CN117057166A - Calculation method of stress intensity factor at crack free surface of stress concentration part - Google Patents
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Abstract
The invention belongs to the field of design development treatment and failure evaluation of high-pressure and ultrahigh-pressure containers, and particularly relates to a calculation method of stress intensity factors at the free surfaces of cracks at stress concentration positions. The invention comprises the following steps: according to the container structure and the load parameters, carrying out elastic stress analysis on the stress concentration part; according to the analysis result, extracting stress distribution data perpendicular to the plane of the crack; discretizing the stress distribution data to obtain discretized data, and respectively solving polynomials for each piece of discretized data to obtain a stress distribution function of the corresponding piece of discretized data; calculating a crack shape coefficient; calculation of stress intensity factor at the crack free surface was performed. The fitting accuracy of the stress distribution data is effectively improved, and the accuracy of the calculation result is further ensured; meanwhile, the calculation method is very efficient and simple, and the practicability in engineering calculation is high.
Description
Technical Field
The invention belongs to the field of design development treatment and failure evaluation of high-pressure and ultrahigh-pressure containers, and particularly relates to a calculation method of stress intensity factors at the free surfaces of cracks at stress concentration positions.
Background
The stress concentration part of the high-pressure and ultra-high-pressure container is the most easily damaged part in the manufacturing and using operation process, and is the most easily surface crack defect-generating area, and is usually expressed as a semi-elliptic or semicircular crack; open hole cracks (type B) and blind bottom cracks (type D), which are well-described in GB/T34019-2017, ultra-high pressure vessels, are typical cracks that occur in such stress concentration sites. In the process of design development treatment and failure assessment of high-pressure and ultrahigh-pressure containers, the stress intensity factor of the crack tip needs to be accurately calculated, because the stress intensity factor is an indispensable key parameter in the assessment of the residual intensity of the crack-containing pressure container and the calculation of the residual life of crack propagation; especially for certain specific cracks, the evaluation process is more focused on the values of the stress intensity factors at the free surface and at the deepest point. Therefore, in practical engineering application, it is important to find a simple calculation method of stress intensity factors at one of the free surface and the deepest point of the crack at the stress concentration part, which can ensure calculation accuracy.
Currently, the calculation methods of stress intensity factors of crack tips mainly include a mathematical analysis method, a finite element method, a boundary configuration method, a photoelastic method, and the like, wherein the finite element method is used in most cases. For the calculation of typical crack stress intensity factors for high and ultra-high pressure vessels, the optional appendix D in ASME BPVC, VIII.3-2021, alternativeRules for Construction of High Pressure Vessels and appendix F in GB 34019-2017, ultra-high pressure vessels, are mentioned, and the detailed calculation steps of type A cracks (barrel inner wall shaft-radial cracks) are also given by two common industry standards, namely: after the stress distribution data are fitted, corresponding stress intensity factor values are calculated according to the fitting coefficients, the crack shapes and the like. However, for the open hole cracks (type B) and blind bottom cracks (type D), the criteria are only mentioned that can be found with reference to the type a crack calculation method, and no specific calculation procedure is seen.
However, the stress distribution at the stress concentration portion of the actual high-pressure and ultra-high-pressure containers is characterized by: the stress gradient is changed greatly, and the attenuation is changed from quick to slow, namely, the stress initially tends to be rapidly reduced along with the increase of the distance measured from the surface of the crack, and then tends to be steadily reduced after a certain distance is reached. Therefore, if the conventional a-type crack calculation method is inertly adopted, due to the influence of the stress gradient factor which greatly changes, the stress distribution data cannot be properly fitted, or the fitted curve is far from the actual data, so that the calculation result of the stress intensity factor at the free surface of the stress concentration part is inevitably greatly deviated from the actual value, and the calculation result cannot be used as an accurate criterion in the evaluation process. Of course, the numerical analysis method can be replaced to perform special fracture mechanics analysis on the crack-containing structure, but the calculation process is complicated, the convergence difficulty is high, and the calculation cost is high, which is one of the main factors of the fracture mechanics analysis rarely adopted at present. Therefore, whether a method for calculating the stress intensity factor at the free surface of the crack at the stress concentration part can be developed is a technical problem to be solved in recent years in the field.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for calculating the stress intensity factor at the free surface of the crack at the stress concentration part, which effectively improves the fitting precision of stress distribution data and further ensures the accuracy of calculation results; meanwhile, the calculation method is very efficient and simple, and the practicability in engineering calculation is high.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for calculating the stress intensity factor at the crack free surface of the stress concentration part is characterized by comprising the following steps:
s1, analyzing elastic stress of a stress concentration part according to a container structure and load parameters;
s2, extracting stress distribution data perpendicular to a plane where the crack is located according to an analysis result;
s3, discretizing the stress distribution data to obtain discretized data, and respectively solving polynomials for each piece of discretized data to obtain a stress distribution function of the corresponding piece of discretized data;
s4, calculating a crack shape coefficient;
s5, calculating stress intensity factors at the free surfaces of the cracks.
Preferably, in step S3, each three sets of stress distribution data adjacent to each other form a piece of discretized data, and each adjacent piece of discretized data is connected to each other to ensure continuity;
the method specifically comprises the following substeps:
s31, obtaining the first according to the following formulaiPolynomial coefficients of segment discretized dataa i0 、a i1 Anda i2 ：
Wherein:
for the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
S32, carrying out the following stepsiStress distribution function of segment discretized datay i (x)Is solved by (1):
wherein:
xthe distance measured for the crack free surface, i.e. depth, is a variable,units ofmm；
nIs the total number of discretized segments.
Preferably, step S5 comprises the sub-steps of:
s51, carrying out stress dividing intensity factorsK I,0 ～K I,4 Is calculated by (1):
wherein:
elliptical crack depth value, constant, unitmm；
S52, calculating stress intensity factors at the free surfaces of the cracks according to the following formula：
Wherein:
p i is the internal pressure of the container, unitMPa；
QIs a crack shape factor;
M 1B ～M 4B all are intermediate coefficients, and the calculation formula is as follows:
G 0 ～G 3 all are coefficients at the free surface of the crack, values are taken according to table F.2 in GB 34019-2017 ultra high pressure vessel, and interpolation is carried out between the values given in table F.2.
Preferably, in step S4, the crack shape coefficient is calculated byQ：
Wherein:
the length value of the elliptical crack is in mm;
is the ratio of the elliptical crack depth value to the elliptical crack length value.
Preferably, in step S1, when the elastic stress analysis is performed on the stress concentration portion, the line elastic stress analysis is performed by using a numerical calculation method through ANSYS analysis software.
Preferably, in step S2, a path is defined along the crack propagation direction by ANSYS analysis software, and stress distribution data along the path is extracted, so as to obtain the required stress distribution data perpendicular to the plane in which the crack is located.
The invention has the beneficial effects that:
1) The accuracy of the calculation result is high. The calculation method provided by the invention is to perform multi-section discretization on stress distribution data of a stress concentration part, respectively solve the stress distribution data, perform high-precision characterization by using the multi-section discretization data, and finally calculate the stress intensity factor value at the free surface of the crack. Therefore, the fitting precision of stress distribution data is ensured, and the defect of insufficient calculation precision of the existing method is overcome.
2) The calculation method is quick and simple. According to the calculation method provided by the invention, a numerical analysis method is not needed to carry out special fracture mechanics analysis on the crack-containing structure, and algebraic calculation is only carried out on the basis of elastic stress analysis. The calculation process is simple and quick, and the practicability in engineering calculation is also ensured.
Drawings
FIG. 1 is a calculation flow chart of example 1;
FIG. 2 is a graph showing the results of analysis of elastic stress at the blind bottom of the ultra-high pressure vessel in example 1;
FIG. 3 is a schematic representation of the path defined at the plane of the blind undercut in example 1;
FIG. 4 is a graph showing the fit of stress distribution data of the present invention to conventional method in example 1;
FIG. 5 is a graph showing the comparison of the stress intensity factor calculation results of the blind bottom crack free surface according to the present invention with those of the conventional method in example 1;
FIG. 6 is a view showing a path defined at a plane where a crack is located in example 2;
FIG. 7 is a graph showing the fit of stress distribution data of the present invention to conventional method in example 2;
FIG. 8 is a graph showing the comparison of the results of calculation of the stress intensity factor at the crack free surface according to the present invention with the conventional method in example 2.
Detailed Description
For ease of understanding, the specific structure and operation of the present invention will be further described herein with reference to FIGS. 1-8:
it should be noted that, to reduce the leakage path of the container and to reduce the uncertainty of the installation process, one end of the small-sized high-pressure and ultra-high-pressure containers are often designed to be a blind bottom structure. For high pressure and ultra-high pressure containers, the blind bottom has a stress concentration phenomenon, and the stress concentration coefficient is very high, so that the blind bottom is the area most prone to initiate surface cracks, and the cracks are usually semi-elliptical initially and mainly initiated and further extended from the blind bottom corners. In the field of design development and failure assessment, for cracks at such blind bottom sites, we are most concerned with at the free surfaceIs a stress intensity factor of (c). Because the stress intensity factor at the free surface of such a crack will grow rapidly as the crack propagates, the free surface will easily enter the destabilization propagation stage, tearing into a full circle of annular crack, resulting in the risk of the container end breaking free entirely, with serious consequences of failure.
For this purpose, as shown in fig. 1, the invention is implemented as follows:
1. and (3) carrying out elastic stress analysis on the blind bottom according to the structure and the running load conditions of the high-pressure and ultrahigh-pressure containers.
In specific operation, the blind bottom position stress distribution of the high-pressure and ultrahigh-pressure containers is complex and cannot be directly obtained by an analytic method, and the line elastic stress analysis can be carried out by utilizing ANSYS or other analysis software and adopting a numerical calculation method. Of course, the analysis result needs to be subjected to steps of model establishment, grid division, loading solution and the like according to the structure and the load of the container, and the steps are conventional processes and are not repeated.
2. And extracting stress distribution data perpendicular to the plane of the crack according to the result of the stress analysis.
In a specific operation, a path can be defined along the crack propagation direction in ANSYS analysis software, and the stress distribution data along the path can be extracted, so that the required stress distribution data perpendicular to the plane of the crack can be obtained.
3. Measuring shape parameters of blind bottom-level cracks, comprising: elliptical crack depth values and elliptical crack length values. And carrying out multi-section discretization on the stress distribution data, and solving each section of discretization data. And each section of discretization data is respectively subjected to polynomial solving, and numerical continuity is kept between each section of functions without interruption.
More specifically, the method comprises the following steps:
3.1, considering the simplicity of the calculation process and the accuracy of the calculation result, the step preferably carries out the second polynomial solving, namely, each three groups of stress distribution data are segmented, and each segment of discretized data is connected end to end, so that the continuity between each segment of data can be ensured, and the method comprises the following steps:
1) The following procedure was followediStress distribution function of segment discretized datay i (x)Is solved by (1):
wherein:
xthe distance measured for the crack free surface, i.e. depth, is a variable,units ofmm；
nIs the total number of discretized segments.
2) First, theiPolynomial coefficients of segment discretized dataa i0 、a i1 、a i2 Calculated as follows:
wherein:
is the>Stress values corresponding to the groups, unitMPa；
Is the>Stress values corresponding to the groups, unitMPa；
Is the>Stress values corresponding to the groups, unitMPa；
Is the>Depth values corresponding to groups, unitmm；
Is the>Depth values corresponding to groups, unitmm；
Is the>Depth values corresponding to groups, unitmm。
4. Calculating crack shape factor as followsQ：
Wherein:
the depth value of the elliptical crack is constant under the crack of the invention, and the unit is thatmm；
Is oval crack lengthValue, unitmm；
Is the ratio of the elliptical crack depth value to the elliptical crack length value.
5. The stress intensity factor at the free surface of the crack is calculated as follows：
Wherein:
p i is the internal pressure of the container, unitMPa；
QIs a crack shape factor;
K I,0 ～K I,4 all are the stress intensity factors, and the calculation process is as follows:
M 1B ～M 4B all are intermediate coefficients, and the calculation formula is as follows:
G 0 ～G 3 all are coefficients at the free surface of the crack, values are taken according to table F.2 in GB 34019-2017 ultra high pressure vessel, and interpolation is carried out between the values given in table F.2.
Example 1:
assume that a certain ultrahigh pressure container is heldThe internal pressure is 200MPa and the temperature is normal temperature; the inner radius of the cylinder body is 150mm, the outer radius is 250mm, and the blind bottom thickness is 140mm. An elliptical crack is arranged at the blind bottom, and the depth value of the elliptical crack16mm oval crack length value +.>48mm.
The calculation method provided by the invention is used for calculating the stress intensity factor at the free surface of the crack, and the specific implementation steps comprise:
1. and (5) carrying out elastic stress analysis on the blind bottom according to the consideration of the axisymmetry problem.
The stress analysis results obtained by the steps of model establishment, grid division, loading solution and the like through ANSYS software are shown in figure 2.
2. According to the defined path of the plane of the crack, the stress distribution data along the path, i.e. the stress distribution data perpendicular to the plane of the crack, can be extracted, and the defined path is shown in fig. 3.
3. According to the flow of the invention, the data are discretized in multiple sections, the quadratic polynomial solution is respectively carried out according to each section of discretized data, and the finally solved function drawing result is shown in fig. 4.
As is apparent from fig. 4, if the stress distribution data is fitted by a polynomial of three times according to the conventional method, the fitting result has a larger difference from the original data, and the fitting effect is poor; the solution value and the original data can be corresponding one by one according to the invention, and the characterization precision is very high.
4. Calculating the crack shape coefficientQ=1.7496。
5. Calculating the stress intensity factor at the free surface of the crack。
Of course, the stress intensity factor values at the free surface at each crack depth can also be solved continuously according to the flow of the invention. Considering that the ratio of the oval crack depth value to the oval crack length value is 1/3, the result obtained by solving the method according to the invention and the traditional method is shown in fig. 5.
As can be seen from FIG. 5, the calculated result of the present invention has a larger difference from the calculated result of the conventional method, and the relative error is nearly 30% at maximum.
Example 1 shows that, by applying the calculation method provided by the invention, the result represented by the piecewise function solution formed by discretization of data is obviously more accurate than the calculation result fitted by the traditional method, which also necessarily leads to more accurate calculation results of the stress intensity factors at the subsequent free surfaces. By applying the calculation method provided by the invention, the numerical analysis method is not needed to carry out special fracture mechanics analysis on the open-pore structure containing the cracks, the calculation result can be obtained by carrying out algebraic operation on the basis of elastic analysis, and the method is simple and quick and is suitable for application in engineering.
This example 1 demonstrates the superiority of the present invention in blind bottom-bit calculations where the stress distribution is complex.
Example 2:
the blind bottom stress distribution of the high-pressure and ultrahigh-pressure containers is complex, so that the traditional method has poor force. However, it should be recognized that, generally, for stress distribution data of a barrel portion, the third order polynomial fitting result in the conventional method can well characterize the stress distribution perpendicular to the plane of the crack, and the accurate stress intensity factor can be obtained by the conventional method. Namely, for stress distribution data of the barrel body part, the accurate stress intensity factor value at the free surface of the crack can be obtained by the traditional method.
In view of this, a comparison of the conventional method with the calculation result of the present invention is performed here by taking a set of stress distribution data along the wall thickness direction of the cylinder as an example, so as to verify the reliability of the calculation flow of the present invention. Note that the object calculated here is not a blind bottom portion where the stress distribution is complex, but a cylindrical body portion where the stress distribution is gentle:
assuming that the internal pressure born by a certain ultrahigh pressure container is 200MPa and the temperature is normal temperature; the inner radius of the cylinder body is 150mm, the outer radius is 250mm, and elliptical cracks exist along the wall thickness direction.
The method comprises the following specific steps:
1. by means of stress analysis, a path is defined according to the plane in which the crack is located, and stress distribution data along the path, namely, stress distribution data perpendicular to the plane in which the crack is located, can be extracted, wherein the defined path is shown in fig. 6.
2. According to the stress distribution data, multi-section discretization of the data is carried out according to the flow of the invention, secondary polynomial solving is respectively carried out according to the discretization data of each section, and the finally solved function drawing result is shown in figure 7.
As is apparent from fig. 7, the calculation result of the present invention almost coincides with the calculation result of the conventional method, and the degree of adhesion between the two is extremely high.
3. When considering that the ratio of the elliptical crack depth value to the elliptical crack length value is 1/3, the stress intensity factor value at the free surface under each crack depth is solved by the method and the traditional method, and the result is shown in figure 8.
As is apparent from fig. 8, the calculated result of the present invention almost coincides with the calculated result of the conventional method in terms of the barrel portion in which the stress distribution is gentle, and the relative error is substantially stabilized at about 0%.
Example 2 demonstrates that the computational flow of the present invention has excellent reliability.
It will be understood by those skilled in the art that the present invention is not limited to the details of the foregoing exemplary embodiments, but includes the same or similar manner which may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
The technical sections of the present invention that are not described in detail are known in the art.
Claims (6)
1. The method for calculating the stress intensity factor at the crack free surface of the stress concentration part is characterized by comprising the following steps:
s1, analyzing elastic stress of a stress concentration part according to a container structure and load parameters;
s2, extracting stress distribution data perpendicular to a plane where the crack is located according to an analysis result;
s3, discretizing the stress distribution data to obtain discretized data, and respectively solving polynomials for each piece of discretized data to obtain a stress distribution function of the corresponding piece of discretized data;
s4, calculating a crack shape coefficient;
s5, calculating stress intensity factors at the free surfaces of the cracks.
2. The method of calculating the stress intensity factor at the free surface of the crack at the stress concentration portion according to claim 1, wherein: in the step S3, each three groups of stress distribution data adjacent to each other form a section of discretization data, and each adjacent section of discretization data are connected with each other so as to ensure continuity;
the method specifically comprises the following substeps:
s31, obtaining the first according to the following formulaiPolynomial coefficients of segment discretized dataa i0 、a i1 Anda i2 ：
Wherein:
for the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Stress values corresponding to the groups, unitMPa；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
For the +.sup.th in the stress distribution data extracted in step S2>Depth values corresponding to groups, unitmm；
S32, carrying out the following stepsiStress distribution function of segment discretized datay i (x)Is solved by (1):
wherein:
xthe distance measured for the crack free surface, i.e. depth, is a variable,units ofmm；
nIs the total number of discretized segments.
3. The method of calculating the stress intensity factor at the free surface of the crack at the stress concentration portion according to claim 2, wherein: step S5 comprises the following sub-steps:
s51, carrying out stress dividing intensity factorsK I,0 ～K I,4 Is calculated by (1):
wherein:
elliptical crack depth value, constant, unitmm；
S52, calculating stress intensity factors at the free surfaces of the cracks according to the following formula：
Wherein:
p i is the internal pressure of the container, unitMPa；
QIs a crack shape factor;
M 1B ～M 4B all are intermediate coefficients, and the calculation formula is as follows:
G 0 ～G 3 all are coefficients at the free surface of the crack, values are taken according to table F.2 in GB 34019-2017 ultra high pressure vessel, and interpolation is carried out between the values given in table F.2.
4. A method of calculating a stress intensity factor at a crack free surface at a stress riser as set forth in claim 3, wherein: in step S4, a crack shape factor is calculated as followsQ：
Wherein:
the length value of the elliptical crack is in mm;
is the ratio of the elliptical crack depth value to the elliptical crack length value.
5. The method for calculating the stress intensity factor at the free surface of the crack at the stress concentration portion according to claim 1 or 2 or 3 or 4, wherein: in step S1, when the elastic stress analysis is performed on the stress concentration portion, the line elastic stress analysis is performed by using a numerical calculation method through ANSYS analysis software.
6. The method for calculating the stress intensity factor at the free surface of the crack at the stress concentration portion according to claim 1 or 2 or 3 or 4, wherein: in step S2, defining a path along the crack propagation direction by using ANSYS analysis software, and extracting stress distribution data along the path to obtain the required stress distribution data perpendicular to the plane of the crack.
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| CN118010621A (en) * | 2024-04-09 | 2024-05-10 | 合肥通用机械研究院有限公司 | Method for calculating fatigue extension life of axial and radial crack based on outer wall of cylindrical longitudinal weld |
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| CN117473839B (en) * | 2023-12-26 | 2024-03-15 | 合肥通用机械研究院有限公司 | Calculation method for fatigue life of crack-containing stress concentration part |
| CN118010621A (en) * | 2024-04-09 | 2024-05-10 | 合肥通用机械研究院有限公司 | Method for calculating fatigue extension life of axial and radial crack based on outer wall of cylindrical longitudinal weld |
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