Limited-discrete element microscopic parameter calibration method for composite material containing interface cracks

Abstract

The invention relates to a finite-discrete element microcosmic parameter calibration method for a composite material containing interface cracks, which comprises the following steps: obtaining a standard-size disc sample containing different materials including a first material, a second material and a composite material containing the first material and the second material; performing a Brazilian splitting FDEM numerical test on the standard-size disc sample to obtain a numerical test result of the standard-size disc sample, and calibrating fracture energy of the joint unit; and according to the fracture energy and other mechanical parameters of the first material and the second material, performing a Brazilian fracture FDEM numerical test on the standard-size disc sample containing other interface fractures with different angles to obtain a numerical test result of the standard-size disc sample containing other interface fractures with different angles. The calibrated microcosmic parameters adopted by the method can be directly used as parameters required for numerical simulation of the composite material containing the interface crack, so that the mechanical property and the failure mode of the composite material containing the interface crack can be accurately simulated.

Description

Technical Field

[0001] This invention relates to the fields of materials mechanics, geotechnical engineering, and numerical simulation technology, and in particular to a finite-discrete element method for calibrating microscopic parameters of composite materials containing interfacial cracks. Background Technology

[0002] Composite materials are widely used in civil engineering, geotechnical engineering, and energy engineering. For example, in geotechnical engineering, rock-mortar composites are commonly used to improve the stability and safety of structures, such as tunnel linings and shaft wall protection. In mining, to maintain the stability of coal mine roadways and improve the safety of coal mining, a layer of mortar is often poured onto the surrounding rock of excavated roadways to form a rock-mortar composite structure. However, due to the effects of in-situ stress and the differences in the properties of the two materials, the interfacial strength between the rock mass and the mortar often decreases, accompanied by the formation of interfacial opening cracks. For such rock-mortar composites with interfacial opening cracks, under the influence of external factors, cracks often propagate along the weak interface, greatly reducing the load-bearing capacity of the composite structure and seriously affecting the stability of underground engineering such as tunnels and coal mine roadways. Therefore, it is urgent to study the mechanical behavior and failure mechanism of composite materials containing interfacial cracks under loading, providing theoretical reference and technical support for the stability analysis and design of composite structure engineering.

[0003] Currently, research on the mechanical behavior and failure mechanisms of composite materials containing interfacial cracks can be divided into laboratory experiments and numerical simulations. In laboratory experiments, Brazilian splitting, uniaxial compression, and triaxial compression tests are commonly used to study the mechanical response and failure mechanisms of composite materials containing interfacial cracks. Research content includes the influence mechanisms of factors such as crack inclination angle, length, and interfacial roughness on the mechanical properties and failure modes of composite materials. Existing experimental studies have made significant contributions to understanding the mechanical response and failure mechanisms of composite materials under various loading conditions. However, although laboratory experiments can more directly study the mechanical parameters and failure modes of composite materials, they also have many limitations, such as non-recovery, high cost, and long cycle time.

[0004] With the rapid development of computer technology, numerical simulation has been increasingly applied in rock mechanics and geotechnical engineering. Commonly used numerical methods include continuum-based methods (finite element method, finite difference method, extended finite element method, and methods for analyzing real fracture processes, etc.) and discontinuous-medium-based methods (discrete element method, block discrete element method, particle discrete element method, and discontinuous deformation methods, etc.). However, continuum-based methods such as the finite element method require the introduction of bonding elements when simulating rock cracking, which cannot accurately capture crack initiation and has significant constraints. Meanwhile, discontinuous-medium-based methods such as the discrete element method suffer from drawbacks when simulating rock fracture, including complex parameter calibration, the inability to achieve a one-to-one correspondence between macroscopic and microscopic parameters, and the lack of intuitive crack morphology. Therefore, the aforementioned methods still have certain shortcomings in simulating rock cracking and parameter calibration.

[0005] The Finite-Discrete Element Method (FDEM) combines the advantages of finite element method for solving solid deformation and stress with discrete element method for simulating particle contact and cracking, making it highly suitable for simulating material fracture problems. This method can model and analyze the deformation and failure of composite materials, serving as a powerful tool for studying the stress characteristics of composite materials. Parameter calibration is an essential step before conducting numerical simulations; reasonable parameter values ​​often determine the accuracy of the simulation results. However, currently, there is no reasonable method for calibrating the microscopic parameters involved in FDEM simulations of the mechanical properties and failure modes of composite materials with interfacial cracks. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a finite-discrete element method for calibrating microscopic parameters of composite materials containing interfacial cracks. The microscopic parameters calibrated using this method can be directly used as the parameters required for numerical simulation of composite materials containing interfacial cracks, thereby enabling accurate simulation of the mechanical properties and failure modes of composite materials containing interfacial cracks.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A finite-discrete element method for calibrating the microscopic parameters of composite materials containing interfacial cracks includes:

[0009] Obtain standard-sized disk samples containing different materials, including: a first material, a second material, and a composite material comprising the first material and the second material;

[0010] The standard-sized disc specimen was subjected to Brazilian splitting FDEM numerical test to obtain the numerical test results of the standard-sized disc specimen and to calibrate the fracture energy of the joint element.

[0011] Based on the fracture energy and other mechanical parameters of the first and second materials, Brazilian splitting FDEM numerical tests were conducted on standard-sized disk specimens containing interface cracks at different angles to obtain numerical test results of standard-sized disk specimens containing interface cracks at different angles.

[0012] Optionally, the numerical test results include: tensile strength, load-displacement curves, and failure modes.

[0013] Optionally, obtaining numerical test results for a standard-sized disk specimen containing the composite material includes:

[0014] Set the target interface crack inclination angle, and based on the target interface crack inclination angle, conduct a Brazilian splitting FDEM numerical test on a standard-sized disk specimen containing the composite material to obtain the numerical test results of the standard-sized disk specimen containing the composite material.

[0015] Optionally, calibrating the fracture energy of the joint element includes:

[0016] The numerical test results and experimental results of standard-sized disk specimens containing the first material and standard-sized disk specimens containing the second material are compared to calibrate the fracture energy of the joint unit.

[0017] Optionally, obtaining the other mechanical parameters includes:

[0018] The first material and the second material were subjected to uniaxial tensile, uniaxial compression and triaxial compression laboratory tests to obtain the other mechanical parameters.

[0019] Optionally, obtaining numerical test results for standard-sized disk specimens containing interface cracks at other different angles includes:

[0020] Other interface cracks with different angles are set up. Based on the other interface cracks with different angles, a standard-sized disk specimen containing the composite material is subjected to Brazilian splitting FDEM numerical test to obtain the numerical test results of the standard-sized disk specimen containing the other interface cracks with different angles.

[0021] Optionally, after obtaining the numerical test results of a standard-sized disk specimen containing interface cracks at other different angles, the following steps are included:

[0022] The numerical test results of standard-sized disk specimens containing interface cracks at other different angles were compared with the experimental results to preliminarily verify the fracture energy of the joint unit.

[0023] Optionally, during the Brazilian splitting FDEM numerical test on a standard-sized disk specimen of the composite material, the mesh is densified at the crack.

[0024] Optionally, the interface cracks at different angles include: open cracks at different angles with a crack length of 30 mm and a width of 1 mm.

[0025] Optionally, the method further includes:

[0026] The numerical test results of standard-sized disk specimens containing interface cracks at other different angles were compared with the experimental results to further verify the micro-parameter calibration results in the Brazilian splitting FDEM numerical test.

[0027] The beneficial effects of this invention are as follows:

[0028] This invention enables the determination of microscopic parameters for FDEM simulation of the mechanical properties and failure modes of composite materials with interfacial fractures. The main calibration parameters are the two fracture energies (Gf) of the joint element. I and Gf II Furthermore, a method for verifying the correctness of parameter calibration results was proposed, which can be applied to the analysis and research of structural stability problems of composite materials containing interfaces.

[0029] Compared to traditional discrete element method (DEM) parameter calibration procedures, this invention is much simpler and more convenient. With the penalty parameter set to 100 times the elastic modulus, the basic rock mechanical parameters input into the FDEM can be directly obtained from experiments. Only the two fracture energies of the joint element need to be calibrated, and the macroscopic and microscopic parameters can correspond one-to-one, possessing clear physical meaning. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This invention provides a finite-discrete element method for calibrating the microscopic parameters of composite materials with interfacial cracks.

[0032] Figure 2 The following are schematic diagrams of Brazilian splitting numerical tests in embodiments of the present invention: (a) is a schematic diagram of Brazilian splitting numerical tests of disk material A; (b) is a schematic diagram of Brazilian splitting numerical tests of disk material B; and (c) is a schematic diagram of Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 0°.

[0033] Figure 3 The following are comparison diagrams of load-displacement curves obtained from Brazilian splitting numerical tests in embodiments of the present invention and experimental results: (a) Comparison diagram of load-displacement curves obtained from Brazilian splitting numerical tests of disk material A and experimental results; (b) Comparison diagram of load-displacement curves obtained from Brazilian splitting numerical tests of disk material B and experimental results; (c) Comparison diagram of load-displacement curves obtained from Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 0° and experimental results; (d) Comparison diagram of failure modes obtained from Brazilian splitting numerical tests of disk material A and experimental results; (e) Comparison diagram of failure modes obtained from Brazilian splitting numerical tests of disk material B and experimental results; (f) Comparison diagram of failure modes obtained from Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 0° and experimental results.

[0034] Figure 4 The following are schematic diagrams of Brazilian splitting numerical tests of disc composite material AB according to embodiments of the present invention: (a) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 15°; (b) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 30°; (c) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 45°; (d) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 60°; (e) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 75°; (f) Schematic diagram of Brazilian splitting numerical test of disc composite material AB with an interface crack angle of 90°.

[0035] Figure 5 The figures show the load-displacement curves and comparisons between the specimen failure model and experimental results obtained from the Brazilian splitting numerical test of the disc composite material AB according to embodiments of the present invention; (a) the load-displacement curves and comparisons between the specimen failure model and experimental results obtained from the Brazilian splitting numerical test of the disc composite material AB with an interface crack angle of 15°; (b) the load-displacement curves and comparisons between the specimen failure model and experimental results obtained from the Brazilian splitting numerical test of the disc composite material AB with an interface crack angle of 30°; and (c) the load-displacement curves and comparisons between the specimen failure model and experimental results obtained from the Brazilian splitting numerical test of the disc composite material AB with an interface crack angle of 45°. (d) Comparison of load-displacement curves and specimen failure models with test results obtained from Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 60°; (e) Comparison of load-displacement curves and specimen failure models with test results obtained from Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 75°; (f) Comparison of load-displacement curves and specimen failure models with test results obtained from Brazilian splitting numerical tests of disk composite material AB with an interface crack angle of 90°.

[0036] Figure 6 The following is a schematic diagram showing the comparison and relative error between the experimental results and the embodiments of the present invention; (a) shows the comparison and relative error between the peak load of the disk composite material AB with different crack angles obtained by FDEM simulation under Brazilian splitting loading and the experimental results; (b) shows the comparison and relative error between the displacement corresponding to the peak load of the disk composite material AB with different crack angles obtained by FDEM simulation under Brazilian splitting loading and the experimental results. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 1 As shown in the figure, this embodiment discloses a finite-discrete element method for calibrating the microscopic parameters of a composite material containing interfacial cracks. The method includes: obtaining standard-sized disk samples containing different materials, including a first material, a second material, and a composite material containing the first material and the second material; conducting Brazilian splitting FDEM numerical tests on the standard-sized disk samples to obtain the numerical test results of the standard-sized disk samples and calibrating the fracture energy of the joint elements; and conducting Brazilian splitting FDEM numerical tests on standard-sized disk samples containing interfacial cracks at other different angles based on the fracture energy and other mechanical parameters of the first material and the second material to obtain the numerical test results of the standard-sized disk samples containing interfacial cracks at other different angles.

[0040] This embodiment discloses a finite-discrete element method for calibrating the microscopic parameters of composite materials containing interfacial cracks, including:

[0041] Step 1: Process materials A and B into standard-sized disc specimens for indoor Brazilian splitting tests, conduct Brazilian splitting FDEM numerical tests on complete disc material A, obtain the tensile strength, load-displacement curve and failure mode of material A, and compare them with the test results;

[0042] Step 2: Conduct Brazilian splitting FDEM numerical tests on the complete disc material B to obtain the tensile strength, load-displacement curve, and failure mode of material B, and compare them with the experimental results. The experimental results can be obtained from self-conducted tests or compared with existing experimental results to determine the fracture energy of the joint element. Since the two materials have different properties, parameter calibration is required for each material. The purpose of comparing the numerical results and experimental results is to determine the fracture energy of the joint element. Only when the fracture energy is taken as a suitable value can the numerical results match the experimental results, thus proving the correctness of the parameter calibration.

[0043] Step 3: Conduct Brazilian splitting FDEM numerical tests on AB composite disk specimens with an interface crack inclination angle of 0° to obtain the tensile strength, load-displacement curves, and failure modes of the composite material AB with an interface crack inclination angle of 0°. Compare these results with the experimental results to preliminarily verify the fracture energy (Gf) of the joint elements calibrated in Steps 1-2. I and Gf II The correctness of );

[0044] Step 4: Calculate the fracture energy (Gf) of the joint element in steps 1-3. I and Gf II Using these as parameter inputs in FDEM, Brazilian splitting FDEM numerical tests were conducted on AB composite disk specimens with interface cracks at different angles. The tensile strength, load-displacement curves, and failure modes of the AB composite materials with interface cracks at different angles were obtained and compared with the experimental results to further verify the correctness of the micro-parameter calibration results (fracture energy) in FDEM. If the verification results were not ideal, the parameters were recalibrated, the fracture energy of the joint elements was adjusted, and the adjustments were repeated multiple times until the ideal verification results were finally obtained.

[0045] Among them, the AB composite disk sample has a tight bond at the interface, that is, the interface strength is taken as the smaller value of the strength of material A and material B.

[0046] Furthermore, during the Brazilian splitting FDEM numerical test on standard-sized disk specimens of composite materials, mesh refinement was performed at the cracks.

[0047] Specifically, the composite specimen model containing interface cracks underwent mesh refinement at the cracks to more accurately capture the initiation and propagation process of cracks at the cracks during loading.

[0048] This embodiment discloses a finite-discrete element method for calibrating the microscopic parameters of composite materials containing interfacial cracks, including:

[0049] Step 1: Process materials A and B into standard-sized disc specimens with a diameter of 50 mm and a thickness of 20 mm for indoor Brazilian splitting tests. Conduct Brazilian splitting FDEM numerical tests on the complete disc material A at a loading rate of 0.001 mm / s. Figure 2 As shown in (a), the tensile strength, load-displacement curves, and failure modes of material A are obtained and compared with experimental results, as shown in (a). Figure 3 As shown in (a) and (d);

[0050] Step 2: Conduct Brazilian splitting FDEM numerical tests on the complete disk material B, with a loading rate of 0.001 mm / s. Figure 2As shown in (b). The tensile strength, load-displacement curves, and failure modes of material B are obtained and compared with experimental results, as shown in (b). Figure 3 As shown in (b) and (e); the test results can be obtained from independently conducted tests or compared with existing test results to determine the fracture energy of the joint element;

[0051] Step 3: Conduct Brazilian splitting FDEM numerical tests on AB composite disk specimens with an interface crack inclination angle of 0°, at a loading rate of 0.001 mm / s. Figure 2 As shown in (c), in the AB composite disk specimen, materials A and B are semi-circular in shape, with equal size and volume, and a crack length of 30 mm and a width of 1 mm. The tensile strength, load-displacement curve, and failure mode of the composite material AB with an interfacial crack inclination angle of 0° were obtained and compared with experimental results to calibrate the fracture energy (Gf) of the joint element. I and Gf II This refers to the preliminary verification of the fracture energy (Gf) of the joint elements identified in steps 1-2. I and Gf II The correctness of ) is as follows Figure 3 As shown in (c) and (f);

[0052] Step 4: Calculate the fracture energy (Gf) of the joint element in steps 1-3. I and Gf II Other mechanical parameters obtained from uniaxial tensile, uniaxial compression, and triaxial compression laboratory tests of materials A and B were used as parameter inputs in the FDEM. Brazilian splitting FDEM numerical tests were conducted on composite disk specimens with interfacial cracks at different angles (15°, 30°, 45°, 60°, 75°, and 90°) using an FDEM loading rate of 0.001 mm / s. Figure 4 As shown in (a)-(f). The crack length is 30 mm and the width is 1 mm. Other mechanical parameters of materials A and B input into FDEM were obtained from indoor uniaxial tensile, uniaxial compression, and triaxial compression tests of materials A and B, respectively. The loading rate for the uniaxial tensile, uniaxial compression, and triaxial compression tests was 0.001 mm / s, and the specimens were cylindrical specimens with a diameter of 50 mm and a height of 100 mm. Finally, the tensile strength, load-displacement curves, and failure modes of the AB composite material with interface cracks at different angles were obtained. These were compared with the experimental results to further verify the correctness of the micro-parameter calibration results (fracture energy) in FDEM. If the verification results were not ideal, the parameters were recalibrated, the fracture energy of the joint elements was adjusted, and this process was repeated multiple times until the ideal verification results were finally obtained, such as... Figure 5 (a)-(f) and Figure 6As shown in (a)-(b). It is worth noting that the mesh was refined at the crack to more accurately capture the crack initiation and propagation process at the crack in the composite specimen under load;

[0053] Among them, the AB composite disk sample has a tight bond at the interface, that is, the interface strength is taken as the smaller value of the strength of material A and material B.

[0054] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A finite-discrete element method for calibrating microscopic parameters of composite materials containing interfacial cracks, characterized in that, include: Obtain standard-sized disk samples containing different materials, including: a first material, a second material, and a composite material comprising the first material and the second material; The standard-sized disc specimen was subjected to Brazilian splitting FDEM numerical test to obtain the numerical test results of the standard-sized disc specimen and to calibrate the fracture energy of the joint element. Based on the fracture energy and other mechanical parameters of the first and second materials, Brazilian splitting FDEM numerical tests were conducted on standard-sized disk specimens containing interface cracks at different angles to obtain numerical test results of standard-sized disk specimens containing interface cracks at different angles.

2. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, The numerical test results include: tensile strength, load-displacement curves, and failure modes.

3. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, Obtaining numerical test results for standard-sized disk specimens containing the composite material includes: Set the target interface crack inclination angle, and based on the target interface crack inclination angle, conduct a Brazilian splitting FDEM numerical test on a standard-sized disk specimen containing the composite material to obtain the numerical test results of the standard-sized disk specimen containing the composite material.

4. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, The fracture energy of the joint element is calibrated as follows: The numerical test results and experimental results of standard-sized disk specimens containing the first material and standard-sized disk specimens containing the second material are compared to calibrate the fracture energy of the joint unit.

5. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, Obtaining the other mechanical parameters includes: The first material and the second material were subjected to uniaxial tensile, uniaxial compression and triaxial compression laboratory tests to obtain the other mechanical parameters.

6. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, Numerical test results for standard-sized disk specimens containing interface cracks at other different angles were obtained, including: Other interface cracks with different angles are set up. Based on the other interface cracks with different angles, a standard-sized disk specimen containing the composite material is subjected to Brazilian splitting FDEM numerical test to obtain the numerical test results of the standard-sized disk specimen containing the other interface cracks with different angles.

7. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 6, characterized in that, After obtaining the numerical test results of the standard-sized disk specimens containing interface cracks at other different angles, the following are included: The numerical test results of standard-sized disk specimens containing interface cracks at other different angles were compared with the experimental results to preliminarily verify the fracture energy of the joint unit.

8. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 6, characterized in that, During the Brazilian splitting FDEM numerical test on the standard-sized disk specimen of the composite material, the mesh was densified at the crack.

9. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, The interface cracks at different angles include: open cracks at different angles with a crack length of 30 mm and a width of 1 mm.

10. The finite-discrete element method for calibrating microscopic parameters of composite materials with interfacial cracks according to claim 1, characterized in that, The method also includes: The numerical test results of standard-sized disk specimens containing interface cracks at other different angles were compared with the experimental results to further verify the micro-parameter calibration results in the Brazilian splitting FDEM numerical test.

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