Load-crack Mouth Opening Displacement Curves Research Articles

Bending damage and fractal characteristics of steel fiber-reinforced concrete under three-point bending test

Steel fiber-reinforced concrete (SFRC) has outstanding mechanical properties and is widely used in the construction industry. To investigate the damage characteristics of SFRC beams with different steel fiber (SF) contents (0, 15, 30, 45, and 60 kg/m3) accurately, this study analyzed the bending damage (including the load-crack mouth opening displacement curve, flexural–tensile strength, fracture toughness, and microstructure and macrostructure) and fractal characteristics of SFRC beams under three-point bending tests. The crack propagation process in the SFRC beams was monitored by the digital image correlation technique. Information on microcrack evolution and macrocrack development during the loading process was collected using acoustic emission techniques. Furthermore, the correlation dimension reflecting the development state of the cracks was obtained based on the Grassberger–Procaccia algorithm. Test results showed that the performance of concrete beams in terms of deformation and cracking significantly improved by adding SFs. The beam with an SF content of 45 kg/m3 had the highest flexural–tensile strength of 6.979 MPa, which was 1.668 times higher than that of a plain concrete beam. The beam with a 60 kg/m3 SF content had the highest fracture toughness of 1.691 MPam1/2, which was 53.87% higher than that of the plain concrete beam. The fractal analysis results showed that when the correlation dimension increased, numerous small-sized, low-evolution microcracks accumulated in the fracture process zone. When the correlation dimension decreased, the microcracks converged and formed macrocracks. The peak value of the correlation dimension can be used as precursor information for SFRC beam fracture prediction.

Three-dimensional numerical study on mode-I local crack propagation of concrete considering boundary effect

A three-dimensional numerical method considering the boundary effect on fracture energy and initial fracture toughness was proposed to simulate the whole propagation process of mode-I local crack in concrete. The initial fracture toughness-based criterion was employed to determine the propagation of local crack surface. The numerical analyses were carried out to obtain the initial cracking load, peak load and load-crack mouth opening displacement curves for a series of concrete beams with a local crack of different sizes. Comparing with the experimental results performed in this study, the numerical results showed good agreements and applicability of the proposed method was verified. After that, the numerical analyses were conducted on the whole fracture process of local crack in concrete. The results indicated the local crack of three-point bending beam always propagated along the thickness direction firstly on the bottom surface of the specimen. The crack front was basically parallel to the upper boundary of specimen after the load decreased to 40%Pmax. For beams with a local crack of different sizes, the variations of the ratio of crack propagation area to ligament area with the ratio of load to peak load were the same so that a function expression was given to predict the increment of crack surface area under different loads. In addition, the fracture process zone evolution during the local crack propagation was discussed.

Micromechanics-based model of single crack propagation in Engineered cementitious composites (ECC)

Engineered Cementitious Composites (ECC) are composites exhibiting strain-hardening behavior accompanied by the formation of multiple cracks. A special feature of ECC is the ability to tune the material composition to meet the different needs of various structural components, which benefits from the special micromechanics-based design theory of ECC. However, these existing micromechanics-based design theories are specific to the case of direct tension and has not been fully discussed and developed for the case where the ECC is subjected to bending load. In this study, a micromechanics-based crack propagation model for ECC under bending load is developed to guide the design of flexural performance of ECC. The entire crack propagation process is simulated by considering the microstructure of ECC and the crack propagation criterion. For ECCs with different types of fiber, the simulated load-crack mouth opening displacement curves agree well with experimental results and the dispersion of the ECC specimens can be captured by imparting randomness to the model. Based on this model, parametric studies of several representative parameters are performed to illustrate the applicability of the model. The results indicate that the material has a higher ultimate flexural bearing capacity near a fiber aspect ratio of 448 for the given material property parameters; and the fiber/matrix bonding should not be excessively strong. Insights from this model can facilitate the design of ECC members with excellent bending properties through fiber tailoring and surface treatment.

Tensile Performance Test Research of Hybrid Steel Fiber-Reinforced Self-Compacting Concrete.

Notched beam specimens were loaded by the three-point bending test device, and the effects of different volume contents and combinations of steel fibers on the tensile properties of hybrid steel fiber-reinforced self-compacting concrete (HSFRSCC) were studied. The failure law and strain field distribution of the specimens were studied by digital image correlation (DIC) technology. Moreover, the curves between the load and crack mouth opening displacement (CMOD) of 18 groups of hybrid steel fiber-reinforced concrete specimens were obtained, and the stress-strain curves of 18 groups of specimens were derived from the load-CMOD curves. The results show that both single and hybrid steel fibers can improve the crack deformation resistance and tensile properties of concrete, but hybrid steel fibers have a more significant improvement effect. Only when the content of steel fiber is more than 0.6% can it have a more obvious postpeak descending section, and hybrid steel fiber has higher postpeak deformation capacity and flexural toughness. The fundamental reason why concrete with hybrid steel fibers has better tensile properties is that micro and macro steel fibers cooperate with each other to resist cracks, improving the toughness of concrete after cracking. Finally, the mechanism of different size and volume content of steel fiber was analyzed from the micro level, which can be used as a reference for the engineering design of HSFRSCC in the future.

Discrete modeling of concrete failure and size-effect

Size-effect in concrete and other quasi-brittle materials defines the relation between the nominal strength and structural size when material fractures. The main cause of size-effect is the so-called energetic size-effect which results from the release of the stored energy in the structure into the fracture front. In quasi-brittle materials and in contrast to brittle materials, the size of the fracture process zone is non-negligible compared to the structural size. As a consequence, the resulting size-effect law is non-linear and deviates from the response predicted by linear elastic fracture mechanics. In order to simulate the size-effect, one needs to rely on numerical modeling to describe the formation, development and propagation of the fracture process zone. Although a number of models have been proposed over the years, it transpires that a correct description of the fracture and size-effect which accounts for boundary effects and varying structural geometry remains challenging. In this study, the Lattice Discrete Particle Model (LDPM) is proposed to investigate the effects of structural dimension and geometry on the nominal strength and fracturing process in concrete. LDPM simulates concrete at the aggregate level and has shown superior capabilities in simulating complex cracking mechanisms thanks to the inherent discrete nature of the model. In order to evaluate concrete size-effect and provide a solid validation of LDPM, one of the most complete experimental data set available in the literature was considered and includes three-point bending tests on notched and unnotched beams. The model parameters were first calibrated on a single size notched beam under three-point bending and on the mechanical response under unconfined compression. LDPM was then used to perform blind predictions on the load-crack mouth opening displacement curves of different beam sizes and notch lengths. Splitting test results on cylinders were also predicted. The results show a very good agreement with the experimental data. The quality of the predictions was quantitatively assessed. In addition, a discussion on the fracturing process and dissipated energy is provided. Last but not least, the Universal Size-Effect Law proposed by Bažant and coworkers was used to estimate concrete fracture parameters based on experimental and numerical data.

Fracture Mechanical Properties of Steel Fiber Reinforced Self-Compacting Concrete under Dry–Wet Cycle Sulfate Attack

Sulfate attack is the most common form of the durability damage of hydraulic concrete, and the performance degradation of cracked structural components is more significant at the position of water level change. Fly ash, a widely utilized supplementary cementitious material, can effectively improve the durability of concrete. In this paper, fly ash was used to partially replace Portland cement at 0 w%, 40 w%, 50 w%, 60 w%, and 70 w%, respectively. Through the three-point bending beam test with notch and the dry–wet cycle of sulfate attack, the change law of the fly ash content on the fracture mechanical properties of steel fiber reinforced self-compacting concrete (SFSCC) and its degradation mechanism under sulfate attack was studied. The results show that the load–crack mouth opening displacement curve of SFSCC changed from a steamed bread peak to a sharp peak under 30 dry–wet cycles of sulfate attack. The fracture toughness, peak load, and fracture energy of SFSCC with a high-volume fly ash increased with the increase in the fly ash content, while they reversed after sulfate attack. When the percentage of fly ash was 70 w%, the retention ratio of the fracture parameters was lower than that of SFSCC without incorporating fly ash, and when the percentage of fly ash was 50 w%, SFSCC had good bearing capacity, fracture mechanical properties, and corrosion resistance. The corrosion product of the reference SFSCC with 30 dry–wet cycles of sulfate attack was ettringite, whereas the SFSCC with a high-volume fly ash had no obvious corrosion products and the microstructure became looser.

Phase-field modeling of fracture in high performance concrete during low-cycle fatigue: Numerical calibration and experimental validation

The development of an elasto-plastic phase-field model is presented which is able to predict nonlinear behavior of high performance concrete (HPC) during low-cycle fatigue. An elasto-plastic damage model which follows the Drucker–Prager yield criterion is formulated. For the modeling of unsymmetric tension–compression behavior of HPC two different continuous stepwise linearly approximated degradation functions for HPC in tension and in compression are used. The experimental three-point bending tests at low-cycle using notched beams of pure HPC are performed. Load–CMOD (crack mouth opening displacement) curves are plotted using the measured experimental data and residual stiffness–CMOD curves are calculated using these experimental Load–CMOD curves. The data used for the interpolation of degradation functions are calibrated using the experimental results for three-point bending tests. For that purpose the uniaxial tension and uniaxial compression tests and three-point bending beam test for HPC are simulated numerically. The accuracy of the proposed numerical model using the presented integration algorithm is verified by comparing the degradation of stiffness in numerical and experimental results.

Experimental investigation on the elastic modulus and fracture properties of basalt fiber–reinforced fly ash geopolymer concrete

A comprehensive experimental study was conducted to explore the fracture characteristics of basalt fiber–reinforced fly ash geopolymer concretes (FAGCs) with different fiber contents (0.025%, 0.05%, 0.1%, 0.15%). The fracture behaviors of the basalt fiber–reinforced FAGCs, such as load-crack mouth opening displacement curve, fracture toughness, fracture energy, crack propagation length, were investigated by three-point bending tests, and their strengthening mechanisms were explored by scanning electron microscopy. In addition, the Mori–Tanaka homogenization (MTH) method was introduced to analyze the elastic properties of the basalt fiber–reinforced FAGCs. It was found that the addition of basalt fibers improved the peak load, fracture toughness, and fracture energy of the basalt fiber–reinforced FAGCs, and the most significant improvements were noticed in the concrete with the basalt fiber content of 0.05%. Moreover, a decrease in the crack length of the basalt fiber–reinforced FAGCs was observed before the load level of the post-80% peak load. The elastic properties of the basalt fiber–reinforced FAGCs were analyzed based on the MTH theory, and numerical results were found to be in good agreement with experimental findings.

Effect of notch depth ratio on mode I and mixed mode I-II fracture properties of engineered cementitious composites (ECC)

The effect of initial notch depth ratios (a/h) on the mode I and mixed mode I-II fracture properties of ECC was studied by using three-point bending test and four-point shear test, respectively. For mode I fracture, the initial fracture toughness KICini and unstable fracture toughness KICun- and KICun+ instead of KICun based on double-K fracture criterion are calculated. The mode I fracture energy GI is calculated by load-crack mouth opening displacement curve (P-CMOD). For mixed mode I-II fracture, the initial effective stress intensity factor (Keffini) are calculated by using nonlinear finite element software and the mixed mode fracture energy GI–II is analyzed. Also, crack propagation mechanism of ECC under mixed mode I-II fracture is analyzed from P-CMOD curve and load-crack mouth sliding displacement (P-CMSD) curve, and mixed mode I-II crack propagation of ECC is divided into six stage. It is found that when 0.3 ≤ a/h ≤ 0.8, the KICini does not change. While, KICun increases when a/h increases from 0.1 to 0.3, decreases when a/h increases from 0.3 to 0.7 and GI decreases with the a/h increasing from 0.3 to 0.8. GI–II is much larger than GI due to an obvious inclined fracture process zone with many micro-cracks dissipating energy in the mixed mode I-II fracture. The GI–II increases with the a/h increasing from 0.1 to 0.6 and decreases with the increase of the a/h from 0.6 to 0.8. While, the crack initiation angle increases with the increase of a/h in the mode I-II fracture.

Fatigue Fracture Investigation of Engineered Cementitious Composites

Abstract The fracture failure and crack propagation of engineered cementitious composites (ECC) are analyzed based on extended finite element method (XFEM) simulation and experiment. Three-point bending notched beam under static and fatigue load is employed in this research. As a result, the peak loads in the experiment were consistent with simulation results, while the simulated crack mouth opening displacement (CMOD) values corresponding to the peak loads were generally smaller than the experimental results. In addition, it was observed that a single crack’s propagation occurred along the initial notch in numerical simulation rather than multiple cracks’ propagation. Though the cycle times of fatigue load were short in the simulation of fatigue fracture under low-stress level and high cycle frequency, the loading cycle frequency had a negligible influence on simulation. However, the higher the stress level was, the greater the effect of the loading cycle frequency on the simulation results. A higher loading frequency will reduce the model’s load carrying capacity. The results showed that the XFEM can simulate the crack propagation behavior and get the strain hardening vertical load–CMOD curve of ECC to a certain extent. XFEM provides a convenient way to solve complex practical engineering problems of ECC with the strain hardening property.

Influence of steel fibers on the flexural performance of concrete incorporating recycled concrete aggregates and dune sand

The flexural performance of steel fiber-reinforced concrete made with recycled concrete aggregates (RCA) and desert dune sand was investigated. Natural aggregates were replaced by 30, 70, and 100% RCA. Steel fibers were incorporated into mixes in 1, 2, and 3% volume fractions. To evaluate the flexural behavior of plain and steel fiber-reinforced RCA concrete mixes, three- and four-point bending tests were conducted. Experimental results showed that RCA replacement had a predominant impact on compression behavior compared to steel fiber addition, while the latter was more influential on flexural performance. Higher pre-peak slope, flexural strength, deflection, toughness, and equivalent flexural ratio were noted when steel fibers were added to RCA-based concrete tested under four-point bending. Similar improvement in flexural performance was reported from load-crack mouth opening displacement curves of three-point bending tests. Accordingly, analytical regression models were developed to correlate the different properties obtained from these two flexural bending test results.

TEST STUDY ON THE BEST PASTING LAYER OF FRP REINFORCED CONCRETE

To optimize the strengthening method using the fiber reinforced polymer (FRP) for the reinforcement of the concrete structure with cracks, the three-point bending test was conducted on the concrete beams wrapped with different layers of FRP materials. The strain gauges were pasted on the surface of the specimens to measure the initial cracking load. The crack mouth opening displacement (CMOD) was utilized to test the load–crack mouth opening displacement curve. According to the improved calculation formula of the fracture toughness, the critical effect crack length [Formula: see text], initiation fracture toughness [Formula: see text] and instability fracture toughness [Formula: see text] of specimens were calculated. The test results showed that, under the same initial crack depth, the peak load of FRP reinforced concrete decreases with the increase of FRP pasting layer. When there was one layer wrapped over the specimen, the instability toughness of the specimen reached the maximum value and the crack resistance was the best. Based on acoustic emission testing method, the acoustic emission parameters of the above-mentioned concrete during fracture process were identified and collected. The optimal layer of the FRP reinforced concrete with cracks was analyzed from the acoustic emission method.

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.

Experimental and numerical analysis of crack evolution in concrete through acoustic emission technique and mesoscale modelling

In this paper, the fracture process zone (FPZ) is investigated on unnotched and notched beams with different notch depths. Three-point bending tests have been realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth is monitored by applying the acoustic emission (AE) technique. The comparison with a numerical model is also realized by using a mesoscopic approach. Such an approach is of particular interest in the analysis of interactions between the cementitious matrix and aggregates. Several AE parameters are examined during the entire loading process, and show that the relative notch depth influences the AE characteristics, the process of crack propagation, and the brittleness of concrete. The numerical load–CMOD curves show that the mesoscopic modelling reproduces well the notch effect and concrete failure. In order to improve our understanding of the FPZ, the width and length of the FPZ are followed based on the AE source locations maps in parallel with the numerical damage fields. An important energy dissipation is observed at the crack initiation in unnotched beams.

Fracture properties of high-strength/high-performance concrete (HSC/HPC) exposed to high temperature

An investigation of the residual fracture properties of high-strength/high-performance concrete (C80 and C100) exposed to high temperatures is reported in this article. Three-point bending test specimens of 100 mm × 100 mm × 515 mm size were prepared according to the RILEM recommendation. The three-point bending beams were exposed to temperatures varying from 200 to 800 °C. The complete load-crack mouth opening displacement curves and load-deflection curves of the specimen were worked out after cooling. The fracture toughness, including the initial and unstable fracture toughness, fracture energy, and characteristic length, was calculated. These four parameters were shown to decrease monotonically with temperature. Other mechanical properties including the compressive strength, compressive Young’s modulus, and splitting strength of post-fire specimens were also obtained. The digital image correlation method was utilized to monitor the whole fracture process, and the results from the digital image correlation method fit well with those from the direct measurements.

An analytical method for determining the crack extension resistance curve of concrete

Owing to its importance in evaluating the fracture behaviour of concrete, crack extension resistance has been studied based mainly on experimental results. In this paper, an analytical method is developed for determining the crack extension resistance curve of concrete. It is assumed that, when the difference in stress intensity factor caused by external forces and by the cohesive stress within the fracture process zone is equal to the initial cracking toughness, crack propagation is initiated. According to this assumption, the crack extension resistance curve of concrete is expressed analytically as either the stress intensity factor caused by external forces, or the sum of the initial cracking toughness and the stress intensity factor by the cohesive stress within the fracture process zone. One advantage of this method is that, unlike other methods, the experimentally measured load–crack mouth opening displacement curve is not required in calculating the crack extension resistance curve. Based on numerical results, it is found that the crack extension resistance curve is independent of initial crack length. Also, for a given fracture energy, the shape of the cohesive stress–crack opening displacement curve exhibits no significant effect on the crack extension resistance curve. It is concluded that the proposed method can predict the crack extension resistance curve of concrete with reasonable accuracy.

Crack Extension Resistance of Normal-Strength Concrete Subjected to Elevated Temperatures

Determination of the residual crack extension resistance curves (KR-curves) associated with cohesive force distribution on fictitious crack zone of complete fracture process is implemented in present research. The cohesive force distributes according to bilinear softening traction-separation law proposed by Petersson. Totally ten temperatures varying from 20°C to 600°C and the specimen size of230×200×200 mm with initial-notch depth ratios 0.4 are considered. The load-crack mouth opening displacement curves (P-CMOD) of postfire specimens are obtained by wedge-splitting method from which the stress intensity factor curves (K-curves) are calculated. In each temperature, with the distribution of cohesive force along the fracture process zone, the residual fracture toughnessKR(Δa) increases with increasing crack lengthΔa, whereas theKR-curves decrease with increasing temperaturesTmfor the thermal damage induced. The stability analysis on crack propagation demonstrates that when the residualKR-curve is higher thanK-curve, the crack propagates steadily; otherwise, the crack propagates unsteadily.

Influence of Fibre Content on Crack Propagation Rate in Fibre-Reinforced Concrete Beams

Experimental study on the influence of fibre content on crack behaviour and propagation in synthetic-fibre reinforced beams has been reported in this paper. The tensile behaviour of metallic fibre concrete is evaluated in terms of residual flexural tensile strength values determined from the load-crack mouth opening displacement curve or load-deflection curve obtained by applying a centre-point load on a simply supported notched prism. The results achieved demonstrate that an increase in fibre content has an almost negligible effect on compressive and tensile splitting properties, causes a marginal increment in flexural tensile strength and increases the Re3 value.

Determination of Double-G Fracture Parameters of Post-Fire Concrete

Double-G fracture model was recently proposed based on the conception of energy release rate to describe the fracture behaviour on cracked concrete. Two fracture parameters, i.e., the initiation fracture energy release GIcini and the unstable fracture energy release GIcun, are termed to distinguish the different crack propagation stages undergoing during the whole fracture process in concrete. In present work, following the Double-G fracture model at ambient temperature, the residual Double-G fracture parameters of post-fire concrete is elaborately introduced. Totally ten temperatures varying from 20oC to 600oC and the specimens size of 230×200×200 mm with initial-notch depth ratios 0.4 were considered. Wedge-splitting method is adopted to measure the loadcrack mouth opening displacement curves (PCMOD) and double-G fracture parameters are experimentally determined.

Equivalence between Two Fracture Methods

Two fracture parameters, i.e., the initiation fracture energy release GIcini and the unstable fracture energy release GIcun, are termed to distinguish the different crack propagation stages. Totally ten temperatures varying from 20oC to 600oC and the specimen size of 230×200×200 mm with initial-notch depth ratios 0.4 were considered. Wedge-splitting method is adopted to measure the loadcrack mouth opening displacement curves (PCMOD) and double-G fracture parameters are experimentally determined. In order to verify the feasibility of this model in post-fire concrete, the effective double-K fracture parameters converted by double-G fracture parameters using are compared with the double-K fracture parameters.