Çentikli beton kirişlerde mod I durumunda kırılma parametrelerinin belirlenmesi
Determination of fracture parameters at the notched concrete beams
Yazar: MEHMET KIZILASLAN
Danışman: PROF. DR. SAİM AKYÜZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Yapı Mühendisliği Ana Bilim Dalı / Yapı Malzemeleri Bilim Dalı
Derece: Yüksek Lisans, 1997
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Beton kirişler = Concrete beams ; Kırılma = Fracture ; İnşaat mühendisliği = Civil engineering

Özet:
Betonun kırılma enerjisi, beton yapıların gevrek kırılmasının mantıklı tahmini için gerekli bir basit malzeme karakteristiğidir. Bazant'ın önerdiği "Boyut etkisi Kuralı"nda kırılma enerjisi, sonsuz büyüklükteki bir numunede çatlak gelişmesi için gerekli birim enerji olarak tanımlanmıştır. Bu çalışmada, betonun kırılma enerjilerinin hesabı Bazant tarafından önerilen "Boyut Etkisi Kuralı"nın kiriş numuneler üzerinde uygulaması yapıldı. Çatlak yayılmasında etkin olan gerilme şiddet çarpanları Mod I durumu için hesaplandı. Deneylerde gevrek kırılmanın daha kolay izlenebilmesi için yüksek mukavemetli çimento kullanıldı ve çimento dozajı yüksek tutuldu. Boyut etkisi metodunda maksimum agrega boyutu önemli olduğundan.kullanılan agrega 8 mmlik elekten elendi ve elek altı malzeme kullanıldı. Betona, kalıba yerleşmesini kolaylaştırmak için süper akışkanlaştırıcı katkı karıştırıldı. Boyut etkisinin uygulanabilmesi için bütün numunelerde aynı karışım kullanıldı ve bu numuneler aynı kür koşullarında saklanıldı. Üç değişik boyutta ve bir seri çentiksiz, üç seri değişik 'çentik boyu/ numune yüksekliği' (a/d) oranına sahip, toplam dört seri beton kiriş numuneler üretildi. Numunelerin kenarlarındaki çentikler aynı kür süresinin sonunda testere ile kesmek suretiyle mesnet ortasına gelecek şekilde oluşturuldu. Deneyler sırasında aynı pres kullanıldı. Hesaplarda bu preste okunan yük değerlerine numune ağırlıkları eklendi. Beton basınç mukavemeti ve elastisite modülü hesaplanması için silindir numuneler üretildi. Bu numuneler üzerinde elastisite modülü ve beton basınç deneyleri yapıldı. Boyut etkisi metodu, kırılma enerjilerinin hesabı ve kırılma bölgesi hakkında bilgiler vermesi bakımından en kolay uygulanan yöntemdir. Çünkü sadece maksimum yük değerlerinin ölçülmesi yeterlidir, tepe noktasının sapması ve boşaltma rijitliğinin hesaplanmasına veya çatlak ucu durumunun incelenmesine gerek yoktur. Aynı zamanda kullanılan aletlerinde aşın rijit veya kapalı-halka yerdeğiştirme kontroluna sahip olması gerekmez. Mod I durumunda hesaplanan gerilme şiddet çarpanları değerleri arasında boyut bakımından sadece %13 dolayında bir fark olduğu gözlendi. Boyut etkisi deneyleri sonucunda değişik (a/d) oranlan için kırılma enerjileri, kırılma süreci bölgesinin etkin uzunluk değerleri ve sonsuz geniş numuneler için kritik efektif çatlak ucu açılması değerleri hesaplandı. Yapıların veya numunenin davranışının, Lineer Elastik Kırılma -Mekaniği'ne mi? yoksa plastik limit analizine mi? yaklaştığını gösteren Bazant tarafından önerilen kırılganlık sayısı (P) 'nın uygulanabilirliği araştırıldı. H

Abstract:
Failure of concrete structures is usually accompanied by cracking of concrete. Understanding and modeling of how and when concrete fails are not only critical for designing concrete structures, but also important for developing new cement-based materials. Many investigations have shown that fracture mechanics has been established as a fundamental approach that can explain certain nonlinear aspect of concrete behavior, help to prevent brittle failures of structure, and be important aid in materials engineering. Even tough concrete is a quasi brittle material, its fracture toughness is currently not used as a design tool. Since concrete structures are usually reinforced, the designer often neglects the tensile strength of plain concrete. But a structural engineer needs to built reliable structures and increase efficiency and accuracy of design. In quasibrittle materials such as concrete, rock, ice and ceramics, a sizeable fracture process zone exists in front of the crack tip. Due to the extensive distributed micro cracking and void formation the fracture process zone consumes a large amount of energy when the crack toughening mechanism, failure of specimen or structure of quasibrittle materials cannot be predicted on the basis of a single parameter such as critical energy release rate or critical stress intensity factor defined in linear elastic fracture mechanics. There are three method for measuring fracture energy of concrete in nonlinear fracture mechanics, all of them recently approved as standard recommendations by RILEM : (1) the work of fracture method proposed by Hillerborg (1985); (2) the two-parameter method proposed by Jenq and Shah (1985) and (3) the size effect method proposed by Bazant (1987). Every test method is based on some material fracture model. -A practical fracture model of a quasibrittle material represents a simplified description of a very complex process of progressive material damage and its localization in the fracture process zone. For this reason, the parameters of any available fracture model to serve as a basis of standardized test can be truly unambiguously defined only by extrapolation to infinite size. According to size effect method, it is proposed to define the fracture energy as the specific energy for crack growth in an infinitely large specimen. We will see, if geometrically similar specimens are considered and the failure load is correctly extrapolated to a specimen of infinite size, the fracture energy obtained must be munique and independent of specimen type, size, and the shape because the fracture process zone in the limit becomes vahishingly small compared to the specimen or structure dimensions. The size effect method, based on the size effect law, is the simplest to apply because it necessitates only the maximum loads of notched fracture specimens to be measured, which can be accomplished even with the most rudimentary test equipment. The postpeak descending load deflection curve, unloading response, measurements of the crack-tip opening displacement, and observation of the crack-tip location are not needed. In this method, during the experimental studies all the specimens must be cast from the same batch of concrete, the quality of concrete and must be as uniform as possible. The curing procedure and environments to which the specimens are exposed, including their histories, must be the same for all specimens. At least three identical specimens should be tested for each specimen size. The second advantage of size effect method is that the measurements are based on the same effect as that needed most for structural design. The model is calibrated by that effect which it is intended to predict. The size-effect method works only if the specimens tested have a sufficient range of brittle number. The fracture energy determination would be exact if we know the exact form of the size-effect law to be used for extrapolation to infinite size. The simplest form of the size effect law results from dimensional analysis and similitude arguments, if it is assumed that earlier the width or length of the fracture process zone is a constant material property. This form is orN = B.ft 1+ 2r (1) in which r = 1 according to initial proposal, on= nominal strength that failure = P^d. where P = maximum load, b=specimen thickness, d = characteristic dimension of the specimen or structure (only geometrically similar specimen are considered), ft' strength parameter, which may be taken as the direct tensile strength, da maximum aggregate size and BJK, = two empirical constants to be determined by fitting test results for geometrically similar specimens of various sizes. Bazant's brittleness number is ( a \ HrV (2) This simple law, which appears acceptable for the presented experimental results, represents a small smooth transition between the case of plasticity at small sizes (P~»0), at which there is no size effect, and the care of linear elastic fracture mechanics at large sizes (£-*») at which the size effect is strongest possible. XlllLi the original form proposed in 1987, size effect method has been amply verified and it is now supported by broad experimental evidence. Recently in an effort to make testing more convenient, three versions of size effect method have been formulated, and so four versions exist at present. Geometrically similar specimens are those in which all the dimensions including the length of the initial traction-free crack or notch are in proportion. Size effect law provides an equation to correlate the nominal strength (ov ) of the specimen the specimen dimension(d). For any geometry there are two constants, (B.ft) and do governing the equation. When the specimen of a geometry increases to a infinitely large size, its fracture behavior must follow linear elastic fracture mechanics (LEFM) because the process zone length becomes negligible in comparison with the crack length and specimen size. Initial crack or notch length also approaches infinity when the size of the structure approaches infinity under the condition that the geometry of the specimen remains the same. Bazant and Pfeiffer showed in 1987 that fracture energy in an infinitely large structure should be independent of structure geometry. With this development the two constants governing the size effect law equation for specimens of any specific geometry are related to each other through a material constant fracture energy (Gf). The generalization of size effect law was completed in 1990 by Bazant and Kazemi. They proposed that not only a constant representing the fracture energy, Gf, but also a constant called the effective process zone length, Cf, can be defined for an infinite specimen as a material parameters and can be evaluated from size effect law. By adapting LEFM formulas for an infinite-size specimen, B.ft' and do can be determined for any specimen geometry from Gf and Cf. Therefore the nominal strength of a structure can be uniquely predicted when Gf, c& the structural geometry and size are known. Conversly, from the maximum loads measured on a series of geometrically similar specimen, B.ft and do, and therefore Gf and Cf, can be obtained. Based on this conditions it was shown that the fracture energy of concrete may be calculated as G=gK) (3) A.EC and effective process length may be calculated as g(«o) (£) cf = g'(a0)UJ (4) in which, Ec = Young's elastic modulus of concrete; A = slope and C=intercept of the size effect regression plot for failure of geometrically similar specimen of very different sizes, g(cto) = nondimensional energy release rate calculated according to linear elastic fracture mechanics, cto = relative notch length = notch length/ characteristic specimen size. In this work, original version and zero-size strength version of size effect method are applied for geometrically similar specimens, and for mode I loading condition stress intensity factor is calculated. XIVThis thesis consists of six parts: First part is an introduction to fracture mechanics, and objective of the investigation is given. The aim and scope of present work are also given in this part. In the second part, Size Effect Law is introduced, fracture parameters are described and some suggestions for the specimens are given. The third part gives the experimental studies. The material used, the principles assumed, mix composition of concrete, the methods of mixing and curing, the types of loading and test methods, and measurements are described. In the fourth part, the experimental results and calculations are given. In the fifth part, the experimental results are discussed and evaluated. The sixth part gives the conclusions. In this work all specimens were cast from the same batch of concrete. The aggregate grading of concrete, water/cement ratio (0,43) and the maximum particle size of aggregate (8 mm) were kept constant. The compressive strength and modulus of elasticity of concrete were determined according to standard procedures using cylinders, 150 mm in diameter, and 300 mm in height. Notched specimens with three different sizes are produced. The cross-section of the beams tested are 70mm x70mm, 100mm xlOOmm and 150mm x 150mm. For each beaam the effective cross- section, however, was obtained at the mid-span by means of a saw cut. The length of the specimens are 280 mm, 515 mm and 600 mm, respectively. The ratio of "notch length /specimen height" (a/d) was chosen as 0,00, 0,15, 0,25 and 0,35. Test results are evaluated in terms of following properties: fresh concrete properties, elastic and fracture properties. The static modili of elasticity were calculated from the ascending part of stress-strain curves in compression for stress approximately 30 percent of ultimate strength using standard cylinder specimens. The main objective of this work was to apply "Size Effect Method" to notched beam specimens with different sizes in mode I loading conditions. All specimens were tested and the results obtained were applied to the model which is proposed by Bazant. At the same time, stress intensity- Jactors for different sizes of specimen were determined. The results obtained in the experimental work can be outlined as follows: 1. As the dimension of specimen increases, the nominal strength decreases both for notched and unnotched specimens. This decrease in unnotched specimens is higher than the others. 2. The test results obtained confirm the existence of size effect and observations agree with size-effect law. XV3. Experimental test results show that a single fracture parameter is not enough to describe fracture of concrete. It is obvious that that more than one parameter or at least two parameters are required. 4. Applicability of Bazant's brittleness number, which indicates how close the behavior of specimen or structure of any geometry is to linear elastic mechanics and to plastic limit analysis, is validated by test results. 5. It can be concluded that fracture process zone becomes more important in specimen with shorter initial notches. XVI