double-K Fracture Parameters Research Articles

Effects of Mix Components on Fracture Properties of Seawater Volcanic Scoria Aggregate Concrete.

The fracture mechanism and macro-properties of SVSAC were studied using a novel test system combined with numerical simulations, which included three-point bending beam tests, the digital image correlation (DIC) technique, scanning electron microscopy (SEM), and ABAQUS analyses. In total, 9 groups and 36 specimens were fabricated by considering two critical parameters: initial notch-to-depth ratios (a0/h) and concrete mix components (seawater and volcanic scoria coarse aggregate (VSCA)). Changes in fracture parameters, such as the load-crack mouth opening displacement curve (P-CMOD), load-crack tip opening displacement curve (P-CTOD), and fracture energy (Gf), were obtained. The typical double-K fracture parameters (i.e., initial fracture toughness (KICini) and unstable fracture toughness (KICun)) and tension-softening (σ-CTOD) curve were analyzed. The test results showed that the initial cracking load (Pini), Gf, and characteristic length (Lch) of the SVSAC increased with decreasing a0/h. Compared with the ordinary concrete (OC) specimen, the P-CMOD and P-CTOD curves of the specimen changed after using seawater and VSCA. The evolution of the crack propagation length was obtained through the DIC technique, indicating cracks appeared earlier and the fracture properties of specimen decreased after using VSCA. Generally, the KICun and KICini of SVSAC were 36.17% and 8.55% lower than those of the OC specimen, respectively, whereas the effects of a0/h were negligible. The reductions in Pini, Gf, and Lch of the specimen using VSCA were 10.94%, 32.66%, and 60.39%, respectively; however, seawater efficiently decreased the negative effect of VSCA on the fracture before the cracking width approached 0.1 mm. Furthermore, the effects of specimen characteristics on the fracture mechanism were also studied through numerical simulations, indicating the size of the beam changed the fracture toughness. Finally, theoretical models of the double-K fracture toughness and the σ-CTOD relations were proposed, which could prompt their application in marine structures.

Prediction of fracture failure and fracture parameters for dam gallery concrete specimens of arbitrary size and age via boundary effect model and fracture extreme theory

Cracking-associated problems may occur in the construction and operation periods of dam galleries, necessitating attention to the fracture characteristics of gallery concrete. The fracture parameters of concrete exhibit size effects and also change with age. A correct evaluation of the cracking risk or crack stability of gallery structures at any given time requires a comprehensive understanding of both the size effect and time-variant characteristics of the gallery concrete fracture parameters. In the present study, 75 wedge-splitting specimens, with effective heights ranging from 200 mm to 600 mm, were cast using gallery concrete produced by the concrete mixing system at the Baihetan Dam construction site. Subsequently, fracture tests were conducted on these specimens at curing ages spanning from 7 days to 90 days. According to the test results, the fracture parameters of concrete with a specific size exhibited an increasing trend with age within 90 days, while the fracture parameters of concrete at specific ages show a significant size effect, tending to stabilize as the effective depth of specimens gradually increases. The boundary effect model was utilized for analyzing the fracture test results of concrete specimens at different ages, yielding the size-independent double-K fracture parameters and scale parameters for concrete at each age, along with their time-varying patterns. Subsequently, equations for predicting the failure loads of concrete specimens of any age and size were established. Based on the prediction results of failure loads, the double-K fracture parameters of concrete specimens of any age and size were solved by the fracture extreme theory. The predicted failure loads and fracture parameters were in good agreement with the experimental results. The findings of this study can be applied to the full lifecycle crack risk analysis or crack stability assessment of Baihetan Dam gallery structures.

Crack resistance properties of carbon nanotube-modified concrete

Incorporating carbon nanotubes (CNTs) into concrete can improve its fracture toughness. The crack resistance properties of reinforced concrete with CNTs were tested by ring test and three-point bending beam fracture test. The fracture parameters of reinforced concrete with CNTs were analysed by using double-K fracture parameters and the results showed that CNTs can improve the crack resistance properties. When the CNT content was 0.10 wt%, the compressive strength at 28 days and the splitting tensile strength of concrete were increased by 1.7 and 11.7%, respectively. When the CNT content was 0.15 wt%, the cracking time of concrete under semi-closed and closed conditions was extended by 42.1 and 41.2%, respectively. The initiation fracture toughness, the unstable fracture toughness and the fracture energy of concrete were increased by 31.0, 32.4 and 24.6%, respectively. It was found that CNTs delay the propagation of micro-cracks by bridging across the micro-cracks in concrete and strengthening the interfacial transition zone.

Fracture Behavior of Steel Slag Powder-Cement-Based Concrete with Different Steel-Slag-Powder Replacement Ratios.

The influence of different replacement ratios of steel-slag powder as cement-replacement material on the fracture performance of concrete is studied in this paper. A three-point bending fracture test is carried out on slag powder-cement-based concrete (SPC)-notched beams with steel-slag powder as cementitious materials, partially replacing cement (0%, 5%, 10%, 15%, and 20%). Load-deflection curves and load-crack-opening displacement curves of SPC-notched beams with five different replacement ratios of steel-slag powder were obtained. The effects of different steel-slag-powder replacement ratios on the fracture properties (fracture energy, fracture toughness, and double-K fracture parameters) of the SPC were analyzed and discussed. The results showed that the incorporation of appropriate steel-slag powder can affect the fracture performance of SPC. Compared with concrete without steel-slag powder, adding appropriate steel-slag powder can effectively improve the bond performance between aggregate and matrix because the steel-slag powder contains hydration activity substances such as calcium oxide and aluminium trioxide. The fracture energy and fracture toughness of SPC increased and then decreased with the increase in steel-slag-powder replacement ratios, and the SPC concrete showed best fracture performance with a 5% steel slag powder replacement ratio. Its fracture energy increases by 13.63% and fracture toughness increases by 53.22% compared with NC.

Simplified equations for determining double-k fracture parameters of concrete for compact tension test

Polynomial equations in non-dimensional form for various fracture parameters of double-K fracture model for compact tension specimen have been derived and presented in this paper. These equations can be used for computing different double-K fracture parameters of concrete for known material properties and specimen size having relative size of initial crack length of 0.3 without involving much complexity in numerical computations. Values of peak load and corresponding crack opening displacement as necessary to compute the double-K fracture parameters of concrete have been derived from the established fictitious crack model in the present study. A simplified equation in non-dimensional form between peak load and critical crack opening displacement as obtained from a fictitious crack model has also been presented.

RILEM Standard: testing methods for determination of the double-K criterion for crack propagation in concrete using wedge-splitting tests and three-point bending beam tests, recommendation of RILEM TC265-TDK

In this recommendation, standard testing methods for determination of the double-K criterion for Mode I crack propagation in concrete using wedge-splitting tests and three-point bending beam tests are specified for the fracture parameters of the initial cracking toughness K_{Ic}^{ini} and the unstable fracture toughness K_{Ic}^{un}. Along with the recommendation of the standard testing methods, the theoretical background of the double-K criterion, the calculation methods and the results of round-robin testing for determining the double-K fracture parameters are presented in technical reports [1, 2]. The recommendation of the standard testing methods includes geometry for specimens, fabrication of specimens, testing machine, load transmission system and supports, measuring instruments, determination of initial cracking load Pini, determination of measured maximum load Pmax and initial compliance ci, calculation methods for wedge-splitting test and three-point bending beam test, as well as the testing results and testing report forms. According to these methods, the measured fracture parameters of double-K criterion can be used to describe the onset of cracking, and the onset of unstable cracking or failure for predicting crack initiation, structure failure and crack stability in concrete structures.

FRACTURE PROPERTIE ANALYSIS OF RECYCLED AGGREGATE CONCRETE BASED ON DIGITAL IMAGE CORRELATION TECHNIQUE

Three point bending fracture tests of recycled aggregate concrete beams with different recycled coarse aggregate replacement ratio (0%, 30%, 50%, 70%, 100%) have been carried out, with results analyzed by digital image correlation (DIC) method and the traditional electrometric method. The double-K fracture parameters, crack-mouth-opening displacement (CMOD), crack-tip-opening displacement (CTOD), crack extension length ( \begin{document}$\Delta a$\end{document} ) and fracture growth path were obtained, and the validity of DIC method was verified. The results show that when the replacement rate is 100%, the crack initiation fracture toughness and unstable fracture toughness of recycled aggregate concrete decrease by 15.81% and 15.39%, respectively. With the increase of the replacement rate of recycled aggregate, the slopes of the descending sections of P-CMOD, P-CTOD and P- \begin{document}$\Delta a$\end{document} curves increase. DIC method can effectively capture the fracture propagation process. The CMOD values measured by DIC method and clip type extenometer are in good agreement. The variation trends of DIC measured value and formula-calculated value of CTOD are relatively consistent. Based on the test results, the estimated values, \begin{document}$\Delta a$\end{document} , of specimens with different replacement rates of recycled aggregate under different loads can be obtained by fitting the curve between \begin{document}$P$\end{document} / \begin{document}${P_{\max }}$\end{document} and \begin{document}$\Delta a$\end{document} / \begin{document}$\Delta {a_{\text{c}}}$\end{document} .

Investigations on fracture properties and analytical solutions of fracture parameters at rock-concrete interface

To investigate fracture properties and find analytical solutions of fracture parameters at rock-concrete interface, three-point bending tests were performed on the composite rock-concrete specimens with different degrees of interface roughness. Numerical simulations were conducted to analyse the crack propagation and the fracture process zone evolution at rock-concrete interface. For convenient applications in practice, a series of analytical solutions were derived or curve-fitted to calculate the fracture parameters of rock-concrete interface. The results indicate that the roughness degree has significant effects on the fracture properties of rock-concrete interface. With the increase of the roughness degree, the fracture energy, the critical crack length and the double-K fracture parameters exhibit obvious increasing tendencies. Meanwhile, the ratio of the unstable fracture toughness of rock-concrete interface to concrete is much less than that of the initial fracture toughness, indicating the much weaker cohesive effect of rock-concrete interface compared with concrete. In addition, with the increase of the roughness degree, the length of the fully formed FPZ and the corresponding ratio of the crack propagation length to the ligament length decrease. The characteristic length of rock-concrete interface is proved to decrease with the increase of the roughness degree, indicating larger brittle behaviour with the increase of the roughness degree. Finally, a series of analytical expressions were curve-fitted or derived to calculate the fracture parameters of rock-concrete interface under three-point bending loading, including the mode-I stress intensity factor, the critical crack length and the characteristic length of rock-concrete interface.

Size effect on double-K fracture parameters of concrete based on fracture extreme theory

Based on fracture extreme theory (FET), the size effect on initial fracture toughness $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and unstable fracture toughness $$K_{\mathrm{I}}^{\mathrm{un}}$$ of concrete for three-point bending beam was investigated. Nine groups of geometrically similar specimen were simulated to obtain peak load and critical crack mouth opening displacement, of which specimen depth was from 200 to 1000 mm and initial crack length-to-depth ratios were from 0.1 to 0.6. The $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ were calculated by FET and double-K method, in which FET adopted the linear, bilinear, and trilinear cohesive stress distribution assumptions and double-K method only used the linear cohesive stress distribution assumption. With linear cohesive stress distribution assumption, $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ determined by FET and double- K method were compared. Then, the influence of specimen depth on $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ was discussed. In addition, $$K_{\mathrm{I}}^{\mathrm{ini}}/K_{\mathrm{I}}^{\mathrm{un}}$$ calculated via FET using different cohesive stress distribution assumptions were analyzed.

Characterization on tensile behaviors of fracture process zone of nuclear graphite using a hybrid numerical and experimental approach

This paper reports an experimental and numerical study on the fracture properties of nuclear graphite NG-CT-01 produced in China. Three-point bending tests were performed on center-notch beams and electronic speckle pattern interferometry (ESPI) technique was employed to measure the full-field deformation of the beams. Besides, finite element analysis was performed by using extended finite element method to simulate the fracture behavior of graphite. Numerical results were compared with the experimental results and excellent agreement was obtained, validating the reliability and accuracy of the numerical model. Based on the strain field measured by ESPI technique, the formation and evolution of the fracture process zone (FPZ) in graphite were observed. The tension softening curve (TSC) of the graphite was determined by using a hybrid numerical and experimental approach. The influences of initial crack length to beam depth ratio on the fracture responses of graphite beam, including the load-displacement curves, double-K fracture parameters, TSCs and the length of the FPZ, were evaluated. In order to explain the correlation between the tension softening behaviors and the fracture mechanism of the FPZ, a tri-linear model was proposed. Furthermore, double-K fracture criterion was employed to predict the crack propagation in graphite.

Fracture performance and numerical simulation of basalt fiber concrete using three-point bending test on notched beam

In this paper, three-point bending tests on precast notched beam and multiscale numerical simulation were used to evaluate and predict the effect of different Basalt Fiber (BF) dosages on the fracture resistance performance for Basalt Fiber Reinforced Concrete (BFRC). The three-point bending test was performed on a series of the notched beams in different sizes and volumetric fiber dosage to obtain the Load-Crack Mouth Opening Displacement (P-CMOD) curves during the loading process. The fracture energy and the double-K fracture parameters were calculated from P-CMOD curves to investigate the influences of fiber volume fraction and beam size on fracture parameters of BFRC. The results indicate that the numerical simulation results are in good coherence with the experimental results. The increase of BF dosage could markedly increase the peak load and the fracture energy of concrete. There was no size effect on fracture energy. Based on the two-parameter fracture theory, the initiation toughness had size effect and increased with the rise of specimen height, while size effect was not significant for unstable toughness. With the augment of fiber dosage, the initiation toughness increased linearly. The unstable toughness varied irregularly with the alteration of fiber dosage but higher than that of ordinary concrete. In addition, this paper developed a homogenization algorithm based on Mori-Tanaka and a multi-scale finite element simulation based on continuum progressive damage theory to evaluate and predict the fracture behavior of BFRC with different sizes and fiber volumetric dosages. The calculated P-CMOD curves from this algorithm were in good agreement with those from experiments and revealed the effects of fiber dosage and size effect on fracture behavior for BFRC.

Influence of Defects on Reinforced Concrete Fracture Performance in Improved Wedge Splitting Tests

Abstract To predict the crack propagation and failure response of reinforced concrete structure, the effect of defects on reinforced concrete fracture characteristics was investigated. Based on the improved wedge splitting test device (an authorized patent No. ZL201410085111.7, China), specimens with various defects were tested. The formulas for the reinforced concrete double-K fracture parameters were derived, and a matrix describing the influence of defects was given. By this matrix, the defects were quantitatively transformed into the sectional loss and the double-K fracture parameters of these specimens were determined. The initial cracking load, unstable load, critical effective crack length, and unstable toughness were found to be improved significantly by the steel bars, but the initial toughness reduced slightly. In addition, with the increasing of sectional loss caused by defects, the initial cracking load, unstable load, and unstable toughness decreased in different proportions. Nevertheless, the defects were irrelevant to the critical effective crack length and the initial toughness. Besides, the critical interval of sectional loss ranged from 14.78 % to 15.48 % in the tests. Once the sectional loss was beyond this range, the steel bar enhancement on unstable toughness could no longer completely offset its attenuation caused by defects.

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.

Research on fracture performance of epoxy asphalt concrete based on double-K fracture criterion

After cracks appear on steel bridge deck epoxy asphalt concrete pavement, cracks propagate fast under vehicle load. This paper studied the fracture performance of epoxy asphalt concrete, utilized single edge notched beam (SEB) three-point bending test, measured the load (P) exerted on epoxy asphalt SEB; utilized digital camera to record the fracture process of epoxy asphalt SEB, extracted the images according to the required sampling frequency and utilized Image-Pro Plus to measure the crack mouth opening displacement (CMOD) of epoxy asphalt SEB on the extracted images; calculated the double-K fracture parameters according to the P-CMOD curve. Results indicate that of epoxy asphalt concrete is 1.11 MPa and of epoxy asphalt concrete is 2.31 MPa at -15°C; of epoxy asphalt concrete is 1.02 MPa and of epoxy asphalt concrete is 1.83 MPa at -5°C; of epoxy asphalt concrete is 0.77 MPa and of epoxy asphalt concrete is 1.82 MPa at 5°C. The double-K fracture parameters of epoxy asphalt concrete increase slightly when the temperature decreases at the scope of -15°C to 5°C. The relation of and is .

Effect of size and cohesive assumptions on the double-K fracture parameters of concrete

This paper studies the effect of size and cohesive assumptions on the double-K parameters in concrete fracture. These two parameters are the fracture toughnesses KIcini and KIcun, related with the crack initiation and the limit of the stable crack propagation, respectively, which are calculated using data from a load-crack mouth opening curve, P-wM (Xu and Reinhardt, 2000). The study starts from three-point bending tests with three different beam sizes, whose results calibrate a numerical model, used to produce additional P-wM curves from a wider beam-size range, with beam depths from 13 to 1300mm. The paper presents a simplification to obtain KIcini experimentally based on the loss of linearity in the P-wM curve, which allows avoiding the use of strain gauges to measure the crack initiation load. The evolution of KIcun and KIcini shows size dependence. The calculated values of KIcun increase slightly with the beam size whereas those of KIcini remain constant but below the experimental range and, later, they diminish for large beam sizes. This points out that KIcini calculation procedure is not correct, especially for sizes out of the usual experimental range. These shortcomings can be overcome by an appropriate selection of the initial stretch of the cohesive law, which leads to a proposal for improving the procedure to calculate KIcini. The analysis includes the calculation of the complete toughness-crack length curves (KIc-a), which are also dependent on the specimen size.

Estimation of real fracture parameters of a dam concrete with large size aggregates through wedge splitting tests of drilled cylindrical specimens

For dam concrete with large size aggregates, large specimen tests are required to obtain size-independent fracture parameters, which are difficult to conduct and such large specimens by no means can be drilled from the dam. The current work attempts to use the results of wedge-splitting tests on 300mm-diameter cylindrical compact tension specimens drilled from Danjiangkou Dam to extrapolate the real fracture parameters that are required to assess the safety of the dam. Load-CMOD curves were obtained from the tests and the experimental double-K fracture parameters were evaluated. For this dam concrete whose maximum aggregate size is 150mm, the experimental double-Ks from these relatively small compact specimens would be underestimated. To overcome this problem, a numerical analysis was performed using a cohesive model. The experimental load-CMOD curves were deeply analyzed to obtain the required softening parameters in the cohesive model, in particular the extension of the tail to calculate the non-measured portion of the fracture energy. With the cohesive model generating the load-CMOD curves for different specimen sizes, the double-K parameters for large sizes were computed, which are applicable for safety assessment of practical structures.

Determining double-K fracture parameters of concrete only by the measured peak load

The peak load and critical crack-mouth opening displacement are two essential parameters that should be measured in the conventional analytical method to determine double-K fracture parameters of concrete. In this study, we propose a method to determine the double-K fracture parameters only by using the measured peak load so that both the measurement of critical crack-mouth opening displacement and the limit to require three or more distinct specimens in the conventional peak load method can be avoided. Furthermore, double-K fracture parameters are computed using the conventional analytical method and proposed method respectively through the three-point bending test and the findings in the scientific literature. The results show that the fracture parameters of the double-K fracture model can be determined by using this proposed method without any appreciable error.

Determination of Double-K Fracture Parameters of Concrete Using Split-Tension Cube: A Revised Procedure

This paper presents a revised procedure for computation of double-K fracture parameters of concrete split-tension cube specimen using weight function of the centrally cracked plate of finite strip with a finite width. This is an improvement over the previous work of the authors in which the determination of double-K fracture parameters of concrete for split-tension cube test using weight function of the centrally cracked plate of infinite strip with a finite width was presented. In a recent research, it was pointed out that there are great differences between a finite strip and an infinite strip regarding their weight function and the solution of infinite strip can be utilized in the split-tension specimens when the notch size is very small. In the present work, improved version of LEFM formulas for stress intensity factor, crack mouth opening displacement and crack opening displacement profile presented in the recent research work are incorporated. The results of the double-K fracture parameters obtained using revised procedure and the previous work of the authors is compared. The double-K fracture parameters of split-tension cube specimen are also compared with those obtained for standard three point bend test specimen. The input data required for determining double-K fracture parameters for both the specimen geometries for laboratory size specimens are obtained using well known version of the Fictitious Crack Model.

Influence of different sizes of concrete and roller compacted concrete on double-K fracture parameters

Affected by physical properties of various components, characteristics and stress states of junction surface and other multiple factors, concrete, as a kind of multi-phase composite material, has complicated failure mechanism, thus making its fracture mechanism research difficult. But concrete has been widely used in engineering construction, so research on concrete fracture theory is of important realistic significance and construction value. This study discusses influence rule of specimen size and crack-depth ratio (?0/h) on doubleK fracture parameters (initial fracture toughness ini ICK and unstable fracture toughness un ICK ) and its size effects by using fracture test. Different sizes of concretes and roller compacted concrete (RCC) specimens are adopted to explore influence of specimen size on concrete double-K fracture parameters. Results reveal that initial fracture toughness ini ICK and unstable fracture toughness un ICK increase as specimen size enlarges, showing a size effect; besides, subcritical crack extends with the increase of specimen size. With regard to specimens with different crack-depth ratios, its unstable fracture toughness un ICK is unrelated to initial crack-depth ratio when crack-depth ratio is more than or equal to 0.4, while initial fracture toughness ini ICK is correlated with initial crack-depth ratio, which indicate that double-K fracture parameters can be considered as material constants describing concrete initial fracture, stable expansion and whole process of stability failure.

Determination of double-K fracture parameters using semi-circular bend test specimens

The present research was conducted to evaluate the double-K fracture parameters using semi-circular bend test. Fracture tests were carried out on semi-circular bend specimens with three different diameters with a range from 200mm to 500mm and four different concrete strengths. The results indicated that double-K fracture parameters KIcini and KIcun values for semi-circular bend specimens were size and strength dependent. All the fracture parameters such as critical effective crack length, critical crack mouth opening displacement and unstable fracture toughness increased as the specimen size increased; while, initial fracture toughness decreased with the increase of specimen size.