s t e e l s -2 w i r e s and 3 .9 k J m f or the high c a r b o n steel, and this d e g r e e of a g r e e m e n t with the
,
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Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
r e s u l t s in the table is c e r t a i n l y as much as can be e x p e c t e d c o n s i d e r i n g the c r u d i t y of the models and the high v a r i a b i l i t y of the t e s t data.
The r e s u l t s suggest f a i r l y
c l e a r l y that f u r t h e r i m p r o v e m e n t s in f r a c t u r e e n e r g y a r e m o r e likely to be gained f r o m using mild steel w i r e s , as long as they can be s a t i s f a c t o r i l y mixed into the c o n c r e t e and s u r f a c e t r e a t e d to i n c r e a s e the i nt erraci al friction. It should be borne in mind that al m os t all of the apparent i m p r o v e m e n t s that have just been d i s c u s s e d o c c u r a f t e r the f i r s t signs of c r a c k i n g in the com posi t e.
This is
b o r n e out by the fact that the values of K higher than those f o r plain c o n c r e t e .
for r e i n f o r c e d c o n c r e t e s a r e v e r y little c The i n c r e a s e in initial cracking r e s i s t a n c e , as
indicated by the I~gher f r a c t u r e s t r e s s f o r a given c r a c k length, this being what K
c
m e a s u r e s , is less than a f a c t o r of 2 for the mild st eel r e i n f o r c e d c o n c r e t e , and a l m o s t nothing f or the high c a r b o n steel.
It is important in design to distinguish
c l e a r l y which f r a c t u r e m e c ha ni c s p a r a m e t e r is the r e l e v a n t one f o r any p a r t i c u l a r 2 requirement. It is c l e a r that K c << 2E ~¢F for the r e i n f o r c e d m a t e r i a l s . F r a c t u r e of Glass F i b r e R e i n f o r c e d Concrete The addition of 2 vol. % gl a s s f i b r e s has i n c r e a s e d the w o r k of f r a c t u r e of c o n c r e t e some 40 t i m e s , but this is still too little for the m a t e r i a l to be c o n s i d e r e d as anything but b r i t t l e .
The s t r e s s / s t r a i n c u r v e s f or t h e s e m a t e r i a l s r e s e m b l e d those of plain
c o n c r e t e s a m p l e s m o r e than those of w i r e r e i n f o r c e d s a m p l e s in that the load fell off v e r y rapidly to z e r o a f t e r the initial onset of c r a c k i n g . c l os e to $ c ' f o r t h e r e was v e r y little fibre pull-out.
The fibre length was c l e a r l y The protruding f i b r e s w ere of
the o r d e r of only 2 m m which suggests that $ ~ 8 ram. The c r i t i c a l s t r e s s intensity c is only r a i s e d above that of plain c o n c r e t e if the m a t e r i a l is wet cured, but the p r e s e n c e of e x c e s s m o i s t u r e a c c e l e r a t e s the alkali attack of the gl ass s u r f a c e and prolonged curing in w a t e r r e d u c e s K c again to the value for plain c o n c r e t e although YF is i n c r e a s e d slightly.
T h e r e is a c r i t i c a l balance h e r e between weakening of
the f ib r e as a r e s u l t of c h e m i c a l action, leading to lower c o n c r e t e st rengt hs (and Kc) and roughening of the fibre, leading to i n c r e a s e d f r i c t i o n w ork (and yF ).
Allen (7) has
s u g g es ted that t h e r e is no evidence that the p r e s e n c e of glass f i b r e s inhibits cracki ng of the c e m e n t .
It a p p e a r s that this is not a c c u r a t e , although the benefits of r e i n f o r -
c e m e n t with s mal l Vf of r a n d o m l y - d i s t r i b u t e d f i b r e s a r e c e r t a i n l y not d r a m a t i c . The fall in f r a c t u r e toughness o b s e r v e d in plain c o n c r e t e on prolonged d r y - c u r i n g is
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461 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
not prevented by the presence of glass fibres, although it is suppressed by steel fibre reinforcement. Acknowledgements This r e s e a r c h was begun as Jane Varlow's third year undergraduate r e s e a r c h project in Materials Science at the University of Sussex.
C.D. Ellis was in receipt
of an S.R.C. studentship for r e s e a r c h on composite materials. References
2.
Fracture Toughness, ISI Publication 121, The Iron & Steel Institute, London (1968). M.F.Kaplan, J . A m e r i c a n Concrete Inst., 58, 581 (1961).
3.
G. B.Welch and B. Haisman, Mat~riaux & Constructions, ~ 171 (1969).
4.
A.H. Cottrell, P r o c . R o y . S o c . , A282, 2 (1964).
5.
J.P.Romualdi and J.A. Mandel, J . A m e r i c a n Concrete Inst., ~
6.
J. Helfet and B. Harris, J. Materials Science, April 1972 (in press).
7.
H.G.AIIen, J. Composite Materials, 5, 194 (1971).
.
657 (1964).
THE F R A C T U R E B E H A V I O U R OF F I B R E R E I N F O R C E D C O N C R E T E
B. H a r r i s , J. V a r l o w and C. D. E l l i s S c h o o l of A p p l i e d S c i e n c e s , U n i v e r s i t y of S u s s e x , B r i g h t o n ,
U. K.
(Communicated by A. M. Neville)
ABSTRACT T h e w o r k of f r a c t u r e , YF, and the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r Kc, have b e e n d e t e r m i n e d f o r the f a i l u r e in b e n d i n g of n o t c h e d s a m p l e s of s a n d / c e m e n t m o r t a r r e i n f o r c e d with s h o r t , r a n d o m l y d i s t r i b u t e d f i b r e s of g l a s s , h i g h c a r b o n s t e e l , and m i l d s t e e l . R e s u l t s w e r e o b t a i n e d on wet and d r y s t o r e d m a t e r i a l a f t e r 7 w e e k s and a g a i n a f t e r 6 m o n t h s c u r i n g . T h e r e is c l e a r e v i d e n c e that the h i g h e s t f r a c t u r e r e s i s t a n c e is o b t a i n e d in the long t e r m by r e i n f o r c e m e n t with m i l d s t e e l . H o w e v e r , w h e r e a s the w o r k of f r a c t u r e of plain c o n c r e t e c a n be i n c r e a s e d by two o r d e r s of m a g n i tude by a d d i n g a s little a s 2 vol. % of s t e e l w i r e s , the m o r e c r i t i cal p a r a m e t e r K c is i n c r e a s e d at m o s t by a f a c t o r of 2. G l a s s f i b r e r a i s e s YF by a f a c t o r of only 40. T h e e x p e r i m e n t a l v a l u e s of "(F f o r w i r e r e i n f o r c e d c o n c r e t e a r e c o m p a r e d with t h e o r e t i c a l e s t i m a t e s b a s e d on c o n s i d e r a t i o n s of f i b r e p u l l - o u t and f i b r e d e formation.
Die B r u c h a r b e i t ~(F und d e r K e r b s p a n n u n g s f a c t o r Kc ftir B i e g e b e l a s t u n g w u r d e ftlr a n g e k e r b t e W e r k s t t i c k e a u s m i t statistisch verteilten Glas-und Stahlfasern verst~irktem Beton b e s t i m m t . M e s s u n g e n w u r d e n n a c h 7 W o c h e n sowie n a c h 6 M o n a t e n T r o c k e n - u n d F e u c h t l a g e r u n g d u r c h geftlhrt. Ganz o f f e n s i c h t l i c h w i r d d i e h~Schste B r u c h f e s t i g k e i t auf lange Sicht bei Verst~irkung m i t W e i c h s t a h l e r z i e l t . W~lhrend j e d o c h die B r u c h a r b e i t von g e w b h n l i c h e m B e t o n d u t c h g e r i n g e Zus/ttze yon 2 V o l u m e n p r o z e n t S t a h l d r a h t u m zwei G r S s s e n o r d n u n g e n e r h S h t w e r d e n kann, w i r d d e r n o c h w i c h t i g e r e K e r b s p a n n u n g s f a k t o r h S c h s t e n s v e r d o p p e l t . D u r c h G l a s f a s e r n w i r d ~(F n u r auf d a s v i e r z i g f a c h e e r h S h t . Die f[ir d r a h t v e r s t ~ i r k t e n B e t o n g e m e s s e n e n W e r t e yon YF w e r d e n m i t t h e o r e t i s c h e n Absch~ttzungen in d e n e n d a s H e r a u s z i e h e n und d i e D e f o r m a t i o n d e r F a s e r n b e r [ i c k s i c h t i g t ist, v e r g l i c h e n . 447
448
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE Introduction If c o n c r e t e is to r e m a i n a cheap s t r u c t u r a l m a t e r i a l , r e i n f o r c e m e n t with strong
f i b r e s may only be feasible if s m al l volume f r a c t i o n s of fibre a r e used and if the addition of the f i br es does not entail s e r i o u s modifications to o n - s i t e p r e p a r a t i o n methods.
Two or t h r e e p e r c e n t by volume of chopped glass or s t e e l w i r e s is about
all that can be s a t i s f a c t o r i l y i n c o r p o r a t e d into c o n c r e t e by o r d i n a r y mixing methods, and the r e s u l t i n g m a t e r i a l may contain e i t h e r a r a n d o m or a pl anar random d i s t r i b ution.
T h e r e is also a limit to the lengths of fibre that can be so i n c o r p o r a t e d ,
since f o r a given d i a m e t e r the w i r e s or f i b r e s must not b e c o m e so flexible that they a r e e a s i l y tangled.
Depending upon the f i b r e / c o n c r e t e bond strength, then, the only
additions that can e a s i l y be made in p r a c t i c e may well t u r n out to be ineffective as fibre s t r e n g t h e n e r s .
F r o m the f r a c t u r e toughness point of view, however, even
f i b r e s that a r e too short to s t r engt hen the c o n c r e t e can, by c r a c k a r r e s t and fibre pull-out, contribute significantly to the m e a s u r e d w ork of f r a c t u r e .
We r e p o r t h e r e
s o me e x p e r i m e n t s in which f r a c t u r e m e c h a n i c s methods have been used to study the toughening of sand/cement= m o r t a r by additions of chopped s t e e l w i r e s and glass f i b r e s , and we c o m p a r e the r e s u l t s with some r e c e n t t h e o r e t i c a l studies of fibre reinforcement.
E x p e r i m e n t a l Work
The mix u s e d throughout this w or k was of fine sand and P o r t l a n d c e m e n t in the weight r a t i o 3 : 1 with a c e m e n t : w a t e r r a t i o of 3 : 2.
T hi s composition was the
d r i e s t m o r t a r that could subsequently be mixed without difficulty with 2% by volume of g las s o r s t e e l f i b r e s .
The c u r e conditions for the basi c m o r t a r w e r e studied by
c o m p r e s s i o n testing c y l i n d r i c a l s a m p l e s 2. 5 c m in d i a m e t e r by 2.5 c m high which had been cas t to shape f r o m s m a l l batch m i x e s in wooden moulds.
These were
r e m o v e d f r o m the moulds a f t e r 24 hours: some w e r e then left to c u r e in a i r , some w e r e s t o r e d in w a t e r , and some w e r e o v e n - c u r e d at 50°C.
Samples c u r e d up to
70 days w e r e c o m p r e s s i o n - t e s t e d between l ubri cat ed s t e e l platens at a s t r a i n - r a t e of 10-3 s e c - 1 The r e s u l t s of t hes e t e s t s , shown in figure 1, suggested that a f t e r 45 days the r a t e of change of s t r engt h of the w a t e r - c u r e d m a t e r i a l was s m a l l enough to be ignored.
Vol. 2, No. 4
449 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE I
¢,q
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10
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CURING PERIOD
60
70
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FIG. 1 Compression strength of plain concrete as a function of curing t i m e . AI! toughness testing was t h e r e f o r e c a r r i e d out on samples aged for 7 weeks in the f i r s t instance.
It is commonly accepted that o r d i n a r y glass and steel fibres are
strongly attacked by a highly alkaline cement matrix, p a r t i c u l a r l y if free m o i s t u r e is present.
In o r d e r to study the deleterious effect of m o i s t u r e , t h e r e f o r e , samples of
all m a t e r i a l s were stored, in w a t e r and in a i r , for a total of 6 months and subjected to a second s e r i e s of f r a c t u r e t e s t s identical with that c a r r i e d out on samples t e s t e d a f t e r 7 weeks. P r e p a r a t i o n of Materials A large batch of m o r t a r was p r e p a r e d in a r o t a r y m i x e r (10 minute mix) and then divided into parts.
One part was poured into a r e c t a n g u l a r ingot mould without any
fibre addition, and each of the remaining parts was s e p a r a t e l y r e t u r n e d to the m i x e r
450
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
f o r a f u r t h e r 5 m i n u t e s d u r i n g which t i m e a p r e - w e i g h e d b a t c h of f i b r e s of the r e q u i r e d kind w e r e s p r i n k l e d into the m o r t a r .
It was found a s long as the f i b r e s
w e r e w e l l s e p a r a t e d b e f o r e s p r i n k l i n g t h e y did not b a l l - u p o r s t i c k t o g e t h e r in the mixer.
A f t e r m i x i n g in the f i b r e s , t h e s e m i x e s w e r e a l s o c a s t into b a r m o u l d s .
A f t e r c a s t i n g the m o u l d s w e r e t a m p e d and t h e n v i b r a t e d f o r about 2 m i n u t e s . A c o n s e q u e n c e of this m e t h o d of p r e p a r a t i o n was that the f i b r e s t e n d e d to s e t t l e into a r a n d o m , p l a n a r d i s t r i b u t i o n r a t h e r t h a n r e m a i n in a genuine 3 - d i m e n s i o n a l a r r a y . When the c o n c r e t e was h a r d e n e d , the ingots w e r e r e m o v e d f r o m t h e i r m o u l d s and cut into two: half of e a c h was then s t o r e d in w a t e r and half in a i r f o r the p r e d e t e r mined cure period. T h r e e t y p e s of f i b r e have b e e n u s e d .
C o l d - d r a w n m i l d s t e e l w i r e s , 2 . 5 c m long
and 0.25 m m in d i a m e t e r , and c o l d - d r a w n high c a r b o n s t e e l w i r e s , 1 . 9 c m long and 0.38 m m in d i a m e t e r , both m a n u f a c t u r e d by National S t a n d a r d L t d . , w e r e u s e d in this work.
The l a t t e r w e r e b r a s s - p l a t e d but the f o r m e r w e r e u n c o a t e d .
f i b r e w a s obtained f r o m F i b r e g l a s s Ltd. 1 . 3 e m long. manufacture
E-glass
It w a s in the f o r m of chopped, s i z e d tows
The s i z e was the c o n v e n t i o n a l PVA s i z e t h a t is put on the f i b r e s d u r i n g to p r o t e c t t h e m f r o m handling d a m a g e .
w a s i n c o r p o r a t e d into one o r two b a t c h e s of m o r t a r .
E a c h of t h e s e t y p e s of f i b r e The s l a b s of m a t e r i a l w e r e
s l i c e d on a w a t e r - c o o l e d d i a m o n d saw and e a c h s l i c e was cut into two t e s t s a m p l e s , a s shown in f i g u r e 2.
T h e s a m p l e s w e r e t h e n n o t c h e d , u s u a l l y t o one t h i r d of t h e i r
depth a s d e s c r i b e d in the next s e c t i o n , a l s o with the d i a m o n d saw. Toughness Testing Most s a m p l e s w e r e t e s t e d in slow t h r e e - p o i n t bending at an I n s t r o n c r o s s - h e a d s p e e d of 1.25 c m min -1.
F r o m the l o a d / d e f l e x i o n t r a c e s the c r i t i c a l s t r e s s
i n t e n s i t y f a c t o r , Kc, and the t o t a l w o r k of f r a c t u r e , ~ F ' w e r e o b t a i n e d a s follows. At the point of r a p i d p r o p a g a t i o n of a c r a c k f r o m the tip of the notch, the load P and the s p e c i m e n d i m e n s i o n s d e t e r m i n e the v a l u e of K c a s : 6Pl 1.93(C/d) ~1 - 3.07(C/d) 3/2 + 1 4 . 5 3 ( C / d ) 5/2 - 25. K =m c bd~
ll(C/d) 7/2 + 2 5 . 8 ( e / d ) 9 / 2 . .
(1)
f o r a s p e c i m e n w h e r e the span L = 4d, w h e r e the p o l y n o m i a l in notch depth r a t i o , C/d, is the f a c t o r that c o r r e c t s the s t r e s s f i e l d solution f o r the e f f e c t s of finite s a m p l e s i z e (1).
The r a w data w e r e a n a l y s e d by c o m p u t e r to obtain K v a l u e s . c
These K
c
Vol. 2, No. 4
45 FRACTURE, MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
I-
FIG. 2 Manner of cutting s a m p l e s f r o m c o n c r e t e slabs, and 3 point bend t e s t g e o m e t r y . must be r e g a r d e d as " a p p a r e n t " o r " e f f e c t i v e " values b e c a u s e of the fact that f r a c t u r e m e c h a n i c s c o n c e p t s apply s t r i c t l y to homogeneous m a t e r i a l s only.
The
i n t e g r a t e d f o r c e / d e f l e x i o n c u r v e gives the total work of f r a c t u r e of the s a m p l e .
If
the a r e a under the c u r v e is U, then the work of f r a c t u r e is U v F
-
. .......
2 ( d - c) b
(2)
w h e r e the f a c t o r 2 is included to give a d i r e c t c o m p a r i s o n with Grfffith e n e r g i e s for f a i l u r e of brittle solids.
Under ideal conditions f o r a b r i t t l e solid KC
2
= 2E%,F =
EG C
w h e r e Gc is the 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 .
........
(3)
F o r m a t e r i a l s such as those
c o n s i d e r e d h e r e , however, it is usually found that 2 "/F >> Gc"
F o r plain c o n c r e t e
452
Vol. 2, No. 4
FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
FIG. 3 O r i e n t a t i o n s of s a m p l e s u s e d to c h e c k a n i s o t r o p y of fracture behaviour. t h e v a r i a t i o n of ~ F w i t h notch depth w a s s t u d i e d .
At l e a s t s i x a n d s o m e t i m e s up to
20 s p e c i m e n s w e r e t e s t e d t o give a m e a n r e s u l t f o r a n y p a r t i c u l a r m a t e r i a l .
For
t h e f i b r e - r e i n f o r c e d c o n c r e t e t h i s w a s e s s e n t i a l b e c a u s e of a t e n d e n c y f o r n o n u n i f o r m f i b r e d i s t r i b u t i o n w h i c h in e x t r e m e c a s e s m e a n t t h a t the r a n g e of m e a s u r e d ~'F o r K c w a s s o m e t i m e s a s w i d e a s + 50%, but the s c a t t e r in t e s t r e s u l t s on p l a i n concrete was much smaller.
B e c a u s e of the m a n n e r in w h i c h the s t e e l w i r e s
s e t t l e d during c a s t i n g of the s l a b s , w h e r e w a s a c o n s i d e r a b l e a n i s o t r o p y in the reinforced concrete.
T h i s w a s i n v e s t i g a t e d by t e s t i n g s a m p l e s cut in the o r i e n t a t i o n s
shown in f i g u r e 3, f r o m one of the d r y - c u r e d ,
mild steel wire reinforced blocks.
T h e s e t e s t s w e r e c a r r i e d out in a H o u n s f i e l d m i n i a t u r e C h a r p y i m p a c t t e s t e r , s a m p l e s s l i g h t l y s m a l l e r t h a n t h o s e u s e d f o r the s l o w b e n d t e s t s : were 1 cmx
1 cmx
5 cm.
using
their dimensions
T h e s e s a m p l e s w e r e a l s o n o t c h e d t o C/d N ½.
Vol. 2, No. 4
453 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
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NOTCH DEPTH RATIO
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FIG. 4 Work of fracture of plain c o n c r e t e as a function of notch depth (material d r y - c u r e d for 7 weeks). Results Plain Concrete The total work of fracture, YF' for plain c o n c r e t e is, like that of most other m a t e r i a l s , dependent on the depth of notch.
This e m p h a s i s e s that only under c l o s e l y
specified conditions does the equality 2 ~F = Gc apply.
Figure 4 shows that for w e t -
c u r e d concrete YF fails from about 80 J m -2 in unnotched s a m p l e s to about 10 J m -2 at C/d ~ 0.6, but the variation of YF with C/d is probably well within experimental s c a t t e r as long as C/d > ½.
Kaplan (2) has determined the c r i t i c a l strain energy
r e l e a s e rate, Gc, for large c o n c r e t e b e a m s containing c o a r s e aggregate using a v a r i e t y of t e s t p r o c e d u r e s and mixes.
His r e s u l t s , which a r e independent of C/d,
range between 14 and 28 J m -2, and his mean value of about 20 J m -2 is t h e r e f o r e in excellent a g r e e m e n t with our values of YF % 10 J m -2 for deep notches.
Kaplan
pointed out that on the b a s i s of the known s u r f a c e e n e r g i e s of t o b e r m o r i t e gel and quartz, the true s u r f a c e energy for his concrete should be about 0. 8 J m -2, assuming no bond failure: this is about an o r d e r of magnitude lower than the m e a s u r e d work of f r a c t u r e .
In our e x p e r i m e n t s t h e assumption of no bond failure would not be
454
Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE TABLE F r a c t u r e Toughness P a r a m e t e r s for Plain and Reinfcr ced Concrete
Reinforcement
~'F kJm-2
6 month cure ~ F (6 months) t-test significance* level for difference in YF Kc Kc MNm-3/2 YF (7 weeks) MNm-3/2 kJm-2 Kc v a l u e s a f t e r 7 weeks and 6 months
7 week c u r e
Condition
Plain c o n c r e t e
Dry
0.02 (6)
0.40
0.023 (5)
0.29
0.8
<0.1%
(no r e i n f o r c e ment)
Wet
0.025(6)
0.41
0.04
(4)
0.44
1.6
> 10~%
> 40%
Mild steel**
High c a r b o n steel*** {brass-plated) E-glass; chopped tows
Dry
2.97 (ll)
0,61
3.20 (23)
0.63
1.1
Wet
3.80(12)
0,74
4.05 (27)
0.83
1.1
1.5%
Dry
3.15 (12)
0,43
2.65 (16)
0.46
0.9
~ 4.5%
Wet
4.56 (10)
0.57
3.60 (14)
0.56
0.8
> 20%
Dry Wet
0.88 (5)
0.47
0.32 (5)
0.35
0.4
0.70 (5)
0.76
0.83 (5)
0.42
1.2
* Figures in brackets indicate n u m b e r s of r e s u l t s used in significance t e s t s . 5% is probably significant, while 0.1% is highly significant. ** Cold drawn mild steel w i r e s , 2 . 5 c m long x 0.24 m m dia;
A [eve[ of
tensile strength 0.9 GNm -2.
*** Cold drawn high c a r b o n steel w i r e s , 1.9 c m long x 0.38 m m dia;
tensile s t r e n g t h 2.1 GNm -2.
valid; in addition to new fracture surfaces created in the gel and in the aggregate particles there was ample m i c r o s c o p i c evidence of interface failure.
But the
tortuous crack path alone could probably account for a single order of magnitude increase in ~F over the true surface energy. A mean notch depth C/d ~ ½ was used for all experiments other than this study of the effect of notch depth.
The table therefore lists fracture properties of plain
concrete for various cure conditions m e a s u r e d at this C/d ratio.
There is little
difference between either the work of fracture or the K values of concrete cured C -2 for 7 weeks in the wet or dry state. ~ F in both c a s e s is about 30 Jm and Kc is 0.4 MNm_3Z2t .
The latter compares with a value of~bout 0. 6 MNm - 3 /~2 reported by
Welch and Haisman (3).
On ageing for a further 17 weeks the w e t - c u r e d concrete
i n c r e a s e s its fracture energy considerably and its K value by a small amount, c w h e r e a s the toughness of the d r y - c u r e d material, as determined by either parameter, decreases.
The increase in K with wet storage is not significant, as the table C
indicates, but the decrease for the d r y - s t o r e d concrete is w e l l outside the range of experimental variation.
This s u g g e s t s that continued curing in the absence of
external water results in f i n e - s c a l e porosity or cracking from shrinkage as the
Vol. 2, No. 4
455 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
hydration process continues: this can c l e a r l y be avoided if an e x t e r n a l source of m o i s t u r e is available, as in wet curing. Wire Reinforced Concrete The most significant r e s u l t is that for so small a fibre volume fraction as 2%, the f r a c t u r e energy of the composite is at least 2 o r d e r s of magnitude g r e a t e r than that of u n r e i n f o r c e d concrete.
F u r t h e r m o r e , in each case the f r a c t u r e e n e r g y of
w e t - c u r e d m a t e r i a l is higher than that of the d r y - c u r e d , and the ratio 7F(wet)/TF(dry) is slightly higher (about 1.5) for the high carbon steel m a t e r i a l than for the mild steel m a t e r i a l (about 1.3).
T h e r e appears to be no v e r y m a r k e d effect of continued curing
in w a t e r or in air, although t h e r e is a slight indication that the toughness of concrete r e i n f o r c e d with mild steel is i n c r e a s e d very slightly as curing continues, w h e r e a s that of the concrete containing b r a s s - p l a t e d wire falls slightly.
It t h e r e f o r e appears
that in the long t e r m r e i n f o r c e m e n t with mild steel wire is likely to give the more s a t i s f a c t o r y r e s u l t s , f r o m a f r a c t u r e e n e r g y point of view. wire has the higher strength and is b r a s s - p l a t e d .
The high-carbon steel
It is t h e r e f o r e more expensive.
But since the short lengths used were below the c r i t i c a l t r a n s f e r length, Lc, for both types of w i r e , the strength advantage of the high carbon steel is partly wasted since no fibres as short as 2.5 cm can be broken during f r a c t u r e .
The b r a s s plating might
be supposed to inhibit attack on the wire by the alkaline m a t r i x and the unplated mild steel ought, in t h e o r y , to be s e r i o u s l y attacked especially in wet concrete.
A small
degree of c h e m i c a l attack could of course account for an i n c r e a s e d f i b r e / m a t r i x bond strength and this, for fibres s h o r t e r than Lc, should i n c r e a s e the work of fracture. Although 7 F is i n c r e a s e d by at least 2 o r d e r s of magnitude by the incorporation of 2 vol. % of w i r e s , K concrete.
C
is only marginally i n c r e a s e d above its value for plain
The effect of continued ageing is again not very significant except for
the w e t - c u r e d mild s t e e l / c e m e n t .
There does, however, appear to be reasonable
evidence that the use of the mild steel r e i n f o r c e m e n t confers g r e a t e r r e s i s t a n c e to c r a c k initiation, as indicated by Kc, than the high carbon steel.
However, it is
c l e a r l y the concrete r a t h e r than the w i r e s that controls this phase of f r a c t u r e . In o r d e r to t e s t the effect of fibre settling during casting, samples cut in the t h r e e orientations shown in figure 3 were impact t e s t e d a f t e r 7 weeks curing.
The
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m a t e r i a l was d r y - c u r e d c o n c r e t e r e i n f o r c e d with 0.25 m m dia. m i l d st eel w i r e s . The ef f ect of f i br e settling is to r e d u c e the n u m b e r of f i b r e s lying in or cl ose to the x 3 direction. cut f a c e s .
In v e r t i c a l cut s l i c e s t h e r e w e r e r a r e l y any of t h e s e visible on the Breaking s a m p l e s of or i e nt a ti on C should r e q u i r e m a x i m u m e n e r g y since
this mode of f r a c t u r e would involve the l a r g e s t num ber of w i r e s , while those in orientations A and B should r e q u i r e roughly s i m i l a r e n e r g i e s , but c o n s i d e r a b l y less than s amp les C.
The means of six Charpy t e s t s f o r ori ent at i ons A, B and C w e r e :
7 F (A) = 3. 8 k J m 7F (B) - 5 . 9 k J m ~F (C) = 9.5 k J m
-2 -2
-2
F r o m these r e s u l t s it can be s e e n that the w o r k of f r a c t u r e of B s a m p l e s is in fact higher than that of A s a m pl es , possibly b e c a u s e in the slicing of A -t ype s a m p l e s , f i b r e s that will ul t i m a t e l y sp~m the c r a c k a r e cut s h o r t e r than t h o s e in B s a m p l e s . A is also the o r i e nt a t i on of all s a m p l e s f o r which t e s t r e s u l t s a r e given in the table. Samples cut f r o m the s a m e b a r as that used for the o r i e n t a t i o n e x p e r i m e n t s and t e s t e d in slow bending gave a m ean value of ~ F = 3 . 4 k J m -2.
This suggests, f i r s t ,
that the v a r i a t i o n f r o m b a r to b a r was not g r e a t (see table) and, second, that the simple and r a p i d Charpy impact t e s t may give a l m o s t the s a m e r e s u l t as the slow bend tes t, a m a t t e r of some i m p o r t a n c e to any d e s i g n e r i n t e r e s t e d in s e r i o u s a p p l i c ation of f r a c t u r e m echani cs to o n - s i t e testing of m a t e r i a l s .
However this is a
hypothesis that r e q u i r e s much f u r t h e r testing. Glass F i b r e R e i n f o r c e d Concrete T h e r e is an i n c r e a s e in ~ F of only 20 or so t i m e s in wet and d r y c u r e d c o n c r e t e r e i n f o r c e d with E - g l a s s , and although a continued w e t - c u r e a p p e a r s to r a i s e this still f u r t h e r , continued dry curing br i ngs about a d e t e r i o r a t i o n in toughness.
T h i s is by
no m e a n s the c a t a s t r o p h i c d e t e r i o r a t i o n that might have been e x p e c t e d f r o m the known e f f e c t s of the alkaline m a t r i x on f i br e strength.
However Kc, which r e f l e c t s the
a c tu al f r a c t u r e s t r engt h instead of the w o rk of f r a c t u r e , is c o n s i d e r a b l y r e d u c e d on prolonged e x p o s u r e even though in the f i r s t instance the w e t - c u r e d gl ass r e i n f o r c e d c o n c r e t e has a higher K value than plain c o n c r e t e . This m a t e r i a l is t h e r e f o r e c i n f e r i o r on mo s t counts to the w i r e r e i n f o r c e d s y s t e m , and even the substitution of
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457 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
a l k a l i - r e s i s t a n t g l a s s could not make it a s e r i o u s c o m p e t i t o r f r o m the point of view of f r a c t u r e toughness.
Discussion F r a c t u r e of Plain Concrete The values of YF and Kc are in reasonable a g r e e m e n t with those c i ~ d by others, viz Welch and Haisman (3) and Kaplan (2) for example.
An indication of the applic-
ability of f r a c t u r e mechanics ideas to a nonhomogeneous s y s t e m such as concrete can be obtained f r o m the equality K
2 c
= EG
C
if independent m e a s u r e m e n t s of K and G can be obtained. C
c
Since for deep notches
our YF for plain concrete a g r e e s almost exactly with Kaplan's value of Gc m e a s u r e d by the compliance method, we have f o r dry and wet c u r e d concrete K = 0. 4 MNm - 3 / 2 , c G = 20 J m -2. If we a s s u m e that E for a s a n d / c e m e n t m o r t a r is about 20 GNm -2, e
then K2 ~ 1 6 x 1010 N2m -3,
and
EG ~ 4 0 x 1 0 1 0 N 2 m -3
c
C
The discrepancy is not too g r e a t considering the complexity of the concrete s t r u c t u r e . F r o m another point of view, given the flexural f r a c t u r e s t r e s s , af, for un-notched samples, and the m e a s u r e d values of YF' we can e s t i m a t e the inherent flaw size in the plain concrete as given by the Grfffith equation 2EY F c = ~
........
(4)
M e a s u r e d values of ~f were as follows: Cured 7 weeks:
~f (wet) = 11.1 MNm -2 ; ~f (dry) = 4.7 MNm -2
Cured 6 months:
~f (wet) = 11.3 MNm-2; vf (dry) = 7.3 MNm -2
With these values and those of YF in the table we find that the inherent c r a c k size is 7 to 10 m m in dry c u r e d concrete and 2 to 3 m m in the w e t - c u r e d .
The implication
is that cracking in w e t - c u r e d concrete occurs at the a g g r e g a t e / c e m e n t interface, since the size of the largest sand particles is of the o r d e r of 2ram, whereas in d r y c u r e d m a t e r i a l much l a r g e r shrinkage c r a c k s a r e p r e s e n t . new - they m e r e l y confirm r e s u l t s of other work.
These ideas are not
458
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F r a c t u r e of R e i n f o r c e d C oncr e t e The s o u r c e of the high f r a c t u r e e n e r g y of c o n c r e t e r e i n f o r c e d with 2 vol. % of s t eel wire is la r gel y the work of pulling f i b r e s out of the m a t r i x a f t e r the latter has cracked.
Cottrell (4} has pr opos e d a simple model which gives the f r a c t u r e e n e r g y
of a composite that r e s u l t s f r o m w or k done in pulling out the fi bre ends against the f i b r e / m a t r i x friction: Wf =
Vf • £2 12d
. ........
~ < ~ c
(5) ........
w her e Vf is the fibre volume fraction, • is the f i b r e / m a t r i x i n t e r f a c i a l friction, ~ is the fibre length and d its d i a m e t e r .
The fri ct i on s t r e s s was d e t e r m i n e d independently
by pulling out lengths of w i r e e m b e d d e d in the c o n c r e t e a f t e r 7 weeks curing. Approximate values w e r e : f o r low carbon s t eel w i r e in w e t - c u r e d c o n c r e t e , ~ ~
1.5 MNm -2, -2 in d r y - c u r e d c o n c r e t e , ~ ~. 0.7 MNm ;
f o r high c a r b o n s t eel w i r e (brass-plated} wet cured, • ~ 0.5 MNm -2, and dry cured, ~ Z 0.5 MNm -2. T hes e r e s u l t s suggest that t h e r e is a c h e m i c a l r e a c t i o n between the c o n c r e t e and s t eel that is intensified by the p r e s e n c e of e x c e s s m o i s t u r e .
The b r a s s plating, as
might be expected, pr e ve nt s any such i nt eract i on however.
The highest value found
in this w o r k was much lower than the range of about 2.5 - 4 . 0 MNm -2 usually quoted f o r bond s t r e n g t h s .
It should be noted however that t hese a r e the dynamic f r i c t i o n
s t r e s s e s and not the much higher static f r i c t i o n s t r e s s e s that a r e usually r e a c h e d only m o m e n t a r i l y until the initial c h e m i c a l bond is b r o k e n and b e f o r e the p r o c e s s of pull-out p r o p e r begins.
Substitution of values of v, £ and d then gives for the
f r i c t i o n a l f r a c t u r e w or k of w e t - c u r e d c o n c r e t e , Wf = 6.5 k J m -2 (mild s t e e l wires} and 0. 8 k J m -2 (high c a r b o n s t eel wires}.
C o t t r e l i ' s model is f o r c o m p o s i t e s
containing aligned f i b r e s , and the effective volume f r a c t i o n of r e i n f o r c e m e n t will be less than the nominal Vf in r a ndom fibre c o m p o s i t e s .
By inspection of a large
n u mb er of f r a c t u r e s u r f a c e s it was possible to e s t i m a t e that an a v e r a g e of 30 f i b r e s 2 i n t e r s e c t e d the c r a c k plane. This is equivalent to about 105 f i b r e s p e r m of f r a c t u r e s u r f a c e , o r about 55% of the nominal fibre content which, f o r Vf = 0.02, is 4 V f / ~ d 2 = 1.8 x 105 f i b r e s m -2.
This is a much higher p r o p o r t i o n than the 41%
e s t i m a t e d by Romualdi and Mandel (5) for a p e r f e c t l y random com posi t e, and this
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459 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
probably r e f l e c t s the fact that the fibre distribution in our m a t e r i a l s was not fully r a n d o m in t h r e e dimensions.
This c o r r e c t i o n f a c t o r for Vf (effective) then gives f o r
the f r i c t i o n a l f r a c t u r e work: Wf = 3.6 k J m -2 f o r mild st eel w i r e s ; Wf = 0.44 kJ m -2 f or high carbon st eel w i r e s . T h e s e r e s u l t s suggest that o v e r t h r e e - q u a r t e r s of the total f r a c t u r e e n e r g y of mild s t e e l r e i n f o r c e d c o n c r e t e is d e r i v e d f r o m the w ork of fibre pull-out, p a r t i c u l a r l y if t h e r e has been s om e s u r f a c e attack of the w i re by the cem ent , butthe pull-out of b r a s s - p l a t e d high car bon s t e e l f i b r e s a p p a r e n t l y c o n t r i b u t e s less than a fifth of the total. Helfet and H a r r i s (6) have shown that an important contribution to the f r a c t u r e e n e r g y of c o m p o s i t e s containing r a n d o m l y - o r i e n t e d f i b r e s is the w ork of plastic s h e a r i n g of any f i b r e s that a r e not lying n o r m a l or p a r a l l e l to the c r a c k plane.
A
m e t a l f ib r e of s h e a r s t r e n g t h ~y, lying at an angle 0 to the c r a c k plane, will be pulled out of one c r a c k face and at the s a me t i m e will be s h e a r e d along the complete pull-out length through the angle 0.
If the pulled out length is ~' and the fibre c r o s s
s ectio n al a r e a is A, the work of plastic sheari ng a non-work hardening wire is • 0 Y p e r unit volume, or v 0 $ ' A Joules p e r fibre. If N f i b r e s p e r square m e t r e of c r a c k Y face a r e involved and t h e i r mean d i s p e r s i o n about the n o r m a l to the c r a c k plane is e , the plastic d ef o r m a t i on w or k is
or
Ws = NVy~ ~' A
J m -2
p e r f r a c t u r e face,
W
Jm -2
if both f r a c t u r e faces a r e
s
= ½N ~ e ~' A y
c o n s i d e r e d by analogy with Wf and ~F"
N is, as we have seen, about 105 f i b r e s m
and ~ ' was found, by inspection, to be always of the o r d e r of 7 m m .
-2
The t ensi l e
s t r e n g t h of the high c a r b o n s t e e l w i r e s is 2.1 GNm -2 and that of the mild st eel is 0.9 GNm -2
"Cy = ay/2
If we make the additional crude assum pt i on that ~ is ~/6, and take , we obtain: W W
s s
= 3.4 k J m
-2
f o r w e t - c u r e d high c a r b o n st eel f i b r e s ,
= 0.8 k J m -2 f o r w e t - c u r e d mild s t e e l f i b r e s .
The total wo r k o f f r a c t u r e , (Wf +W ), is thus some 4 . 4 kJm -2 f o r the mild s t e e l s -2 w i r e s and 3 .9 k J m f or the high c a r b o n steel, and this d e g r e e of a g r e e m e n t with the
,
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Vol. 2, No. 4 FRACTURE MECHANICS, FIBRE, REINFORCEMENT,CONCRETE
r e s u l t s in the table is c e r t a i n l y as much as can be e x p e c t e d c o n s i d e r i n g the c r u d i t y of the models and the high v a r i a b i l i t y of the t e s t data.
The r e s u l t s suggest f a i r l y
c l e a r l y that f u r t h e r i m p r o v e m e n t s in f r a c t u r e e n e r g y a r e m o r e likely to be gained f r o m using mild steel w i r e s , as long as they can be s a t i s f a c t o r i l y mixed into the c o n c r e t e and s u r f a c e t r e a t e d to i n c r e a s e the i nt erraci al friction. It should be borne in mind that al m os t all of the apparent i m p r o v e m e n t s that have just been d i s c u s s e d o c c u r a f t e r the f i r s t signs of c r a c k i n g in the com posi t e.
This is
b o r n e out by the fact that the values of K higher than those f o r plain c o n c r e t e .
for r e i n f o r c e d c o n c r e t e s a r e v e r y little c The i n c r e a s e in initial cracking r e s i s t a n c e , as
indicated by the I~gher f r a c t u r e s t r e s s f o r a given c r a c k length, this being what K
c
m e a s u r e s , is less than a f a c t o r of 2 for the mild st eel r e i n f o r c e d c o n c r e t e , and a l m o s t nothing f or the high c a r b o n steel.
It is important in design to distinguish
c l e a r l y which f r a c t u r e m e c ha ni c s p a r a m e t e r is the r e l e v a n t one f o r any p a r t i c u l a r 2 requirement. It is c l e a r that K c << 2E ~¢F for the r e i n f o r c e d m a t e r i a l s . F r a c t u r e of Glass F i b r e R e i n f o r c e d Concrete The addition of 2 vol. % gl a s s f i b r e s has i n c r e a s e d the w o r k of f r a c t u r e of c o n c r e t e some 40 t i m e s , but this is still too little for the m a t e r i a l to be c o n s i d e r e d as anything but b r i t t l e .
The s t r e s s / s t r a i n c u r v e s f or t h e s e m a t e r i a l s r e s e m b l e d those of plain
c o n c r e t e s a m p l e s m o r e than those of w i r e r e i n f o r c e d s a m p l e s in that the load fell off v e r y rapidly to z e r o a f t e r the initial onset of c r a c k i n g . c l os e to $ c ' f o r t h e r e was v e r y little fibre pull-out.
The fibre length was c l e a r l y The protruding f i b r e s w ere of
the o r d e r of only 2 m m which suggests that $ ~ 8 ram. The c r i t i c a l s t r e s s intensity c is only r a i s e d above that of plain c o n c r e t e if the m a t e r i a l is wet cured, but the p r e s e n c e of e x c e s s m o i s t u r e a c c e l e r a t e s the alkali attack of the gl ass s u r f a c e and prolonged curing in w a t e r r e d u c e s K c again to the value for plain c o n c r e t e although YF is i n c r e a s e d slightly.
T h e r e is a c r i t i c a l balance h e r e between weakening of
the f ib r e as a r e s u l t of c h e m i c a l action, leading to lower c o n c r e t e st rengt hs (and Kc) and roughening of the fibre, leading to i n c r e a s e d f r i c t i o n w ork (and yF ).
Allen (7) has
s u g g es ted that t h e r e is no evidence that the p r e s e n c e of glass f i b r e s inhibits cracki ng of the c e m e n t .
It a p p e a r s that this is not a c c u r a t e , although the benefits of r e i n f o r -
c e m e n t with s mal l Vf of r a n d o m l y - d i s t r i b u t e d f i b r e s a r e c e r t a i n l y not d r a m a t i c . The fall in f r a c t u r e toughness o b s e r v e d in plain c o n c r e t e on prolonged d r y - c u r i n g is
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461 FRACTURE MECHANICS, FIBRE, REINFORCEMENT, CONCRETE
not prevented by the presence of glass fibres, although it is suppressed by steel fibre reinforcement. Acknowledgements This r e s e a r c h was begun as Jane Varlow's third year undergraduate r e s e a r c h project in Materials Science at the University of Sussex.
C.D. Ellis was in receipt
of an S.R.C. studentship for r e s e a r c h on composite materials. References
2.
Fracture Toughness, ISI Publication 121, The Iron & Steel Institute, London (1968). M.F.Kaplan, J . A m e r i c a n Concrete Inst., 58, 581 (1961).
3.
G. B.Welch and B. Haisman, Mat~riaux & Constructions, ~ 171 (1969).
4.
A.H. Cottrell, P r o c . R o y . S o c . , A282, 2 (1964).
5.
J.P.Romualdi and J.A. Mandel, J . A m e r i c a n Concrete Inst., ~
6.
J. Helfet and B. Harris, J. Materials Science, April 1972 (in press).
7.
H.G.AIIen, J. Composite Materials, 5, 194 (1971).
.
657 (1964).