Fracture toughness tests for concrete

92

FRACTURE TOUGHNESS TESTS FOR CONCRETE

T. J. Bear and B. Barr Department of Civil Engineering and Building The Polytechnic of Wales Pontypridd, Mid Glamorgan CF37 1DL UK tel: (0443)405 133

Kaplan [I] was one of the first to apply fracture mechanics to the study of the fracture of concrete. He performed tests on concrete beams containing crack-simulating notches to evaluate fracture toughness, and other research workers [2-4] have carried out similar experiments. Moavenzadeh and Kuguel [4] also used the energy method to determine the fracture toughness of conrete. Brown [5] has performed a series of tests to measure the fracture toughness of cement paste and mortar, and more recently Schmidt [6] has investigated the fracture toughness of limestone. The principal disadvantage of the above tests is that the specimens have to be molded or require extensive machining and are therefore unsuitable for testing in situ concrete.

In this report the authors describe two tests which have been applied to both rock and fine-grained concrete specimens. The tests use circumferentially notched round bar specimens which are subjected to two loading systems. In the first case the notched round bar is subjected to four-point bending and the test is referred to as the CNRBB test (see Fig. i). In the second case the notched round bar is subjected to an eccentric longitudinal load and the test is referred to as the CNRBEL test (Fig. 2).

From the work of Neuber [7], Harris [8], and Bowie [9] it can be shown [i0] that for a CNRBB specimen

KIIM = 3 1 ( 2 / [ ~ r S { l - t l r ) 5 ( 0 . 8 9 + O . l l r / t ) ] } {i)

It can also be shown that for a CNRBEL specimen

KI/P = 3e/(2/[~r 5(l-t/r)5(0.89+0.11 r/t)]}

- i/(2/[~r3(l-t/r)3(0.8+0.2 r/t) ]} (2)

Eqns (i) and (2) are shown graphically in Figs. 1 and 2, respectively.

To ensure that the grain size of the concrete specimens was suf- ficiently small compared to the specimen dimensions, a fine-grained concrete was used. The aggregate used was in the range 0.6 - 2.4mm and gave a relatively homogeneous material in the test specimens. The concrete was a mix of 4.5 : 2.7 : 1 aggregate : cement : water. Beams were prepared in standard molds and the concrete cured under water for 28 days.

The samples were c o r e d from t h e c o n c r e t e beams u s i n g a r a d i a l d r i l l and w a t e r was u s e d as a l u b r i c a n t . Each c o r e was c u t i n t h e same d i r - e c t i o n r e l a t i v e t o t h e beam and so e n s u r e d t h a t each s p e c i m e n from t h e beam would have a p p r o x i m a t e l y t h e same p r o p e r t i e s . The samples were

Int Journ of Fracture 13 (1977)

93

then notched on a lathe using a tool-post grinder. A 0.025cm wide dia- mond blade was used for introducing the notches and the specimens were left for seven days to dry at room temperature. The ends of the cylin- ders to be used for the CNRBEL tests were then machined to give a flat loading surface.

The rock specimens were prepared in the same manner as the concrete specimens. Two rocks were tested - dolomite and slate. Dolomite was chosen as the first rock to be tested as it is relatively isotropic with no discernible bedding direction. Cores were taken in three mutually perpendicular directions (denoted A, B, and C in Table 3) in order to test for any anisotropy.

The slate used in the experiments had a well defined cleavage, but was not too friable and hence gave a suitable test material. As the slate specimens were drilled, perpendicular to the bedding plane, the cores broke off at about 8cm intervals. As a result only CNRBEL tests were used to determine the fracture toughness of slate.

The CNRBB specimens were tested under four-point loading in an Instron 1251 Model testing machine. To ensure a uniformity of bending moments for each test a Perspex rig held steel rods in place to give major and minor spans of 10cm and 0.8cm respectively. The experiments were conducted in displacement control at nominal room temperature. The failure load, used to evaluate Klc, was taken as the maximum during a test. The CNRBEL tests were carried out under the same conditions. The points of application of the load were taken as the inside edges of the steel bars (see Fig. 2) since the load is concentrated to the inside edges as deformation of the specimens takes place.

Table 1 gives a typical set of results for CNRBB and CNRBEL tests on concrete specimens. For these tests the external diameter was 5.36cm and the diameter at notch was nominally 3.34cm. The average values for Klc are similar for the two methods of loading. The initial tests on concrete suggest that Klc increases with increasing notch depth. Further information regarding tests on additional concrete specimens has been given elsewhere [11,12].

Table 2 gives a typical set of results for slate specimens subjected to the CNRBEL method of loading. Good correlation was obtained for specimens drilled perpendicularly to the bedding plane (referred to as PEB specimens in Table 2). The Klc value for specimens drilled par- allel to the bedding plane (PAB in Table 2) is less than half that for PEB specimens and the scatter of the results is considerably greater as expected.

A typical set of results for dolomite rock is given in Table 3. As the scatter of the results was large, a histogram of the frequency of occurrence of Klc values was drawn. From the histogram it was ap- parent that there were three populations or groups of results. The three groups are shown in Table 4 which gives the results of Table 3 together with further results from a second block of dolomite. The three groups occur as a result of the various mineral components in the dolomite; Group Z represents fracture of the dolomite matrix, whereas Group Y was obtained by fracture of calcite veins within the samples tested and Group X represents weathered rock.

Int Journ of Fracture 13 (1977}

94

The two tests are thus found to be economic of material and are suitable for testing in situ samples. The loading is simple and elim- inates some of the difficulties of testing rectangularly notched beams. The plane of crack propagation is governed by the circumferential notch and assures that the nominal crack area is constant.

The two tests are reproducible and the results show that the vari- ability of the data is low compared with other traditional tests on concrete and rock specimens. The tests have been shown to be suffi- ciently sensitive to separate the fracture toughness values of the various mineral components in a rock. Further research work is in progress on the application of these two tests.

REFERENCES

[I] M. F. Kaplan, Journal of American Concrete Institute Proceedings 58 (1961) 591-610.

[2] D. S. Naus and J. L. Lott, Journal of American Concrete Institute Proceedings 66 (1969) 481-489.

[3] J . L. Lo t t and C. E, Kes le r , Symposium on Structure of Portland Cement Paste and Concrete, Washington, D.C., Highway Research Board, Special Report 90, (1966) 204-218.

[4] F. Moavenzadeh and R. Kuguel, Journal of Materials 4 (1969) 497- 519.

[5] J . H. Brown, Magazine o f Concrete Research 24 (1972) 185-196.

[6] R. A. Schmidt, Experimental Mechanics 16 (1976) 161-167.

[7] H. Neuber, Theory of Notch Stresses: Principles for Exact Calcu- lation of Strength with Reference to Structural Form and Material, U.S. Atomic Energy Commission, Office of Technical Information (1958).

[8] D. O. Harris, Journal of Basic Engineering 89 (1967) 49-54.

[9] O. L. Bowie, Journal of Applied Mechanics 31 (1964) 208-212.

[lO] T. J. Bear, New Fracture Toughness Tests for Rock and Concrete with Particular Reference to Rock Structure Design, Ph.D. Thesis, CNAA, London (1976).

[ii] T. J. Bear and B. Barr, Concrete I0 (1976) 25-27.

[12] T. J . Bear and B. Barr , Concrete ( to a p p e a r ) .

18 October 1976


95

i L ~F

i

0.1 0,2 0-3 0.4 0.5 0-6 t/r

Fig1 Graphical representation of equotion (1) for r:2-7cm. together with CNRBB specimen details.

Specimen Failure x lO Number Load (N) Klc (N/m~l

2 3 4 5 6 7 8 9

,,,,

1587 1487 1575 17oo 1675 155o 1762 :575 :750

KI°= 8.O4!0.43

CNRBEL iO 2700 Ii 2180 12 2575 13 2460 14 2250 15 2550 :6 2550

17 21~o

Klc= 8.o6_+o.63

7.87 7.44 b.20 8.36 8.17 7.5o 8.60 7.69 ~.,54 ,J

x lO 5 a/m%'2

8.74 7.31 8.40 6.32 7.54 8.55 8.55 7.:4

1o 5 N/~-

Table 1. Klc results for concrete.

o

S

~L

16[ p ..... /~~

I 4

o11 o:2 6.% o14 o% o:6 t/r

Fig 2 GrophicQt representotion ot equotion (2) for r=2.7cm, together with CNRBEL specimen details

Specimen Number

I 2 3 4 5 6 7 8 9

iO

Failure Loa~ (N)

5.98 6.62 6.29 6.62 6.37 7.13 7.39 6.86 6.20 7.70

Klc= 2.25+_O.18

L

K. x 105

2.02 2.21 2.13 2.21 2.:3 2.38 2.47 2.31 2.07

,2.77 x lO 5 N/m~/~

PAB ll 1.97 12 2.19 13 3.25 :4 3.92 15 3.95 16 2.78 17 4.60 18 3.33

Klc= 1.06+0.30

0.65 0.72 1.O8 1.33 1.28 0.93 1.52 1.12

x lO 5

Table 2. Klc results for slate.


96

Specimen Failure hox i0 ~ Number

IA 2A 3A 4A 5A 6A 7A 8A 9A

lOA

IB 2B 3B 4B 5B

IC 2C 30 40 5c 60

Load (N)

1362 1.27 ii00 1.86 1385 1.33 965 0.93

1185 1.11 199o 1.91 1747 1.5o 2005 1.87 14o5 1.37 1847 1.72

2010 1.96 2077 2.02 1060 1.84 1365 1.33 1217 1.17

1847 1.82 1850 1.78 1837 1.71 1245 1.20 1847 1.74 2018 1.88

Table 3. Klc results for dolomite.

Group xlOL

"°(N/m'Z) 0.93 0.92 0.79

o=O. 88

Var. =8.9%

Group K~ xlO-

1.27 1.33 I.Ii 1.5o 1.37 1.33 1.17 1.20 1.09 1.20 1.40 1.53 1.38 1.28 1.21 1.44 1.~7 Klo=l.30 Var.=9.9~

Table 4.

Group K~ xlO _

J-O (N/m~/~)

1.86 1.91 1.87 1.72 I. 96 2.02 1.84 1.82 1.78 1.71 1.74 1.88 1.71 1.73

I<1o=1.82 K10=5.4%

Dolomite results divided into three groups.


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Fracture toughness tests for concrete