CN117272686A - Method for automatically tracking rock crack tip based on DIC technology - Google Patents

Method for automatically tracking rock crack tip based on DIC technology Download PDF

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CN117272686A
CN117272686A CN202311540933.5A CN202311540933A CN117272686A CN 117272686 A CN117272686 A CN 117272686A CN 202311540933 A CN202311540933 A CN 202311540933A CN 117272686 A CN117272686 A CN 117272686A
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rock
crack
preset
crack tip
objective function
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沈沐傲
杜瑞雪
张鸣原
李英骏
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China University of Mining and Technology Beijing CUMTB
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/70Determining position or orientation of objects or cameras
    • G06T7/73Determining position or orientation of objects or cameras using feature-based methods
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14Force analysis or force optimisation, e.g. static or dynamic forces
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/30Subject of image; Context of image processing
    • G06T2207/30108Industrial image inspection
    • G06T2207/30132Masonry; Concrete

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Abstract

The invention discloses a method for automatically tracking rock crack tips based on a DIC technology, and belongs to the technical field of rock engineering. The method comprises the following steps: manufacturing a rock test piece with prefabricated cracks; carrying out speckle experiments on the rock test piece to obtain speckle images of crack propagation; processing the speckle image to obtain displacement field data of the rock test piece in the breaking process; a plurality of crack tips are preset initially, coordinates and displacement parameters of the preset crack tips are extracted from displacement field data, and an objective function value of each preset crack tip is calculated by utilizing a formula; taking the preset crack tip with the smallest objective function value as a new center, resetting a plurality of crack tips, and calculating to obtain a new preset crack tip with the smallest objective function value; and (3) carrying out loop iteration until a final crack tip is obtained, wherein the obtained final crack tip is more approximate to the actual crack tip through verification, and the calculated rock stress intensity factor is more reliable for evaluating the stability of engineering.

Description

Method for automatically tracking rock crack tip based on DIC technology
Technical Field
The invention relates to the technical field of rock engineering, in particular to a method for automatically tracking the tip of a rock crack based on the DIC technology.
Background
Rock fracture is widely used in the field of construction engineering, tunnel engineering, mining engineering and other practical engineering, and because of the sudden occurrence, the rock fracture has a great influence on engineering safety.
The stress intensity factor is a physical quantity used for representing the intensity of the elastic stress field of the crack tip in rock fracture, and plays an important role in evaluating engineering safety and stability. Therefore, in practical application, the engineering safety and stability can be evaluated by using the stress intensity factors.
Currently, three main methods for calculating stress intensity factors of rock exist. One is an empirical formula, i.e., under fixed geometry and loading conditions, substituting measured parameters into the formula (such parameters include sample geometry and peak load). The critical stress intensity factor of the rock is mainly calculated by the method, and is considered as a fixed parameter of the material, and the difficulty of the rock in achieving fracture is described (references can be made to KURUPPU M D, OBARA Y, AYATOLLAHI M R, et al 2014, ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular bond specification Rock Mechanics and Rock Engineering [ J ], 47:267-274 ]. Since the critical stress intensity factor determined by the method only describes the state of the rock when cracks are initiated, and the breaking of the rock is finished after the breaking, the critical stress intensity factor actually comprises three processes of crack initiation, propagation and crack stopping. Therefore, the critical stress intensity factor obtained by the method only describes the crack growth difficulty degree when cracks are initiated, and the difficulty degree when the cracks are expanded is not related, so that the critical stress intensity factor cannot be used for engineering evaluation. In the second method for determining the stress intensity factor, strain changes of the sample during crack propagation are determined mainly by attaching strain gages. Since stress is a linear relationship with strain during the online elastic phase, the stress intensity factor can be determined from the change in strain. However, this method requires the attachment of strain gages (see, e.g., liqing, lesion, xu Wenlong, et al, comparative test study of dynamic stress intensity factor type I for different distance strain gages [ J ]. Coal journal, 2018,43 (12): 3348-3355.), and is complicated and expensive. The third is a non-contact measurement method, mainly represented by DIC (Digital Image Correlation, digital image correlation method), which measures the strain field of the crack tip from an image of the sample crack propagation process (see Pan Bing, xie Huimin. Full field strain measurement based on displacement field partial least squares fitting in digital image correlation [ J ]. Optical journal, 2007 (11): 1980-1986.) to calculate stress intensity factors. Obviously, the method can be calculated by taking a picture of the fracture process, and is simple and convenient. However, this method requires first determining the location of the crack tip. Currently, the location of crack tips is generally determined by the naked eye of a researcher (see, e.g., treeing, ma Shengli, pan Yishan, etc. digital speckle correlation methods determine the stress intensity factor [ J ] of rock type I, proc. Of rock mechanics and engineering, 2012,31 (12): 2501-2507). Because the crack tip is tiny when the crack tip is initiated in the rock breaking process, the accurate position of the crack tip can not be obtained due to the limitation of the image resolution ratio in the visual recognition process, so that errors can be generated in the rock breaking process by utilizing the image recognition technology, further errors in calculation of stress intensity factors are caused, and the engineering safety and stability can not be reliably evaluated by utilizing the stress intensity factors.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides the following technical scheme.
The first aspect of the invention provides a method for automatically tracking rock crack tips based on DIC technology, comprising the following steps:
manufacturing a rock test piece with prefabricated cracks;
carrying out speckle experiments on the rock test piece to obtain speckle images of crack propagation;
processing the speckle image to obtain displacement field data of the rock test piece in the breaking process;
a plurality of crack tips are preset initially, coordinates and displacement parameters of the preset crack tips are extracted from the displacement field data, and the objective function value of each preset crack tip is calculated by using the following formula
Wherein,for the objective function value->For the displacement component matrix>Is a coefficient matrix->For the matrix to be solved +.>Is the abscissa of the preset crack tip +.>Is the ordinate of the preset crack tip; matrix->Sum matrix->Obtaining through the displacement field data;
taking the preset crack tip with the smallest objective function value as a new center, resetting a plurality of crack tips, and calculating to obtain a new preset crack tip with the smallest objective function value; and (3) performing loop iteration until the difference between the minimum objective function value obtained by the next calculation and the minimum objective function value obtained by the last calculation does not exceed a preset value, and taking the preset crack tip corresponding to the minimum objective function value obtained by the last calculation as a final crack tip.
Preferably, extracting from the displacement field dataData points, resulting in a matrix->Matrix->Sum matrix->
First, theDisplacement component of rigid translational displacement coordinate axis in data point in transverse axis directionFirst->Displacement component of rigid translational displacement coordinate axis in longitudinal direction in data pointWherein (1)>For the number of data points extracted from the displacement field data, each data point comprises coordinates and displacements, +.>Series developed for Williams equation, +.>Is->Displacement component in the horizontal axis direction of the rigid body translational displacement coordinate axis in the data point, +.>Is->Displacement component in the longitudinal axis direction of the rigid body translational displacement coordinate axis in the data point, +.>Is->Abscissa in data points, +.>Is->Ordinate in data point, +.>Is the component of the rigid translational displacement coordinate axis horizontal axis direction of the rock test piece, +.>For the component of the rigid translational displacement coordinate axis longitudinal axis direction of the rock specimen,/->For the rigid body rotation component of the rock specimen, +.>For shear modulus of rock specimen +.>,/>Poisson's ratio->And->Respectively, with a preset crack tip (+)>) As polar parameter of origin, +.>And->The coefficients of the series term developed for the Williams equation.
Preferably, the method comprises the steps of,>2n+3。
preferably, the method comprises the steps of,=10,/>>23。
preferably, prior to the speckle test, speckle is prepared on rock test pieces as follows: firstly, spraying a primer on a rock test piece, and then preparing scattered spots on the primer; wherein the size of the speckles is required to be 5-10 pixels in diameter in the speckle image, and the speckles and the primer are prepared with a non-reflective color-difference coating.
Preferably, the performing a speckle experiment on the rock specimen comprises: and carrying out speckle experiments on the rock test piece by using an ultrafast digital speckle system based on pulse laser.
Preferably, the initial preset plurality of crack tips includes: taking the tip of the pre-crack of the rock test piece as an initial center, and arranging a plurality of preset crack tips within a preset range of the initial center at a set grid interval.
Preferably, the preset value is not more than 0.05 in the case that the difference between the minimum objective function value calculated at the next time and the minimum objective function value calculated at the last time is not more than a preset value.
According to a second aspect of the invention, a method for obtaining a rock stress intensity factor is provided, the rock stress intensity factor is obtained through calculation by using a Williams polynomial according to displacement field data of a rock crack tip and a rock test piece in a breaking process, wherein the rock crack tip and the displacement field data of the rock test piece in the breaking process are obtained through the method for automatically tracking the rock crack tip based on the DIC technology according to the first aspect.
The beneficial effects of the invention are as follows: according to the method, a DIC technology is combined with a Williams equation, a method for automatically tracking crack tips is provided, a target crack tip is determined by calculating the minimum value of an objective function in a plurality of preset crack tips in each iteration, the target crack tip determined in the last iteration is used as the center of the plurality of preset crack tips in the next iteration to set the crack tip, and multiple iterations are carried out until the distance between the target crack tips obtained in the previous iteration and the subsequent iteration does not exceed the preset value. The final crack tip obtained by this method was verified to be more similar to the actual crack tip. And the crack tip and the displacement field data of the rock test piece in the breaking process, which are obtained by the method, are more reliable in evaluating the stability of engineering by using the rock stress intensity factor obtained by Williams polynomial calculation.
Drawings
FIG. 1 is a schematic flow chart of a method for automatically tracking rock crack tips based on DIC technology according to the present invention;
FIG. 2 is a schematic diagram showing the variation trend of rock crack tip coordinates under different expansion stages calculated by the method provided by the invention;
FIG. 3 is a schematic diagram showing the variation trend of the stress intensity factor under different expansion stages calculated by the method provided by the invention;
FIG. 4 is a schematic diagram of the variation trend of rock crack tip coordinates under different expansion stages calculated by using a nonlinear least square method;
fig. 5 is a schematic diagram of a variation trend of stress intensity factors under different expansion stages calculated by using a nonlinear least square method.
Detailed Description
In order to better understand the above technical solutions, the following detailed description will refer to the accompanying drawings and specific embodiments.
As shown in fig. 1, an embodiment of the present invention provides a method for automatically tracking a rock crack tip based on DIC technology, comprising: s101, manufacturing a rock test piece with a prefabricated crack; s102, carrying out a speckle experiment on the rock test piece to obtain a speckle image of crack propagation; s103, processing the speckle image to obtain displacement field data of the rock test piece in the fracture process; s104, a plurality of crack tips are preset initially, coordinates and displacement parameters of the preset crack tips are extracted from the displacement field data, and the objective function value of each preset crack tip is calculated by using the following formula
Wherein,for the objective function value->For the displacement component matrix>Is a coefficient matrix->For the matrix to be solved +.>Is the abscissa of the preset crack tip +.>Is the ordinate of the preset crack tip; matrix->Sum matrix->And obtaining through the displacement field data.
Taking the preset crack tip with the smallest objective function value as a new center, resetting a plurality of crack tips, and calculating to obtain a new preset crack tip with the smallest objective function value; and (3) performing loop iteration until the difference between the minimum objective function value obtained by the next calculation and the minimum objective function value obtained by the last calculation does not exceed a preset value, and taking the preset crack tip corresponding to the minimum objective function value obtained by the last calculation as a final crack tip.
Wherein, in step S101, before the speckle test, speckle is prepared on a rock specimen according to the following method: firstly, spraying a primer on a rock test piece, and then preparing scattered spots on the primer; wherein the size of the speckles is required to be 5-10 pixels in diameter in the speckle image, and the speckles and the primer are prepared with a non-reflective color-difference coating. Wherein, the primer can be white primer, and the scattered spots can be prepared by using black paint.
In step S102, the performing a speckle experiment on the rock specimen includes: the rock test piece was subjected to a speckle experiment using an ultrafast digital speckle system based on pulsed laser (see patent CN 113251941B). In the system, a light source is pulse laser, an ultrafast camera is used for shooting digital speckle images, the frame rate of the ultrafast camera is consistent with the repetition frequency of laser output by the pulse laser, and the exposure time of the system is consistent with the half-width of picosecond order of laser output by the pulse laser. Not only can the scattered spots of the rock test piece be clearly shot, but also the time resolution of the strain field of the rock test piece can be improved to the picosecond level, more accurate displacement data can be obtained, and further more accurate crack tips can be obtained by utilizing the displacement data.
In step S103, the speckle image may be processed with VIC-2D software as follows: the image of the rock test piece before the experiment (loaded) is imported into software to serve as an initial reference image; importing a series of shot speckle images of crack propagation into software, and inputting the longest boundary dimension of a rock test piece shot in the images into the software; setting the calculated displacement field range and starting calculation to obtain displacement field data.
In step S104, m data points extracted from the displacement field data are substituted into the following equation:
first, theDisplacement component of rigid translational displacement coordinate axis in data point in transverse axis directionFirst->Displacement component of rigid translational displacement coordinate axis in longitudinal direction in data pointObtaining matrix after deformation>Matrix->Sum matrix->
Wherein,for the number of data points extracted from the displacement field data, each data point comprises coordinates and displacements, +.>Determination of the rock I-II composite crack stress intensity factor [ J ] by digital image correlation, for Williams equation (Williams equation, or Williams expansion, or crack tip region displacement field equation, reference is made to treeing, ma Shengli, pan Yishan)]Geotechnical engineering report 2013,35 (07): 1362-1368 expansion series, ++>Is->Abscissa in data points, +.>Is->Ordinate in data point, +.>Is the component of the rigid translational displacement coordinate axis transverse axis direction of the rock test piece,for the component of the rigid translational displacement coordinate axis longitudinal axis direction of the rock specimen,/->For the rigid body rotation component of the rock specimen, +.>For shear modulus of rock specimen +.>,/>Poisson's ratio->And->Respectively, with a preset crack tip (+)>,/>) As polar parameter of origin, +.>The coefficients of the series term developed for the Williams equation.
In the invention, takeThe value of (2) is greater than the matrix to be solved>The number of unknown quantities in (2)>+3 (wherein, < >>Series developed for the Williams equation), the actual study found +_s>When the numerical value of (2) is more than or equal to 10, the stress intensity factors obtained by solving are all stable. Therefore, in the present invention ∈ ->=10, get->>An integer value of 23.
In a preferred embodiment of the present invention, the initial preset plurality of crack tips may include: taking the tip of the pre-crack of the rock test piece as an initial center, and arranging a plurality of preset crack tips within a preset range of the initial center at a set grid interval. In the specific implementation process, the tip of the pre-crack is taken as an initial center, and preset crack tip points of L rows and P columns are arranged at set grid intervals within a range of 5mm×5mm around the tip.
Calculating to obtain preset crack tips with minimum objective function values for a plurality of crack tips preset for the first time; then, step S105 is executed, in which a plurality of crack tips are preset again with the preset crack tip having the smallest objective function value as a new center, and a new preset crack tip having the smallest objective function value is calculated; in this way, the iteration is circulated until the difference between the minimum objective function value obtained by the next calculation and the minimum objective function value obtained by the last calculation does not exceed the preset value, and the minimum objective function value obtained by the last calculation is corresponding toThe crack tip is preset as the final crack tip. Wherein, the same method as the first time can be adopted for presetting a plurality of crack tips each time, namely, preset crack tip points of L rows and P columns are arranged at a set grid interval within a range of 5mm×5mm around the center point. The same method as the first time may be adopted for calculating the objective function value of each preset crack tip each time. And obtaining a final crack tip through multiple iterations, wherein the final crack tip is used for calculating the stress intensity factor of the rock. Wherein, in the case that the difference between the minimum objective function value obtained by the next calculation and the minimum objective function value obtained by the last calculation does not exceed a preset value, the preset value does not exceed 0.05. That is, for example, the preset crack tip corresponding to the smallest objective function value calculated last time is [ ],/>) The preset crack tip corresponding to the smallest objective function value calculated next time is (++>±0.05,/>(+ -0.05), the crack tip can be preset (/ -0)>,/>) As the final crack tip.
In the invention, in each iteration, a target crack tip is determined by calculating the minimum value of an objective function in a plurality of preset crack tips, and the target crack tip determined in the previous iteration is used as the center of the plurality of preset crack tips in the next iteration to set the crack tip. When the coordinate distance of the target preset crack tip obtained in the previous and later iterations reaches a preset value, the final crack tip is obtained and used for the subsequent calculation of the stress intensity factor. The final crack tip obtained by this method was verified to be more similar to the actual crack tip. And the crack tip and the displacement field data of the rock test piece in the breaking process, which are obtained by the method, are more effective for evaluating the stability of engineering by using the rock stress intensity factor obtained by Williams polynomial calculation.
In practical application, the nonlinear least square method and the method provided by the invention are used for calculating the coordinates and stress intensity factors of the crack tip of the rock (corresponding calculation is carried out under the stage of each Williams equation expansion of 1 to 10) respectively, the obtained results are shown in figures 2-5, wherein the stage expansion term is the stage of the Williams equation expansion, the crack tip coordinates are the coordinates of the crack tip (abscissa x 0 Ordinate y 0 ),Representing a stress intensity factor of type->Representing the type two stress intensity factor. As can be seen from the graph, compared with the nonlinear least square method, the coordinate of the crack tip and the fluctuation of the stress intensity factor obtained by calculation by the method are small, and the data are more stable and accurate.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention. It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.

Claims (9)

1. A method for automatically tracking rock crack tips based on DIC technology, comprising:
manufacturing a rock test piece with prefabricated cracks;
carrying out speckle experiments on the rock test piece to obtain speckle images of crack propagation;
processing the speckle image to obtain displacement field data of the rock test piece in the breaking process;
a plurality of crack tips are preset initially, coordinates and displacement parameters of the preset crack tips are extracted from the displacement field data, and the objective function value of each preset crack tip is calculated by using the following formula
Wherein,for the value of the objective function,hin order to be a matrix of displacement components,Bis a coefficient matrix->For the matrix to be solved +.>Is the abscissa of the preset crack tip +.>Is the ordinate of the preset crack tip; matrix arrayhSum matrixBObtaining through the displacement field data;
taking the preset crack tip with the smallest objective function value as a new center, resetting a plurality of crack tips, and calculating to obtain a new preset crack tip with the smallest objective function value; and (3) performing loop iteration until the difference between the minimum objective function value obtained by the next calculation and the minimum objective function value obtained by the last calculation does not exceed a preset value, and taking the preset crack tip corresponding to the minimum objective function value obtained by the last calculation as a final crack tip.
2. The method of automatically tracking rock crack tips based on DIC technology of claim 1, wherein extracting from the displacement field dataData points, resulting in a matrix->Matrix->Sum matrix->
First, theDisplacement component of rigid translational displacement coordinate axis in data point in transverse axis directionFirst->Displacement component of rigid translational displacement coordinate axis in longitudinal direction in data pointWherein (1)>For the number of data points extracted from the displacement field data, each data point comprises coordinates and displacements, +.>Series developed for Williams equation, +.>Is->Abscissa in data points, +.>Is->Ordinate in data point, +.>Is the component of the rigid translational displacement coordinate axis horizontal axis direction of the rock test piece, +.>Rigid body translational displacement seat for rock test pieceThe component in the direction of the longitudinal axis of the target,for the rigid body rotation component of the rock specimen, +.>For shear modulus of rock specimen +.>,/>Poisson's ratio->And->Respectively, with a preset crack tip (+)>) As polar parameter of origin, +.>The coefficients of the series term developed for the Williams equation.
3. The method for automatically tracking rock crack tips based on DIC technology as recited in claim 2,>2n+3。
4. the method for automatically tracking rock crack tips based on DIC technology as recited in claim 3,=10,/>>23。
5. the method of automatically tracking rock crack tips based on DIC technology of claim 1, wherein prior to the speckle test, speckle is prepared on a rock specimen according to the following method: firstly, spraying a primer on a rock test piece, and then preparing scattered spots on the primer; wherein the size of the speckles is required to be 5-10 pixels in diameter in the speckle image, and the speckles and the primer are prepared with a non-reflective color-difference coating.
6. The method of automatically tracking rock crack tips based on DIC technology of claim 1, wherein the performing a speckle experiment on the rock specimen comprises: and carrying out speckle experiments on the rock test piece by using an ultrafast digital speckle system based on pulse laser.
7. The method of automatically tracking rock crack tips based on DIC technology of claim 1, wherein the initially pre-setting a plurality of crack tips comprises: taking the tip of the pre-crack of the rock test piece as an initial center, and arranging a plurality of preset crack tips within a preset range of the initial center at a set grid interval.
8. The method of automatically tracking rock crack tips based on DIC technology of claim 1, wherein the preset value is not more than 0.05 in the difference between the smallest objective function value calculated next and the smallest objective function value calculated last is not more than a preset value.
9. A method for obtaining a rock stress intensity factor, characterized in that the rock stress intensity factor is obtained by calculating a Williams polynomial according to displacement field data of a rock crack tip and a rock test piece in a breaking process, wherein the displacement field data of the rock crack tip and the rock test piece in the breaking process are obtained by using the method for automatically tracking the rock crack tip based on the DIC technology according to any one of claims 1-8.
CN202311540933.5A 2023-11-20 2023-11-20 Method for automatically tracking rock crack tip based on DIC technology Pending CN117272686A (en)

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