CN112906255B - Method for measuring crack tip stress intensity factor - Google Patents
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Abstract
The invention discloses a method for measuring a crack tip stress intensity factor, which comprises the following steps: determining the shape of crack opening displacement, and deducing an opening displacement value at any position; deriving a theoretical model corresponding to the crack tip stress intensity factor and the crack opening displacement; aiming at actual engineering conditions, researching the influence of model size; aiming at actual engineering conditions, researching the form of an additional load; and (5) establishing a measurement method of the stress intensity factor of the limited plate model containing the center penetrating crack. The method for measuring the stress intensity factor of the crack tip is low in operation difficulty, is not limited by the specific requirements of the size of a test piece and the borne load form, enables the method for measuring the stress intensity factor at the laboratory stage to be further close to actual engineering, lays a foundation for grasping the state of the stress intensity factor of the crack tip of an actual engineering structure with crack damage in real time, and enables the application of the stress intensity factor measurement in the engineering structure to be possible.
Description
Technical Field
The invention relates to the technical field of structural engineering, in particular to a method for measuring a crack tip stress intensity factor.
Background
The defects of the weld toe part with serious stress concentration are easy to develop into surface cracks with the shape close to a semi-ellipse under the action of various alternating loads when in operation. Under the action of continuous external load, surface cracks can be continuously expanded to penetrate the steel plate to form penetration cracks. Because the engineering structure has a large amount of redundancy, the occurrence of surface cracks and even penetrating cracks does not mean the damage of the crack-containing area, and only when the fracture parameter of the crack tip, namely the stress intensity factor reaches a critical value, the cracks are instable and expand, so that the bearing capacity of the corresponding structure reaches a limit to damage. Therefore, in order to ensure that the engineering structure does not generate integral fracture and damage in the effective service period, the main control factor directly related to the ultimate strength of the structure, namely the crack tip stress strength factor, needs to be mastered.
The stress intensity factor is a mechanical parameter which is very important for the safety assessment of the residual intensity of the structure, the life estimation, the failure analysis, the fracture toughness measurement of the material and the like. Researchers have been striving to find stress intensity factor solutions as accurate as possible using various analytical, numerical, experimental, or engineering methods. At present, various stress intensity factor analysis methods are obtained by taking a basic equation of a stress field and a displacement field in a region near a crack tip as a starting point and performing series deduction based on a complex function theory, integral transformation, an elastic mechanics conservation law and a complex transformation-variation method. However, these analytical methods stay on ideal models and simple boundary conditions, are difficult to be applied to complex structures under the action of complex loads in actual engineering, and require solving stress intensity factors by other methods. Along with the rapid development of computer technology, the finite element method has been widely applied in engineering by using the powerful simulation and numerical calculation functions, and in particular, the stress intensity factor of the crack tip can be calculated by directly using the calculation value of the finite element node force or displacement near the crack tip. However, when solving the problem of a practical large structure, the finite element method still has the following difficulties, such as (1) it is difficult to accurately obtain external load and deformation data with complex structure, so that a calculation result of a stress field near a crack tip may have a larger error, and the calculation accuracy of a stress intensity factor is directly affected; (2) The whole three-dimensional structure is required to be discretized, and due to the singularity of stress fields near crack tips, very dense grids have to be divided, or special finite element technologies such as singular elements are adopted, so that the data preparation workload is large, and the real-time mastering of crack tip stress intensity factors is difficult to realize. The real-time measurement of the stress intensity factor is the most direct method for grasping the safety state of the structure with crack damage, however, the existing methods for measuring the stress intensity factor, such as a photoelastic method, a caustic line method, a PVDF measuring method and the like, are all in experimental stages, have definite requirements on the size of a test piece and the load form of the test piece, have high experimental operation difficulty and cannot be used for measuring the actual engineering structure.
Disclosure of Invention
The present invention aims to solve, at least to some extent, one of the above technical problems in the prior art. In view of this, the present invention needs to provide a method for measuring the stress intensity factor in laboratory stage, which has low operation difficulty and is not limited by the specific requirements of the size of the test piece and the type of the load, so that the method is further close to the actual engineering, lays a foundation for grasping the state of the stress intensity factor of the crack tip of the crack damage actual engineering structure in real time, and makes the application of the stress intensity factor measurement in the engineering structure possible.
The invention provides a method for measuring a crack tip stress intensity factor, which comprises the following steps:
s1, determining the shape of crack opening displacement, and deducing an opening displacement value at any position;
s2, deducing a theoretical model corresponding to the crack tip stress intensity factor and the crack opening displacement;
s3, researching the influence of the model size aiming at the actual engineering situation;
s4, researching the form of an additional load according to actual engineering conditions;
s5, establishing a measuring method of the stress intensity factor of the limited plate model containing the center penetrating crack.
According to one embodiment of the present invention, the crack opening displacement formula is used in the calculation in step S1:
determining crack opening displacement value:
wherein a is the crack half length, sigma is the film stress of external load, E is the elastic modulus, y is the opening displacement, a x And x is the position of any point of the crack, and the origin of coordinates is the center position of the crack length.
In step S2, the stress intensity factor formula is used in the derivation according to an embodiment of the present invention
And a crack opening displacement formula, and determining a relative relation between the stress intensity factor and the opening displacement at any position:
wherein K is I As a crack tip stress intensity factor, deltau measured in this formula is near the crack maximum opening displacement and far from the crack tip.
In step S3, the effect of the boundary effect of the model is analyzed by finite element numerical simulation using the center-containing penetrating crack plate subjected to uniform tensile load as a subject of study:
the formula applies to a finite flat model in the range of a/w=0.1 to 0.667, where W is the half-width of the model.
According to one embodiment of the present invention, the flat plate containing the center through crack in the step S3 is taken as a research object, and the step S4 is performed by adopting a finite element numerical simulation technology, wherein the step S4 includes the following two steps:
first, analyzing non-uniform symmetrical loads:
the formula is suitable for any non-uniform symmetrical load condition that the maximum opening displacement occurs at the center of the crack;
secondly, analyzing the non-uniform asymmetric load: the shape of the opening displacement is not a symmetrical ellipse, the maximum opening displacement of the crack no longer appears at the center of the crack, and four measuring points are arranged near the maximum opening displacement according to the shape of the crack opening displacement, wherein two measuring points (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) The other two points are far to the right and the other two points are far to the left, and one group of two points is represented by the formula:
the crack length on each side is determined, and the crack opening displacement shape can be regarded as a result of two different long axes (a L 、a R ) Semi-elliptical composition of the same minor axis, again according to:
will left semi-elliptic long axis a L And the measured left opening displacement value is brought in, and a stress intensity factor of the left tip is obtained; right semi-elliptical major axis a R And a measured opening displacement value to the right is taken in, a stress intensity factor of the tip on the right is obtained, wherein a L And a R Representing half lengths of cracks at the left and right ends respectively.
According to one embodiment of the present invention, step S5 includes the following three steps:
the first step, arranging four measuring points to obtain corresponding data;
step two, carrying out a crack half-length formula, and determining crack half-lengths a at the left end and the right end;
thirdly, the stress intensity factors K of the left and right tips of the crack are determined by substituting the stress intensity factors into a stress intensity factor formula I Values.
For flat-panel models containing central penetrating cracks that are subjected to tensile loading,
according to one embodiment of the invention, for a flat plate model with a central penetration crack subjected to tensile loading, first 4 measuring points are arranged, two of which (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) And the other two points are biased to one side and the other two points are biased to the other side. According to the values of the two measuring points, respectively determining the corresponding crack half length a L And a R The method comprises the steps of carrying out a first treatment on the surface of the Then according to the opening displacement value Deltau measured on each side i Corresponding a xi And length of a, combine:
the stress intensity factor value of each side of the tip is estimated, wherein i is an integer value from 1 to 4.
According to one embodiment of the invention, the shape of the opening displacement is determined to be elliptical by using a crack opening displacement formula.
The invention provides a method for measuring a crack tip stress intensity factor, which is a method for measuring the crack tip stress intensity factor of a plate member with a central penetrating crack, wherein the method for measuring the stress intensity factor of the crack tip is provided based on the form of crack opening displacement and the corresponding relation between the crack opening displacement and the crack tip stress intensity factor, and on the basis of the influence of model size and load form, under the action of any tensile load, the method for measuring the stress intensity factor of the corresponding tip is determined based on the opening displacement far away from the crack tip and near the maximum opening displacement, so that the method for measuring the stress intensity factor can be applied to engineering members.
Drawings
FIG. 1 is a schematic representation of three symmetrical tensile load models in a method of measuring crack tip stress intensity factors in accordance with the present invention.
FIG. 2 is a graph showing maximum opening displacement of a crack under asymmetric tensile loading in a method for measuring crack tip stress intensity factor according to the present invention.
FIG. 3 is a schematic diagram of an asymmetric tensile load model in a method of measuring crack tip stress intensity factor according to the present invention.
Fig. 4 is a schematic view of crack opening displacement under the load shown in fig. 3.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
As shown in fig. 1 to 4, a method for measuring a crack tip stress intensity factor includes the steps of:
s100, determining the shape of crack opening displacement, and deducing an opening displacement value at any position;
s200, deducing a theoretical model corresponding to the crack tip stress intensity factor and the crack opening displacement;
s300, researching the influence of the model size according to actual engineering conditions;
s400, researching the form of an additional load according to actual engineering conditions;
s500, establishing a measuring method of the stress intensity factor of the limited plate model containing the center penetrating crack.
The invention provides a method for measuring a crack tip stress intensity factor, which is a method for measuring the crack tip stress intensity factor of a plate member with a central penetrating crack, wherein the method for measuring the stress intensity factor of the crack tip is provided based on the form of crack opening displacement and the corresponding relation between the crack opening displacement and the crack tip stress intensity factor, and on the basis of the influence of model size and load form, under the action of any tensile load, the method for measuring the stress intensity factor of the corresponding tip is determined based on the opening displacement far away from the crack tip and near the maximum opening displacement, so that the method for measuring the stress intensity factor can be applied to engineering members.
As shown in fig. 1, the crack opening displacement formula is used in the calculation in step S100:
determining crack opening displacement value:
and the opening displacement has an elliptical shape, so that it can be determined based on the measured given crack position (x=a x0 ) Opening displacement value of (2), predicting crack opening displacement shape and opening displacement value of any other positionWherein a is the crack half length, sigma is the film stress of external load, E is the elastic modulus, y is the opening displacement, a x And x is the position of any point of the crack, and the origin of coordinates is the center position of the crack length.
As shown in fig. 1, in step S200, the stress intensity factor formula is used in the derivation
And a crack opening displacement formula, and determining a relative relation between the stress intensity factor and the opening displacement at any position:
wherein K is I As the stress intensity factor of the crack tip, the delta u measured in the formula is near the maximum opening displacement of the crack and far away from the crack tip, so that the stress intensity factor of the crack tip can be predicted according to the opening displacement measured by 2-3 measuring points, when the predicted stress intensity factor values are very close, the accuracy of the measured opening displacement values can be proved, and the average value of the measured opening displacement values can be taken as the final result of the stress intensity factor.
As shown in fig. 1, in step S300, the effect of the boundary effect of the model is analyzed by finite element numerical simulation using a flat plate with a central through crack, which is subjected to uniform tensile load, wherein the effect coefficient is 1 (see table 1):
TABLE 1 calculation results of maximum normal opening displacement and stress intensity factor for cracks of different plate width models
From the above calculation result, it is deduced that the formula (5) in step S200 is applied to a finite-plane model, and the formula (5) is applied to a finite-plane model in the range of a/w=0.1 to 0.667, where W is the half-width of the model.
As shown in fig. 1, the step S400 is performed by using the plate containing the center through crack in the step S300 as a study object and adopting a finite element numerical simulation technique, wherein the step S400 includes the following two steps:
in a first step, the effect of the non-uniform symmetrical load was first analyzed, and, taking three types as shown in fig. 1 as an example, the effect coefficient was found to be 1 (see table 2):
table 2 calculation results under three symmetrical tensile loads
From the calculation result, it is deduced that the formula (5) in the step S200 is applicable to the non-uniform and symmetrical tensile load, and the formula (5) is applicable to any non-uniform and symmetrical load condition in which the maximum opening displacement occurs at the center of the crack;
secondly, analyzing the non-uniform asymmetric load: the shape of the opening displacement is not a symmetrical ellipse, the maximum opening displacement of the crack no longer appears at the center of the crack, and four measuring points are arranged near the maximum opening displacement according to the shape of the crack opening displacement, wherein two measuring points (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) The other two points are far to the right and the other two points are far to the left, and one group of two points is represented by the formula:
the crack length on each side is determined, and the crack opening displacement shape can be regarded as a result of two different long axes (a L 、a R ) The semi-ellipse with the same minor axis is formed, and the left semi-ellipse major axis a is calculated according to the formula (5) L And the measured left opening displacement value is brought in, and a stress intensity factor of the left tip is obtained; right semi-elliptical major axis a R And a measured opening displacement value to the right is taken in, a stress intensity factor of the tip on the right is obtained, wherein a L And a R Representing half lengths of cracks at the left and right ends respectively.
As shown in fig. 1, the step S500 includes the following three steps:
the first step, arranging four measuring points to obtain corresponding data;
step two, carrying out a crack half-length formula, and determining crack half-lengths a at the left end and the right end;
thirdly, the stress intensity factors K of the left and right tips of the crack are determined by substituting the stress intensity factors into a stress intensity factor formula I Values.
Wherein according to the above procedure, for a flat plate model with a central penetration crack subjected to tensile load, first 4 measuring points are arranged, two of which (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) The other two points are deviated to one side and the other two points are deviated to the other side, and the corresponding crack half length a is respectively determined according to the values of the two measuring points L And a R The method comprises the steps of carrying out a first treatment on the surface of the Then according to the opening displacement value Deltau measured on each side i Corresponding a xi And a length, estimating stress intensity factor value of each side of the tip in combination with the formula (5), wherein i is an integer value in 1 to 4.
As shown in fig. 1 to 4, a specific measurement procedure of a crack tip stress intensity factor measurement method according to the present invention is as follows:
firstly, according to the displacement form of crack opening in a known model, 4 measuring points are arranged, wherein the measuring points are arranged far away from the tip of the crack and near the maximum crack opening displacement, two points are right and the other two points are left so as to obtain the crack opening displacement value (a x1 ,Δu 1 )、(a x2 ,Δu 2 )、(a x3 ,Δu 3 ) And (a) x4 ,Δu 4 ) The corresponding crack length a is calculated by two points which are far right and far left according to the formula (6) R And a L Last measured a xi 、Δu i And determining the stress intensity factor K of the flat plate component corresponding to the a and being brought into the formula (5) R And K L Values.
Taking the model of fig. 3 as an example, the crack half-length a=10m, the plate half-width w=100, the half-length l=150mm, the external load maximum value of 100MPa, the elastic modulus e=210 GPa, the poisson ratio of 0.3 are calculated, and the calculated opening displacement form is shown in fig. 4.
The comparison of the crack tip stress intensity factor determined from the measured values with the finite element calculation results is given in table 3 below, from the relative error between the two, the measurement method has higher measurement accuracy:
table 3 comparison of the determined stress intensity factor with the finite element results
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
Claims (7)
1. A method for measuring a crack tip stress intensity factor, comprising the steps of:
s1, determining the shape of crack opening displacement, and deducing an opening displacement value at any position;
s2, deducing a theoretical model corresponding to the crack tip stress intensity factor and the crack opening displacement;
s3, researching the influence of the model size aiming at the actual engineering situation;
s4, researching the form of an additional load according to actual engineering conditions;
taking the flat plate containing the center penetrating crack in the step S3 as a research object, and adopting a finite element numerical simulation technology to carry out the step S4, wherein the step S4 comprises the following two steps:
first, analyzing non-uniform symmetrical loads:
the formula is suitable for any non-uniform symmetrical load condition that the maximum opening displacement occurs at the center of the crack;
second step, analysisNon-uniform asymmetric loading: the shape of the opening displacement is not a symmetrical ellipse, the maximum opening displacement of the crack no longer appears at the center of the crack, and four measuring points are arranged near the maximum opening displacement according to the shape of the crack opening displacement, wherein two measuring points (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) The other two points are far to the right and the other two points are far to the left, and one group of two points is represented by the formula:
the crack length on each side is determined, and the crack opening displacement shape can be regarded as a result of two different long axes (a L 、a R ) Semi-elliptical composition of the same minor axis, again according to:
will left semi-elliptic long axis a L Substituting the measured left opening displacement value to obtain the stress intensity factor of the left tip; right semi-elliptical major axis a R And a measured opening displacement value to the right is taken in, a stress intensity factor of the tip on the right is obtained, wherein a L And a R Respectively representing half lengths of cracks at the left end and the right end;
s5, establishing a measuring method of the stress intensity factor of the limited plate model containing the center penetrating crack.
2. The method for measuring a crack tip stress intensity factor according to claim 1, wherein the calculation in step S1 uses a crack opening displacement formula:
determining crack opening displacement value:
wherein a is the crack half length, sigma is the film stress of external load, E is the elastic modulus, y is the opening displacement, a x And x is the position of any point of the crack, and the origin of coordinates is the center position of the crack length.
3. The method for measuring a crack tip stress intensity factor as claimed in claim 1, wherein in the step S2, the stress intensity factor formula is used in the deriving
And a crack opening displacement formula, and determining a relative relation between the stress intensity factor and the opening displacement at any position: />
Wherein K is I As a crack tip stress intensity factor, deltau measured in this formula is near the crack maximum opening displacement and far from the crack tip.
4. The method according to claim 1, wherein in step S3, the effect of the boundary effect of the model is analyzed by finite element numerical simulation using a center-containing penetrating crack plate subjected to uniform tensile load as a subject:
the formula applies to a finite flat model in the range of a/w=0.1 to 0.667, where W is the half-width of the model.
5. The method for measuring a crack tip stress intensity factor as claimed in claim 1, wherein the step S5 comprises the following three steps:
the first step, arranging four measuring points to obtain corresponding data;
step two, carrying out a crack half-length formula, and determining crack half-lengths a at the left end and the right end;
thirdly, the stress intensity factors K of the left and right tips of the crack are determined by substituting the stress intensity factors into a stress intensity factor formula I Values.
6. The method according to claim 5, wherein for a flat plate model with a center penetration crack subjected to a tensile load, 4 measuring points are first arranged, two of which (a x1 ，Δu 1 ) And (a) x2 ，Δu 2 ) The other two points are deviated to one side and the other two points are deviated to the other side, and the corresponding crack half length a is respectively determined according to the values of the two measuring points L And a R The method comprises the steps of carrying out a first treatment on the surface of the Then according to the opening displacement value Deltau measured on each side i Corresponding a xi And length of a, combine:
the stress intensity factor value of each side of the tip is estimated, wherein i is an integer value from 1 to 4.
7. The method of claim 1, wherein the crack tip stress intensity factor is determined to have an elliptical shape using a crack opening displacement formula.
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| CN103984860A (en) * | 2014-05-13 | 2014-08-13 | 大连理工大学 | Method for estimating stress intensity factors of surface cracks on typical welding structure of ship body |
| CN104390860A (en) * | 2014-11-27 | 2015-03-04 | 西安交通大学 | Determination method for failure parameters of materials with complex defects |
| CN105352433A (en) * | 2015-10-23 | 2016-02-24 | 武汉理工大学 | Device and method for measuring surface crack depth and shape of hull typical welding structure |
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| CN111651924B (en) * | 2020-06-04 | 2022-05-10 | 北京航空航天大学 | Weight function-based surface crack stress intensity factor database establishment method |
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| CN103984860A (en) * | 2014-05-13 | 2014-08-13 | 大连理工大学 | Method for estimating stress intensity factors of surface cracks on typical welding structure of ship body |
| CN104390860A (en) * | 2014-11-27 | 2015-03-04 | 西安交通大学 | Determination method for failure parameters of materials with complex defects |
| CN105352433A (en) * | 2015-10-23 | 2016-02-24 | 武汉理工大学 | Device and method for measuring surface crack depth and shape of hull typical welding structure |
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