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In this research, the fracture processes in concrete subjected to monotonic and fatigue loadings are characterized and the differences in failure mechanisms are studied using acoustic emission (AE) and digital image correlation (DIC) techniques. Experiments are performed on notched plain concrete beams under three-point bending. The micro and macro structural activities are classified based on acoustic energy levels to differentiate between the formation of a fracture process zone (FPZ) under monotonic and fatigue loadings. It is observed that a FPZ within its conventional definition is formed under monotonic loading. On the contrary, the AE results under fatigue loading indicate isolated and dispersed micro cracks up to 95% of fatigue life. A damage index based on AE energy is proposed for concrete subjected to fatigue loading which could be used in health monitoring of structures.

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... Length of FPZ was evaluated by Zhang & Wu [44] using Acoustic Emission (AE) in concrete notched beams and stated that length Presence of fracture core zone in fracture process zone, [46]. was rather specimen size dependent than being a material property. ...

... Keerthana and Kishan [46] combined AE and DIC techniques to determine the existence of FPZ and more localised fracture core zone (FCZ) to distinguish between FPZ of cyclic and monotonic loading. FPZ length and width along with its microcrack distribution in the thickness for monotonic loading is shown in Fig. 4. It was observed that higher energy AE events (shown by red colour) fall into FCZ and rest into the FPZ. ...

... The size effect refers to the phenomenon in which the same mechanical characteristics exhibit different values depending on the size of the fundamental structural parts. Bazant's size effect law establishes a correlation between the strength criteria and LEFM for concrete like materials as seen from 12. Size effect phenomena in quasi-brittle material have been thoroughly explained in Section 3. Various researchers have investigated the properties of FPZ and incorporated the size effect [37,46,[60][61][62][63][64]. The authors have provided an understanding of the size effect in regard to FPZ in this section. ...

Concrete structures are exposed to various loading scenarios in real-time performance, which affects their effective lifespan. Fatigue loading is one of the key influencers which leads to major crack failures at a load smaller than the design load when subjected to longer period of time. Hence, a comprehensive analysis of fatigue behaviour is essential to predict the lifespan of a structure. To date, significant progress has been attained in this field and a detailed literature survey has been provided here which covers all studies addressing the factors affecting the fatigue life of concrete. Firstly, a brief introduction is given describing the necessity of fatigue analysis followed by the evolution of crack propagation laws in concrete from Paris Law established for metallic structures. A detailed study of size effect is presented which mentions the different types of size effect laws that evolved with time. The existence of a Fracture Process Zone and estimation of its shape and size has been highlighted in view of advanced crack detection techniques. Furthermore, a rigorous study has been done on various fatigue crack growth characterising factors such as loading rate, reinforcement, corrosion, bond slip, and temperature. Finally, the review is concluded with the advent of artificial neural networks, machine learning, and deep learning in the domain of fatigue and fracture analysis of concrete. Based on this review, a critical analysis of exisiting limitations have been performed and open problems are identified for future reference.

... Hence, utilizing these values without regard to the size effect can result in a possible erroneous estimation of the real-life structural performance [1,6]. Recently, the application of advanced fracture monitoring techniques has provided new insights in this fundamental issue [9][10][11][12][13][14][15]. Acoustic emission (AE) [9][10][11][12][13][14][15], digital image correlation (DIC) [9,10,15], and X-ray imaging techniques [13] have been used to study the effect of specimen size on the energy release rate, the time of crack initiation, and the size of the fracture process zone (FPZ). ...

... Recently, the application of advanced fracture monitoring techniques has provided new insights in this fundamental issue [9][10][11][12][13][14][15]. Acoustic emission (AE) [9][10][11][12][13][14][15], digital image correlation (DIC) [9,10,15], and X-ray imaging techniques [13] have been used to study the effect of specimen size on the energy release rate, the time of crack initiation, and the size of the fracture process zone (FPZ). ...

... Recently, the application of advanced fracture monitoring techniques has provided new insights in this fundamental issue [9][10][11][12][13][14][15]. Acoustic emission (AE) [9][10][11][12][13][14][15], digital image correlation (DIC) [9,10,15], and X-ray imaging techniques [13] have been used to study the effect of specimen size on the energy release rate, the time of crack initiation, and the size of the fracture process zone (FPZ). ...

The size effect is a phenomenon where the strength and the ductility of a material depend on the size of the structure. Investigating size effects and related crack formation in brittle materials requires advanced monitoring methods. The aim of this research is to experimentally investigate the impact of size effect with the acoustic emission (AE) technique. Brazilian splitting tests with AE monitoring were performed on cement-based mortar cylinders of three sizes. It was found that in addition to the size, the boundary condition affects the final strength. When adopting similar boundary conditions in samples with different sizes, the larger samples had the lowest tensile splitting strength. For the larger samples, initially, there were fewer AE activities. However, there was a surge of high-amplitude AE events near the peak load. This indicates that as size increases, there is a lack of micro-cracking before macro-crack propagation, and the material fails in a more brittle manner. The width of the fracture process zone was quantified with AE and increased with sample size. A further analysis of the AE amplitude distribution demonstrated a change in the distribution in the pre-peak phase for the larger samples and for the smaller samples in the post-peak phase, signifying the brittle to ductile failure transition that occurs as size decreases.

... The research found that damage in fatigue develops in three stages; the initial increase in AE activity is followed by a linear rate of growth, and finally there is a steep rise of AE events prior to failure. More recently, Keerthana and Kishen (2020) used AE monitoring to compare the formation of the fracture process zone (FPZ) between monotonic and fatigue three-point bending tests of plain concrete beams. The research concluded that in monotonic loading, a more localized inelastic zone in front of the fracture front can be found. ...

... The slower increase in AE activity during fatigue cycles in contrast to monotonic loading indicates progressive and cumulative damage. Also similar to Keerthana and Kishen (2020), more low-energy AE events are found in fatigue loading than in monotonic loading. ...

... It can be observed that the estimated width of FPZ for the step-wise fatigue sample (28.9 mm) is larger than for the monotonic test (18.1 mm). When comparing monotonic and fatigue three-point bending tests of plain concrete beams, Keerthana and Kishen (2020) reported that even though there is a well-defined fracture zone for monotonic loading, micro-cracks were found to be isolated and scattered for fatigue loading, which led to the conclusion that the FPZ in their definition does not exist for fatigue loading. Here, both loading schemes generate localized cracks mainly thanks to the test setup (i.e. ...

In this work, acoustic emission (AE) sensors are used to detect micro-cracking in mortar cylinders subjected to monotonic
and step-wise fatigue loads, in a Brazilian splitting test setup. The difference in damage progression between monotonic
and fatigue tests was analyzed by using AE monitoring. The rate of AE events in monotonic tests was initially low, but
there is a sudden rise of AE events with high amplitude and energy prior to failure. On the other hand for fatigue tests,
three damage stages were identified. In addition, the width of a fracture process zone (FPZ) measured with AE, was found
to be higher for the fatigue tests. Finally, crack types throughout the fracture process are classified using AE parameter
analysis. In both tests, initially, AE due to tensile cracks dominated. However, after the major crack has formed, more shear
noises were observed.

... However, concrete structures would be subjected to various fatigue loading (e.g. vehicle loads) during their service life [2,3], where the mechanical properties and permeability performance of concrete materials will be weakened with the accumulation of damage caused by fatigue loading [4,7]. Therefore, it is of great significance to investigate the structural performance deterioration and fatigue behavior of concrete materials under fatigue loading. ...

... Various fatigue loading tests (e.g. cyclic loading and unloading, constant-amplitude fatigue loading, variable amplitude fatigue loading, and discontinuous fatigue loading) were carried out to understand the fatigue behavior of the concrete materials [5][6][7][8][9]. Some distinctive and important observations were obtained from laboratory testing. ...

... Some distinctive and important observations were obtained from laboratory testing. For example, under fatigue loading, the cyclic strain, the indicator of irreversible fatigue life, cyclic creep, and fatigue range that is higher than monotonic state strain, and the accumulated ultimate and plastic strains after each cycle before rupture, are dependent on the applied fatigue loading cycles of the concrete materials [1,7,[10][11][12][13][14]. Nucleation, interaction, and multi-microdefects growth are the main causes for the weakening of Young's modulus of elasticity in the fatigue process [15][16][17], and the mechanical behavior of concrete materials under fatigue loading is governed by microdefects like kinetics of the microstructure of the concrete materials. ...

A R T I C L E I N F O Keywords: Post-fatigue characteristics High-strength concrete Coupled 3D fatigue-static loading Physico-mechanical properties Fatigue damage model Empirical prediction model A B S T R A C T Concrete structures suffer some damage yet not failed under fatigue load, and then continue to bear 3D redistributed stress. For this, the 3D fatigue loading considering various fatigue factors (e.g. confining stress, axial static stress (ASS) and force amplitude (FA), frequency, and cycle number) is first carried out, and then the 3D static loading is performed. The post-fatigue characteristics of high-strength concrete (e.g. P-wave velocity, S-wave velocity, porosity, gas permeability, triaxial compression strength, and elastic modulus) are gained. The results indicate that 3D fatigue loading weakens mechanical properties, delays wave propagation, and increases seepage paths. An obvious stress threshold is exhibited with increasing axial static stress and force amplitude, that is 80% triaxial compressive strength, where the physico-mechanical characteristics are rapidly weakened due to the energy dissipation caused by crack growth rises increasingly. Compared with 1D fatigue loading, the frequency turning point of weakening effect from decreasing to increasing is advanced under 3D fatigue loading due to the application of 3D stress exacerbates the heat accumulation and creep damage generation. Interestingly , the fatigue damage is likely to be more sensitive to axial load compared to confining stress during 3D fatigue loading. In other words, the promotion effect of axial fatigue load on damage is larger than the restriction of confining stress. Furthermore, the fatigue damage models considering various fatigue factors are proposed. Then, the empirical prediction models of this damage variable to mechanical parameters (strength and elastic modulus) and permeability are established to predict the capacity loss caused by fatigue loading in the design of concrete construction. The testing results in this context could facilitate our understanding of post-fatigue characteristics of high-strength concrete subjected to 3D fatigue loading and guide the safe design of concrete construction.

... Due to the similar microstructure of matrix consisting of smaller grains, larger grains, pores and micro-cracks, refractories exhibit largely similar behaviour with regard to civil engineering concrete and rocks. For both concrete and rocks, qualitative and quantitative differences in crack propagation under monotonic and cyclic loading has been reported [15,16]. For rocks, deviations from monotonic failure trends were observed for stress and strain ("damage") controlled cyclic fatigue [15]. ...

... For rocks, deviations from monotonic failure trends were observed for stress and strain ("damage") controlled cyclic fatigue [15]. For concrete, whether the force-displacement curves of cyclic fatigue failure exceed or fall within the envelope of monotonic loading is assumed to be determined by the combined effect of loading amplitude and frequency, by the concrete's strength and by its heterogeneity [16]. Generally, the cyclic failure is distinguished by higher capacity of energy absorption [17] resulting from wider FPZ with crack branching [15,17]. ...

... The cyclic fatigue mechanisms feature de-cohesion of the larger grains and matrix loosening [15]. Final fatigue failure involves coalescence of micro-cracks [15,16]. The same phenomenon controls the saturation of the microstructural damage during repetitive thermal shock in technical ceramics [19]. ...

Refractory masonry (refractories) is exposed to in-service loads of different types. To rationalise the masonry design and failure analysis, differences of failure under cyclic and monotonic loading were studied. For samples of silica refractories tested in wedge splitting set-up global failure parameters and crack trajectories were assessed. Under cyclic loading, higher fracture energy and lower brittleness at failure were seen. Cracks of different modes had similar non-linearity and branching. However, the size and microstructural characteristics of the fracture process zone was different. In addition, higher energy dissipation during cyclic loading is promoted by repetitive friction events along the crack trajectory.

... Due to similar microstructure of matrix consisting of smaller grains, larger grains, pores and micro-cracks, refractories have largely similar mechanical behaviour to the civil engineering concrete and rocks. For both, the concrete, and the rocks, qualitatively and quantitatively different crack propagation under monotonic and cyclic loading has been reported [15,16]. For rocks, deviations from monotonic failure trends were observed both for stress and strain ("damage") controlled cyclic fatigue of high and low amount of cycles [15]. ...

... For rocks, deviations from monotonic failure trends were observed both for stress and strain ("damage") controlled cyclic fatigue of high and low amount of cycles [15]. For concrete, whether the force-displacement curves of cyclic fatigue failure exceed or fall within the envelope of monotonic loading is believed to be determined by the combined effect of loading amplitude and frequency, by the concrete's strength and its heterogeneity [16]. Generally, the cyclic failure is distinguished by higher capacity of energy absorption [17] resulting from wider FPZ with crack branching [15,17]. ...

... The cyclic fatigue mechanisms feature decohesion of the larger grains and matrix loosening [15]. Final fatigue failure involves coalescence of micro-cracks [15,16]. The same phenomenon controls the saturation of the microstructural damage during repetitive thermal-shock in technical ceramics [19]. ...

Refractory masonry (refractories) of industrial furnaces experience loads of various nature during service. Microstructural aspects of failure in silica refractories under monotonic and cyclic fatigue wedge splitting loading was studied. Knoop hardness measurements assisted the analysis. Monotonic and cyclic loading resulted in similar average strength with lower fracture energy for the first. With similar average crack non-linearity and trans granular failure, due to lower matrix damage and higher energy input the monotonic crack follows preferably grain-matrix interfaces (lowest energy consuming route). In cyclic mode, repeated loading increases energy dissipation. Within one loading mode, the brittleness correlates with trans granular failure.

... By analyzing the AE signal, researchers studied the initiation and propagation of fractures in UHPC and understand the different toughening mechanisms that influence its behavior [10][11][12]. For example, the AE technique can be used to determine the critical load at which a UHPC beam will fail, the number of microcracks formed in the beam, and the rate at which the crack is growing, thereby providing valuable information for the analysis of UHPC beams [13][14][15][16][17]. ...

... The AE technique allows researchers to study various fracture properties of UHPC beams, such as crack propagation, parametric-based properties, and the size of the fracture process zone (FPZ) [9,15,16,18]. By monitoring the AE signals generated by the microcracks as they form in the UHPC beam, researchers can determine the critical load at which the beam will fail and the rate at which the cracks are growing. ...

... The average width of FPZ determined from the AE events in small, medium and large concrete beams of depth of 75 mm, 150 mm and 300 mm (with maximum aggregate size of 12.5 mm) was found to be about 38 mm, 71 mm and 167 mm. The ratio of length of FPZ to the depth of the concrete beam was found to be constant (¼0.78) (Keerthana & Kishen, 2020). Similar investigations carried out using AE technique demonstrated that the width of FPZ is 2.75 times the maximum aggregate size (Hadjab et al., 2004). ...

... The FPZ also continues to exist in the post peak region. The maximum width of FPZ in plain concrete is found to be 60 mm (¼thrice the maximum size of aggregate) which is in line with the values reported in the literature (Alam et al., 2014;Hadjab et al., 2004;Keerthana & Kishen, 2020;Mihashi & Nomura, 1996). In the case of fibrous concrete, the maximum width of FPZ is much higher (¼ 90 mm, 4.5 times the maximum size of aggregate or 3 times the length of fiber used in this study). ...

Different types of fiber reinforced concrete are being developed with the aim to improve the desired mechanical properties like tensile strength, strain carrying capacity and energy absorption capacity. Fracture characteristics of fiber reinforced concrete are quite different from conventional concrete and much more complicated when chemically active fibers, capable to the unique strain hardening properties due to both mechanical and chemical bond in heterogeneous medium, are incorporated. Characterization of such material, specifically fracture behaviour, is very important for better understanding of—and efficient design for—the material. In the present study, detailed investigations are carried out using the complementary image- and acoustic wave-based techniques to obtain the complete information on the fracture characteristics of the strain hardened concrete, as the conventional strain/displacement sensors may not completely capture the behavior due to heterogeneity and brittleness. Thorough analysis of acoustic parameters including clustering and image processing at different stages of damage are carried out. It is found that the major fracture characteristics like determining the location of crack formation, monitoring the crack propagation, fracture energy and most importantly, fracture process zone of fiber reinforced concrete, can be evaluated by the proposed technique as discussed and demonstrated in this paper.

... The more the dissipation energy, the greater the damage becomes. This dissipated mechanism was observed in many experiments reported in the literature (Bazant & Xu, 1991;Isojeh et al., 2017;Keerthana & Kishen, 2020;Cho et al., 2021), wherein the area of the hysteresis loops become larger with the increasing number of loading cycles until tested specimens fail (Fig. 1). Therefore, capturing realistic hysteresis of the material is one of the key features to developing a modelling model capable of predicting fatigue crack propagation. ...

This paper proposes a modelling approach that combines the discrete element method (DEM) and a novel bonded contact model to characterise the fatigue response of cemented materials. While DEM is commonly used to simulate bonded materials undergoing cracking, the centrepiece of the present method is the development of the novel bonded fatigue model. This new model couples damage mechanics and bounding surface plasticity theory to capture fatigue crack growth in cement bridges between aggregates. Thanks to the incorporation of the bounding
surface plasticity, the proposed model provides a smooth transition from static to fatigue damages and vice-versa in a unified manner, making it more flexible to capture damage responses of cemented materials under different loading conditions (i.e. monotonic and cyclic loadings). Moreover, the proposed approach automatically captures the hysteretic response in cement bridges between aggregates under fatigue loadings without ad-hoc treatments. More importantly, by removing the direct dependence of the fatigue damage variable on the number of loading cycles, the modelling approach can be applied to simulate the fatigue behaviour of cemented materials under cyclic variable load amplitudes. The proposed modelling approach is evaluated against several strength tests to examine its predictive capability. Satisfactory agreements with fatigue experiments are achieved for flexural modulus degradations, lifetimes and sensitivity of stress levels under constant and variable amplitude cycles. This result suggests that the proposed discrete modelling approach can be used to conduct numerical experiments for insights into the fatigue behaviour of cemented materials.

... Cracking and stress redistribution also cause concrete to shrink and creep, which are both reversible and irreversible volume changes that are detrimental to the long-term performance of concrete structures. [11,12]. Failure of cementitious materials is often a gradual process. ...

The present experimental and analytical study aims to modify conventional cement to create a higher strength-to-weight ratio concrete using hybrid nanomaterials, i.e., Carbon Nanotubes (CNTs) and Nano-Silica (NS), as a partial replacement for cement (Nano-blended cement). In this study, three CNTs and four NS contents were chosen to evaluate the mechanical properties of concrete. 234 tests for specimens at 7, 28, and 90 days were carried out to achieve the optimum composition of the nanoparticles for the compressive strength and splitting tensile strength. Test results of the specimens examined at 28 days illustrate that the compressive strength and tensile strength were improved by 125 % by the inclusion of 0.1 % CNT + 1.5 % NS and by 110 % by using 0.5 % CNT + 1.0 % NS, respectively. Moreover, the strength-enhancement mechanism of novel concrete was visualized by scanning electron microscopy (SEM). Since conventional high-performance concretes, due to the high amount of cement required, are not environmentally friendly, the novel Nano-blended cement can create high-performance concretes without adding more cement or any concrete ingredients. In addition, using Nano-blended concrete results in a lighter structure with smaller members' size and a more lightweight foundation, and therefore is more cost-effective and sustainable than conventional concrete.

... Especially under the fatigue load, severe local stress concentration will be generated at the crack tip [1], which makes each phase in cementitious composites more susceptible to fracture or separation from each other. The fatigueinduced cracks are believed to be randomly distributed inside cementitious composites, affecting the service life of cementitious composites structure, and especially increasing the uncertainty about the safety of infrastructures, such as bridge deck and airport pavement [2][3][4]. ...

The compressive fatigue performance of cementitious composites largely depends on the generation and connection of fatigue nano/micro-cracks in the composites. These types of cracks are beyond the scope that traditional fibers can restrain, but can be effectively eliminated and inhibited by incorporating nano-materials, especially those with fiber shape, such as carbon nanotube (CNT). Unfortunately, the effect of CNT and its physical and chemical characteristics on the compressive fatigue performance of cementitious composites remains unclear. Therefore, this paper systematically investigated the effect of CNT with different contents and sizes, functional groups and coating layers on the compressive fatigue performance of cementitious composites, including fatigue life, strength, deformation behavior and cracking characteristics. The morphology of the fatigue fracture surface of cementitious composites shows that CNT can refine pore structure, bridge nano/micro-cracks and result in the generation of the multi-directional and network-like fatigue micro-cracks as well as the appearance of the fatigue striation around aggregates. Consequently, by increasing the integrity among each phase of cementitious composites, CNT significantly maximizes the compressive fatigue life (in logarithmic form), strength and failure strain of cementitious composites by 160%, 43.4% and 20.6%, respectively, showing great potential for extending the service life of concrete structures.

... Videographs with a frame rate of 25 images per second were captured during fatigue loading. More details on the DIC and AE parameters can be found in Keerthana and Chandra Kishen (2020). ...

This study investigated the effect of loading frequency on the fatigue damage process in concrete using digital imaging and acoustic emission techniques. It was found that the complex fatigue damage process in heterogeneous concrete is reflected in the amplitude of acoustic energy. The distribution of acoustic energy levels was utilized to classify micro- and macro-structural activities. It was found that fatigue failure at higher frequencies is governed predominantly by microcracks, while at lower frequencies both micro- and macro-cracks contribute to failure. The applied loading frequency had a marked influence on the size of the fracture process zone (FPZ). A fatigue model encapsulating frequency effects in terms of FPZ width is proposed using a unified damage and fracture mechanics approach within the framework of dimensional analysis and similitude concepts.

... Videographs with a frame rate of 25 images per second were captured during fatigue loading. More details on the DIC and AE parameters can be found in Keerthana and Chandra Kishen (2020). ...

... Videographs with a frame rate of 25 images per second were captured during fatigue loading. More details on the DIC and AE parameters can be found in Keerthana and Chandra Kishen (2020). ...

... There are a large number of pores or micro-cracks in concrete, which may be the original existence of the material, or induced by stress. These defects have a great influence on mechanical properties such as stiffness and strength of materials [1][2][3], and leads to the complex cracking behaviors on material, which have a significant influence on its mechanical properties and failure modes. From meso-level, the concrete can be considered as a composite material, which is composed of aggregate, mortar, pore and interface transition zone (ITZs). ...

The PeriDynamics (PD) model of material fracture can simulate the nucleation and propagation of cracks naturally with a simple bond breakage criterion. Combined with its advantages in multi-scale, the crack characteristics of concrete can be simulated from micro-scale. Therefore, the micro-calculation model of concrete was established by the spherical growth model based on the MATLAB-ABAQUS co-simulation method. Meanwhile, combined with the plastic softening characteristics of concrete, a quasi-plastic damage fracture constitutive model for concrete was established. Finally, the mode-I fracture test and two typical mixed-mode fracture tests were simulated by this model, and the PD-FEM (finite element method) method was used to reduce the calculation cost, in which the cracking regions were set as the PD model and other regions were set as the FEM model. The results show that the crack initiation and propagation of different calculation samples can be well described by the calculation model. Moreover, the proposed material model can better reflect the comprehensive mechanical behavior of concrete, and the crack path of the specimens is consistent with the test results. For the simulation of the I-II (tension shear) mixed fracture test, the crack paths of different calculation samples with small shear load are obviously different, and the range of crack paths can be predicted by the simulation of calculation samples. Furthermore, for the calculation samples with large shear load, the crack path and macro-behavior of different calculation samples are close to each other.

... An example is that plain concrete subjected to repeated uniaxial tensile stresses appeared to fail before N reaches 2 10 cycles regardless of the stress level [14]. To quantify the fatigue damage of materials, different damage variables are introduced, and they are based on fracture mechanics [15][16][17], numerical approach [18,19], or continuum damage mechanics [20][21][22]. The fracture mechanics method estimates fatigue crack propagation by measuring the stress intensity factor which indicates the stress state of the materials. ...

There is limited research reported on the effect of cyclic loading on cement-based repair materials as conducting such tests is time consuming. To overcome this issue, this study utilized a novel loading regime consisting of cycle groups with increasing stress amplitude to accelerate the test process. The Palmgren-Minder rule was used to estimate the fatigue life of repaired specimens. Specimens repaired with Mix M (cementitious repair mortar), which was estimated to have the highest 2-million-cycle fatigue endurance limit (77.4%), showed the longest fatigue life (95,991 cycles) during the cyclic loading test, the highest slant, and splitting bond strength among all repair mixes. The estimated two-million cycle fatigue endurance limit of Mix S (70.8%) was very similar to that was reported in literature (71%) using the traditional loading method. This study confirms the usefulness of Palmgren-Minder rule on estimating the fatigue life of repaired specimens. Additionally, the use of the novel loading regime showed the benefit of shortening the test process while producing results similar to those from using traditional loading methods. To improve the prediction accuracy, future research is required to modify the failure criteria to accommodate specimens that may not fail even when the average flexural strength is met.

The use of microorganisms that induce calcium carbonate or calcite precipitation has been proposed as an alternative to solve cracking problems in cement-based materials and to reduce the environmental impact from construction. This review aims to overview the use of microorganisms in concrete or mortar mixtures to enhance the properties of these materials, and was based on published research. Several microorganisms have been applied to concrete or mortar in different ways over the last decades. These experiments tested mechanical strength, porosity, resistance to aggressive environments and crack healing. The application of microbial suspensions directly into concrete or mortar mixtures showed increased compressive and tensile strengths, decreased porosity and lower penetration of aggressive agents when these materials were exposed to sulfates and chlorides. Other studies applied the microbial culture to specific components of the cement mixture, or immobilized the microorganisms in specific materials, and then added it to the concrete or mortar mixture. These studies demonstrated healing of induced cracks in the samples. Altogether, these results suggest that the application of microorganisms that induce calcite precipitation is viable and effective in enhancing the properties of concrete or mortar and repairing cracks in the material.

Owing to high strength to weight ratio, durability, corrosion resistance and design flexibility, composite materials are extensively used in engineering applications. While these materials have several useful properties, they often exhibit complex failure modes that arise from their heterogeneous microstructure details. A continuum model for composites should accordingly exploit the microstructural information for an accurate prediction of the non-local and non-linear behavior preceding failure. In simulating discontinuities such as cracks, a derivative-free continuum theory – peridynamics, to wit – has an advantage in that the integro-differential balance laws work even with discontinuities. It does not need the special measures required with continuum models using partial differential equations (PDEs) for simulating cracks. In this work, we use a novel non-local variant of the deformation gradient and propose a constitutive model for composite materials within a derivative-free set-up whilst incorporating the microstructural information, which enables a faithful reproduction of the macroscopic response leading to failure. Since concrete is perhaps the most commonly used composite material in large scale engineering applications, we implement the model to study fracture/damage and size effect in concrete. Our results are in close conformity with the experimental data available in the literature. We also show that complex phenomena like crack propagation and branching are accurately simulated via the proposed model with considerably reduced computational overhead.

In order to study the flexural behaviors of concrete beams under monotonic and cyclic loadings, three-point bending tests were performed on center-notched beams made of normal strength concrete (NSC) and high strength concrete (HSC) respectively. From the P-CMOD curves of the beams, it was found that nonlinear deformation occurred before the cracking load. The P-CMOD curves were further normalized to characterize the flexural performance of the beams by a nominal stiffness EIR. Based on the normalized EIR-CMODR curves, formulas for predicting the flexural behaviors of the beams were proposed. With these formulas, the P-CMOD curve of a specimen can be estimated if only the specimen dimension, E, Pmax and CMODun are known. Finally, the P-CMOD hysteresis curve was analyzed, a hysteresis loop model was proposed, and the hysteresis curve of XFEM was adjusted with Python to make it closer to the experimental results.

The critical crack propagation length is essential to calculate the fracture toughness of concrete and the further safety evaluation of the cracked concrete structures. In this study, the critical crack propagation lengths of the notched three-point bending (TPB) beams with various geometric dimensions and concrete strength grades are measured with two experimental methods. One way is to paste strain gauges on the sides of the crack propagation path, and another way is to arrange clip gauges along the depth direction. The results indicate that the effective crack propagation lengths derived based on the existing fracture model are smaller than the experimentally measured critical crack propagation lengths with the maximum relative error of 45%. To obtain the critical crack propagation length with the simple theoretical model accurately, a modified analytical method is proposed, where the elastic equivalent crack propagation length corresponding to 95% of the peak load in the post-peak section is treated as a good approximation of the critical crack propagation length. With the modified method for determining the critical crack propagation length, the fracture toughness of concrete can be derived reasonably. It is expected that the modified method would provide a valuable reference for determining the fracture property of concrete using the small size TPB beams in practical engineering.

In this study, analytical formulations for energy dissipation rate and critical energy dissipation have been derived for concrete under cyclic loading conditions. Initially, the formulation for micro-crack growth rate has been derived adopting nano-mechanistic approach, which subsequently has been extended to express the critical energy dissipation. In order to eliminate the scale effect encountered between the micro and macro-scale stress properties, a multi-scale approach has been adopted in the present work. A new damage parameter has been proposed for the quantification of damage on the basis of critical energy dissipation.

The propagation of fatigue cracks leads to the degradation of the load-carrying capacity of concrete structures and even fatigue failure. An in-depth investigation of the fatigue crack propagation process is essential to reveal the fracture mechanism and further assess the safety of concrete structures. This paper presents an experimental study of mixed mode I–II fatigue crack propagation in concrete. Fatigue tests are conducted on three-point bending (TPB) beams with an off-center initial crack with different fatigue load levels. The digital image correlation (DIC) method is employed to observe the complete fatigue crack propagation process, and the method is verified to be applicable. The results indicate that the mixed mode I–II fatigue crack propagation process can be divided into three stages, namely, the rapid propagation in the initial stage, a stable propagation stage, and the final fast propagation until unstable failure. The mixed mode I–II crack propagation path under static loading is a good approximation of that under fatigue loading. The results also show that the crack tip opening displacement (CTOD), crack tip sliding displacement (CTSD), mode I stress intensity factor (SIF), and mode II SIF corresponding to the unstable failure of the TPB beam are approximately constant and independent of the fatigue load level. In particular, the negligible CTSD and mode II SIF demonstrate that the mixed mode I–II fatigue failure of concrete is dominated by the mode I component.

This study showed a method of selecting appropriate foundation models for fatigue stress analysis of cement concrete pavement. Based on the strength and damage conditions of the base and the correlation between the crack rate of the base (Cb) and modulus of the base (Et), the integrity and stiffness of the base were evaluated. Moreover, the applicability of the base to the Winkler foundation model and the elastic half-space foundation model for each road section was clarified based on the evaluation results. The cement concrete pavement's load stresses and temperature stresses under different technical conditions were calculated by combining the parameters of the thickness of the cement concrete surface layer (hc), modulus of the cement concrete surface layer (Ec), and Et of each road section and the compatible foundation models. The effects of the changes of parameters hc, Ec, and Et on the load and temperature stresses of cement concrete surface layers under different foundation models were also investigated. It was observed that the effects of Ec and Et on the temperature stresses of the cement concrete surface layer are more pronounced compared to hc. hc is the parameter that has the most significant influence on the internal load stress of the cement concrete surface layer. The Winkler foundation model is more sensitive to the change in hc, and the Elastic half-space foundation model is more sensitive to the change of Ec and Et. No matter what kind of technical condition the pavement is and what type of foundation model is adopted, the influence degree of each structural parameter on the load stress of the cement concrete surface layer is not different obviously, and the influence ratio is relatively stable. However, for the temperature stress, under different pavement technical conditions, the changing amplitude of temperature stress caused by the changes of hc, Ec, and Et is significantly different, and the greater the hc is, the greater the influence of the changes of hc, Ec, and Et on the temperature stress is.

To investigate the mechanical properties and acoustic emission (AE) response of cemented tailings backfill (CTB) under the action of compression–shear, 30°, 45°, and 60° variable angle shear tests (VAST) were conducted. Based on the stress–strain law and AE parameter characteristics, the rupture law of the CTB with different shear angles was analyzed. The evolution of the fractal dimension (FD) and b-value and the relationship between them were investigated. The results indicate the following: (1) With increasing shear angle, the peak stress and normal stress show a decreasing trend, the plastic yield stage shortens or disappears, and damage evolution is accelerated; with a shear angle greater than 45°, the specimen deformation and damage mode change. (2) The AE ringing counts and energy evolution at 30° and 45°, and the ringing count evolution at 60° show an inverted U-shaped distribution; the energy evolution at 60° shows a stepped distribution. As the shear angle increases, the active and decline periods move rearward, and the proportion of ringing count and AE events before peak stress decreases. (3) With increasing shear angle, the crack evolution mode of the specimen changes from intermittent local failure repeatedly to progressive expansion. The fracture evolution is a dimensionality reduction and an orderly process; before failure, crack development is a process from disorder to order, producing a state in which large-scale crack propagation stabilizes and small-scale cracks expand. The conclusion provides a basis for analyzing the rupture evolution of CTB under different compression–shear angles and provides a reference for the stability analysis of CTB backfilled goaf.

Developments of scaling laws are crucially important for modeling an engineering phenomenon. Based on the type of physical problems scaling laws have been developed in conjunction with the concept of self-similarity. Scale effect should take into account when the size of an object reduces to extremely small-scale level. Therefore, scaling/power laws and similarity concepts have been considered to be important in nano mechanics in the recent times. In the case of quasi-brittle materials like concrete, crack growth phenomenon can considered as a multi-scale problem comprising of atomistic separation, nano scale level coalesce to form micro and subsequently, major crack. Therefore, it is necessary to have a clear understanding of cracking phenomenon in concrete at different length scales under the action of repetitive loading cycles.
In this work, an attempt has been made out to understand the micro-fracture scale effect on the crack growth rate in concrete material under the action of fatigue loading. A theoretical model has been developed based on atomic fracture mechanics theory. Using the concept, the activation energy controls the random movement of the nano-crack front in the subcritical environment of micro-crack growth within the cyclic fracture process zone of quasi-brittle material. Kramer’s formula has been used for the prediction of net frequency of the forward crack front jumps by assuming, fatigue crack propagation rate is governed by thermally activated breakage of interatomic bonds. A multi-scale transition approach has been adopted from micro to the macro using scaling law considering energy dissipation in each cycle to grow a macro-crack is equal to the sum of the energy dissipations associated with the propagation of all the active micro-cracks inside the cyclic fracture process zone.

This study showed a method for calculating the fatigue stress under different foundation models based on the evaluation results of the thickness, strength, and damage conditions of each structural layer of cement concrete pavement by Falling Weight Deflectometer (FWD) and Ground Penetrating Radar (GPR). This method corrected the deviation of load and temperature stress of cement concrete layer calculated by inaccurate pavement structural parameters under different foundation models. At the same time, we analyzed the influence of pavement structural parameters on the load and temperature fatigue stress and the sensitivity of load and temperature fatigue stress to the change of pavement structural parameters. The research results show that the load and temperature stress of the cement concrete layer in various foundation models are mainly affected by the thickness of the cement concrete layer and the base and are much higher than other structural parameters. Although the influence of structural parameters on load and temperature stress in different foundation models is consistent, the difference of load and temperature stress calculated under different foundation models is pronounced. Therefore, selecting the appropriate foundation model for the fatigue performance evaluation of old cement concrete pavement is particularly important. We recommended selecting the proper foundation model for the fatigue stress analysis of pavement in the future according to the internal structural condition of pavement and the applicable scope of different foundation models.

In this study, a continuum-based model was proposed to characterise the flexural performance and damage evolution process of a plain concrete beam under high-cycle fatigue loads. The plain concrete beam under three-point bending load was modelled by combining the damaged constitutive model of concrete and the Euler–Bernoulli beam theory with varied stiffness. The dynamic stiffness matrix method, in conjunction with the discretization technique, was adopted to solve the nonlinear governing equations of motion. A global damage index corresponding to natural frequencies was introduced to quantify the performance degradation of the beam. To improve the analysis efficiency of the high-cycle fatigue problems, the accelerated algorithm, namely the jump-in-cycle method, was employed in this model. It is demonstrated that the numerical results agree well with the experimental data under fatigue harmonic loads. Performance degradation under fatigue bending loads only occurs at the midspan of the beam. Adopting the jump-in-cycle methods significantly improves the analysis efficiency of the high-cycle fatigue problem, and the calculation time is reduced by approximately 90% compared with the cycle-by-cycle method. This model is capable of rationally predicting damage evolutions, stiffness degradation processes, stress redistributions, and loading level-fatigue life (S–N) curves and can provide a basis for simulating the flexural behaviours of reinforced concrete (RC) beams under fatigue bending loads.

Представлены основные результаты совместного российско-индийского проекта «Исследование процессов деформирования и разрушения конструкционных материалов с учетом их многоуровневого структурного состояния для обеспечения прочности, надежности, долговечности и безопасности высоконагруженных конструкций». В рамках совместного проекта было осуществлено комплексное расчетно-экспериментальное исследование процессов деформирования и разрушения образцов и конструктивных элементов выполненных из двух типов основных конструкционных материалов: (1) металлических имеющих выраженные участки упругого и пластического деформирования в широком диапазоне деформаций с сопоставимыми диаграммами деформирования в области растяжения и сжатия; (2) бетонов, имеющих сопоставимую с металлом упругую деформацию и низкую неупругую составляющую деформаций, и существенно различающиеся диаграммы растяжения и сжатия. Выполненные российскими и индийскими специалистами сопоставительные исследования прочности, деформативности, трещиностойкости, безопасности и рисков конструкций из металлических и цементных композиций показали принципиальную возможность использования унифицированных моделей деформирования, повреждения и разрушения и определяющих уравнений линейного и степенного вида с существенно различающимися параметрами этих уравнений.

The fracture process zone (FPZ) was investigated on unnotched and notched beams with different
notch depths. Three point bending tests were realized on plain concrete under crack mouth opening
displacement (CMOD) control. Crack growth was monitored by applying the acoustic emission (AE) technique.
In order to improve our understanding of the FPZ, the width and length of the FPZ were followed based on
the AE source locations maps and several AE parameters were studied during the entire loading process. The bvalue
analysis, defined as the log-linear slope of the frequency-magnitude distribution of acoustic emissions, was
also carried out to describe quantitatively the influence of the relative notch depth on the fracture process. The
results show that the number of AE hits increased with the decrease of the relative notch depth and an
important AE energy dissipation was observed at the crack initiation in unnotched beams. In addition, the
relative notch depth influenced the AE characteristics, the process of crack propagation, and the brittleness of
concrete.

In this paper, the fatigue behavior of concrete subjected to combined stresses in the compression-tension region of the biaxial stress space is studied. Hollow cylindrical concrete specimens are subjected to combined stresses through torsional loading. The load-deflection responses of specimens subjected to cyclic and constant amplitude fatigue loading are presented. Damage imparted to the specimens during cyclic and fatigue loading processes was monitored using mechanical measurements and a nondestructive evaluation technique based on the measurement of structural resonance frequencies of vibration. The complete load response of the specimen subjected to cyclic loading was obtained by unloading the specimen at different points in the postpeak part (descending branch) of the quasistatic response. Changes in the resonant frequencies during the loading procedure were monitored. Fatigue tests were performed to failure with three different torsional load ranges. The decrease in rotational stiffness duringfatigue tests was obtained from mechanical measurements, and the resonance frequencies are presented. It was observed that the decrease in rotational stiffness at failure for the constant amplitude fatigue loading was comparable to the corresponding load in the postpeak part of the quasistatic response. The number of cycles to failure is closely related to the rate of the reduction of stiffness of the specimen as well as the resonant frequencies in linear portion of the fatigue response. This relationship is independent of the applied load range. The fatigue failure of concrete subjected to torsional loading is a local phenomenon similar to failure for quasistatic loading; the damage is seen to localize to a crack in the first few cycles, and the subsequent fatigue behavior is governed by the propagation of that crack. An approach for predicting the fatigue life and the stiffness of a pavement structure is finally presented using the results of this paper.

Digital Image Correlation (DIC) is an important and widely used non-contact technique for measuring material deformation. Considerable progress has been made in recent decades in both developing new experimental DIC techniques and in enhancing the performance of the relevant computational algorithms. Despite this progress, there is a distinct lack of a freely available, high-quality, flexible DIC software. This paper documents a new DIC software package Ncorr that is meant to fill that crucial gap. Ncorr is an open-source subset-based 2D DIC package that amalgamates modern DIC algorithms proposed in the literature with additional enhancements. Several applications of Ncorr that both validate it and showcase its capabilities are discussed.

This paper presents a structural health monitoring methodology that uses Acoustic Emission (AE) features to predict the crack growth in structural elements subjected to fatigue. This allows for the prediction of the failure of the structural element at the current load level. The methodology uses Bayesian inference to account for different sources of uncertainty such as: uncertainty in the data (AE signal), unknown fracture mechanics parameters and model inadequacy. The methodology is divided in two main components: a model updating component that uses available data to build a joint probability distribution of the different unknown fracture mechanics parameters, and a prognosis component in which this multivariable probability distribution is sampled to predict the stress intensity factor range at a future number of cycles. The application of the methodology does not require the knowledge of the load amplitude nor the initial crack length. The methodology is validated using experimental data from a compact test specimen under cyclic loading.

In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (K(IC)). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage when there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the R-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.

Threshold condition and rate of fatigue crack growth appear to be significantly affected by the degree of deflection of cracks. In the present paper, the reduction of the fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared to that for a straight counterpart is quantified via the Paris–Erdogan law modified according to some simple theoretical arguments. It is shown that such a reduction increases as the value of the kinking angle increases. Then, a so-called ‘continuously-kinked crack’ (the kink length tends to zero) is considered and modelled as a self-similar invasive fractal curve. The sequence of kinking angles in the crack is such that the fatigue crack path is ‘on average’ straight. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. It is shown that the fatigue crack growth rate in the Paris range depends not only on the above fractal dimension and in turn on the kinking angle, but also, in an explicit fashion, on the crack length. Some experimental results related to concrete and showing a crack size effect on the fatigue crack growth rate are analysed.

An acoustic emission (AE) is a localized rapid release of strain energy in a stressed material. Quantitative acoustic emission measurement techniques have recently been developed to estimate the location, size, orientation, and fracture mode of individual microcracks. Quantitative AE techniques were applied to a laboratory study of plain concrete beams under four point loading. Center-notched and off-center-notched beams were loaded in order to produce, respectively, mode I and mixed mode failure. Using AE seismic moment tensor representation, microcracking was characterized as mode I, mode II, or mixed mode. The mode of microcracking was compared to the mode of the visible crack. Most microcrack planes were in a direction normal to the tensile stress for a mode I macrocrack (center-notched), whereas microcrack planes were relatively uniformly distributed for a mixed-mode macrocrack (off-center notched). A large number of mixed-mode microcracks were observed even for the center-notched beam indicating that fracture mechanisms of microcracks may differ from the main macromechanical crack. It is shown that AE measurements can provide a potentially powerful tool in assessing damage.

A series of experiments has been conducted to determine the effect of loading variables such as cyclic frequency, load ratio,
and material on acoustic emission from fatigue-crack propagation. It is shown that the applied-stress intensity range (ΔK) is the controlling parameter for all materials studied while the other parameters have lesser effects. Two potential methods
for engineering application of acoustic emission during fatigue loading are described.

During the fracture of concrete the formation of microcracks is a continuous process where new microcracks are formed in the vicinity of the macrocrack. As the fracture grows, these microcracks interact with the macrocrack and disrupt its smooth opening. In fracture mechanics based approaches; a smooth stress-crack opening softening behaviour is generally used to describe the local fracture process, where the effect of micro-macro crack interactions is lacking. This paper presents firstly an experimental study on the interaction between microcracking and the macrocrack opening (COD) in concrete using digital image correlation and acoustic emission techniques. The study reveals a transient behaviour of macrocrack opening as microcracks are formed in the surrounding. Based on the experimental results, the paper presents a new approach based on fracture mechanics to consider the effects of micro-macro crack interaction on the stress-crack opening softening behaviour. Local fracture energy is determined using the new softening model with micro-macro crack interaction for different geometrically similar sizes of the beams and at different locations on the crack profile.

In this work, an attempt has been made to understand the evolution of fracture process zone in plain concrete member utilizing Digital Image Correlation (DIC) technique. Series of experiments have been performed in centre point bending under the action of monotonic and repetitive loadings and DIC technique is used during the entire test process. A systematic procedure has been developed to monitor the evolution and propagation of the fracture process zone and traction free crack. Size of fully developed FPZ has been found to be approximately equal in both static and fatigue loading cases. It has been also seen that traction free crack propagation has occurred only in medium and large size beams. DIC analysis results have been compared with the measured CMOD values through validation study and both are found to be in good agreement. An analysis has been performed for evaluating the resolution and standard uncertainty in the DIC measured displacements and strains.

A three-dimensional (3D) realistic numerical modelling method is proposed to simulate the fracture process of concrete based on its meso-structure. In the 3D realistic numerical modelling method, CT technology is first applied to capture the microstructure of the concrete as a series of cross-sectional CT images. An improved digital image processing (DIP) technique is then developed to identify and characterize the aggregates and the interfacial transition zones (ITZ) in the CT images. After that, a 3D realistic three-phase structure model of the concrete is reconstructed on the basis of the processed CT images using the vectorized transformation and volume rendering method, which is integrated into a well-established 3D Realistic Failure Process Analysis (RFPA3D) code. In this way, the 3D realistic numerical modelling method is developed. It is validated by building a 3D realistic numerical model of the concrete and comparing the results between numerically and experimentally obtained. Finally, using the 3D realistic numerical modelling method, the effects of the ITZ strength on the fracture process of the concrete under uniaxial compression and tension are studied and further clarified. The proposed 3D realistic numerical modelling method provides a new tool to study the fracture mechanism of concrete at the mesoscopic/microscopic levels under complex loading conditions.

A fatigue model for plain concrete under variable amplitude loading is proposed by unifying the concepts of damage mechanics and fracture mechanics through an energy equivalence, in conjunction with the principles of dimensional analysis and self-similarity. The effects of stress ratio and overloads that accelerate the crack growth rate is included in the model, in order to capture the realistic behaviour under variable amplitude loading. Experiments are performed under variable amplitude fatigue loading in order to calibrate and verify the validity of the model. The model proposed in this work encapsulates the complex behaviour of concrete under fatigue and provides a more rational method for computing fatigue life of concrete structures.

An experimental investigation of the behavior of fiber reinforced concrete under cyclic flexural loading is presented. One type of polypropylene and two types of steel fibers in two different volume concentrations are studied. Load-deflection response is obtained for constant amplitude fatigue loading as well as for static loading. The damage level is recorded under static and fatigue loading using acoustic emission techniques. Data is presented in terms of complete load-deflection diagrams (for static loading) and in terms of S-N diagrams (for fatigue loading). Damage evolution is described in terms of acoustic emission activity as a function of deflection (static loading) or cycles (fatigue loading). The test results show that the addition of steel fibers increases the flexural fatigue strength considerably. Compared with plain concrete the fatigue strength for 2 million cycles is changed from 60 percent to 90 percent of the ultimate flexure strength when the steel fiber content is 1 volume percent. High-fiber volume concentrations (2 percent) further increase absolute fatigue strength; however, fatigue performance measured relative to the static strength is decreased compared to the lower fiber volume concentration. Furthermore, the results show that the accumulated damage level at failure in the static test of unreinforced concrete is of the same order of magnitude as in the fatigue testing of the same material. However, using fiber reinforced concrete the accumulated damage level in fatigue testing is 1-2 order of magnitude higher than the level reached in static testing of the same material. Finally, the tests show that the deflection at failure of the fiber reinforced concrete specimens under constant stress range fatigue loading can be predicted using the static load-deflection curve, provided the testing time is short enough to neglect creep effects.

Sealed specimens of paste and concrete were tested under the maximum cyclic or sustained compressive stresses of 60 to 90% of the ultimate stress. Volumetric strains, ultrasonic velocity and attenuation, and internal microcrack propagation were examined. Sustained or cyclic loading resulted in progressive crack propagation. Crack growth under sustained stresses appeared to result from the phenomenon of stress corrosion while under cyclic loading the process of load repetition played an important role.

Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with the size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of a size-adjusted stress intensity factor. The size adjustment is based on the brittleness number of the structure, representing the ratio of the structure size d to the transistional size d0, which separates the responses governed by nominal stress and stress intensity factor. Experiments show that d0 for cyclic loading is much larger than d0 for monotonic loading, which means that the brittleness number for cyclic loading is much less than that for monotonic loading. The crack growth is alternatively also characterized in terms of the nominal stress amplitude.

In this work we are interested in how micromechanical phenomena affect bulk mechanical properties. Specifically we are interested in microfracture characteristics and how they influence damage evolution and fracture toughness. Toward this end, quantitative acoustic emission techniques were used to measure microfracture properties in an array of cement-based materials of varying microstructure. Microcracks were modeled using a seismic moment tensor, which could be estimated through deconvolution of the measured acoustic emission waveforms. Results of the experiments indicate that materials with higher bulk fracture toughness had larger numbers of sliding mode microcracks, while materials with lower bulk fracture toughness had fewer numbers of tensile mode microcracks.

When concrete is subjected to uniaxial compression, the failure process is normally initialed from a localized zone. The localization of failure governs structural behaviors of concrete. In particular, the post-peak region of load–deformation curve is greatly affected. Therefore, it is necessary to investigate the extent of the localized failure zone in compression. In this study, acoustic emission (AE) method is applied to distinguish the damage level of concrete, because the method can be applied to quantify the damage in concrete structures. The length of compressive failure zone is quantified by AE activity, which is compared with visual observation of cracks, the distribution of the local energy consumption by the acrylic rod method, and the calculated length by the simplified relation. Then, AE method is applied to a reinforced concrete deep beam which fails under shear compression, and of which two dimensional failure zone is identified.

The acoustic emission technique is used for monitoring the fatigue crack growth in plain concrete beams under three-point loading. Variable amplitude loading with step-wise increase in the maximum load is applied. The fatigue crack growth is continuously monitored using six acoustic sensors. The results of load, displacement, crack mouth opening displacement, acoustic events, and acoustic energy are simultaneously acquired during the test. It is seen that a Paris law type of relationship exists between the rate of increase of acoustic emission count per cycle and the stress intensity factor range. Using b-value analysis, different stages of fatigue fracture is explained.

This study investigated acoustic emission behavior during fatigue crack growth test under constant and variable amplitude loading in 304 stainless steel. To describe the acoustic emission behavior, counts rate(dη/dn) was related with stress intensity factor range (SIFR, ΔK) in log-log plot. As a result of test, the relationship was represented a curve, which forms rise and fall behavior in counts rate as the SIFR increases. AE response to a single overload was sudden drop and slow recovery in counts rate, which was similar to crack growth retardation behavior. Under block loading, counts rate of each loading block was same as that of constant amplitude loading. Overall experimental results indicated that stress intensity factor controls the counts rate (dη/dn) as well as crack growth rate (da/dn) regardless of load range or crack length.

Center-notched mortar plate specimens are loaded in tension. A multiple sensitivity vector holographic setup is developed to record several deformation stages during the stable crack propagation range. The three-sensitivity vector setup enables the calculation of both crack opening displacements and strain fields around the crack trajectories. An image analysis system is used to isolate the interferometric effect from the sandwich holograms, resulting in fringe patterns with perfect contrast. Image analysis is also used as a faster, more accurate, and more consistent method for fringe count. After evaluation of the holograms, the existence of tensile forces transmitted through the crack faces is associated with the presence of tensile strain behind the crack tip. A definition of the fracture process zone (FPZ) is proposed based on the difference between experimentally observed and linear elastic fracture mechanics (LEFM) strain fields. Deviations from the linear elastic solution show a relatively small zone of nonlinearity in front of the crack tip and a wake fracture process zone (WFPZ) behind the crack tip. A cohesive crack type of model with a bilinear closing process zone is used to predict the experimental observations.

Experiments were carried out with X-rays using contrast medium and three-dimensional (3D) Acoustic Emission (AE) techniques to investigate the behavior of the fracture process zone in concrete. The results show that, as the loading increases, a zone consisting of numerous microcracks accompanied by AE events develops ahead of the notch tip in the concrete compact tension specimen. The energy of each individual AE event was calculated and plotted on the (3D) map. The results obtained by the two methods were compared and related to provide a clear view of the fracture process zone of concrete.

This paper focuses on the development of a thermodynamic approach to constitutive modelling of concrete materials, with emphasis on the use of non-local damage models. Effort is put on the construction of a consistent and rigorous thermodynamic framework, which readily allows the incorporation of non-local features into the constitutive modelling. This is an important feature in developing non-local constitutive models based on thermodynamics. Examples of non-local constitutive models derived from this framework and numerical examples are given to demonstrate the promising features of the proposed approach.

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation.

Acoustic emission (AE) has been used to investigate characteristics of the fracture process zone (length, width and macro crack propagation) in a concrete specimen subjected to four-point bending, using probability and statistical methods. To understand the process of crack growth and fracture, a technique based on AE has been developed. The results are treated according to the laws of probability and statistics. It is shown that these results agree more or less in comparison to those obtained using other techniques.

Extensive research and studies on concrete fracture and failure by means of the acoustic emission (AE) technique have shown that fracture and damage growth can be characterized through a single synthetic parameter, namely the b-value, which changes systematically during the different stages of the failure process, as shown by several AE tests carried out from the specimen to the structural scale [Sammonds PR, Meredith PG, Murrel SAF, Main IG. Modelling the damage evolution in rock containing porefluid by acoustic emission. In: Proceedings of the Eurock’94; 1994; Colombo S, Main IG, Forde MC. Assessing damage of reinforced concrete beam using “b-value” analysis of acoustic emission signals. J Mater Civil Eng ASCE 2003;15:280–6; Carpinteri A, Lacidogna G, Niccolini G. Critical behaviour in concrete structures and damage localisation by Acoustic Emission. Key Eng Mater 2006;312:305–10]. This parameter can be linked to the value of the exponent α of the power-law distribution of the crack size in a damaged structure. In this paper, we propose a statistical interpretation for the variation of the b-value during the evolution of damage, based on a treatment originally proposed by [Carpinteri A. Mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. Dordrecht: Martinus Nijhoff Publishers; 1986; Carpinteri A. Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics. Int J Solid Struct 1989;25:407–29; Carpinteri A. Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solid Struct 1994;31:291–302]. The proposed model captures the transition from the condition of criticality, in which α = 3, to that of imminent failure, characterized by α = 2, in terms of damage localisation.

Recently acoustic emission (AE) techniques have been used to study crack propagation in materials. The application of these techniques to heterogeneous, quasi-brittle materials such as concrete requires a better understanding of how the signal generated from a microfracture is transformed due to wave propagation and due to the transducer response. In this study, piezoelectric transducers were calibrated using displacement transducers. The validity of an elastodynamic Green's function approach was examined for cement-based materials. The acoustic emission source was characterized using moment tensor analysis. Acoustic emission measurements were analyzed for center-cracked-plate specimens of mortar and concrete. It was observed that, as expected, the dominant mode of cracking was mode I (tensile). However, mode II (shear) and mixed mode cracks also occurred, perhaps due to grain boundary sliding and interface debonding. Microfractures appear to localize prior to critical crack propagation. Mode I cracks generally required more energy release than mode II and a smaller inclusion provided a stronger interface bond than the larger ones.

In this study, three-point bending tests were carried out on notched beams to investigate mode I crack propagation in plain concrete under fatigue. The first part of the study focused on microscopic observations of the crack growth features. Microscopic observations were made using the replica method associated with scanning electron microscopy (SEM). Observations of fatigue crack growth both on the surface and inside the specimens are presented as a comparison between the observed crack lengths and those estimated by the compliance calibration method. In the second part, a finite element model of mode I crack propagation under fatigue is presented. According to the cohesive crack concept, a cohesive force distribution on the crack at various loading stages is assumed, according to both the stress-crack opening relation worked out by Hordijk (1991; Thesis, Technische Universiteit) and a new proposed relation with hysteresis loop. Finite element computation is used to evaluate the crack extension in the bending beams. Numerical predictions are discussed in comparison with experimental results. Copyright © 2002 John Wiley & Sons, Ltd.

The method of compliance calibration for estimating crack growth in notched beams of metallic materials and nonmetallic materials such as rock has been used extensively with success. This method has also been used with concrete, but recently its suitability for this material has been questioned. The validity of this method has been evaluated using concrete beams in three-point bending in which the crack surface is revealed by a dye-penetrant technique.
The results of this study, which utilized twelve specimens precracked to varying depths and thirteen companion specimens using 0.076-mm thick Teflon notches of various depths, are presented. It was found that the compliance estimates of crack length agreed exactly with the actual length for the beams with Teflon notches. For the precracked beams the compliance estimates for crack length were in good agreement with the actual length observed at the beam surface (thus confirming previously reported results) but were greater than the average crack length revealed by dye.

This report contains results of acoustic emission studies on flawed and unflawed specimens of aluminum and beryllium. Acoustic emission from the flawed specimens is found to begin at stress levels far below the general yield stress. A theoretical model given here indicates that the total number of acoustic emission signals from a specimen containing a crack should be proportional to the fourth power of the stress intensity factor obtained from a sharp-crack fracture mechanics analysis. This is in disagreement with experimental data from single-edge-notched fracture toughness specimens of the two materials, which indicate that acoustic emission varies more like the sixth to eighth power of the stress intensity factor. An example is given to show how the acoustic emission data obtained on fracture toughness specimens can be used to nondestruetively test the fracture strength of an engineering structure.

The size effect on the fracture process zone in notched and unnotched three
point bending tests of concrete beams is analysed by a meso-scale approach.
Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft
matrix separated by weak interfaces. The mechanical response of the three
phases is modelled by a discrete lattice approach. The model parameters were
chosen so that the global model response in the form of load-crack mouth
opening displacement curves were in agreement with experimental results
reported in the literature. The fracture process zone of concrete is determined
numerically by evaluating the average of spatial distribution of dissipated
energy densities of random meso-scale analyses. The influence of size and
boundary conditions on the fracture process zone in concrete is investigated by
comparing the results for beams of different sizes and boundary conditions.

The use of acoustic emission to investigate fracture process zone in notched concrete beams. Current Sci

- H Hadjab
- J.-F Thimus
- M Chabaat

Hadjab, H., Thimus, J.-F., Chabaat, M., 2007. The use of acoustic emission to investigate
fracture process zone in notched concrete beams. Current Sci. 648-653.