Beton disk numunede mod I halinde göçme: Boyut etkisi kuralı /
Yazar: HAKAN NURİ ATAHAN
Danışman: PROF. DR. MEHMET TAŞDEMİR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1996
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Beton dayanımı = Concrete strength

Özet:
Bu çalışmada, Bazant tarafından çentikli kiriş için önerilen "Boyut Etkisi Kuralı" nın Mod I (Açılma modu) durumunda çentikli ve çentiksiz beton disk yarma numunesine uygulanması yapıldı. Bu yükleme durumunda Mod I gerilme şiddet çarpardan hesaplandı. Üretilen numunelerde boyut etkisi kuralının uygulanması için aynı karışım kullanıldı ve dört değişik boyutta ve bir seri çentiksiz olmak üzere, üç seri den oluşan değişik "çentik boyu/çap" (2a/2R) oranına sahip beton disk numuneler üretildi. Yüksek mukavemetli betonlar gibi çekme halinde yan gevrek davranış gösteren bir malzemede Mod I durumunda gerilme şiddet çarpanının hesaplanabilmesi için Brezilya yöntemi olarak da bilinen bir deney tekniği seçildi. Numunelerin merkezlerindeki çentikler üretim sırasında oluşturuldu. Bunun için disk merkezine yerleştirilen çelik levhalar kalıplara beton dökümünden sonra piriz sona ermeden çekildi ve böylece çekilen levhaların yerleri çentik olarak kaldı. Ayrıca üretilen betonun basınç mukavemeti ve elastisite modülünün saptanabilmesi için silindir numuneler üretildi ve bu numuneler üzerinde basınç mukavemeti ve elastisite modülü deneyleri de yapıldı. Mod I durumunda hesaplanan gerilme şiddet çarpanı değerleri arasmda boyut bakımından sadece %17 dolaylarında bir fark olduğu gözlendi. Elde edilen değerler, literatürde aynı mukavemet değerine sahip betonlar için kiriş numunelerde saptanan gerilme şiddet çarpanı değerlerine yalan olduğu görüldü. Bu da disk üzerinde Lineer Elastik Kırılma Mekaniği (LEKM) esasına göre bulunan gerilme şiddet çarpanı değerlerinin saptanmasında belirli bir düzeltme yapılarak, yani daha hassas şekil değiştirme ölçümlerim ve betonda agrega kenetlenmesini gözönünde bulunduran modelleri kullanarak disk numunede gerilme şiddet çarpanının elde edilmesine imkan verecektir. Disk numunenin şimdiye dek önerilen ve üzerinde çalışılmakta olan kiriş numuneye bir alternatif olabileceği düşünülmektedir. Özellikle disk numune geometrisi karot numuneler için daha uygun olacağı ve böylece kiriş numunelerdeki gibi sadece üretilen betonlarda gerilme şiddet çarpanının bulunması sakıncasının ortadan kalkacağı düşünülmektedir. Disk numunelerde, yarma-çekme mukavemeti değerlerinin disk çapının büyümesiyle birlikte belirgin biçimde azaldığı ve bu azalmanın %50 mertebelerinde olduğu görüldü. Yarı gevrek bir malzeme olan betonun aksine, sinterlenmiş karbid, pleksiglas ve grafit gibi gevrek malzemelere LEKM nin uygulanmasının mükemmel olduğu kanıtlandı. Boyut etkisi kuralının, LEKMne göre betonun kırılma davranışını daha iyi ifade ettiği görüldü. Böylece bu çalışma boyut etkisi kuralının Mod I halinde disk numuneler için de geçerli olacağını kanıtlamış oldu. Yapılan bu disk yarma deneyleri sonucunda, çatlağın önce çentik uçlarında oluştuğu, önceden oluşturulan çatlak düzleminde yayıldığı ve yük uygulanan noktalar yakınında çatlakların çatallaşdığı ve kama oluşurak göçtüğü gözlendi. ix

Abstract:
Structural engineering changes its scope related to the new needs and new technologies. Because of progress in fracture mechanics, engineers and designers have gained the new concepts about crack propagation and residual strength of structures containing crack. Since concrete is widely used material in structural engineering, it is necessary to know sufficent information about crack initiation and propagation in the material. The information is especially needed for analytical finite element studies of concrete behaviour. Modern computer-aided analysis and use of concrete for special structures such as reactor containtment vessels, dams, high rise concrete buildings and missile storage silos has led to a growing interest in the cracking behaviour of concrete. The widespread application of the concepts and methods of fracture mechanics to practical testing of the mechanical properties of materials and to the calculation of the strength and deformation of structures has stimulated considerable interest in investigations of the stressed state of finite bodies with cracks. The pertinent problems of the theory of elasticity are, as a rule, very complex, so that one has to be satisfied with computing approximate stress intensity factors at the crack tip. Among the many problems concerning finite bodies, one of particular interest is the case of a disk of radius R with an internal diametric crack of length 2a, has many advantages as an experimental sample, wich has been solved analyticaly in Russian literature in the form of a series in the power of a/R. Recently, a number of investigations have been carried out on the failure of concrete for Mode I loading. The acceptability of fracture mechanics to the design of concrete structures presupposed the availability of methods of testing to obtain appropriate material properties. To date, a number of such methods have been proposed to RILEM eg. Hillerborg (and RILEM Commitee TC 50), Gf ; Bazant Gf and cf ; and Jenq/Shah, KS1C, CTODc, where Gf is fracture energy of concrete subjected to three point bending type of loading using beam specimens. KS1C is the critical value of stress intensiy factor and CTODc is the critical value of crack tip opening displacement. These methods determine the indicated Mode I fracture properties as well as brittieness number, characteristic dimension and effective crack length. These methods and comparisons between equivalent results, as well as other methods, are given in recent publications..Studies to determine the influence of test set-up and geometry of specimens on various materials parameters are being conducted by various technical commities. However, there is no acceptable testing technique to determine fracture parameters. Recent studies are show that due to determine fracture process zone and precritical crack growth, a single fracture parameters of concrete, such as the critical stressintensity factor can not be applied to quasi-brittle materials. In order to determine the size independent fracture parametrs, nonlinear type of fracture mechanics models will be used in the near future by using well developed experimental techniques based on observations of fracture process. Generally, the critical value of the parameter during fracture can be determined with laboratory specimens. Hence, the value obtained as a material property can be used in a wide range of engineering structures of different geometric shapes and sizes. Accurancy in the determination of fracture parameters is needed for readable predictions of crack growth and crack propagations in structures. Under Mode I loading crack instability begins when the crack tip stress intensity factor Ki reachs a critical value K^. This critical value is described in the literature as the plain strain toughness of the material and it is independent of the geometry and loading conditions of the body containing crack. This critical value can be considered as a material property. Due to difficulty in applying direct tension to concrete, the split-cylinder test has gained wide popularity. In this test, also called Brazilian, a cylinder is loaded between two planets. The split-cylinder test method to. determine tensile strength of the concrete material is attributed to Carneiro and was adopted by the national standart method of Brazil, thus the method was named as "Brazilian Test". According the theory of elasticity, this loading produces a nearly uniform maximum principle tensile stress along approximately seventy five percent of the diameter which causes the cylinder to fail by splitting. The tensile strength at failure is calculated using the theory of elasticity and ignoring the effect of multiaxial state of stress near loading planets. Although the stress state is not uniaxial due to significant compressive stress in the transverse direction and there is redistribution of stress due to nonlinearity of materials, the tensile stress value in the cylinder at failure has proven to be a useful measure of the tensile strength. Experimental test results obtained in recent years have showed that the flexural strength of concrete usually decreases with increasing size of specimens and then remains constant. Fracture growth generally relieves stress from the zones on the sides of the fracture, which causes release of stored energy of structure into the fracture front. The size effect on concrete strength may be primarily explained by the fracture process zone. When a concrete structure is loaded, the strain energy produced by applied load is converted to the energy absorbed in the fracture process zone. For large sized structures, the letter is negligible compared to the former, whereas for small sized structures, the letter can be comparable compared to the former. However, the concrete strength approaches a constant when sizes of concrete structures become very large. The size effect on nominal strength of structures is the most important practical consequence of the global energy release associated with large fractures. Therefore it is natural to exploit the size effect for measuring material fracture parerneters. The measured values of the parameters characterizing material properties must be independent of the specimen or structure size, or else they would not represent properties of the material alone but also properties of the structure. The size effect method, based on the size effect law, is the simplest to apply because only the maximum loads of specimens are needed. No measurements of post-peak displacement and unloading stiffness, nor observations of crack tip location are needed, the testing machine need not be very stiff, and there is no need for closed- XIloop displacement control. During the experimental studies all specimens must be cast from the same batch of concrete, the quality of concrete must be as uniform as possible. The curing procedure and the environments to which the specimens are exposed, including their histories, must be the same for all specimens. The main objective of this work was to apply the "Size Effect Method" to the notched disk concrete specimens with different sizes in mode I loading conditions. After a brief introduction to the notched cylinder and the experimental procedure employed, the observed modes of failure of the cylinder are discussed. This is followed by a quantitative description of fracture and notch effect, and a critical examination of alternate ways of computing Kj stress intensity factor. In this work all speciments are cast from the same batch of concrete. The aggregate grading of concrete, water/cement ratio (0,38) and the maximum particle size of aggregate (12,7mm) were kept constant. The compressive strength and modulus of elasticity of concrete were determined according to standart procedures using 100mm diameter and 200mm long cylinders. Notched disk specimens with four different sizes were cast in steel molds to simplify notched. The used disk specimens are 600mm, 300mm, 150mm and 100mm in diameters and 300mm, 150mm, 60mm and 50mm in thickness, respectively. The notches stated at the centre of the specimens are produced during casting. A strip of thin steel metal was left in the diameter of the fresh concrete to form the notch. The steel sheet was removed before setting for easy removal. The ratio of 2a/2R was chosen as 0,0, 0,1, 0,3 and 0,5 where 2a is the length of the notch and 2R is the diameter of the disk specimen. Test results obtained are evaluated in terms of following properties: fresh concrete properties, elastic and fracture properties. The static moduli of elasticity were calculated from the ascending part of stress-strain curves in compression for stress approximately 30 percent of the ultimate strength using standart cylinder specimens. The main objective of this work was to apply the "Size Effect Method" to the notched disk concrete specimens with different sizes in mode I loading conditions. All the specimens were tested and the results obtained were applied to the model which is proposed by Bazant. At the same time, the stress intencity factors for different sizes of disk specimens were determined. From theoritical and experimental analysis of models of the notched cylinder, and from experiments on concrete disks of various axial and initial notch lengths, several conclusions may be drawn. This thesis consists of six parts: In the first part, an introduction is given containing the objective of the investigation and revelant general information. In this part the aim and scope of the present work are also given. The secont part is devoted to a survey of the present knowledge on the disk specimen geometry. The third part gives the experimental studies. The material used, the princples assumed, the mix composition, the methods of mixing and curing, the types of loading and the methods employed in testing and measurements made are described. xuThe fourth part is devoted the experimental results. In the fifth part the experimental results are discused and evaluated in the light of experimental findings. In the sixth part the conclucions are summirized and suggestions for further studies are given. The results obtained in the experimental work can be outlined as follows: 1) Size effect in the split-disk tensile test is studied experimentally and analyzed theoritically. The size effect law proposed by Bazant in two dimensions is defined in terms of nominal stress at failure; «.=e.^ (1) in which Pu= maximum load (ultimate load), b=specimen or structure thickness, d=characteristic dimension (size) and cn=coefficent introtuced for convenience. The size effect of fracture mechanics type can be approximately described by the size effect law proposed by Bazant; aN=B.ftV(l + p)a5, p = d/d0 (2) in which f \= a measure of material tensile strength, B and d0 = emprical constants, and P=brittleness number. This simple law, which appears, acceptable for the presented experimental results, represents a smooth transition between the case of plasticity at small sizes (P- >0), at which there is no size effect, and the case of linear elastic fracture mechanics at large sizes (J3- »<») at which the size effect is the strongest possible. The test results obtained confirm the existence of size effect in the notched disk specimens. In all (2a/2R) ratios, observations agree with size-effect law proposed by Bazant. 2) As the diameter of disk specimen increases, the splitting-tensile strength decreases significantly for both notched and unnotched specimens. 3) Experimental test results show that a single fracture parameter is not enough to describe fracture of concrete. It is obvious that more than one parameter or at least two parameter is required. 4) A central crack initiates at the tip of a notch propagates towards the loading points, and is followed by wedge formation. It has been observed that the wedge formation in the disk test configuration constitues a secondary failure mode and occurs after a single crack has propagated through the diameter of the specimen. 5) It can be concluded that fracture process zone becomes more important in specimens with shorter initial notches. xniFor the feature research, both theoritical and experimental, should establish criteria for crack initiation and propagation at every instance in an experiment. At this point, useful directions seem to be related to the use of crack tip opening displacement and rotation between two cracked parts, measured using CMOD (Crack Mouth Opening Displacement) and CTOD (Crack Tip Opening Displacement), for determining the crack length and the onset of crack propagation. The fracture toughness may then be calculated from this length and the corresponding load, and evaluated with respect to order specimen and material parameters. Because of observed ductility and different crack propagation rates, the dynamic aspects of crack propagation, continuous stress redistribution ahead of a crack tip and the size effect of specimen on the fracture parameters of concrete should also be investigated. The notched cylinder is a good fracture mechanics specimen with many advantages, and future investigations of cracking in concrete may be carried out on this specimen with a strong potential for standardization. The limitatious of the present work also suggest new directions for further studies on combined mode fracture of quasi-brittle materials like concrete. In testing such a disk shaped specimen with inclined crack subjected to diametral compression test, there are the following advantages: i) By changing the inclination of the notch with respect to the loading direction, it will be possible to change the fracture mode from Mode I (tensile) to Mode II (shear) and to obtain combined loading condition with a wide range of Kj/Kjc versus Kq/Kjc where Kjj is the Mode II intensity factor, and Kj is the Mode I intensity factor. The value of Kjc (critical value of stress intensity factor in Mode I) is a material parameter and may depend on the rate of loading. These efforts will help in better understanding of crack growth in concrete under combined Mode I and Mode II loadings. ii) It is not diffûcult to obtain higher Kjj/Kj ratios using this type of loading configuration. One can also obtain both positive and negative values of Kjj/Kj ratio. The same specimen can be used to obtain test results in pure Mode I and combined Mode cases. iii) To obtain loading rate effects on both Mode I and mixed mode fracture of concrete, crack propagation studies should also be used at slow and high rates. xiv