CN-121997611-A - Isotropic rock I/III type mixed cracking mode and in-plane cracking angle calculation method and system

CN121997611ACN 121997611 ACN121997611 ACN 121997611ACN-121997611-A

Abstract

The invention discloses a calculation method and a system of an isotropic rock I/III type mixed cracking mode and an in-plane cracking angle, comprising the steps of obtaining material attribute parameters to construct a geometric model; the method comprises the steps of obtaining stress intensity factors, obtaining fitted I/III type geometric form factors, constructing an expression of crack tip stress intensity factors under a new coordinate system, obtaining the maximum value of the I/III type crack tip stress intensity factors, comparing the maximum value with I/III type fracture toughness to obtain an isotropic rock I/III type mixed cracking mode, constructing an expression of an in-plane cracking angle, and calculating to obtain the in-plane cracking angle of the isotropic rock I/III type mixed cracking. The method can calculate the isotropic rock I/III type mixed cracking mode and the in-plane cracking angle more accurately, and can determine the in-plane cracking angle only according to the geometric form factor and the fixed parameters under the condition that the crack tip stress intensity factor is not required to be acquired.

Inventors

QIAO WENZHENG
YAN XIAOYAN
Hou wencui
JIAO JINFENG

Assignees

吕梁学院

Dates

Publication Date: 20260508
Application Date: 20260207

Claims (8)

1. The calculation method of the isotropic rock I/III type mixed cracking mode and the in-plane cracking angle is characterized by comprising the following steps: s1, acquiring material attribute parameters of a target isotropic rock, and constructing a geometric model of a corresponding edge slotting disk bending sample according to preset parameters; s2, performing numerical simulation on the geometric model by using software to obtain I-type and III-type stress intensity factors under different loading angles; S3, according to the I-type stress intensity factors and the III-type stress intensity factors under different loading angles obtained in the step S2, combining preset parameters to obtain corresponding I-type geometric form factors and III-type geometric form factors, and performing numerical fitting on the corresponding I-type geometric form factors and III-type geometric form factors to obtain fitted I-type geometric form factors and III-type geometric form factors; S4, constructing expressions of I-type and III-type crack tip stress intensity factors under a new coordinate system characterized by I-type and III-type geometric form factors and preset parameters by carrying out coordinate rotation transformation on the crack tip and combining the multistage mapping relation of stress components and the stress intensity factors; S5, respectively solving the maximum value of the tip stress intensity factors of the I-type and III-type cracks in a set range according to the expressions of the tip stress intensity factors of the I-type and III-type cracks obtained in the step S4, and comparing the maximum value with the I-type and III-type fracture toughness of the isotropic rock to obtain a calculation result of the I/III-type mixed cracking mode of the isotropic rock; s6, constructing an expression of an in-plane cracking angle represented by the type I geometric form factors and the type III geometric form factors according to a three-dimensional maximum tangential stress rule by utilizing a proportional relation between a stress intensity factor and the geometric form factors; S7, substituting the fitted I-type and III-type geometric form factors obtained in the step S3 into the expression of the in-plane cracking angle obtained in the step S6, and calculating to obtain the in-plane cracking angle of the isotropic rock I/III-type mixed cracking.
2. The method according to claim 1, wherein the predetermined parameters in step S1 include a specimen diameter, a specimen thickness, a crack length, a half-pitch between lower supports, a loading angle between a direction of a loading applied and a crack face of the model, and a loading load applied from above the specimen in an axial direction of the specimen, and singular units are arranged at crack tips of the geometric model of the edge grooved disk bending specimen.
3. The method for determining the isotropic rock I/III type mixed cracking mode and the in-plane cracking angle according to claim 2, wherein the step S2 is specifically to calculate stress intensity factors of a model by adopting a J integration method, and change loading angles by performing angle rotation on a geometric model, so as to obtain I type and III type stress intensity factors under different loading angles.
4. The method for determining an isotropic rock type I/III hybrid initiation mode and an in-plane initiation angle according to claim 3, wherein the step S3 comprises the steps of: A1. According to the I-type and III-type stress intensity factors under different loading angles obtained in the step S2, calculating the discrete values of the corresponding I-type and III-type geometric form factors by using the following formula aiming at the geometric model of the edge slotting disk bending sample, Wherein, the For loading angle Discrete values of the type I geometry factor below, In order to obtain the diameter of the sample, For the thickness of the sample, Is under an initial coordinate system and the loading angle is The type I stress intensity factor at the time of the test, In order to apply an axial load to the bearing, For half the distance between the two lower supports, For the length of the crack to be a crack, For loading angle Discrete values for the type III geometry factor below, Is under an initial coordinate system and the loading angle is Type III stress intensity factor at that time; A2. based on the discrete values of the type I and type III geometric factors obtained in the step A1, carrying out numerical fitting on the discrete values by adopting the following formula to obtain the fitted type I and type III geometric factors and the expression of the loading angle, Wherein, the For the fitted loading angle The lower type I geometry factor is that of, For the zeroth fitting parameter, As a first of the parameters of the fit, As a second fit parameter, As a third fitting parameter, For the fourth fitting parameter, a second fitting parameter, For the fitted loading angle The lower type III geometry factor is that of, Is a fifth fitting parameter, Is a sixth fitting parameter, For a seventh fitting parameter, Is an eighth fitting parameter, And a ninth fitting parameter.
5. The method for determining the isotropic rock type I/III hybrid initiation mode and the in-plane initiation angle according to claim 4, wherein the step S4 comprises the steps of: B1. for the geometric model of the edge slotting disk bending test piece, the stress intensity factor of the crack tip under the initial coordinate system is calculated by adopting the following steps: in the formula, For loading angle And the I-type stress intensity factor of the crack tip under the initial coordinate system, In order to apply an axial load to the bearing, For half the distance between the two lower supports, In order to obtain the diameter of the sample, For the thickness of the sample, For the length of the crack to be a crack, For the fitted loading angle The lower type I geometry factor is that of, For loading angle And III type stress intensity factors of crack tips under an initial coordinate system, For the fitted loading angle The lower type III geometry factor; B2. And (2) calculating a crack tip stress field according to a geometric model of the edge slotting disk bending sample and combining the stress intensity factors of the crack tips under the initial coordinate system obtained in the step (B1), wherein the stress fields are shown in the following formula: in the formula, In the initial coordinate system The stress component in the direction of the force, Is the I-type stress intensity factor of the crack tip under the initial coordinate system, For the radial distance of the crack tip to any point near the tip, To make a counterclockwise rotation angle around the crack tip, In the initial coordinate system The stress component in the direction of the force, In the initial coordinate system - The stress component in the plane of the wafer, In the initial coordinate system - The stress component in the plane of the wafer, Is a type III stress intensity factor of the crack tip in the initial coordinate system, In the initial coordinate system - Stress components in the plane; B3. By rotating at the crack tip Angle generating new coordinate system Obtaining a new coordinate system At the corners And (3) with : In the formula, In a new coordinate system The stress component in the direction of the force, For the purpose of the coordinate transformation angle, In a new coordinate system Stress components in the plane; B4. Combining the definition of the local stress intensity factors with the new coordinate system obtained in the step B3 At the corners And (3) with Substituting the expression of the stress intensity factor of the crack tip under the initial coordinate system, and deriving the expression of the stress intensity factors of the crack tip of the type I and the type III under the new coordinate system characterized by the geometric form factors of the type I and the type III and preset parameters, wherein the expression of the stress intensity factor of the crack tip of the type I and the type III under the new coordinate system is as follows: in the formula, Under a new coordinate system and loading angle The type I stress intensity factor at the time of the test, In order to apply an axial load to the bearing, For half the distance between the two lower supports, In order to obtain the diameter of the sample, For the thickness of the sample, For the length of the crack to be a crack, For the fitted loading angle The lower type I geometry factor is that of, For the purpose of the coordinate transformation angle, Under a new coordinate system and loading angle The type III stress intensity factor at the time, For the fitted loading angle The following type III geometry factor.
6. The method for determining an isotropic rock type I/III hybrid initiation pattern and an in-plane initiation angle according to claim 5, wherein the calculation result of the isotropic rock type I/III hybrid initiation pattern in step S5 is represented by the following formula: wherein, the stress intensity factor is the maximum value of the III type stress intensity factor; is the fracture toughness of the III type, Is the maximum value of the I-type stress intensity factor; Is type I fracture toughness.
7. The method for determining the isotropic rock type I/III hybrid initiation mode and the in-plane initiation angle according to claim 6, wherein the step S6 comprises the steps of: D1. the local cylindrical coordinate system is established by taking the crack tip as an origin, and the tangential normal stress is obtained by the following expression: in the formula, In the case of tangential normal stresses, Is a stress intensity factor of the type I, The polar angle calculated for the original crack plane, Is a type III stress intensity factor, The in-plane shear stress expression is as follows: in the formula, Is in-plane shear stress; D2. according to the three-dimensional maximum tangential stress criterion, assuming that the crack is initiated in the direction of the maximum tangential stress, the in-plane shear stress in this direction is equal to 0, and the in-plane initiation angle The control equation of (2) is as follows: in the formula, In order to make the symbol of the partial guide, In the event of a tangential stress, To pair(s) The deviation is calculated and guided, and the deviation is calculated, Is in-plane shear stress; D3. according to the expression of the in-plane shear stress obtained in the step D1 and the control equation of the in-plane crack initiation angle obtained in the step D2, the following formula is obtained: in the formula, The crack angle is in-plane; Solving the variable replacement to obtain an in-plane cracking angle The expression of (2) is as follows: Due to And (2) and Thus, the in-plane angle of attack characterized by type I and type III geometry factors is derived The expression of (2) is as follows: 。
8. The computing system for the isotropic rock I/III type mixed cracking mode and the in-plane cracking angle is characterized by comprising a geometric model building module, an I type and III type stress intensity factor obtaining module, an I type and III type geometric form factor fitting module, an I type and III type crack tip stress intensity factor expression building module, an I/III type mixed cracking mode computing module, an in-plane cracking angle expression building module and an in-plane cracking angle computing module, wherein the geometric model building module, the I type and III type stress intensity factor obtaining module, the I type and III type geometric form factor fitting module, the I type and III type crack tip stress intensity factor expression building module, the I/III type mixed cracking mode computing module, the in-plane cracking angle expression building module and the in-plane cracking angle computing module are sequentially connected in series; The geometric model construction module is used for acquiring material attribute parameters of the target isotropic rock, constructing a geometric model of a corresponding edge slotting disc bending sample according to preset parameters, and uploading data to the I-type and III-type stress intensity factor acquisition module; The I-type and III-type stress intensity factor acquisition module is used for carrying out numerical simulation on the geometric model by utilizing software according to the received data, acquiring I-type and III-type stress intensity factors under different loading angles, and uploading the data to the I-type and III-type geometric shape factor fitting module; The I-type and III-type geometric form factor fitting module is used for obtaining corresponding I-type and III-type geometric form factors according to the received data and the I-type and III-type stress intensity factors under different loading angles obtained in the step S2 by combining preset parameters, performing numerical fitting on the I-type and III-type geometric form factors to obtain fitted I-type and III-type geometric form factors, and uploading the data to the expression construction module of the I-type and III-type crack tip stress intensity factors; The expression construction module of the I-type and III-type crack tip stress intensity factors is used for constructing the expressions of the I-type and III-type crack tip stress intensity factors under a new coordinate system characterized by the I-type and III-type geometric form factors and preset parameters by carrying out coordinate rotation transformation on the crack tip according to the received data and combining the multistage mapping relation of the stress components and the stress intensity factors, and uploading the data to the calculation module of the I/III-type mixed cracking mode; The calculation module of the I/III type mixed cracking mode is used for respectively solving the maximum value of the I type and III type crack tip stress intensity factors in a set range according to the received data and the expressions of the I type and III type crack tip stress intensity factors obtained in the step S4, comparing the maximum value with the I type and III type fracture toughness of isotropic rock to obtain the calculation result of the isotropic rock I/III type mixed cracking mode, and uploading the data to the expression construction module of the in-plane cracking angle; The in-plane cracking angle expression construction module is used for constructing an in-plane cracking angle expression represented by the I type geometric form factor and the III type geometric form factor according to the received data and the three-dimensional maximum tangential stress criterion and the proportional relation between the stress intensity factor and the geometric form factor, and uploading the data to the in-plane cracking angle calculation module; The in-plane cracking angle calculation module is used for substituting the fitted I-type and III-type geometric form factors obtained in the step S3 into the expression of the in-plane cracking angle obtained in the step S6 according to the received data, and calculating to obtain the in-plane cracking angle of the isotropic rock I/III-type mixed cracking.

Description

Isotropic rock I/III type mixed cracking mode and in-plane cracking angle calculation method and system Technical Field The invention relates to the field of civil engineering, in particular to an isotropic rock I/III type mixed cracking mode and an in-plane cracking angle calculation method. Background In engineering scenes such as ground rock pavement, rock slope and the like, the destabilization and the expansion of cracks in isotropic rock are one of important reasons for inducing engineering disasters, and the essential appearance is that the I/III type mixed mode cracks in the rock start from cracking, undergo evolution and aggregation, and finally pass through. The initiation mode of the crack determines to a large extent its subsequent propagation path, whereas the initiation angle directly influences the final failure mode of the rock mass. Therefore, the method accurately predicts the cracking mode and the cracking angle of the I/III type rock mass cracks, and has important guiding significance for engineering safety evaluation and support scheme design. Existing methods for determining crack initiation modes and initiation angles mostly use end b (Edge-Notched Disc Bend) samples to implement mixed mode loading, or use Digital Image Correlation (DIC) techniques to observe crack initiation morphology. However, the initiation mode determination based on the ENDB sample generally requires microscopic scanning of the fracture after the test and reverse derivation of the initiation mode based thereon, while the digital image correlation technique requires microscopic scale analysis of the acquired displacement field to extract and identify the mode features of the crack initiation stage, which is difficult to implement. Other scholars have proposed methods of calculating stress intensity factors for type I/III cracks, but many have been less common for fracture toughness, and for determination of the initiation mode and in-plane initiation angle of an ENDB sample. Disclosure of Invention The invention aims to provide a more accurate calculation method for an isotropic rock I/III type mixed cracking mode and an in-plane cracking angle. The invention provides a calculation method of an isotropic rock I/III type mixed cracking mode and an in-plane cracking angle, which comprises the following steps: s1, acquiring material attribute parameters of a target isotropic rock, and constructing a geometric model of a corresponding edge slotting disk bending sample according to preset parameters; s2, performing numerical simulation on the geometric model by using software to obtain I-type and III-type stress intensity factors under different loading angles; S3, according to the I-type stress intensity factors and the III-type stress intensity factors under different loading angles obtained in the step S2, combining preset parameters to obtain corresponding I-type geometric form factors and III-type geometric form factors, and performing numerical fitting on the corresponding I-type geometric form factors and III-type geometric form factors to obtain fitted I-type geometric form factors and III-type geometric form factors; S4, constructing expressions of I-type and III-type crack tip stress intensity factors under a new coordinate system characterized by I-type and III-type geometric form factors and preset parameters by carrying out coordinate rotation transformation on the crack tip and combining the multistage mapping relation of stress components and the stress intensity factors; S5, respectively solving the maximum value of the tip stress intensity factors of the I-type and III-type cracks in a set range according to the expressions of the tip stress intensity factors of the I-type and III-type cracks obtained in the step S4, and comparing the maximum value with the I-type and III-type fracture toughness of the isotropic rock to obtain a calculation result of the I/III-type mixed cracking mode of the isotropic rock; s6, constructing an expression of an in-plane cracking angle represented by the type I geometric form factors and the type III geometric form factors according to a three-dimensional maximum tangential stress rule by utilizing a proportional relation between a stress intensity factor and the geometric form factors; S7, substituting the fitted I-type and III-type geometric form factors obtained in the step S3 into the expression of the in-plane cracking angle obtained in the step S6, and calculating to obtain the in-plane cracking angle of the isotropic rock I/III-type mixed cracking. The preset parameters in the step S1 comprise the diameter of the sample, the thickness of the sample, the crack length, the half distance between lower supports, the loading angle between the direction of the applied load and the crack surface of the model, and the loading load applied from the upper part of the sample along the axial direction of the sample, and singular units are configured at the crack tips of the