Critical Effective Crack Length Research Articles

The effects of loading rates on the fracture characteristics at the bonding interface between steam concrete and self-compacting concrete using three-point bending test

The properties of bonding interface of Chinese Railway Track System III (CRTS III) slab ballastless track structure is important for the stability of operation, however, little is known about the interface fracture behaviors of CRTS III slab ballastless track structure. In this work, the three-point bending test under different loading rates was conducted on concrete specimens with a bonding interface between steam concrete (SC) and self-compacting concrete (SCC). The influences of loading rate on the fracture parameters and characteristics were investigated. The experimental results indicate that the failure patterns of concrete with bonding interface changed from debonding failure to spalling failure as the loading rate increased. The P-CMOD curve of concrete with a bonding interface demonstrated a similar pattern under different loading rates, which mainly included three stages: linear growth stage, crack development stage and failure destruction stage. The fracture parameters exhibited an obvious loading rate effect: the higher the loading rate, the higher the fracture energy, as well as the critical relative effective crack length, fracture toughness, and the deformation resistance of the bonding interface. It also revealed that more tortuous main crack and multiple crack paths could be observed with the increase in loading rate. A higher loading rate can promote the conversion of fracture process zone to macroscopic crack zone and also increase the fracture energy in the bonding interface.

Fatigue life and fracture behaviors of aligned steel fiber reinforced cementitious composites (ASFRC)

Aligned and random steel fiber reinforced cementitious composites (ASFRC, SFRC) are prepared to study how fiber orientation and volume fraction affect the fatigue life and fracture behaviors of composites. The experimental results indicate the fatigue life of ASFRC exceeds that of SFRC by more than 8 times. Compared with SFRC, the critical effective crack length of ASFRC is improved by more than 17%, which can withstand greater deformation and crack propagation. And the improvement increases with enlarging fiber volume fraction (Vf). Furthermore, based on the experimental results, a two-parameters fracture model considering Vf is developed to predict the fatigue life.

Fracture model for predicting tensile strength and fracture toughness of concrete under different loading rates

For the sake of safety evaluation of concrete structures under dynamic loading conditions, the rate dependences of concrete fracture parameters are necessary to be elucidated rationally first. Therefore, the aim of this study is to develop a fracture model for determining the size-independent tensile strength (ft), the fracture toughness (KIC) and the fracture energy (GF) under different loading rates. The fracture mechanism was analyzed comprehensively using three-point bending tests on concrete beams with varied depths (h) and ratios of the initial crack length to the beam depth (a0/h). As the loading rate increases, the number of fractured coarse aggregates is increased, and the shape of the load–displacement curve around the maximum fracture load (Fmax) becomes sharper. Subsequently, a fracture model was proposed to predict the size-independent parameters ft, KIC and GF by incorporating the average aggregate size (davg) and a discrete coefficient (β) to indicate material heterogeneity and discontinuity, respectively. The critical effective crack length (Δac) was discretized and quantified as davg multiplied by β. Closed-form solutions of ft, KIC and GF were obtained using Fmax based on the boundary effect model. ft, KIC and GF can be explicitly predicted after determining Fmax from the fracture tests, and were generally irrelevant to h and a0/h under individual loading rates, indicating their size-independence. The scatters in the ft, KIC and GF values were determined using a statistical analysis. The rate dependences of the fracture parameters were clarified quantitatively through elucidating the variations in ft, KIC and GF with respect to the loading rate. Moreover, the predicted fracture parameters based on the proposed model were insensitive to the possible variations of davg and β. This study brings a new insight into the fracture behaviors of concrete under different loading rates and provides scientific guidance for the disaster prevention of concrete structures.

Experimental Research on Fracture Characteristics of Reactive Powder Concrete in Different Volume Content of Steel Fiber

The fracture characteristics of reactive powder concrete in different volume content of steel fiber are researched in this paper, combining with the photoelastic coating method and the mathematical analytical software MATLAB. More precisely, the wholly integrated initiation, stable propagation, and final failure stages of precast cracks in three-point bending specimens of reactive powder concrete in different volume content of steel fiber are directly recorded and systematically analyzed. Besides, the photoelastic fringe distribution graphs from the vicinity of the precast cracks of specimens are obtained. Based on the experimental results and fracture mechanics theory, the mechanical property of reactive powder concrete, fracture energy, ductility index, initial fracture toughness, and unstable fracture toughness are quantitatively and qualitatively analyzed. The research achievements indicate that there is a stable crack propagation process before the instability failure of the three-point bending beam specimen of reactive powder concrete. The fracture process of the structure includes three stages, namely, the crack initiation, stable propagation, and instability failure. The order of the photoelastic fringe, critical effective crack length, crack initiation load, and maximum load of test parameters in the three-point bending beam specimen of reactive powder concrete increases with the increase of the fiber volume ratio. Based on the numerical treatment for the whole curves of each specimen group, the softening curve and the double fracture parameters of reactive powder concrete are obtained. Besides, the calculated critical effective joint length, initiation toughness, toughness increment, and unstable fracture toughness increase with the increase of the steel fiber volume ratio, by analyzing the measured initiation load, maximum load, and critical effective joint length. The research results can be treated as an important basis and reference for the engineering design and safety assessment of reactive powder concrete.

Time-dependent crack propagation in concrete under constant loading

This paper presents an experimental study on the fracture characteristics of concrete under constant loading, focusing on the crack propagation and the unstable fracture criterion. The test involves three-point bending (TPB) notched beams and compact tension (CT) specimens with different heights, and four constant loads are considered. The results show that the specimens fail within 0.37–4566 h and a higher constant load results in a shorter lifetime of concrete. Furthermore, the time-dependent crack mouth opening displacement and crack length, CMOD(t) and a(t), show three stages with the loading time, t. In the first stage, CMOD(t) and a(t) increase rapidly whereas their growth rates decrease. In the second stage, CMOD(t) and a(t) increase at constant growth rates, indicating cracks propagate stably. In the third stage, CMOD(t) and a(t) increase at greater growth rates than those in the second stage and the growth rates are increasing, indicating the unstable fracture occurs. Accordingly, the time of the boundary point between the second and third stages is defined as the critical time of the unstable fracture of concrete under constant loading, tc. CMOD(tc) and a(tc) are found to be greater than the critical CMOD and effective crack length under static loading, CMODc and ac, and decrease with increasing the constant load. Moreover, it is found that the unstable fracture toughness of concrete under static loading, KunIC, can also be used to determine whether the unstable fracture occurs under constant loading, i.e., when the stress intensity factor at tc reaches KunIC, the unstable fracture occurs.

Fracture properties of slag-based alkali-activated seawater coral aggregate concrete

The development of cracks inside concrete is harmful to the structural durability of seawater coral aggregate concrete (CAC) subjected to an aggressive marine environment. Thus, three-point bending (TPB) tests were performed on the notched beams to determine the fracture properties of cement-based CAC and slag-based alkali-activated CAC (AACAC) at different initial crack-depth ratios (a0/H = 0.2, 0.3, 0.4, and 0.5) and alkaline contents (Na2O-to-binder ratios of 3%, 4%, and 6% by mass). The initial fracture toughness (KICini), critical effective crack length (ac), and unstable fracture toughness (KICun) of the CAC and AACAC were calculated and analyzed based on the double-K fracture criterion. Then, the fracture energy (GF) and characteristic length (lch) were introduced to analyze the energy consumption and brittleness of concrete. It was found that increasing the a0/H ratio reduced the initial cracking load (Pini), peak load (Pmax), ac, GF, and lch, but increased the Pini/Pmax ratio, KICini, KICun, and KICini/KICun ratio, implying that a higher a0/H ratio had a detrimental effect on the crack propagation and increased the brittleness of the AACAC. Additionally, a higher alkaline content, i.e., a greater compressive strength of concrete, upgraded the values of Pini, Pmax, KICini, KICun, and GF due to better mechanical interaction at paste-aggregate interfaces. However, the Pini/Pmax ratio, ac, and lch were steadily lowered with increasing concrete strength, justified by an increase in brittleness. Moreover, the notched AACAC beams contained higher ac (approximately 12.2% increase) and lower KICini/KICun (approximately 4.6% decrease) than those of the notched CAC beams, demonstrating that the existence of alkali-activated materials (AAMs) was beneficial to crack propagation due to improved interfacial transition zone (ITZ) between the paste matrix and aggregates.

Mechanical and fracture properties of steel fiber-reinforced geopolymer concrete

Abstract In this study, the effects of steel fibers on the mechanical properties of the geopolymer concrete – compressive, splitting tensile, and flexural strength; compressive elastic modulus; and fracture properties – were evaluated. Milling steel fibers were incorporated into the geopolymer concrete, and the volume fraction of the steel fibers was varied from 0 to 2.5%. Fly ash and metakaolin were chosen as the geopolymer precursors. Fracture parameters – critical effective crack length, initial fracture toughness, and unstable fracture toughness – were measured by a three-point bending test. The results indicated that all the mechanical properties of the geopolymer concrete are remarkably improved by the steel fibers with the optimum dosage. When the steel fiber content was under 2%, the cubic and axial compressive strength and the compressive elastic modulus increased. The inclusion of 2% steel fibers enhanced the cubic and axial compressive strength and the compressive elastic modulus by 27.6, 23.7, and 47.7%, respectively. When the steel fiber content exceeded 2%, the cubic and axial compressive strength and the compressive elastic modulus decreased, having values still higher than those of the geopolymer concrete without steel fibers. The splitting tensile strength and flexural strength of the concrete were enhanced with increasing steel fiber content. When the steel fiber content was 2.5%, the increment of the splitting tensile strength was 39.8%, whereas that of the flexural strength was 134.6%. The addition of steel fibers effectively improved the fracture toughness of the geopolymer concrete. With 2.5% steel fibers, the initial fracture toughness had an increase of 27.8%, and the unstable fracture toughness increased by 12.74 times compared to that of the geopolymer concrete without the steel fibers.

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.

Determining concrete fracture parameters using three-point bending beams with various specimen spans

The effects of specimen spans on concrete fracture parameters were firstly investigated using three-point bending beams. The calculation formulae of the fracture parameters for specimens with span-depth ratios commonly used in testing were put forward based on linear interpolation method. Six span-depth ratios (2, 2.5, 3, 4, 5 and 6) for concrete specimens were explored. Results show that (1) with the increase of span-depth ratio, the critical effective crack length increased linearly whilst constant initial and unstable fracture toughness were obtained; (2) furthermore, the applicability of the proposed linear interpolation method was verified by the available methods in literatures.

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.

Post cracking behaviour of fibre reinforced concrete with mineral wool fibers residues

The research concerns the feasibility of recycling fibers from mineral wool residues from construction and demolition waste, by incorporating them into a fine grained concrete. All the specimens of concrete with various types of fibers have been subjected to the mechanical tests of flexural and compressive strength. Also the pre-cracking and postcracking softening behaviour of concrete with fiber residues has been investigated. The flexural load-CMOD and load-deflection relationships, obtained in three-point bending test, have been used to determine the fracture parameters: fracture energy, critical stress intensity factor, critical crack tip opening displacement, critical effective crack length. It was verified that the incorporation of mineral residues to a cement concrete is a viable alternative for their recycling; the new composites analyzed maintain adequate mechanical properties for different application.

Experimental validation and fracture properties analysis on wedge splitting concrete specimens with different initial seam-height ratios

In order to study the fracture properties of non-standard concrete wedge splitting tensile specimens with different initial seam-height ratios and the impact on concrete fracture toughness based on aggregates cohesive force, five groups non-standard concrete wedge splitting specimens with different initial seam height ratios as 0.2, 0.25, 0.3, 0.35 and 0.4 were designed and constructed for the experiment. Based on double-K fracture model and fictitious crack model, a new fracture toughness calculation model for non-standard concrete wedge splitting tensile specimen with different initial seam height ratios was built. The results showed that: the value of initial cracking load Pini and unstable fracture load Pun decreased gradually with the increase of specimens’ initial seam height ratio. With the increase of seam height ratios, the value of the critical effective crack length ac showed a linearly increasing trend, but the subcritical crack propagation length Δac showed a decrease trend. The unstable fracture toughness KunIC and the cohesive toughness KcIC were affected by seam height ratios, decreased with initial seam height ratios increasing, and the initial fracture toughness KiniIC was independent of it that could be treated as material constant. When calculating the initial fracture toughness KiniIC, the model in this paper could eliminate the errors caused at the moment of determining initial cracking load Pini, which proved its advantage. For the specimens with smaller initial seam height ratio, its fracture features was influenced by maximum tension stress and showed some shearing 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.

Predicting unstable toughness of concrete based on initial toughness criterion

The fracture processes of concrete were described by a cohesive crack model based on initial toughness criterion. The corresponding analytical method to predict the instability state was proposed. In this model, the initial toughness was adopted as the crack propagation criterion and the weight function method was used to calculate the stress intensity factor and the crack opening displacement caused by the cohesive stress. The unstable toughness can be easily obtained using the proposed method without measuring parameters at the critical state that was necessary in traditional methods. The proposed method was verified by existing experimental data of wedge splitting specimens with different grades of concrete and the sensitivity of the results on the tensile softening curve was discussed. The results demonstrate that the proposed method can well predict the peak load, the critical effective crack length, and the unstable toughness of concrete specimens. Moreover, the calculated unstable toughness is not sensitive to the tensile softening curve.

A theoretical method for determining initiation toughness based on experimental peak load

A theoretical method for determining the initiation toughness was proposed using input conditions of the peak load and the tensile softening curve. In this method, the cohesive stress is considered to calculate the values of critical effective crack length, crack tip opening displacement, and the initiation toughness. The calculated results using the proposed method were compared with those by the double-K method+. The comparison showed that the values obtained by the proposed method were slightly greater than those by the double-K method. Moreover, the calculation results of initiation toughness by the proposed method were verified to be independent of the specimen size and not sensitive to the tensile softening curve.

Dynamic Fracture Toughness of Sandstone Masonry Beams Bound with Fiber-Reinforced Mortars

AbstractThis paper reports the fracture parameters of bond in stone masonry beams bound with plain and fiber-reinforced mortar. Sandstone blocks were joined together with a modern Type S mortar conforming to the Canadian standard. A companion series was examined employing a hydraulic lime mortar, typically used in the restoration of historical masonry. Based on a previous study, polypropylene microfibers were incorporated at up to 0.50% by volume to achieve superior crack growth resistance. This study evaluated the critical stress intensity factor, the critical effective crack length, and the critical crack mouth opening displacements. The masonry beams were subjected to quasi-static flexure as per ASTM and dynamic bending through a drop weight impact machine that generated stress rates up to 107 kPa/s. The study reveals that there is an improvement in the bond strength due to fibers but a difference in the fracture performance between the Type S and hydraulic lime mortars. Whereas with Type S mortar, fi...

Experimental Study on Fracture Properties of Hybrid Fiber Reinforced Concrete

Though fracture test on the fifteen specimens with notch of hybrid fiber reinforced concrete with the size of 100mm×100mm×400mm, this paper explores the hybrid effect between steel fiber and polypropylene fiber and impact on the fracture properties, such as critical effective crack length, critical crack tip opening displacement, effective stress intensity factors and fracture energy. The test results indicate that the addition of fiber is helpful to improve the fracture properties of concrete. Synergistic effect of two kinds of fibers is good, the steel fiber with high elastic module can restrain the cracking of concrete when the crack displacement is small, polypropylene macro-fiber with high ductility is more beneficial to increase the fracture properties of concrete than steel fiber when the crack displacement is big. The best fiber compounding can be gotten when the volume fractions of steel fiber and polypropylene fiber is respectively 0.5％and 1.0％in this experiment.

Experimental Study on Fracture Properties of Hybrid Fiber Reinforced Concrete

Though fracture test on the fifteen specimens with notch of hybrid fiber reinforced concrete with the size of 100mm×100mm×400mm, this paper explores the hybrid effect between steel fiber and polypropylene fiber and impact on the fracture properties, such as critical effective crack length, critical crack tip opening displacement, effective stress intensity factors and fracture energy. The test results indicate that the addition of fiber is helpful to improve the fracture properties of concrete. Synergistic effect of two kinds of fibers is good, the steel fiber with high elastic module can restrain the cracking of concrete when the crack displacement is small, polypropylene macro-fiber with high ductility is more beneficial to increase the fracture properties of concrete than steel fiber when the crack displacement is big. The best fiber compounding can be gotten when the volume fractions of steel fiber and polypropylene fiber is respectively 0.5％and 1.0％in this experiment.

A comparative study on five approaches to evaluate double- K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double- K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double- K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.