Method and system for calculating I / III type mixed crack initiation mode and in-plane crack initiation angle of isotropic rock

Abstract

The invention discloses a method and a system for calculating an I / III type mixed crack initiation mode and an in-plane crack initiation angle of isotropic rock. The method comprises the following steps: acquiring material attribute parameters to construct a geometric model; obtaining a stress intensity factor; obtaining a fitted I / III type geometrical shape factor; constructing an expression of a crack tip stress intensity factor under the new coordinate system; solving the maximum value of the I / III type crack tip stress intensity factor, and comparing the maximum value with the I / III type fracture toughness to obtain an isotropic rock I / III type mixed crack initiation mode; and an expression of the in-plane crack initiation angle is constructed, and the in-plane crack initiation angle of isotropic rock I / III type mixed crack initiation is obtained through calculation. According to the method, the isotropic rock I / III type mixed crack initiation mode and the in-plane crack initiation angle can be calculated more accurately, and the in-plane crack initiation angle can be determined only according to the geometrical shape factor and the fixed parameter under the condition that the crack tip stress intensity factor does not need to be obtained.

Description

Technical Field

[0001] This invention relates to the field of civil engineering, specifically to a method for calculating the mixed crack initiation mode of isotropic rock (Type I / III) and the in-plane crack initiation angle. Background Technology

[0002] In engineering scenarios such as ground rock pavements and rock slopes, the unstable propagation of isotropic rock internal cracks is one of the important causes of engineering disasters. Essentially, this manifests as a process in which mixed-mode Type I / III cracks within the rock initiate, evolve, aggregate, and eventually penetrate. The crack initiation mode largely determines its subsequent propagation path, while the initiation angle directly affects the final failure mode of the rock mass. Therefore, accurately predicting the initiation mode and initiation angle of Type I / III rock mass cracks is of great guiding significance for engineering safety assessment and support scheme design.

[0003] Existing methods for determining crack initiation modes and initiation angles mostly employ ENDB (Edge-Notched DiscBend) specimens for mixed-mode loading or utilize digital image correlation (DIC) techniques to observe crack initiation morphology. However, determining the initiation mode based on ENDB specimens typically requires microscopic scanning of the fracture surface after the test, followed by reverse derivation of the initiation mode. Methods using DIC require microscale analysis of the acquired displacement field to extract and identify the modal characteristics of the crack initiation stage, a process that is quite challenging. Some researchers have proposed methods for calculating stress intensity factors for type I / III cracks, but these primarily focus on fracture toughness, and methods for determining the initiation mode and in-plane initiation angle of ENDB specimens remain relatively rare. Summary of the Invention

[0004] One of the objectives of this invention is to provide a more accurate method for calculating the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III.

[0005] The method for calculating the mixed fracture initiation mode and in-plane fracture initiation angle of isotropic rocks (Type I / III) provided by this invention includes the following steps:

[0006] S1. Obtain the material property parameters of the target isotropic rock, and construct the geometric model of the corresponding edge-grooved disk bending specimen according to the preset parameters;

[0007] S2. Use software to perform numerical simulation of the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles;

[0008] S3. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and combined with preset parameters, obtain the corresponding Type I and Type III geometric shape factors, and then perform numerical fitting on them to obtain the fitted Type I and Type III geometric shape factors.

[0009] S4. By performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, expressions for the stress intensity factors at the crack tip of Type I and Type III cracks in a new coordinate system characterized by Type I and Type III geometric shape factors and preset parameters are constructed.

[0010] S5. Based on the expressions for the stress intensity factors at the tips of Type I and Type III cracks obtained in step S4, within the set range, calculate the maximum values ​​of the stress intensity factors at the tips of Type I and Type III cracks respectively, and compare them with the fracture toughness of Type I and Type III of isotropic rocks to obtain the calculation results of the mixed initiation mode of Type I / III cracks in isotropic rocks.

[0011] S6. Based on the three-dimensional maximum tangential stress criterion, and utilizing the proportional relationship between stress intensity factor and geometric shape factor, construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors;

[0012] S7. Substitute the fitted Type I and Type III geometric shape factors obtained in step S3 into the expression for the in-plane initiation angle obtained in S6 to calculate the in-plane initiation angle of the isotropic rock with mixed initiation of Type I / III cracks.

[0013] The preset parameters in step S1 include: specimen diameter, specimen thickness, crack length, half-spacing between lower supports, loading angle between the direction of applied load and the crack surface of the model, and an applied load from above the specimen along the axial direction of the specimen. Singular elements are configured at the crack tip of the geometric model of the edge-grooved disk bending specimen.

[0014] Step S2 specifically involves: calculating the stress intensity factor of the model using the J-integral method, and changing the loading angle by rotating the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles.

[0015] Step S3 includes the following steps:

[0016] A1. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, for the geometric model of the edge-grooved disk bending specimen, the discrete values ​​of the corresponding Type I and Type III geometric shape factors are calculated using the following formula.

[0017] in, For loading angle Discrete values ​​of the Type I geometry factor under the given conditions. The diameter of the sample is 1. For the sample thickness, In the initial coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The length of the crack. For loading angle Discrete numerical values ​​of the Type III geometry factor under the following conditions In the initial coordinate system and with the loading angle being... Type III stress intensity factor at that time;

[0018] A2. Based on the discrete values ​​of the Type I and Type III geometric shape factors obtained in step A1, the following formula is used to numerically fit them, resulting in the fitted expressions for the Type I and Type III geometric shape factors in relation to the loading angle.

[0019] in, The fitted loading angle Type I geometry factor below, The zeroth fitted parameter, The first fitted parameter is... The second fitting parameter, The third fitting parameter, The fourth fitting parameter, The fitted loading angle Type III geometry factor, For the fifth fitting parameter, For the sixth fitting parameter, For the seventh fitting parameter, For the eighth fitting parameter, This is the ninth fitting parameter.

[0020] Step S4 includes the following steps:

[0021] B1. For the geometric model of the edge-grooved disk bending specimen, the stress intensity factor at the crack tip in the initial coordinate system is calculated using the following formula:

[0022] In the formula, For loading angle Below, the Type I stress intensity factor at the crack tip in the initial coordinate system. For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For loading angle Below, the Type III stress intensity factor at the crack tip in the initial coordinate system. The fitted loading angle Type III geometry factor;

[0023] B2. For the geometric model of the edge-grooved disk bending specimen, and combining the stress intensity factor at the crack tip in the initial coordinate system obtained in step B1, calculate the stress field at the crack tip, as shown in the following equation:

[0024] In the formula, In the initial coordinate system Stress components in the direction, Let be the Type I stress intensity factor at the crack tip in the initial coordinate system. This represents the radial distance from the crack tip to any point near the tip. The angle of rotation is counterclockwise around the crack tip. In the initial coordinate system Stress components in the direction, In the initial coordinate system - In-plane stress components In the initial coordinate system - In-plane stress components This represents the Type III stress intensity factor at the crack tip in the initial coordinate system. In the initial coordinate system - In-plane stress components;

[0025] B3. By rotating the crack tip Angle generates a new coordinate system To obtain the new coordinate system corner and :

[0026] In the formula, For the new coordinate system Stress components in the direction, For coordinate transformation angle, For the new coordinate system In-plane stress components;

[0027] B4. Based on the definition of the local stress intensity factor, and combined with the new coordinate system obtained in step B3... corner and Substituting the expression for the stress intensity factor at the crack tip in the initial coordinate system, the expressions for the stress intensity factors at the crack tip in the new coordinate system, characterized by the type I and type III geometry factors and preset parameters, are derived as follows:

[0028] In the formula, In the new coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For coordinate transformation angle, In the new coordinate system and with the loading angle being... Type III stress intensity factor at that time The fitted loading angle Type III geometry factor.

[0029] The calculation results of the isotropic rock type I / III mixed fracturing mode described in step S5 are expressed by the following formula:

[0030] In the formula, This is the maximum value of the Type III stress intensity factor; It has a type III fracture toughness. This represents the maximum value of the Type I stress intensity factor; Type I fracture toughness;

[0031] and Obtained through experimental measurement;

[0032] Step S6 includes the following steps:

[0033] D1. Establish a local cylindrical coordinate system with the crack tip as the origin, and derive the expression for the tangential normal stress as follows:

[0034] In the formula, For tangential and normal stress, It is a type I stress intensity factor. The polar angle is calculated from the original crack plane. It is a type III stress intensity factor.

[0035] The expression for in-plane shear stress is as follows:

[0036] In the formula, This refers to in-plane shear stress;

[0037] D2. According to the three-dimensional maximum tangential stress criterion, assuming the crack initiates along the direction of the maximum tangential stress, then the in-plane shear stress in that direction is equal to 0, and the in-plane crack initiation angle is... The governing equations are as follows:

[0038] In the formula, The sign of the partial derivative. For tangential stress, To Find the partial derivative. This refers to in-plane shear stress;

[0039] D3. Based on the expression for in-plane shear stress obtained in step D1 and the governing equation for in-plane crack initiation angle obtained in step D2, the following equation is derived:

[0040] In the formula, For in-plane cracking;

[0041] Solving the above equation by variable substitution yields the in-plane crack initiation angle. The expression is as follows:

[0042] because ,and Therefore, the in-plane crack initiation angle, characterized by type I and type III geometry factors, is derived. The expression is as follows: .

[0043] A second objective of this invention is to provide a calculation system for the mixed type I / III crack initiation mode and in-plane crack initiation angle of isotropic rocks. This system comprises: a geometric model construction module, a type I and type III stress intensity factor acquisition module, a type I and type III geometric shape factor fitting module, a type I and type III crack tip stress intensity factor expression construction module, a type I / III mixed crack initiation mode calculation module, an in-plane crack initiation angle expression construction module, and an in-plane crack initiation angle calculation module. These modules are connected in series.

[0044] The geometric model construction module is used to obtain the material property parameters of the target isotropic rock, construct the corresponding geometric model of the edge-grooved disk bending specimen according to the preset parameters, and upload the data to the Type I and Type III stress intensity factor acquisition module.

[0045] The Type I and Type III stress intensity factor acquisition module is used to perform numerical simulation of the geometric model using software based on the received data, obtain the Type I and Type III stress intensity factors under different loading angles, and upload the data to the Type I and Type III geometric shape factor fitting module.

[0046] The Type I and Type III geometry factor fitting module is used to obtain the corresponding Type I and Type III geometry factors based on the received data, the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and preset parameters. Then, it performs numerical fitting to obtain the fitted Type I and Type III geometry factors, and uploads the data to the expression construction module for the Type I and Type III crack tip stress intensity factors.

[0047] The expression construction module for the stress intensity factor at the crack tip of Type I and Type III cracks is used to construct expressions for the stress intensity factor at the crack tip of Type I and Type III cracks in a new coordinate system characterized by the geometric shape factor of Type I and Type III and preset parameters, based on the received data, by performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, and then upload the data to the calculation module for the mixed crack initiation mode of Type I / III.

[0048] The calculation module for the mixed initiation mode of type I / III cracks is used to calculate the maximum value of the stress intensity factor at the tip of type I and type III cracks within a set range based on the received data and the expressions for the stress intensity factor at the tip of type I and type III cracks obtained in step S4. The maximum value is then compared with the fracture toughness of type I and type III cracks in isotropic rocks to obtain the calculation results of the mixed initiation mode of type I / III cracks in isotropic rocks. The data is then uploaded to the expression construction module for the in-plane initiation angle.

[0049] The expression construction module for the in-plane crack initiation angle is used to construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors based on the received data, according to the three-dimensional maximum tangential stress criterion and the proportional relationship between stress intensity factor and geometric shape factor, and upload the data to the in-plane crack initiation angle calculation module.

[0050] The in-plane crack initiation angle calculation module is used to calculate the in-plane crack initiation angle of isotropic rocks by substituting the fitted type I and type III geometric shape factors obtained in step S3 into the expression of the in-plane crack initiation angle obtained in step S6, based on the received data.

[0051] This invention constructs an expression for the crack tip stress intensity factor, characterized solely by geometric shape factors and preset parameters, to obtain the maximum values ​​of the stress intensity factors at the crack tips of Type III and Type I cracks. The ratio of these two values ​​is then compared with the ratio of Type III to Type I fracture toughness to derive the calculation results for the mixed Type I / III crack initiation mode. Furthermore, the in-plane initiation angle for the mixed Type I / III crack initiation in isotropic rocks is calculated. The calculation method for the mixed Type I / III crack initiation mode and in-plane initiation angle in isotropic rocks provided by this invention yields more accurate results. Attached Figure Description

[0052] Figure 1 This is a schematic flowchart illustrating a method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to the present invention.

[0053] Figure 2 This is a schematic diagram of the structure of a grooved disk bending specimen constructed with preset parameters for a target isotropic rock in an embodiment of the method of the present invention.

[0054] Figure 3 This refers to the Abaqus mesh model used in the method of this invention to calculate the geometric shape factor.

[0055] Figure 4 This is a schematic diagram comparing the in-plane crack initiation angle results calculated using the method of this invention with those calculated using existing technologies in an embodiment of this invention. Detailed Implementation

[0056] like Figure 1 The diagram shown is a flowchart of the method of the present invention: The method for calculating the mixed fracture initiation mode of isotropic rocks (Type I / III) and the in-plane fracture initiation angle disclosed in this invention includes the following steps:

[0057] S1. Obtain the material property parameters of the target isotropic rock, and construct the geometric model of the corresponding edge-grooved disk bending specimen according to the preset parameters;

[0058] The material property parameters of the target isotropic rock include: elastic modulus and Poisson's ratio; the preset parameters include: specimen diameter, specimen thickness, crack length, half-spacing between lower supports, loading angle between the direction of applied load and the crack surface of the model, and loading load applied from above the specimen along the axial direction of the specimen, with singular elements configured at the crack tip of the geometric model of the edge-grooved disk bent specimen.

[0059] S2. Use software to perform numerical simulation of the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles;

[0060] Specifically, the stress intensity factor of the model is calculated using the J-integral method. By rotating the geometric model to change the loading angle, the type I and type III stress intensity factors under different loading angles are obtained.

[0061] S3. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and combined with preset parameters, obtain the corresponding Type I and Type III geometric shape factors, and then perform numerical fitting on them to obtain the fitted Type I and Type III geometric shape factors.

[0062] Includes the following steps:

[0063] A1. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, for the geometric model of the edge-grooved disk bending specimen, the discrete values ​​of the corresponding Type I and Type III geometric shape factors are calculated using the following formula.

[0064] in, For loading angle Discrete values ​​of the Type I geometry factor under the given conditions. The diameter of the sample is 1. For the sample thickness, In the initial coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The length of the crack. For loading angle Discrete numerical values ​​of the Type III geometry factor under the following conditions In the initial coordinate system and with the loading angle being... Type III stress intensity factor at that time;

[0065] A2. Based on the discrete values ​​of the Type I and Type III geometric shape factors obtained in step A1, the following formula is used to numerically fit them, resulting in the fitted expressions for the Type I and Type III geometric shape factors in relation to the loading angle.

[0066] in, The fitted loading angle Type I geometry factor below, The zeroth fitted parameter, The first fitted parameter is... The second fitting parameter, The third fitting parameter, The fourth fitting parameter, The fitted loading angle Type III geometry factor, For the fifth fitting parameter, For the sixth fitting parameter, For the seventh fitting parameter, For the eighth fitting parameter, This is the ninth fitting parameter.

[0067] S4. By performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, expressions for the stress intensity factors at the crack tip of Type I and Type III cracks in a new coordinate system characterized by Type I and Type III geometric shape factors and preset parameters are constructed.

[0068] Includes the following steps:

[0069] B1. For the geometric model of the edge-grooved disk bending specimen, the stress intensity factor at the crack tip in the initial coordinate system is calculated using the following formula:

[0070] In the formula, For loading angle Below, the Type I stress intensity factor at the crack tip in the initial coordinate system. For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For loading angle Below, the Type III stress intensity factor at the crack tip in the initial coordinate system. The fitted loading angle Type III geometry factor;

[0071] B2. For the geometric model of the edge-grooved disk bending specimen, and combining the stress intensity factor at the crack tip in the initial coordinate system obtained in step B1, calculate the stress field at the crack tip, as shown in the following formula:

[0072] In the formula, In the initial coordinate system Stress components in the direction, Let be the Type I stress intensity factor at the crack tip in the initial coordinate system. This represents the radial distance from the crack tip to any point near the tip. The angle of rotation is counterclockwise around the crack tip. In the initial coordinate system Stress components in the direction, In the initial coordinate system - In-plane stress components In the initial coordinate system - In-plane stress components This represents the Type III stress intensity factor at the crack tip in the initial coordinate system. In the initial coordinate system - In-plane stress components;

[0073] B3. By rotating the crack tip Angle generates a new coordinate system To obtain the new coordinate system corner and :

[0074] In the formula, For the new coordinate system Stress components in the direction, For coordinate transformation angle, For the new coordinate system In-plane stress components;

[0075] B4. According to the definition of local stress intensity factor , Combined with the new coordinate system obtained in step B3 corner and Substituting the expression for the stress intensity factor at the crack tip in the initial coordinate system, the expressions for the stress intensity factors at the crack tip in the new coordinate system, characterized by the type I and type III geometry factors and preset parameters, are derived as follows:

[0076] In the formula, In the new coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For coordinate transformation angle, In the new coordinate system and with the loading angle being... Type III stress intensity factor at that time The fitted loading angle Type III geometry factor.

[0077] S5. Based on the expressions for the stress intensity factors at the tips of Type I and Type III cracks obtained in step S4, within a set range, calculate the maximum values ​​of the stress intensity factors at the tips of Type I and Type III cracks respectively, and compare them with the fracture toughness of Type I and Type III cracks in isotropic rocks to obtain the calculation results of the mixed initiation mode of Type I / III cracks in isotropic rocks; the set range is −180° to 180°.

[0078] The calculation results of the mixed fracture initiation mode of type I / III isotropic rock are expressed by the following formula:

[0079] In the formula, This is the maximum value of the Type III stress intensity factor; It has a type III fracture toughness. This represents the maximum value of the Type I stress intensity factor; It is a type I fracture toughness.

[0080] S6. Based on the three-dimensional maximum tangential stress criterion, and utilizing the proportional relationship between stress intensity factor and geometric shape factor, construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors;

[0081] Includes the following steps:

[0082] D1. Establish a local cylindrical coordinate system with the crack tip as the origin, and derive the expression for the tangential normal stress as follows:

[0083] In the formula, For tangential and normal stress, It is a type I stress intensity factor. The polar angle is calculated from the original crack plane. It is a type III stress intensity factor.

[0084] The expression for in-plane shear stress is as follows:

[0085] In the formula, This refers to in-plane shear stress;

[0086] D2. According to the three-dimensional maximum tangential stress criterion, assuming the crack initiates along the direction of the maximum tangential stress, then the in-plane shear stress in that direction is equal to 0, and the in-plane crack initiation angle is... The governing equations are as follows:

[0087] In the formula, The sign of the partial derivative. For tangential stress, To Find the partial derivative. This refers to in-plane shear stress;

[0088] D3. Based on the expression for in-plane shear stress obtained in step D1 and the governing equation for in-plane crack initiation angle obtained in step D2, the following equation is derived:

[0089] In the formula, For in-plane cracking;

[0090] Solving the above equation by variable substitution yields the in-plane crack initiation angle. The expression is as follows:

[0091] because ,and Therefore, the in-plane crack initiation angle, characterized by type I and type III geometry factors, is derived. The expression is as follows: .

[0092] S7. Substitute the fitted Type I and Type III geometric shape factors obtained in step S3 into the expression for the in-plane initiation angle obtained in S6 to calculate the in-plane initiation angle of the isotropic rock with mixed initiation of Type I / III cracks.

[0093] The method for calculating the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III provided by this invention can more accurately determine the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III.

[0094] The effects of the method of the present invention will be illustrated below with reference to an embodiment:

[0095] Taking the experimental parameters and results from Shui Xin's 2024 paper "Investigation of the fracture characteristics of mixed-mode I / III crack by using two kinds of sandstone specimens" published in *Engineering Fracture Mechanics* as an example: the specimens were sandstone from Sichuan province, with an elastic modulus E = 5.00 GPa, Poisson's ratio ν = 0.25, and a density ρ = 2500 kg / m³. 3 The longitudinal wave velocity is 2498 m / s. ; Figure 2 This is a schematic diagram of a grooved disk bending specimen constructed for a target isotropic rock and pre-defined parameters. Figure 3 For the Abaqus mesh model used to calculate the geometric shape factor, the radius R = 37.5 mm, sample thickness B = 30 mm, crack length a = 9 mm, bottom support span 2S = 71 mm (span ratio 2S / D = 0.95), crack width 0.45 mm, and crack inclination angles β = 0°, 10°, 20°, 30°, 40°, and 50° were used. Three-point bending static loading was applied, with the upper loading end being a semi-cylindrical steel bar with a diameter of 10 mm, at a speed of 0.1 mm / min (displacement control). The results are shown in Table 1 below.

[0096] First, the parameters obtained are shown in Table 1;

[0097] Then, the calculations shown in Table 2 are obtained. and ;

[0098] Next, through comparison and The size of the sample determines the crack initiation mode;

[0099] Finally, the crack initiation angle of the specimen was calculated using the specimen's geometric shape factor. .

[0100] Meanwhile, Jamal Bidadi's 2022 article, "Development of maximum tangential strain (MTSN) criterion for prediction of mixed-mode I / III brittle fracture," published in the *International Journal of Solids and Structures*, provides a formula for calculating the crack initiation angle. By comparing the calculations, we can obtain the calculated fracture parameters of the ENDB specimen shown in Table 2.

[0101] The crack initiation angle calculated by the method of this invention is compared with the crack initiation angle calculated by the prior art. The comparison results are as follows: Figure 4 As shown; according to Figure 4 As can be seen, the crack initiation angle (square) of the ENDB specimen calculated by the method of this invention is more consistent with the experimental test results (triangular) than the result (spherical) obtained by Jamal Bidadi's method. Compared with the maximum tangential strain method used by Jamal Bidadi, the method of this invention considers the three-dimensional maximum tangential stress to determine the crack initiation angle, resulting in more accurate calculation results.

[0102] This invention also discloses a calculation system for the mixed type I / III crack initiation mode and in-plane crack initiation angle of isotropic rocks. The calculation system for the mixed type I / III crack initiation mode and in-plane crack initiation angle of isotropic rocks includes: a geometric model construction module, a type I and type III stress intensity factor acquisition module, a type I and type III geometric shape factor fitting module, a type I and type III crack tip stress intensity factor expression construction module, a type I / III mixed crack initiation mode calculation module, an in-plane crack initiation angle expression construction module, and an in-plane crack initiation angle calculation module; the geometric model construction module, the type I and type III stress intensity factor acquisition module, the type I and type III geometric shape factor fitting module, the type I and type III crack tip stress intensity factor expression construction module, the type I / III mixed crack initiation mode calculation module, the in-plane crack initiation angle expression construction module, and the in-plane crack initiation angle calculation module are connected in series.

[0103] The geometric model construction module is used to obtain the material property parameters of the target isotropic rock, construct the corresponding geometric model of the edge-grooved disk bending specimen according to the preset parameters, and upload the data to the Type I and Type III stress intensity factor acquisition module.

[0104] The Type I and Type III stress intensity factor acquisition module is used to perform numerical simulation of the geometric model using software based on the received data, obtain the Type I and Type III stress intensity factors under different loading angles, and upload the data to the Type I and Type III geometric shape factor fitting module.

[0105] The Type I and Type III geometry factor fitting module is used to obtain the corresponding Type I and Type III geometry factors based on the received data, the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and preset parameters. Then, it performs numerical fitting to obtain the fitted Type I and Type III geometry factors, and uploads the data to the expression construction module for the Type I and Type III crack tip stress intensity factors.

[0106] The expression construction module for the stress intensity factor at the crack tip of Type I and Type III cracks is used to construct expressions for the stress intensity factor at the crack tip of Type I and Type III cracks in a new coordinate system characterized by the geometric shape factor of Type I and Type III and preset parameters, based on the received data, by performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, and then upload the data to the calculation module for the mixed crack initiation mode of Type I / III.

[0107] The calculation module for the mixed initiation mode of type I / III cracks is used to calculate the maximum value of the stress intensity factor at the tip of type I and type III cracks within a set range based on the received data and the expressions for the stress intensity factor at the tip of type I and type III cracks obtained in step S4. The maximum value is then compared with the fracture toughness of type I and type III cracks in isotropic rocks to obtain the calculation results of the mixed initiation mode of type I / III cracks in isotropic rocks. The data is then uploaded to the expression construction module for the in-plane initiation angle.

[0108] The expression construction module for the in-plane crack initiation angle is used to construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors based on the received data, according to the three-dimensional maximum tangential stress criterion and the proportional relationship between stress intensity factor and geometric shape factor, and upload the data to the in-plane crack initiation angle calculation module.

[0109] The in-plane crack initiation angle calculation module is used to calculate the in-plane crack initiation angle of isotropic rocks by substituting the fitted type I and type III geometric shape factors obtained in step S3 into the expression of the in-plane crack initiation angle obtained in step S6, based on the received data.

[0110] This invention also discloses a method for calculating the in-plane crack initiation angle of isotropic rocks of type I / III, comprising the following steps:

[0111] S1. Obtain the material property parameters of the target isotropic rock, and construct the geometric model of the corresponding edge-grooved disk bending specimen according to the preset parameters;

[0112] S2. Use software to perform numerical simulation of the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles;

[0113] S3. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and combined with preset parameters, obtain the corresponding Type I and Type III geometric shape factors, and then perform numerical fitting on them to obtain the fitted Type I and Type III geometric shape factors.

[0114] S4. Based on the three-dimensional maximum tangential stress criterion, and utilizing the proportional relationship between stress intensity factor and geometric shape factor, construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors;

[0115] S5. Substitute the fitted Type I and Type III geometric shape factors obtained in step S3 into the expression for the in-plane initiation angle obtained in S4 to calculate the in-plane initiation angle of the isotropic rock with mixed initiation of Type I / III cracks.

[0116] The method for calculating the in-plane initiation angle of isotropic rock type I / III mixed fracture provided by this invention can bypass cumbersome calculation steps and directly determine the in-plane initiation angle of isotropic rock type I / III mixed fracture based solely on geometric shape factors and preset parameters, without needing to obtain the stress intensity factor at the crack tip.

[0117] This invention also discloses a calculation system for the in-plane crack initiation angle of isotropic rocks of type I / III hybrid composition. The system comprises: a geometric model construction module, a type I and type III stress intensity factor acquisition module, a type I and type III geometric shape factor fitting module, an in-plane crack initiation angle expression construction module, and an in-plane crack initiation angle calculation module; these modules are connected in series.

[0118] The geometric model construction module is used to obtain the material property parameters of the target isotropic rock, construct the corresponding geometric model of the edge-grooved disk bending specimen according to the preset parameters, and upload the data to the Type I and Type III stress intensity factor acquisition module.

[0119] The Type I and Type III stress intensity factor acquisition module is used to perform numerical simulation of the geometric model using software based on the received data, obtain the Type I and Type III stress intensity factors under different loading angles, and upload the data to the Type I and Type III geometric shape factor fitting module.

[0120] The Type I and Type III geometry factor fitting module is used to obtain the corresponding Type I and Type III geometry factors based on the received data, the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and preset parameters. Then, it performs numerical fitting to obtain the fitted Type I and Type III geometry factors, and uploads the data to the expression construction module for in-plane crack initiation angle.

[0121] The expression construction module for the in-plane crack initiation angle is used to construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors based on the received data, according to the three-dimensional maximum tangential stress criterion and the proportional relationship between stress intensity factor and geometric shape factor, and upload the data to the in-plane crack initiation angle calculation module.

[0122] The in-plane crack initiation angle calculation module is used to calculate the in-plane crack initiation angle of isotropic rocks by substituting the fitted type I and type III geometric shape factors obtained in step S3 into the expression of the in-plane crack initiation angle obtained in step S6, based on the received data.

Claims

1. A method for calculating the mixed fracture initiation mode and in-plane fracture initiation angle of isotropic rocks of type I / III, characterized in that, Includes the following steps: S1. Obtain the material property parameters of the target isotropic rock, and construct the geometric model of the corresponding edge-grooved disk bending specimen according to the preset parameters; S2. Use software to perform numerical simulation of the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles; S3. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and combined with preset parameters, obtain the corresponding Type I and Type III geometric shape factors, and then perform numerical fitting on them to obtain the fitted Type I and Type III geometric shape factors. S4. By performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, expressions for the stress intensity factors at the crack tip of Type I and Type III cracks in a new coordinate system characterized by Type I and Type III geometric shape factors and preset parameters are constructed. S5. Based on the expressions for the stress intensity factors at the tips of Type I and Type III cracks obtained in step S4, within the set range, calculate the maximum values ​​of the stress intensity factors at the tips of Type I and Type III cracks respectively, and compare them with the fracture toughness of Type I and Type III of isotropic rocks to obtain the calculation results of the mixed initiation mode of Type I / III cracks in isotropic rocks. S6. Based on the three-dimensional maximum tangential stress criterion, and utilizing the proportional relationship between stress intensity factor and geometric shape factor, construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors; S7. Substitute the fitted Type I and Type III geometric shape factors obtained in step S3 into the expression for the in-plane initiation angle obtained in S6 to calculate the in-plane initiation angle of the isotropic rock with mixed initiation of Type I / III cracks.

2. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 1, characterized in that, The preset parameters in step S1 include: specimen diameter, specimen thickness, crack length, half-spacing between lower supports, loading angle between the direction of applied load and the crack surface of the model, and an applied load from above the specimen along the axial direction of the specimen. Singular elements are configured at the crack tip of the geometric model of the edge-grooved disk bending specimen.

3. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 2, characterized in that, Step S2 specifically involves: calculating the stress intensity factor of the model using the J-integral method, and changing the loading angle by rotating the geometric model to obtain the Type I and Type III stress intensity factors under different loading angles.

4. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 3, characterized in that, Step S3 includes the following steps: A1. Based on the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, for the geometric model of the edge-grooved disk bending specimen, the discrete values ​​of the corresponding Type I and Type III geometric shape factors are calculated using the following formula. in, For loading angle Discrete values ​​of the Type I geometry factor under the given conditions. The diameter of the sample is 1. For the sample thickness, In the initial coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The length of the crack. For loading angle Discrete numerical values ​​of the Type III geometry factor under the following conditions In the initial coordinate system and with the loading angle being... Type III stress intensity factor at that time; A2. Based on the discrete values ​​of the Type I and Type III geometric shape factors obtained in step A1, the following formula is used to numerically fit them, resulting in the fitted expressions for the Type I and Type III geometric shape factors in relation to the loading angle. in, The fitted loading angle Type I geometry factor below, The zeroth fitted parameter, The first fitted parameter is... The second fitting parameter, The third fitting parameter, The fourth fitting parameter, The fitted loading angle Type III geometry factor, For the fifth fitting parameter, For the sixth fitting parameter, For the seventh fitting parameter, For the eighth fitting parameter, This is the ninth fitting parameter.

5. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 4, characterized in that, Step S4 includes the following steps: B1. For the geometric model of the edge-grooved disk bending specimen, the stress intensity factor at the crack tip in the initial coordinate system is calculated using the following formula: In the formula, For loading angle Below, the Type I stress intensity factor at the crack tip in the initial coordinate system. For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For loading angle Below, the Type III stress intensity factor at the crack tip in the initial coordinate system. The fitted loading angle Type III geometry factor; B2. For the geometric model of the edge-grooved disk bending specimen, and combining the stress intensity factor at the crack tip in the initial coordinate system obtained in step B1, calculate the stress field at the crack tip, as shown in the following equation: In the formula, In the initial coordinate system Stress components in the direction, Let be the Type I stress intensity factor at the crack tip in the initial coordinate system. This represents the radial distance from the crack tip to any point near the tip. The angle of rotation is counterclockwise around the crack tip. In the initial coordinate system Stress components in the direction, In the initial coordinate system - In-plane stress components In the initial coordinate system - In-plane stress components This represents the Type III stress intensity factor at the crack tip in the initial coordinate system. In the initial coordinate system - In-plane stress components; B3. By rotating the crack tip Angle generates a new coordinate system To obtain the new coordinate system corner and : In the formula, For the new coordinate system Stress components in the direction, For coordinate transformation angle, For the new coordinate system In-plane stress components; B4. Based on the definition of the local stress intensity factor, and combined with the new coordinate system obtained in step B3... corner and Substituting the expression for the stress intensity factor at the crack tip in the initial coordinate system, the expressions for the stress intensity factors at the crack tip in the new coordinate system, characterized by the type I and type III geometry factors and preset parameters, are derived as follows: In the formula, In the new coordinate system and with the loading angle being... Type I stress intensity factor at that time For the applied axial load, The spacing between the two lower supports is half the distance between them. The diameter of the sample is 1. For the sample thickness, The length of the crack. The fitted loading angle Type I geometry factor below, For coordinate transformation angle, In the new coordinate system and with the loading angle being... Type III stress intensity factor at that time The fitted loading angle Type III geometry factor.

6. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 5, characterized in that, The calculation results of the isotropic rock type I / III mixed fracturing mode described in step S5 are expressed by the following formula: In the formula, represents the maximum value of the Type III stress intensity factor; It has a type III fracture toughness. This represents the maximum value of the Type I stress intensity factor; It is a type I fracture toughness.

7. The method for determining the mixed initiation mode and in-plane initiation angle of isotropic rocks of type I / III according to claim 6, characterized in that, Step S6 includes the following steps: D1. Establish a local cylindrical coordinate system with the crack tip as the origin, and derive the expression for the tangential normal stress as follows: In the formula, For tangential and normal stress, It is a type I stress intensity factor. The polar angle is calculated from the original crack plane. It is a type III stress intensity factor. The expression for in-plane shear stress is as follows: In the formula, This refers to in-plane shear stress; D2. According to the three-dimensional maximum tangential stress criterion, assuming the crack initiates along the direction of the maximum tangential stress, then the in-plane shear stress in that direction is equal to 0, and the in-plane crack initiation angle is... The governing equations are as follows: In the formula, The sign of the partial derivative. For tangential stress, To Find the partial derivative. This refers to in-plane shear stress; D3. Based on the expression for in-plane shear stress obtained in step D1 and the governing equation for in-plane crack initiation angle obtained in step D2, the following equation is derived: In the formula, For in-plane cracking; Solving the above equation by variable substitution yields the in-plane crack initiation angle. The expression is as follows: because ,and Therefore, the in-plane crack initiation angle, characterized by type I and type III geometry factors, is derived. The expression is as follows: 。 8. A calculation system for mixed fracture initiation modes and in-plane fracture initiation angles of isotropic rocks of type I / III, characterized in that, The calculation system for the mixed type I / III crack initiation mode and in-plane crack initiation angle of isotropic rocks includes: a geometric model construction module, a type I and type III stress intensity factor acquisition module, a type I and type III geometric shape factor fitting module, a type I and type III crack tip stress intensity factor expression construction module, a type I / III mixed crack initiation mode calculation module, an in-plane crack initiation angle expression construction module, and an in-plane crack initiation angle calculation module; the geometric model construction module, the type I and type III stress intensity factor acquisition module, the type I and type III geometric shape factor fitting module, the type I and type III crack tip stress intensity factor expression construction module, the type I / III mixed crack initiation mode calculation module, the in-plane crack initiation angle expression construction module, and the in-plane crack initiation angle calculation module are connected in series; The geometric model construction module is used to obtain the material property parameters of the target isotropic rock, construct the corresponding geometric model of the edge-grooved disk bending specimen according to the preset parameters, and upload the data to the Type I and Type III stress intensity factor acquisition module. The Type I and Type III stress intensity factor acquisition module is used to perform numerical simulation of the geometric model using software based on the received data, obtain the Type I and Type III stress intensity factors under different loading angles, and upload the data to the Type I and Type III geometric shape factor fitting module. The Type I and Type III geometry factor fitting module is used to obtain the corresponding Type I and Type III geometry factors based on the received data, the Type I and Type III stress intensity factors obtained in step S2 under different loading angles, and preset parameters. Then, it performs numerical fitting to obtain the fitted Type I and Type III geometry factors, and uploads the data to the expression construction module for the Type I and Type III crack tip stress intensity factors. The expression construction module for the stress intensity factor at the crack tip of Type I and Type III cracks is used to construct expressions for the stress intensity factor at the crack tip of Type I and Type III cracks in a new coordinate system characterized by the geometric shape factor of Type I and Type III and preset parameters, based on the received data, by performing coordinate rotation transformation at the crack tip and combining the multi-level mapping relationship between stress components and stress intensity factors, and then upload the data to the calculation module for the mixed crack initiation mode of Type I / III. The calculation module for the mixed initiation mode of type I / III cracks is used to calculate the maximum value of the stress intensity factor at the tip of type I and type III cracks within a set range based on the received data and the expressions for the stress intensity factor at the tip of type I and type III cracks obtained in step S4. The maximum value is then compared with the fracture toughness of type I and type III cracks in isotropic rocks to obtain the calculation results of the mixed initiation mode of type I / III cracks in isotropic rocks. The data is then uploaded to the expression construction module for the in-plane initiation angle. The expression construction module for the in-plane crack initiation angle is used to construct an expression for the in-plane crack initiation angle characterized by type I and type III geometric shape factors based on the received data, according to the three-dimensional maximum tangential stress criterion and the proportional relationship between stress intensity factor and geometric shape factor, and upload the data to the in-plane crack initiation angle calculation module. The in-plane crack initiation angle calculation module is used to calculate the in-plane crack initiation angle of isotropic rocks by substituting the fitted type I and type III geometric shape factors obtained in step S3 into the expression of the in-plane crack initiation angle obtained in step S6, based on the received data.

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