Critical Crack Opening Displacement Research Articles

Experimental Study on the Influence of Humidity on Double-K Fracture Toughness and Fracture Energy of Concrete under Water Environment

Saturated concrete is significantly different from dry concrete in fracture mechanical properties. Using the wedge-splitting tensile method to research the rule of change in moisture content, double-K fracture toughness and fracture energy of three strength grades (C20, C30, and C40) of concrete immersed in a free water environment for 0 h, 2 h, 5 h, 24 h, and 120 h were studied in order to provide support for the safety evaluation of concrete structures in a water environment. The initial cracking fracture toughness of C20, C30, and C40 concrete in saturated state were, respectively, 29.6%, 23.2%, and 33.4% lower than that in dry state. The unstable fracture toughness of C20, C30, and C40 concrete in saturated state were, respectively, 22.7%, 23.9% and 33.8% lower than that in dry state. The fracture energy of C20, C30, and C40 concrete in saturated state are only 71.99%, 70.29%, and 66.11% of that in dry state, respectively. The initial cracking fracture toughness and unstable fracture toughness of concrete all show a linear, decreasing trend with an increase in moisture content. Before the crack initiation, the measured P–CMOD curve had an obvious linear elastic stage, stable expansion stage, and unstable expansion stage. The critical crack opening displacement gradually decreases with an increase in moisture content; the deformation capacity and toughness of concrete are shown to decrease. The humidity state should be fully considered when evaluating the fracture mechanical properties of concrete.

Fracture process zone of high-strength concrete under monotonic and cyclic loading

To evaluate the characteristics of the fracture process zone (FPZ) of high-strength concrete (HSC) under monotonic and cyclic loading, three-point bending (TPB) tests were carried out on single-edge notched HSC beams and digital image correlation (DIC) technique was employed to obtain the full-filed deformation of the beams. Based on the displacement and strain fields measured by the DIC technique, a defined strain threshold (εxx) was used to determine the tip of the FPZ and critical crack opening displacement (wc) was used to judge the rear of the FPZ. The length of the FPZ (lFPZ) was defined as the vertical distance between the tip and rear of the FPZ and the width of the FPZ was determined from the strain concentration zone surrounded by the εxx. The results indicates that the envelope of the load versus the lFPZ (P-lFPZ) curve under cyclic loading is consistent with that under monotonic loading and it can be divided into 4 stages, namely linear elastic deformation stage, stable crack propagation stage, unstable stage before fully developed FPZ and unstable stage after fully developed FPZ, respectively. When the FPZ is fully developed, the lFPZ of the beams is about 80.04 mm ∼ 89.72 mm while the maximum width of the FPZ (bm) is about 8.43 mm ∼ 10.31 mm which is equivalent to the maximum size of the coarse aggregates. Both the lFPZ and bm first increases and then decreases in the unloading stage of each cycle and this can be explained by the variation of the stress intensity factor (SIF) which indicates that the driving force of crack growth is greater than the fracture resistance at the initial stage of unloading. Both the lFPZ and bm first decreases and then increases in the early stage of reloading, which may be caused by the lagging recovery of the deformation of the specimen as the rate of reloading is much lower than that of unloading.

Stochastic evolution characteristics of fracture process zone in concrete

In this study, the stochastic characteristics of the fracture process zone (FPZ) of concrete are analysed. The impacts of specimen size on the critical crack opening displacement, the distribution of cohesive stress, and the critical length of FPZ are studied, and calculations are performed for the stochastic energy consumption curves of concrete. The dispersion of the variance of critical crack tip opening displacement CTODc and the critical length of FPZ are obtained. Combined with the existing experiments, comparative verification is performed. The results show that the critical crack tip opening displacement CTODc and critical length of FPZ increased with the specimen size, whereas the critical cohesive stress at the tip of the initial crack decreased with the specimen size. The dispersion of the variance of critical crack tip opening displacement CTODc and the critical length of FPZ increased with the specimen size.

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.

Thermoplastic cohesive fracturing model of thermally-treated granite

Thermoplastic fracturing is a prominent characteristic of thermally-treated granite for temperature-dependent underground geotechnical engineerings , such as geothermal energy exploration and high-level nuclear waste disposal. More specifically, the tension-open of the cohesive crack in the fracture process zone (FPZ) presents a plastic softening feature dependent on temperature. However, understanding granite thermoplastic fracturing remains challenging. This work proposes a thermoplastic cohesive fracturing model of thermally-treated granite, incorporating temperature-dependent softening rule and completely coupled stress-strain-temperature constitutive relation. Several new thermoplastic fracturing properties in the proposed model are determined by further analyses of published fracturing test data (Miao et al., 2020) done on Beishan granite suffering high-temperature treatments (200–500 °C). The initial yield parameter (cohesive tensile strength) decreases linearly with the rising high-temperature treatments. The critical yield parameter (the critical crack opening displacement (COD)) follows a two-stage linear increasing rule with 300 °C as a boundary, similar to the temperature-dependent FPZ length. The plastic modulus, delineating the cohesive crack's softening rule, increases quadratically with the enhanced high-temperature treatment. The temperature sensitivity modulus ( T ), characterizing the contraction/expansion of yield surface with increasing temperatures, decreases from positive to negative with the increasing COD. Both the fracture energy and the accumulated dissipated energy present remarkable nonlinearities with several inflection points , implying the complex temperature-dependent fracture resistance . This proposed model was validated with three-point-bending fracturing tests of thermally-treated Beishan granite, fitting well (coefficient: 88.8%–99.7%) with the experimental cohesive tensile strength , critical COD, and the accumulated dissipated energy. Besides, by analyzing the softening curves of cohesive cracks in thermally-treated granite, the positive-negative change of T was consistent with the contraction-expansion transition of the yield surface. This work provides a modeling approach for temperature-dependent fracturing of rock-like materials. • The thermoplastic softening of FPZ is characterized via a thermoplastic framework. • This work proposes a thermoplastic cohesive fracturing model for rocks. • New model parameters were proposed to characterize temperature-dependent fracturing. • The correlation coefficient between the model and test data reaches 88.8%–99.7%. • This work provides a modeling approach for temperature-dependent fracturing of rock.

Investigation of fracture properties and size effects of mass concrete using wedge splitting tests on large specimens

This work presents experimental results of fracture tests on very large concrete specimens of mass concrete mixture with a maximum aggregate size of 100 mm. Wedge splitting tests were performed on very large concrete specimens and on moderate-size specimens sawn from large concrete blocks to investigate both size and temperature effects. The digital image correlation (DIC) technique allowed to assess the fracture parameters of these specimens, including the critical crack opening displacement and crack growth length at the peak. These parameters were compared to theoretical computed parameters based on linear elastic fracture mechanics or LEFM theory. Cyclic splitting tests were additionally performed on very large and moderate-size concrete specimens. Interpretation of the results of these cyclic tests via DIC enabled to formulate important conclusions regarding the evolution of the fracture process zone length and critical opening displacement during the tests and to validate the hypotheses associated with the recently developed disturbed fracture process zone theory in terms of the size effect on the fracture energy.

Experimental study on development characteristics and size effect of rock fracture process zone

In order to investigate the development characteristics and size effect of rock fracture process zone (FPZ), the GCTS RTX-3000 rock mechanics testing machine was used to carry out on semi-circular bend (SCB) sandstone specimens with diameters of 50 mm, 100 mm, 150 mm and 200 mm, respectively. Combined with the digital image correlation (DIC) method, the variations of the displacement field at the crack tip of specimens with different sizes were analyzed. The results show that the crack opening mode of the SCB sandstone specimen has experienced three stages of slow, linear and accelerated growth. Its critical crack opening displacement is about 20 μm. When the load reaches around 65% pre-peak, the FPZ begins to develop. The range of the FPZ reaches the maximum at the peak. The closer to the peak, the faster the development of the FPZ, and the length of the FPZ that increases from 90% pre-peak to peak accounts for 50% of the total FPZ length. The FPZ length of specimens of different sizes at the peak is about 2–2.5 times of the width. As the size of the specimen increases, the length and width of the FPZ increase. The thickness of the specimen has a significant effect on the width of the FPZ.

Investigation on crack propagation perpendicular to mortar–rock interface: experimental and numerical

The initiation and propagation of cracks perpendicular to mortar–aggregate interfaces have a significant influence on the mechanical behaviour of concrete materials. Although existing studies have revealed that a perpendicular crack to the interface can penetrate into the aggregate for high strength concrete owing to the stronger interfacial bond strength, the crack propagation penetrating into aggregates has not been fully understood. In this paper, a crack propagation criterion based on the stress intensity factor (SIF) is developed for layered mortar–rock beams with a crack normal to the interface. Based on this criterion, a numerical method is proposed to predict the crack propagation process of layered mortar–rock beams under mode I fracture. After the validity of the numerical method is verified with experimental data obtained in this paper, the effects of the fracture parameters on the crack propagation characteristics in layered mortar–rock beams are evaluated. The results show that the crack propagation behaviour is greatly affected by the difference of the initial fracture toughness and the tension-softening constitutive law between the two materials. If a crack approaches a material with a larger initial fracture toughness, the load increases suddenly when the crack passes through the interface due to the higher resistance against crack penetration. Conversely, when the crack approaches a material with a smaller initial fracture toughness, it rapidly penetrates into the material after reaching the interface, resulting in an obvious discontinuity in the load response. It is also shown that, when a crack grows across the interface and propagates inside a material with a smaller critical crack opening displacement, the cohesive stress distributes discontinuously along the ligament where a traction-free crack is formed in the vicinity of the interface. This paper concludes that the proposed numerical method is effective in predicting the crack propagation process of layered composite beams with a crack normal to the interface.

Experimental study on fracture and fatigue crack propagation processes in concrete based on DIC technology

A method to determine crack tip position and fracture process zone (FPZ) in concrete was proposed based on Bažant Crack Band Model (CBM) and digital image correlation (DIC) technique, which was described as: firstly, the critical crack opening displacement of concrete (wcr) was determined based on CBM and the basic mechanical properties; secondly, DIC method was used to obtain the displacement field on the surface of specimens; thirdly, the position where the crack opening displacement equaled to wcr was defined as the crack tip position. In the fatigue crack propagation tests, the whole fatigue crack was FPZ at the beginning of fatigue loading until the non-cohesive crack grew and the length of FPZ decreased. The length of FPZ tended to be stable when the number of loading cycles was close to half of the fatigue life. Fatigue crack propagation curves (a-N curves) were obtained and fitted by logistic function to reduce the influence of the data scattering. Fatigue crack propagation rate da/dN was separated into descending and ascending crack propagation functions based on the increment of crack Δa and stress intensity factor ΔK, respectively. The da/dN-Δa curves for the descending segment showed obvious scatter. Paris’ law was applied to describe fatigue crack propagation rate well for the ascending segment.

Plastic deformation and mixed-mode I/II fracture behavior of un-plasticized polyvinyl chloride

To further understand the mixed-mode I/II fracture behavior of Un-plasticized Polyvinyl Chloride (UPVC), a series of mixed-mode I/II experiments on analogy compact tension specimens have been conducted using an MTS 810 hydraulic test machine. The evolution of the displacement field during stable crack extension was monitored by two-dimensional digital image correlation technique. Results obtained from the mechanical testing demonstrate that the maximum load of mode II is about 100% higher than that of mode I, and the load-carrying capacity is dependent on orientation and load condition. Fractography observations indicate that the fracture surface can be divided into fatigue region with relatively smooth characters and stable crack extension region with randomly distribution of honeycomb-like voids. Furthermore, mode I failure (opening) should be the main failure mechanism of UPVC rather than mode II (shear failure). The results also suggest that the value of crack opening displacement (COD) tends to be nearly constant when the length of crack exceeds the thickness of the sample, which is independent on orientation and load condition. Therefore, COD criterion can be used to describe the overall severity of plastic deformation in the near-tip region of UPVC, and components of COD, which is perpendicular to the crack surface, should be the predominant controlling parameter of crack propagation.

Comparative experimental study of the mechanical and fracture properties of Portland limestone and Corsehill sandstone

An experimental investigation of the mechanical and fracture characteristics of Portland limestone and Corsehill sandstone is undertaken, aiming at enhancing understanding of the structural behaviour of these natural building stones commonly used in both new and restoration projects in Edinburgh, Scotland. A series of three-point bending and four-point bending tests on appropriately cut prismatic samples, in the presence of U-shape notches, were performed and results were interpreted following the concepts of crack mouth opening displacement and fracture energy. The critical crack opening displacement could be further investigated as a fracture criterion, in­dependently of the method used for its determination. At a second stage, the effect of specimen shape and size on flexural strength, deflection at mid-span, crack mouth opening displacement and fracture energy was studied for Port­land limestone. Despite the scattering of results, trends observed comprise (a) the negative correlation between the flexural strength of Portland limestone and the specimen span length and (b) the positive correlation between fracture energy and specimen size. Conclusions drawn are in good agreement with similar ones for other quasi-brittle materials and contribute to the assessment of the fracture behaviour of full size structural members that are often beyond the range of possible failure testing.

Shear strength of reinforced concrete beams with recycled aggregates

This article presents an experimental program on the shear behavior of beams without transversal reinforcement manufactured with natural aggregate concrete and 100% recycled aggregate concrete. The beams were tested under four-point bending for a shear span-to-depth ratio ( a/ d) equal to 1.5 and 3.0. The mechanical properties of two mixes were characterized in terms of compressive strength, splitting tensile strength, and elastic modulus. Three-point bending tests were performed on plain pre-notched samples in order to determine the fracture properties by an inverse analysis of experimental force–crack mouth opening displacement curves using the analytical nonlinear hinge model and a power law strain-softening relationship. The strain-softening law is described by two parameters being, respectively, the power n and the critical crack opening displacement wc. The experimental results show that, for the same class of compressive strength, tensile strength, fracture energy, and the shear strength of recycled aggregate concrete are lower than natural aggregate concrete. The decrease in the fracture energy and the shear strength is consistent with the decrease in the splitting tensile strength of the recycled aggregate concrete mixes compared to the natural aggregate concrete. Critical shear crack theory was adopted to model the shear behavior of beams tested with a/ d = 3.0. For an accurate evaluation of the deformation capacity of tested beams, the nonlinear hinge model for recycled concrete members was extended to recycled concrete sections. For deep beams ( a/ d = 1.5), the strut-and-tie model was used. Finally, comparisons of prediction models to a wide range of experimental data are presented.

Visual detection of a cohesionless crack in rock under three-point bending

Crack initiation and propagation in rock involve the development of a nonlinear zone around the crack tip called fracture process zone. The existence of fracture process zone influences the fracture behavior and therefore it must be carefully investigated. This zone is normally idealized as a cohesive zone whose mechanical properties are difficult to measure. In this study, a relatively simple approach is proposed to identify the properties of the cohesive zone and the length of the cohesionless crack in a sandstone specimen under three-point bending. Two types of specimens were tested: beams with center notch and with smooth boundary. The digital image correlation (DIC) was utilized to obtain the opening displacement around the position where the fracture initiated. For a small length of a horizontal section around the specimen center, the material is considered to be in the state of uniaxial tension and its behavior is interpreted by the cohesive zone model.The proposed approach discusses three types of opening displacement distribution patterns (I), (II), (III). Pattern (I) is related to tensile loading of the material, pattern (II) suggests the development of material softening within the cohesive zone and pattern (III) indicates the development of the cohesionless crack. These displacement patterns together with the appropriate reference loadings are used to identify the length of the cohesionless crack. For example, observation of pattern (III) is consistent with the development of the cohesionless crack when the reference loading is the beginning of experiment. Further, the proposed method is useful for measuring the critical crack opening displacement and the fracture energy.

In-situ microscale visualization experiments on microcracking and microdeformation behaviour around a pre-crack tip in a three-point bending sandstone

A new microscale visualization experimental system is proposed for in-situ measurement of microcracking and microdeformation behaviour of macroscopic specimens during real-time loading. A series of three-point bending experiments were conducted on sandstone beam specimens containing a Mode I pre-crack. The newly developed microscopic experimental system and two other traditional experimental techniques, including acoustic emission (AE) monitoring and macroscopic charge coupled device (CCD) monitoring, were applied together to capture and measure the cracking process and deformation characteristics around the pre-crack tip in real-time. The results show that the crack initiation determined by the proposed microscopic monitoring system was earlier than that determined by AE monitoring and macroscopic CCD monitoring. The microscopic monitoring system observed that the cracks initiated at multiple locations at the pre-crack tip, and they continuously propagated, opened, and coalesced with each other to eventually form a main crack in a zigzag and irregular way, which is significantly different from the macroscopic CCD monitoring observations that suggested that the crack only initiated from the pre-crack tip and rapidly extended upwards along the pre-crack length direction in a relatively simple way. Furthermore, the full-field deformation characteristics at the pre-crack tip were quantitatively obtained by the macrograph-based digital image correlation (DIC) and the micrograph-based DIC calculations. The results indicate that the calculated localized strain zones from the micrograph-based DIC were narrower than those calculated from the macrograph-based DIC. The former had a very similar morphology to realistic microscopic cracks, whereas the latter was wider and longer than the induced macroscopic cracks. The average critical crack opening displacement (COD) calculated using the micrograph-based DIC was approximately 1.3 times larger than that calculated using the macrograph-based DIC.

Comprehensive sandstone fracturing characterization: Integration of fiber Bragg grating, digital imaging correlation and acoustic emission measurements

Prominent characteristics of rock fracturing can be described mainly by crack opening displacement (COD), fracture process zone (FPZ) and fracture energy. In view of lack of real-time and comprehensive measurement techniques for characterizing rock fracturing in field applications, this paper developed a characterizing method of rock fracturing by utilizing and integrating Fiber Bragg Grating (FBG), Digital Imaging Correlation (DIC) and Acoustic Emission (AE). In this paper, mode I fracturing test was performed on sandstone using three-point bending, and the fracturing process was simultaneously detected and recorded by FBG, DIC and AE. The experimental results showed that (1) DIC-based measurement of horizontal displacements across the fracture presented a localized discontinuity, in accordance with FBG-based real-time measurement. At the onset of traction-free zone formation (peak load), the critical COD (δc) was found to be 76 μm as identified by DIC and FBG. (2) Moreover, the dissipated energy distribution and cohesive crack profile in FPZ characterized by the integrated measurement, indicated that 70%–90% of AE energy (dissipated energy) populated in the FPZ, little AE energy concentrated in the traction-free zone, and the position of δc delineated a boundary for specifying FPZ. The length of fully developed FPZ was 20 mm (±2 mm) in length. (3) The integrated measurement delineated the cohesive crack, which was not available previously. The integrated measurement revealed the softening curve followed a straight line; the relationship between FPZ length and crack tip opening displacement (CTOD) was linear, and the relationship between dissipated energy and FPZ length was quadratic. Based on the interrelations of cohesive crack characteristics identified by the integrated measurements, real-time fracturing can be captured by one technique (e.g. FBG) in field application.

A multiscale model for post-peak softening response of concrete and the role of microcracks in the interfacial transition zone

The effect of microcracks ahead of a macrocrack on the post-peak behavior of concrete-like quasi-brittle material is studied. The critical length of a microcrack is estimated by considering a small element near the macrocrack tip and defining the critical crack opening displacement of the microcrack that exist in the interface region between the aggregate and cement paste. A fracture model is proposed to predict the post-peak response of plain concrete. This model is validated using the experimental results for normal-strength, high-strength and self-consolidating concretes available in the literature. Through a sensitivity analysis, it is observed that the elastic modulus of concrete and the fracture toughness of the interface have a substantial influence on the critical microcrack length.

Influence of recycled coarse aggregates incorporation on the fracture properties of concrete

This paper presents the mechanical and fracture properties of a structural concrete incorporating coarse recycled aggregate. Four mixes were designed according to the standard EN 206-1 to achieve S4 consistence class and C35/45 class of strength. Concrete specimens were prepared with different recycled gravel content of 0%, 30%, 65% and 100% by volume of the total coarse gravel.Three points bending tests were performed on 10×10×40cm pre-notched samples in order to determine the flexural strength and fracture properties according to the RILEM recommendations. From experimental Force-CMOD curves, the intrinsic fracture properties were obtained by an inverse analysis using an analytical model and a power law strain-softening relationship. The strain-softening law is described by two parameters being respectively the power n and the critical crack opening displacement wc. It was found that the difference between the calculated fracture energy, GF, and the RILEM fracture energy, GFRILEM, is more pronounced for recycled aggregate concrete.The evolution of n and wc, the parameters of the power strain-softening law, was also studied. It appeared that the power, n, depends on the compressive strength, the aggregate size and the water to binder ratio. For the same class of compressive strength, it remains substantially unchanged when the recycled aggregates content increases. For the critical crack opening wc, it decreases when the substitution ratio increases. Finally, the relationship between fracture properties and the tensile strength has been established.

Determination of Fracture Toughness by Single and Double Action Tensile Impact Fracture Tests

The characterization of the loading rate dependence of the fracture behavior of polymers is of prime theoretical and practical interest for supporting demanding engineering applications. To gain more insight into the high rate fracture behavior of polymers, fracture tests were performed under tensile loading conditions up to 12 m/s loading rate using a neat model polymer (PVC grey) in this study. A conventional single actuator test set-up for compact tension C(T) specimens was developed based on the previous experience of the authors and implemented on a new high rate servohydraulic testing machine. In addition, a novel double action test set-up was developed by applying two twin actuators and implemented in a rigid horizontal test frame. The conventional load and force measurement was extended by instrumented test specimens and by a high speed optical strain analysis system for both set-ups. Force based fracture toughness values using the peak load values, KIcPL and displacement based values using the critical crack opening displacement (CTOD) KICCTOD were determined up to a loading rate of 10 m/s. While the KIcPL values decreased up to a loading rate 103 MPam1/2s-1 an increase with a high data scatter was observed above them. Corresponding to the CTOD values the calculated KICCTOD values revealed a slight decrease and moderate data scatter up to the maximal loading rate.

Fracture behavior of fly ash concrete containing silica fume

Effect of silica fume on fresh properties, compressive strength at 28 days and fracture behavior of fly ash concrete composite were studied in this paper. Test results indicated that the fluidity and flowability of fly ash concrete composites decreased and fly ash concrete composite are more cohesive and appear to be sticky with the addition of silica fume. Addition of silica fume was very effective in improving the compressive strength at 28 days of fly ash concrete composite, and the compressive strength of fly ash concrete composite has a trend of increase with the increase of silica fume content. Results also indicated that all the fracture parameters of effective crack length, fracture toughness, fracture energy, the critical crack opening displacement and the maximum crack opening displacement of fly ash concrete composite decreased with the addition of silica fume. When the content of silica fume increased from 3% to 12%, these fracture parameters decreased gradually with the increase of silica fume content. Furthermore, silica fume had great effect on the relational curves of the three-point bending beam specimen. As the silica fume content increased from 3% to 12%, the areas surrounded by the three relational curves and the axes were becoming smaller and smaller, which indicated that the capability of concrete composite containing fly ash to resist crack propagation was becoming weaker and weaker.

Approach to Critical Crack Opening Displacement Modeling of Damage in Metal Sheets after Composite Patch Bonded Repair

Abstract The paper proposes a method of calculating the maximum displacement in the aircraft metal structure repaired by CPBR (bonded composite patch repair). The calculations were made based on specimens. The specimens were prepared according to the current requirements used in aviation. The 2024-T3 alloy metal sheet was a structure. To repair the structure used the boron-epoxy composite patch in prepreg technology was used. The metal structure was modeled as an isotropic elastic body. The metal structure coated with the composite patch was modeled as an orthotropic structure. Based on this, the stress was determined in the metal structure. The size opening displacement in the metal structure was determined based on the model of linear elastic fracture mechanics for the plane stress state. The calculation results were verified by measuring the displacement in laboratory conditions. The laboratory tests made it possible to demonstrate the accuracy of the proposed approach.