Tensile fatigue evolution in sandstone under lower cyclic stress: Coupled Brazilian disc experiments and enhanced mesoscale damage modeling

The validity and rationality of the Brazilian disc test have attracted much attention since it was proposed. To verify the validity of four Brazilian disc tests, red sandstone and yellow rust granite were employed. In these experiments, uniaxial tensile tests and four Brazilian disc tests were performed. Meanwhile, the typical location of the Brazilian discs was arranged with gages to detect the crack initiation location. By analyzing the rationality of the four Brazilian disc tests from two aspects, the crack initiation location and the difference between indirect tensile strength and direct tensile strength, it was found that the Brazilian disc tests without cushion and the Brazilian disc tests with two small-diameter steer rods are suitable for determining the indirect tensile strength of rock materials. However, the Brazilian disc tests with arc loading jaws should be carefully adopted to measure the indirect tensile strength due to their overestimation of the indirect tensile strength. Additionally, flattened Brazilian disc tests were found to be not suitable for measuring the indirect tensile strength of rock materials.

Static and dynamic Brazilian disk tests for mechanical characterization of annealed and chemically strengthened glass

Revisiting the Brazilian disc test with split Hopkinson pressure bar by high-speed digital image correlation analysis

The dynamic fracture process of rock materials is of importance for several industrial applications, such as drilling for geothermal installation. Numerical simulation can aid in increasing the understanding about rock fracture; however, it requires precise knowledge about the dynamical mechanical properties alongside information about the initiation and propagation of cracks in the material. This work covers the detailed dynamic mechanical characterisation of two rock materials—Kuru grey granite and Kuru black diorite—using a Split-Hopkinson Pressure Bar complemented with high-speed imaging. The rock materials were characterised using the Brazilian disc and uniaxial compression tests. From the high-speed images, the instant of fracture initiation was estimated for both tests, and a Digital Image Correlation analysis was conducted for the Brazilian disc test. The nearly constant tensile strain in the centre was obtained by selecting a rectangular sensing region, sufficiently large to avoid complicated local strain distributions appearing between grains and at voids. With a significantly high camera frame rate of 671,000 fps, the indirect tensile strain and strain rates on the surface of the disc could be evaluated. Furthermore, the overloading effect in the Brazilian disc test is evaluated using a novel methodology consisting of high-speed images and Digital Image Correlation analysis. From this, the overloading effects were found to be 30 and 23%. The high-speed images of the compression tests indicated fracture initiation at 93 to 95% of the peak dynamic strength for granite and diorite, respectively. However, fracture initiation most likely occurred before this in a non-observed part of the sample. It is concluded that the indirect tensile strain obtained by selecting a proper size of the sensing region combined with the high temporal resolution result in a reliable estimate of crack formation and subsequent propagation.

This paper evaluates the fracture of notched epoxy matrix composites using the Brazilian disk (BD) test from both numerical and experimental points of view. The study began with a comprehensive experimental program covering three different composite lay-ups (quasi-isotropic, unidirectional, and cross-ply) and various geometries of U and V notches. Specifically, the BD samples combined the three layouts, four different notch angles, and three notch radii with three specimens per combination, leading to an overall number of 108 fracture tests. The experiments showed the appropriateness of the BD test for the study of the fracture behavior of composite materials and provided a good pool of data for further investigations. Subsequently, the virtual isotropic material concept (VIMC) was applied in combination with two fracture criteria to theoretically predict the experimentally acquired fracture loads. This study demonstrated that using the VIMC approach can provide robust predictions while incurring much lower computational costs compared to the conventional approaches found in the literature.

Accurately simulating the compressive and tensile mechanical behavior of rock is one of the challenges faced by numerical simulation. In this paper, the rock’s triaxial compression experiment and the Brazilian disk simulation were simulated, and the propagation process of the rock crack was simulated in Brazilian disk test in the finite element method. According to the experimental data, the KCC model was completely modified and the triaxial compression experiment was carried out with the modified model. The modified model was applied to the Brazilian disk test simulation, and the crack propagation in Brazilian disk test was simulated by inducing the erosion algorithm, which verifies the applicability of the erosion algorithm in the finite element method of material continuity loss.

Observation of damage evolution is of great importance to the understanding of the failure process of rock materials. High-speed DIC system is constructed and used to observe the strain field evolution of the granodiorite disc in Brazilian test. The strain fields at different load levels are analyzed based on the stain abnormality indicator (SAI) which is the ratio of the strain measured in experiment to the strain from theoretical solution in an isotropy and elastic model. SAI could be used to indicate the damage in the specimen. The process of damage and failure of the specimen in Brazilian disc test is quantitatively analyzed and deeply discussed according to the strain fields and the statistics of SAI. Experimental results in this paper show that the failure process of the disc specimen in Brazilian test is not simple crack propagation under tensile load, but a complicated damage evolution procedure.

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.

The incurved Brazilian disc as an alternative to the standardized Brazilian disc test

The objective of this work was to understand matrix cracking mechanisms in a unidirectional α2 titanium matrix composite (TMC) in possible hypersonic applications. A [0]8 SCS-6/Ti-24Al-11Nb (atomic %) TMC was first subjected to a variety of simple isothermal and nonisothermal fatigue cycles to evaluate the damage mechanisms in simple conditions. A modified ascent mission cycle test was then performed to evaluate the combined effects of loading modes. This cycle mixes mechanical cycling at 150 and 483°C, sustained loads, and a slow thermal cycle to 815°C. At low cyclic stresses and strains more common in hypersonic applications, environment-assisted surface cracking limited fatigue resistance. This damage mechanism was most acute for out-of-phase nonisothermal cycles having extended cycle periods and the ascent mission cycle. A simple linear fraction damage model was employed to help understand this damage mechanism. Time-dependent environmental damage was found to strongly influence out-of-phase and mission life, with mechanical cycling damage due to the combination of external loading and CTE mismatch stresses playing a smaller role. The mechanical cycling and sustained loads in the mission cycle also had a smaller role.

A comprehensive investigation of grain effect (size and distribution) in discrete element modelling of intact rock is carefully conducted through simulating Brazilian disc and uniaxial compressive tests on an intact rock using Universal Distinct Element Code. All the investigations are performed based on the same group of material parameters. Six sizes of Voronoi tessellation grains ranging from 1 to 6 mm are investigated. To investigate the influence of grain assemblage distribution, five different polygonal grain assemblages are created and tested for uniaxial compression and Brazilian disc tests. The simulation results demonstrate that grain size and assemblage distribution play a significant role in the numerical modelling of intact rock using discrete element method. It is found that larger particle size produces higher stiffness and strength. It is also observed that a more homogeneous model can produce higher strength (compressive strength, tensile strength). The modelled Young's modulus and Poisson's ratio have been demonstrated to be dependent on the grain effect.

Numerical and experimental investigation of the anisotropic tensile behavior of layered rocks in 3D space under Brazilian test conditions

In this work, various tensile tests, including Brazilian disc test (BDT), flattened Brazilian disc (FBD) test and semi- circular bending (SCB) test, were carried out on a highly particle-filled composite by using a split Hopkinson pressure bar (SHPB). With the consideration of low strength and low wave impedance of the materials, a quartz crystal transducer was embedded in SHPB to measure the loading forces. A high-speed camera was used to capture the deformation and fracture process of materials. Digital image correlation (DIC) method was used to process these digital images to obtain the dynamic deformation information. Based on the measured strain fields, the crack growth path was determined and the failure mechanism of samples was analyzed. Combining SHPB and DIC method, the indirect tensile stress strain plots of disc samples were obtained, and the dynamic fracture toughness of materials was measured using both FBD and SCB tests. The results show that the tensile failure strength and fracture toughness increases with the increase of strain rates, exhibiting strain rate dependence. The high-speed DIC method combined with SHPB is effective to study the dynamic tensile behaviour of brittle materials with low strengths.

The difference between rock tensile strength measured by a direct tensile test and a Brazilian test is always attributed to external testing conditions and the natural heterogeneity of rock. There are few studies focusing on achieving a substantial understanding and quantifiable analysis of this difference. Methodologically, the relationship between the dominant frequency characteristics of acoustic emission and micro-failure has been preliminarily verified in the direct tensile test. To further explore the relationship between micro-failure types and dominant frequency characteristics and to quantitatively study the relationship between micro-failure and macro-mechanical behaviour, direct tensile tests and Brazilian disc tests were carried out to determine rock tensile strength. Furthermore, the acoustic emission technique was used to monitor the micro-failure of rock during the loading process. Detailed temporal and spatial distribution, as well as spectrum analyses of the acoustic emission signals, were conducted. Based on the statistical analysis of dominant frequency of AE signals, comparisons were made in rock tensile strength and micro-failure components from direct tensile tests and Brazilian tests. Then, a new parameter of strength factor was established to evaluate the contribution of micro-cracks produced by micro-tensile and micro-shear failures to the strength indirectly. The parameter also reflects the statistical relationship between micro-failure events and macro-failure process. By virtue of this parameter, it has been demonstrated that the difference between direct tensile strength and Brazilian splitting strength results from the higher proportion of micro-shear failure in the Brazilian test. Finally, the “ideal” tensile strength under the specific condition was obtained based on the statistical relationship between the strength and micro-failure component and suggested as a conservative design parameter for rock engineering.

Mechanical properties of rocks/soils are key inputs in the design and analysis of surface structures (e.g., slope, foundation) and underground excavations (e.g., tunnel, cavern, borehole, and fracture) in earth engineering practice. Brazilian disc test has been extensively used to measure tensile strength for various rocks. In this study, we propose to measure Young’s modulus, Poisson’s ratio and tensile strength in one Brazilian test through making two additional measurements, i.e., two relative displacements using LVDT, or normal strains by pasting two strain gauges, which are perpendicular to each other, at the center of the disc’s side faces. The analytical solutions of the equivalent strains calculated from LVDT measurements or measured directly by strain gauges are derived from elasticity theory. The analytical solutions are verified with measurements in a numerical model. New formulae for calculating Young’s modulus and Poisson’s ratio from two measured strains are provided and their insensitivity to gauge size is illustrated.