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Yüksek mukavemetli betonların kırılma parametreleri

Yüksek mukavemetli betonların kırılma parametreleri

##### Dosyalar

##### Tarih

1995

##### Yazarlar

Çakır, Ayhan

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Kırılma mekanizması çatlak yayılması ve yapısal tepkiler sonucu oluşur. Normal çalışma koşullarında kınlan yapı elemanlan üzerinde yapılan incelemelere göre kırılmanın başlıca kaynağının malzemede mevcut veya üretim sırasmda oluşan çatlak türünde kusurlar olduğu sonucuna vanlmıştır. Başlangıçta önemsiz görünen veya gözden kaçan bu kusurlar zamanla büyüyerek kritik bir değere ulaşmakta ve ani kırılmalara neden olmaktadır. Bu tezde genel olarak bir malzemede mevcut çatlağın yayılması ve sonuçta kınlma oluşması için gereken koşullan saptamakta kullanılan eneıji yaklaşımı parametrelerinin tanımı ve özellikleri üzerinde duruldu. Literatürden alınan kınlma eneıjisi ve karakteristik uzunluk gibi kınlma parametrelerinin özellikle beton basınç mukavemetleriyle, agrega boyutuyla, su / bağlayıcı oranıyla olan ilişkileri incelendi. Beton mukavemetinin artmasıyla kınlma eneıjisinin özellikle yüksek mukavemetli betonlarda arttığı görüldü. Karakteristik uzunluk, beton basmç mukavemeti arttıkça azalmakta ve malzeme daha gevrek bir yapı kazanmaktadır. Aynı agrega ile hazırlanmış yüksek mukavemetli betonun karakteristik uzunluk değerleri, normal mukavemetli betona göre üçte iki oranında daha düşük çıkmıştır. Kınlma mekaniği parametrelerine yükleme tipinin ve maksimum agrega boyutunun etkisi incelenmiş, sonuçta kınlma mekaniği parametrelerinde agrega boyutunun tek başına bir etkisi gözlenmemiştir. Betonun bünyesel ilişkilerine dair geniş bilgi içermekte olan CEB-FIB Model Kod’da verilen basmç mukavemeti - kınlma eneıjisi’ne ilişkin tabloların silis dumanı içeren yüksek mukavemetli betonlan, malzemede çatlakların agrega içinden geçmesi ve yük – sehim eğrisinde inen kısmın daha ani olması ve daha kısa bir kuyruk göstermesi nedeniyle kapsamayabileceği görülmüştür. Bu nedenle yüksek mukavemetli betonlarda kınlma eneıjisi azalmakta ve daha gevrek bir davranış elde edilmektedir. Böylelikle silis dumanı içeren ve içermeyen betonlan birbirinden ayırmak gerekmektedir.

The mechanical behaviour of concrete that is designed to have high strength is different in many aspects from that of normal concrete. These differences have yielded some characteristics that are not beneficial, such as britdeness. Fracture models can be used to understand the microstructural mechanics that control brittleness and crack resistance (toughness),and to provide reliable means of quantifying them. New high- performance concretes can then be engineered to possess higher toughness and lower brittleness. Increased resistance to cracking may also lead to better durability, long-term reliability and seismic resistance. The application of fracture mechanics to structural analysis and design is motivated by the fact that the failure of concrete structures is primarily due to cracking, and several types of failures could occur catastrophically, especially in high-strength concrete structures.Certain aspects of such failures cannot be predicted satisfactorily by empirical relations obtained from tests, but can be explained rationally through fracture mechanics. In general, structural analysis based on fracture principles can lead to better estimates of crack widths and deformations under service loads, the safety factors under ultimate loads, and post-failure response during collapse.The use of fracture mechanics principles in the design of materials with higher toughness and ductility has produced encouraging results in the ceramics industry, and a similar approach is needed for high-performance concretes. Other aspects of concrete behaviour including the bond between steel and concrete, which is more brittle in silica iiime concrete than normal concrete, will also benefit from an increase in crack resistance and a decrease in brittleness. The durability, long-term reliability and thermal performance, which are greatly affected by cracking, would also be enhanced. Compressive strength is usually employed as the main parameter for the design of concrete structures. Nevertheless, as in other brittle materials, its fracture is governed by tensile mechanism. Not only is the strength important but so also is the whole behaviour of concrete under tensile stresses, especially its toughness. In many cases it would not be possible to build concrete structures that were safe enough if the material had no capacity to absorb energy. Although fracture mechanics has been extensively developed for brittle materials, the applicability of conventional concepts to concrete is not easy, due to the characteristics of the material. Concrete is heterogeneous (a composite, multiphase material); cracking itself is a heterogeneous process (initiation of cracks, slow stable crack growth, crack arrest and unstable crack propagation);the surface area formed in many times larger than the effective fracture area ( multiple crack formation occurs) and as a result, the energy dissipating mechanism in concrete is not merely confined to surface energy. The resistance of the material to fracture, G, can defined as the energy needed to create a crack of unit area. When a notched specimen, such as the beam in Fig.l, is tested until failure, the total work done gives the total energy dissipated. Assuming that all the energy has been consumed in extending the crack, determination of the work done and the crack area would yield G. This value is usually called fracture energy. The area under a load-displacement curve provided the total energy. Taking the unnotched part of the cross-section (i.e.,the ligament area) as the area of the crack, the fracture energies for different types of concretes can be determined. For Linear Elastic Fracture Mechanics (LEFM) type behaviour, the fracture energy is a constant equal to the critical strain energy release rate,i.e. Gf=GC. In practice however, Gy is not always constant. Researchers found that the fracture energy increased with specimen size and decreased with a significant decrease in stiffness of testing machine.Researchers showed that the determination of Gf was not straightforward. Since cracking in concrete is tortuous,they argued that the exact crack area should be determined instead of simply using the ligament area. They obtained the crack area from microscopic techniques, and thereby computed the fracture energies that were almost the same for hardened ce-ment past, mortar and concrete. Since the measurement of 'true' crack area is difficult, and to a certain extent subjective, later researchers have usually circumvented the problem by taking the ligament (or projected) area as the nominal area of the crack. Then, the fracture energy is also a nominal value. As the sizes of ligament and specimen increase, G would approch asimtotically towards a constant value. Therefore, G tend to be a material property when the fracture zone is negligible compared to the specimen size. Accordingly, the test method was recommended by RILEM with a lower limit on the specimen size. For concrete with a maximum aggregate size of 16-32 mm, the required beam depth is 200 mm and the length is 1.2 m. The notch length should be half of the depth of the beam. If the total energy consumed (including the work done by the weight of the beam) is G, the fracture energy is: where Alig= area of the ligament.It has been shown that the specimen sizes recommended by RILEM do not always provide size-independent values for Gy. The work-of-fracture of beams with depths ranging from 150 mm to 300 mm was determined. It was shown that Gy increased with an increase in beam depth, and decreased with an increase in notch depth.Though the method yields size dependent values, it has widely been used due to its simplicity. Availability of extensive data has led to empirical 'code-type' relations linking fracture energy to conventional design properties. One such equations is provided by the CEB-FIP where xF is a tabulated coefficient that depends on the aggregate size (e.g.,for a maximum aggregate size = 16 mm, xF = 6), fcm means compressive strength of the concrete in MPa, and Gy is obtained in N/m.It should be emphasized that Gy,by itself is not a reliable measure of toughness or ductility, and that using Gy as the sole fracture parameter could lead to erroneous conclusions. If one were to conclude from the observed increase in Gy the increase in with compressive strength that ductility increases with the increas in compressive strength, this would be wrong. With the use of additional parameters (i.e.characteristic length), the higher brittleness in high strength concrete can be adequately characterized. The failure of plain concrete is generally brittle, but not as brittle as that of glass. This ductility, that concrete possesses can be quantified through fracture mechanics. In this work ductility is taken to be the inverse of brittleness.In almost all of the nonlinear fracture models, the brittleness of the material can be related to parameters that depend on the dimensions or the deformations of the fracture process zone. Hillerborg defined a characteristic length lch that is proportional to the process zone length:Where E:Elasticity Modulus and f: tensile strength of the concrete. A smaller lch implies that the material is more brittle. It was verified that the characteristic length increase as the aggregate size increases. Characteristic length strongly decrease as concrete strength increases. A specific method has been proposed by the RILEM Technical Committee TC-50 to quantify the fracture energy, and recommended values have been included in the last CEB Model At the same time the use of high-strength concretes is continuously increasing, but despite the amount of research that has been performed there are still many areas which need to be studied. Fracture toughness is one of them because questions about the "brittleness" of high-strength concretes usually appear. This paper presents results for the fracture energy of concrete obtained from a wide range of high-strength concretes. The behaviours of notched and unnotched specimens with different water-cement ratios were examined and compared. Relationships between fracture parameters ( fracture energy and brittleness ) and basic strength properties are also presented. The influence of maximum aggregate size and type of loading on fracture mechanics parameters are studied. The effect of microsilica and aggregate size on the strain localization, softening response and brittleness of high strength concretes were investigated by measuring the fracture energy. The energy of fracture increases as concrete strength increases. As the strength increases, concretes have a greater peak load deflection followed by a steeper gradient of the softening branch. The final displacements are similar for concretes with different strength. The final displacement is much lower for mortar than for concrete, and it depends on the type (and size) of aggregate. Based on the fracture tests and microscopic studies at the aggregate matrix interface, it is concluded that in concretes which contain microsilica, the cracks usually travel through the aggregates; the interfacial zone for these concretes becomes stronger and more heterogeneuos, and the fracture occurs in a more brittle manner. However, in concretes without microsilica, the cracks usually develop around the coarse aggregate resulting in an inter-coarse aggregate type of fracture. Brittleness of normal and high strength concretes are the compressive strength, splitting tensile strength, net flexural tensile strength; dynamic modulus and fracture energy of concrete increases while characteristic length of the concrete decreases when water/binder ratio decreases. This study, relations for an estimate of fracture parameters as given in CEB Model Code as well as their justification are summarized. This new model code for the design of concrete structures includes extensive information on constitutive relations for concrete and reinforcing steel. In this model code relations are also proposed to predict fracture properties of concrete on the basis of fracture mechanics concepts. In particular fracture energy is given as a function of concrete grade, maximum aggregate size and temperature.Another work reported in this thesis was to try to compare the relative values of the long tail in the latter part of the strain softening part of the curves.

The mechanical behaviour of concrete that is designed to have high strength is different in many aspects from that of normal concrete. These differences have yielded some characteristics that are not beneficial, such as britdeness. Fracture models can be used to understand the microstructural mechanics that control brittleness and crack resistance (toughness),and to provide reliable means of quantifying them. New high- performance concretes can then be engineered to possess higher toughness and lower brittleness. Increased resistance to cracking may also lead to better durability, long-term reliability and seismic resistance. The application of fracture mechanics to structural analysis and design is motivated by the fact that the failure of concrete structures is primarily due to cracking, and several types of failures could occur catastrophically, especially in high-strength concrete structures.Certain aspects of such failures cannot be predicted satisfactorily by empirical relations obtained from tests, but can be explained rationally through fracture mechanics. In general, structural analysis based on fracture principles can lead to better estimates of crack widths and deformations under service loads, the safety factors under ultimate loads, and post-failure response during collapse.The use of fracture mechanics principles in the design of materials with higher toughness and ductility has produced encouraging results in the ceramics industry, and a similar approach is needed for high-performance concretes. Other aspects of concrete behaviour including the bond between steel and concrete, which is more brittle in silica iiime concrete than normal concrete, will also benefit from an increase in crack resistance and a decrease in brittleness. The durability, long-term reliability and thermal performance, which are greatly affected by cracking, would also be enhanced. Compressive strength is usually employed as the main parameter for the design of concrete structures. Nevertheless, as in other brittle materials, its fracture is governed by tensile mechanism. Not only is the strength important but so also is the whole behaviour of concrete under tensile stresses, especially its toughness. In many cases it would not be possible to build concrete structures that were safe enough if the material had no capacity to absorb energy. Although fracture mechanics has been extensively developed for brittle materials, the applicability of conventional concepts to concrete is not easy, due to the characteristics of the material. Concrete is heterogeneous (a composite, multiphase material); cracking itself is a heterogeneous process (initiation of cracks, slow stable crack growth, crack arrest and unstable crack propagation);the surface area formed in many times larger than the effective fracture area ( multiple crack formation occurs) and as a result, the energy dissipating mechanism in concrete is not merely confined to surface energy. The resistance of the material to fracture, G, can defined as the energy needed to create a crack of unit area. When a notched specimen, such as the beam in Fig.l, is tested until failure, the total work done gives the total energy dissipated. Assuming that all the energy has been consumed in extending the crack, determination of the work done and the crack area would yield G. This value is usually called fracture energy. The area under a load-displacement curve provided the total energy. Taking the unnotched part of the cross-section (i.e.,the ligament area) as the area of the crack, the fracture energies for different types of concretes can be determined. For Linear Elastic Fracture Mechanics (LEFM) type behaviour, the fracture energy is a constant equal to the critical strain energy release rate,i.e. Gf=GC. In practice however, Gy is not always constant. Researchers found that the fracture energy increased with specimen size and decreased with a significant decrease in stiffness of testing machine.Researchers showed that the determination of Gf was not straightforward. Since cracking in concrete is tortuous,they argued that the exact crack area should be determined instead of simply using the ligament area. They obtained the crack area from microscopic techniques, and thereby computed the fracture energies that were almost the same for hardened ce-ment past, mortar and concrete. Since the measurement of 'true' crack area is difficult, and to a certain extent subjective, later researchers have usually circumvented the problem by taking the ligament (or projected) area as the nominal area of the crack. Then, the fracture energy is also a nominal value. As the sizes of ligament and specimen increase, G would approch asimtotically towards a constant value. Therefore, G tend to be a material property when the fracture zone is negligible compared to the specimen size. Accordingly, the test method was recommended by RILEM with a lower limit on the specimen size. For concrete with a maximum aggregate size of 16-32 mm, the required beam depth is 200 mm and the length is 1.2 m. The notch length should be half of the depth of the beam. If the total energy consumed (including the work done by the weight of the beam) is G, the fracture energy is: where Alig= area of the ligament.It has been shown that the specimen sizes recommended by RILEM do not always provide size-independent values for Gy. The work-of-fracture of beams with depths ranging from 150 mm to 300 mm was determined. It was shown that Gy increased with an increase in beam depth, and decreased with an increase in notch depth.Though the method yields size dependent values, it has widely been used due to its simplicity. Availability of extensive data has led to empirical 'code-type' relations linking fracture energy to conventional design properties. One such equations is provided by the CEB-FIP where xF is a tabulated coefficient that depends on the aggregate size (e.g.,for a maximum aggregate size = 16 mm, xF = 6), fcm means compressive strength of the concrete in MPa, and Gy is obtained in N/m.It should be emphasized that Gy,by itself is not a reliable measure of toughness or ductility, and that using Gy as the sole fracture parameter could lead to erroneous conclusions. If one were to conclude from the observed increase in Gy the increase in with compressive strength that ductility increases with the increas in compressive strength, this would be wrong. With the use of additional parameters (i.e.characteristic length), the higher brittleness in high strength concrete can be adequately characterized. The failure of plain concrete is generally brittle, but not as brittle as that of glass. This ductility, that concrete possesses can be quantified through fracture mechanics. In this work ductility is taken to be the inverse of brittleness.In almost all of the nonlinear fracture models, the brittleness of the material can be related to parameters that depend on the dimensions or the deformations of the fracture process zone. Hillerborg defined a characteristic length lch that is proportional to the process zone length:Where E:Elasticity Modulus and f: tensile strength of the concrete. A smaller lch implies that the material is more brittle. It was verified that the characteristic length increase as the aggregate size increases. Characteristic length strongly decrease as concrete strength increases. A specific method has been proposed by the RILEM Technical Committee TC-50 to quantify the fracture energy, and recommended values have been included in the last CEB Model At the same time the use of high-strength concretes is continuously increasing, but despite the amount of research that has been performed there are still many areas which need to be studied. Fracture toughness is one of them because questions about the "brittleness" of high-strength concretes usually appear. This paper presents results for the fracture energy of concrete obtained from a wide range of high-strength concretes. The behaviours of notched and unnotched specimens with different water-cement ratios were examined and compared. Relationships between fracture parameters ( fracture energy and brittleness ) and basic strength properties are also presented. The influence of maximum aggregate size and type of loading on fracture mechanics parameters are studied. The effect of microsilica and aggregate size on the strain localization, softening response and brittleness of high strength concretes were investigated by measuring the fracture energy. The energy of fracture increases as concrete strength increases. As the strength increases, concretes have a greater peak load deflection followed by a steeper gradient of the softening branch. The final displacements are similar for concretes with different strength. The final displacement is much lower for mortar than for concrete, and it depends on the type (and size) of aggregate. Based on the fracture tests and microscopic studies at the aggregate matrix interface, it is concluded that in concretes which contain microsilica, the cracks usually travel through the aggregates; the interfacial zone for these concretes becomes stronger and more heterogeneuos, and the fracture occurs in a more brittle manner. However, in concretes without microsilica, the cracks usually develop around the coarse aggregate resulting in an inter-coarse aggregate type of fracture. Brittleness of normal and high strength concretes are the compressive strength, splitting tensile strength, net flexural tensile strength; dynamic modulus and fracture energy of concrete increases while characteristic length of the concrete decreases when water/binder ratio decreases. This study, relations for an estimate of fracture parameters as given in CEB Model Code as well as their justification are summarized. This new model code for the design of concrete structures includes extensive information on constitutive relations for concrete and reinforcing steel. In this model code relations are also proposed to predict fracture properties of concrete on the basis of fracture mechanics concepts. In particular fracture energy is given as a function of concrete grade, maximum aggregate size and temperature.Another work reported in this thesis was to try to compare the relative values of the long tail in the latter part of the strain softening part of the curves.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1995

##### Anahtar kelimeler

Kırılma değeri,
Yüksek dayanımlı beton,
Fracture degree,
High strength concrete