Flattened Brazilian Disc Specimens Research Articles

Dynamic mode II fracture mechanism of rocks using a novel double-edge notched flattened Brazilian disc specimen in the split Hopkinson pressure bar tests

The dynamic mode I fracture behaviors of rocks have been extensively investigated during recent decades, while the dynamic mode II fracture mechanism of rocks and its comparison with dynamic mode I fracture are poorly understood. In this study, a novel double-edge notched flattened Brazilian disc (DNFBD) specimen is introduced for dynamic mode II fracture toughness tests of rocks in the split Hopkinson pressure bar (SHPB) tests. First, using the finite element method (FEM), the stress distribution of the DNFBD specimen is analyzed and the stress intensity factors (SIFs) and the T-stress at the crack tips are determined. Then, dynamic mode II fracture tests are conducted on sandstone using the DNFBD specimen with proper specimen geometry configuration. High-speed photography and digital image correlation (DIC) results show that the shear crack initiates from the notch tips and propagates along the shear ligament of the DNFBD specimen, which demonstrates the reliability of the DNFBD-SHPB method for dynamic mode II fracture tests of rocks. Experimental results show that the dynamic mode II fracture toughness KIIC of rocks generally increases with increasing loading rate, exhibiting significant loading-rate dependence. For comparative investigation, dynamic mode I fracture tests using the notched semi-circular bend (NSCB) specimen are conducted on the same rocks. The results indicate that the mode II fracture toughness KIIC values are always higher than the mode I fracture toughness KIC values of rocks over a wide range of loading rates. The microscopic fracture mechanism of sandstone is interpreted based on the thin section observations. Under quasi-static loading, trans-granular (TG) fractures are more popular in the mode II fracture tests, while inter-granular (IG) fractures dominate the failure of mode I fracture. However, with the increase of loading rate, TG fracture becomes increasingly prevalent in both the dynamic mode II fracture and the dynamic mode I fracture of rocks. The results of this study are of great significance for understanding the dynamic mode II fracture mechanism of rocks.

Fracture characteristics of sustainable crumb rubber concrete under a wide range of loading rates

The dynamic mechanical properties of concrete materials significantly influences the safety of construction under impact loads. In this study, a comprehensive experiment on the crack straight-through flattened Brazilian disc specimens of crumb rubber concrete (CRC) is undertaken. Three specific experiments were performed to obtain the wide loading-rate ranges of fracture characteristics, i.e., the quasi-static test, drop-hammer impact test, and split Hopkinson pressure bar test. The measured and calculated results are also discussed. The results reveal that the fracture toughness and energy are both positively correlated with loading rate. Moreover, a transition loading rate (around 1 GPa × m1/2/s) exists between the high and low loading rates, and the enhancing effect of high loading rate on fracture toughness cannot be neglected. The analysis of the dynamic increased factor (DIF) on the fracture toughness (DIFk) and fracture energy (DIFg) of CRC shows that DIFk and DIFg are related to the rubber content. Furthermore, the analysis demonstrates that crumb rubber particles can enhance the crack resistance of concrete under dynamic loads. Accordingly, empirical models for the DIFk and DIFg of CRC are proposed based on the experimental data. In addition, the mechanisms by which the loading-rate affects the fracture characteristics were preliminarily identified by observing the failure modes under various loading-rate loads. This study is intended to help spread the application of crumb rubber in concrete materials.

Tensile mechanical behavior and fracture characteristics of sandstone exposed to freeze-thaw treatment and dynamic loading

Rock masses in high-elevation or cold areas are vulnerable to the joint results of freeze-thaw (F-T) action and dynamic loading, it is thus significant to evaluate the tensile mechanical behavior and fracture characteristics of F-T treated rocks under dynamic loading. In this study, based on the split-Hopkinson pressure bar (SHPB) device, the dynamic flattened Brazilian disc (FBD) tests are performed on sandstone to investigate the degradation mechanism of dynamic tensile response and fracture characteristics of rock induced by F-T treatment. Recur to high-speed photography and digital image correlation (DIC) technique, 3D scanning and scanning electron microscope (SEM), the macroscopic and microscopic fracture characteristics of F-T treated sandstone are comprehensively observed and discussed. Experimental results show that the dynamic tensile strength of sandstone constantly decreases with increasing F-T cycles at a specified loading rate. The failure mode of FBD specimen gradually transforms from slash mode to ‘Y’-shaped mode and then to ‘X’-shaped mode with increasing loading rates. 3D scanning results show that the roughness of the central fracture surface of FBD specimen decreases with increasing loading rate or freeze-thaw cycles. Furthermore, both microscopic tensile and shear fracture patterns are observed by SEM, and it is found that the trans-granular (TG) fracture become more prevalent under higher loading rate or higher freeze-thaw cycles. In addition, some hidden connection between microscopic fracture mechanism and macroscopic mechanical properties of F-T treated sandstone is analyzed and discussed.

New insights into the fracture mechanism of flattened Brazilian disc specimen using digital image correlation

As a simple and convenient testing method, the flattened Brazilian disc (FBD) specimen has been widely used to determine the tensile strength and mode-I fracture toughness of rocks. However, the precision of the mechanical parameters calibrated by FBD testing method needs to be further evaluated. In this paper, digital image correlation (DIC) technique is used to capture the progressive failure process of FBD specimen, and some new insights are provided for further understanding the fracture mechanism of FBD specimens. Firstly, the horizontal tensile strain history in the center region of FBD specimen is obtained via DIC technique, and combined with loading force history, the tensile stress–strain curve of rocks can be determined. Then, by analyzing the horizontal strain and displacement field near the central crack of FBD specimen, the central crack tip positions are identified. The progressive failure process of FBD specimen shows that the micro-crack and fracture process zone (FPZ) has grown at the center of FBD specimen at the moment of first peak force Pmax. After the Pmax, the central crack propagates unsteadily towards the flattened ends of FBD specimen, while is hindered after the loading force declined to the local minimal force Pmin. Therefore, it is not proper to determine the mode-I fracture toughness KIC using the local minimal force Pmin in FBD tests. In this study, a modified calculation method to determine KIC is proposed using the first peak force Pmax and its corresponding central effective crack length observed via DIC technique. In addition, the cracking nature of the secondary crack is identified, and the second rise of the loading force is induced by the compression-shear failure near the flattened ends of FBD specimen. These results are beneficial to better understanding the progressive fracture mechanism of FBD specimen and improving the accuracy of KIC calibrated by FBD testing method.

Splitting tensile mechanical behavior and failure characteristics of thermally-damaged rock

The Brazilian disc specimen (BDS) and flattened Brazilian disc specimen (FBDS) test was conducted on the thermally damaged rock (from room temperature to 1000°C) that was subjected to static loads....

Dynamic tensile behavior of rocks under static pre-tension using the flattened Brazilian disc method

Rocks in underground engineering projects, are likely to be subjected to static pre-stress and dynamic loading simultaneously. To measure the tensile strength of brittle rocks under coupled static-dynamic loads, a coupled static-dynamic flattened Brazilian disc (FBD) testing method is proposed in this study via a modified split Hopkinson pressure bar (SHPB) system. Our method has unique advantages on coupled static-dynamic tests using SHPB, because under different static pre-loads, the contact area between the loading platens and the specimen remain nearly constant, contributing to maintaining a consistent contact condition. Using the method, we experimentally and numerically investigate the tensile response of sandstone subjected to different static pre-tensions and different dynamic loading rates. By careful pulse shaping, the dynamic force equilibrium on both loading ends of FBD specimens can be satisfied. Detailed progressive fracture processes of tested specimens are captured via a high-speed camera, and the central crack initiation is observed in all our coupled static-dynamic tests. The dynamic tensile strength of sandstone decreases with the increase of the pre-tension, while the total tensile strength features an increase, and both the dynamic tensile strength and total tensile strength show the obvious rate dependence. The numerical simulation reveals that under a higher pre-tension ratio, more microcracks are observed at the static pre-tension stage, suggesting that more damage is induced in the rock. Our method is feasible to indirectly measure the tensile strength of rocks under coupled static-dynamic loads.

Experimental study on dynamic split tensile properties of rubber concrete

Static and dynamic split tensile tests were conducted on rubber concrete with varied volume fractions of rubber particles that replaced fine aggregate (10%, 20%, 30%, 40%, and 50%, named as RC10, RC20, RC30, RC40, and RC50, respectively). The flattened Brazilian disc specimens were applied to determine the tensile properties and energy absorption capabilities under high strain rate by an SHPB (Split Hopkinson Pressure Bar) and medium strain rate by a drop-hammer testing machine. With a high-speed camera, the crack growth of specimens in the SHPB and drop-hammer impacting tests was observed and validated. The experimental result of five rubber concretes and one normal concrete without rubber particles was obtained, and the strain-rate effect on tensile strength of rubber concretes and normal concrete was confirmed. For high strain rate, RC10, RC20 and RC30 were sensitive to strain rate dependence, but rate dependence of RC40 and RC50 was lower than normal concrete. RC30 exhibited the most sensitivity and excellent energy absorption capability in static and dynamic tests. Excessive rubber content did not continually increase the toughness of the concrete under dynamic loadings.

Cyclic flattened Brazilian disc tests for measuring the tensile fatigue properties of brittle rocks.

We propose a cyclic flattened Brazilian disc (FBD) testing method to measure the tensile fatigue properties of brittle rocks. Our method has obvious merits in its specimen preparation and experimental operation. Two parallel flattens are introduced in the disc specimen, which facilitate easily and uniformly loading the specimen without special loading devices required. Moreover, the contact regions between two flattens and loading planes barely change during the entire loading and unloading process, ensuring a consistent contact condition. With certain appropriate loading angles, this method guarantees that the very first breakage of the specimen occurs at the center of the disc, which is the prerequisite of the Brazilian-type indirect tensile tests. To demonstrate our new method, nine cyclic FBD tensile tests are conducted. The fatigue load-deformation characteristics of FBD specimens are revealed. The tensile fatigue lives of tested specimens are observed to increase with the increase in cyclic loading frequency. Our proposed method provides a convenient and reliable approach to indirectly measure the fatigue tensile properties of brittle rocks and other brittle solids subjected to cyclic tensile loadings.

Experimental Study of Strain Rate Sensitivity to Fracture Toughness of Rock using Flattened Brazilian Disc

Brazilian splitting test with arc loading condition may result in a reduction of the concentration of stress in the disc. Additionally, crack initiation from the central position of the Brazilian disc cannot be guaranteed because of the non-uniformity of stress-loading arcs. In order to achieve the theoretical foundation of the Brazilian splitting test, a Flattened Brazilian Disc (FBD) specimen can be used as an alternative, which prevents local crack initiation. An FBD specimen, because of its ease of sample preparation and loading geometry, can be used to estimate different geomechanical properties of rocks such as tensile strength (σt) and mode I fracture toughness (KIC). To validate the indirect tensile test by using the complete Brazilian disc, the crack must be initiated from the central region of the specimen, and the loading angle that corresponds to the arc of the disc must be greater than 19.5°. In the current study, an attempt has been made to investigate the sensitivity of the strain rate to various geomechanical properties (tensile strength and fracture toughness) of a homogeneous fine-grained sandstone by using FBD specimens. The strain rates were varied between low and intermediate rates in the range of 10-5 to 10-2 s-1. Two sets of specimens were tested with a loading angle of 2α = 20° and 2α = 30° in order to ensure better experimental observation of the strain rate sensitivity to various geomechanical properties. The test results indicate that with increasing strain rates, the fracture toughness, and tensile strength gradually increase. The fracture toughness that corresponds to a loading angle of 20° overestimates the fracture toughness of the rock.

Determination of elastic modulus, tensile strength and fracture toughness of bioceramics using the flattened Brazilian disc specimen: analytical and numerical results

Ceramics and bioceramic composites are materials characterized with strong but quite low crack-resistance properties. Indeed, their application is hindered by their brittleness and low ability to deform, and the accurate measurement of their fracture toughness can often be challenging. This measurement along with that of tensile strength and elastic modulus were conducted using a novel configuration of the Brazilian test. The flattened Brazilian specimens, which are in the shape of discs having parallel flat ends, are subjected to compression for the determination of opening mode I fracture toughness KIC. The experiments were conducted using tricalcium phosphate–fluorapatite composites which were tested by compressive loading on the parallel flat ends. The loading angle corresponding to the flat end width is about 2α=20° to guarantee crack initiation at the specimen center according to the Griffith criteria. Finite element program, called ABAQUS, is used for the numerical modeling for finding stress intensity factors. The effects of fluorapatite additives and fracture toughness were studied. The fracture toughness values of tricalcium phosphate–fluorapatite composites were found to increase with the increase in fluorapatite addition until an appropriate value. It is shown that there is a good agreement between the experimental, analytical and numerical results.

The Contrast of Concrete Brazilian and Flattened Brazilian Disc Specimen under Quasi Static Diametral Compression Tests

Reference the test method of the rock mechanical properties, through the concrete Brazilian and flattened Brazilian disc specimen under quasi static diametral compression tests and compared, research shows that flattened Brazilian disc specimens split eventually destroy the formation more than one cracks, on both sides along the platform has large cracks, even cracks in some specimens from the platform to the next platform throughout the ipsilateral endpoint, and complete Brazilian disc does not appear this phenomenon. Complete Brazilian disc specimens and flattened Brazilian disc test specimen loading force curves form remains the same, but flattened Brazilian disc specimens eventually reach the extreme loading force has a higher value than the first extreme loading force.

Quantification of dynamic tensile behavior of cement-based materials

The modified split Hopkinson pressure bar testing method was used to quantify the dynamic tensile behavior of cement mortar using flattened Brazilian disc specimens. Experimental procedure for testing dynamic behavior of cement-based materials under high loading rate is presented. Employing a proper pulse shaper in the conventional split Hopkinson pressure bar (SHPB) test helps to achieve dynamic equilibrium in the test specimen. Strain histories from strain gauges offer comprehensive information to evaluate the stress equilibrium of specimen under dynamic loading. A numerical analysis was conducted to verify the experimental data. In addition, the results of the strain rate sensitivity of cement mortar are analyzed. Based on the experimental results and an existing quasi-static model, a tensile constitutive model with strain rate effects was formulated. This model provides a good description of dynamic experimental results for cement mortar.

Experimental Study on Impact Compression and Spliting of Granite

In order to systematically study on dynamic mechanics character of granite, impact compression experiments and impact flattened Brazilian disc specimens of granite have been investigated with modified split Hopkinson pressure bar (SHPB) experimental facility, curve about stress versus strain and other parameter at strain rates of 23.9/s～108.4/s were obtained from impact compression. The dynamic tensile strength and critical tensile failure strain at strain rates of 2.3/s～25.6/s were obtained from impact flattened Brazilian. The experimental result show that dynamic compression strength , elastic modulus and failure strain，dynamic tensile strength significantly increase comparing to quasi-static experiment, and the above mechanics parameter include dynamic strength etc will increase with strain rate increasing, granite have the character of impact harding and ductility enhancement. The failure degree of failure will increase with increasing strain rate under impact compression; the failure configurations of the specimens present an center splitting mode under impact flattened Brazilian experiments. Whether impact compression or impact splitting under strain rate including this paper ’s experiments, the relationship between the DIFC or DIFT and the logarithm of strain rate is linear.

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (KI(t) for opening mode I, and KII(t) for sliding mode II), mode mixture ratio (KI(t)/KII(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (KId and KIId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ϕ50mm specimen, however it is 10° for the ϕ130mm and ϕ200mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. KIId is generally greater than KId. Both KId and KIId increase with increment of specimen size, and this trend for KIId is more remarkable than that for KId.

Impact Experimental Study for Dynamic Character of Reactive Powder Concrete

In order to systematically study dynamic mechanics character of reactive powder concrete (RPC), impact compression experiments and impact flattened Brazilian disc specimens of RPC have been investigated with modified split Hopkinson pressure bar (SHPB) experimental facility using brass pulse shaper, curves about stress versus strain and other parameters at strain rates of 20.3/s~137.0/s were obtained from impact compression. The dynamic tensile strength and tensile failure strain at strain rates of 3.4/s~26.2/s were obtained from impact flattened Brazilian. For comparison, the quasi-static compress and split tension of RPC were obtained with an MTS 810 materials test system and CSS-88500 electron universal material testing machine.The experimental result show that dynamic compression strength , elastic modulus and failure strain,dynamic tensile strength and failure strain significantly increase comparing to quasi-static experiment, RPC have the character of impact harding and ductility enhancement. RPC exhibit excellent failure patterns at high strain rate. Whether impact compression or impact splitting under strain rate including this paper ’s experiments, the relationship between the DIFC or DIFT and the logarithm of strain rateis linear.

Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method

Investigation of geometrical parameters for flattened Brazilian disc method is important, since this is a simple and attractive method for mode I fracture toughness testing on rock cores. Evaluating numerical modeling results, a parametric equation in terms of principal stresses at the center of the disc and the loading angle of the flattened end was developed. An equation was proposed for maximum stress intensity factors at critical crack lengths around stable to unstable crack propagation. Comparing fracture toughness results of flattened Brazilian disc method to the results of the suggested cracked chevron notched Brazilian disc method, geometrical parameters for flattened Brazilian discs were investigated. Diameter, loading angle of flattened ends, and thickness of andesite rock core specimens were changed to obtain comparable results to the suggested method. The closest results to the suggested method were obtained by 54 mm diameter discs with loading angles larger than 32°, and thicknesses between 19 and 34 mm. Results were confirmed by the flattened Brazilian disc tests on a marble rock. In flattened Brazilian disc tests with smaller loading angles and larger diameters, larger fracture toughness values than the results of the suggested cracked chevron notched were obtained. However, excluding tests with large loading angles over 27°; specimen size was less effective on the results of these tests. Critical crack length parameters computed from modeling and experiments were close to each other for the flattened Brazilian disc specimens with smaller loading angles around 20° and thickness/radius ratio equal or less than 1.1.

Dynamic split tensile test of Flattened Brazilian Disc of rock with SHPB setup

The Flattened Brazilian Disc (FBD) specimens were impacted diametrically by a pulse shaping split Hopkinson pressure bar to measure dynamic tensile strength of a brittle rock. With application of strain gauge technique, the stress waves traveling through the incident bar, the transmission bar as well as the FBD specimen were recorded and analyzed. The loading history was determined based on the one-dimensional stress wave theory. The dynamic equilibrium condition in the specimen was approximately satisfied, this claim was supported by the numerical simulation of dynamic stress evolution in the specimen, with the conclusion that a short time after impact the pattern of dynamic stress distribution in the specimen was symmetric and similar to that of the counterpart static loading. The validity of the test was further verified experimentally, as the waveforms acting on the two flat ends of the FBD specimen, respectively, were of nearly the same shape, and the rupture modes of the specimens were generally such that crack first initiated at the center of the disc and subsequently propagated along the loading diameter, whereas crush zones were implied to form lastly near the two flat ends of the broken specimen. The dynamic tensile strength of marble was measured at the critical point when the tensile strain wave recorded at the disc center got peak value of the strain derivative with respect to time.

A Method for Testing Dynamic Tensile Strength and Elastic Modulus of Rock Materials Using SHPB

An experimental procedure for testing dynamic tensile strength and elastic modulus of rock materials at high strain rate loading is presented in this paper. In our test the split Hopkinson pressure bar (SHPB) was used to diametrally impact the Brazilian disc (BD) and flattened Brazilian disc (FBD) specimens of marble. A tensile strain rate of about 45 1/s was achieved at the center of the specimen. In order to improve the accuracy of the analysis, the initiation time difference between the strain waves acting on the two flat ends of the FBD specimen was treated properly. Typical failure modes corresponding to different loading conditions were observed. It was verified with a finite-element simulation that the equilibrium condition was established in the specimen before its failure. This numerical simulation validates the experimental procedure and also proves the suitability of formulation for the basic equations.

The flattened Brazilian disc specimen used for determining elastic modulus, tensile strength and fracture toughness of brittle rocks: experimental results

The flattened Brazilian disc specimen used for determining elastic modulus, tensile strength and fracture toughness of brittle rocks: experimental results

The flattened Brazilian disc specimen used for determining elastic modulus, tensile strength and fracture toughness of brittle rocks: experimental results

The flattened Brazilian disc specimen used for determining elastic modulus, tensile strength and fracture toughness of brittle rocks: experimental results