- Email: [email protected]
Variations in fracture energy of concrete subjected to cyclic freezing and thawing
archives of civil and mechanical engineering 13 (2013) 254–259
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/acme
Original Research Article
Variations in fracture energy of concrete subjected to cyclic freezing and thawing M. Kosior-Kazberuk Faculty of Civil and Environmental Engineering, Bialystok University of Technology, 45E Wiejska Street, 15-351 Bialystok, Poland
ar t ic l e in f o
abs tra ct
Article history:
Fracture energy is one of the fundamental parameters representing cracking resistance
Received 16 November 2012
and fracture toughness of concrete. The paper deals with the effect of internal frost
Accepted 4 January 2013
damage on the fracture energy of concrete. The fracture energy value was assessed on
Available online 11 January 2013
beams with initial notches in three-point bend test assuring stable failure of the specimen.
Keywords:
It was found, that the internal damages due to cyclic freezing and thawing have a
Concrete
significant effect on variations in fracture energy, related to changes in destructive load
Frost damage
value as well as in deformability of material. The analysis of load-deflection curves
Fracture energy
obtained made it possible to fit the simple function, describing the post-peak behaviour of
Load-deflection curve
concrete subjected to frost damages, which can be useful for the calculation of GF value. It was proved that it is reasonable and feasible to study the freeze-thaw damage process of concrete using fracture mechanics methods. & 2013 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved.
1.
Introduction
Concrete is a heterogeneous material of high compressive strength, but its resistance to cracking is low [1,2]. The destruction of concrete under the influence of external loads is affected, among other things, by material discontinuities, disruptions, and local differences in mechanical properties of material [3,4]. Local stress concentrations occurring in the vicinity of concrete defects can cause rapid propagation of damage, and finally lead to the destruction of the entire element [5–7]. The most dangerous stress concentrators are the tips of cracks where the greatest stress values are achieved [8,9]. Considering the complex microstructure and quasi-brittle character of the failure of concrete, the strength properties are not sufficient to describe the material’s behaviour. Thus, the fracture mechanics can help analyse the response of microstructure to external load.
Applications of fracture mechanics to concrete structures can provide a rational basis for both service performance and failure analysis and lead to better understanding of design methods [8]. One of the severe types of deterioration in concrete microstructure is caused by freezing and thawing. Internal freezethaw damage results from tensile stresses generated by water on freezing when the pore system in concrete is saturated above the critical value. Internal damage, which is likely to occur in concrete subjected to long-term wet/saturated conditions [10,11], is manifested macroscopically by irreversible tensile deformations and randomly oriented microcracking [12,13]. In the progress of freezing and thawing, recurrent frost expanding and stress act on concrete, causing inner flaws accumulation and forming new damages. Hence, the freezing and thawing action can be looked upon as a complex fatigue crack propagation process [14].
n
Tel.: þ48 85 746 96 94; fax: þ48 85 746 95 59. E-mail address: [email protected]
1644-9665/$ - see front matter & 2013 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2013.01.002
archives of civil and mechanical engineering 13 (2013) 254–259
The most of previous works on the freeze-thaw durability of concrete were focused on the strength properties degradation, weight change, length change or ultrasonic signature change after different numbers of freeze-thaw cycles, sometimes in the presence of salt solution [10–15]. Assuming the fracture parameters are strongly influenced by flaws development in concrete microstructure, they can be useful to assess the degradation process caused by different factors [8,16,17]. The ways of using fracture mechanics parameters for the assessment and prediction of the durability of structure, are being sought. The influence of freeze-thaw on fracture parameters of cement concrete were investigated by Hanjari et al. [11], and on fracture parameters of polymer concrete—by Reis and Ferreira [18]. Karihaloo and Santhikumar [19] used the energy based criterion of fracture mechanics to elaborate tension-softening model to cracked and ageing concrete structures subjected to environmental influences. The variations in fracture energy of normal strength and high strength concretes subjected to thermal cycling were investigated by Bazˇant and Prat [20] and Kanellopoulos et al. [21]. The analysis of research works, described in references, has shown the sensitivity of fracture parameters to material’s microstructure changes caused by repetitive actions resulting in accumulation of internal damages. Despite the evidence of fracture mechanics methods applicability to the analysis of concrete degradation process, there are no coherent theory and experimental studies on changes in fracture parameters during cyclic freezing and thawing of water-saturated concrete. The fracture energy is a fundamental fracture parameter of cohesive crack model, representing cracking resistance and fracture toughness of quasi-brittle materials e. g. concrete [7,22]. The model is able to capture the essential features of a progressively fracturing surface and its evolution until the failure. The crack is assumed to propagate when the stress at the crack tip reaches the tensile strength of concrete. When the crack opens the stress does not fall to zero at once, but it decreases with increasing crack width [6]. As a result, the energy dissipation for crack propagation can be completely characterised by the cohesive stress-separation relationship. It characterises the softening response of a crack that could develop anywhere in a concrete structure. A unique load-displacement curve is very often used to quantify the value of energy [8,22]. The choice of descending softening function (or cohesive law) influences the prediction of the structural response and the local fracture behaviour. Some of fitted functions were discussed in [8,23,24]. The aim of the research work was the analysis of the effect of internal damages due to freezing and thawing on the fracture energy GF of concrete. In order to determine the value of fracture energy three-point bend tests were performed for a notched beam of non aerated concrete as well as aerated one. On the basis of load-deflection curves analysis, the power function was proposed to describe the post-peak behaviour of concrete.
2.
Experimental investigations
2.1.
Materials and specimens preparation
The tests were carried on for non-aerated concrete (NAE) as well as for aerated concrete (AE). The cement (CEM I 42,5NHSR/NA) content in concretes tested was constant—350 kg/m3,
255
and water to cement ratio was equal to 0.40. The river sand, fraction 0C2 mm and the natural aggregate with maximum diameter of 8 mm were used. The air-entraining agent (AEA) content was 0.10% related to cement mass. The specimens were vibrated in forms. After de-moulding they were stored in water at temperature 2072 1C. The compressive strength, tested after 28 days of curing, was equal to 59.7 MPa for non-air-entrained concrete and 55.2 MPa for concrete with AEA, respectively. The airentrained concrete was characterised by the following air void characteristics: specific surface a¼ 29.60 mm1; spacing factor L ¼0.15 mm; total air-content A ¼6.57% and the pore volume below 0.3 mm A300 ¼ 2.56%. The specimen with sizes 100 100 400 mm were prepared for fracture energy determination. The central saw-cut notch depth was equal to 30 mm and width was 3 mm. The notches were sawn under wet conditions one day before the test.
2.2.
Test procedure
After 28 days of water storage the specimens for fracture energy determination were subjected to cyclic freezing in air and thawing in water. The temperature changed from 18 1C to 18 1C. The duration of single cycle was 8 h and the freezing period duration was 6 hours. The freezing and thawing process was finished one day before testing. The tests for fracture energy determination for specimens of non aerated concrete were performed after 60, 90, 120, 150, 180 and 210 cycles and aerated concrete specimens were tested after 150, 250, 300 and 350 cycles. The reference specimens were stored in water at temperature 2072 1C until the time of testing. The fracture parameter was assessed in three-point bend test on beams with initial notches according to procedure [25]. The geometry of specimen and the way of load were presented in Fig. 1. Each series was composed of 4 replicates. The testing machine with closed-loop servo control was used to achieve a stable failure. The complete load-time curve was recorded to check the stability during the test. The mid-span deflection d of specimen and the applied load P were recorded continuously until the beam was completely separated into two halves. The test was performed with constant rate of deformation, so that the maximum load
Fig. 1 – Configuration of three-point bending beam.
256
archives of civil and mechanical engineering 13 (2013) 254–259
Fig. 3 – Complete load-deflection (P–d) curves for non aerated concrete specimens after different number of cycles n. Fig. 2 – Beam specimen during testing.
was reached within 30–60 s after start of the test, depending on the degree of concrete degradation. The image of specimen destruction during testing, after freeze–thaw cycles, was presented in Fig. 2 The fracture energy is defined as the amount of energy necessary to create one unit area of a crack [5]. The values of fracture energy GF are obtained by dividing the area under P–d curve, the measured work of fracture, by area of the ligament, Alig, which is defined as the projection of the fracture zone on a plane perpendicular to the beam axis [7,25]: Z dmax PðdÞdd þ mgdmax =½ðda0 Þb ð1Þ GF ¼ 0
where g¼ 9,81 m/s2, d—beam depth, b—beam width, a0—notch depth and dmax—maximum deflection. In connection with the test, the weight of the beam m was determined and included into calculation of GF. The load-deflection curve was corrected for possible nonlinearities at initial low loads, according to [9]. The scatter in GF calculation comes from inherent randomness in the tail part of P–d curve, uncertainty in extrapolating the tail end of curve to zero load and difficulty in elimination of nonfracture sources of energy dissipation [7,16]. In order to limitation the influence of factors mentioned above, the plot of curve was cut at load value approximately equal to 0.05 Pmax (100C250 N) and in this way dmax value was determined. The experimental load-deflection data of three-point bending tests were used to obtain the softening function which characterises the post-peak behaviour of concrete.
3.
Results and discussion
3.1.
Effect of freezing and thawing of fracture energy GF
The complete curves of the load P versus mid-span deflection d for selected specimens of concrete tested are presented in Figs. 3 and 4. Considering the fracture energy is the product of load and deflection due to load applied, the variation of plot of P–d curve reflects the variation of GF.
Fig. 4 – Complete load-deflection (P–d) curves for aerated concrete specimens after different number of cycles n.
It was found that cyclic freezing and thawing had significant influence on the plot of load-deflection curve. At first, the changes in concrete microstructure due to cyclic freezing and thawing caused the increase in mid-span deflection of specimen, connected with the deformability of material, but the changes in the value of maximum load were small. As a result, the value of GF increased. The following cycles, causing the accumulation of internal damages, resulted in the further growth of deflection and at the same time significant decrease in maximum load for specimen. Similar effects, during frost degradation, were observed for both non aerated and aerated concretes, although the damage process rate was higher for concrete without AEA. The results obtained for frozen concrete (Cfroz) were compared with the values of GF for control concrete specimens (Cref) cured in water (Fig. 5). Fracture energy of control concrete only slightly increased with age. The analysis of fracture energy dependence on the number of freeze-thaw cycles, for concretes of varied frost resistance, showed the significant differences in the rate of GF development. The essential changes in fracture energy of freezing concretes comparing to control concretes and considering the scatter of results were observed after 90 cycles for non aerated concrete and after 150 cycles for concrete
archives of civil and mechanical engineering 13 (2013) 254–259
257
dissipation through friction and some bridging across the crack. The crack tip can be terminated by air voids, which produces a blunt tip. Additional energy is required to propagate the crack with a new blunt tip. The crack may propagate into several branches due to heterogeneity of concrete and more energy should be consumed to form new crack branches [7,8,24].
3.2.
Post-peak behaviour of concrete
The data sets collected during test of specimens after different number of cycles were used to find the softening function describing the post-peak behaviour of concrete with proper accuracy. The following expression was employed to fit the descending part of P–d curve: c2 dp , ð2Þ PðdÞ ¼ Pmax c1 þ ð1c1 Þ d where Pmax is peak load and dp—deflection value corresponding to Pmax. The coefficients c1 and c2 are determined by means of the last-square method. The plots of post-critical range of P–d curves approximated by expression (2), after different number of cycles n, were presented in Figs. 6 and 7.
Fig. 5 – Variations in fracture energy GF of concrete specimens subjected to freeze-thaw cycles Cfroz in comparison to control specimens Cref: (a) non aerated concrete; (b) aerated concrete.
with AEA additive. Initially, cyclic freezing and thawing caused the significant increase in fracture energy in comparison to GF value determined for control specimens. The greater increase (about 25%) was observed after 150 cycles for non aerated concrete and after 250 cycles for aerated concrete. Further freezing (frost influence), connected with the development in the process of concrete microstructure degradation, resulted in instant decrease in fracture energy. Similar effect of damages on fracture energy changes, after different number of cycles, was observed by Hanjari et al. [11], Prasad et al. [24] and Reis and Ferreira [18]. The fracture energy increase can be explained by the presence of several flaws (microcracks, pores, air voids), randomly oriented in microstructure of concrete, arisen or developed due to cyclic freezing and thawing, which influence the fracture process by toughening mechanisms that appear around the main crack when it propagates. The microcracks of different orientation, with respect to the main crack plane, can connect to each other and deviate from initial propagation direction. During grain pullout or the opening of a tortuous crack, there may be some contact (or interlock) between the crack faces. This causes energy
Fig. 6 – Plot of post-critical range of P–d curves for non aerated concrete specimens after different number of cycles n.
Fig. 7 – Plot of post-critical range of P–d curves for aerated concrete specimens after different number of cycles n.
258
archives of civil and mechanical engineering 13 (2013) 254–259
The integration of expression (2) in the range from deflection value dp corresponding to Pmax to the maximum value of deflection df at final fracture and dividing the value obtained by area of the ligament, Alig, gives the value of GF: " # c2 ðc1 1Þ df dp =df dp ð3Þ =½ðda0 bÞ: GF ¼ Pmax df dp c1 þ ðc2 1Þ df dp
aerated concrete (AE), the essential decrease in c2 was found after 250 cycles.
The weight of the beam should also be included in the same manner as in Eq. (1). The fracture energy was calculated according to Eq. (3) for both non aerated (NAE) and aerated (AN) concretes tested after different number of freeze/thaw cycles and compared with the values obtained from experiment. The result of the comparison, presented in Fig. 8, confirmed good fit of approximated function. The value of the coefficient c1 (in expression(2)) varied from 0.979 to 0.078 in dependence on Pmax and dp values. However, the shape of softening curve was determined by c2 coefficient. The values of c2 coefficient of power function (2) in relation to the number of freeze-thaw cycles n for both concretes tested were presented in Fig. 9. The change of c2 in case of non aerated concrete (NAE) was almost linear. For
The results obtained from the test, performed on non aerated as well as on aerated concretes, made it possible to analyse the variations in fracture energy due to cyclic freezing and thawing. It was found that the fracture energy is strongly influenced by the accumulation of internal damages in concrete microstructure. The long-term destructive factors have an effect on the modification of the load-displacement curve in fracture process. The degradation process causes the decrease in destructive load value and the increase in material deformability. The internal degradation influences the crack propagation process and thus, it causes the variations in fracture energy GF. The initial increase in fracture energy due to cyclic freezing and thawing can be explained by the introduction of several cracks as an effect of internal frost damage prior to mechanical testing. Thus, greater amount of energy was dissipated, by opening several dominant cracks, to fully fracture the specimen. However, further degradation of concrete microstructure resulted in the drop of fracture energy. The analysis of load-deflection curves, recorded for concrete specimens after different number of cycles, made it possible to fit the simple function describing the post-peak behaviour of concrete subjected to frost damages. On the basis of softening function obtained, the value of GF can be calculated. The applicability of fracture mechanics characteristics to study the freeze-thaw damage rules of concrete was proved.
4.
Conclusion
r e f e r e n c e s
Fig. 8 – Comparison between calculated GFcal and measured in experiment GFexp values.
Fig. 9 – Dependency of c2 coefficient value on the number of freeze-thaw cycles n.
[1] B. Goszczyn´ska, G. S´wit, W. Tra˛pczyn´ski, A. Krampikowska, J. Tworzewska, P. Tworzewski, Experimental validation of concrete crack identification and location with acoustic emission method, Archives of Civil and Mechanical Engineering 12 (1) (2012) 23–28. [2] E. Raue, H.G. Timmler, R. Garke, On the physically non-linear analysis of cyclic loaded reinforced concrete cross-sections with mathematical optimisation, Journal of Civil Engineering and Management 15 (2) (2009) 189–195. [3] T. Gorzelan´czyk, J. Hoła, Pore structures of self-compacting concretes made using different superplasticizers, Archives of Civil and Mechanical Engineering 12 (3) (2011) 611–621. [4] J.G.M. Van Mier, M.R.A. Van Vliet, Influence of microstructure of concrete on size/scale effects in tensile fracture, Engineering Fracture Mechanics 70 (2003) 2281–2306. [5] Y.S. Jenq, S.P. Shah, Features of mechanics of quasi-brittle crack propagation in concrete, International Journal of Fracture 51 (1991) 103–120. [6] Z.P. Bazˇant, Concrete fracture models: testing and practice, Engineering Fracture Mechanics 69 (2002) 165–205. [7] B.L. Karihaloo, Failure of concrete, in: Comprehensive Structural Integrity, Elsevier Pergamon, UK, 2003, pp. 477–548. [8] S.P. Shah, S.E. Swartz, Ch. Ouyang, Fracture mechanics of concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials, John Wiley & Sons, Inc., New York, 1995.
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[9] C. Rossello´, M. Elices, G.V. Guinea, Fracture of model concrete: 2. Fracture energy and characteristic length, Cement and Concrete Research 36 (2006) 1345–1353. [10] G. Fagerlund, Mechanical damage and fatigue effects associated with freeze-thaw of materials, in: Proceedings of the 2nd International RILEM Workshop on Frost Resistance of Concrete, Essen, 18–19 April, 2002, pp. 117–132. [11] K.Z. Hanjari, P. Utgenannt, K. Lundgren, Experimental study of the material and bond properties of frost-damaged concrete, Cement and Concrete Research 41 (2011) 244–254. [12] M. Pigeon, J. Marchand, R. Pleau, Frost resistant concrete, Construction and Building Materials 10 (1996) 339–348. [13] J. Sˇelih, Performance of concrete exposed to freezing and thawing in different saline environments, Journal of Civil Engineering and Management 16 (2) (2010) 306–311. [14] M. Hasan, T. Ueda, Y. Sato, Stress-strain relationship of frostdamaged concrete subjected to fatigue loading, Journal of Materials in Civil Engineering 20 (2008) 37–45. [15] D. Jo´z´wiak-Niedz´wiedzka, Scaling resistance of high performance concretes containing a small portion of prewetted lightweight fine aggregate, Cement and Concrete Composites 27 (2005) 709–715. [16] Z.P. Bazˇant, Q. Yu, G. Zi, Choice of standard fracture test for concrete and its statistical evaluation, International Journal of Fracture 118 (2002) 303–337. [17] H. Mang, On contemporary computational mechanics, Journal of Civil Engineering and Management 15 (1) (2009) 113–128. [18] J.M.L. Reis, A.J.M. Ferreira, Freeze-thaw and thermal degradation influence on the fracture properties of carbon
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and glass fiber reinforced polymer concrete, Construction and Building Materials 20 (2006) 888–892. B.L. Karihaloo, S. Santhikumar, Application of a visco-elastic tension-softening constitutive model to cracked and ageing concrete, Construction and Building Materials 13 (1999) 15–21. Z.P. Bazˇant, P.C. Prat, Effect of temperature on fracture energy of concrete, ACI Materials Journal 85 (1988) 262–271. A. Kanellopoulos, F.A. Farhat, D. Nicolaides, B.L. Karihaloo, Mechanical and fracture properties of cement-based bimaterials after thermal cycling, Cement and Concrete Research 39 (2009) 1087–1094. Z. Zhao, S.H. Kwon, S.P. Shah, Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy, Cement and Concrete Research 38 (2008) 1049–1060. X.H. Guo, F. Tin-Loi, H. Li, Determination of quasibrittle fracture law for cohesive crack models, Cement and Concrete Research 29 (1999) 1055–1059. B.K.R. Prasad, R.K. Saha, A.R. Gopalakrishnan, Fracture behaviour of plain concrete beams—experimental verification of one parameter model, in: Proceedings of the International Conference on Computational & Experimental Engineering and Science, Las Vegas, USA, 2010, vol. 14, pp. 65–83. Draft RILEM Recommendation, Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, Materials and Structures 18 (1985) 287–290.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/acme
Original Research Article
Variations in fracture energy of concrete subjected to cyclic freezing and thawing M. Kosior-Kazberuk Faculty of Civil and Environmental Engineering, Bialystok University of Technology, 45E Wiejska Street, 15-351 Bialystok, Poland
ar t ic l e in f o
abs tra ct
Article history:
Fracture energy is one of the fundamental parameters representing cracking resistance
Received 16 November 2012
and fracture toughness of concrete. The paper deals with the effect of internal frost
Accepted 4 January 2013
damage on the fracture energy of concrete. The fracture energy value was assessed on
Available online 11 January 2013
beams with initial notches in three-point bend test assuring stable failure of the specimen.
Keywords:
It was found, that the internal damages due to cyclic freezing and thawing have a
Concrete
significant effect on variations in fracture energy, related to changes in destructive load
Frost damage
value as well as in deformability of material. The analysis of load-deflection curves
Fracture energy
obtained made it possible to fit the simple function, describing the post-peak behaviour of
Load-deflection curve
concrete subjected to frost damages, which can be useful for the calculation of GF value. It was proved that it is reasonable and feasible to study the freeze-thaw damage process of concrete using fracture mechanics methods. & 2013 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved.
1.
Introduction
Concrete is a heterogeneous material of high compressive strength, but its resistance to cracking is low [1,2]. The destruction of concrete under the influence of external loads is affected, among other things, by material discontinuities, disruptions, and local differences in mechanical properties of material [3,4]. Local stress concentrations occurring in the vicinity of concrete defects can cause rapid propagation of damage, and finally lead to the destruction of the entire element [5–7]. The most dangerous stress concentrators are the tips of cracks where the greatest stress values are achieved [8,9]. Considering the complex microstructure and quasi-brittle character of the failure of concrete, the strength properties are not sufficient to describe the material’s behaviour. Thus, the fracture mechanics can help analyse the response of microstructure to external load.
Applications of fracture mechanics to concrete structures can provide a rational basis for both service performance and failure analysis and lead to better understanding of design methods [8]. One of the severe types of deterioration in concrete microstructure is caused by freezing and thawing. Internal freezethaw damage results from tensile stresses generated by water on freezing when the pore system in concrete is saturated above the critical value. Internal damage, which is likely to occur in concrete subjected to long-term wet/saturated conditions [10,11], is manifested macroscopically by irreversible tensile deformations and randomly oriented microcracking [12,13]. In the progress of freezing and thawing, recurrent frost expanding and stress act on concrete, causing inner flaws accumulation and forming new damages. Hence, the freezing and thawing action can be looked upon as a complex fatigue crack propagation process [14].
n
Tel.: þ48 85 746 96 94; fax: þ48 85 746 95 59. E-mail address: [email protected]
1644-9665/$ - see front matter & 2013 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2013.01.002
archives of civil and mechanical engineering 13 (2013) 254–259
The most of previous works on the freeze-thaw durability of concrete were focused on the strength properties degradation, weight change, length change or ultrasonic signature change after different numbers of freeze-thaw cycles, sometimes in the presence of salt solution [10–15]. Assuming the fracture parameters are strongly influenced by flaws development in concrete microstructure, they can be useful to assess the degradation process caused by different factors [8,16,17]. The ways of using fracture mechanics parameters for the assessment and prediction of the durability of structure, are being sought. The influence of freeze-thaw on fracture parameters of cement concrete were investigated by Hanjari et al. [11], and on fracture parameters of polymer concrete—by Reis and Ferreira [18]. Karihaloo and Santhikumar [19] used the energy based criterion of fracture mechanics to elaborate tension-softening model to cracked and ageing concrete structures subjected to environmental influences. The variations in fracture energy of normal strength and high strength concretes subjected to thermal cycling were investigated by Bazˇant and Prat [20] and Kanellopoulos et al. [21]. The analysis of research works, described in references, has shown the sensitivity of fracture parameters to material’s microstructure changes caused by repetitive actions resulting in accumulation of internal damages. Despite the evidence of fracture mechanics methods applicability to the analysis of concrete degradation process, there are no coherent theory and experimental studies on changes in fracture parameters during cyclic freezing and thawing of water-saturated concrete. The fracture energy is a fundamental fracture parameter of cohesive crack model, representing cracking resistance and fracture toughness of quasi-brittle materials e. g. concrete [7,22]. The model is able to capture the essential features of a progressively fracturing surface and its evolution until the failure. The crack is assumed to propagate when the stress at the crack tip reaches the tensile strength of concrete. When the crack opens the stress does not fall to zero at once, but it decreases with increasing crack width [6]. As a result, the energy dissipation for crack propagation can be completely characterised by the cohesive stress-separation relationship. It characterises the softening response of a crack that could develop anywhere in a concrete structure. A unique load-displacement curve is very often used to quantify the value of energy [8,22]. The choice of descending softening function (or cohesive law) influences the prediction of the structural response and the local fracture behaviour. Some of fitted functions were discussed in [8,23,24]. The aim of the research work was the analysis of the effect of internal damages due to freezing and thawing on the fracture energy GF of concrete. In order to determine the value of fracture energy three-point bend tests were performed for a notched beam of non aerated concrete as well as aerated one. On the basis of load-deflection curves analysis, the power function was proposed to describe the post-peak behaviour of concrete.
2.
Experimental investigations
2.1.
Materials and specimens preparation
The tests were carried on for non-aerated concrete (NAE) as well as for aerated concrete (AE). The cement (CEM I 42,5NHSR/NA) content in concretes tested was constant—350 kg/m3,
255
and water to cement ratio was equal to 0.40. The river sand, fraction 0C2 mm and the natural aggregate with maximum diameter of 8 mm were used. The air-entraining agent (AEA) content was 0.10% related to cement mass. The specimens were vibrated in forms. After de-moulding they were stored in water at temperature 2072 1C. The compressive strength, tested after 28 days of curing, was equal to 59.7 MPa for non-air-entrained concrete and 55.2 MPa for concrete with AEA, respectively. The airentrained concrete was characterised by the following air void characteristics: specific surface a¼ 29.60 mm1; spacing factor L ¼0.15 mm; total air-content A ¼6.57% and the pore volume below 0.3 mm A300 ¼ 2.56%. The specimen with sizes 100 100 400 mm were prepared for fracture energy determination. The central saw-cut notch depth was equal to 30 mm and width was 3 mm. The notches were sawn under wet conditions one day before the test.
2.2.
Test procedure
After 28 days of water storage the specimens for fracture energy determination were subjected to cyclic freezing in air and thawing in water. The temperature changed from 18 1C to 18 1C. The duration of single cycle was 8 h and the freezing period duration was 6 hours. The freezing and thawing process was finished one day before testing. The tests for fracture energy determination for specimens of non aerated concrete were performed after 60, 90, 120, 150, 180 and 210 cycles and aerated concrete specimens were tested after 150, 250, 300 and 350 cycles. The reference specimens were stored in water at temperature 2072 1C until the time of testing. The fracture parameter was assessed in three-point bend test on beams with initial notches according to procedure [25]. The geometry of specimen and the way of load were presented in Fig. 1. Each series was composed of 4 replicates. The testing machine with closed-loop servo control was used to achieve a stable failure. The complete load-time curve was recorded to check the stability during the test. The mid-span deflection d of specimen and the applied load P were recorded continuously until the beam was completely separated into two halves. The test was performed with constant rate of deformation, so that the maximum load
Fig. 1 – Configuration of three-point bending beam.
256
archives of civil and mechanical engineering 13 (2013) 254–259
Fig. 3 – Complete load-deflection (P–d) curves for non aerated concrete specimens after different number of cycles n. Fig. 2 – Beam specimen during testing.
was reached within 30–60 s after start of the test, depending on the degree of concrete degradation. The image of specimen destruction during testing, after freeze–thaw cycles, was presented in Fig. 2 The fracture energy is defined as the amount of energy necessary to create one unit area of a crack [5]. The values of fracture energy GF are obtained by dividing the area under P–d curve, the measured work of fracture, by area of the ligament, Alig, which is defined as the projection of the fracture zone on a plane perpendicular to the beam axis [7,25]: Z dmax PðdÞdd þ mgdmax =½ðda0 Þb ð1Þ GF ¼ 0
where g¼ 9,81 m/s2, d—beam depth, b—beam width, a0—notch depth and dmax—maximum deflection. In connection with the test, the weight of the beam m was determined and included into calculation of GF. The load-deflection curve was corrected for possible nonlinearities at initial low loads, according to [9]. The scatter in GF calculation comes from inherent randomness in the tail part of P–d curve, uncertainty in extrapolating the tail end of curve to zero load and difficulty in elimination of nonfracture sources of energy dissipation [7,16]. In order to limitation the influence of factors mentioned above, the plot of curve was cut at load value approximately equal to 0.05 Pmax (100C250 N) and in this way dmax value was determined. The experimental load-deflection data of three-point bending tests were used to obtain the softening function which characterises the post-peak behaviour of concrete.
3.
Results and discussion
3.1.
Effect of freezing and thawing of fracture energy GF
The complete curves of the load P versus mid-span deflection d for selected specimens of concrete tested are presented in Figs. 3 and 4. Considering the fracture energy is the product of load and deflection due to load applied, the variation of plot of P–d curve reflects the variation of GF.
Fig. 4 – Complete load-deflection (P–d) curves for aerated concrete specimens after different number of cycles n.
It was found that cyclic freezing and thawing had significant influence on the plot of load-deflection curve. At first, the changes in concrete microstructure due to cyclic freezing and thawing caused the increase in mid-span deflection of specimen, connected with the deformability of material, but the changes in the value of maximum load were small. As a result, the value of GF increased. The following cycles, causing the accumulation of internal damages, resulted in the further growth of deflection and at the same time significant decrease in maximum load for specimen. Similar effects, during frost degradation, were observed for both non aerated and aerated concretes, although the damage process rate was higher for concrete without AEA. The results obtained for frozen concrete (Cfroz) were compared with the values of GF for control concrete specimens (Cref) cured in water (Fig. 5). Fracture energy of control concrete only slightly increased with age. The analysis of fracture energy dependence on the number of freeze-thaw cycles, for concretes of varied frost resistance, showed the significant differences in the rate of GF development. The essential changes in fracture energy of freezing concretes comparing to control concretes and considering the scatter of results were observed after 90 cycles for non aerated concrete and after 150 cycles for concrete
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dissipation through friction and some bridging across the crack. The crack tip can be terminated by air voids, which produces a blunt tip. Additional energy is required to propagate the crack with a new blunt tip. The crack may propagate into several branches due to heterogeneity of concrete and more energy should be consumed to form new crack branches [7,8,24].
3.2.
Post-peak behaviour of concrete
The data sets collected during test of specimens after different number of cycles were used to find the softening function describing the post-peak behaviour of concrete with proper accuracy. The following expression was employed to fit the descending part of P–d curve: c2 dp , ð2Þ PðdÞ ¼ Pmax c1 þ ð1c1 Þ d where Pmax is peak load and dp—deflection value corresponding to Pmax. The coefficients c1 and c2 are determined by means of the last-square method. The plots of post-critical range of P–d curves approximated by expression (2), after different number of cycles n, were presented in Figs. 6 and 7.
Fig. 5 – Variations in fracture energy GF of concrete specimens subjected to freeze-thaw cycles Cfroz in comparison to control specimens Cref: (a) non aerated concrete; (b) aerated concrete.
with AEA additive. Initially, cyclic freezing and thawing caused the significant increase in fracture energy in comparison to GF value determined for control specimens. The greater increase (about 25%) was observed after 150 cycles for non aerated concrete and after 250 cycles for aerated concrete. Further freezing (frost influence), connected with the development in the process of concrete microstructure degradation, resulted in instant decrease in fracture energy. Similar effect of damages on fracture energy changes, after different number of cycles, was observed by Hanjari et al. [11], Prasad et al. [24] and Reis and Ferreira [18]. The fracture energy increase can be explained by the presence of several flaws (microcracks, pores, air voids), randomly oriented in microstructure of concrete, arisen or developed due to cyclic freezing and thawing, which influence the fracture process by toughening mechanisms that appear around the main crack when it propagates. The microcracks of different orientation, with respect to the main crack plane, can connect to each other and deviate from initial propagation direction. During grain pullout or the opening of a tortuous crack, there may be some contact (or interlock) between the crack faces. This causes energy
Fig. 6 – Plot of post-critical range of P–d curves for non aerated concrete specimens after different number of cycles n.
Fig. 7 – Plot of post-critical range of P–d curves for aerated concrete specimens after different number of cycles n.
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The integration of expression (2) in the range from deflection value dp corresponding to Pmax to the maximum value of deflection df at final fracture and dividing the value obtained by area of the ligament, Alig, gives the value of GF: " # c2 ðc1 1Þ df dp =df dp ð3Þ =½ðda0 bÞ: GF ¼ Pmax df dp c1 þ ðc2 1Þ df dp
aerated concrete (AE), the essential decrease in c2 was found after 250 cycles.
The weight of the beam should also be included in the same manner as in Eq. (1). The fracture energy was calculated according to Eq. (3) for both non aerated (NAE) and aerated (AN) concretes tested after different number of freeze/thaw cycles and compared with the values obtained from experiment. The result of the comparison, presented in Fig. 8, confirmed good fit of approximated function. The value of the coefficient c1 (in expression(2)) varied from 0.979 to 0.078 in dependence on Pmax and dp values. However, the shape of softening curve was determined by c2 coefficient. The values of c2 coefficient of power function (2) in relation to the number of freeze-thaw cycles n for both concretes tested were presented in Fig. 9. The change of c2 in case of non aerated concrete (NAE) was almost linear. For
The results obtained from the test, performed on non aerated as well as on aerated concretes, made it possible to analyse the variations in fracture energy due to cyclic freezing and thawing. It was found that the fracture energy is strongly influenced by the accumulation of internal damages in concrete microstructure. The long-term destructive factors have an effect on the modification of the load-displacement curve in fracture process. The degradation process causes the decrease in destructive load value and the increase in material deformability. The internal degradation influences the crack propagation process and thus, it causes the variations in fracture energy GF. The initial increase in fracture energy due to cyclic freezing and thawing can be explained by the introduction of several cracks as an effect of internal frost damage prior to mechanical testing. Thus, greater amount of energy was dissipated, by opening several dominant cracks, to fully fracture the specimen. However, further degradation of concrete microstructure resulted in the drop of fracture energy. The analysis of load-deflection curves, recorded for concrete specimens after different number of cycles, made it possible to fit the simple function describing the post-peak behaviour of concrete subjected to frost damages. On the basis of softening function obtained, the value of GF can be calculated. The applicability of fracture mechanics characteristics to study the freeze-thaw damage rules of concrete was proved.
4.
Conclusion
r e f e r e n c e s
Fig. 8 – Comparison between calculated GFcal and measured in experiment GFexp values.
Fig. 9 – Dependency of c2 coefficient value on the number of freeze-thaw cycles n.
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