CN111916160A - Method for calculating stress field coefficient of crack tip of material - Google Patents
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Abstract
The invention discloses a method for calculating stress field coefficients of a material crack tip, which comprises the following steps: p1, dividing the crack-containing area into a potential energy area, a complementary energy area and a boundary thereof according to a partition generalized variation principle, and establishing a partition generalized variation equation; p2, two full-field plane high-definition photographic images before and after sample deformation are obtained based on DIC technology, the image before deformation is a reference image, the derivation process is clearer and more accurate through simulation analysis, the problems of crack tip displacement data loss and inaccurate calculation result of the strain field in the existing DIC technology are effectively solved by combining DIC technology and EFG method, meanwhile, gridding division is not needed in modeling based on DIC-EFG method, modeling is convenient, rapid and accurate, the calculation derivation process is more direct and concise, and calculation accuracy is improved by increasing the number of nodes in units, so that the division number of the units is effectively reduced.
Description
Technical Field
The invention relates to the technical field of analysis of materials containing defects, in particular to a method for calculating stress field coefficients of a crack tip of a material.
Background
The stress field coefficient of the crack tip of the material is an important parameter for describing the stress intensity and the distribution condition of the crack tip.
At present, a meshless method needs to determine some unknown parameters, such as the size of an interpolation domain, the size of a background integral domain and the like, so that the defects of large calculation amount, low efficiency and the like exist, a DIC technology is usually adopted in combination with a finite element analysis theory to analyze and calculate a strain field in the prior art, the specific mode is to calculate the surface displacement of a test piece through the DIC technology, then perform strain calculation based on the finite element theory, in order to facilitate grid division, a triangular unit or a tetrahedral unit is usually adopted to analyze, the calculation is complex, simplicity and clearness cannot be realized, and the calculation result is possibly inaccurate.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a method for calculating stress field coefficients of a crack tip of a material.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating stress field coefficients of a tip of a material crack, the method comprising the steps of:
p1, dividing the crack-containing area into a potential energy area, a complementary energy area and a boundary thereof according to a partition generalized variation principle, and establishing a partition generalized variation equation;
p2, obtaining two full-field plane high-definition photographic images before and after sample deformation based on DIC technology, wherein the image before deformation is a reference image, and the image after deformation is a target image;
p3, searching and obtaining node information and a displacement field of the target image based on DIC technology, wherein the result around the crack is lost;
p4, establishing expressions of potential energy of the potential energy region, residual energy of the residual energy region and mixed work on the boundary of the potential energy region and the residual energy region, and performing discrete approximation on numerical integration and differentiation in the expressions by using a weak form integral method;
p5, analyzing and identifying a crack path and a crack tip by adopting a small subset aiming at the crack tip part to obtain encrypted node information and a displacement field around the crack;
p6, establishing a meshless calculation model for the derived node information;
p7, obtaining an algebraic equation set containing the stress field coefficient by applying the variable stagnation condition, and directly obtaining the stress field coefficient by solving the algebraic equation set.
Preferably, the P3 step specifically includes the following steps:
s1, selecting a full field range, and searching by adopting a proper subset size to obtain a displacement measurement result and node distribution information of the surface of the sample;
s2, setting an integral reference coordinate system Oxy;
and S3, distributing the field nodes according to the first distance, and deriving the coordinate positions (x, y) and the displacements (ux, uy) of the field nodes in the full field range.
Preferably, in the step P4, the potential energy Π P of the potential energy region is: and n P1/2 dTKd, wherein K is an integral rigidity matrix and Q is an integral load vector.
Preferably, in the step P4, the residual energy Π C of the residual energy region is: and in the equation of 1/2 ATMA, A is a stress field coefficient vector of the crack tip, AT is the transposition of A, and M is an integral matrix corresponding to the stress field coefficient vector of the crack tip.
Preferably, in the step P4, the combined work Π PC at the boundary between the potential energy region and the residual energy region is: in the ATWd equation, W is a matrix corresponding to the number vector of stress fields at the tip of the crack and the overall displacement vector.
Preferably, the displacement fields obtained by the steps of P3 and P5 are introduced into a meshless model, and the stress and strain of the crack tip are calculated based on the EFG method.
Preferably, the appropriate subset size in step S1 is selected on the premise that the correlation is maximum.
According to the method for calculating the stress field coefficient of the crack tip of the material, provided by the invention, the derivation process is clearer and more accurate through simulation analysis, the problems of crack tip displacement data loss and inaccurate strain field calculation result of the existing DIC technology are effectively solved by combining the DIC technology and the EFG method, meanwhile, gridding division is not needed on the basis of DIC-EFG method modeling, modeling is convenient, rapid and accurate, the calculation derivation process is more direct and concise, and the calculation accuracy is improved by increasing the number of nodes in a unit, so that the division quantity of the unit is effectively reduced.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A method for calculating stress field coefficients of a tip of a material crack, the method comprising the steps of:
p1, dividing the crack-containing area into a potential energy area, a complementary energy area and a boundary thereof according to a partition generalized variation principle, and establishing a partition generalized variation equation;
p2, obtaining two full-field plane high-definition photographic images before and after sample deformation based on DIC technology, wherein the image before deformation is a reference image, and the image after deformation is a target image;
p3, searching and obtaining node information and a displacement field of the target image based on DIC technology, wherein the result around the crack is lost;
p4, establishing expressions of potential energy of the potential energy region, residual energy of the residual energy region and mixed work on the boundary of the potential energy region and the residual energy region, and performing discrete approximation on numerical integration and differentiation in the expressions by using a weak form integral method;
p5, analyzing and identifying a crack path and a crack tip by adopting a small subset aiming at the crack tip part to obtain encrypted node information and a displacement field around the crack;
p6, establishing a meshless calculation model for the derived node information;
p7, obtaining an algebraic equation set containing the stress field coefficient by applying the variable stagnation condition, and directly obtaining the stress field coefficient by solving the algebraic equation set.
Preferably, the P3 step specifically includes the following steps:
s1, selecting a full field range, and searching by adopting a proper subset size to obtain a displacement measurement result and node distribution information of the surface of the sample;
s2, setting an integral reference coordinate system Oxy;
and S3, distributing the field nodes according to the first distance, and deriving the coordinate positions (x, y) and the displacements (ux, uy) of the field nodes in the full field range.
Preferably, in the step P4, the potential energy Π P of the potential energy region is: and n P1/2 dTKd, wherein K is an integral rigidity matrix and Q is an integral load vector.
Preferably, in the step P4, the residual energy Π C of the residual energy region is: and in the equation of 1/2 ATMA, A is a stress field coefficient vector of the crack tip, AT is the transposition of A, and M is an integral matrix corresponding to the stress field coefficient vector of the crack tip.
Preferably, in the step P4, the combined work Π PC at the boundary between the potential energy region and the residual energy region is: in the ATWd equation, W is a matrix corresponding to the number vector of stress fields at the tip of the crack and the overall displacement vector.
Preferably, the displacement fields obtained by the steps P3 and P5 are introduced into a meshless model, and the stress and strain of the crack tip are calculated based on the EFG method.
Preferably, the appropriate subset size in step S1 is selected on the premise that the correlation is maximum.
According to the method for calculating the stress field coefficient of the crack tip of the material, provided by the invention, the derivation process is clearer and more accurate through simulation analysis, the problems of crack tip displacement data loss and inaccurate strain field calculation result of the existing DIC technology are effectively solved by combining the DIC technology and the EFG method, meanwhile, gridding division is not needed on the basis of DIC-EFG method modeling, modeling is convenient, rapid and accurate, the calculation derivation process is more direct and concise, and the calculation accuracy is improved by increasing the number of nodes in a unit, so that the division quantity of the unit is effectively reduced.
Example 1
A method for calculating stress field coefficients of a tip of a material crack, the method comprising the steps of:
p1, dividing the crack-containing area into a potential energy area, a complementary energy area and a boundary thereof according to a partition generalized variation principle, and establishing a partition generalized variation equation;
p2, obtaining two full-field plane high-definition photographic images before and after sample deformation based on DIC technology, wherein the image before deformation is a reference image, and the image after deformation is a target image;
p3, searching and obtaining node information and a displacement field of the target image based on DIC technology, wherein the result around the crack is lost;
p4, establishing expressions of potential energy of the potential energy region, residual energy of the residual energy region and mixed work on the boundary of the potential energy region and the residual energy region, and performing discrete approximation on numerical integration and differentiation in the expressions by using a weak form integral method;
p5, analyzing and identifying a crack path and a crack tip by adopting a small subset aiming at the crack tip part to obtain encrypted node information and a displacement field around the crack;
p6, establishing a meshless calculation model for the derived node information;
p7, obtaining an algebraic equation set containing the stress field coefficient by applying the variable stagnation condition, and directly obtaining the stress field coefficient by solving the algebraic equation set.
Preferably, the P3 step specifically includes the following steps:
s1, selecting a full field range, and searching by adopting a proper subset size to obtain a displacement measurement result and node distribution information of the surface of the sample;
s2, setting an integral reference coordinate system Oxy;
and S3, distributing the field nodes according to the first distance, and deriving the coordinate positions (x, y) and the displacements (ux, uy) of the field nodes in the full field range.
Preferably, in the step P4, the potential energy Π P of the potential energy region is: and n P1/2 dTKd, wherein K is an integral rigidity matrix and Q is an integral load vector.
Preferably, in the step P4, the residual energy Π C of the residual energy region is: and in the equation of 1/2 ATMA, A is a stress field coefficient vector of the crack tip, AT is the transposition of A, and M is an integral matrix corresponding to the stress field coefficient vector of the crack tip.
Preferably, in the step P4, the combined work Π PC at the boundary between the potential energy region and the residual energy region is: in the ATWd equation, W is a matrix corresponding to the number vector of stress fields at the tip of the crack and the overall displacement vector.
Preferably, the displacement fields obtained by the steps P3 and P5 are introduced into a meshless model, and the stress and strain of the crack tip are calculated based on the EFG method.
Preferably, the appropriate subset size in step S1 is selected on the premise that the correlation is maximum.
Claims (7)
1. A method for calculating stress field coefficients of a material crack tip is characterized by comprising the following steps: the method for calculating the stress field coefficient of the tip of the material crack comprises the following steps:
p1, dividing the crack-containing area into a potential energy area, a complementary energy area and a boundary thereof according to a partition generalized variation principle, and establishing a partition generalized variation equation;
p2, obtaining two full-field plane high-definition photographic images before and after sample deformation based on DIC technology, wherein the image before deformation is a reference image, and the image after deformation is a target image;
p3, searching and obtaining node information and a displacement field of the target image based on DIC technology, wherein the result around the crack is lost;
p4, establishing expressions of potential energy of the potential energy region, residual energy of the residual energy region and mixed work on the boundary of the potential energy region and the residual energy region, and performing discrete approximation on numerical integration and differentiation in the expressions by using a weak form integral method;
p5, analyzing and identifying a crack path and a crack tip by adopting a small subset aiming at the crack tip part to obtain encrypted node information and a displacement field around the crack;
p6, establishing a meshless calculation model for the derived node information;
p7, obtaining an algebraic equation set containing the stress field coefficient by applying the variable stagnation condition, and directly obtaining the stress field coefficient by solving the algebraic equation set.
2. A method of calculating the stress field coefficient at the tip of a material crack according to claim 1, characterized in that: the step P3 specifically comprises the following steps:
s1, selecting a full field range, and searching by adopting a proper subset size to obtain a displacement measurement result and node distribution information of the surface of the sample;
s2, setting an integral reference coordinate system Oxy;
and S3, distributing the field nodes according to the first distance, and deriving the coordinate positions (x, y) and the displacements (ux, uy) of the field nodes in the full field range.
3. A method of calculating the stress field coefficient at the tip of a material crack according to claim 1, characterized in that: in the step P4, the potential energy Π P of the potential energy region is: and n P1/2 dTKd, wherein K is an integral rigidity matrix and Q is an integral load vector.
4. A method of calculating the stress field coefficient at the tip of a material crack according to claim 3, characterized in that: in the step P4, the residual energy Π C of the residual energy region is: and in the equation of 1/2 ATMA, A is a stress field coefficient vector of the crack tip, AT is the transposition of A, and M is an integral matrix corresponding to the stress field coefficient vector of the crack tip.
5. A method of calculating the stress field coefficient at the tip of a material crack according to claim 4, characterized in that: in the step P4, the combined power Π PC at the boundary between the potential energy region and the complementary energy region is: in the ATWd equation, W is a matrix corresponding to the number vector of stress fields at the tip of the crack and the overall displacement vector.
6. A method of calculating the stress field coefficient at the tip of a material crack according to claim 1, characterized in that: the displacement fields obtained by the steps of P3 and P5 introduce a meshless model, and the stress and strain of the crack tip are calculated based on an EFG method.
7. A method of calculating the stress field coefficient at the tip of a material crack according to claim 2, characterized in that: the appropriate subset size in step S1 is selected on the premise that the correlation is at most.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| 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 |
| CN114563267A (en) * | 2022-01-11 | 2022-05-31 | 武汉大学 | Sandstone crack path prediction method based on pixel unit energy level division |
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| CN104850683A (en) * | 2015-04-20 | 2015-08-19 | 重庆大学 | Method for calculating material crack tip stress field coefficient on basis of weak form quadrature element method |
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| CN104850683A (en) * | 2015-04-20 | 2015-08-19 | 重庆大学 | Method for calculating material crack tip stress field coefficient on basis of weak form quadrature element method |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| 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 |
| CN114563267A (en) * | 2022-01-11 | 2022-05-31 | 武汉大学 | Sandstone crack path prediction method based on pixel unit energy level division |
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