CN111398057A - Heterogeneous material crack stress intensity factor calculation method applying DIC technology - Google Patents
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Abstract
The invention discloses a heterogeneous material crack stress intensity factor calculation method applying DIC technology, which comprises the following steps: preparing a standard compression or tension test piece of the heterogeneous material, and performing unidirectional compression or tension to obtain the elastic modulus and the Poisson ratio; preparing a standard fracture test piece of a heterogeneous material with cracks, and preparing speckles for DIC test on the surface of a region around the cracks; carrying out a fracture experiment on the test piece to obtain a displacement field and a crack size of an area near the tip of the crack under different loads; selecting different integral paths, dividing subunits in the integral area, and calculating J-integral values of the subunits; filtering the J-integral value, then superposing the J-integral value to obtain the J-integral value on an integral path, and converting the J-integral value into a stress intensity factor K; and repeating the steps, and calculating J-integral values under different loads/displacements to obtain the stress intensity factor K at each loading moment. The invention has the characteristics of high efficiency, high precision, strong universality and the like.
Description
Technical Field
The invention relates to the technical field of fracture mechanics and engineering thereof, in particular to a calculation method of a crack stress intensity factor of a heterogeneous material by using DIC technology.
Background
The stress intensity factor K of the crack problem in the complex structure is difficult to calculate by using a theoretical expression, but if the displacement field or the stress field of the area near the crack tip in the complex structure is obtained by other methods, the stress intensity factor K of the crack can be calculated, in recent years, the stress intensity factor of the crack in the complex structure can be calculated by using a Digital Image Correlation (DIC) method, which has the advantages of high precision, simplicity in use, non-contact, post-processing of displacement data, and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a calculation method of a crack stress intensity factor of a heterogeneous material by using DIC technology. According to the method, a displacement field of a region near a crack of the heterogeneous material is measured through DIC technology, then a program is programmed to calculate J-integral on an integral path around the crack, and after the calculated value is filtered, the J-integral is converted into a stress intensity factor K.
The purpose of the invention can be realized by the following technical scheme:
a stress intensity factor calculation method for a crack problem in a heterogeneous material comprises the following steps:
preparing a standard compression or tension test piece of the heterogeneous material, and performing a unidirectional compression or tension experiment on the standard test piece to obtain the elastic modulus E and the Poisson ratio mu of the heterogeneous material;
preparing a standard fracture test piece of a heterogeneous material with cracks, and preparing speckles which are in black and white phase and are appropriate in size and uniformly distributed on the surface of a region around the cracks; the area around the crack is an area which takes the tip of the prefabricated crack as the center of a circle and takes 5-7 times of the length of the prefabricated crack as the radius; the maximum speckle of the speckle is no more than 6 pixels;
performing a fracture experiment on the test piece, synchronously recording the deformation of the area (speckle) around the crack in the loading process by adopting a CCD (charge coupled device) camera, and obtaining the displacement field U and the crack size of the area near the tip of the crack under different loads after the processing by DIC (digital computer) software;
selecting different integration paths, compiling a calculation program according to the obtained elastic modulus E and the displacement field U, dividing subunits in the integration regions, and calculating J-integral values of the subunits on the different paths;
carrying out filtering processing on the calculated J-integral value;
superposing the J-integral values of the remaining subunits after filtering to obtain the J-integral value on the integral path, and converting the J-integral value into a stress intensity factor K under the same load/displacement;
and repeating the steps of calculating the J-integral values of all the subunits on different paths, filtering the integral values, converting the integral values into stress intensity factors K, calculating the J-integral values under different loads/displacements, and filtering to obtain the stress intensity factors K at all the loading moments.
Preferably, the heterogeneous material is concrete, composite, fiber reinforced composite (FRP), rock, or the like.
Preferably, the standard fracture test piece is a unidirectional tensile Central Crack (CCT) test piece, a Compact Tension (CT) test piece, or a three-Point Bending (3-Point Bending) test piece.
Specifically, the method for dividing the sub-units in the integration area comprises the following steps: and dividing the subunits in the integration region in a triangular unit or quadrilateral unit mode according to the principle that the subunits are full, do not overlap and completely cover the whole integration region.
Specifically, the calculation formula of the J-integral value after superposition of each subunit on different paths is as follows:
in the formula, n is the number of subunits divided by the annular integral domain; gp represents the number of Gaussian integration points in each subunit; u. ofiDisplacement field, σ, measured for DIC methodsijFor the stress on each subunit node, i, j is 1, and 2 represents x and y directions respectively; omega is the strain energy density; q. q.s1Take 0 at the outer boundary and 0 at the inner boundary0Taking 1 above;1jis the kronecker tensor; x is the number ofk、ηkThe coordinates of the real parameter unit and the form parameter unit are respectively, and k represents the x direction and the y direction;
is the weight coefficient of the gaussian integration point.
Specifically, the J-integrated values of the subunits to be filtered are classified into the following two types:
j-integrated value J of sub-unit near the removed crackedge；
Filtering out J-integral singular value J of subunit satisfying formula (2) by applying 3 sigma-5 sigma principle of probability theorysingular：
In the formula, JAIIs the J-integral value of the subunit; e is JAIExpected value (mean value) of; d is JAIThe variance of (a); the value of the coefficient n is 3-5 (3 is taken when 3 sigma is adopted, and 5 is taken when 5 sigma is adopted).
Preferably, the crack-near subunit is a subunit having a shortest distance between the centroid and the crack boundary of 1 to 4 mm.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the method, a Digital Image Correlation (DIC) technology is combined with a J-integral calculation method, a displacement field of a region around a crack is extracted through the DIC technology, the numerical integration idea of finite element discretization is combined, the concussion of the displacement field of the surface of a heterogeneous material/component and the error of the displacement field of the free boundary of an object measured through DIC are considered, and the calculation of J-integral and a stress intensity factor K is achieved through Matlab programming. The method combines the DIC technology with the J-integral calculation method and the filtering technology, has the characteristics of high efficiency, high precision, strong universality and the like, and is suitable for calculating the J-integral and the stress intensity factor K of crack problems in various structures or components containing heterogeneous materials.
Drawings
FIG. 1 is a schematic view of a three-point bending test piece.
FIG. 2 is a schematic illustration of a speckle pattern of a concrete surface.
FIG. 3 shows the displacement field U in the X-direction of the region around the crackXCloud pictures.
FIG. 4 is a schematic diagram of the closed-loop integration domain (integrator rail) and subunits of a crack.
FIG. 5 is a diagram illustrating the J-integration values of the sub-units in the integration domain.
Fig. 6 is a schematic diagram of the sub-unit in the vicinity of the crack.
Fig. 7 is a graph of the stress intensity factor K as a function of the load point displacement v.
Fig. 8 is a graph comparing the calculated value of the stress intensity factor K with the theoretical value.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
A stress intensity factor calculation method for a crack problem in a heterogeneous material comprises the following steps:
(1) preparing a standard compression or tension test piece of the heterogeneous material, and carrying out a unidirectional compression or tension experiment on the standard test piece to obtain the elastic modulus E and the Poisson ratio mu of the heterogeneous material.
Before calculating the J-integral of the crack problem in the heterogeneous material, the mechanical parameters of the material need to be obtained. Therefore, in this embodiment, taking a concrete material as an example, a standard compression test piece is prepared according to general concrete mechanical property test method standard (GB/T50081-2002), and the standard compression test piece is unidirectionally compressed, so that the mechanical parameters of the concrete material test piece are: the elastic modulus E is 33.73GPa, and the Poisson ratio mu is 0.2.
(2) Preparing a standard fracture test piece of a heterogeneous material with cracks, and preparing speckles which are black and white and alternate, have the maximum spot size not more than 6 pixels and are uniformly distributed on the surface of a region around the cracks. The area around the crack is an area which takes the tip of the prefabricated crack as the center of a circle and takes 5-7 times of the length of the prefabricated crack as the radius.
FIG. 1 shows the preparation of three-point bend concrete test pieces containing type I pre-cracks. The test piece has a span S of 600mm, a width w of 150mm, a height h of 150mm, and an initial crack height a of 1/3h of 50 mm. Before the three-point bending experiment is carried out, speckles for DIC test need to be manufactured in the area around the crack on the surface of the test piece, and the manufacturing method comprises the following steps: and (3) uniformly coating white putty powder on the area around the crack, and spraying black matte paint after the area is dried to form a layer of uniformly distributed black spots. The speckle size is required to be moderate to ensure the measurement accuracy of DIC, and the speckle obtained by the manufacturing method is shown in figure 2.
(3) And (3) performing a fracture experiment on the test piece, synchronously recording the deformation of the area (speckle) around the crack in the loading process by adopting a CCD (charge coupled device) camera, and obtaining the displacement field U of the area near the tip of the crack under different loads and the size of the crack after the processing by DIC (digital computer) software.
In the process of the three-point bending experiment, a CCD camera of the DIC device is adopted to synchronously acquire displacement information of the concrete surface of the area around the crack in the loading process, and the height of the crack is tracked and determined. The loading speed in this embodiment is 0.005mm/s and the acquisition frequency of the camera is set to 1 Hz. Utilizing DIC system software to process displacement information of a certain moment (a certain picture) collected by a CCD camera so as to obtain a displacement field on the surface of the test area at the moment, wherein the displacement field U in the X directionXAs shown in fig. 3.
(4) Selecting different integration paths, compiling a calculation program according to the obtained elastic modulus E and the displacement field U, dividing subunits in the integration regions, and calculating J-integration values of the subunits on the different paths.
After the displacement field of the concrete in the area around the crack is determined, the J-integral value of each subunit AI in a certain integral path is calculated, and the concrete solving process is as follows:
fig. 4 shows a schematic diagram of a closed-loop integration domain (i.e., an integral peripheral path) and subunits of the crack in this embodiment.
Setting the node coordinate, the node displacement and the q function of a certain subunit as follows:
wherein m is the number of nodes in the unit, a triangle unit when m is 3, a quadrangle unit when m is 4, and qmTaking 0 at the outer boundary of the integration path (the envelope), and taking 0 at the inner boundary0Get 1 above.
The coordinate, the displacement and the function q of any point of the subunit are obtained by an interpolation method, and the function q is as follows:
[x y u v q]＝N[x y u v q](4)
in the formula, N can be represented as:
N＝[N1N2… Nm](1)
wherein i is 1,2, …, m, ξiThe coordinates of the form parameter units are ξ and η, and the coordinates a, b and c are coordinate constants.
The derivative is:
the jacobian matrix is:
the derivative of the shape function to the coordinates is:
according to the displacement field U measured by DIC on the unit node, the strain field can be obtained as follows:
similarly, the partial derivative of the function q can also be found as:
at this time, the stress at the gaussian integration point is:
in the formula:
the strain energy density can be expressed as:
the J-integral within a certain subunit AI can be calculated by:
in the formula (I), the compound is shown in the specification,
with gaussian integration, the J-integral of the subunit is:
wherein GP is the number of Gaussian integration points, ξP、ηPThe coordinates of the gaussian integration points. For a triangle unit, GP is generally taken to be 3; the unit of quadrilateral generally takes GP 4. The coordinate of the two-dimensional Gaussian integral point and the corresponding weight coefficient can be obtained by looking up the weight function table
Therefore, the method comprises the following steps:
thus, the J-integral over the entire integration domain (the corridor) is:
in the formula, n is the number of subunits in the crack periphery annular integral domain (surrounding channel).
(5) Carrying out filtering processing on the calculated J-integral value;
triangular subunits are divided by using a Delaunay triangulation algorithm in Matlab, the triangular subunits are divided into 1165 subunits in an annular integral domain (enclosed road), each subunit contains 3 Gaussian integral points, and the J-integral value J of each subunit can be obtained by using the formulas (3) to (21)AIAs shown in fig. 5.
The crack-neighborhood subunits within the integral domain (the corridors) are shown in fig. 6. Since the DIC method cannot accurately measure the displacement field of subunits near the crack in the integral domain (enclosed channel), the J-integral value J of the subunits needs to be determinededgeAnd deleted. In the present embodiment, the crack vicinity subunit is defined as: the shortest distance from the centroid of the triangular unit to the crack edge was 2 mm. By this definition, the calculated J-integral of 9 subunits is filtered outedgeThe center (○) point in FIG. 5, the filtered J-integral value is denoted as J2The method comprises the following steps:
J2＝ΣJedge(23)
for J-integral singular value J3J for each subunit using the 5 σ principle and equation (2)AIWhen the judgment is made, the singularities (points of triangle (△) in fig. 5) appearing in the J-integrated values of 6 subunits are found and filtered out.
After removing the J-integrated values of the 9 subunits near the crack and the J-integrated singular values of the 6 subunits, the J-integrated values (the solid square (■) points in fig. 5) for the remaining 1150 subunits can be calculated using the following formula:
J＝J1-J2-∑Jsingular(24)
equation (24) is the J-integral calculation equation in a certain integral path (enclosed road) obtained by the method of the present invention.
And processing the displacement picture acquired by the CCD camera at each moment, and calculating the J-integral value in the integral domain (the enclosed channel) according to the method to obtain a relation graph of the displacement v-J-integral of the loading point of the test piece.
(6) Superposing the J-integral values of the remaining subunits after filtering to obtain the J-integral value on the integral path, and converting the J-integral value into a stress intensity factor K under the same load/displacement;
(7) and (5) repeating the steps (4) to (6), calculating J-integral values under different loads/displacements, and performing filtering treatment to obtain a stress intensity factor K at each loading moment.
In addition, because the number of displacement pictures acquired by the CCD camera is large, it is sometimes difficult to avoid environmental interference during the acquisition process, and therefore, smoothing (filtering) processing needs to be performed on the stress intensity factor K converted in step (6). The specific calculation and processing method is as follows:
from the J-integral value obtained above, the stress intensity factor K of the crack front can be obtained by the following formulaorign：
In the process of loading the test piece, if the collection frequency of DIC is h Hz, h displacement pictures can be collected every second, and each picture corresponds to 1 stress intensity factor Korign. Invoking smooth filter function of Matlab to obtain stress intensity factor K at all loading momentsorignPerforming smoothing (filtering) treatment, i.e.
K＝smooth(Korign,span) (26)
A final stress intensity factor K versus load point displacement v can be obtained as shown in fig. 7.
In the formula (26), span is a filtering window, and is generally 150 to 250, and in this embodiment, is 200.
The method for calculating the stress intensity factor K of the crack problem in the heterogeneous material is described above.
In order to verify the effectiveness of the method of the present invention, the stress intensity factor K obtained from 4 different integration paths (corridors) shown in fig. 8 is compared with the stress intensity factor K calculated by using the linear elastic fracture theory.
According to the theory of linear elastic fracture (stress intensity factor handbook), the theoretical calculation formula of the stress intensity factor K of the three-point bending test piece is as follows:
wherein P is load, S is test piece span, h is test piece height, B is test piece thickness, α is crack relative height a/h, a is crack height, β is span-height ratio S/h, and geometric modification factor kβ(α) is:
in the three-point bending test, the crack height a at each time was measured by the DIC system, and the theoretical value of the stress intensity factor of the I-type crack in the concrete three-point bending test piece was obtained by using the equations (27) and (28), as shown in fig. 8.
As can be seen from fig. 8, in the initial loading stage, since the load is small, the deformation of the test piece is also small, which results in the test result of the DIC and the calculation result of K having an error; in addition, in the stage of crack destabilization and propagation (the stress intensity factor K is larger than the fracture toughness K of the material)IC1.4 MPam), the crack is rapidly expanded, and the testing precision is difficult to ensure by adopting a DIC method. In addition to the two special stages described above, the mean relative error of the stress intensity factor K calculated by the method of the invention (i.e. the integral peripheral 1) from its theoretical value is about 5% when the crack is steadily propagating. In addition, the fracture toughness K obtained by calculating the integral surrounding road 1-4ICThe relative errors from their experimental values were 3.2%, 4.3%, 3.7% and 3.0%, respectively. This indicates to adoptThe method of the present invention is effective and feasible for calculating the stress intensity factor K of the crack problem in heterogeneous materials, and the characteristics of the J-integral value independent of the integral path are also demonstrated again.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (9)
1. A heterogeneous material crack stress intensity factor calculation method applying DIC technology is characterized by comprising the following steps:
preparing a standard compression or tension test piece of the heterogeneous material, and performing a unidirectional compression or tension experiment on the standard test piece to obtain the elastic modulus and the Poisson ratio of the heterogeneous material;
preparing a standard fracture test piece of a heterogeneous material with cracks, and preparing speckles with black and white phases and proper sizes on the surface of a region around the cracks;
performing a fracture experiment on the test piece, synchronously recording the deformation of the area around the crack in the loading process by adopting a CCD (charge coupled device) camera, and obtaining the displacement field of the area near the tip of the crack under different loads and the size of the crack after the processing by DIC (digital computer) software;
selecting different integral paths, compiling a calculation program according to the obtained elastic modulus and displacement field, dividing subunits in the integral regions, and calculating J-integral values of the subunits on the different paths;
carrying out filtering processing on the calculated J-integral value;
superposing the J-integral values of the remaining subunits after filtering to obtain the J-integral value on the integral path, and converting the J-integral value into a stress intensity factor K under the same load/displacement;
and repeating the steps of calculating the J-integral values of all the subunits on different paths, filtering the integral values, converting the integral values into stress intensity factors K, calculating the J-integral values under different loads/displacements, and filtering to obtain the stress intensity factors K at all the loading moments.
2. The method of claim 1, wherein the heterogeneous material is concrete, composite, fiber reinforced composite, or rock.
3. The method of claim 1, wherein the standard fracture specimen is a unidirectional tensile center crack specimen, a compact tensile specimen, or a three point bend specimen.
4. The method of claim 1, wherein the sub-cell division method in the integration area is: and dividing the subunits in the integration region in a triangular unit or quadrilateral unit mode according to the principle that the subunits are full, do not overlap and completely cover the whole integration region.
5. The method of claim 1, wherein the J-integral value of the superposed subunits on different paths is calculated by the formula:
in the formula, n is the number of subunits divided by the annular integral domain; gp represents the number of Gaussian integration points in each subunit; u. ofiDisplacement field, σ, measured for DIC methodsijFor the stress on each subunit node, i, j is 1, and 2 represents x and y directions respectively; omega is the strain energy density; q. q.s1Take 0 at the outer boundary and 0 at the inner boundary0Taking 1 above;1jis the kronecker tensor; x is the number ofk、ηkThe coordinates of the real parameter unit and the form parameter unit are respectively, and k represents the x direction and the y direction;
is the weight coefficient of the gaussian integration point.
6. The method of claim 1, wherein J-integrated values of subunits to be filtered are classified into the following two categories:
j-integrated value J of sub-unit near the removed crackedge；
Filtering out J-integral singular value J of subunit satisfying the following formula by applying 3 sigma-5 sigma principle of probability theorysingular：
In the formula, JAIIs the J-integral value of the subunit; e is JAIThe expected value of (d); d is JAIThe variance of (a); the value of the coefficient n is 3-5.
7. The method of claim 6, wherein the crack-near subunits are subunits having a shortest distance between the centroid and the crack boundary of 1-4 mm.
8. The method according to claim 1, wherein the CCD camera acquires a large number of displacement pictures, which are sometimes inevitably interfered by the environment during the acquisition process, and therefore the stress intensity factor K after conversion needs to be smoothed, and the specific calculation and processing method is as follows:
from the J-integral value obtained, the stress intensity factor K of the crack front can be obtained by the following formulaorign：
In the process of loading the test piece, if the collection frequency of DIC is h Hz, h displacement pictures can be collected every second, and each picture corresponds to 1 stress intensity factor Korign(ii) a Invoking smooth filter function, and applying stress intensity factor K at all loading momentsorignIs subjected to a smoothing treatment, i.e.
K＝smooth(Korign,span)
In the formula, span is a filtering window, and the span is 150-250.
9. The method according to claim 1, wherein the area around the crack is an area which takes the tip of the prefabricated crack as a center of a circle and takes 5-7 times of the length of the prefabricated crack as a radius; the maximum speckle for said speckle is no more than 6 pixels.
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| CN113008669A (en) * | 2021-01-22 | 2021-06-22 | 天津大学 | Method for dynamically monitoring stress intensity factor of crack tip |
| CN113029817A (en) * | 2021-01-14 | 2021-06-25 | 华南理工大学 | Unilateral J-integration method for interface cracks |
| CN113158465A (en) * | 2021-04-23 | 2021-07-23 | 中国石油大学(华东) | Nano SiO based on crack failure mechanism2Nano SiO in modified composite material2Preferred method of content |
| CN114169209A (en) * | 2021-12-24 | 2022-03-11 | 哈尔滨工业大学 | Numerical method for extracting tip parameters of heterogeneous material mixed type dispersion cracks |
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| CN113029817A (en) * | 2021-01-14 | 2021-06-25 | 华南理工大学 | Unilateral J-integration method for interface cracks |
| CN113008669A (en) * | 2021-01-22 | 2021-06-22 | 天津大学 | Method for dynamically monitoring stress intensity factor of crack tip |
| CN112903442A (en) * | 2021-01-26 | 2021-06-04 | 北京市理化分析测试中心 | Method for testing I-type fracture toughness of bonding interface of composite material bonding structure |
| CN113158465A (en) * | 2021-04-23 | 2021-07-23 | 中国石油大学(华东) | Nano SiO based on crack failure mechanism2Nano SiO in modified composite material2Preferred method of content |
| CN113158465B (en) * | 2021-04-23 | 2022-05-27 | 中国石油大学(华东) | Optimal selection method of content of nano SiO2 in nano SiO2 modified composite material based on crack failure mechanism |
| DE102021124940A1 (en) | 2021-09-27 | 2023-03-30 | Technische Universität Bergakademie Freiberg, Körperschaft des öffentlichen Rechts | Method for determining the fracture-mechanical stress of at least one crack when a component is loaded, computer program product and device for carrying out the method, and their use |
| WO2023046751A1 (en) | 2021-09-27 | 2023-03-30 | Technische Universität Bergakademie Freiberg | Method for determining the fracture mechanical load of at least one crack when a component is loaded, computer program product and device for carrying out the method, and use thereof |
| CN114169209A (en) * | 2021-12-24 | 2022-03-11 | 哈尔滨工业大学 | Numerical method for extracting tip parameters of heterogeneous material mixed type dispersion cracks |
| CN114818340A (en) * | 2022-04-29 | 2022-07-29 | 西北核技术研究所 | Method for obtaining physical equivalent strength of heterogeneous rock under strong impact load |
| CN116046533A (en) * | 2023-01-10 | 2023-05-02 | 中国人民解放军陆军工程大学 | Crack tip stress intensity factor measuring method based on DIC and stress field reconstruction |
| CN116046533B (en) * | 2023-01-10 | 2023-09-22 | 中国人民解放军陆军工程大学 | Crack tip stress intensity factor measuring method based on DIC and stress field reconstruction |
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