Critical Crack Mouth Opening Displacement Research Articles

MIXED MODE FRACTURE OF THE GEOPOLYMER COMPOSITES REINFORCED WITH RECYCLED STEEL FIBERS

For the fiber-reinforced composites, strength-based criteria alone may fail to evaluate the bending response due to the long tail of the load-displacement curve. Hence, the fracture characterization of fibered composites has gained great attention worldwide. In this study, the mixed-mode fracture performance of the recycled steel fiber-reinforced geopolymer concrete was examined experimentally. The main test parameters were the amount of steel fibers (0 and 2% by mass) and the offset ratios of the edge notch (β = 0, 0.2, and 0.4). Several notched prisms were produced and tested under a deformation-controlled three-point bending test. Deformation maps on the surface of the specimens were derived through the digital image correlation method. Experimental results were discussed concerning the first cracking load, ultimate load, critical crack mouth opening displacement, critical crack mouth sliding displacement, and fracture energy. Based on the experimental findings, it can be stated that the peak flexural loads were increased by 666%, 1327%, and 400%, respectively for the 0, 0.2, and 0.4 notch offset ratios due to the use of recycled steel fiber. The fracture energies of the plain specimens were proportional to the notch offset ratio, but they fluctuated for the fiber-reinforced specimens because of the uneven distribution of fibers.

Effect of loading rate on mode I fracture behavior of red sandstone: Insights from AE and DIC techniques

The loading rate is an essential factor that influences the fracture characteristics and behavior of rock materials. In the study, a series of mode I fracture tests were performed on semi-circular bending (SCB) specimens of red sandstone under a range of static loading rates (0.005 mm/min–2 mm/min). The results showed that fracture toughness increases linearly with the logarithm of loading rates but the critical crack mouth opening displacement (CMODc) almost keeps constant. The fracture processes of rock were monitored using the acoustic emission (AE) and digital image correlation (DIC) techniques. The accumulated ringing counts increases with the loading rates at a natural logarithm relationship. The quantitative analysis for RA-AF data reveals that the contribution of shear cracks to mode I fracture increases with the loading rates. Prior to the DIC analysis, the DIC parameters were firstly calibrated by comparing the CMOD obtained from the clip gauge with that from the DIC data. By virtue of the strain and displacement fields, the fracture process, including post-peak fracture behavior, was analyzed using the cohesion zone model (CZM) in detail. Some fracture parameters, such as fracture process zone (FPZ) length and width, critical crack tip opening displacement (CTODc) were identified. The results indicate that FPZ length decreases with the loading rates but FPZ width and CTODc are nearly unaffected. The FPZ length at post-peak stage is lower than that at peak, regardless of the loading rate. Finally, the FPZ length measured by DIC is compared to that estimated by five theoretical models. The results show that the FPZ length calculated by the modified Irwin model is very closed to that from DIC.

Influence of initial crack length on fracture properties of limestone using DIC technique

Due to limitations in equipment and testing methods, there is currently little literature studying the effect of initial crack length (a0) on fracture parameters. Considering that limestone is often associated with the construction of cultural heritage buildings, monuments, tunnels, subways and power stations, so limestone beams were used as the experimental objects, and were used to conduct three-point bending (3-p-b) tests based on digital image correlation (DIC) technique to study the influence of a0 on fracture parameters, including critical crack tip opening displacement (CTODc), nominal strength without considering the crack (σN), nominal strength considering the crack (σn), critical mid-span deflection (δc), critical crack mouth opening displacement (CMODc), unstable fracture toughness (KIcun), fracture energy (Gf) and fully developed fracture process zone length (lmFPZ). In addition, based on the boundary effect model (BEM), the relationships between the crack-to-depth ratio (α0 = a0/D) with KIcun and Gf were analyzed. The findings indicate that, as a0 increases, σN, KIcun, Gf, and lmFPZ decrease gradually, while CMODc, CTODc, and δc increase gradually; as two important parameters of the BEM, the boundary influence length (A1) and size-independent fracture energy (GF) are 27.08 mm and 74.67 N/m, respectively.

Effects of pressurized carbonation with presoaking in calcium hydroxide solution on the fracture behaviours of recycled coarse aggregate concrete

Carbonation is effective in enhancing recycled coarse aggregate, but the shortage of carbonizable Ca2+ in recycled coarse aggregate and the low permeability efficiency of CO2 at ambient pressure limit the carbonation efficiency and industrial application. To solve these issues, the Ca2+ content in recycled coarse aggregate and the carbonation effectiveness were increased by presoaking recycled coarse aggregate in calcium hydroxide and enhancing the carbonation pressure, respectively. The optimal carbonation condition was obtained based on the physical properties of the recycled coarse aggregate and the strength of recycled coarse aggregate concrete: the carbonation pressure was 4 bar, and the concentration of the calcium hydroxide solution was 0.04 mol/kg. The fracture behaviour and microstructure of the recycled coarse aggregate concrete under different carbonation conditions were evaluated. The recycled coarse aggregate concrete after pressurized carbonation with presoaking in calcium hydroxide solution (RCAC-C0.04-P4) has higher toughness and a more stable crack propagation process than untreated recycled coarse aggregate concrete. Pressurized carbonation with presoaking in calcium hydroxide solution significantly increased the initial cracking load, peak load, Young's modulus, initial toughness, unstable toughness, and fracture energy of the recycled coarse aggregate concrete by 67.35%, 2.83%, 12.19%, 60.77%, 2.31%, and 5.38%, respectively, and reduced the critical crack mouth (CMODc) and tip opening displacement (CTODc) by 9.13% and 10.96%. Simple pressurized carbonation made the toughness of the specimens worse than that of untreated recycled coarse aggregate concrete. Compared with untreated recycled coarse aggregate concrete, although the initial toughness, unstable toughness, and fracture energy of recycled coarse aggregate concrete after simple pressurized carbonation (RCAC-P4) were increased by 16.02%, 1.86%, and 0.28%, respectively, the Young's modulus was slightly reduced by 1.35%, and the CMODc and CTODc were increased by 5.37%. In addition, a microstructural analysis showed that the contents of Ca(OH)2 and CaCO3 of RCAC-C0.04-P4 were increased by 50.56% and 37.62% compared to untreated recycled coarse aggregate concrete, respectively, and the average indentation modulus of the old aggregate and old mortar interface of RCAC-C0.04-P4 was increased by 24.37% compared to untreated recycled coarse aggregate concrete, which confirmed that pressurized carbonation with presoaking in a calcium hydroxide solution made CaCO3 fill the cracks in the interface and improved the macroperformance. These results can promote the application of recycled coarse aggregate in engineering.

The Effect of Polypropylene Fibers on the Fracture Characteristics of Lightweight Aggregate Crumb Rubber Concrete Composites

The increasing use of rubber tires and their low recycling ratio have made them a serious environmental problem. This work aims to develop and investigate enhanced lightweight aggregate crumb rubber concrete (PFLWACRC) composites regarding the fracture properties of concrete. Polypropylene (PP) fibers are commonly familiar with increased crack growth endurance of concrete. On the other hand, the reuse of waste rubber in concrete plays a major role in the mitigation of the effects of climate change. Various concrete mixtures were designed with conventional Portland cement and common lightweight coarse aggregates. The variables considered in this study are PP fibers in different percentages (0.2%, 0.4%, and 0.6% volume fraction), and crumb rubber with various substitution proportions (0%, 5%, 10%, 15%, 20%, and 25% of fine aggregates). Cement with 450kg/m3 density with 10% silica fume was used. The fracture characteristics, which involve fracture toughness (KIC) and fracture energy generation (GF), of all concrete mixtures were evaluated by testing two types of samples, i.e. 54 notched concrete beams with dimensions of 10×10×52cm and 54 cylinders with diameter×height equal to 15×30cm. The results showed that the fracture toughness generation addresses the energy scattering limit of concrete mixtures. The findings showed that the existence of PP fibers increased the fracture energy and critical Crack Mouth Opening Displacement (CMOD)c. The PP fibers had a limited effect on the compressive strength and may even reduce it, but a remarkable enhancement of the energy absorption was observed.

Influence of Graphite Powder on the Mechanical and Acoustic Emission Characteristics of Concrete

In this paper, uniaxial compressive strength (UCS) test and three-point bending (TPB) test, together with an acoustic emission (AE) system, were performed to investigate the mechanical properties and AE characteristic changes of concrete with different graphite powder (GP) content. The results show that: (1) Poor adhesion and low interlocking of graphite with cement stone increase the initial defects of concrete, reducing its elastic modulus and the cyclo-hoop effect, and thus weakening the compressive strength. (2) For concrete with a low graphite content, the second sharp rise in ringing counts or energy released during the compressive process can be regarded as a failure alarm. However, as GP content increases, the second sharp rise fades away, while the first sharp rise becomes more visible. At high GP content, the first sharp rise is better for predicting failure. (3) The initial defects caused by GP significantly lower the initial fracture toughness, but its bridging effect greatly increases the critical crack mouth opening displacement and thus significantly enhances the unstable fracture toughness of concrete, by up to 9.9% at 9% GP content. (4) In contrast to compressive process, the sharp increase in AE signals preceding failure during the fracture process cannot be used to predict failure because it occurs too close to the ultimate load. However, as GP can significantly increase the AE signals and damage value in the stable period, such failure precursor information can provide a safety warning for damage development.

Fracture properties of concrete under cyclic loading

Three-point bending tests were performed on pre-notched beams to investigate the fracture properties of concrete under cycling loading. Electronic speckle pattern Interferometry (ESPI) technique was used to measure the full-field displacement of the beams. The influence of loading history on the fracture properties of concrete were analyzed. Results measured by ESPI were compared with that measured by a clip gauge and good agreement was observed, which validates the reliability of using ESPI to measure the deformation of fracture process zone during crack extension. The experimental results indicate that load–displacement curves under monotonic loading are an envelope line for that under cyclic loading. The load–displacement curves of each loading cycle can be divided into five stages and in both loading and unloading process, elastic deformation responses earlier than inelastic deformation. The critical crack mouth opening displacement (CMODc) increases with the loading cycles and reaches about 0.090 mm while the critical crack tip opening displacement (CTODc) is almost constant about 0.034 mm which can be used as a fracture characteristic of the material. The cumulative dissipative energy tends to reach about 21 N/m as the loading cycles increase and can be used as a fracture parameter under cyclic loading.

Experimental Study on the Fracture Parameters of Concrete.

This study aimed to determine the influence of the volume fraction of steel fibers on the fracture parameters of concrete. Fifty notched steel-fiber-reinforced concrete (SFRC) beams and ordinary concrete beams with 100 mm × 100 mm × 515 mm were cast and tested via a three-point bending test. Among them, the type of steel fiber was the milling type (MF), and the volume fraction of steel fiber added was 0%, 0.5%, 1%, 1.5% and 2%, respectively. The effects of the steel fiber volume fraction (VF) on the critical stress intensity factor (KIC), fracture energy (GF), the deflection at failure(δ0), the critical crack mouth opening displacement (CMODC) and the critical crack tip opening displacement (CTODC) were studied. Through the analysis of test phenomena and test data such as the load-deflection (P-δ) curve, load-crack mouth opening displacement (P-CMOD) curve and load-crack tip opening displacement (P-CTOD) curve, the following conclusions are drawn: with the increase of the steel fiber volume fraction, some fracture parameters increase gradually and maintain a certain linear growth. The gain ratio of the fracture parameters increases significantly, and the gain effect is obvious. Through this law of growth, the experimental statistical formulas of fracture energy and the critical stress intensity factor are summarized.

Fracture behaviors of concrete incorporating different levels of recycled coarse aggregate after exposure to elevated temperatures

This study focuses on the fracture behavior of recycled aggregate concrete (RAC) after exposure to elevated temperatures, thus, a total of 128 cubic specimens and 64 notched beams were cast to analysis the effects of recycled coarse aggregate (RA) substitutions (0%, 30%, 70% and 100%) and elevated temperatures (20 °C, 100 °C, 200 °C and 300 °C) on fracture parameters of RAC, such as peak load (Pmax), critical crack mouth opening displacement (CMODc), critical crack tip opening displacement (CTODc), effective crack length (ac), fracture energy (GF), initiation fracture toughness (KICini), unstable fracture toughness(KICun), the characteristic length (Lch) and so on. The result showed that the values of Pmax decreased as the increase of exposure temperature and the decrease rate grew slower as the increase of RA substitution. In contrast, the values of GF increased with elevated temperature and the increased rate grew slow with the incremental of RA replacement. As the increase of RA substitution, the CMODc and CTODc of specimens slightly increased first and then decreased at ordinary temperature and elevated temperature. The KICini and KICun of concrete with different RA substitution decreased with the elevated temperatures. In addition, the RA substitution had a positive impact on the KICini of concrete after exposure to 200 °C and 300 °C. At each high temperature, the Lch of RAC was smaller than that of natural aggregate concrete (NAC), indicating that the ductility of RAC was worse than that of NAC.

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.

Determining the tensile strength of concrete for wedge splitting specimens based on the fracture extreme theory

Two theoretical methods were developed to determine the tensile strength ft of concrete using wedge splitting specimens based on nil-stress intensity factor (nil-SIF) criterion and force equilibrium theory, respectively. With the fracture extreme theory (FET), only experimental peak load of one specimen was needed and did not require the measurement of critical crack mouth opening displacement CMODc for calculation. The existing experimental data were utilized to verify the two methods. Results show that the values of ft were insensitive to the initial notched ratios a0/D and agreed well with the experiment data. The influence of the size of the specimen was analyzed, ft was affected by the specimen size when the nil-SIF criterion was adopted. Nevertheless, ft calculated by the force equilibrium theory appeared to be kept a constant when the height of the specimen varied from 200 mm to 600 mm. Finally, the critical effective crack length ac and critical crack tip opening displacement CTODc were obtained and compared using the two methods.

Mechanical properties and prediction of fracture parameters of geopolymer/alkali-activated mortar modified with PVA fiber and nano-SiO2

Properties of fly ash (FA) and metakaolin (MK) based geopolymer/alkali-activated mortar modified with polyvinyl alcohol (PVA) fiber and nano-SiO2, including workability, compressive strength, flexural performance, elastic modulus and fracture property were tested in this study. PVA fiber content varies from 0 to 1.2%. Nano-SiO2 content is 0 and 1%. Adaptive neuro-fuzzy interfacial systems (ANFIS) method was used to establish the artificial intelligence (AI) model to predict the fracture parameters of geopolymer/alkali-activated mortars. The inputs of ANFIS models include PVA fiber content, nano-SiO2 content, compressive strength, flexural strength, elastic modulus, critical crack mouth opening displacement, crack load and peak load. The outputs of ANFIS model include critical effective crack length, initiation fracture toughness, unstable fracture toughness, and fracture energy. Experiment results showed that PVA fiber addition enhanced the mechanical properties especially the compressive strength and fracture performance, but decreased the workability. 0.8%–1.0% was considered as the optimal content of PVA fiber. Addition of 1% nano-SiO2 shows a slight improvement on both workability and mechanical properties of the mortar no matter how much fiber is added. Based on the ANFIS algorithm and 42 sets of experimental data, the trained models were proved to have high accuracy with root mean square error (RMSE) under 0.15, mean absolute error (MAE) under 0.01, and coefficient of determination (R2) over 0.85. The ANFIS model established in this study combined the fracture properties with the basic mechanical properties of geopolymer/alkali-activated composites, which can provide a new method to assess the fracture performance of geopolymer/alkali-activated mortars modified with PVA fiber and nano-SiO2 in the future.

Fracture analysis of Beishan granite after high-temperature treatment using digital image correlation

A systematical knowledge of the fracture characteristics and thermal damage mechanism of granite at elevated temperature is an important issue in the high-level nuclear waste disposal and geothermal energy exploration field. To investigate the influence of high temperature on the fracture behaviors and characteristics of Beishan granite, three-point bending tests were conducted on specimens subjected to different high temperatures, i.e. 200 °C, 300 °C, 400 °C, 500 °C, 600 °C and 800 °C, and specimens at room temperature (25 °C) were also tested for comparison. An innovative technique called digital image correlation (DIC) was used in this study to trace the fracture process, and important fracture parameters, such as the fracture process zone (FPZ) size and critical opening displacement, were measured by full-field displacement and strain measurement. The experimental result illustrates that thermal treatment has a significant influence on the fracture behavior of the Beishan granite. Comparisons reveal that the enhanced ductile feature, a linear decline in the peak load and a rapid increase in critical crack mouth opening displacement is observed with the increase of temperature from 200 °C to 600 °C. Moreover, the increasing temperatures also reduce the applied load for fracture initiation. The FPZ length and critical opening displacement are significantly affected by the thermal treatment, while the FPZ width almost does not change with the increasing temperatures. The fracture toughness for Beishan granite shows a decreasing trend with the increase of temperature from 25 °C to 300 °C, while a valid fracture toughness value cannot be obtained for granite specimens subjected to temperature over 300 °C due to the existing of a large FPZ above the notch tip. Finally, the thermal-induced damage mechanism is also revealed by optical microscopic observation, and the thermal-induced microcracks are considered as the essential cause for the change of the fracture behavior of Beishan granite.

Loading‐rate dependence of mode I crack growth in concrete

AbstractMode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.

A general framework for determining fracture parameters of concrete based on fracture extreme theory

A general theoretical framework for determining the fracture parameters of concrete was presented based on fracture extreme theory (FET). The method for determining tensile strength ft and initial fracture toughness KIini was established using nil-stress intensity factor (nil-SIF) criterion and initial fracture toughness criterion, respectively. Using the nil-SIF criterion, the ft was determined by the proposed method and verified by experimental values. In addition, the values of KIini calculated using the initial fracture toughness criterion were compared with those using an existing analytical method. The influence of the cohesive stress distribution on KIini was analyzed. With FET, only the experimental peak load of one specimen was needed, and the measurement of the critical crack mouth opening displacement was not required for the calculation.

Determining initial fracture toughness of concrete for split-tension specimens based on the extreme theory

A theoretical method to determine the initial fracture toughness KIini of concrete for central-notched split-tension specimens was developed based on the extreme theory. In this method, the KIini, critical crack tip opening displacement CTODc, and half critical effective crack extension Δɑc could be obtained by the experimental peak load of a single specimen. The measurement of critical crack mouth opening displacement CMODc was unnecessary in this method. The fracture parameters were calculated using the cube and cylinder split-tension specimens. Results showed that the values of KIini obtained by the proposed method were slightly smaller than those obtained by the double-K method, and the difference between them generally decreases with the loading rates. And the values of CTODc and Δɑc obtained by the proposed method were more stable compared with those obtained by the double-K method.

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.

Effect of Prefabricated Crack Length on Fracture Toughness and Fracture Energy of Fly Ash Concrete Reinforced by Nano-SiO2 and Fibers

This paper summarizes the test data obtained from an experimental investigation of nanoparticles and steel fiber-reinforced concrete. Tests were conducted to investigate the effect of prefabricated crack length on determining fracture parameters of concrete composite. The results reveal that most of the fracture parameters and the fracture relational curves of the concrete composite are influenced greatly by the prefabricated crack length of beam specimens, while the prefabricated crack length has little effect on the critical crack tip opening displacement. There is a tendency for effective crack length and the critical crack mouth opening displacement to increase with the increase in prefabricated crack length, while the initial fracture toughness, unstable fracture toughness and fracture energy gradually decrease. Besides, when the prefabricated crack length decreases from 50 to 20 mm, these relational curves become much larger, and the nonlinear stage of the curves become longer and longer, and the descent stage of the curves become flatter and flatter.

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.

The Effects of Tensile Softening Curve Parameters on Fracture in Concrete Based on Initial Fracture Toughness Criterion

The effects of tensile softening curve parameters on the crack propagation P-CMOD and P-CTOD curves were analyzed using a calculation method which adopted the initial fracture toughness as the crack propagation criterion. The results showed that: the whole process of the P-CMOD and P-CTOD curves were affected by the tensile softening curve parameters, especially for the descending segment of the curves, but the peak load and critical crack mouth opening displacement were less affected.