Concrete, which was hitherto considered as a brittle material, has shown much better softening behavior after the post peak load than anticipated. This behavior of concrete did put the researchers in a quandary, whether to categorize concrete under brittle materials or not. Consequently concrete has been called a quasi-brittle material. Fracture mechanics concepts like Linear elastic fracture mechanics (LEFM) and Plastic limit analysis applicable to both brittle and ductile materials have been applied to concrete to characterize the fracture behavior. Because of quasi-brittle nature of concrete, which lies between ductile and brittle response and due to the presence of process zone ahead of crack/notch tip instead of a plastic zone, it is found that non-linear fracture mechanics (NLFM) principles are more suitable than linear elastic fracture mechanics (LEFM) principles to characterize fracture behavior. Fracture energy, fracture process zone (FPZ) size and the behavior of concrete during fracture process are the fracture characteristics, which are at the forefront of research on concrete fracture. Another important output from the research on concrete fracture has been the size effect. Numerous investigations, through mathematical modeling and experiments, have been carried out and reported in literature on the effect of size on the strength of concrete and fracture energy. Identification of the sources of size effect is of prime importance to arrive at a clear analytical model, which gives a comprehensive insight into the size effect. With the support of an unambiguous theory, it is possible to incorporate the size effects into codes of practices of concrete design. However, the theories put forth to describe the size effect do not seem to follow acceptable regression. After introduction in Chapter-1 and literature survey in Chapter-2, Chapter-3 details the study on size effect through three point bend (TPB) tests on 3D geometrically similar specimens. Fracture behavior of beams with smaller process zone size in relation to ligament dimension approaches LEFM. The fracture energy obtained from such beams is said to be size independent. In the current work Size effect law (Bazant et al. 1987) is used on beams geometrically similar in three dimensions with the depth of the largest beam being equal to 750mm, and size independent fracture energy G Bf is obtained. In literature very few results are available on the results obtained from testing geometrically similar beams in three dimensions and with such large depth. In the current thesis the results from size effect tests yielded average fracture energy of 232 N/m. Generally the fracture energies obtained from 2D-geometrically similar specimens are in the range of 60-70 N/m as could be seen in literature. From 3D-geometrically similar specimens, the fracture energies are higher. The reason is increased peak load, could be due to increased width. The RILEM fracture energy Gf , determined from TPB tests, is said to be size dependent. The assumption made in the work of fracture is that the total strain energy is utilized for the fracture of the specimen. The fracture energy is proportional to the size of the FPZ, it also implies that FPZ size increases with increase in (W−a) of beam. This also means that FPZ is proportional to the depth W for a given notch to depth ratio, because for a given notch/depth, (W−a) which is also W(1 − a ) is proportional to W`because (1 − a ) is a constant. WWThis corroborates the fact that fracture energy increases with size. Interestingly, the same conclusion has been drawn by Abdalla & Karihaloo (2006). They have plotted a curve relating fracture process zone length and overall depth the beam. In the present study a new method namely Fracture energy release rate method is suggested. In the new method the plot of Gf / (W−a) versus (W−a) is obtained from a set of experimental results. The plot is found to follow power law and showed almost constant value of Gf / (W−a) at larger ligament lengths. This means that fracture energy reaches a constant value at large ligament lengths reaffirming that the fracture energy from very large specimen is size independent. The new method is verified for the data from literature and is found to give consistent results. In a quasi-brittle material such as concrete, a fracture process zone forms ahead of a pre-existing crack (notch) tip before the crack propagates from the tip. The process zone contains a scatter of micro-cracks, which coalesce into one or more macro-cracks, which eventually lead to fracture. These micro-cracks and macro-cracks release stresses in the form of acoustic waves having different amplitudes. Each micro or macro crack formation is called an acoustic emission (AE) event. Through AE technique it is possible to locate the positions of AE events. The zone containing these AE events is termed the fracture process zone (FPZ). In Chapter-4, a study on the evolution of fracture process zone is made using AE technique. In the AE study, the fracture process zone is seen as a region with a lot of acoustic emission event locations. Instead of the amplitudes of the events, the absolute AE energy is used to quantify the size of the process zone at various loading stages. It has been shown that the continuous activities during the evolution of fracture process zone correspond to the formation of FPZ, the size of which is quantified based on the density of AE events and AE energy. The total AE energy released in the zone is found to be about 78% of the total AE energy released and this is viewed as possible FPZ. The result reasonably supports the conclusion, from Otsuka and Date (2000) who tested compact tension specimens, that zone over which AE energy is released is about 95% can be regarded as the fracture process zone. As pointed out earlier, among the fracture characteristics, the determination of fracture energy, which is size independent, is the main concern of research fraternity. Kai Duan et al. (2003) have assumed a bi-linear variation of local fracture energy in the boundary effect model (BEM) to showcase the size effect due to proximity of FPZ to the specimen back boundary. In fact the local fracture energy is shown to be constant away from boundary and reducing while approaching the specimen back boundary. The constant local fracture energy is quantified as size independent fracture energy. A relationship between Gf , size independent fracture energy GF , un-cracked ligament length and transition ligament length was developed in the form of equations. In the proposed method the transition ligament length al is taken from the plot of histograms of energy of AE events plotted over the un-cracked ligament. The value of GF is calculated by solving these over-determined equations using the RILEM fracture energies obtained from TPB tests. In chapter-5 a new method involving BEM and AE techniques is presented. The histogram of energy of AE events along the un-cracked ligament, which incidentally matches in pattern with the local fracture energy distribution, assumed by Kai Duan et al. (2003), along the un-cracked ligament, is used to obtain the value of GF , of course using the same equations from BEM developed by Kai Duan et al. (2003). A critical observation of the histogram of energy of AE events, described in the previous chapter, showed a declining trend of AE event pattern towards the notch tip also in addition to the one towards the specimen back boundary. The pattern of AE energy distribution suggests a tri-linear rather than bi-linear local fracture energy distribution over un-cracked ligament as given in BEM. Accordingly in Chapter-6, GF is obtained from a tri-linear model, which is an improved bi-linear hybrid model, after developing expressions relating Gf , GF , (W−a) with two transition ligament lengths al and blon both sides. The values of Gf , and GF from both bi-linear hybrid method and tri-linear method are tabulated and compared. In addition to GF , the length of FPZ is estimated from the tri-linear model and compared with the values obtained from softening beam model (SBM) by Ananthan et al. (1990). There seems to be a good agreement between the results. A comparative study of size independent fracture energies obtained from the methods described in the previous chapters is made. The fracture process in concrete is another interesting topic for research. Due to heterogeneity, the fracture process is a blend of complex activities. AE technique serves as an effective tool to qualitatively describe the fracture process through a damage parameter called b-value. In the Gutenberg-Richter empirical relationship log 10N=a−bM, the constant ‘b’ is called the b-value and is the log linear slope of frequency-magnitude distribution. Fault rupture inside earth’s crust and failure process in concrete are analogous. The b-value, is calculated conventionally till now, based on amplitude of AE data from concrete specimens, and is used to describe the damage process. Further, sampling size of event group is found to influence the calculated b-value from the conventional method, as pointed out by Colombo et al. (2003). Hence standardization of event group size, used in the statistical analysis while calculating b-value, should be based on some logical assumption, to bring consistency into analytical study on b-value. In Chapter-7, a methodology has been suggested to determine the b-value from AE energy and its utilization to quantify fracture process zone length. The event group is chosen based on clusters of energy or quanta as named in the thesis. Quanta conform to the damage stages and justify well their use in the determination of the b-value, apparently a damage parameter and also FPZ length. The results obtained on the basis of quanta agree well with the earlier results.

No description available.

Concrete has established itself as the most widely used structural material. There is hardly any place where human life and concrete structure do not exist together. It's use is seen in wide variety of structures like buildings, bridges, dams, nuclear structures, floating and submerged structures and so on. Hence, in view of safety, serviceability and economy, proper understanding of the behaviour of concrete is imperative in designing these complex structures. Current reinforced concrete codes are based on strength and serviceability concepts. The tensile strength of concrete is totally neglected in the limit state method of analysis. The concrete in tension is assumed to be fully cracked and conservative method of design is adopted. The crack causes a considerable degradation of stiffness of overall structure and gives rise to regions of stress concentration, which are not accounted for, in the present design methods. Besides, it is found that the size of the structural component significantly influences the stress at failure. It has been fairly well established that large specimens fail by catastrophic crack propagation while small specimens tend to fail in a ductile manner with considerable amount of slow crack growth preceding fracture. Initial attempts to understand the cracking of concrete through the principles of fracture mechanics was made in 1960's. It was concluded that the LEFM and small scale yielding fracture mechanics which are developed for metals are inapplicable to concrete structures except for certain limiting situations such as the behaviour at extremely large sizes. The reasons for the inapplicability of LEFM principles to concrete structures are attributed to slow crack growth, formation of nonlinear fracture process zone, and softening behaviour of concrete in tension. Several analytical and numerical models have been proposed to characterize the fracture behaviour of concrete. In the present work a simple numerical method is proposed to analyse the Mode-I fracture behaviour of concrete structures, using finite element method. The stiffness matrices calculated at the beginning of the analysis are used till the end without any modification. For this reason, the method is named as Initial Stiffness Method (ISM). An attempt has also been made to modify the lattice model existing in literature. The contents of the thesis are organised in six chapters. In chapter 1, a brief introduction to basic principles of fracture mechanics theory is presented. This is included mainly for the completeness of the thesis. In chapter 2, a brief review of literature regarding the application of principles of fracture mechanics to concrete structures is presented. The need for the introduction of fracture mechanics to concrete is presented. Early work, applying LEFM principles to concrete structures is discussed. The reasons for the inapplicability of linear elastic fracture mechanics principles to concrete structures are discussed. Necessities for nonlinear fracture mechanics principles are pointed out. Attention is focused on the influence of the factors like slow crack growth, formation of nonlinear fracture process zone and softening behaviour of concrete in tension on the fracture behaviour. Besides a possible use of fracture energy as an alternative fracture criterion for concrete is contemplated. Several analytical and numerical models (assuming concrete as homogeneous continuum), proposed so far to characterize the fracture behaviour of concrete, are presented and discussed in detail. Different heterogeneous models presented so far are also discussed. In chapter 3, a simple numerical method to analyse the fracture of concrete (strain softening material) in Mode-I, using FEM is proposed. The stiffness matrices are generated only once and are used till the end of the analysis. This feature makes the model simple and computationally efficient. A new parameter namely, strain softening parameter α has been introduced. It is found that this strain softening parameter ‘α’ is a structural property. The results obtained from the present method are found to converge with increasing number of elements thus making the method mesh independent, and thus objective. The method was validated by analysing the beams tested and reported by various researchers. The predicted values of maximum load by the present method are found to agree well with the experimental values. Initially, all the beams are analysed using uniform meshes and load-deflection diagrams are plotted. All the beams are again analysed using graded meshes. The load-deflection, load-CMOD diagrams are plotted from the results obtained from the analysis using graded meshes. In chapter 4, the results obtained in chapter 3 are analysed for size effect. Literature regarding size effect of concrete structures has been reviewed. In addition to the size effect on nominal stress at failure which exists in literature, two new parameters namely, post peak slope and softening slope parameter α have been used to confirm the size effect. This does not exist in the literature. In chapter 5, an attempt is made to modify the lattice model existing in literature. This is done with a view to model concrete as a heterogeneous medium, which would be nearer to reality. The softening property of concrete has been incorporated. The model was validated against some of the experimental results existing in literature. The results are found to be encouraging. The results from this model show the post peak softening similar to the experimentally observed ones. The effects of different probabilistic distributions to the properties of mortar on the maximum load of the beam are studied. It is found that normal distribution of properties to mortar gives the best results. A study is made regarding the sensitivity of various properties of mortar on the maximum load of the beam. It is concluded that load carrying capacity of the beam can be increased by using a mortar of higher tensile strength. Finally in chapter 6, general conclusions and suggestions for further investigations are discussed.

Polyethylene is a widely-used material in package industries. The fracture behavior of this material has not been studied in the plastic region in many years. In this thesis work, the J-Integral which is one material property used to represent the plastic material strength is calculated through the numerical analysis. To build a correct numerical model, the material behavior is summarized from previous uniaxial tensile test. The result from the fracture experiment for variable initial crack length is used to validate the reliability of the numerical model. The numerical analysis is done by the software ABAQUS which has the function to get the value of J-Integral directly. The final result contains the comparison between experiments and numerical analysis and the value of J-Integral at the crack initiation.

In the present work, the non-linear vibrations and the corresponding dynamic fracture mechanics of cables of cable-stayed bridges are studied. The cables are among the most critical components in cable-stayed bridges and there are different damage sources such as corrosion, vibration, fatigue and fretting fatigue that can significantly affect them, thereby reducing the cable’s service life and even producing their failure. Cable-Parametric Resonance is the specific non-linear vibration studied in this research. This type of vibration occurs due to displacements presented at the cable supports. These displacements are induced by the wind and traffic loads acting on the pylon and deck of the bridge. Under certain conditions, unstable cable-vibration of significant amplitude can be registered. Therefore, numerical and experimental analyses are carried out in order to describe this phenomenon and to determine the corresponding instability conditions. Two non-linear models of cable-parametric resonance are studied to predict the cable response. In the simulation method, the non-linear components are treated as external forces acting on the linear systems, which are represented by Single Degree of Freedom systems and described by digital filters. A clear non-linear relationship between the excitation and the cable response is observed in the simulations and the experiments. The corresponding experimental analysis is based on a scaled model (1:200) of the Öresund bridge and a good agreement between the numerical and experimental results is found. After obtaining the relationship between the cable response and the excitation, the cable instability conditions are determined. This is done by finding the minimum displacement required at the cable supports in order to induce nonlinear cable vibration of considerable amplitude. The instability conditions are determined within a wide range of excitation frequencies and conveniently expressed in a simplified and practical way by a curve. The determination process is rather fast and offers the possibility to evaluate all bridge cable stays in a rather short time. Finally, the dynamic fracture mechanics of the cable is considered by studying the fracture toughness characteristics of the material under dynamic conditions. Finite Element simulations on a pre-cracked three-point bending specimen under impact loading are performed. The observed cable instability is equivalently considered as the associated response to impact load conditions, and a crack as a defect on the wires of a cable stay. The simulations are based on an experimental work by using the Split Hopkinson pressure bar (Jiang et al). The dynamic stress intensity factor KI(t) up to crack initiation is then obtained by different methods. The numerical estimations based on the specimen’s crack tip opening displacement (CTOD) and mid-span displacement were closest to the experimental results. It is observed that a better estimation of the dynamic stress intensity factor relies on a proper formulation of the specimen’s stiffness. / Lic March 2011

Acrylic bone cement is widely used as a structural material in orthopaedics, dentistry, and orofacial surgery. Although bone cement celebrates four decades of success, it remains susceptible to fatigue fracture. This type of failure can directly lead to implant loosening, revision surgery, and increased healthcare expenditures. The mechanism of fatigue failure is divided into three stages: 1) fatigue crack initiation, 2) fatigue crack propagation, and 3) fast, brittle fracture. Adding reinforcing fibers and particles to bone cement is a proposed solution for improving fatigue performance. The mechanical performance of these reinforced bone cements is limited by fiber ductility, fibermatrix de-bonding, elevated viscosity, and mismatch of fiber size and scale of fatigue induced damage. In this dissertation, I report that adding small amounts (0% - 10% by weight) of multiwall carbon nanotubes (MWNTs) enhances the strength and fatigue performance of single phase bone cement. MWNTs (diameters of 10-9 10-8 m; lengths of 10-6 10-3 m) are a recently discovered nanomaterial with high surface area to volume ratios (conferring MWNT bone cement composites with large interfaces for stress transfer) that are capable of directly addressing sub-microscale, fatigue induced damage. MWNTs (2wt%) significantly increased the flexural strength of single phase bone cement by a modest 12%; whereas, similar additions of MWNTs dramatically enhanced fatigue performance by 340% and 592% in ambient and physiologically relevant conditions, respectively. Comparing the fatigue crack propagation behaviors of reinforced and unreinforced single phase bone cements revealed that the reinforcing mechanisms of MWNTs are strongly dependent on stress intensity factor, K, a numerical parameter that accounts for the combinatorial effect of the applied load and the crack size. As the crack grows the apparent stress at the crack tip intensified and the MWNTs lost their reinforcing capabilities. For that reason, it is likely that the predominant role of the MWNTs is to reinforce the bone cement matrix prior to crack initiation and during the early stages of crack propagation. Therefore, MWNTs are an excellent candidate for improving the clinical performance of bone cement, thereby improving implant longevity and reducing patient risk and healthcare costs.

Yucca Mountain, Nevada is the proposed site for the underground storage of high-level civilian nuclear waste in the United States. The repository must be isolated from the general environment for at least 10,000 years. Ground water and gases are potential carriers of radioactive materials. Fractures and connected pores in the host rock are the major pathways for ground water and gases. Therefore, the mechanical and flow properties of the host rock should be understood and utilized in the design of the underground repository. Samples of Topopah Spring tuff from Yucca Mountain were used in this study. Cylindrical specimens were prepared to perform uniaxial and triaxial "damage" tests where specimens are loaded to a particular stress level to induce damage and fracturing and then unloaded. Mechanisms of microcracking at different fracturing levels have been studied by using both an optical microscope and a Scanning Electron Microscope (SEM). The original rock sample without loading was also observed under the microscopes. Many kinds of defects including pores, preexisting fractures, and soft inclusions were found in the undamaged Apache Leap tuff samples. Pores were determined to be the main microstructures in Topopah Spring tuff that could influence the mechanical and hydrologic properties. Under compressive stresses, microcracking initiates from some of the pores. These microcracks will interact and coalescence to form large microcracks or macroscopic cracks as the load is increased. Crack propagation phenomena, such as pore cracking, pore linking, pore collapse and the formation of en echelon arrays were all found in specimens unloaded prior to complete failure. The failure of tuff specimens is often through a process of shear localization. In summary, the deformation and failure of both tuffs occurred by progressive fracturing, starting from microcracking on the small scale, and ending as fractures coalesced to form macroscopic fractures and shear localization. On the basis of the experimental studies, micromechanical models such as the pore collapse model and the pore linking model have been developed based on fracture mechanics theory. These models are used to predict the constitutive behavior for tuff and the predicted stress-strain curves match well with the experimental curves.

This thesis details an experimental study on the determination of the fracture parameters for a crack located at the interface between two dissimilar materials using the method of photoelasticity. The interface is potential1y an inherent weak spot of any composite material, structure"or adhesively bonded joint. Accurate description of the state of stress at the crack tip is required for strength prediction. The concept of the complex stress intensity factor is used to characterise the elastic crack tip stress field for an interface crack. Complex stress intensity factors and their moduli have been measured experimental1y for standard bimaterial crack geometries using the wel1 established technique of photo elasticity. Bimaterial specimens comprising aluminium al10y and epoxy resin components were used. This creates a large material mismatch at the interface and al10ws data to be col1ected from the epoxy component of the specimen using transmission photoelasticity. An automated ful1 field photoelastic technique was developed to significantly reduce the data col1ection time. The technique comprises elements from the approaches of three wavelength and phase stepping photoelasticity and is a significant improvement on techniques previously available. Stress intensity factors were determined by fitting a theoretical stress field solution for the bimaterial crack to the experimental data. A computational routine automatical1y selects the region of best fit between the experimental data and the theoretical solution. This data is then used to determine the complex stress intensity factor and its modulus value. In order to provide a robust fit between the experimental data and the theoretical field solution a weighting function was incorporated into the routine. The measured bimaterial stress intensity factors are compared with those determined experimental1y for equivalent homogeneous specimens made from epoxy resin. The differences between the two are then discussed. The experimental results agree with the wel1 known concept that tension and shear effects are inherently coupled at the crack tip. However, the effects of changing the load angle with respect to the interface also demonstrate that some contrasts exist with known numerical solutions.

The main aim of this research was to investigate the behaviour of adhesive joints exposed to repeated low-velocity impact i.e. impact fatigue (IF), and to compare this loading regime with standard fatigue (SF), i.e. non-impacting, constant amplitude, sinusoidal loading conditions. Two types of lap joint configuration using rubber toughened modified epoxy adhesives were used and exposed to various loading conditions in order to determine the fatigue behaviour of the joints for each load conditions. The fatigue life was investigated using bonded aluminium alloy (7075-T6) single lap joint (SLJ) specimens, where it was seen that IF is an extremely damaging load regime compared to SF. Different trends were visible in force-life plots for these two types of loading. In SF a gradual decrease in the fatigue life with increasing load was observed, whereas, in IF a significant decrease in life was seen at relatively modest levels of maximum force after relatively few cycles. Comparisons of the fatigue life show a considerably earlier failure in IF than in SF for comparable levels of force and energy. Additionally, it was demonstrated that the maximum force per cycle, loading time, stiffness and strength decreased as a result of damage generated in the sample during IF.

Carbon Capture and Storage (CCS) is recognised as having a significant role to play in tackling climate change and reducing carbon dioxide (CO2) emissions. In CCS schemes, CO2 is captured from anthropogenic sources, and transported to suitable sites either for EOR (Enhanced Oil Recovery) or storage. The transport of such huge amount of CO2 causes new challenges. The main concern is in the difference between natural gas and CO2 transportation pipelines. CO2 phase behaviour during decompression, existence of different impurities and very high operating pressure are some of the new challenges for pipeline designer and operators. This PhD study has taken a systematic approach to understand the mechanics involved in the fracture of pipes containing high pressure flue-gas CO2. The work involved the development of a novel weight function stress intensity factor solution that can be used with complex stress fields induced by residual and/or thermal stresses in addition to applied pressure. In addition, the thesis reports a substantial experimented test programme which involved low temperature fracture toughness tests linked to a detailed finite element based stress analysis. Overall, the thesis presents an integrated engineering criticality means to assess the suitability or otherwise of a pipeline system to transport high pressure flue-gas CO2.