Method for calculating rock crack tip position and mode i fracture toughness under dynamic-static combined loading

Abstract

The application discloses a rock crack tip position and I-type fracture toughness calculation method under dynamic and static combined loading, which comprises the following steps: preparing a disc rock sample with a straight cutting groove, and making a speckle pattern on the surface; after prestatic loading, superimposing a dynamic disturbance load to carry out a fracture experiment, and collecting whole-process images of the sample observation surface by using a digital image correlation system; performing correlation calculation on the images, and extracting crack tip area displacement fields at each time before cracking; taking crack tip coordinates as unknown quantities, and establishing polar coordinates of observation points relative to the crack tip; substituting displacement data and corresponding polar radii and polar angles into a Williams series displacement field equation, constructing a nonlinear over-determined equation group with stress intensity factors and crack tip positions as unknown quantities, and solving the equation group by numerical iteration to obtain dynamic I-type stress intensity factors and crack tip coordinates; and frame-by-frame calculation is performed on the whole process to obtain a stress intensity factor time history curve. The method has high precision, good reliability, and is easy to operate.

Description

Technical Field

[0001] This invention pertains to material performance testing methods, specifically relating to methods for testing the location of rock crack tips and the toughness of type I fractures. Background Technology

[0002] With the continuous depletion of shallow mineral resources, deep resource mining has become an inevitable trend in the mining industry. In the high-stress environment of deep rock formations, the surrounding rock not only bears high in-situ stress but is also inevitably affected by dynamic disturbances caused by earthquakes, blasting operations, and mechanical drilling. This combined static and dynamic loading condition, with both pre-static and dynamic loads present, results in significant differences in the fracture behavior of deep rocks compared to shallow rocks. Studying the fracture characteristics of rocks under combined static and dynamic loading conditions is of significant theoretical and engineering application value for revealing the mechanisms of deep rock mass disaster development and ensuring engineering safety.

[0003] Type I fracture toughness is a key mechanical parameter characterizing the ability of rock to resist crack initiation and propagation, and its accurate value directly affects the reliability of rock engineering safety assessments. In deep engineering, Type I fracture of rock is often closely related to typical engineering hazards such as rockburst and zonal fracturing. Accurately determining the Type I fracture toughness of rock under combined dynamic and static loading conditions not only helps to deepen the understanding of the fracture mechanism of deep rocks, but also provides key mechanical parameter basis for the stability analysis and disaster prevention of deep surrounding rock. In rock dynamic fracture mechanics tests, the standard test recommended by the International Society for Rock Mechanics and Rock Engineering is based on linear elastic fracture mechanics theory, calculating dynamic fracture toughness by recording the peak load during the loading process and combining it with the corresponding dimensionless stress intensity factor formula.

[0004] However, as a typical quasi-brittle material, rock exhibits a fracture process zone in front of the crack tip during loading, encompassing the initiation, aggregation, and evolution of microcracks. This leads to significant nonlinear deformation characteristics in the specimen near the peak load. Existing fracture toughness calculation methods based on linear elastic fracture mechanics directly substitute the peak load into the linear elastic formula, essentially treating the nominal value containing nonlinear damage effects as the material's true fracture resistance. The resulting values ​​may deviate from the material's true fracture toughness. Furthermore, in these traditional calculation methods, the crack tip location is not treated as an independent variable. The stress intensity factor is calculated based on a pre-defined crack geometry, while the actual crack tip location during loading is difficult to accurately determine using traditional methods. This introduced uncertainty further affects the accuracy of the fracture toughness calculation results.

[0005] Therefore, it is necessary to provide a method for calculating the location of rock fracture tips and the toughness of type I fracture under combined dynamic and static loading. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the crack tip location and Type I fracture toughness of rocks under combined dynamic and static loading. This method can use DIC technology to obtain crack tip displacement data and use the crack tip location as an unknown quantity to participate in the solution, directly calculating the dynamic Type I fracture toughness of rocks under combined dynamic and static loading conditions. It has good testing accuracy and reliability, and the operation process is standardized and easy to implement.

[0007] To achieve the above-mentioned objectives, this invention provides a method for calculating the location of rock fracture tips and the toughness of type I fracture under combined dynamic and static loading, comprising the following steps: A) Prepare a disc rock specimen with a straight groove, and create a randomly distributed speckle pattern on the observation surface of the specimen. B) After applying a pre-static load to the target load level to the specimen, a dynamic disturbance load is superimposed, and a fracture test is carried out under the combined dynamic and static loading conditions. A digital image correlation system is used to collect digital images of the specimen observation surface in real time during the entire loading process. C) Perform relevant calculations on the acquired digital images to extract the displacement field data of the crack tip region of the sample at each moment before crack initiation; D) Using the crack tip position coordinates as unknowns, determine the polar radius and polar angle of each point in the crack tip region in the polar coordinate system with the crack tip as the origin, based on the geometric relationship between the pixel coordinates of each point in the observation surface of the sample and the crack tip position coordinates. E) Substitute the displacement data of each point in the crack tip region and the corresponding polar radius and polar angle into the crack tip displacement field equation in Williams series form to construct a nonlinear overdetermined set of equations with stress intensity factor and crack tip position coordinates as unknowns. F) The nonlinear overdetermined equations are solved by numerical iteration to obtain the dynamic type I stress intensity factor and crack tip location coordinates of the specimen. G) Calculate frame by frame throughout the loading process to obtain the dynamic Type I stress intensity factor time history curve. The critical value of the stress intensity factor at the crack initiation moment is the dynamic Type I fracture toughness. At the same time, determine the crack tip position based on the crack tip position coordinates obtained in step F).

[0008] Specifically, the straight groove in step A) is located in the middle of the sample and penetrates the sample along the thickness direction.

[0009] More specifically, the steps for creating the speckle pattern described in step A) include: a) Clean the observation surface and evenly spray a thin layer of matte white paint; b) Print black speckles on the matte white paint thin layer. The speckles should be uniform in size and randomly distributed, with each speckle occupying 5-10 pixels. c) The coverage of the black speckle pattern is 50% ± 5%, that is, the area of ​​the matte white paint and the area of ​​the black speckle should be approximately equal.

[0010] Furthermore, the fracture test described in step B) is conducted using a Hopkinson bar apparatus. During the experiment, a pre-static load is first applied to the specimen to the target load level, followed by a dynamic disturbance load. The Hopkinson bar apparatus includes a spindle-shaped impact bar, an incident bar, a transmission bar, and a pre-static load device. The specimen is clamped between the incident bar and the transmission bar, and a dynamic disturbance load is applied to the specimen by the spindle-shaped impact bar striking the incident bar.

[0011] Furthermore, the digital image correlation system in step B) includes a high-speed camera, a high-intensity lighting device, and a computer. The high-speed camera is electrically connected to the computer to acquire digital images of the observation surface in real time.

[0012] Furthermore, the computer includes DIC analysis and calculation software, which is used to perform relevant calculations on the acquired digital images and extract the displacement field data of the crack tip region of the sample in step C).

[0013] Furthermore, in step D), the polar radius and polar angle of each point in the crack tip region in the polar coordinate system with the crack tip as the origin are obtained through the geometric relationship between the pixel coordinates of each point in the observation surface of the sample and the position coordinates of the crack tip.

[0014] Furthermore, the nonlinear overdetermined equations are constructed using the dynamic stress intensity factor and crack tip position coordinates as unknowns, through displacement data of a series of monitoring points in the crack tip region and the corresponding polar radius, polar angle, and crack tip displacement field equations in Williams series form.

[0015] Furthermore, the calculation parameters of the nonlinear overdetermined equation system include shear modulus, Kolosov constant, elastic modulus, and Poisson's ratio; Furthermore, the dynamic stress intensity factor and the crack tip location are obtained by solving the nonlinear overdetermined equations, and the stress intensity factor time history curve is obtained by calculating the digital image frame by frame.

[0016] Furthermore, the dynamic type I fracture toughness is obtained by the critical value of the crack initiation time of the dynamic stress intensity factor time history curve.

[0017] The beneficial effects achieved by adopting the above solution are as follows: The method for calculating the location of rock crack tip and type I fracture toughness under dynamic and static combined loading of the present invention involves creating a randomly distributed speckle pattern on the observation surface of the CSTBD sample and using a digital image correlation system to perform full-field measurement of the displacement field of the crack tip region of the sample during dynamic and static combined loading, thereby obtaining displacement field data of the crack tip region at each moment. Since the Williams series displacement field equation is a function expression with the crack tip as the origin of polar coordinates, the crack tip position coordinates are directly introduced into the equation as unknowns. Together with the stress intensity factor, a nonlinear overdetermined equation system is constructed for joint iterative solution. This allows the actual spatial position of the crack tip during loading to be automatically determined without prior assumptions or subsequent manual calibration of the crack tip position. Based on this actual crack tip position, the displacement field equation in polar coordinates is accurately established, thereby improving the accuracy of dynamic stress intensity factor calculation. Furthermore, this method, based on DIC full-field displacement data and combined with a frame-by-frame calculation strategy, can continuously capture the time-varying evolution of the stress field before crack initiation, obtain the dynamic type I stress intensity factor time history curve, and simultaneously acquire the dynamic migration trajectory of the crack tip position, providing richer experimental data support for studying the fracture mechanism of rocks under dynamic and static combined loads. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an embodiment of the present invention; Figure 2 This is a schematic diagram of the experimental apparatus in an embodiment of the present invention; Figure 3 This is a front view of the sample in an embodiment of the present invention; Figure 4 This is a cross-sectional view of the sample in an embodiment of the present invention; Figure 5 This refers to the speckle field on the observation surface of the sample in an embodiment of the present invention; Figure 6 This is the sample crack tip displacement monitoring area of ​​the present invention; Figure 7 This is a schematic diagram of the displacement coordinate transformation of the present invention; Figure 8 This is the time history curve of the stress intensity factor of the present invention; Figure 9 This is a schematic diagram showing the location of the crack tip in this invention.

[0019] The labels in the diagram are as follows: 1-Pre-static load, 2-Transmission rod, 3-Incident rod, 4-High-intensity lighting equipment, 5-Spindle-shaped impact rod, 6-High-speed camera, 7-Computer. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation steps. It should be understood that the specific embodiments described herein are only for illustrating and explaining the embodiments of the present invention and are not intended to limit the embodiments of the present invention.

[0021] like Figure 1 As shown, the method for calculating the location of rock fracture tips and the toughness of type I fracture under combined dynamic and static loading provided by the present invention includes the following steps: A) Prepare CSTBD disc rock specimens with straight grooves, and fabricate randomly distributed speckle patterns on the observation surface of the specimens. B) After applying a pre-static load to the target load level to the specimen, a dynamic disturbance load is superimposed, and a fracture test is carried out under the combined dynamic and static loading conditions. A digital image correlation system is used to collect digital images of the specimen observation surface in real time during the entire loading process. C) Perform relevant calculations on the acquired digital images to extract the displacement field data of the crack tip region of the sample at each moment before crack initiation; D) Using the crack tip position coordinates as unknowns, determine the polar radius and polar angle of each point in the crack tip region in the polar coordinate system with the crack tip as the origin, based on the geometric relationship between the pixel coordinates of each point in the observation surface of the sample and the crack tip position coordinates. E) Substitute the displacement data of each point in the crack tip region and the corresponding polar radius and polar angle into the crack tip displacement field equation in Williams series form to construct a nonlinear overdetermined set of equations with stress intensity factor and crack tip position coordinates as unknowns. F) The nonlinear overdetermined equations are solved by numerical iteration to obtain the dynamic type I stress intensity factor and crack tip location coordinates of the specimen. G) Calculate frame by frame during the entire loading process to obtain the dynamic Type I stress intensity factor time history curve. The critical value of the stress intensity factor at the crack initiation moment is the dynamic Type I fracture toughness. At the same time, the crack tip position is obtained according to the crack tip position coordinates obtained in step F).

[0022] The method for calculating the location of rock crack tip and type I fracture toughness under dynamic and static combined loading of the present invention involves creating a randomly distributed speckle pattern on the observation surface of the CSTBD sample and using a digital image correlation system to perform full-field measurement of the displacement field of the crack tip region of the sample during dynamic and static combined loading, thereby obtaining displacement field data of the crack tip region at each moment. Since the Williams series displacement field equation is a function expression with the crack tip as the origin of polar coordinates, the crack tip position coordinates are directly introduced into the equation as unknowns. Together with the stress intensity factor, a nonlinear overdetermined equation system is constructed for joint iterative solution. This allows the actual spatial position of the crack tip during loading to be automatically determined without prior assumptions or subsequent manual calibration of the crack tip position. Based on this actual crack tip position, the displacement field equation in polar coordinates is accurately established, thereby improving the accuracy of dynamic stress intensity factor calculation. Furthermore, this method, based on DIC full-field displacement data and combined with a frame-by-frame calculation strategy, can continuously capture the time-varying evolution of the stress field before crack initiation, obtain the dynamic type I stress intensity factor time history curve, and simultaneously acquire the dynamic migration trajectory of the crack tip position, providing richer experimental data support for studying the fracture mechanism of rocks under dynamic and static combined loads.

[0023] In one embodiment of the method for calculating the location of rock fracture tips and the toughness of type I fracture under combined dynamic and static loading provided by the present invention, like Figure 2 As shown, a fracture test is carried out on the sample based on the Hopkinson pressure bar device. Specifically, the Hopkinson pressure bar device includes a spindle-shaped impact bar, an incident bar, a transmission bar, and a pre-static load device. The sample is clamped between the incident bar and the transmission bar. The sample is pre-statically loaded to the target value by hydraulic pressure. The sample is subjected to dynamic disturbance by the impact of the spindle-shaped impact bar on the incident bar, which can cause cracks to be generated in the sample along the groove.

[0024] The structure of the sample can be as follows: Figure 3 and Figure 4 As shown, in one embodiment of the method for calculating the location of rock crack tip and type I fracture toughness under dynamic and static combined loading provided by the present invention, the specimen can be set as a disc specimen, and the straight groove is preferably set in the middle of the upper plane of the disc specimen and penetrates the disc specimen along the thickness direction of the disc specimen.

[0025] Specifically, in one embodiment of the method for calculating the location of rock fracture tips and the toughness of type I fracture under dynamic and static combined loading provided by the present invention, the measurement of the location of rock fracture tips and the toughness of type I fracture is based on a digital image correlation system.

[0026] like Figure 2As shown, the digital image measurement device includes a high-speed camera, high-intensity lighting equipment, and a computer. The high-speed camera is electrically connected to the computer to acquire digital images of the observation surface in real time. The high-speed camera is installed at a position 1 m away from the center normal of the observation surface of the sample. The lens surface is adjusted to be parallel to the observation surface, and the parameters of the high-speed camera are reasonably set according to the size of the sample and the working distance to ensure that the captured image (observation surface) is clear and located at the exact center of the camera target surface. Preferably, the high-speed camera is capable of high-speed shooting at the microsecond level. Therefore, the shooting speed is preferably 80,000 frames / second to facilitate the correlation of the displacement change of the speckle with time. The high-intensity lighting equipment can be set up with two high-intensity LED point light sources for high-speed cameras, and placed on both sides of the sample respectively to ensure that the sample is not obstructed and that the distance between the light source and the sample observation surface is more than 20 cm, so as to provide a stable light source during the shooting process. The computer includes DIC (Digital Image Correlation) analysis and calculation software, which is used to calculate the displacement of measurement points in the image.

[0027] The specific method for testing the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading is as follows: First, the observation surface of the sample is cleaned. After cleaning, the entire observation surface is sprayed to form a base layer. The preferred spraying material is matte white paint to prevent excessive reflection from making the DIC analysis software unable to clearly and accurately identify the speckles. After the base coat has hardened and dried, black speckles are created on the base coat using stamping or spraying techniques, such as... Figure 5 As shown, it is important to note that the paint color of the undercoat and the color of the speckles need to have a high contrast. In particular, the speckles need to be randomly distributed and cover 50% ± 5% of the undercoat area to ensure that the speckles can shift with the deformation of the sample. Furthermore, the speckles need to occupy 5-10 pixels so that the DIC analysis software in the computer can clearly and accurately identify the speckles and calculate the displacement of each speckle captured by the high-speed camera in the dynamic fracture experiment.

[0028] Secondly, such as Figure 6 As shown, a certain number of measuring points are selected in the area surrounding the groove, and the horizontal displacement of each measuring point is extracted. x and vertical displacement y Assume the coordinates of the origin at the crack tip are ( x 0, y 0), and calculate the extreme diameter of each measuring point in the region surrounding the crack tip according to the following formula. r and polar angle θ ,like Figure 7 As shown:

[0029]

[0030] Next, measure the extreme diameter of each measuring point in the area surrounding the crack tip. r and polar angle θ Substituting the Williams series form of the crack tip displacement field equation, a nonlinear overdetermined system of equations is constructed with the dynamic stress intensity factor and the crack tip position coordinates as unknowns, as follows:

[0031] μ = E / [2(1+ ν )]

[0032]

[0033] in, U , V These represent the horizontal and vertical displacements of the measuring points in the crack tip region, respectively. μ Shear modulus κ It is the Kolosov constant. E and ν These are the elastic modulus and Poisson's ratio, respectively.

[0034] Again, repeat the above steps to calculate the stress intensity factor of each frame of digital images before crack initiation, obtain the stress intensity factor time history curve, and obtain the dynamic mode I fracture toughness through the critical value of the crack initiation time of the dynamic stress intensity factor time history curve, such as... Figure 8 As shown, the crack tip position is obtained through the corresponding crack tip coordinates, such as... Figure 9 As shown.

[0035] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0036] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading, characterized in that, Includes the following steps: A) Prepare a disc rock specimen with a straight groove, and create a randomly distributed speckle pattern on the observation surface of the specimen. B) After applying a pre-static load to the target load level to the specimen, a dynamic disturbance load is superimposed, and a fracture test is carried out under the combined dynamic and static loading conditions. A digital image correlation system is used to collect digital images of the specimen observation surface in real time during the entire loading process. C) Perform relevant calculations on the acquired digital images to extract the displacement field data of the crack tip region of the sample at each moment before crack initiation; D) Using the crack tip position coordinates as unknowns, determine the polar radius and polar angle of each point in the crack tip region in the polar coordinate system with the crack tip as the origin, based on the geometric relationship between the pixel coordinates of each point in the observation surface of the sample and the crack tip position coordinates. E) Substitute the displacement data of each point in the crack tip region and the corresponding polar radius and polar angle into the crack tip displacement field equation in Williams series form to construct a nonlinear overdetermined set of equations with stress intensity factor and crack tip position coordinates as unknowns. F) The nonlinear overdetermined equations are solved by numerical iteration to obtain the dynamic type I stress intensity factor and crack tip location coordinates of the specimen. G) Calculate frame by frame during the entire loading process to obtain the dynamic Type I stress intensity factor time history curve. The critical value of the stress intensity factor at the crack initiation moment is the dynamic Type I fracture toughness. At the same time, obtain the crack tip position based on the crack tip position coordinates obtained in step F).

2. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 1, characterized in that, The straight groove in step A) is located in the middle of the sample and penetrates the sample along the thickness direction.

3. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 2, is characterized in that... The steps for creating the speckle pattern described in step A) include: a) Clean the observation surface and evenly spray a thin layer of matte white paint; b) Print black speckles on the matte white paint thin layer. The speckles are uniform in size and randomly distributed, with each speckle occupying 5-10 pixels. c) The coverage of the black speckle pattern is 50% ± 5%, that is, the area of ​​the matte white paint and the area of ​​the black speckle are approximately equal.

4. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 3, is characterized in that... The fracture test described in step B) is conducted using a Hopkinson pressure bar apparatus, which includes a spindle-shaped impact bar, an incident bar, a transmission bar, and a pre-static load device. The specimen is clamped between the incident bar and the transmission bar, and a dynamic disturbance load is applied to the specimen by the spindle-shaped impact bar striking the incident bar.

5. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 4, characterized in that, The digital image correlation system in step B) includes a high-speed camera, a high-intensity lighting device, and a computer. The high-speed camera is electrically connected to the computer and acquires digital images of the observation surface in real time.

6. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 5, characterized in that, The computer includes DIC analysis and calculation software, which is used to perform relevant calculations on the acquired digital images and extract the displacement field data of the crack tip region of the sample in step C).

7. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 6, characterized in that, The computational parameters of the nonlinear overdetermined equations include shear modulus, Kolosov constant, elastic modulus, and Poisson's ratio.

8. The method for calculating the location of rock crack tips and the toughness of type I fracture under combined dynamic and static loading as described in claim 7, characterized in that, In step G), the dynamic migration trajectory of the crack tip position is obtained synchronously by calculating frame by frame of the digital image of the entire loading process.

Images