CN117494482B - Calculation method of high-pressure thick-wall spherical shell outer wall crack stress intensity factor - 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 a crack stress intensity factor of the outer wall of a high-pressure thick-wall spherical shell. The invention comprises the following steps: determining structural parameters, crack shape parameters and load working conditions of the high-pressure thick-wall spherical shell; obtaining the stress vertical to the plane where the crack of the outer wall of the high-pressure thick-wall spherical shell is located; calculating a reference fitting coefficient and an actual fitting coefficient; calculation of the shape factor and stress intensity factor at the deepest point of the outer wall crack and/or at the free surface is performed. The invention realizes the simple and quick calculation requirement of the stress intensity factor at the deepest point of the crack on the outer wall surface of the container and/or at the free surface under the working condition that the container synchronously bears the internal and external pressure load, and can meet the use requirement of the current mainstream high-pressure thick-wall spherical shell calculation occasion.
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 a crack stress intensity factor of the outer wall of a high-pressure thick-wall spherical shell with a diameter ratio of 1.2 to 2.0.
Background
Spherical shell refers to spherical shell, and mainly comprises spherical sealing heads, spherical containers and the like in the application field of pressure containers. Compared with a cylindrical shell, the spherical shell has two main characteristics: (1) the stress of the spherical shell in all directions is equal and is only half of the hoop stress of the cylindrical shell with the same diameter and the same wall thickness, and the calculated wall thickness of the spherical shell can be thinned to half of the wall thickness of the cylindrical shell with the same diameter; (2) at the same volume, the surface area of the spherical shell is the smallest. The two characteristics also make the design weight of the spherical shell be the lightest under the same working pressure and volume, so the spherical shell is mostly used in the design scheme of the high-volume high-pressure even ultra-high-pressure container.
The thick-wall spherical shell is generally formed by hot stamping of a steel plate or a forging plate special for a pressure vessel, and the material performance is recovered through multiple heat treatment processes; the intermediate process causes the workpiece to undergo multiple plastic deformations and generate harmful residual stresses, which all cause the spherical shell to easily generate tiny surface crack defects during the manufacturing and using operation and further spread to the outer wall, thereby causing the pressure vessel to crack and fail. Spherical shell outer wall surface cracks, similar to spherical shell inner wall surface cracks, are generally considered semi-elliptical. From the point of view of damage tolerance of the pressure vessel, it is necessary to accurately calculate the stress intensity factor of the crack front, especially at the deepest point of the crack and at the free surface, since it is a key parameter for crack-containing pressure vessel residual strength assessment and residual life prediction based on crack propagation. The calculation method of the crack tip stress intensity factor mainly comprises a mathematical analysis method, a finite element method, a boundary configuration method, a photoelastic method and the like, and most students aiming at various cracks currently use the finite element method. The finite element numerical calculation method needs to model, load and calculate a crack-containing structure, has very large workload, is greatly influenced by finite element grids, and is not suitable for the engineering field.
For typical cracks in high pressure vessels, the optional appendix D in ASME BPVC. VIII.3-2021, another rule of construction for high pressure vessels, and appendix F in GB/T34019-2017, ultra high pressure vessels, are both mentioned, both sets of criteria have detailed calculation steps for type A cracks (cylinder outer wall shaft-radial cracks). For cracks on the outer wall of the thick-wall spherical shell, reference can also be made to the calculation method of the A-type crack, namely: (1) the elastic analysis obtains stress distribution data perpendicular to the plane of the crack; (2) performing related cubic polynomial fitting on the stress distribution data, and solving fitting coefficients; (3) the stress intensity factor at the deepest point of the crack and at the free surface is derived from the actual shape of the crack based on the stress intensity factor coefficients given in the table. Therefore, the key point of the calculation of the stress intensity factor of the crack of the outer wall of the high-pressure thick-wall spherical shell is that the third-order polynomial fitting coefficient related to the stress distribution data along the thickness direction of the spherical shell is solved.
However, on the one hand, in the elastography process, mathematical deductions or computational analysis with ANSYS are required; in the process of solving the cubic polynomial fitting coefficient, special mathematical analysis software such as Maple, MATLAB, math CAD, matheca and the like is used for carrying out least square method solving. It follows that these calculation processes are too complex and are not suitable for the rapid and compact calculation requirements in engineering. On the other hand, the existing calculation method generally only considers the working condition that the container bears the internal pressure load, but in actual engineering, the container can bear the internal and external pressure load or bear the external pressure load, such as a spherical container or a spherical sealing head in a deep sea environment; for this special situation, the prior art is insufficient, and needs to be solved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for calculating the crack stress intensity factor of the outer wall of the high-pressure thick-wall spherical shell; the invention realizes the simple and quick calculation requirement of the stress intensity factor at the deepest point of the crack on the outer wall surface of the container and/or at the free surface under the working condition that the container synchronously bears the internal and external pressure load, and can meet the use requirement of the current mainstream high-pressure thick-wall spherical shell calculation occasion.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for calculating the crack stress intensity factor of the outer wall of the high-pressure thick-wall spherical shell is characterized by comprising the following steps of:
1) Determining structural parameters, crack shape parameters and load working conditions of the high-pressure thick-wall spherical shell;
2) Fitting according to the following formula to obtain a plane vertical to the crack of the outer wall of the high-pressure thick-wall spherical shellStress of (2)：
Wherein:
A i the' is the reference fitting coefficient,iis an integer of 0 to less than or equal toi≤3：
xThe distance measured from the free surface of the crack is variable inmmAnd is less than or equal to 0 percentx≤t；
tIs the thickness of the spherical shell, unitmm；
3) Calculating a reference fitting coefficient:
for the diameter ratioKA high-pressure thick-wall spherical shell between 1.2 and 2.0, and a reference fitting coefficient is calculated by the following formulaA i ′：
Wherein:
p i is the internal pressure load, unitMPa；
p o For external pressure load, unitMPa；
4) Calculating the actual fitting coefficient under the outer wall crack shape according to the following formulaA i ：
Wherein:
ais the depth of crackmm；
5) Calculating a shape factor at the deepest point of the outer wall crack and/or at the free surface;
6) The calculation of the stress intensity factor at the deepest point of the outer wall crack and/or at the free surface is performed.
Preferably, the shape factor of the outer wall crack in step 5)QThe method is characterized by comprising the following steps:
wherein:
ais the depth of crackmm；
Is the crack length, unitmm；
q y Is a plastic correction coefficient;
to design the yield strength of a material at temperature, unitsMPa；
G 0 ～G 3 Are coefficients.
Preferably, the stress intensity factor at the deepest point of the outer wall crack and/or at the free surface in step 6)K I The method is obtained by the following formula:
preferably, in step 1), the structural parameters of the high-pressure thick-wall spherical shell include: outer radiusr o Inner radiusr i Using materials; the shape parameters of the crack include: depth of crackaCrack lengthlThe method comprises the steps of carrying out a first treatment on the surface of the The load conditions include: internal pressure loadp i External pressure loadp o Design temperature, and determining yield strength of the material used at the design temperature。
The invention has the beneficial effects that:
1. the calculation method is quick and simple.
The calculation method provided by the invention can obtain the calculation result without the help of finite element calculation software, professional mathematical analysis software and the like; the whole calculation process is quick and simple, the calculation result has high accuracy, and the application calculation in engineering is greatly facilitated.
2. The load conditions are considered comprehensively.
The calculation method provided by the invention considers the working condition that the inner wall and the outer wall of the ultrahigh pressure container bear pressure load, and improves the applicability in engineering. In addition, the diameter ratio of most of high-pressure thick-wall spherical shells is between 1.2 and 2.0 at present, namely, the invention can meet the calculation requirements of most of high-pressure thick-wall spherical shells, and has the advantages of comprehensive consideration of load working conditions and wide application range.
Drawings
FIG. 1 is a computational flow diagram of the present invention;
FIG. 2 is a schematic illustration of the appearance of crack in the outer wall and the stressed structure of a thick-walled spherical shell subjected to compressive loading for both the inner and outer walls;
fig. 3 is a graph comparing the fitted curve with the original data in example 1.
FIG. 4 is a graph comparing the calculated stress intensity factors at the deepest point of a crack and at the free surface using the method of the present invention with the conventional complex method in example 1.
Fig. 5 is a graph comparing the fitted curve with the original data in example 2.
FIG. 6 is a graph comparing the calculated stress intensity factors at the deepest point of a crack and at the free surface using the method of the present invention with the conventional complex 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 fig. 1-6:
for the high-pressure thick-wall spherical shell with the inner wall and the outer wall bearing pressure load, the stress distribution function perpendicular to the plane of the crack of the outer wall can be obtained by mathematical derivation, and the following stress distribution function formula is obtained:
wherein:
is the stress perpendicular to the plane of the crack of the outer wall of the high-pressure thick-wall spherical shellMPa；p i Is the internal pressure load, unitMPa；p o For external pressure load, unitMPa；r i Is of inner radius, unitmm；r o Is of outer radius, unitmm；xDistance, variable, unit measured for crack free surfacemm；tIs the wall thickness of the spherical shell, unitmm. As can be seen from the above functional formula, asxIncrease in value, stress value->Will decrease with it.
Based on the method, for the crack of the outer wall of the thick-wall spherical shell, which is usually a semi-elliptic crack, the stress intensity factors at the deepest point and the free surface are simultaneously obtained; of course, the actual operation can be selected according to the situation.
Referring to fig. 1 to 2, the actual steps of the present invention are as follows:
1) Determining structural parameters of the high-pressure thick-wall spherical shell, comprising: outer radiusr o Inner radiusr i Using materials; measuring a shape parameter of an outer wall crack, comprising: depth of crackaCrack lengthThe method comprises the steps of carrying out a first treatment on the surface of the Determining load conditions, comprising: internal pressure loadp i External pressure loadp o Design temperature, etc.; searching performance parameters of the used material to obtain yield strength of the used material at design temperature。
2) The stress distribution perpendicular to the plane of the crack is fitted as follows:
3) Calculating relevant fitting coefficients:
for the diameter ratioK(ratio of outer diameter to inner diameter) between 1.2 and 2.0, the required fitting coefficient is calculated by the following formula, namely, the reference fitting coefficientA i ', includeA 0 ′、A 1 ′、A 2 ′、A 3 ′：
Wherein:
p i is the internal pressure load, unitMPa；
p o For external pressure load, unitMPa；
4) Calculating another fitting coefficient under the outer wall crack shape, namely the actual fitting coefficientA i ：
Wherein:
ais the depth of crackmm；
5) The shape coefficients at the deepest point and the free surface of the crack of the outer wall are calculated respectively by the following methodQ：
Wherein:
ais crack depth, constant, unitmm；
Is crack length, constant, unitmm；
q y Is a plastic correction coefficient;
to design the yield strength of a material at temperature, unitsMPa。
6) Calculating stress intensity factors at the deepest point of the outer wall crack and at the free surface byK I ：
Wherein:
G 0 ～G 3 the values of (2) can be obtained by looking up a table; specifically, according to whether the target is the deepest point of the crack of the outer wall or the free surface of the crack of the outer wall, the values are respectively taken according to the tables F.1 and F.2 in GB/T34019-2017 ultra-high pressure container, and the values are given by the tables, and the values are interpolated, so that a conventional table lookup is adopted, and the description is omitted.
Example 1:
assuming that a certain high-pressure container is of a round cylinder body and spherical end socket structure, bearing internal pressure loadp i 98MPa, external pressure loadp o 10MPa, the design temperature is normal temperature, and the selected material is Q345R; inner radius of spherical seal headr i 500mm, outer radius ofr o Measuring the crack depth of the outer wall of the spherical sealing head to 750mma10mm, crack lengthIs 3 (3)0mm。
The calculation method provided by the invention is used for calculating stress intensity factors at the deepest point of the outer wall crack and at the free surface, and comprises the following specific implementation steps:
1. obtaining the diameter ratio of the cylinder body according to the outer radius and the inner radius of the spherical sealing headKA value of 1.5, meets the requirements in the present invention.
2. Calculation ofTo get->The method comprises the following steps of: 45.58, 20.85, 0.61, 22.54. The cubic polynomial fitting curve drawn according to the obtained fitting coefficient is shown in figure 3, the fitting curve is basically coincident with the trend of the original stress distribution data, and the coefficient of the fitting curve can be determinedR 2 The (statistic for measuring the goodness of fit) is 0.9999, which shows that the fitting precision is high and the characterization effect is good.
3. Calculation ofA i To obtainA 0 、A 1 、A 2 、A 3 The method comprises the following steps of: 45.58, 0.834, 9.76X10 −4 、0.0014。
4. Calculating the shape factor at the deepest point of the crack and at the free surfaceQ1.7446, 1.7457, respectively.
5. Calculating stress intensity factor at the deepest point of crack and at the free surfaceK I 8.05 MPa.m respectively 1/2 、7.09MPa·m 1/2 。
In fact, when the crack depth-to-length ratioWhen considered according to 1/3, the calculation results of the stress intensity factors at the deepest points of cracks and at the free surface of the outer wall of the high-pressure thick-wall spherical shell can be easily obtained at each crack depth. The stress intensity factor values calculated by the method of the invention are compared with those calculated by a general complex method, as shown in fig. 4; FIG. 4 shows the calculation of the stress intensity factor, either at the crack deepest point or at the free surface, for two methodsThe results are very consistent, with a relative error of no more than 0.5% between the two methods.
In fig. 4, the right triangular broken line indicates the relative error between the two methods at the deepest point, and the left triangular broken line indicates the relative error between the two methods at the free surface; in view of the size of the drawing, a simplified text processing is shown in fig. 4, and is described in detail herein.
Example 1 shows that:
the calculation method provided by the invention can obtain the calculation result according to the calculation formula without the help of other finite element calculation software, professional mathematical analysis software and the like, is simple and quick, and is suitable for application in engineering; the relative error between the calculation method and the result calculated by the general complex method is small, which indicates that the method has high accuracy and can be applied to engineering.
Example 2:
assuming that a certain high-pressure container is of a round cylinder body and spherical end socket structure, bearing internal pressure loadp i 98MPa, external pressure loadp o 10MPa, the design temperature is normal temperature, and the selected material is Q345R; inner radius of spherical seal headr i 500mm, outer radius ofr o Measuring the crack depth of the outer wall of the spherical sealing head to 1000mma20mm, crack lengthl60mm.
The calculation method provided by the invention is used for calculating stress intensity factors at the deepest point of the outer wall crack and at the free surface, and comprises the following specific implementation steps:
1. obtaining the diameter ratio of the cylinder body according to the outer radius and the inner radius of the spherical sealing headKThe value is 2, which meets the requirements in the invention.
2. Calculation ofTo get->The method comprises the following steps of: 8.86, 18.01, -32.25, 58.24. A third-order polynomial fitting curve drawn according to the calculated fitting coefficient is shown as a figure5, the fitted curve is basically coincident with the trend of the original stress distribution data, and the determinable coefficient of the fitted curveR 2 The (statistic for measuring the goodness of fit) is 0.9985, which shows that the fitting precision is high and the characterization effect is good.
3. Calculation ofA i To obtainA 0 、A 1 、A 2 、A 3 The method comprises the following steps of: 8.857, 0.720, -0.0516, 0.00373.
4. Calculating the shape factor at the deepest point of the crack and at the free surfaceQ1.7490, 1.7492, respectively.
5. Calculating stress intensity factor at the deepest point of crack and at the free surfaceK I Respectively 3.91 MPa.m 1/2 、3.41MPa·m 1/2 。
Also, when the crack depth-to-length ratioWhen considered according to 1/3, the calculation results of the stress intensity factors at the deepest points of the cracks of the outer wall of the high-pressure thick-wall spherical shell and at the free surface at each crack depth can be obtained easily. The stress intensity factor values calculated by the method of the present invention are compared with those calculated by a general complex method, as shown in fig. 6. Fig. 6 also shows that the calculation results of the two methods are very consistent whether the stress intensity factors are at the deepest point of the crack or at the free surface, and the relative error between the two methods is not more than 3%, which also proves the simplicity, rapidity and accuracy of the calculation of the invention, and the calculation method can be suitable for engineering application.
Similarly, in fig. 6, the right triangular broken line indicates the relative error between the two methods at the deepest point, and the left triangular broken line indicates the relative error between the two methods at the free surface; in view of the size of the drawing, a simplified text processing is shown in fig. 6, and is described in detail herein.
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.
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 (2)
1. The method for calculating the crack stress intensity factor of the outer wall of the high-pressure thick-wall spherical shell is characterized by comprising the following steps of:
1) Determining structural parameters, crack shape parameters and load working conditions of the high-pressure thick-wall spherical shell;
2) Fitting according to the following formula to obtain the stress vertical to the plane of the crack of the outer wall of the high-pressure thick-wall spherical shell
Wherein:
A i the' is the reference fitting coefficient,iis an integer of 0 to less than or equal toi≤3；
xThe distance measured from the free surface of the crack is variable inmmAnd is less than or equal to 0 percentx≤t；
tIs the thickness of the spherical shell, unitmm；
3) Calculating a reference fitting coefficient:
for the diameter ratioKA high-pressure thick-wall spherical shell between 1.2 and 2.0, and a reference fitting coefficient is calculated by the following formulaA i ′：
Wherein:
p i is the internal pressure load, unitMPa；
p o For external pressure load, unitMPa；
4) Calculating the actual fitting coefficient under the outer wall crack shape according to the following formulaA i ：
Wherein:
ais the depth of crackmm；
5) Calculating a shape factor at the deepest point of the outer wall crack and/or at the free surface;
6) Calculating stress intensity factors at the deepest point and/or the free surface of the outer wall crack;
shape factor of outer wall crack in step 5)QThe method is characterized by comprising the following steps:
wherein:
ais the depth of crackmm；
lIs the crack length, unitmm；
q y Is a plastic correction coefficient;
to design the yield strength of a material at temperature, unitsMPa；
G 0 ～G 3 Are all coefficients;
stress intensity factor at the deepest point of the outer wall crack and/or at the free surface in step 6)K I By passing throughThe following formula is used for obtaining:
。
2. the method for calculating the crack stress intensity factor of the outer wall of the high-pressure thick-wall spherical shell according to claim 1, wherein the method comprises the following steps of: in the step 1), the structural parameters of the high-pressure thick-wall spherical shell comprise: outer radiusr o Inner radiusr i Using materials; the shape parameters of the crack include: depth of crackaCrack lengthlThe method comprises the steps of carrying out a first treatment on the surface of the The load conditions include: internal pressure loadp i External pressure loadp o Design temperature, and determining yield strength of the material used at the design temperature。
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