Results of notched beam (fracture) tests on a 60 MPa silica fume concrete at the ages of 4,
10, 31 and 232 days are presented. Fracture parameters at the different ages were obtained
using the size effect and cohesive crack models, which indicate that the fracture resistance
(toughness and energy) decreases and the brittleness increases with the age of the concrete.
This trend is attributed to the increase in the strength of the hardened cement paste and the
interfaces that leads to less bond cracking and more aggregate rupture, and consequently, to
more brittle failure and lower toughening.Peer Reviewe

Aguado de Cea, Antonio

García Álvarez, Víctor Óscar

Gettu, Ravindra

English

UPCommons. Portal del coneixement obert de la UPC

EFFECT OF AGING ON THE FRACTURE CHARACTERISTICS AND BRITTLENESS OF A HIGH-STRENGTH CONCRETERavindra Gettu, Víctor O. García-Álvarez and Antonio AguadoUniversitat Politècnica de CatalunyaETSECCPB, Gran Capitán, s/n, E-08034 Barcelona, SpainABSTRACTResults of notched beam (fracture) tests on a 60 MPa silica fume concrete at the ages of 4,10, 31 and 232 days are presented. Fracture parameters at the different ages were obtainedusing the size effect and cohesive crack models, which indicate that the fracture resistance(toughness and energy) decreases and the brittleness increases with the age of the concrete.This trend is attributed to the increase in the strength of the hardened cement paste and theinterfaces that leads to less bond cracking and more aggregate rupture, and consequently, tomore brittle failure and lower toughening.IntroductionThe failure of high-strength silica fume concrete is characteristically more brittle than that ofconventional concretes. This can be attributed to the compact high-strength matrix and interfaces, whichreduce the toughening that can occur during crack propagation (1,2) although increasing the strength andimpermeability of the concrete. This phenomenon can be studied using models based on fracturemechanics that are capable of quantifying the effectiveness of the toughening mechanisms, as well as thecrack resistance, through material parameters. In the present work, the evolution of the fracture parameters with age (ranging from 4 days to 8months) is studied using two different models. One of them is an effective crack model, known as the sizeeffect model, through which fracture parameters can be derived from the peak loads of notchedspecimens of different sizes (3,4). Here the model is applied to data from beams undergoing mode Ifracture. The second is a cohesive crack model, defined through a constitutive relation for the stressversus crack separation response (5), which in the present work is implemented in a finite elementframework using joint elements and a discrete crack approach. Experimentally obtained load versus crackmouth opening displacement (CMOD) curves of notched beams have been used to determine theparameters of the latter model.Details of the Material, Specimens and TestsThe concrete used in this study was designed for a 28-day compression strength of 60 MPa, with theproportions of cement:sand:gravel:microsilica:water as 1:1.25:1.8:0.2:0.3. Spanish type I/55A cement(1)(equivalent to European Standard CEM I 52.5R cement), densified silica fume, crushed basalt gravel(5-12 mm), and siliceous sand (0-5 mm) were used. A melamine-based superplasticizer was alsoincorporated in the concrete. Four batches of the concrete were fabricated for the experimental study.The slump of each of them is given in Table 1. Three 150 mm×300 mm cylinders and nine beams werecast from each batch. The ends of the cylinders were polished with a diamond wheel and they weretested in compression 28 days after casting; the average strengths (f c) are reported in Table 1. The beamshad the same thickness (b) of 50 mm, depths (d) of 80, 160 and 320 mm, lengths equal to 3.125d, andspans equal to 2.5d. Three beams were cast for each d. A notch of length a0 = 0.275d was cut at themid-span of each beam with a diamond disc saw. All specimens were stored in a fog room until testing.TABLE 1.  Concrete propertiesBatch 28-day cylinder compressive strength (MPa) Slump (cm)ABCD64.3 (± 6.9%)67.5 (± 5.3%)60.6 (± 1.5%)68.1 (± 6.6%)23242220The tests of the notched beams were conducted in a 1 MN INSTRON servohydraulic machine underclosed-loop CMOD control. Constant CMOD rates were imposed such that the peak loads occurred atabout 3 minutes. Each batch of beams was tested at a different age (see Table 2) and the load-CMODcurves of the specimens were recorded. Visual observations of the crack surfaces showed, as expected,a significant increase in the number of ruptured gravel aggregates with an increase in age; for example, itdoubled between the ages of 4 days and 8 months in the largest beams. The peak loads obtained in thetests are given in Table 2 (except for one 160 mm specimen of series C that was not registered). Ingeneral, there is no major increase in the failure loads with age, especially in the larger specimens.TABLE 2.  Peak Loads of the Notched Beams at Different AgesBatch Age(days)Peak loads of individual specimens, Pu (N)d = 80 mm d = 160 mm  d = 320 mm   A 4     3925, 4125, 3500 6424, 6408, 6400 12370, 12650, 12650   B 10     3888, 3950, 3950 7175, 7150, 7725 12150, 12100, 13300   C 31     4250, 3910, 4738 6900, 8025 12250, 12600, 11700   D 232     4782, 4750, 5100 7450, 8125, 7441 12190, 12640, 12620Application of the Size Effect ModelThe size effect model (SEM) of Bažant is based on the ductile-brittle transition of the failure mode ofgeometrically-similar fracture specimens with an increase in size. The basic form of this nonlinearfracture mechanics model, which gives the size-dependence of the nominal failure stress, is (3):where FN = Pu/bd is the maximum nominal stress, Pu is the maximum load, d is a characteristic dimension(2)of the specimen (note that here d is the beam depth), and B and d0 are empirical parameters. $ is calledthe brittleness number and denotes the proximity of the failure mode to ideal-brittle linear elastic fracturemechanics (LEFM) behavior; FN has a constant value at $60 and is proportional to d-1/2 (whichcorresponds to the LEFM failure criterion) at $64 (Fig. 1). Parameters B and d0 are obtained by fittingEq. 1 to the FN -values determined experimentally from different sizes of specimens.The values of B and d0 can be used to obtain material fracture parameters defined unambiguously byBažant in terms of an infinite size specimen, whose behavior is theoretically independent of geometryeffects (3):where KIc = fracture toughness, cf = effective fracture process zone length, Gf = fracture energy,E = modulus of elasticity (for plane stress), and "0 = a0 /d is the relative notch length. Function g is thedimensionless energy release rate and gN is its derivative with respect to the relative crack length. Thesefunctions depend only on the specimen geometry, and can be obtained from LEFM analysis (see Ref. 4for beam geometries).The SEM parameters were obtained by regression analysis of FN -values (from the Pu-data in Table 2corrected for self-weight, as in Ref. 4) at different ages with Eq. 1, using the Marquardt-Levenberg least-squares algorithm. The normalized experimental data are shown in Fig. 1, where a shift of the data towardthe LEFM asymptote, indicating increasing brittleness, is seen with an increase in age. The parametersare given in Table 3, along with the coefficient of variation of the fits (T). It can be seen that B increaseswith age while d0 decreases. Considering that the parameter B is a measure of the strength, the trendobserved is logical. The decrease in d0 indicates an increase in the structural brittleness $.The modulus of elasticity (E) of each specimen was computed from its initial load-CMOD complianceusing LEFM functions; the average value at each age is given in Table 3. As expected, there is anincrease in E  with age. The values g("0) = 10.6 and gN("0) = 47.7 (for "0 = 0.275), obtained by finiteelement analysis (6), were used in Eq. 2 to determine the material fracture parameters at different ages(given in Table 3). All of them exhibit a decreasing trend with age; the trends of KIc and Gf indicate adecrease in the toughening and crack resistance, and the decrease in cf indicates an increase in thebrittleness of the material with age (1,7).TABLE 3.  Fracture Parameters Obtained with the Size Effect Model at Different AgesAge (days) B (MPa) d0 (mm) T E (GPa) KIc (MPa-mm1/2) cf (mm) Gf (J/m2)4        1.02 413 0.08 32.7 67.5 92 139.310        1.10 361 0.04 35.5 67.9 80 129.531        1.30 172 0.08 36.8 55.6 38 84.1232        1.70 82 0.04 38.3 50.3 18 66.0Application of the Cohesive Crack ModelThe toughening or crack-shielding effect of the fracture process zone that occurs in front of aprogressing crack (2) is modeled as closing stresses in cohesive crack models (see Fig. 2). One suchmodel is the fictitious crack model, proposed for concrete by Hillerborg et al. (5). The constitutive relationfor the cohesive crack is given by a stress versus crack separation curve, F = f(T). In the present work,the exponential curve shown in Fig. 3, characterized by two independent parameters, namely the fractureenergy (the area under the curve) GF  and the tensile strength f t , is used. This model has beenimplemented in a finite element code with the cracking simulated by quadratic joint elements. Furtherdetails of the numerical analysis are available in Ref. 6. FIG. 1Size effect model with normalized experimentaldata for different agesFIG. 2Cohesive crack model, where FPZ = fracture process zoneFIG. 3Exponential stress versus crack separation law used in the cohesive crack modelThe parameters of the cohesive crack for each age were obtained by back-fitting of the experimentalload-CMOD curves of all the specimens at that age. Note that all the sizes were fitted together in order toreduce the uncertainty of the parameter set. However, the choice of the optimum parameters wasinfluenced by the trends seen in the size effect analysis, and they are, therefore, not considered to becompletely unique or objective. The parameter set, GF and f t , which gave the best fits of the experimentalload-CMOD data for the three sizes are given in Table 4 for each age. It can be seen that an increase in the tensile strength with age is accompanied by a decrease in GF,which is similar to the trend of Gf in the SEM, though the absolute values of GF are higher, as also seenby other researchers (8). The characteristic length (which is related to the process zone length), definedby Hillerborg (5,9) as lch = EGF /f t2, also decreases with age (Table 4) indicating an increase in brittleness.TABLE 4.  Parameters of the Cohesive Crack Model at Different AgesParameter Age (days)4 10 31 232GF (J/m2) 150 140 120 88f t (MPa) 4.7 5.2 6.0 7.0lch (mm) 220 180 120 70DiscussionThe trends observed in the size effect analysis suggest that the brittleness of a structure composed ofthe concrete used in this study would increase with age. This is implied by the shift in the data in Fig. 1 tothe right (toward ideal-brittle LEFM behavior) and the decrease in cf with age. The parameter cf is ameasure of the size of the zone where energy is dissipated during crack propagation. This conceptualfracture process zone includes the effects of toughening mechanisms such as crack-deflection, bridgingand microcracking. Therefore, a decrease in cf , as in the present results, implies an increase in thebrittleness of the material. The lower values of KIc and Gf indicate a slight decrease in the crackresistance due to the reduced toughening or crack-shielding. A similar trend is seen in the cohesive crackanalysis, where an increase in tensile strength with age is accompanied by a decrease in the fractureenergy GF and characteristic length lch.The main reason for the increase in brittleness and the decrease in toughening with age seems to bethe strengthening of the hardened cement paste and the aggregate-matrix interface due to hardeningprocesses. Moreover, as shown by Alexander (10), the fracture energy of the hardened cement pastedecreases with age implying an increase in its brittleness. Consequently, in high strength concretes withhigh matrix and interface strengths, there would be an increase in aggregate rupture and a decrease ininterface cracking with age, as observed here in the crack surfaces. The resulting decrease in cracktortuosity would effectively cause a higher stress intensity at the crack-tip or lower toughening, leading tomore brittle crack propagation. In conventional concretes, the failure mechanisms can be significantly different from that of highstrength concretes. At early ages, it has been observed that fracture toughness and fracture energyincrease significantly with age (11-13). However, the trends given in the literature for brittleness arecontradictory; Petersson (11), and Berra and Castellani (14) found that lch decreased with age (as in thepresent results) while Zollinger et al. (13) concluded that cf increases due to aging. The reasons for thedifferent tendencies seen in the higher strength concretes could be due to the relative strength, toughnessand brittleness of the aggregate, interfaces and paste, which are obviously influenced by the presence ofsilica fume and the low water/cement ratio.ConclusionsHigh-strength concrete notched beams of three different sizes were tested at the ages of 4, 10, 31and 232 days. The results were analyzed using the size effect model and the cohesive crack model (withan exponential constitutive law) to obtain the fracture parameters at different ages. The data indicate thatthe crack resistance decreases and the brittleness increases with age. This can be attributed to theprogressive increase in strength and brittleness of the paste, and the strengthening of the interfaces, whichlead to more aggregate rupture and less crack tortuosity, causing a decrease in the toughening or crack-shielding.AcknowledgmentsPartial financial support from Spanish CICYT grants PB93-0955 and MAT96-0967, and theGeneralitat de Catalunya (DGR-CUR) grant 1995SGR-517 is gratefully appreciated. The doctoral studiesof V.O.García-Álvarez at the UPC were supported by a pre-doctoral fellowship from the Generalitat deCatalunya (Spain). The authors thank I.Carol and P.C.Prat for the use of the DRAC finite elementpackage in the numerical analysis, and O.M.García-Álvarez for his help during the tests. References1. R.Gettu, Z.P.Bažant and M.E.Karr, ACI Mater. J., 87, 608-618 (1990).2. R.Gettu and S.P.Shah, in High Performance Concrete and Applications, pp. 161-212, Edward Arnold,London, 1994. 3. Z.P.Bažant and M.T.Kazemi, Int. J. Fract., 44, 111-131 (1990).4. RILEM Technical Committee TC89-FMT, Mater. Struct., 23, 461-465 (1990).5. A.Hillerborg, M.Modéer and P.-E.Petersson, Cem. Concr. Res., 6, 773-782 (1976).6. V.O.García-Álvarez, Study of Mixed Mode Fracture in Quasi-brittle Materials (in Spanish), Doctoralthesis, Universitat Politècnica de Catalunya, Barcelona, Spain, 1997.7. R.Gettu, P.C.Prat and M.T.Kazemi, in Fracture Mechanics of Concrete Structures, ProceedingsFramCoS 1, pp. 430-436, Elsevier Applied Science, London, 1992.8. M.Elices and J.Planas, Adv. Cem. Bas. Materials, 4, 116-127 (1996).9. A.Hillerborg, in Fracture Mechanics of Concrete, pp. 223-249, Elsevier Science, Amsterdam, 1983.10. M.G.Alexander, Cem. Concr. Res., 24, 1277-1285 (1994).11. P.E.Petersson, Cem. Concr. Res., 10, 91-101 (1980).12. F.H.Wittmann, P.E.Roelfstra, H.Mihashi, Y.-Y.Huang, X.-H.Zhang and N.Nomura, Mater. Struct., 20, 103-110 (1987).13. D.G.Zollinger, T.Tang, and R.H.Yoo, ACI Mater. J., 90, 463-471 (1993).14. M.Berra and A.Castellani, in Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-2,pp. 85-94, Aedificatio Publishers, Freiburg, Germany, 1995.

Effect of aging on the fracture characteristics and brittleness of a high-strength concrete

Results of notched beam (fracture) tests on a 60 MPa silica fume concrete at the ages of 4,

10, 31 and 232 days are presented. Fracture parameters at the different ages were obtained

using the size effect and cohesive crack models, which indicate that the fracture resistance

(toughness and energy) decreases and the brittleness increases with the age of the concrete.

This trend is attributed to the increase in the strength of the hardened cement paste and the

interfaces that leads to less bond cracking and more aggregate rupture, and consequently, to

more brittle failure and lower toughening.Peer Reviewe

Effect of aging on the fracture characteristics and brittleness of a high-strength concrete

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