The microstructure of concrete contains random features over a wide range of length scales in which each length scale possess a new random composite. The influence of individual material constituents at different scales and their mutual interactions are responsible for the formation of fracture process zone (FPZ). The presence of the FPZ and the various toughening mechanism occurring in it, influences the fatigue and fracture behavior of concrete which also gets influenced by the geometry, spacial distribution and material properties of individual material constituents and their mutual interactions. Hence, in order to study the influence of interfacial transition zone, microcrack and aggregate bridging on the fracture and fatigue behavior of concrete, a multiscale analysis becomes necessary. This study aims at developing a linearized model which helps in understanding the fracture and fatigue behavior of cementitious materials by considering the predominant fracture process zone (FPZ) mechanisms such as microcracking and aggregate bridging. This is achieved by quantifying the critical microcrack length and the bridging resistance offered by the aggregates. Further, the moment carrying capacity of a cracked concrete beam is determined by considering the effect of aggregate bridging. A modified stress intensity factor (SIF) is derived based on linear elastic fracture mechanics (LEFM) approach by considering the material behavior at different scales through a multiscale approach. The model predicts the entire crack growth curve for plain concrete by considering these process zone mechanisms. Furthermore, the fracture and fatigue response of concrete is studied through the development of analytical models which include the properties of the mix constituents using the multiscale based SIF. The effect of the interfacial transition zone, microcracks and resistance offered through aggregate bridging on the resistance to crack initiation and propagation are studied. A fatigue crack growth law is proposed using the concepts of dimensional analysis and self-similarity. Through sensitivity analyses, the influence of different parameters on the overall fracture and fatigue behavior are studied. In addition, studies related to concrete-concrete bi-material interfaces are conducted in order to understand the influence of repair materials on the service life of damaged concrete structures when subjected to fatigue loading. An analytical model is proposed in this study to predict the crack growth curve using the concepts of dimensional analysis and self-similarity in conjunction with the human population growth model. It is seen that a repair done with a patch having similar elastic properties as those of the parent concrete will have a larger fatigue life.

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.

This work is focused on the application of advanced elasto-plastic material model intended for shotcrete. Spatial mathematical models of two laboratory tests are created, where this model is used. The first test is a three-point bending concrete specimen. Next, the behavior of the material is analyzed, in which input parameters are entered. Consequently, two reverse analyzes of the available data are analyzed where a match between prediction and measurement can be obtained. The second test is a modified tensile test, where is describe the material behavior in changing of input parameters. Subsequently, reverse data analysis is created, where an acceptable match between prediction and measurement is possible. In every study, the stress waveform in the fracture process zone is analyzed to more detail.

This work is focused on the evaluation of the selected fracture parameters of quasi-brittle material, especially concrete, and an assessment of their dependence on the size and shape of the fracture process zone developing at the tip of the macroscopic crack during fracture. For this purpose, experimentally obtained loading diagrams published in the scientific literature have been utilized. These diagrams have been processed into a form enabling creation and calibration of numerical models of these tests in the ATENA FEM program. The results obtained from simulations of the three-point bending tests on beams of four sizes, with three notches lengths, using the created numerical models were used for determination of fracture parameters of concrete. Results of the work consist of the determined values of the specific energy dissipated for creation of new surfaces of the effective crack and an estimation of the specific energy dissipated in the volume of the fracture process zone, which exhibits specific parameters for each beam size and notch length.

The integrity of nearly all engineering structures are threatened by the presence of cracks. Structural failure occurs if a crack larger than a critical size exists. Although most well designed structures initially contain no critical cracks, subcritical cracks can grow to failure under fatigue loading, called fatigue crack growth (FCG). Because it is impossible or impractical to prevent subcritical crack growth in most applications, a damage tolerant design philosophy was developed for crack sensitive structures. Design engineers have taken advantage of the FCG threshold concept to design for long fatigue lives. FCG threshold (DKth) is a value of DK (crack-tip loading), below which no significant FCG occurs. Cracks are tolerated if DK is less than DKth. However, FCG threshold is not constant. Many variables influence DKth including microstructure, environment, and load ratio. The current research focuses on load ratio effects on DKth and threshold FCG. Two categories of load ratio effects are studied here: extrinsic and intrinsic. Extrinsic load ratio effects operate in the crack wake and include fatigue crack closure mechanisms. Intrinsic load ratio effects operate in the crack-tip process zone and include microcracking and void production. To gain a better understanding of threshold FCG load ratio effects (1) a fatigue crack closure model is developed to consider the most likely closure mechanisms at threshold, simultaneously, and (2) intrinsic load ratio mechanisms are identified and modeled. An analytical fatigue crack closure model is developed that includes the three closure mechanisms considered most important at threshold (PICC, RICC, and OICC). Crack meandering and a limited amount of mixed-mode loading are also considered. The rough crack geometry, approximated as a two-dimensional sawtooth wave, results in a mixed-mode crack-tip stress state. Dislocation and continuum mechanics concepts are used to determine mixed-mode crack face displacements. Plasticity induced crack closure is included by modifying an existing analytical model, and an oxide layer in the crack mouth is modeled as a uniform layer. Finite element results were used to verify the analytical solutions for crack-tip stress intensity factor and crack face displacements. These results indicate that closure for rough cracks can occur at two locations: (1) at the crack-tip, and (2) at the asperity nearest the crack-tip. Both tip contact and asperity contact must be considered for rough cracks. Tip contact is more likely for high Kmax levels, thick oxide layers, and shallow asperity angles, a. Model results indicate that closure mechanisms combine in a synergistic manner. That is, when multiple closure mechanisms are active, the total closure level is greater than the sum of individual mechanisms acting alone. To better understand fatigue crack closure where multiple closure mechanisms are active (i.e. FCG threshold), these interactions must be considered. Model results are well supported by experimental data over a wide range of DK, including FCG threshold. Closure-free load ratio effects were studied for aluminum alloys 2024, 7050, and 8009. Alloys 7050 and 8009 were selected because load ratio effects at FCG threshold are not entirely explained by fatigue crack closure. It is believed that closure-free load ratio mechanisms occur in these alloys. Aluminum alloy 2024 was selected for study because it is relatively well behaved, meandering most load ratio effects are explained by fatigue crack closure. A series of constant Kmax threshold tests on aluminum alloys were conducted to eliminate fatigue crack closure at threshold. Even in the absence of fatigue crack closure load ratio (Kmax) effects persist, and are correlated with increased crack-tip damage (i.e. voids) seen on the fatigue crack surfaces. Accelerated FCG was observed during constant Kmax threshold testing of 8009 aluminum. A distinct transition is seen the FCG data and is correlated with a dramatic increase in void production seen along the crack faces. Void production in 8009 aluminum is limited to the specimen interior (plane-strain conditions), promoting crack tunneling. At higher values of Kmax (+_ 22.0 MPaà m), where plane-stress conditions dominate, a transition to slant cracking occurs at threshold. The transition to slant cracking produces an apparent increase in FCG rate with decreasing DK. This unstable threshold behavior is related to constraint conditions. Finally, a model is developed to predict the accelerated FCG rates, at higher Kmax levels, in terms of crack-tip damage. The effect of humidity (in laboratory air) on threshold FCG was studied to ensure that environmental effects at threshold were separated from load ratio effects. Although changes in humidity were shown to strongly affect threshold FCG rates, this influence was small for ambient humidity levels (relative humidity between 30% and 70%). Transient FCG behavior, following an abrupt change in humidity level, indicated environmental damage accumulated in the crack-tip monotonic plastic zone. Previous research implies that hydrogen (a component of water vapor) is the likely cause of this environmental damage. Analysis suggests that bulk diffusion is not a likely hydrogen transport mechanism in the crack-tip monotonic plastic zone. Rather, dislocation-assisted diffusion is presented as the likely hydrogen transport mechanism. Finally, the (extrinsic) fatigue crack closure model and the (intrinsic) crack-tip damage model are put in the context of a comprehensive threshold model. The ultimate goal of the comprehensive threshold model is to predict fatigue lives of cyclically loaded engineering components from (small) crack nucleation, through FCG, and including failure. The models developed in this dissertation provide a basis for a more complete evaluation of threshold FCG and fatigue life prediction. The research described in this dissertation was performed at NASA-Langley Research Center in Hampton, Virginia. Funding was provided through the NASA GSRP program (Graduate Student Researcher Program, grant number NGT-1-52174). / Ph. D.

[pt] O trincamento de camada de mistura asfáltica é o principal tipo de deterioração das rodovias, e o presente estudo pretende contribuir para conhecimento dos processos de fissuramento com o objetivo de incorporar novos parâmetros mecânicos para melhorar projetos de pavimentação rodoviária . A modelagem computacional através do Método dos Elementos Discretos (MED), permitiu fazer uma simulação da iniciação e da propagação do trincamento em um ensaio de tração direta chamado de Disco Circular com Fenda (Disk Shaped compact), considerando uma abordagem da teoria da mecânica da fratura elástica linear (MFEL) e a incorporação do modelo constitutivo de zona coesiva (MZC). As modelagens realizadas permitiram inferir o comportamento de corpos de prova de Disco Circular com Fenda DC(T) feitos em laboratório. O método dos elementos discretos monstrou-se uma ferramenta apropriada para realizar este tipo de simulação. Também foram feitas análises da sensibilidade da resposta do modelo em relação a diversos parâmetros mecânicos do material: módulo de Young (E), resistência à tração (RT) e energia da fratura (Gf). Este último parâmetro foi obtido da área sob a curva tração-deslocamento da abertura da boca da trinca (CMOD). A análise foi realizada considerando o corpo como material homogêneo atribuindo-se a todas as partículas propriedades idênticas. A modelagem numérica 2D foi executada através do programa comercial PFC2D baseado no MED. / [en] The cracking of asphalt mixture layers is the main type of deterioration of roads in Brazil, and this study aims to contribute to improve the knowledge of cracking processes in order to incorporate new mechanical parameters into road pavement projects. Computer modeling by the Discrete Element Method (DEM), permitted the simulation of the initiation and the propagation of cracking in a tensile test called Direct Circular Slotted Disc (Disk Shaped Compact), whose interpretation is based on the theory of linear elastic fracture mechanics and considering an specific elastoplastic model known as the cohesive zone model (CZM). Results of Direct Circular Slotted Disc tests were obtained in laboratory and interpreted by numerical simulations using the discrete element method, with good results. The sensitivity of model response with respect to various mechanical parameters, such as the Young s modulus (E), the tensile strength (RT) and the fracture energy (Gf) was also analyzed. This last parameter (Gf) was obtained considering the area under the traction-displacement curve from the Crack Mouth Opening Displacement (CMOD) test. The analyses were carried out considering the body as a homogeneous material, assigning to all particles identical properties. The 2D numerical model was analyzed using the commercial software PFC2D based on the discrete element method (MED).

The thesis is focused on a test on determination of the fracture-mechanical parameters of quasi-brittle materials, especially concrete. What is referred to as the wedge-splitting test is considered, for which a variety of shapes of notched specimen can be used. This work is exclusively focused on the cylinder-shaped specimen of diameter 150 mm and breadth of 100 mm. The test is performed virtually using Atena 2D FEM software. Progress of failure is observed during loading of the specimen for various notch lengths. The amount of energy released for the development the failure outside of the tested cross-sectional area (weakened by the notch) is quantified and the size of the fracture process zone is investigated. The described analysis is performed for several material sets witch differ in cohesive properties of the quasi-brittle material expressed via the so-called characteristic length. Suitable proportions of the test specimen are sought, in order to avoid the failure and thus also the energy dissipation outside of the specimen ligament area during the experimental tests, which shall lead to more accurate estimates of fracture-mechanical parameters of the tested material.