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Investigating the crack initiation stress of rocks is vital for understanding the gradual damage process of rocks and the evolution law of internal cracks. In this paper, the particle flow code method is used to conduct biaxial compression tests on a marble model with an elliptical crack under different confining pressures. According to the evoluti...
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Citations
... Studies on the Young's modulus, elasticity modulus, and Poisson's ratio, in particular, were generally completed in field conditions utilizing geophysical methods, with very few sensitive studies having been completed in the laboratory environment. [17][18][19][20][21][22][23] In these models, applicability and validity were low, whereas error values were quite high for these rock types. ...
This study attempted to determine both the presence and the appearance of the surface of a crack artificially created in a marble block without axial loading or compression by FFT analysis of ultrasonic longitudinal sound waves by scanning the surface. In such respect, the study differs from other studies in the literature. The aim of the study was to minimize marble waste by determining the most appropriate slab cut direction based on the orientation of the fracture or discontinuity within the marble block. During location-controlled scanning of the marble surface, mean longitudinal wave velocity, Young modulus, Poisson ratio and longitudinal wave velocity variation data were obtained using a V-Meter Mark IV™ ultrasonic test device. For each location, longitudinal ultrasonic velocity data was taken at 250 kHz sampling rate and 256 data points were created. Data from the computer environment were subsequently reorganized using the MATLAB software and FFT conversions for such velocity data were obtained for each location. Then, the peaks of the FFT transformation components were determined by using the “Findpeaks” function in MATLAB‘s signal processing toolbox. The number of peaks in the 50-60 kHz range was determined for each location. A single difference was determined between the peak numbers at the locations within the cracked and uncracked regions. By examining the FFT graphs, it was determined that such additional peak occurring in the cracked regions appeared as a second frequency component near the dominant frequency values. Points with secondary frequency were recorded as 1, while all other points were recorded as 0 in a new matrix. Such data matrices created for each sample were examined by visualization in the form of surface graphics. Using these graphics, the orientations of discontinuities within the marble block may be determined according to the scanning surface.
... Griffith's crack simulations are also an interesting research topic. In the literature, there are publications by Yin et al. [8] or Dewapriya et al. [9] where the simulation of symmetrical fracture in graphene was performed with the use of Molecular Dynamic Simulations, or, for example, the work by Wang et al. [10], in which the kinked Griffith's crack was analyzed using the Discrete Element Method. The topic of kinked crack has appeared in the literature for a long time [11,12]. ...
... where: μ is the shear modulus, ν is the Poisson's ratio (for all calculations assumed as 0.2), u x and u y are horizontal and vertical displacements at any point in the polar system around the crack tip, respectively. The diagram of these displacements is shown in Fig. 4. The displacements can be also rotated to the local coordinate system: (10) u r will be called as displacements along the radius and u θ as displacements perpendicular to the radius. u are resultant displacements. ...
... In the case of stresses, theoretically, they grow to infinity at the crack tip, while the displacements according to the formula (8a) tend to 0. In fact, in various simulations, depending on the model, the displacements at the crack tip will not be equal to 0, hence the displacements at all points need to be decreased by values obtained at the crack tip. Then the displacements along the radius u r , the displacements perpendicular to the radius u θ, and the resultant displacements u are calculated as in equation (10). In the same way, as in the previous criteria, they are placed on the graph, reduced to a unit radius, according to the assumption in the formula (8a) that the displacements increase at the rate . ...
The paper presents the results of numerical simulation of brittle material fracture initiated by Griffith's crack situated at any angle with respect to the load direction. The simulations were performed with the Simulia Abaqus FEA system using the X-FEM method. The direction of the crack propagation was determined using the user's subroutine written in Fortran, implemented in the Abaqus system. The authors programmed several conditions for the direction of the fracture propagation: maximum principal stress criterion, Ottosen-Podgórski criterion, three criteria based on displacements around the crack tip, and the MTS criterion, which is based on stress intensity factors. For the purposes of this study, two shapes of the crack tip were analyzed - sharp and blunted. The relationship between the direction of the initial fracture and the direction of crack propagation was found. The simulations were carried out for the angles of the initial crack from 0° to 90°, every 10°. A theoretical analysis of the implemented criteria was also carried out and compared to numerical results. The influence of the shape of the crack tip on the simulation result was analyzed. It was shown that the simulation results closest to the theoretical results were obtained for the own implementation of the stress-based criteria. It has also been proven that the shape of the crack tip has little effect on the result if the finite element mesh is properly densified. However, the sharp crack has a disadvantage for small initial crack angles. The Author’s method of predicting the crack propagation has been proven correct and effective. This work is also the basis for the further development of the described method.
... Griffith's crack simulations are also an interesting research topic. In the literature, there are publications by Yin et al. [8] or Dewapriya et al. [9] where the simulation of symmetrical fracture in graphene was performed with the use of Molecular Dynamic Simulations, or, for example, the work by Wang et al. [10], in which the kinked Griffith's crack was analyzed using the Discrete Element Method. The topic of kinked crack has appeared in the literature for a long time [11,12]. ...
... where: μ is the shear modulus, ν is the Poisson's ratio (for all calculations assumed as 0.2), u x and u y are horizontal and vertical displacements at any point in the polar system around the crack tip, respectively. The diagram of these displacements is shown in Fig. 4. The displacements can be also rotated to the local coordinate system: (10) u r will be called as displacements along the radius and u θ as displacements perpendicular to the radius. u are resultant displacements. ...
... In the case of stresses, theoretically, they grow to infinity at the crack tip, while the displacements according to the formula (8a) tend to 0. In fact, in various simulations, depending on the model, the displacements at the crack tip will not be equal to 0, hence the displacements at all points need to be decreased by values obtained at the crack tip. Then the displacements along the radius u r , the displacements perpendicular to the radius u θ, and the resultant displacements u are calculated as in equation (10). In the same way, as in the previous criteria, they are placed on the graph, reduced to a unit radius, according to the assumption in the formula (8a) that the displacements increase at the rate . ...
The paper presents the results of numerical simulation of brittle material fracture initiated by Griffith's crack situated at any angle with respect to the load direction. The simulations were performed with the Simulia Abaqus FEA system using the X-FEM method. The direction of the crack propagation was determined using the user's subroutine written in Fortran, implemented in the Abaqus system. The authors programmed several conditions for the direction of the fracture propagation: maximum principal stress criterion, Ottosen-Podgórski criterion, three criteria based on displacements around the crack tip, and the MTS criterion, which is based on stress intensity factors. For the purposes of this study, two shapes of the crack tip were analyzed-sharp and blunted. The relationship between the direction of the initial fracture and the direction of crack propagation was found. The simulations were carried out for the angles of the initial crack from 0° to 90°, every 10°. A theoretical analysis of the implemented criteria was also carried out and compared to numerical results. The influence of the shape of the crack tip on the simulation result was analyzed. It was shown that the simulation results closest to the theoretical results were obtained for the own implementation of the stress-based criteria. It has also been proven that the shape of the crack tip has little effect on the result if the finite element mesh is properly densified. However, the sharp crack has a disadvantage for small initial crack angles. The Author's method of predicting the crack propagation has been proven correct and effective. This work is also the basis for the further development of the described method.
To ensure the safety of coal mining, lots of coal pillars were reserved in the coal mine. The stability of coal pillar and roof composite structures determines the safety of stope. Under the action of cyclic loading and unloading such as mining face, chamber blasting, and roadway excavation, the coal pillar, and roof composite structure will gradually instability, which will affect the safety production of the coal mine. Therefore, this paper takes the dynamic disaster of coal pillar and roof composite structure as the research background, carries on the cyclic loading and unloading test of the coal-rock composite structure with different coal-rock height ratios, and studies the influence of coal-rock height ratio on the progressive instability characteristics, mechanical properties and damage variables of the coal-rock composite structure. The crack initiation stress, crack propagation time and failure pattern of coal-rock composite structure are analyzed. The improved load-unload response ratio considering the damage variable is established, and the stability of the coal-rock composite structure under cyclic loading and unloading is quantitatively analyzed. It is concluded that the larger the coal-rock height ratio is, the greater the load-unload response ratio of the composite structure is, and the more unstable the composite structure is. This conclusion is consistent with the crack initiation stress and fracture propagation time, and can quantitatively reflect the progressive instability process of coal-rock composite structure, and provide a basis for revealing the dynamic disaster of coal pillar and roof composite structure.
