CN117057166A - Calculation method of stress intensity factor at crack free surface of stress concentration part - Google Patents

Abstract

The invention belongs to the field of design, development, processing and failure assessment of high-pressure and ultra-high-pressure vessels, and specifically relates to a method for calculating the stress intensity factor at the free surface of cracks in stress concentration locations. The invention includes: conducting elastic stress analysis on the stress concentration part according to the container structure and load parameters; extracting stress distribution data perpendicular to the plane where the crack is located based on the analysis results; discretizing the stress distribution data to obtain discretized data, The discretized data of each segment is solved with polynomials to obtain the stress distribution function of the discretized data of the corresponding segment; the crack shape coefficient is calculated; and the stress intensity factor at the free surface of the crack is calculated. The invention effectively improves the fitting accuracy of stress distribution data, thereby ensuring the accuracy of calculation results; at the same time, the calculation method is also very efficient and simple, and has high practicability in engineering calculations.

Description

Calculation method of stress intensity factor at the free surface of cracks at stress concentration locations

Technical field

The invention belongs to the field of design, development, processing and failure assessment of high-pressure and ultra-high-pressure vessels, and specifically relates to a method for calculating the stress intensity factor at the free surface of cracks in stress concentration locations.

Background technique

The stress concentration parts of high-pressure and ultra-high-pressure vessels are the places most susceptible to damage during manufacturing and operation, and are also the areas most prone to surface crack defects, which usually appear as semi-elliptical or semi-circular cracks; GB/T The cracks at the opening (type B) and the blind bottom crack (type D) clearly stated in 34019-2017 "Ultra-High Pressure Vessel" are typical cracks that appear in such stress concentration locations. In the design, development and failure assessment process of high-pressure and ultra-high-pressure vessels, it is necessary to accurately calculate the stress intensity factor at the crack tip, because it is indispensable in the residual strength assessment and crack propagation remaining life calculation of cracked pressure vessels. Key parameters; especially for some specific cracks, it is necessary to focus on the stress intensity factor values at the free surface and the deepest point during the assessment process. Therefore, in practical engineering applications, it is particularly important to find a simple and accurate calculation method for the stress intensity factor at one of the crack free surface and the deepest point at the stress concentration location.

At present, the main methods for calculating the stress intensity factor at the crack tip include mathematical analysis method, finite element method, boundary configuration method and photoelastic method, among which the finite element method is the most common. For the calculation of typical crack stress intensity factors of high-pressure and ultra-high pressure vessels, the non-mandatory appendix D in ASME BPVC. Both are mentioned in F. Two common standards in the industry also provide detailed calculation steps for type A cracks (axial-radial cracks on the inner wall of the cylinder), that is: after fitting the stress distribution data, and then according to the simulated Combination coefficient and crack shape, etc., and then calculate the corresponding stress intensity factor value. However, for cracks at openings (type B) and blind bottom cracks (type D), the standard only mentions that they can be calculated by referring to the calculation method for type A cracks, without specifying the calculation process.

However, the stress distribution characteristics of the actual stress concentration parts of high-pressure and ultra-high-pressure vessels are: the stress gradient changes greatly, and the attenuation changes from fast to slow, that is, the stress will initially "decline rapidly" as the distance measured from the crack surface increases. trend, and then show a "steady downward" trend after reaching a certain distance. Therefore, if the traditional A-type crack calculation method is followed inertially, due to the above-mentioned greatly changing stress gradient factors, the stress distribution data often cannot be appropriately fitted, or the fitted curve is far from the actual data. As a result, the calculated result of the stress intensity factor at the free surface of the stress concentration part will inevitably deviate greatly from the actual value, and thus cannot be used as an accurate criterion in the assessment process. Of course, at this time, numerical analysis methods can be used to perform specialized fracture mechanics analysis on structures containing cracks, but the calculation process will be very cumbersome and difficult to converge, resulting in high calculation costs. This is why this type of fracture mechanics analysis is rarely used at present. one of the main reasons. Therefore, whether a method for calculating the stress intensity factor at the crack free surface at the stress concentration location can be developed is a technical problem that needs to be solved urgently in this field in recent years.

Contents of the invention

The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art and provide a method for calculating the stress intensity factor at the crack free surface at the stress concentration location. The present invention effectively improves the fitting accuracy of the stress distribution data, thereby ensuring the accuracy of the calculation results. at the same time, the calculation method is also very efficient and simple, and has high practicability in engineering calculations.

In order to achieve the above objects, the present invention adopts the following technical solutions:

The calculation method of the stress intensity factor at the free surface of the crack at the stress concentration location is characterized by including the following steps:

S1. According to the container structure and load parameters, perform elastic stress analysis on the stress concentration parts;

S2. Based on the analysis results, extract the stress distribution data perpendicular to the plane where the crack is located;

S3. Discretize the stress distribution data to obtain discretized data. Perform polynomial solution for each segment of discretized data to obtain the stress distribution function of the corresponding segment of discretized data;

S4. Calculate the crack shape coefficient;

S5. Calculate the stress intensity factor at the free surface of the crack.

Preferably, in step S3, each three adjacent groups of stress distribution data form a segment of discretized data, and the adjacent segments of discretized data are connected to each other to ensure continuity;

Specifically, it includes the following sub-steps:

S31. Obtain the polynomial coefficients a _{0 i} , a _{1 i} and a _{2 i} of the i -th section of discretized data according to the following formula:

In the formula:

is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

S32. Solve the stress distribution function y _i (x) of the i -th segment of discretized data using the following formula:

In the formula:

x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ;

n is the total number of discretized segments.

Preferably, step S5 includes the following sub-steps:

S51. Calculate the component stress intensity factors K _I,0 ~ K _I,4 :

In the formula:

is the depth value of the elliptical crack, which is a constant and the unit is mm ;

S52. Calculate the stress intensity factor at the free surface of the crack with the following formula :

In the formula:

p _i is the internal pressure of the container, in MPa ;

Q is the crack shape coefficient;

M _1B ~ M _4B are all intermediate coefficients, and the calculation formula is as follows:

G ₀ ~ G ₃ are all coefficients at the free surface of the crack. The values are taken according to Table F.2 in GB 34019-2017 "Ultra-high pressure vessels", and the values given in Table F.2 are interpolated.

Preferably, in step S4, the crack shape coefficient Q is calculated by the following formula:

In the formula:

is the length value of the elliptical crack, in mm;

is the ratio of the elliptical crack depth value to the elliptical crack length value.

Preferably, in step S1, when performing elastic stress analysis on the stress concentration part, ANSYS analysis software is used to perform linear elastic stress analysis using numerical calculation methods.

Preferably, in step S2, ANSYS analysis software is used to define a path along the crack expansion direction, and the stress distribution data along the path is extracted, that is, the required stress distribution data perpendicular to the plane where the crack is located is obtained.

The beneficial effects of the present invention are:

1) The calculation results are highly accurate. The calculation method proposed by the present invention is to perform multi-segment discretization to solve the stress distribution data of the stress concentration part separately, use the multi-segment discretization data to perform high-precision characterization, and then finally calculate the stress intensity factor value at the free surface of the crack. In this way, the fitting accuracy of stress distribution data is ensured, and the shortcomings of insufficient calculation accuracy of existing methods are overcome.

2) The calculation method is fast and concise. The calculation method proposed by the present invention does not require the use of numerical analysis methods to conduct special fracture mechanics analysis on cracked structures, and only performs algebraic calculations based on elastic stress analysis. The calculation process is simple and fast, which also ensures the practicality in engineering calculations.

Description of the drawings

Figure 1 is a calculation flow chart of Embodiment 1;

Figure 2 is a diagram showing the elastic stress analysis results of the blind bottom of the ultra-high pressure vessel in Example 1;

Figure 3 is a path display diagram defined at the plane where the blind bottom crack is located in Embodiment 1;

Figure 4 is a comparison diagram of stress distribution data fitting between the present invention and the traditional method in Example 1;

Figure 5 is a comparison chart of the calculation results of the stress intensity factor at the free surface of the blind bottom crack of the present invention and the traditional method in Example 1;

Figure 6 is a path display diagram defined at the plane where the crack is located in Embodiment 2;

Figure 7 is a comparison diagram of stress distribution data fitting between the present invention and the traditional method in Example 2;

Figure 8 is a comparison chart of the calculation results of the stress intensity factor at the free surface of the crack between the present invention and the traditional method in Example 2.

Detailed ways

For ease of understanding, the specific structure and working mode of the present invention are further described as follows in conjunction with Figures 1-8:

First of all, it needs to be explained that in order to reduce the leakage channel of the container and reduce the uncertainty of the installation process, one end of small high-pressure and ultra-high-pressure containers is often designed with a blind bottom structure. For high-pressure and ultra-high-pressure vessels, there is stress concentration at the blind bottom, and the stress concentration coefficient is very high. It is the area where surface cracks are most likely to initiate. Cracks are usually semi-elliptical at first, and mainly originate from the corners of the blind bottom and then expand. . In the field of design development and failure assessment, for such cracks at the blind bottom, we are most concerned about the free surface. The value of the stress intensity factor. Because the stress intensity factor on the free surface of such a crack will increase rapidly as the crack expands, the free surface will easily enter the unstable expansion stage and be torn into a full circle of annular cracks, resulting in the risk of the end of the container being detached as a whole and the consequences of failure. serious.

To this end, as shown in Figure 1, the implementation steps adopted by the present invention are as follows:

1. According to the structure and operating load conditions of high-pressure and ultra-high-pressure vessels, conduct elastic stress analysis on the blind bottom position.

During specific operations, the stress distribution at the blind bottom of high-pressure and ultra-high-pressure vessels is complex and cannot be directly obtained by analytical methods. ANSYS or other analysis software can be used to conduct linear elastic stress analysis using numerical calculation methods. Of course, the analysis results require steps such as model establishment, mesh division, and loading solution based on the structure and load of the container. This is a routine process and will not be described in detail.

2. Based on the results of stress analysis, extract the stress distribution data perpendicular to the plane where the crack is located.

During specific operations, you can define a path along the crack expansion direction in the ANSYS analysis software and extract the stress distribution data along the path to obtain the required stress distribution data perpendicular to the plane where the crack is located.

3. Measure the shape parameters of the crack at the blind bottom, including: elliptical crack depth value and elliptical crack length value. The stress distribution data is discretized into multiple segments, and the discretized data of each segment is solved. Polynomial solutions are performed for each section of discretized data, and the numerical continuity between each section of function should be maintained without any discontinuity.

More specifically include:

3.1. Taking into account the simplicity of the calculation process and the accuracy of the calculation results, this step gives priority to quadratic polynomial solution, that is, every three sets of stress distribution data are segmented, and each segment of discretized data is connected end to end, so that It can ensure the continuity between each piece of data, including:

1) Use the following formula to solve the stress distribution function y _i (x) of the i-th segment of discretized data:

In the formula:

x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ;

n is the total number of discretized segments.

2) The polynomial coefficients a _{0 i} , a _{1 i} , and a _{2 i} of the i -th segment of discretized data are calculated as follows:

In the formula:

is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

is the stress distribution data/> The depth value corresponding to the group, in mm ;

is the stress distribution data/> The depth value corresponding to the group, in mm ;

is the stress distribution data/> The depth value corresponding to the group, in mm .

4. Calculate the crack shape coefficient Q according to the following formula:

In the formula:

It is the depth value of the elliptical crack, which is a constant under the crack of the present invention, and the unit is mm ;

is the length value of the elliptical crack, in mm ;

is the ratio of the elliptical crack depth value to the elliptical crack length value.

5. Calculate the stress intensity factor at the free surface of the crack with the following formula :

In the formula:

p _i is the internal pressure of the container, in MPa ;

Q is the crack shape coefficient;

K _I,0 ~ K _I,4 are all stress intensity factors. The calculation process is as follows:

M _1B ~ M _4B are all intermediate coefficients, and the calculation formula is as follows:

G ₀ ~ G ₃ are all coefficients at the free surface of the crack. The values are taken according to Table F.2 in GB 34019-2017 "Ultra-high pressure vessels", and the values given in Table F.2 are interpolated.

Example 1:

Assume that the internal pressure of an ultra-high pressure vessel is 200MPa, the temperature is normal temperature; the inner radius of the cylinder is 150mm, the outer radius is 250mm, and the blind bottom thickness is 140mm. There is an elliptical crack at the blind bottom, and the depth value of the elliptical crack is 16mm, oval crack length value/> is 48mm.

The stress intensity factor at the free surface of the crack is calculated through the calculation method proposed by the present invention. The specific implementation steps include:

1. Considering the axial symmetry problem, conduct elastic stress analysis on the blind bottom position.

The stress analysis results obtained through the steps of model establishment, mesh division, and loading solution using ANSYS software are shown in Figure 2.

2. Define the path according to the plane where the crack is located, and extract the stress distribution data along the path, that is, the stress distribution data perpendicular to the plane where the crack is located. The defined path is shown in Figure 3.

3. Carry out multi-segment discretization of data according to the process of the present invention, and solve the quadratic polynomial according to each segment of discretized data. The final solved function drawing result is shown in Figure 4.

It can be clearly seen from Figure 4 that if the cubic polynomial fitting is performed on the stress distribution data according to the traditional method, the fitted result is greatly different from the original data, and the fitting effect is very poor; while according to the present invention, the solution value is different from the original data. They can all correspond to each other one by one, and the representation accuracy is very high.

4. Calculate the crack shape coefficient Q= 1.7496.

5. Calculate the stress intensity factor at the free surface of this crack .

Of course, according to the process of the present invention, the stress intensity factor value at the free surface under each crack depth can also be continuously solved. Considering that the ratio of the elliptical crack depth value to the elliptical crack length value is 1/3, the results obtained by the present invention and the traditional method are as shown in Figure 5.

It can be seen from Figure 5 that the calculation results of the present invention are quite different from the calculation results of the traditional method, and the maximum relative error can be close to 30%.

Example 1 shows that by applying the calculation method proposed in the present invention, the results represented by the piecewise function solution formed by data discretization are obviously more accurate than the calculation results fitted by the traditional method, which will inevitably make the subsequent free The calculated results of the stress intensity factor at the surface are more accurate. By applying the calculation method proposed in the present invention, there is no need to use numerical analysis methods to carry out special fracture mechanics analysis on structures containing cracked openings. The calculation results can be obtained by simply performing algebraic operations on the basis of elastic analysis, which is simple and fast. , suitable for engineering applications.

This Example 1 demonstrates the superiority of the present invention in calculating blind bottom locations with complex stress distribution.

Example 2:

The stress distribution at the blind bottom of high-pressure and ultra-high-pressure vessels is complex, so traditional methods are inadequate. However, it needs to be acknowledged that usually for the stress distribution data of the cylinder, the cubic polynomial fitting results in the traditional method can well represent the stress distribution perpendicular to the plane where the crack is located, and the accurate stress intensity can be obtained using the traditional method. factor. That is to say, for the stress distribution data of the cylinder part, the accurate stress intensity factor value at the crack free surface can be obtained using traditional methods.

In view of this, a set of stress distribution data along the cylinder wall thickness direction is used as an example to compare the calculation results between the traditional method and the present invention, thereby verifying the reliability of the calculation process of the present invention. It should be noted that the object calculated here is not the blind bottom part with complex stress distribution, but the cylinder part with gentle stress distribution:

Assume that the internal pressure of an ultra-high pressure vessel is 200MPa, the temperature is normal temperature; the inner radius of the cylinder is 150mm, the outer radius is 250mm, and there are elliptical cracks along the wall thickness direction.

Specific steps include:

1. Through stress analysis, the path is defined according to the plane where the crack is located, and the stress distribution data along the path can be extracted, that is, the stress distribution data perpendicular to the plane where the crack is located. The defined path is shown in Figure 6.

2. According to the stress distribution data, perform multi-segment discretization of the data according to the process of the present invention, and solve the quadratic polynomial according to the discretized data of each segment. The final solved function drawing result is shown in Figure 7.

It can be clearly seen from Figure 7 that the calculation results of the present invention almost coincide with the calculation results of the traditional method, and the degree of fit 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 at each crack depth is solved through the present invention and the traditional method respectively. The results are shown in Figure 8 .

It can be clearly seen from Figure 8 that as far as the cylinder part with gentle stress distribution is concerned, the calculation results of the present invention almost coincide with the calculation results of the traditional method, and the relative error is basically stable at about 0%.

Example 2 shows that the calculation process of the present invention has excellent reliability.

Of course, for those skilled in the art, the present invention is not limited to the details of the above-described exemplary embodiments, but also includes the same or similar embodiments that can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Way. Therefore, the embodiments should be regarded as illustrative and non-restrictive from any point of view, and the scope of the present invention is defined by the appended claims rather than the above description, and it is therefore intended that all claims falling within the claims All changes within the meaning and scope of equivalent elements are included in the present invention.

In addition, it should be understood that although this specification is described in terms of implementations, not each implementation only contains an independent technical solution. This description of the specification is only for the sake of clarity, and those skilled in the art should take the specification as a whole. , the technical solutions in each embodiment can also be appropriately combined to form other implementations that can be understood by those skilled in the art.

The technical parts not described in detail in the present invention are all known technologies.

Claims (6)

1. The calculation method of the stress intensity factor at the free surface of the crack at the stress concentration location is characterized by including the following steps: S1. According to the container structure and load parameters, perform elastic stress analysis on the stress concentration parts; S2. Based on the analysis results, extract the stress distribution data perpendicular to the plane where the crack is located; S3. Discretize the stress distribution data to obtain discretized data. Perform polynomial solution for each segment of discretized data to obtain the stress distribution function of the corresponding segment of discretized data; S4. Calculate the crack shape coefficient; S5. Calculate the stress intensity factor at the free surface of the crack. 2. The method for calculating the stress intensity factor at the crack free surface at the stress concentration location according to claim 1, characterized in that: in step S3, every three groups of stress distribution data adjacent to each other form a segment of discretized data, each adjacent Segments of discretized data are connected to each other to ensure continuity; Specifically, it includes the following sub-steps: S31. Obtain the polynomial coefficients a _{0 i} , a _{1 i} and a _{2 i} of the i -th section of discretized data according to the following formula: In the formula: is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; S32. Solve the stress distribution function y _i (x) of the i -th segment of discretized data using the following formula: In the formula: x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ; n is the total number of discretized segments. 3. The method for calculating the stress intensity factor at the free surface of the crack at the stress concentration location according to claim 2, characterized in that step S5 includes the following sub-steps: S51. Calculate the component stress intensity factors K _I,0 ~ K _I,4 : In the formula: is the depth value of the elliptical crack, which is a constant and the unit is mm ; S52. Calculate the stress intensity factor at the free surface of the crack with the following formula : In the formula: p _i is the internal pressure of the container, in MPa ; Q is the crack shape coefficient; M _1B ~ M _4B are all intermediate coefficients, and the calculation formula is as follows: G ₀ ~ G ₃ are all coefficients at the free surface of the crack. The values are taken according to Table F.2 in GB 34019-2017 "Ultra-high pressure vessels", and the values given in Table F.2 are interpolated. 4. The method for calculating the stress intensity factor at the free surface of the crack at the stress concentration location according to claim 3, characterized in that: in step S4, the crack shape coefficient Q is calculated by the following formula: In the formula: is the length value of the elliptical crack, 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 in the stress concentration part according to claim 1 or 2 or 3 or 4, characterized in that: in step S1, when performing elastic stress analysis on the stress concentration part, ANSYS analysis is performed. Software, using numerical calculation methods to conduct linear elastic stress analysis. 6. The method for calculating the stress intensity factor at the crack free surface at the stress concentration location according to claim 1 or 2 or 3 or 4, characterized in that: in step S2, ANSYS analysis software is used to define a path along the crack expansion direction and extract the The stress distribution data along this path is the required stress distribution data perpendicular to the plane where the crack is located.