Tensile Strength Of Brittle Materials Research Articles

Diametral Compression of Short Cylinders with a Central Hole as a Method for Assessing the Tensile Strength of Brittle Materials

Diametral Compression of Short Cylinders with a Central Hole as a Method for Assessing the Tensile Strength of Brittle Materials

Innovative tensile test for brittle materials: Validation on graphite R4550

This paper proposes an innovative ultrasonic tensile test methodology for the assessment of quasi-static uniaxial mechanical properties and tensile strength of brittle materials. An ultrasonic testing machine, commonly employed for very high cycle fatigue tests, had its control and data acquisition systems adapted to induce specimen failure in about 100 cycles, avoiding cyclic load damage. The mechanical properties are thereafter estimated with a finite element model which simulates the experimental test. The proposed method has been validated by assessing the tensile strength of graphite R4550, characterized by brittle behaviour. The mechanical properties for graphite R4550 estimated with this experimental-numerical approach were found to be close to literature values obtained in different quasi-static testing configurations, confirming the effectiveness of the proposed method and the feasibility of employing the ultrasonic fatigue testing machine for studying the behaviour of brittle materials. Furthermore, the proposed methodology eliminated issues caused by mechanical fixtures and tensile testing machine alignment, while also allowing a considerable increase of the material loaded volume when compared to that of traditional test methods. The experimental and numerical approaches are successfully validated on graphite R4550, also highlighting its capability of characterizing the material nonlinear behaviour, including viscoelasticity and asymmetrical response in tension and compression.

Diametral compression of short cylinders with a central hole as a method for assessing the tear resistance of brittle materials

The possibility of evaluating the tear resistance of brittle materials by diametral compression test of short cylinders (solid and central with a central hole) has been analyzed. The computational analysis was performed by the finite element method using the ANSYS program. It is shown that the stress distribution in a disk with a hole is similar that without a hole but contains disturbances introduced by a stress concentrator in the form of a hole. The normalized values of the maximum first principal stresses for a disk with a hole exceed the values for a disk without a hole by more than 5 times. The experimental analysis was carried out by testing short cylinders, both solid and with a central hole, made of brittle materials: cast iron and graphite. It is noted that the fracture resistance, determined by the formula recommended by the ASTM D3967 – 95a standard, practically does not differ for solid cast iron samples, and for graphite differs by 1.5 times from the true tear resistance of materials; when testing samples with a central hole, the tear resistance differs from the standard values by a factor of 1.5 and almost 2.5, respectively. The different nature of the sample destruction is also noted: slow controlled rupture of cast iron and dynamic destruction of graphite with the corresponding deformation diagrams. The results of testing fuel pellets of uranium dioxide are given as an example of testing real cylindrical samples with a central hole. It is shown that the test results of ARV-1 graphite samples are in good agreement with the test results of fuel samples. Thus, the possibility of testing small-sized short cylinders according to the diametral compression scheme for indirect assessment of the tensile strength of brittle materials has been confirmed. A calculation formula is proposed for an indirect assessment of the tensile strength of brittle materials based on the results of testing small-sized short cylinders, both with and without a central hole according to the diametral compression scheme.

Investigating the Flexural Performance of Basalt Fiber Reinforced Polymer (BFRP) Bars at Elevated Temperatures

The FRP-reinforced concrete constructions may be subjected to elevated temperatures, which may compromise the structural integrity of the bars and, finally, the whole structure. As a result, the thermal stability of the FRP bars needs to be properly examined before they can be completely used in the construction field. Flexural strength testing has been utilized as a standard approach for determining the uniaxial tensile strength of brittle materials since it is less costly and easier to perform than the direct tension test. While the findings achieved were not absolute tensile data, they can offer a prediction of the relative tensile strength of the FRP bars. The flexural behavior of basalt fiber-reinforced polymer (BFRP) bars with different nominal diameters (8.0 mm, 10.0 mm, 12.0 mm, and 14.0 mm) exposed to increased temperatures (up to 150 °C) was examined in this research. According to the findings, when the temperature rises, the stiffness and flexural strength of the BFRP bars reduce. As the temperature approached the glass transition temperature (Tg) of the bars, a significant decrease in stiffness and strength was noted. These outcomes were also seen in other studies' pure tension tests of FRP bars. At higher temperatures, bigger nominal diameter bars are superior to smaller nominal diameter bars in terms of flexural strength decaying resistance. Although a comparable flexural stiffness degradation was noted as temperature increased.

Investigating the Fracture Process and Tensile Mechanical Behaviours of Brittle Materials under Concentrated and Distributed Boundary Conditions

In this study, concrete was selected to investigate the real-time splitting tensile mechanical and fracture behaviours of brittle materials using the Brazilian test under concentrated and distributed boundary conditions. The digital image correlation (DIC) method was adopted to evaluate the tensile strength and failure process in Brazilian tests using a high-resolution camera. The DIC results showed that the position of the crack initiation randomly occurred at the centre of a disc and at the boundary in Brazilian tests with concentrated loads (BTC). Comparatively, the crack initiated at the centre of discs in most Brazilian tests with distributed loads (BTD), as validated by the DIC results. Our results indicated that the average nominal tensile strength of specimens cracking at the boundary was larger than that of specimens cracking at the centre in the BTC, suggesting that the nominal tensile strength measured by the Brazilian test was related to the failure process of the discs. Moreover, this study demonstrated that the tensile strength measured by the Brazilian test was dependent on the boundary conditions. The equation recommended by the ISRM (International Society for Rock Mechanics) might slightly overestimate the tensile strength of brittle materials based on the pure elastic theory and hyperbolic-distributed loading conditions at the boundaries.

Biaxial Loading of Brazilian Disc Samples

The Brazilian test method has been widely used over the past 50 years to determine the indirect tensile strength of brittle materials, such as rocks and concrete. While the behaviour of Brazilian samples under conventional indirect tensile testing has been the subject of much research, the biaxial loading of a Brazilian sample under both horizontal and vertical compressive forces has rarely been studied. This study investigates the ultimate strength, crack propagation speed, fracture mode, and damage evolution in sandstone Brazilain samples using high-speed photography methods integrated with a newly designed hybrid biaxial-impact testing facility. The result shows that the samples fail under lower tensile stress than their Indirect Tensile Strength based on the principle of superposition.

ANALYSIS OF THE METHODS FOR BENDING SMALL-SIZED DISKS ON A RING SUPPORT

A number of methods for testing bending of thin discs on an annular support designed to determine the tensile strength of brittle materials, are considered. The methods differ in the type of a loading indenter (with flat, spherical, or toroidal tips), support devices, and calculation equations for determination of the breaking stress. The results of testing samples on an annular support made of two model materials which differ in the degree of brittleness, i.e., cast iron and graphite, are presented. It is shown that the calculated strength of the tested materials depends on the character of the sample destruction and on the type of bending diagram. Cast iron samples were destructed under a significant plastic deformation (characteristic bending diagram passed through the maximum), and the tensile strength of the samples corresponded to the compressive strength of the material being several times higher than the tensile strength of the material. Graphite samples underwent brittle fracture (within the linear section of the bending diagram), and the calculated strength value was comparable to the tensile strength of the material. A conclusion is made that the use of the test method of thin disk samples on an annular support for determination of the tensile strength of the material is substantiated only in the case of absolutely brittle fracture of samples with a bending diagram similar to the fracture diagram of graphite samples. Disk samples made of aluminum oxide obtained by electro-pulse sintering were tested using two methods (with flat and spherical tips). In both cases, the bending diagram of aluminum oxide samples was similar to that of graphite samples, i.e., their destruction occurred at the initial linear section of the diagram and was absolutely brittle. The results of comparative testing of the samples made of aluminum oxide, taking into account the results of testing samples made of model materials (cast iron and graphite), showed that tests on the annular support of disks using a flat-tipped indenter are the most grounded. The samples should be made of brittle materials having a linear bending diagram up to the sample destruction.

Effects of damage evolution on tensile strength measurement of nuclear graphite material by ring compression test

• Effects of damage evolution on tensile strength measurements were studied. • Damage evolution should be considered if an indirect method is used for strength measurement. • Uniaxial tensile strength can be measured via the diametrical ring compression test. Because of the limitations of the direct tension method, indirect methods such as Brazil tests or ring compression tests are widely applied to measure the tensile strength of brittle materials. However, in most cases of indirect method application, empirical equations that have been derived based on the assumption of a linear elastic material are used, and the effects of damage on the tensile strength measurements are ignored. Thus, in this study, ring-shaped nuclear graphite IG-11 specimens were subjected to diametrical compression tests to study the effects of damage evolution on tensile strength measurements. By analysing the experimental results and the damage evolution law obtained via an inverse method and finite element analysis, the true uniaxial tensile strength of IG-11 was accurately obtained. The results indicate that damage plays an important role in the tensile strength measurement of the nuclear graphite material when an indirect method is used. This study is also useful as a reference for obtaining accurate tensile strength predictions for other types of brittle materials.

Size-effect on the apparent tensile strength of brittle materials with spherical cavities

The decrease of the apparent uniaxial tensile strength resulting from a single flawless spherical cavity in an infinite linear elastic continuum under uniaxial tension is investigated. To this end, a new generalized semianalytical expression for the stress intensity factor of an annular crack surrounding the spherical cavity under different loading conditions is proposed and validated. The apparent tensile strength is then estimated by four different approaches: two criteria implement a single condition, either on the stress field (Theory of Critical Distances) or on the energy release rate (equivalent Linear Elastic Fracture Mechanics), whereas the other two are stress-energy coupled criteria, namely the Finite Fracture Mechanics and the Cohesive Zone Model. Finally, theoretical predictions are discussed and compared with experimental data and atomistic simulations available in the literature, showing good correlation.

Determination of uniaxial tensile strength of brittle materials using tubular samples

Tensile strength of brittle materials is usually obtained through Brazilian tests. It is accepted that failure is initiated at the centre of the sample and that it propagates through the material, creating a tensile failure plane along the vertical diameter or at the majority of it. Then, the tensile stress developed at the centre of the disc is considered as the tensile strength of the material tested. However, the stress state along the vertical diameter is always biaxial, even in the centre of the sample. This implies that the strength measured using such technique is not the uniaxial tensile strength. In this article, the expressions of the stress state supported by a tubular sample subjected to a novel device to determine the tensile strength of brittle materials are described. Besides, it is noticed that the failure plane contains points with the maximum uniaxial tensile strengths so the testing method is adequate to determine the uniaxial tensile strength of brittle materials.

Brazilian Tensile Strength Test Conducted on Ductile Unsaturated Soil Samples

Abstract The tensile strength of soil is often neglected. Because of the presence of matric suction, unsaturated soils may have substantial tensile strengths with implications for a range of geotechnical problems, such as slope stability, bearing capacity, and the integrity of clay liners. Direct measurement of the tensile strength of soils is complex to carry out, while the simplicity of the Brazilian tensile strength (BTS) test offers an attractive alternative. However, this method was developed to measure the tensile strength of brittle materials. While suction-bound unsaturated soils may behave in a brittle fashion at low moisture contents, such materials become more ductile as the moisture content increases. This study investigated the application of the BTS test to measure the tensile strength of unsaturated soil samples over a range of moisture contents. Because of the low sample strength of these soils, the use of curved loading platens is recommended. The required load angle depends on the ratio between the compressive and tensile strength of the material tested. When brittle behavior is obtained during testing, conventional interpretation may be used, i.e., the maximum mobilized load during load application is used for tensile strength calculation. This is not appropriate when testing ductile materials. During load application on ductile samples, the initial mobilized load-deformation behavior is approximately linear and becomes nonlinear when tensile yielding starts to occur, originating from the sample center where the full tensile strength is first mobilized. It is recommended that, to obtain a conservative estimate of tensile strength, the inflection point where behavior becomes nonlinear should be taken as representative of soil tensile strength.

EXPERIMENTAL ANALYSIS OF PROCESS AND TENSILE STRENGTH FOR CONCRETE BRAZILIAN SPLITTING TEST WITH DIFFERENT LOADING BOUNDARIES BY DIC METHOD

Brazilian splitting test was widely used in the evaluation of tensile strength of brittle materials, but the results of strength are difference with different loading boundaries, such as flat plates, bearing strips, arc die, and flattened Brazilian disc,which has always been a research focus. In this paper, the splitting test was designed under different loading boundaries of direct flat plates and bearing strips, and analyzed theoretically, carried out experimentally as well. By the high-speed camera and digital image correlation (DIC) method, the process of the evolution of strain field, crack initiation and propagation on the surface of the specimen were studied in the splitting test. The influence of different loading boundaries on the tensile strength and the strain concentration evolution were further discussed. The results show that: (1) The evolution characteristics of strain concentration caused by the nonlinear tensile properties of concrete are sensitive to loading conditions, which lead to strain concentration earlier from the loading ends and evolves to the of the specimen when loaded by flat plates . In this case, even the experimental condition of center cracking is satisfied, its strength still lower than that of bearing strips, the difference can reach 17.9%; (2) As long as the contact angles of bearing strips loading is designed properly, the stress field of the specimen can develop stably than that of direct flat plate loading, which is conductive to ensure strain concentration as well as fracture starting from the center. It is better to meet the requirements of the Brazilian splitting test; (3) It is not sufficient to only verify the validity condition of center cracking, which must be carefully considered in the test design and analysis. The research results have important reference significance for the design and test analysis of the Brazilian splitting experiment of brittle materials.

Determination of Tensile Strength by Modified Brazilian Disc Method for Nuclear Graphite

The Brazilian disc test has been used widely to measure the tensile strength of brittle materials, such as rock and ceramic. However, the Brazilian disc method developed for rock has not been applicable for nuclear graphite due to the large ratio of tensile to compressive strength in the material. According to the results of stress analysis and Griffith’s strength criteria, the graphite compressive stress near the contact area must be decreased for the Brazilian tensile strength method. In this paper, the Brazilian disc test has been modified by using a newly developed anvil with a V-shaped cavity. According to finite element analysis, the stress concentration around the contact area between graphite samples and anvils was significantly reduced by the new design of anvils. The design has been proved to be effective by comparing with the direct methods. The method also has been proved to be valid for different samples sizes considered in this study, which indicates that it has a wide applicability.

A simple formula for calculating the tensile strength of brittle materials by means of the circular semi‐ring test and the optical method of caustics

The tensile strength of brittle materials is here obtained by applying the experimental method of caustics to the circular semi-ring test (CSR). In this context, first the equations of the initial and the respective caustic curves are obtained for the CSR for light reflected from the front and rear face of the CSR as well as for transmitted light, thus covering all cases for both opaque and transparent materials. It is seen that the radii of the initial curves assume complex and real values with only the latter being accepted to form the loci on the CSR to provide the caustics. Then, simple closed-form formulae are provided for determining the critical stresses at the critical points A and B on the inner and outer perimeter of the CSR, in terms of the caustics' horizontal diameter DX.

Enlightening the role of critical parameters for the determination of the tensile strength by means of the Circular Semi Ring test

Analytic formulae for stresses and displacements are provided for the Circular Semi Ring under either compression or tension. The respective expressions for the tensile strength for both tests are obtained and compared to existing ones. In addition, it is shown that smooth contact between the specimen and the loading device should be preferred. The suggested tests seem to remove some drawbacks of existing methods for obtaining the tensile strength of brittle materials: Fracture is achieved at points where the stress field is purely tensile and, also, very low external force is required thus avoiding premature fracturing at the specimen-loading device contact region. From the theoretical point of view the tension test appears to be more advantageous regarding the very low fracture load and the fact that the maximum tensile stress is higher in absolute value from the respective compressive one.

Numerical assessment of rupture mechanisms in Brazilian test of brittle materials

Due to the difficulties associated with performing a direct uniaxial tensile test, the tensile strength of brittle materials is commonly estimated indirectly. The Brazilian test is probably the most widely accepted indirect technique among others. Since the development of the Brazilian test, the test has received considerable attention due to its ease of sample preparation and interpretation. However, the accuracy of this method has also been criticized for a long time in the literature. This paper aims to numerically study some of these criticisms by mainly focusing on failure mechanisms, the effect of contact loading conditions and stress distributions induced in the Brazilian test. Brazilian discs having contact angles ranging from 1 to 30° (i.e. concentrated to distributed loading scenarios) were simulated in the Fast Lagrangian Analysis of Continua (FLAC) based on the finite difference model. Results of this study show that at low contact loading angles, zones of high compressive stresses are generated at the vicinity of loading rims which is followed by an initiation and propagation of the cracks from these high-stressed zones. With an increase in the contact loading angle, the magnitude of compressive stresses at the vicinity of loading rims decreases leading to the disc's tensile rupture initiation at its centre. Also, it was found that the transition in the observed failure mode from cracking under the loading rims to central tensile cracking is material dependent in a Brazilian test. Finally, the ratio of uniaxial compressive strength to tensile strength was suggested as a controlling parameter for the evaluation of failure transition in a Brazilian test.

Determination of tensile strength of brittle materials by bending thin discs on the annular support

It is proposed to use the test of bending small thin disk specimens simply supported along the contour, to determine the resistance of material to tensile strain. The results of computer analysis of stress-strain state and test a thin disk specimens made of brittle materials are cast iron and graphite as a possible model, and directly samples made by electric pulse methods are presented. It is shown the effect of size of specimens on the resistance to their destruction and different character of deformation and destruction of cast iron and graphite samples. The possibility of application of thin disc samples for the determination the resistance to tensile strain of the composite ceramics based on SiAlON with various additives Y2O3, SiC, and TiN is confirmed.

Application of the “Brazilian test” to determine the strength of materials obtained by electric pulse consolidation of powders

Testing of short cylinders according to the “Brazilian test” scheme is considered as a method of assessing the tensile strength of brittle materials obtained by electric pulseconsolidation of powders. The paper presents a calculated using FEM and an experimental analysis of the behavior of short cylinders (thick disks) when loaded according to the “Brazilian test” scheme. The calculation shows the weak influence of the disk thickness on the average and maximum tensile stresses in the plane of symmetry of the disk. Results of testing of small samples made of cast iron and graphite are presented. It is shown a good correspondence between the results of the test samples from cast iron when using formula recommended by the ASTM Standard D3967-95a, and the strength of the material when tested in tension. The results of testing samples of graphite were 1.5–2 times less than its tensile strength. The results of testing of small-size samples of heavy alloy WNiFe and aluminum oxide obtained by electric pulse consolidation of powders are presented. The influence of the pressure and current pulse on the fracture resistance of the alloy WNiFe and the sample thickness on the strength of Al2O3 is investigated. Thus, the possibility of testing small samples according to the “Brazilian test” scheme to determine the tensile strength of materials obtained by electric pulse consolidation of powders is demonstrated.

Brazilian disk test and digital image correlation: a methodology for the mechanical characterization of brittle materials

In this paper, an optimized and reliable approach for the evaluation of the mechanical properties of brittle materials is proposed and applied to the characterization of geopolymer mortars. In particular, the Young’s modulus, the Poisson’s ratio and the tensile strength are obtained by means of a Brazilian disk test combined with the digital image correlation (DIC) technique. The mechanical elastic properties are evaluated by a special routine, based on an over-deterministic method and the least square regression, that allows to fit the displacement fields experienced by the samples during the experiment. Error sources, like center of the disk location and rigid-body motion components, were analyzed and estimated automatically with the proposed procedure in order to perform an accurate evaluation of the elastic constants. The strain field measured by DIC and the computed elastic properties were then used to perform a local stresses analysis. This latter was exploited to investigate the failure mechanisms and to evaluate the tensile strength of the investigated material and the obtained data were compared with those predicted by the ASTM and ISMR standards. Three different loading platens (flat, rod and curved) were adopted for the Brazilian test in order to evaluate their effect on the elastic properties calculation, on the failure mechanisms and tensile strength evaluation. Results reveal that the curve platens are the most suitable for the tensile strength calculation, whereas the elastic properties did not show any influence from the loading configuration. Furthermore, the proposed procedure, of easy implementation, allows to accurately calculate Young’s modulus, Poisson’s ratio and the tensile strength of brittle materials in a single experiment.

Modeling for Distribution of Compressive Stress from Loading Platens in Diametrical Compression Test

Diametrical Compression test is one of indirect tests to investigate the tensile strength of brittle materials. This test is spread because of easiness to perform. However, results from this test are not stable. Traditionally, calculations for this test are performed under a pair of opposite concentrated loading on the diameter of specimen. However, contact areas appear just before fracture of specimen in the fact and the stress distribution from loading platens is not obvious. It seems be one of reasons why the result from this test is not stable. In this study, the attempt to establish the modeling for distribution on loading platens in the diametrical compression test is shown. The aim of this modeling is to calculate stresses and displacement of specimen using complex stress function by Lekhnitskii. Therefore, this model is expanded in Fourier expansion. Accuracy of calculation using Fourier expansion depends on the number of terms. Therefore, the influence of contact area and number of terms to accuracy is also discussed.