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International Journal o f Fracture 41: R55-R58 1989. R5 5

1989

KluwerAcademic Publishers.Printed n the Netherlands.

F A T I G U E C R A C K P R O P A G A T I O N I N C O N C R E TE

Y i W a n g a n d H e n r y J . P e t ro s k i

D e p a r t m e n t o f C iv i l a n d E n v i r o n m e n t a l E n g i n e e r i n g

D u k e U n i v e r si t y

D u r h a m , N o r t h C a r o li n a 2 7 7 0 6 U S A

t e l: 9 1 9 ) 6 8 4 - 2 4 3 4

I t is n o w g en e ra l l y r eco g n i ze d th a t a u n i q u e r e la t io n b e t w ee n c rack

p ro p ag a t i o n r a t e d a / d N an d s t re s s i n t en s i t y f ac t o r r an g e A K ex i s t s fo r a m a t e r i a l ,

i .e . , in t he no ta t ion of Pa ds e t a l. [1 ]

d a

= f ( A K )

(1)

F o r m an y en g i n ee r i n g m a t e r i a ls , t h e r e la t i o n o f t en t ak es t h e fo rm [2]

d a

= C(zXK)

d N

(2)

w h e re t h e v a l u e s o f C an d n a r e co n s i d e red t o b e m a t e r i a l co n s t an ts .

N u m e r o u s s tu d i es h a v e b e e n p u b l i s h e d o n p o r t la n d c e m e n t c o n c r e t e f r ac t u r e

[3 -1 2] . B u t n o a t t em p t h a s b een r ep o r t ed t o r e l a t e t h e c r ack p ro p ag a t i o n r a t e in

co n c re t e to s t r es s i n t en s i t y f ac t o r r an g e . A t e s t i s b e i n g p rep a red t o o b t a in su ch

i n fo rm a t i o n an d d e t e rm i n e i f (2 ) ap p l ie s t o co n c re t e .

A l a rg e f r ac t u re p ro ces s z o n e , a s r ep o r t ed i n co n c re t e f r ac t u re te s ts , i s

ex p ec t ed ah ea d o f a c r ack t ip , a s su g g es t ed in F i g . 1 . T h i s f a c t m ak es i t

i n ap p ro p r i a t e t o u se t h e p h y s i ca l c r ack s i z e a i n t h e ca l cu l a t io n o f s t re s s i n t en s i t y

fac t o r K . I t i s n ece s sa ry to ad d a p o r ti o n o f t h e f r ac t u re p ro ces s z o n e s i z e g t o th e

p h y s i ca l c r ack l en g t h t o o b t a i n an e f f ec t i v e c r ack s i z e a

ao = a + g (3)

W h i l e i t i s p o s s i b le

to

num erica l ly eva lu a te ao by as sum ing a s t ress d i s t r ibu t ion in

t h e f r ac t u re p ro ces s zo n e an d ca l cu l a t e th e zo n e s i ze , t h e s am e g o a l c an b e

a c h i e v e d u s i n g a c o m p l i a n c e m e t h o d [ 9 ,1 3 ,1 4 ]. T h i s m e t h o d c a n a v o i d th e

u n ce r t a i n t ie s i n t ro d u ced i n t h e s t r e ss d i s t r ib u t i o n a s su m p t i o n an d p h y s i ca l c r ack

s iz e m e a s u r e m e n t a n d t h e c o m p u t a t i o n i n v o l v e d i n z o n e s iz e d e t e r m i n a ti o n .

I n t J o u r n o f r a c t u r e 4 1 1 9 8 9 )

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R56

In develop ing the complianc e vs . crack s ize (C,-a) curve, a set of specimen s

with know n crack s izes wil l be s tatically loaded. The crack mo uth openin g

displacem ent (CMO D) wil l be plot ted against the appl ied nominal s tess o, as in

Fig. 2. The inverse of the CMOD -G l ine s lope is the comp liance C~. Since a

signif icant f racture process zone appears in concrete unde r mode rate G, the

magn i tude of G needs to be kept low to ensure that the or iginal kno wn crack s ize a

is not chan ged by the process zone. Plot t ing the data obtained from the test in a

graph as in Fig. 3, a regression curve can be dev eloped.

To est imate the ma xim um appl ied a , the s tress dis t r ibut ion in the process

zone is assumed parabolic and reaching f, at a distance (8+dy) from the physical

crack tip, whe re f, is the tensile strength, as show n in Fig. 1.- The m aterial be yo nd

that distance is elastic and the stress profile follows that fr om linear elastic

fracture mechan ics . The elastic s t ress prof i le is then extended back into the

process zone by the dot ted l ine. The ver t ical asymptote of the extended curve

determines the effect ive crack t ip, a t a dis tance 8 f rom the physical crack t ip.

From these assumptions and Irwin s model [15]

8 5 K ~ 2

= t77,

4)

where K is the stress intensity factor calculated with effective crack size (a+8).

Wh en neglect ing the boundary correct ion in the K calculat ion

5(1 + ~x)

5)

wh ere o~ = 8/a. To kee p 8/a < 0.05, (5) gives 8/f, < 0.138. Con side ring the

assump tions made, i t i s safe to l imit the maxi mu m appl ied nomin al s t ress G to 10

perce nt o f f ,.

Center-cracked-spl i t t ing-disk (CCSD) and edge-cracked-four-point-bend-

ing-bea m (EC BB) specime ns of port land cement concrete , as show n in Fig. 4, are

being used in the experiments . AS TM Standard E647-88 [16] is used to guide the

specime n and exper iment designs. To minim ize crack s ize mea surem ent error , an

increm ental-poly nomia l met hod [16] is used to reduce crack s ize ao and crack

propag t ion rate dao/dN from raw measu rements .

REFERENCES

[1] P.C. Par is , M.P. G omez, and W.E. A nderson,

The Trend in Engineering

13

(1961) 9-14.

[2] P.C. Paris and F. Erdogan, Journal of Basic Engineering 85 (1963) 528-534.

[3] M.F. Kaplan,

Journal of American Concrete Institute

58 (1961) 591-610.

[4] O.E.Gjorv, S.I. Sorensen, and A .Arnesen, Cement and Concrete Research

(1977) 333-344.

Int Journ of racture 41 1989)

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R 5 7

[5] Y.S. Jen q and S.P. Shah, in Application of Fracture Mechanics to Cementi-

tious Composites

S.P. Sha h ed.), Mart inus N ijho ff Publishers, Bo ston 1985)

319-359.

[6] H. K itagawa , S. Kim , and M. Suyama,

The 19th Japan Congress on Materials

Reseach - Nonmetallic Materials 1976) 160-163.

[7] V.C. Li , in Application o f Fracture Mechanics to Cementitious Composites

Martinus N ijho ff Pub lishers, Bo ston 1985) 431-449.

[8] R.P. O jdrov ic and H.J. Petrosk i , Journal of Engineering Mechanics 113 1987)

1551-1564.

[9] P.C. Perdikar i s and A.M. Calom ino, Load His tory Effect on the Fracture

Proper t ies of P la in Concrete , a repor t on NSF Research Grant CEE-83-07937,

Case Western Univers i ty , Cleveland, Oh io 1986).

[10] M. W ech aran a and S.P. Shah, Journal o f Structural Division 108 1982)

1400-1413.

[11] M.W echarana an d S .P . Shah, Journal of Engineering Mechanics 109 1983)

1231-1246.

[12] S.P. Shah and F.J. McGarry,

Journal of Engineering Mechanics Division

47

1971) 1663-1676.

[13] S.E. Sw artz and C.G. Go ,

Experimental Mechanics

24 1984) 129-134.

[14] S.E. Swartz, K.K. Hu, and G.L. Jones,

Journal o f Engineering Mechanics

Division

EM 4 1978) 789-800.

15] G.R. Irw in, in

Mechanical and Metallurgical Behavior of Sheet Material

Procee dings of 7th S agam ore Ordn ance M ater ia l Research Co nference, Syracuse ,

NY 1960) IV-63.

[16] ASTM E647-88, in Annual Book of ASTM Standards 03.01 1988) 714-736,

2 November 1988

y

ft

\

\

\

a

C ~ 1 I

F i g u r e i . S t r e s s d i s t r i b u t i o n i n c o n c r e t e a h e a d o f c r a c k t ip .

fnt Journ of racture 41 1989)

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R 5 8

aV;OD

Cp

F i g u r e 2. C o m p l i a n c e e v a l u a t i o n .

F i g u r e 3. C o m p l i a n c e - c r a c k s i z e

c u r v e .

~ ~

t t

F i g u r e 4 . S p e c i m e n s b e i n g u s e d .

Int Journ of racture

41 1989)