Materials and Structures/Mat~riaux et Constructions, Vol.31, January-February1998, pp 36-41

Size effect and fracture energy studies using compact compression specimens Ben I. G.Barr 1, Hadi F. Abusiaf e, Siddik Sener 3 (1) Professorof Civil Engineering, University of Wales Cardiff,, CF2 1XH, UK (2) PhD student of Division of Civil Engineering, University of Wales Cardif, UK (3) Visitingscholarat University of Wales Cardiff, on leavefrom Gazi University, Ankara 06571, Turkey Paper received:August 20, 1996; Paperaccepted:November I3, 1996

RI~SU

ABSTRACT

MI~

The size effect has been investigated and fracture energy, G F, determined for a range of different strength concretes. The test specimen geometry used in the study was a compact compression prism. Five sizes of geometrically similar specimens with increasing square crosssectional area (length = depth) and constant thickness (100 ram) were used in the experimental work; the length/depth dimensions of the test specimens were 100, 150, 200, 300, and 400 ram, giving an overall size range ratio of 1:4. The grades of concrete used in this study were C50, C70, C80 and C90, and the maximum coarse aggregate (crushed limestone) size was 10 ram. A strong size effect was observed in the results and it is concluded that the test geometry is good for size effect studies in concrete. Furthermore, it was observed that with increasing strength the size effect becomes more pronounced as the brittleness is increased.

On a dtudid l'effet de taille et l'&ergie de rupture, GF, d&ermin& pour une gamme de bdtons want des r&istames diff&entes. La g domdtrie des dprouvettes choisie pour cette dtude dtait le prisme compact de compression. Cinq tailles d'dprouvettes de gdomdtrie similaire, ayant une dpaisseur constante (100 ram) et de section transversale cart& (longueur - profondeur) croissante ont ~td utilis&s pour ce travail. Les dimensions longueur/profondeur des dprouvettes dtaient de 100, 150, 200, 300 et 400 ram, r&ultant en un rapport gdn&al de 1:4. Les b~tons utilis& dans cette itude ~taient de quah't~s C50, C70, C 8 0 et C90, et la dimension maximale des granulats (calcaire concassd) dtait de 10 ram. On a observd clans les r&ultats un fort effet de taille et on a conclu que la gdomdtrie utilis& pour l'essai convient pour des dtudes d'e~t de taille sur le bdton. Qui plus est, on a observd qu'avec une r&istance croissante, l'effet de taille devient plus prononcd Iorsque lafiagilitd a ugmente.

1. INTRODUCTION

effects in the fracture of concrete for use by researchers in this area. The existing literature in this area is extensive and researchers new to this topic are referred to proceedings o f an international workshop on "Size Effect in Concrete Structures" organised by the Japan Concrete Institute [1], the proceedings of the IUTAM Symposium on "Size-Scale Effects in the Failure Mechanisms of Materials and Structures" held at Turin in 1994 [2] and papers of a Conference Workshop on "Size Effects: Theoretical Concepts, Experimental Verifications, and Implications in Structural Design" organised as a part of FRAMCOS 2 held at Zurich in 1995 [3]. A discussion of the relative merits of the probabilistic model for quasibrittle failure of concrete proposed by Mihashi [4], the

In the last decade, a considerable amount of research effort has been devoted to so-called "high performance concrete" which, more often than not, can be equated to high strength concrete. There has also been a trend for concrete structures to increase in size over a period of time. These trends have occurred alongside the better understanding of the fracture process in concrete and, in particular, the size effect observed in the fracture of concrete whereby the nominal strength is reduced as the size of geometrically similar test specimens is increased. Although the phenomenon of size effect in the fracture of concrete is generally accepted, the purpose of this paper is to provide further experimental evidence of size

Editorialnote Prof. BenjaminI. G. Barris a RILEM SeniorMember.He participatesin the EditorialGroupof TC 090-FMA' "FractureMechanicsof ConcreteApplications", and is a memberof TC 162-TDF, "Test and Design Methodsfor Steel Fibre reinforcedConcrete!'and TC QFS, "Size effectand Scalingof QuasibrittleFracture". 0025-5432/98 9 RILEM

36

Barr, Abusiaf, Sener

Ba~ant size-effect law proposed by p P Ba~ant and Pfeiffer [5], and the scaling ~_~_____~ LVDT(8) lip gauge (CTOD) laws based on multifractal aspects of damage proposed by Carpinteri et al . . . . . ,,rr,,o..........~.... ~ (CMOD) [6], is beyond the scope of this paper. P On the other hand, the test results reported, for a range of concrete strength, should prove useful for experimentalists as well as colleagues work/////,~//////////////////////////// ing on numerical analysis of the sizeeffect phenomenon. P A large amount of experimental results has already been published in this All test specimens have thickness,B= 100ram area. One of the main requirements in traditional size-effect studies is the need for test specimens which are geometriP cally similar and which provide a range of sizes. In the case of beam specimens P subjected to flexure, the biggest test specimens tend to be large, requiring attention to be given to the influence of a a gEE D self-weight. Ideally, tests should be carried out on compact test specimen geometries where the problems of selfweight are minimal. Current developments in this field suggest that the size Fig. 1 - Test specimens and loading details. effect method (expressed in terms of the from the same batch for the range of concrete grades energy release function) can be used for dissimilar geomeinvestigated. The average uniaxial 28-day compressive tries, and in that case, all the specimens can be of the same and average splitting tensile strengths (together with size, expect that the notch length is varied. their coefficients of variation) are given in Table 1. A number of compact test geometries have been All specimens were tested at the age of 28 days as reported in the literature. For example, the wedge splitting soon as possible after taking them from the curing tank. test fulfils all the necessary requirements of a compact test Notches for all specimens were introduced by means of a specimen geometry. A comparison between the wedge masonry saw one day prior to testing, and thereafter clip splitting test and the three-point bend test has been given gauge holders were glued on the surfaces adjacent to the recently by Linsbauer and Sajna [7]. A second compact test notch mouth. Testing was carried out by a (Shenck) specimen geometry is provided by notched cylinders subclosed-loop testing machine with a m a x i m u m load jected to three-point bending, as reported by Jefferson and capacity of 250 kN. The rate of loading was controlled Barr [8]. However, an even more compact test geometry is via the clip gauge located across the mouth of the notch provided by the compact compression test geometry used (i.e. crack opening displacement was linear with time). in this study (on which a preliminary, abbreviated report Four grades of concrete were tested in the study: has been given at a recent conference [9]). nominal C50 (nominal compressive cube strength of 50 MPa at 28 days), C70, C80 and C90 concrete mixes having the proportions (together with the water/cement 2. TEST SPECIMENS AND EXPERIMENTAL ratio) given in Table 2. The cement was Ordinary DETAILS "//////

///////~/////~////////////////////~

/7,~///• " / / / 2 / I / / ~ / / / / / / / / / / / / / / / / / / 2 / ~ 2 2 7

The compact compression test specimen was developed a decade ago as a compact Mode I fracture test specimen [10]. In this case, the double-edge-notched standard cube specimens are subjected to eccentric loading as shown (Fig.l). Five test specimen sizes have been investigated in this study with the overall size ranging as follows: 100, 150, 200, 300, and 400 mm. In all cases, the notch depth ratio was 0.25 for both notches, resulting in a uniform ligament/depth ratio of 0.50. A total of 15 prisms together with three companion 100 m m cubes (to evaluate 28 day compressive strength) and three companion 200 m m long 100mm diameter cylinders (to evaluate splitting tensile strength) were cast

1/////, I / / / / / / / / /

Table 1 - Concrete strengths and coefficients of variation Concrete Grades

fcu (N/mm2) (coy %)

ft' (N/mm2) (coy %)

C50

48.10 (4.06)

3.86 (2.72)

C70

37

66.03

5.01

(o.86)

(o.48)

C80

82.37 (0.74)

5.94 (4.89)

C90

88.40 (0.30)

6.16 (5.85)

Materials and Structures/Mat~riaux et Constructions,Vol. 31, January-February1998

displacements CTOD (crack tip opening displacement) and CMOD (crack mouth opening displacement) were measured via clip gauges attached to knife edges on the test specimens. The nominal vertical displacement, 8, was measured via LVDT readings, as shown in Fig. 1. The Load-CMOD, Load-CTOD and Load-8 curves were recorded autographically by means of X-Y plotters and the same data was also recorded on a PC.

Table 2 - Mix details (proportion by weight) Concrete Cement Fine Coarse Grade Agg. Agg. C 50 C 70 C80 C90

1 1 1 1

1.87 1.87 1.80 1.76

3.13 3.13 3.00 2.94

w/c

Micro- Supersilica plasticizer

0.50 0.46 0.34 0.30

0.11 0.11 0.11

0.005 0.01 0.015

Portland Cement (BS12:1991, Class 42.5N), the fine aggregate was a local sea-dredged sand and the coarse aggregate was crushed limestone. The maximum coarse aggregate size, da, was 10 mm and the maximum fine aggregate size was 5 mm. In the case of the C70, C80, and C90 concrete, microsilica in slurry form (50:50 slurry) was used together with a superplasticizer (Conplast SP430). The mixes were prepared in a pan mixer and the specimens, including the control cubes, were compacted by means of a vibrating table. The tests were carried out under crack mouth opening displacement-control at a strain rate of approximately 3 • 10-4/sec. t o reach the peak load in approximately 2-4 min, with the entire tests taking some 10-20 min to complete, depending to the size of the specimen. Previous work [11] has shown that a variation in the rate of loading within a factor of 2 does not have a significant effect on the test results. All the tests were carried out at room temperature (20~ The test specimens were loaded eccentrically, the load being applied through steel loading strips as illustrated in Fig.1. All the dimensions were kept geometrically similar in two dimensions, including those of the steel loading strips. During the tests three softening curves were obtained, the first being the P-8 curve (normal load-deflection curve for G F tests), the second being the P-CMOD curve (loadcrack mouth opening displacement) and the third the PCTOD curve (load-crack tip opening displacement). The

3. RESULTS AND ANALYSIS Three identical specimens were tested in all cases. The test results are summarised in Table 3 which shows the peak load (Pu) values in kN. In this table, typical CTOD, CMOD and vertical displacement (8) values at peak load are also reported. Full details of the test results obtained in the study are provided elsewhere [12]. For the size effect diagram, maximum (ultimate) stresses, (~N, were obtained according to equation (1), given below, which is applicable for eccentrically loaded prisms. P,+~ 2 ON-- A

P,e I Y

(1)

where g - weight of specimens, A = ligament (concrete section) area, e - eccentricity of load- 9/20D, I = moment of inertia of ligament, and y - distance between the crack tip and centre of the ligament. The above expression for (~N is somewhat simplistic for the complex stress-strain state in the ligament area, but provides a reasonable first approximation. In this study, 50 mm compact specimens were also tested. Unfortunately, the required mode of failure could not be achieved for this specimen size, since shear failure occurred at the point of application of the load rather than flexure failure in the ligament. In all other tests, the failure surfaces were horizontal in the ligament zone as expected.

Table 3 - Measured peak load, Pu, and typical values of CMOD, CTOD and (3 for different concrete grades Specimen Size Sm (

)

C50 Pu (kN)

CMOD CTOD ~ (ram) (mm) (ram)

C70

C80

C90

Pu CMOD CTOD 8 ( k N ) (mm) (ram) ( m m )

Pu (kN)

(mm) (mm) (mm)

Pu CMOD CTOD ,3 ( k N ) (mm) (mm) (mm)

CMOD CTOD

6

100

10.31 8.71 0.0232 0.0230 0.109 10,50

13.26 12.59 0.0164 0.0057 0.200 14.97

15.89 14.98 0.0171 0.0054 0.213 16.51

14.86 16.28 0.0229 0.0068 0.239 13.65

150

13.50 12,98 0.0246 0.0258 0.121 13,56

14,08 14.87 0.0184 0.0064 0,224 14.57

18.61 18.95 0.0228 0.0072 0.283 19.84

20.35 19.46 0.0235 0.0053 0.288 20.12

200

23.51 16.00 19.84 0.0099 23.96 16.78 0.0353 0.0362 0.194 19.00 0.0246 0.345 22.58 0.0285 0.0091 0.354 25.08 0.0312 0.0085 0.329 17.13 20.00 25.20 26.10

300

20.10 21.44 0.0503 0.0477 0.213 20.33

25.18 31.67 33.45 24.90 0.0371 0.0124 0.432 30.45 0.0368 0.0116 0.457 32.87 0.0385 0.011 24.80 20.33 30.06

400

27.06 26.24 0.0418 0.0119 0.209 27.00

27.24 35.10 30.43 28.09 0.0364'0.0146 0.510 32.22 0.0399 0.0216 0.496 37.87 0.0479 0.0091 0.346 28.01 27.00 33.65

38

0.358

Barr, Abusiaf, Sener

0.00

9

2

a)C

-0.20

50

c) c 80

"",.,,1

~ ""., 2 & ~ . . l

8

-0.10

", LEFM

s g _a

t~,~.

-0.40

LEFM

-0.20 =2.84MPa Do=151.01mm

o

B

=4.46 M P a

9

Do=36.14turn

-0.30 -0.25 -0.10

"'.

0.00

-0.60 0.50 0.25

0.25

"',.

b) C Z0 "'~"

-0.25

0.50

""-..

0.75

",,

1.00

1.25

Fig. 2 - Size effect curves for different concrete grades.

d) C 90

"-. " ' . . . 2

2

-0.30

~"~..~E~ -0.50

-1

-0.50

9

B =4.13MPa Do=39.13mm

"'-

-0.70

0.25

0.50

0.75

1.00

1.25

-0.75 0.50

0.75

where

f5 = D / D o

1.25

the peak loads measured in individual tests. All these plots clearly indicate a strong size effect in the test results. However, according to current Codes of Practice, the size effect observed would be ignored. Comparing the size effect plots of different strength concrete shows that as the strength of concrete increases (i.e. concrete is more brittle) the size effect becomes more pronounced and is observed to approach that represented by the LEFM line for the highest strength concrete used in the study. This is not surprising, since a high strength concrete specimen stores more strain energy than a normal strength specimen of the same dimension. Data points in Fig. 3 represent the average (~N value for each group of three identical specimens, and the plots for all strengths are gathered in the same figure. The brittleness of concrete has previously been characterized

Based on previous theoretical arguments of general validity, the size effect can be described by the following approximate size effect law proposed by Ba~ant [13]: Bf[

1.00 Log

Log IB

(~N- /1+[5

"o.

B =4.96MPa Do=27.07mm

(2)

in which Bf[ and D O are two empirical constants. The tensile strength, ft', (determined from splitting tests) is introduced merely for convenience to make B nondimensional9 The optimal fits for this size-effect law are shown by solid curves in Fig. 2. For small specimen sizes these curves approach a horizontal asymptote, and for large sizes they approach an inclined asymptote of slope -1/2, which corresponds to LEFM. The size effect plot of Log (~N versus Log D (D = characteristic dimension of the structure), which represents the standard sizeeffect plot, is given for C50 con0.00 crete in Fig. 2a with correlation ""... coefficient - 0.949 and coeffi""', 2 cient of variation (vertical devia~.~..~ ""..-~..1 tions from the regression line) "",,, 0.101, for C70 in Fig. 2b with -0.25 correlation coefficient - 0.968 and coefficient of variation = ~ ' &, 0.112, for C80 in Fig. 2c with correlation coefficient - 0.969 -0.50 and coefficient of variation = 0.112 and for C90 in Fig. 2d B =4.10 MPa ~ , with correlation coefficient = Do=63.34 nlm 0.912 and coefficient of variation = 0.2199 In these plots the -0.75 data points show, separately for -0.25 0.00 0.25 0.50 each strength, the value of nomLog IB inal strength, (SN, (calculated according to equation (1)) for Fig. 3 - Test results on size effect plots for different concrete

9 C90 C80 ,c70 o CSO

9

o~

'

, k

.

T

,

39

0.75

grades.

1.00

1.25

Materials and Structures/Matdriaux et Constructions,Vol. 31, January-February1998

I

C80

C70

C50

40 j

~

20

C90

II

- - 3o t ~ D = 4 0 0 D=IO0

0

CMOD (ram)

0

CMOD (miTt)

CMOD (mm)

1

CMOD (mm)

40

0

CTOD (mm)

CTOD (ram)

0

CTOD (mm)

1

0

CTOD (mm)

0,00

Displ (mm)

0,75

0.00

Displ (ram)

Fig. 4 - Typical P-CMOD, P-CTOD and P-8 curves for different concrete grades.

40

o "11o 0 0.00

Oispl (ram)

0.75

0.00

Displ (mm)

0.75

0,75

observed for the P-8 re@onses. The sn@-back relationship which is observed in the P-8 curves is particularly clear in the case of the three higher strength concretes. The negative slopes observed in the P-8 curves for the C70, C80 and C90 concretes could be due to the increased brittleness introduced by the use ofmicrosilica. The work done ,W D, was calculated by measuring the area under the P-8 plots, and the fracture energy, GF, was calculated from equation (3), in which the area of the unnotched ligament, All, was equated to B(D - 2a). The fact that 8 was measure~ slightly off-load was ignored in these calculations. Furthermore, great care is required in the interperation of the results obtained via the P-8 curves due to the possible local crushing of the concrete near the lines of application of the load. The W D values were deter-

by the so-called brittleness number, [} = D / D o. The point [3 = 1 (i.e. D - Do) corresponds to the intersection of the horizontal and inclined asymptotes on the size effect plots. From the test data shown here, it is observed that for the small size normal strength concrete [3 < 1, whereas for the larger test specimens of low strength and all high strength concrete specimens 13> 1. A major advantage of using compact specimens [14, 15] in size effect studies is that self-weight is kept to a minimum. With the compact specimen geometry it is possible to test specimens with a large size range ratio extending to possibly 1:8. Also, as in other size effect tests, it is easy to test these specimens in aW laboratory with any loading frame. The simplicity of the size effect approach in fracture makes it suitable not only for the laboratory but also for field quality control.

Table 4 - Work Done, W D results during fracture process

4. FRACTURE ENERGY OF CONCRETE For any situation where the crack growth is stable, it can be assumed that all the work done by the external load goes into crack extension and that the energy required by the latter is independent of the test specimen geometry. Thus, the work done by the applied load in these tests can be assumed to have been consumed in fracturing the unnotched part of the specimen cross-section, i.e. the ligament ahead of the pre-existing crack. This work (or work of fracture) ,WD, and the area of ligament, Ali,, which was intact before the test began, gives the energ~ needed to create a crack of unit area, G> or fracture energy [16] from the following: G F = WD/Alig

Concrete Grade

Specimen Size D (mm)

C50

100 150 200 300 400

104.5 118.3 71.3 160.7 402.0

100 150 200 300 400

110.3 147.5 181.3 243.8 345

92.3 100.3 172.5 193 261.5

100 150 200 300 400

91.0 98.8 200.5 231.8

109.5 133.0 204.5 262

221.5

100 150 200 300 400

157.3 102.0 121.8 164.3 274.5

70.5 102.8 95.0

134.5 160.3

204.5

195.8

C70

C80

(3) C90

Typical P-8, P-CMOD and P-CTOD curves for the different grades of concrete are shown in Fig. 4. The curves showing the P-CTOD and P-CMOD responses are similar, whereas there is a significant difference 40

WD((~) (kN-mm) 91.3 79.5

205.0

191.5

217.5 B

146.5 247.5 329.3 91.3 129.0

Barr, Abusiaf, Sener

ACKNOWLEDGEMENT

Table 5 - Coefficients of variation for GF values obtained from P-8 curves D (mm)

C50

C70

C80

C90

400 300 200 150 100

0.30 14.97 1.16 47.88 9.57

14.22 13.35 20.47 20.55 12.58

8.83 1.40 16.19 10.60

18.02

Broken

The last author wishes to express his gratitude for a fellowship from The Scientific and Technical Research Council of Turkey (TUBITAK), and further partial financial support from The Royal Society (UK) to support his visit to the University of Wales Cardiff, where some of the work reported was carried out.

1.17

30.27 18.18 53.87

mined from the P-8 curves as an average of four measurements. In the calculation of Work Done, the self-weight of specimens was only 0.2 kN for the largest specimens (400 mm) and hence the effect of self-weight was ignored. Table 4 provides details of the work done (in kN-mm) during the fracture process and illustrates the very significant variation in the test results for any given combination of concrete grade and test specimen size. Whereas the spread of results was limited in the case of the maximum load recorded in similar tests, the variation in the work done was an order of magnitude greater in some cases. Table 5 presents the results for the coefficients of variation for the G F values, and it is observed that the variation is of the order of 50% in some cases. Whereas the geometry does have clear advantages in terms of size effect studies, it requires further thought before it can be recommended for use to determine G F values.

REFERENCES [1] Mihashi, H., Okamura, H. and Ba~ant, Z.P. (Eds.), 'Size Eeffect in Concrete Structures' (E&FN Spon, London, 1994). [2] Carpinteri, A. (Ed.), 'Size-scale Effects in the Failure Mechanisms of Materials and Structures' (E&FN Spon, London, 1996). [31 Wittmann, F.H. (Ed.), 'Fracture Mechanics of Concrete Structures', Vol III, (AEDIFICATIO Publishers, Freiburg, Germany, 1996). [4] Mibashi, H., 'A stochastic theory for fracture of concrete,' in 'Fracture Mechanics of Concrete', Ed. F.H. Wittmann (Elsevier Science Publishers, Amsterdam, 1983) 301-339. [5] Ba~ant, Z.P., and Pfeiffer, P.A., 'Determination of fracture energy from size effect and brittleness number,' ACI Materials Journal 84 (1987) 463-480. [6] Carpinteri, A., Chiaia, B. and Ferro, G., 'Multifractal scaling law: an extensive application to nominal strength size effect of concrete structures', Report 51, Politccnico di Torino, Torino, ]995, 145 p. 171 Linsbauer, H.N. and Sajna, A., 'Size-effect sensitivity - threepoint bending test versus wedge splitting test,' in [2] above, 427439. [8] Jefferson, A.D., and Barr, B.I.G., 'Unified test procedure fbr evaluating the fracture characteristics of concrete' in [3] above, 5564. [9] Abusiaf, H.F., Barr, B.I.G. and Sener, S., 'Size effect in eccentrically loaded compact specimens', in 'Concrete Technology for Developing Countries', Proceedings of Fourth International Conference, North Cyprus, November, 1996 (Eastern Mediterranean University, North Cyprus). [10] Barr, B.I.G, and Sabir, B.B., 'Fracture toughness testing by means of the compact compression test specimen', Magazine of ConcreteResearch37 (1985), 88-94. [11] Ba~ant, Z.P. and Gettu, R., 'Rate effects and load relaxation in static fracture of concrete', ACI MaterialsJournal 89 (5) (1992) 456-468. [12] Abusiaf, H.F., 'Damage and Fracture of High Strength Concrete', PhD Thesis under preparation (University of Wales Cardiff, 1997). [13] Ba~ant, Z.P., 'Size eft?ct in blunt fracture: concrete, rock, metal', Journal of EngineeringMechanicsASCE 110 (1984) 518-535. [14] Barr, B.I.G., Brokenshire, D.R. and A1-Oraimi, S.K.A., 'Size effect study in three fracture test specimens', in 'Size-Scale Effects in the Failure Mechanisms of Materials and Structures' (E&FN Spon, London 1996) 385-398. [15] Barr, B.I.G. and Tokatly, Z.Y., 'Size effects in two compact test specimen geometries', Chapter 4 in 'Applications of Fracture Mechanics to Reinforced Concrete' (Elsevier Applied Science, 1992) 63-93. [16] RILEM Committee FMC 50, Draft Recommendation 'Determination of the fracture energy of mortar and concrete by means of the three point bend tests on notched-beams', Mater. Struct. 18 (1985) 285-290.

5. CONCLUSIONS The following conclusions may be drawn from this study of the use of the compact compression test specimen geometry to investigate size effects in the fracture of medium and high strength concrete: 1. The compact compression test specimen exhibits a strong size effect during the fracture of concrete. Hence, this is a good geometry for size effect studies in concrete and similar materials. 2. P-CTOD and P-CMOD curves are very similar (as expected), and for high strength concrete the slope of the softening branch is much steeper than for normal strength concrete. 3. The test results are in good agreement with the size effect law, as defined by equation (2). 4. With increasing strength of concrete, the size effect becomes more pronounced and the brittleness number increases. 5. G F values were obtained in the study for a range of concrete grades. Since the maximum load varied with the grade of concrete, but the G F values were almost constant (or decreasing with increasing strength), it follows that the shape of the strain softening curves were different. This is an area for future research since the shape of the softening branch is probably a better indication of the brittleness of the material. 6. The possible effect of microsilica in increasing the brittleness observed in the softening branch requires further research studies. 41