InternationalJournalof Fracture41: R55-R58, 1989. © 1989KluwerAcademicPublishers.Printedin the Netherlands.

R55

FATIGUE CRACK PROPAGATION IN CONCRETE Yi Wang and Henry J. Petroski Department of Civil and Environmental Engineering Duke University Durham, North Carolina 27706 USA tel: (919) 684-2434

It is now generally recognized that a unique relation between crack propagation rate da/dN and stress intensity factor range AK exists for a material, i.e., in the notation of Pads et al. [1] da

=f(AK) (1)

For many engineering materials, the relation often takes the form [2] da = C(zXK)" dN (2) where the values of C and n are considered to be material constants. Numerous studies have been published on portland cement concrete fracture [3-12]. But no attempt has been reported to relate the crack propagation rate in concrete to stress intensity factor range. A test is being prepared to obtain such information and determine if (2) applies to concrete. A large fracture process zone, as reported in concrete fracture tests, is expected ahead of a crack tip, as suggested in Fig. 1. This fact makes it inappropriate to use the physical crack size a in the calculation of stress intensity factor K. It is necessary to add a portion of the fracture process zone size g to the physical crack length to obtain an effective crack size a ao = a + g

(3)

While it is possible to numerically evaluate ao by assuming a stress distribution in the fracture process zone and calculate the zone size, the same goal can be achieved using a compliance method [9,13,14]. This method can avoid the uncertainties introduced in the stress distribution assumption and physical crack size measurement and the computation involved in zone size determination.

Int Journ of Fracture 41 (1989)

R56

In developing the compliance vs. crack size (C,-a) curve, a set of specimens with known crack sizes will be statically loaded. The crack mouth opening displacement (CMOD) will be plotted against the applied nominal stess o, as in Fig. 2. The inverse of the CMOD-G line slope is the compliance C~. Since a significant fracture process zone appears in concrete under moderate G, the magnitude of G needs to be kept low to ensure that the original known crack size a is not changed by the process zone. Plotting the data obtained from the test in a graph as in Fig. 3, a regression curve can be developed. To estimate the maximum applied a, the stress distribution in the process zone is assumed parabolic and reaching f, at a distance (8+dy) from the physical crack tip, where f, is the tensile strength, as shown in Fig. 1.- The material beyond that distance is elastic and the stress profile follows that from linear elastic fracture mechanics. The elastic stress profile is then extended back into the process zone by the dotted line. The vertical asymptote of the extended curve determines the effective crack tip, at a distance 8 from the physical crack tip. 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). When neglecting the boundary correction in the K calculation

5(1 + ~x)

(5) where o~ = 8/a. To keep 8/a < 0.05, (5) gives 8/f, < 0.138. Considering the assumptions made, it is safe to limit the maximum applied nominal stress G to 10 percent of f,. Center-cracked-splitting-disk (CCSD) and edge-cracked-four-point-bending-beam (ECBB) specimens of portland cement concrete, as shown in Fig. 4, are being used in the experiments. ASTM Standard E647-88 [16] is used to guide the specimen and experiment designs. To minimize crack size measurement error, an incremental-polynomial method [16] is used to reduce crack size ao and crack propagtion rate dao/dN from raw measurements.

REFERENCES [1] P.C. Paris, M.P. Gomez, and W.E. Anderson, 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 7 (1977) 333-344. Int Journ of Fracture 41 (1989)

R57

[5] Y.S. Jenq and S.P. Shah, in Application of Fracture Mechanics to Cementitious Composites, S.P. Shah (ed.), Martinus Nijhoff Publishers, Boston (1985) 319-359. [6] H. Kitagawa, S. Kim, and M. Suyama, The 19th Japan Congress on Materials Reseach - Nonmetallic Materials (1976) 160-163. [7] V.C. Li, in Application of Fracture Mechanics to Cementitious Composites, Martinus Nijhoff Publishers, Boston (1985) 431-449. [8] R.P. Ojdrovic and H.J. Petroski, Journal of Engineering Mechanics 113 (1987) 1551-1564. [9] P.C. Perdikaris and A.M. Calomino, Load History Effect on the Fracture Properties of Plain Concrete, a report on NSF Research Grant CEE-83-07937, Case Western University, Cleveland, Ohio (1986). [10] M. Wecharana and S.P. Shah, Journal of Structural Division 108 (1982) 1400-1413. [11] M.Wecharana and 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. Swartz and C.G. Go, Experimental Mechanics 24 (1984) 129-134. [14] S.E. Swartz, K.K. Hu, and G.L. Jones, Journal of Engineering Mechanics Division EM4 (1978) 789-800.

[15] G.R. Irwin, in Mechanical and Metallurgical Behavior of Sheet Material, Proceedings of 7th Sagamore Ordnance Material Research Conference, Syracuse, NY (1960) IV-63. [16] ASTM E647-88, in Annual Book of ASTM Standards 03.01 (1988) 714-736, 2 November 1988 Cy \ \

\ \

ft

J

a

-C

~1-

I

Figure i. Stress distribution in concrete ahead of crack tip.

fnt Journ of Fracture 41 (1989)

R58

Cp

!

J

f

aV;OD Figure 2. Compliance evaluation.

P~ Pt

Figure 3. Compliance-crack size curve.

~P tP

Figure 4. Specimens being used.

Int Journ of Fracture 41 (1989)