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3 D s ur f ac e i ma ge a n al ys is f o r f r ac tu re m od e li ng o f c em en t- ba s ed m at er ia ls

A n ne B . N i ch o ls a ,, D av id A . L an ge b

a Te x a s A & M U n i v e r s i ty , D e p a r t m e n t o f A r c hi t e c t u re , C o l l e g e S t a t i o n , T X 7 7 8 4 3 , U S Ab U n i ve r s it y o f I l l in o is , D e p ar t me n t o f C i v il E n gi n e er i ng , U r b an a , I L 6 1 80 1 , U S A

R e c ei v e d 8 A p r il 2 0 05 ; a c c ep t e d 1 0 J a n ua r y 2 0 0 6

Abstract

T h e t e xt u re a n d e x po s ed p h as e s o f a f r ac t ur e s u rf a ce a r e d i re c t e v id e nc e o f t h e m e ch a ni c al b e ha v io r o f a c e me n t- b as e d m a te r ia l . D e fl e ct i on ,

m i c r o c r a c k i n g a n d b r i d g i n g a r e t o u g h e n i n g m e c h a n i s m s i n v o l v e d i n f r a c t u r e o f b r i t t l e m a t r i c e s t h a t a f f e c t s u r f a c e r o u g h n e s s . T h i s s t u d y m e a s u r e s

c r a c k d e f l e c t i o n a n d b r a n c h i n g u s i n g 3 D s u r f a c e m e a s u r e m e n t t e c h n i q u e s w i t h c o n f o c a l l a s e r m i c r o s c o p y o f m e c h a n i c a l l y f r a c t u r e d m o r t a r p r i s m s

a n d 3 D s t er e o p a ir m i cr o sc o py o f m e ch a ni c al l y f r ac t ur e d p l ai n c o nc r et e p r is m s. I m ag e a n al y si s t e ch n iq u es w e re u s ed t o i d en t if y p h as e

c o m p os i t io n a n d o u t - o f - s u rf a c e c r a c k b r a n c h i n g f r o m p r o f i l e s o f c r a c ks i n t ru d e d w i t h a l o w m e l t i n g- p o i nt a l l oy . T h e r e s u lt i n g d a t a w a s t h e b a s i s

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

t h e m a t ri x i n d e pe n d e nt f r o m t h e c o m p os i t e b e h a vi o r.

2 0 06 E l se v ie r L t d. A l l r i g h ts r e se r ve d .

Keywords: Image an aly sis; Micro stru ctu re; SEM; Fractu re to u g h n ess; Micro mech an ics

1. Introduction

I n o rd er t o u nd er s ta nd t he f ra ct ur e b eh av io r o f c om pl ex

c e me n t- b as e d c o mp o si t es , r e s ea r c he r s h a ve b e en d r aw n t o a

w i de a r ra y o f t e st in g , i ma g in g a n d m o de l in g t e ch n iq u es [1].

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

t h e r o l e o f t o u g h e n i n g m e c h a n i s m s [2]. W i t h o u t a c c e s s t o d i r e c t

o b se r va t io n o f t h e t o ug h en i ng m e ch a ni c s d u ri n g f r ac t ur e , t h e

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

t h e m i cr o st r uc t u ra l r e s po n se t o s t ra i n [3] . F ra ct ur e m od el s o f

c r ac k o pe ni ng b eh av io r t ha t r el y o n l in e ar e la st ic f ra ct ur e

m e c h a ni c s t h e o r i e s h a v e b e e n a p p l ie d t o p r o v id e s o m e i n s ig h t t ot h e b e h a vi o r o f t h e s e n o n - l i n ea r e l a s ti c , q u a s i -b r i t tl e m a t er i a l s

[2,4] . I ma gi ng t ec hn iq ue s s uc h a s l as er - sc an ni ng c on fo ca l

mi croscopy [5], 3 D t om og ra ph y [6], s te r eo m ic ro sc op y a nd

st ereophot ogramy [7] h a v e b e e n u s e d t o c h a r a c t e r i z e a s u r f a c e

o r v ol um e f ro m r ep re s en ta ti ve s ur f ac e o r s ec ti on i ma ge s o f

c e m e n t- b a s e d m a t e r i a ls . I m a g in g o f s e c t io n s f i l l ed w i t h v a r i o u s

penet rant s, i ncl udi ng dyes and l ow-t emperat ure mol t en met al s,

by opt i cal or el ect ri cal mi croscopy such as scanni ng el ect ron

m i cr o sc o py ( S EM ) o r d i gi ta l i ma g in g , i s u s ef u l f o r c a pt u ri n g

sl i ces o f c r ac k b e ha v io r [710]. S ec ti on i ma ge s h av e b ee n

u s ed e x te n si v el y t o c h ar a c te r iz e t h e p h as e s a n d m o rp h ol o gy o f

t h e m i c r os t r u c tu r e [11,12] .

T he i nf or ma ti on c ol le ct ed b y c ha ra ct er iz in g t he s ur f ac e

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

c o mp u ta t io n al m o de l s. T h e s u r fa c e t o rt u os i ty d a ta a l on e h a s

been used t o correl at e t he roughness t o mechani cal propert i es

[13,14], a s w el l a s t o e xa mi ne t he r el at io ns h ip o f s ca li ng o r

f r a c t a l n a t u r e o f t h e s u r f a c e w i t h t h e t o u g h n e s s [15] . A d d i t i o n a l

C e m en t a n d C o n c r et e R e s ea r c h 3 6 ( 2 0 06 ) 1 0 9 81107

C o r r e s po n di n g a u t h o r. Te l . : + 1 9 7 9 8 4 5 6 5 40 ; f a x : + 1 9 7 9 8 4 5 6 5 4 0.

E -mail address: an ich o ls@tamu .ed u ( A . B. N i c ho l s ) .

T ab l e 1

Mo rtar mix sp ecificatio n s

S et N o. of

sp ecimen s

W/

C

Cemen t/

s a n d r a t i o

b y weig h t

Flu o rescen t

d y e ( b y

w e i g ht w a t er )

(%)

Air

en train men t

( b y w e i gh t

c e m en t ) ( % )

Fresh

m o r t ar a i r

co n ten t

(%)

A 6 0.5 1:1 5 0. 82

B 6 0.5 1:1 5 0 .3 3. 57

C 6 0.5 1:2 5 1. 85

D 6 0.5 1:2 5 0 .3 7. 70

E 6 0.5 1:1a 5 0. 82

a B a s ed o n e q u iv a l e nt v o l um e o f c e r am i c b a l l s.

0 0 0 8- 8 8 46 / $ - s e e f r o n t m a t t e r 2 0 06 E l s e vi e r L t d . A l l r i g h t s r e s e r v e d.d o i:10.1016/j.cemconres.2006.01.002

mailto:anichols@tamu.edumailto:anichols@tamu.eduhttp://dx.doi.org/10.1016/j.cemconres.2006.01.002mailto:anichols@tamu.eduhttp://dx.doi.org/10.1016/j.cemconres.2006.01.002

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i n ve s ti g at io n s h a ve c o mp a r ed t h e i n te r f ac e t r an s it io n z o ner o u g h n e s s t o f r a c t u r e t o u g h n e s s i n c o n c r e t e [16] . M e a s u r e m e n t s

o f t h e o r ie n ta t io n a n d v o lu m e f r a c t io n o f a g gr e ga t e h a ve a l so

been used t o st udy effect s of bri dgi ng at t he crack face wi t h

r e s p e c t t o m a t r i xa g g r e g a t e b o n d [17] . M o d e l s f o r t h e b e h a v i o r

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

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

o n t h e i n fl u en c e o f t h e d e f l ec t io n a n gl e o f t h e c r a c k p a t h [18] .

M a ny m o de l s a r e l i mi te d t o p l an a r e x pl o ra t io n s o f t o ug h ne s s

a l th o ug h s u bs u r fa c e o r 3 D m e ch a ni s ms s u ch a s b r an c hi n g a r e

c o n s id e r e d t o c o n t ri b u t e t o t h e f r a c t u r e e n e r g y.

T hi s p ap er d es cr ib es t he f ra ct ur e s ur fa ce a nd p ro fi le

c h a r a ct e r i za t i o n a n d i m a g e a n a l y s i s m e t h od o l o gy f o r o b t a in i n g

d a ta i n t h e f o rm o f s u rf a c e t o po l og y, c r ac k b r an c hi n g m e as u r ea n d p h as e c l as s i fi c at i on o f t h e s u rf a c e e l e m e nt s . T h is d a ta i s

i n te n de d f o r u s e i n m ic r om e ch a ni c al m od e li n g t h at c o ns i de r s

t h e e f f ec t o f s u rf a c e t o rt u os i ty a n d m a te r ia l p h as e p r op e rt i es

o n t he s tr ai n e ne rg y r el ea se r at e o f m or ta r a nd c on cr et e

mat eri al s.

2. Experimental technique

To e x am i ne t h e r e la t io n sh i p o f m ic r os t r uc t ur a l g e om e tr y

t o f ra ct ur e t he t es t m at er ia l s w er e d es ig ne d w it h a gg re ga te

s iz e, a gg re ga te v ol um e a nd e nt ra in ed a ir a s t he v ar ia bl e

paramet ers i n order t o exami ne t he degree of porosi t y,i nd uc e d c ra ck s , c ra ck d ef le c ti on a nd c ra ck p la ne . T he t es t

s pe ci me ns w he re m ec ha ni ca ll y t es te d a nd t he f ra ct ur e

e vi de nc e w as p re pa re d f or e xa mi na ti on o f c ra ck p ro fi le s

a n d s u r f a c es .

2 . 1 . M a t e r i al s

F iv e m ix es w er e c as t f or t he m or ta r s pe ci me ns a nd o ne

m ix w as c as t f or t he c on cr et e s pe ci me ns . A ll m ix es u se d

Ty pe I P or tl an d C em en t a t a w /c r a ti o o f 0 .5 . F lo re s ce nt d ye

( pr op yl en e g ly co l m on om et hy l e th er ) w as a dd ed a t 5 % b y

w ei gh t o f w at e r. T he s an d f or t he m or ta r s w as 2 0/ 30 A ST MC 7 78 s ili ca s an d. An a ir e nt ra ini ng a ge nt wa s a dd ed a t

0 .3 % b y w ei gh t o f c em en t. T he a gg re ga te f or o ne s et ( E)

w as 0 .7 91 .1 8 m m a lu mi na c er am ic b al ls . T he c on te nt o f

a lu mi na b al ls i n t he m or ta r w as b as ed o n t he e qu iv al en t

v ol um e o f s il ic a s an d f or a 1 :1 r at io o f c em en t t o s an d b y

w ei gh t. T he b ul k d en si ti es o f t he s il ic a s an d a nd c er am ic

bal l s were measu red as 1.755 g/ cm3 a nd 2 .1 04 g / cm3,

r es pe ct iv el y. T he a gg re ga te f or t he c on cr et e w as c r us he d

l im e st o ne w it h m a xi m um s i ze o f 3 / 4 i n . a n d w a sh e d g r av e ll y

s a nd . T h e m o rt a r m i x s p ec i fi c at i on s a r e p r es e nt e d i n Ta b le 1,

a nd t he c on cr et e m ix s pe ci fi ca t io n d et er mi ne d b y t he A CI

2 11 .1 m ix d es ig n m et ho d i s p re se nt ed i n Ta bl e 2. Thepropert i es for t he aggregat es of t he concret e are l i st ed i n

Ta b le 3. T he f re sh a ir c on te nt o f t he m or ta r w as m ea su re d

by ASTM C185 adj ust ed for si l i ca sand cont ent and i s al so

present ed i n Ta b le 1.

A ll m or ta r s pe ci me ns we re c as t a s 1 7. 8 3 .8 2 .4 c m

( 7 1 . 5 1 i n . ) b e a m s w i t h a n o t c h a t m i d s p a n o f 1 . 2 7 c m ( Fig.

1) . S e t E w a s c a s t w i t h m o r t a r c o n t a i n i n g d y e a n d a l u m i n a b a l l s

f or t he c en te r 1 .5 c m . T he r es t o f t he b ar w as c as t w it h p la in

past e and no dye. Al l ot her mort ar bars were cast and cured i n

t h e h o r i zo n t a l p o s it i o n .

T he c on cr et e s pe ci me ns w er e c as t a s 7 1. 1 1 5. 2 1 0. 2 c m

( 2 8 6 4 i n . ) b e a m s w i t h a n o t c h a t m i d s p a n o f 5 . 1 c m ( 2 i n . ) .

T h e c o nc r et e b e am s w e re g e om e tr i ca l ly p r op o rt i on a l t o t h em o r t a r b e a m s b y a f a c t o r o f 4 .

A ll s pe ci me ns w er e c ur ed i n l ab or a to ry c on di ti on s f or

1 d ay a nd th en mo is t c ur ed f or a t ot al of 1 4 da ys pr io r t o

m ec ha ni ca l t es ti ng o f t he n ot ch ed b ea ms i n t hr ee -p oi nt

bendi ng usi ng t he RILEM t wo-paramet er fract ure model

met hod [19] . F ou r b ea ms f r om e a ch m or ta r a nd c on cr et e s et

w er e l oa de d t o s ep ar a ti on a ft er c om pl et io n o f m ec ha n ic al

t e st i ng . Tw o b e am o f e a ch m o rt a r s e t w e re l o ad e d t o 7 5 % a n d

8 5% o f p ea k l oa d o n t he s ec on d l oa di ng c yc le a nd a w ed ge

w as i ns er te d i nt o t he c as t n ot ch es t o k ee p t he c ra ck s f ro m

cl osi ng.

2 . 2 . C r a c k i n f i l t r at i o n

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

f o r i n tr u si o n, s e ct io n s w e re r e mo v ed a t m id s pa n t h ro u gh t h e

Table 2

Co n crete mix sp ecificatio n s

Set No. of

sp ecimen s

W/

C

Water

(k g /m3)

Cement

(k g /m3)

Coarse

aggregate a

(k g /m3)

Fin e

a g g re g at e a

(k g /m3)

Concret e 4 0.5 1 78 (3 00

lb /y d3

)

3 5 6 (6 0 0

lb /y d3

)

1 1 9 7 (2 0 1 8 lb /

y d3

)

6 8 1 (1 1 4 8 lb /

y d3

)a Su rface satu rated d ry.

Table 3

Co n crete ag g reg ate p ro p erties

Coarse aggregat e Fine aggregate

TM = 0.8% TM = 2.0 8%

AD = 1.4% AD = 1.8 %

SSD = 2 . 6 8 SSD = 2 . 6

U n i t w t .SSD = 1 0 1 .4 0 l b / f t 3 F M = 2 . 6 3

dyed mortar section

b) Set Ea) Sets A, B, C, D

F i g . 1 . M o r ta r b a r g e o m e t ry.

1099 A .B . Nichols, D.A . Lange / Cement and Concrete R esearch 36 (2006) 10981107

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c r os s s e ct i on ( F i g . 2a ) . T h e s e p i e c e s w e r e t h e n s e c t i o n e d i n t o a

c en te r p ro fil e a nd a n e dge p ro fi le (F ig . 2b), whi ch were

g e ne r al l y 1 c m w id e . T h e s p e c im e n s a m p le s w e re o v en d r ie d

( 1 05 C ) p r io r t o i n tr u si o n.

T he i nt ru s io n p ro ce du re w as d er iv ed f r om t he i nt ru si on

porosi met ry t echni que i nvol vi ng Wood's met al , an al l oy wi t h a

l o w m e l ti n g p o i n t, u s ed b y W il l is e t a l . [20] Wo o d' s m e ta l i s

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

poi nt near 66 C wi t h no appreci abl e vol ume change. The

m or ta r s pe ci me ns a nd Wo od 's m et al w er e l oa de d i nt o a n

a u to c la v e, w h ic h w a s e v ac u at e d, h e at e d a b ov e 9 0 C , p r es s ur -i ze d t o 1 0. 3 MP a ( 150 0 ps i) a nd a llo we d t o c oo l to r oo m

t emperat ure.

2 . 3 . C o n f oc a l m i c r os c o p y

A l a s e r- s c a n ni n g c o n f o c a l m i c r o s c o p e w a s u s e d t o o p t ic a l l y

o bt ai n s ur f ac e e le va ti on d at a a nd i ma ge s c on ta in in g p ha se

i n f o r ma t i o n u s i n g r e f l e c ti v e l a s e r l i g ht u n d e r n o n - f l u o r e sc i n g

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

s p e c i m e n s ( F i g . 3) . T h e c o n f o c a l m i c r o s c o p e r e c o r d s a s e r i e s o f

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

i m a g e i n w h i c h e a c h p i x e l i s a s s i g n e d a v a l u e t h a t r e p r e s e n t s t h ez l e v e l o f t h e i n - f o c u s p l a n e . T h e e l e v a t i o n d a t a c o n t a i n e d i n t h e

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

n um er ic al ly. T he 2 56 5 12 p ix el d ig it al i ma ge s c on ta in t he

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

a pp ea rs a s a f oc us ed i ma ge o f t he s ur f ac e, i n t he b ot to m h al f

( F i g . 4).

T he i ma ge s w er e a cq ui re d w it h a n a r go n l as er s ou rc e a nd

r e d- d e te c ti n g p h ot o mu l ti p li e r u s in g s q ua r e p i xe l s, a 2 . 5 l e ns

a t 2 0 t im e s f o r a 5 0 m a g ni f ic a ti o n, a n d a f l uo r es c en t f i lt e r f o r

t h e f l u o r e s c e n t i m a g i n g . A s q u a r e m a t r i x o f 1 6 i m a g e s o n e a c h

s u rf a c e w e r e r e qu i re d t o p r ov i de a 9 5 % d e g r ee o f c o nf i de n ce

a n d c o nf i de n ce i n te r va l o f 8 % b a se d o n t h e s t an d ar d d e vi a ti o n

o f t he r ou gh ne s s n um be r ( a m ea su re o f s ur f ac e r ou gh ne s s)

f ro m p re vi ou s m ea su re me nt s o n a m or ta r w it h t he s am e

a g gr e ga t e s i ze a n d d i st r ib u ti o n [21] . T he f ie ld s iz e f or th e

i m a g e s w a s a p p r o x i m a t e l y 3 . 5 m m 3 . 5 m m ( 0 . 0 1 3 8 m m / p i x e l ) .

The z s l ic e t h ic k ne s s w a s 1 3 .5m . T h e c o nf o ca l m i cr o sc o pe

s ca nn ed t he s ur fa ce o nc e p er z e l ev a ti on . C on tr a st a n d

bri ght ness was cont rol l ed t o avoi d sat urat i on of dark or bri ght

a r e as ( l ow a n d h i gh ) r e su l ti n g i n a r ti f ic i al l y f l at t o po g r ap h y.

S at ur at io n d id o cc ur o n o r a r ou nd t he a gg re ga te d ue t o t he

f a c e t e d f e a t u r e s o f t h e s i l i c a g r a i n s i n 1 5 % o f t h e i m a g e p i x e l s .

T hi s r ef le ct io n o f t he l as er l ig ht c ou ld n ot b e d ir ec te d o r

i de nt if ie d a s n oi se a nd i ma ge f il te ri ng w as n ec es sa ry t oi n t e rp o l a te t h e m i s s in g d a t a [22] .

a) midspan section

edge section

center section

b) center line profile and edge profile

F i g . 2 . C r a ck s e c t i on g e om e t r y.

Set A Set B Set C Set D Set E

10 mm

F i g . 3 . T yp i c a l f r a c t u re s u r fa c e s o f m o r ta r b e a ms .

F i g . 4 . D a t a f i l e o f r a n g e i m a g e ( t o p ) a n d c o nf o c al i m a ge ( b ot t o m ).

1100 A . B. N i c ho l s, D . A. L a n ge / C e m en t a n d C o nc re t e R e se a rc h 3 6 ( 2 0 06 ) 1 0 981107

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I ma ge s w er e a ls o t ak en w it h t he f lu or es ce nt f il te r o f t he

i d en t ic a l a r e a a s t h e e l ev a ti o n i ma g e . T h e c o nt r as t a n d b r ig h tn e ss

f o r t h e f l uo r e sc e nt i m ag e s w e re c o nt r ol le d t o s a tu r at e t h e d a rk

v a l ue s r e c o r d ed f o r t h e n o n - r ef l e c ti n g a g g re g a t e s. F ig . 5 s ho ws a

pai r of confoca l i mages wi t hout t he fi l t er and wi t h t hefl uorescent fi l t er.

T h e c o n f oc a l i m a g es a n d c o r r e s po n d i ng f l u o r es c e n t i m a g e s

w er e a na ly ze d t o i de nt if y a gg re ga te s, b ro ke n a gg re ga te s,

i mp re ss io ns o f w he re a gg re ga te s h ad b ee n, a s w el l a s t o

i d en t if y v i si b le v o id s a n d p o re s p ac e s .

2 . 4. 3 D s t er eo p a ir m i c ro s co p y

A 3 D s t er e o p a ir m ic r os c op y e v al u at io n w a s p e rf o r me d o n

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

based on a shi ft of t he opt i cal focal poi nt as a poi nt of

c om pa r is on a nd b ec au se o f t he r an ge l im it a ti on o f t he l as er -

s c a n n i n g c o n f o c a l t e c h n i q u e . T h e f r a c t u r e s u r f a c e s o f t h e m o r t a r s p ec i me n s a n d c o nc r et e s p ec i me n s (F ig . 6) w er e i ma ge d a s

s t er e o p a ir s w it h a s c an n in g e l ec t ro n m i cr o sc o pe , a n d a C CD

v i de o c a me r a a n d s o f tw a re , r e s pe c ti v el y. E x am p le p a ir s a r e

s h o w n i n F i g . 7. T h e p a i r s s i m u l a t e h o w w e p e r c e i v e d e p t h w i t h

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

o f t he m ic ro sc op e o r c am er a . T he d if fe re nc e i n d ep th f r om a

r e fe r e nc e p l an e c a n b e d e te r mi n ed b a se d o n t h e s h i f t b e tw e en

a) non filtered image b) fluorescent image

1 mm

F i g . 5 . C o n fo c a l i m a g e s .

F i g . 6 . Ty p i ca l f r a ct u r e s u r f a c e o f c o nc r e t e b e a m s .

1 mm

a) mortar stereo pair (50X)

10 mm

(left) (right)(left) (right)

b) concrete stereo pair (4X)

F i g . 7 . S u r fa c e s t e r e o p a i r s .

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F i g . 8 . S a m pl e B S E m i c r o g ra p h o f c r a ck p r o fi l e ( 5 0 ) a n d h i s t o g ra m o f g r a y v a l u es .

F i g . 9 . C o m pl e t e e d g e c r a c k p r o f i l e f o r m o r t a r s a m p l e A 6 ( 5 0 ) .

F i g . 1 0 . F u l l c r a c k p r o f i l e a n d p r o fi l e w i t h b r a n c he s r e m ov e d ( f i e l d w i d t h 1 5 . 86 m m ) .

F i g . 1 1 . E x a mp l e s t a c k i m a g es f o r a m o r ta r c o n fo c al i m a g e.

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

f o c a l l e n g th .

F iv e i ma ge s w er e t ak en f or e ac h f ra ct ur e s ur fa ce . T he

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

a n d t h e c e nt e r o f t h e s u r f a ce .

T h e 3 D s t er e o p a ir i m ag e s w e re p r oc e s se d u s in g s o ft w ar e

programs i ncl uded wi t h t he IMIX i magi ng syst em1. T he t ex t

f i le s o f x,y,z g r id p o in t v a lu e s w e re a s se m bl e d a n d c o nv e rt e d

t o b i n a ry r a ng e f i le s . T h e l e ft s t er e o i m a g e t a k en a t 0 t il t w a s

u se d f or i ma ge a na ly si s t o i de nt if y a gg re ga te s, a gg re ga te

i mp r es s io n s, b r ok e n a g gr e ga t es , a n d v i si b le v o id s a n d p o re

spaces.

3. Image analysis

3 . 1 . C r a c k p r of i l e

To e xt ra ct i nf or ma ti on a bo ut t he c ra ck g eo me tr y, t hei n tr u de d c r ac k s p ec i me n s w e re i m ag e d a n d p r oc e s se d w i th a

s er ie s o f i ma ge a na ly si s s te ps t o o bt ai n a d is cr et e c ra ck

c en te rl in e. T he t wo i nt ru de d c ra ck s ec ti on s f r om e ac h

u n f r a ct u r e d m o r t a r b e a m w e r e i m a g ed u s i n g B S E m i c r os c o p y.

T h e h i g h a t o m i c w e i g h t o f t h e W o o d ' s m e t a l a l l o y , c o m p a r e d t o

t h e c e me n t p h as e s a n d s i li c a s a nd , p r ov i de d s h ar p c o nt r as t i n

back sca t t er mode . A t ypi cal cra ck segm ent i mage and

c o rr e sp o nd i ng h i st o gr a m a r e p r es e n te d i n F ig . 8. T he s il ic a

s an d g ra in s a pp ea r t he d ar ke s t, t he c em en t p as te m at ri x i s a

l i gh t er g r ay, a n d t h e Wo o d' s m e ta l i s b r ig h t. T h e b a ck s ca t te r

b) aggregate

impression in range

plot

a) aggregate

impression feature in

confocal image

Fig . 1 2 . Ag g reg ate imp ressio n ch aracterizatio n.

a) stereo composite

image in grayscale

b) void binary image

F i g . 1 3 . Vo i d i d e n t i f i ca t i o n f o r a m o r ta r 3 D s t e r eo i m a ge .

b) aggregate holesa) aggregates d) broken aggregatesc) voids

F i g . 1 4 . E x a mp l e s t a c k b i n a r y i m a g e s f o r a 3 D s t e r e o m o r t a r i m a g e .

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

5 0 a nd w er e s ti tc he d t o c re at e a c om pl et e c r ac k i ma ge . A n

e x am p le i s s h ow n i n F i g . 9 .

T he m ic ro gr ap hs r e ve al ed i mp er f ec t f il li ng o f c ra ck s,possi bl y due t o resi dual wat er vapor pressure present duri ng

m o lt e n m e ta l i n tr u s io n . To o b ta i n t h e c o mp l et e c r ac k p r of i le ,

a n a dd it io na l i ma ge p ro ce s s w as u se d. T he u nf il le d c ra ck

s eg me nt s ( ve ry d ar k a re as ) w er e a dd ed t o t he f il le d c ra ck

s eg me nt s ( ve ry b r ig ht a re as ) t o c re at e t he f ul l c ra ck p ro fi le .

T he c ra ck t hi ck ne ss w as r ed uc ed t o a s in gl e p ix el - wi de l in e

w i th a s k el e to n iz i ng f u nc t io n f o r t h e c o mp l et e d l in e p r of i le .

T he b ra nc hi ng c ra ck s w er e r em ov ed a nd t he l in e p ro fi le

w it ho ut b ra nc hi ng w as r ec or de d. E xa mp le p ro fi le s o f

c om pl et e c ra ck a nd c r ac k w it ho ut b ra nc hi ng a re s ho wn i n

F ig . 1 0.

3 . 2 . M o r t a r p h a s e s e p a r a t i on

F o r b o t h t h e c o n f oc a l i m a g es a n d t h e S E M m i c r og r ap h s o f

t he m or t ar s pe ci me ns , a s er i es o f i ma ge a na ly si s s te ps w er eperformed t o i dent i fy areas of past e, aggregat e, aggregat e

i mp re ss io ns a nd v oi ds a s s ho wn i n F ig . 1 1. T h e f l uo r es c en t

c on fo ca l i ma ge f ro m t he b ot to m h al f o f t he 5 12 2 5 6 p ix el

d ig it al i ma ge w as u s ed t o i de nt if y t he a gg re ga te a re a o n t he

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

t o d is ti ng ui sh t he a gg re ga te a nd a t hr es ho ld w as a pp li ed t o

i de nt if y t he a gg re ga te s a s b la ck t o c on st r uc t a b in ar y i ma ge

(F i g. 1 1b).

T he b in ar y r ep re se nt at io n o f t he a re as o f a gg re ga te

i mp re ss io ns w as d et er mi ne d b y u si ng a g ra y d en si ty s li ce

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

t h e e d ge o u tl i ne . F ig . 1 2 i ll u s t r at e s t h e a g g r e ga t e i m p r es s i o nf ea tu re a nd t he p rof il e i n t he r an ge i ma ge . T he b in ar y

a) aggregate area c) air void areab) aggregate holes d) broken aggregate

F i g . 1 5 . E x a mp l e s t a c k b i n a r y i m a g e s f o r a 3 D s t e r e o c o n c r e te i m a g e.

F i g . 1 6 . C o n cr e t e v i d e o i m a g e a n d e d g e i m a ge .

T ab l e 4

Av e r ag e c r a ck m e a su r e me n t s a n d b r a nc h i ng r a t i o f o r m o r ta r s p e ci m e ns

Samp le

set

L e n gt h o f m a i n

crack (p ix els)

L e n gt h o f

b ran ch es

(p ix els)

Total

len g th

(p ix els)

Bran ch in g ratio

(to tal/main crack )

A 22 61 4 70 2731 1.2 1

B 26 32 6 81 3313 1.2 7

C 42 77 2 659 6939 1.6 6

D 29 14 1 092 4006 1.3 6

E 26 26 4 49 3075 1.1 7

Direction ofcrack propagation

Twist of crack

Tilt of crack

F i g . 1 7 . S u r fa c e s c h em a t i c f o r m i c r om e c ha n i ca l m o d el .

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r e pr e s en t at i on o f v o id s a n d p o re s w a s c o ns t r uc t ed i n t h e s a m e

manner.

T h e f i lt e re d r a ng e i ma g e, a g gr e ga t e b i na r y, h o le b i na r y a n d

v o i d b i n a r y i m a g e s w e r e c o m b i n e d i n t o a n i m a g e s t a c k f i l e . Fig.

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

r a n g e i m a g e .

T h e c o m p o s i t e i m a g e o f e a c h l e f t , r i g h t 3 D s t e r e o p a i r ( Fig.13a ) w a s u s e d t o i d en t if y t h e a r e a s o f i n ta c t a g g r e ga t e, b r ok e n

a gg re ga te , a gg re ga te i mp re ss io ns a nd v is ib le v oi ds o n t he

s u rf a c e. I m ag e a n al y si s u s in g a r a ng e o f t h re s ho l di n g v a lu e s

w a s p e rf o rm e d t o i d en t if y e d ge b o un d a ri e s. A g gr e g at e a r ea s

w e re i d en t if i ed f i rs t w it h r e sp e ct t o t h e c o mp o si t e i ma g e a n d

s to re d i n a b in ar y f il e. W he n a r ea s o f b ro ke n a gg re ga te w er e

i d e n t i f i e d , t h e a r e a w a s r e m o v e d f r o m t h e a g g r e g a t e b i n a r y a n d

a dd ed t o t he b ro ke n a gg re ga te b in ar y f or t he s am pl e. F or

d et er mi ni ng t he v oi d a re a, t he p ix el s pa ce n ot c on ta in in g

a g gr e ga t es o r a g gr e ga t e i mp r es s io n s w a s u s ed t o i d en t if y e d ge

boundari es as descri bed. F i g . 1 3 i l l u s t r a t e s t h e c o m p o s i t e i m a g e

a n d t h e r e su l ti n g v o id b i na r y i ma g e.

T he a gg re ga te b in ar y, b ro ke n a gg re ga te b in ar y, h ol ebi nary and voi d bi nary were combi ned i nt o an i mage st ack

fi l e. F i g. 1 4 s h ow s a n e x am p le o f b i na r y f i le s c o rr e s po n di n g

t o t he r an ge d at a f or a m or ta r 3 D s te re o p ai r. T he c on fo ca l

i ma ge s ta ck f il e f or t he m or ta r d at a d id n ot i nc lu de a b ro ke n

a g gr e ga t e b i na r y i m ag e .

3 . 3 . C o n c r e t e p h a s e s e p a ra t i o n

F or t he v id eo i ma ge s o f t he c on cr et e, a s er ie s o f i ma ge

a na ly si s s te ps w er e p er fo rm ed t o i de nt if y a re as o f p as te ,

a g gr e ga t e, a g gr e ga t e i mp r e ss i on s a n d v o id s (F ig . 1 5) . I ma ge

a na ly si s w as u se d t o i de nt if y t he a gg re ga te a re as u si ng t hem a xi m um v a lu e f o un d b y a n e d ge d e te c to r k e rn e l f o r e a ch o f

e i gh t d i re c ti o ns a r ou n d a p i xe l . F ig . 1 6 i l l us t ra t es t h e v i de o

i ma g e a n d r e s ul ti n g e d ge i ma g e .

T he e dg e d et ec ti on d id n ot d is cr im in at e b et we en v ar ia -

t io ns o f c om po si ti on w it hi n a l ar ge a gg re ga te . O ne o r t wo

o pe ni ng o pe ra ti on s w er e p er f or m ed o n t he e dg e i ma ge s uc h

t ha t t he v er y s ma ll o ut li ne s w er e r em ov ed f r om w it hi n t he

l ar ge a gg re ga te s ha pe s. T he f in e a gg re ga te p ar ti cl es w er ei d en t if i ed f r o m t h e e d ge i m ag e a r ea e x cl u di n g l a rg e a g gr e ga t e

a r ea s u s in g a s e ri e s o f t h re s ho l di n g o p er a ti o ns a n d a d di t io n s .

F ig . 1 6a s hows t he th re sh old ed e dg e i ma ge . A s er ie s o f

e r os i on s w i th d i ff e r en t n e ig h bo r in g p i xe l c o un t s w e re a p pl i ed

t o c le an t he i ma ge o f s in gl e p ix el s n ot i de nt if ie d w it h a ny

aggregat e.

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

v i si b le v o id s w e r e d e t e r mi n ed i n t h e s a me m a no r a s p r es e nt e d

f o r t h e m o rt a r s p ec i me n i ma g e s. T h es e i ma g es w e re c o mb i ne d

i n to a n i ma g e s t ac k f i le . F ig . 1 5 s h ow s a n e x am p le o f b i na r y

f i le s c o r re s po n di n g t o t h e r a n g e d a ta f o r a c o nc r et e 3 D s t er e o

pai r.

4. Results

4 . 1 . C r a c k b r a n ch i n g m e a s u re m e n t

T he l in ea r iz ed c ra ck p ro fi le s w er e m ea s ur ed u si ng t he

rel at i onshi p:

Lengt h 0:948 num: o f o r t h og o n a l n e i g h b o rs 1:340 num: o f d i a g on a l n e i g h b o r s 1

w h er e t h e n u mb e r o f o r th o go n al a n d d i ag o na l n e ig h bo r s w e re

m e a s u r e d b y s c a n n i n g r o w s o f t h e p r o f i l e i m a g e . T h e r e s u l t s f o r t h e m o rt a r s p ec i me n s a r e p r es e n te d i n Ta b l e 4. T h e c a lc u la t ed

branchi ng rat i os di d not show a rel at i onshi p bet ween t he

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

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

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

t h at t h e a s su m ed c o nd i ti o n o f p l ai n s t ra i n w a s v a li d .

4 . 2. P h as e a re a f r a ct i o ns

T he a re a f r ac ti on s c al cu la te d f or t he c on fo ca l i ma ge s o f

m o r t a r a r e p r e s e n t e d w i t h t h o s e c a l c u l a t e d f o r t h e S E M i m a g e s

i n T a b l e 5. T h e i m a g e a n a l y s i s s h o w s g o o d a g r e e m e n t b e t w e e n

m ic r os c op y m e th o d a n d i ma g e a n al y si s t e ch n iq u es f o r p h as ei dent i fi cat i on.

A re a f r ac ti on c al cu la ti on s w er e p er f or me d o n t he p ha se

bi nari es for t he mort ar 3D st ereo pai rs. The area fract i ons

c or r el at e w it h v ol um e f ra ct io ns . T he r es ul ts f or t he m or ta r

s am pl e s et s a r e r ep or te d i n Ta b le 6 a l on g w it h t he v ol um e

Table 5

M o r ta r c o nf o c al a n d 3 D i m a g e a n a l y s i s a r e a m e a s ur e m en t s

C e m en t p a s t e a r e a

(%)

Sand area (%) Air area (%)

Con focal 3D Confo cal 3D Co nfo cal 3D

Set A 68. 26 65.09 3 1.14 33.0 2 0. 60 1 .89

Set B 70. 42 63.35 2 7.56 33.7 5 2. 02 2 .89Set C 56. 26 52.23 4 1.90 46.8 5 1. 84 0 .92

Set D 52. 76 51.51 4 1.06 40.8 2 6. 18 7 .67

Set E 75. 28 72.70 2 3.85 26.5 0 0. 87 0 .80

Table 6

M o r ta r 3 D i m a g e a n a ly s i s a r e a m e a su r e me n t s a n d m i x d e s i g n v o l u m e s

C e m en t p a s t e

v o l um e ( % )

San d vol um e ( %) Ai r vo lum e (% )

Mix Imag es Mix Images Mi x Images

Set A 49 .79 65 .09 49.39 3 3.02 0.82 1.89

Set B 51 .39 63 .35 47.71 3 3.75 3.57 2.89

Set C 24 .28 52 .23 73.87 4 6.85 1.85 0.92

Set D 22 .47 51 .51 69.83 4 0.82 7.70 7.67

Set E 58 .27 72 .70 40.91 2 6.50 0.82 0.80

Table 7

C o nc r e t e 3 D m i x d e s i gn v o l um e s a n d i m a ge a n a l ys i s v o l um e m e a s ur e m en t s

C e m en t p a s t e

v o l um e ( % )

Aggregate

v o l um e ( % )

San d v o lu me

(%)

A i r v o l u m e ( % )

Mix Images Mi x Images Mi x Images Mix Images

27.73 41.49 44.7 8 35.98 26.4 9 21.31 1.0 0 1.22

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f r a ct i on s d e te r mi n ed f r om m ix w e ig h t f r a ct i on s a n d m e as u r e-

m e nt . T h e m e as u re d a g gr e ga t e v o lu m e f r a ct i on s a r e c o ns i s-

t en tl y l ow er t ha n t ho se f ro m m ix w ei gh t f r ac ti on s , a s w as

s e en w i th t h e c o n f oc a l i ma g es , b e ca u se o f t h e b i a s t o wa r d t h e

past e.

A re a f ra ct io n c al cu la ti on s w er e p er f or me d o n t he p ha se

bi nari es for t he 3D st ereo pai r i mages of concret e. The resul t sa re r ep or te d i n Ta bl e 7 a lo ng w it h t he v ol um e f ra ct io ns

d e te r mi n ed f r om m ix w e ig h t f r a ct i on s a n d m e as u r em e nt . T h e

m e as u r ed a g gr e ga t e v o lu m e f r a ct i on s a r e c o ns i st e nt ly l o we r

t ha n t ho se f r om m ix w ei gh t f r ac ti on s , a s w as s ee n w it h t he

m o rt a r i ma g es , b e ca u se o f t h e b i as t o wa r d t h e p a s t e .

4 . 3 . A p p l i ca t i o n i n m i c r om e c h a ni c a l m o d e l i ng

T h e r e s u l t o f t h e c h a r a c t e r i z a t i o n a n d i m a g e a n a l y s i s o f c r a c k

branchi ng rat i o pl ot fi t , range el evat i ons and bi nary i mage

s t a c k s a r e e s s e n ti a l g e o me t r i c a n d m o r p ho l o g ic a l i n f o rm a t i on

r e qu i re d i n a m i cr o me c h an i ca l m o de l o f f r ac t ur e . T h e m o de ld e t e r m i n e s a n a v e r a g e s t r a i n e n e r g y r e l e a s e r a t e b a s e d o n t h e t i l t

a n d t w i s t a n g l e s o f t h e c r a c k p a t h a n d t h e Y o u n g ' s m o d u l u s o f

t h e p h a s e s o n t h e c r a c k s e g m e n t ( m a t r i x , a g g r e g a t e , i n t e r f a c e o r

v oi d) . T he l oc al a ng le o f t il t a lo ng t he c ra ck p ro gr e ss io n i s

d e te r mi n ed f r om t h e c h an g e i n e l ev a ti o n b e tw e en p r og r e ss i ve

pi xel s i n t he bi nary range i mage represent i ng surface geomet ry,

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

e l e v a t i o n b e t w e e n o r t h o g o n a l p i x e l s ( i l l u s t r a t e d i n F i g . 1 7) . T h e

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

s t r e s s i n t e n s i t y f a c t o r s t h a t a r e a f u n c t i o n o f P o i s s o n ' s r a t i o , t h e

u n kn o wn f l at c r ac k s t re s s i n te n s it y f a ct o r, t r ig o no m et r y o f t h e

a n gl e s a n d t h e Yo u ng ' s m od u lu s o f t h e c r a c k s e gm e nt w h os e

phase i s det ermi ned from t he correspondi ng bi nary phase i magesw i th i n t h e s t ac k . W h en a c r ac k s e gm e nt s p an s t wo p h as e s, t h e

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

e n er g y r e l ea s e r a t e f o r t h e s u rf a c e w i th r e sp e ct t o t h a t o f a f l at

c r a ck c a n b e d e te r mi n ed a n d s u bs e qu e nt l y m a gn i fi e d w it h t h e

branchi ng rat i o (t aki ng i nt o account t he subsurface cracki ng) i n

o rd er t o i de nt if y t he c ri ti ca l s tr es s i nt en si ty f ac to r f or a

t h eo r e ti c al f l at c r ac k i n t h e m a tr i x, i n e s se n c e, e x tr a c ti n g t h e

c o nt r ib u ti o n o f t o rt u os i ty a n d i n cl u si o ns f r o m t h e c o mp o si t e

s t r a i n e n e r g y r e l e a s e r a t e [22].

5. Summary

T h e r e se a r ch d e sc r i be s t h e i m ag e a c qu i si ti o n o f m o rt a r a n d

c o nc r et e f r ac t ur e s u rf a c es u s in g c o nf o ca l l a se r m i cr o sc o py,

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

f r ac tu re s ur f ac e m or ph ol og y a nd g eo me tr y. A n i nt ru si on

t e ch n iq u e u s in g Wo o d' s m e ta l a l lo w ed c r ac k p r of i le s p e rp e n-

d i cu l ar t o t h e f r a ct u re s u rf a c e t o b e c a pt u re d w it h b a ck s ca t te r

e le ct ro n m ic r os c op y. I ma ge a na ly s is w as p er f or me d o n t he

c r a ck m i cr o gr a p hs t o i d en t if y a m e as u re o f c r a ck b r a nc h in g ,

w h il e c o nf o ca l i m ag e s a n d t h e 3 D s t er e o p a i r s f r om v i de o a n d

e l ec t ro n m i cr o sc o py w e re u s ed t o i d en t if y a r ea s o f a g gr e ga t e,

past e, voi ds, broken aggregat es and aggregat e i mpressi ons. The

r es ul ti ng b in ar y a nd r an ge m ap s w er e d at a r eq ui re d f or a

m i c r om e c h an i c a l m o d e l , w h i c h c a n c a l c ul a t e a n a v e r a ge s t r a i n

r e le as e r a te b as ed o n t he a ng le a nd p ha se o f c ra ck s e gm en t i n

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

c r a c k b r a n c hi n g .

T h e i m a g e a n a l ys i s s o l ut i o n p r e s e n t s a q u a n ti f i a bl e m e t h od

o f o b ta i ni n g s u rf a c e m o rp h ol o gy a n d s u bs u rf a ce c r ac k in g t h at

c a n b e r e la t ed d i re c tl y t o t h e m e ch a ni s ms o f c r ac k b r an c hi n g

a n d d e f l e ct i o n i n c e m e nt - b a s ed m a t er i a l s.

Acknowledgements

Th is r es ea rch wa s s up por te d b y t he N SF Ce nt e r f or

A dv an ce d C em en t- Ba se d M at er ia ls ( NS F G ra nt N o. D MR

88808432-01).

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