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

Calculation method of stress intensity factor at crack free surface of stress concentration part Download PDF

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CN117057166A
CN117057166A CN202311311170.7A CN202311311170A CN117057166A CN 117057166 A CN117057166 A CN 117057166A CN 202311311170 A CN202311311170 A CN 202311311170A CN 117057166 A CN117057166 A CN 117057166A
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stress
crack
free surface
stress distribution
distribution data
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汪志福
范志超
周煜
秦宗川
牛铮
范海俊
戴兴旺
危书涛
朱金花
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Hefei General Machinery Research Institute Co Ltd
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Abstract

本发明属于高压及超高压容器的设计开发处理及失效评定领域,具体涉及一种应力集中部位裂纹自由表面处应力强度因子的计算方法。本发明包括:根据容器结构及载荷参数,对应力集中部位进行弹性应力分析;根据分析的结果,提取出垂直于裂纹所在平面的应力分布数据;把应力分布数据进行离散化,获得离散化数据,各段离散化数据分别进行多项式求解,获得相应段离散化数据的应力分布函数;进行裂纹形状系数的计算;进行裂纹自由表面处应力强度因子的计算。本发明有效提升了应力分布数据的拟合精度,进而确保了计算结果的准确性;同时,计算方法也非常高效简洁,工程计算中的实用性高。

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

应力集中部位裂纹自由表面处应力强度因子的计算方法Calculation method of stress intensity factor at the free surface of cracks at stress concentration locations

技术领域Technical field

本发明属于高压及超高压容器的设计开发处理及失效评定领域,具体涉及一种应力集中部位裂纹自由表面处应力强度因子的计算方法。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.

背景技术Background technique

高压及超高压容器的应力集中部位,是在制造及使用运行过程中最易损伤的地方,更是最易出现表面裂纹缺陷的区域,通常表现为半椭圆形或半圆形裂纹;GB/T 34019—2017《超高压容器》中明确表述的开孔处裂纹(B型)和盲底裂纹(D型),便是此类应力集中部位中出现的典型裂纹。在高压及超高压容器的设计开发处理及失效评定过程中,需要准确地计算出裂纹尖端的应力强度因子,因为它在含裂纹压力容器剩余强度评定和裂纹扩展剩余寿命计算中是不可或缺的关键参数;尤其对于某些特定裂纹,评定过程中更需重点考察自由表面处以及最深点处应力强度因子的值。因而,在实际工程应用中,找到一种简洁又能保证计算精度的应力集中部位裂纹自由表面和最深点其中之一处的应力强度因子的计算方法,显得尤为重要。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.

当前,裂纹尖端的应力强度因子的计算方法主要有数学分析法、有限元法、边界配置法及光弹性法等,其中以有限元法居多。对于高压及超高压容器典型裂纹应力强度因子的计算,ASME BPVC.Ⅷ.3-2021《AlternativeRules for Construction of High PressureVessels》中的非强制性附录D和GB 34019—2017《超高压容器》中的附录F中都有所提及,两个业内常见标准也都给出了A型裂纹(筒体内壁轴-径向裂纹)的详细计算步骤,即:将应力分布数据进行拟合后,再根据拟合系数及裂纹形状等,进而计算出相应的应力强度因子值。但,对于开孔处裂纹(B型)和盲底裂纹(D型),标准仅是提到可以参照A型裂纹计算方法得出,而并未见具体计算流程。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.

然而,实际高压及超高压容器应力集中部位的应力分布特点为:应力梯度变换大,且衰减由快变慢,即应力起初会随着从裂纹表面所测得距离的加大呈“快速下降”趋势,到一定的距离后再呈“平稳下降”趋势。因此,如果惯性地按照传统的A型裂纹计算方法,由于上述大幅度变化的应力梯度因素影响,其应力分布数据往往无法进行合适的拟合,或者拟合出来的曲线与实际数据相差甚远,随之导致应力集中部位自由表面处应力强度因子的计算结果必然会和实际值有较大偏差,从而无法作为评定过程中的准确判据。当然,此时可以换用数值分析方法对含裂纹结构进行专门的断裂力学分析,但计算过程会很繁琐且收敛难度大,造成的计算成本很高,这也是目前极少采用这类断裂力学分析的主因之一。因而,是否能研发出一种针对应力集中部位裂纹自由表面处应力强度因子计算方法,为本领域近年来所亟待解决的技术难题。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.

发明内容Contents of the invention

本发明的目的是克服上述现有技术的不足,提供一种应力集中部位裂纹自由表面处应力强度因子的计算方法,本发明有效提升了应力分布数据的拟合精度,进而确保了计算结果的准确性;同时,计算方法也非常高效简洁,工程计算中的实用性高。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.

为实现上述目的,本发明采用了以下技术方案:In order to achieve the above objects, the present invention adopts the following technical solutions:

应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于包括以下步骤: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.根据容器结构及载荷参数,对应力集中部位进行弹性应力分析;S1. According to the container structure and load parameters, perform elastic stress analysis on the stress concentration parts;

S2.根据分析的结果,提取出垂直于裂纹所在平面的应力分布数据;S2. Based on the analysis results, extract the stress distribution data perpendicular to the plane where the crack is located;

S3.把应力分布数据进行离散化,获得离散化数据,各段离散化数据分别进行多项式求解,获得相应段离散化数据的应力分布函数;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.进行裂纹形状系数的计算;S4. Calculate the crack shape coefficient;

S5.进行裂纹自由表面处应力强度因子的计算。S5. Calculate the stress intensity factor at the free surface of the crack.

优选的,步骤S3中,每三组彼此相邻的应力分布数据形成一段离散化数据,各相邻段离散化数据之间彼此衔接,以保证连续性;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;

具体包括以下子步骤:Specifically, it includes the following sub-steps:

S31.按下式求取第i段离散化数据的多项式系数a 0i 、a 1i a 2i 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:

式中:In the formula:

为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ;

为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ;

S32.以下式进行第i段离散化数据的应力分布函数y i (x)的求解:S32. Solve the stress distribution function y i (x) of the i -th segment of discretized data using the following formula:

式中:In the formula:

x为裂纹自由表面起所测得的距离,也即深度,为变量,,单位mm x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ;

n为离散化的总段数。 n is the total number of discretized segments.

优选的,步骤S5包括以下子步骤:Preferably, step S5 includes the following sub-steps:

S51.进行分应力强度因子K I,0 ~K I,4的计算:S51. Calculate the component stress intensity factors K I,0 ~ K I,4 :

式中:In the formula:

为椭圆形裂纹深度值,为常量,单位mm is the depth value of the elliptical crack, which is a constant and the unit is mm ;

S52.以下式计算裂纹自由表面处应力强度因子S52. Calculate the stress intensity factor at the free surface of the crack with the following formula :

式中:In the formula:

p i为容器的内压力,单位MPa p i is the internal pressure of the container, in MPa ;

Q为裂纹形状系数; Q is the crack shape coefficient;

M 1B ~M 4B均为中间系数,计算公式如下: M 1B ~ M 4B are all intermediate coefficients, and the calculation formula is as follows:

G 0 ~G 3均为裂纹自由表面处系数,按GB 34019—2017《超高压容器》中的表F.2取值,在表F.2所给出值之间的取插值。 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.

优选的,步骤S4中,以下式计算裂纹形状系数QPreferably, in step S4, the crack shape coefficient Q is calculated by the following formula:

式中:In the formula:

为椭圆形裂纹长度值,单位mm; is the length value of the elliptical crack, in mm;

为椭圆形裂纹深度值与椭圆形裂纹长度值的比值。 is the ratio of the elliptical crack depth value to the elliptical crack length value.

优选的,步骤S1中,对应力集中部位进行弹性应力分析时,通过ANSYS分析软件,采用数值计算方法进行线弹性应力分析得出。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.

优选的,步骤S2中,使用ANSYS分析软件沿裂纹扩展方向定义路径,提取出沿该路径上的应力分布数据,即得到所需的垂直于裂纹所在平面的应力分布数据。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.

本发明的有益效果在于:The beneficial effects of the present invention are:

1)计算结果精度高。本发明所提的计算方法,是把应力集中部位的应力分布数据进行多段离散化分别求解,用多段的离散化数据进行高精度表征,进而最终计算出裂纹自由表面处应力强度因子值。如此,也就保证了应力分布数据的拟合精度,克服了现有方法计算精度不足的缺点。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)计算方法快速简洁。本发明所提的计算方法,不需要采用数值分析方法对含裂纹结构进行专门的断裂力学分析,仅在弹性应力分析的基础之上进行代数计算即可。计算过程简洁快速,也保证了工程计算中的实用性。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.

附图说明Description of the drawings

图1为实施例1的计算流程图;Figure 1 is a calculation flow chart of Embodiment 1;

图2是实施例1中,超高压容器盲底部位弹性应力分析结果图;Figure 2 is a diagram showing the elastic stress analysis results of the blind bottom of the ultra-high pressure vessel in Example 1;

图3是实施例1中,盲底裂纹所在平面处定义的路径显示图;Figure 3 is a path display diagram defined at the plane where the blind bottom crack is located in Embodiment 1;

图4是实施例1中,本发明与传统方法应力分布数据拟合对比图;Figure 4 is a comparison diagram of stress distribution data fitting between the present invention and the traditional method in Example 1;

图5是实施例1中,本发明与传统方法盲底裂纹自由表面处应力强度因子计算结果对比图;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;

图6是实施例2中,裂纹所在平面处定义的路径显示图;Figure 6 is a path display diagram defined at the plane where the crack is located in Embodiment 2;

图7是实施例2中,本发明与传统方法应力分布数据拟合对比图;Figure 7 is a comparison diagram of stress distribution data fitting between the present invention and the traditional method in Example 2;

图8是实施例2中,本发明与传统方法裂纹自由表面处应力强度因子计算结果对比图。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.

具体实施方式Detailed ways

为便于理解,此处结合图1-图8,对本发明的具体结构及工作方式作以下进一步描述: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:

首先需要说明,为了减少容器的泄漏通道及降低安装过程的不确定性,小型的高压及超高压容器一端往往都设计为盲底结构。对于高压及超高压容器来说,盲底部位存在应力集中现象,并且应力集中系数很高,是最易萌生表面裂纹的区域,裂纹通常起初为半椭圆形,主要从盲底拐角处萌生进而扩展。在设计开发及失效评定领域,对于此类盲底部位处的裂纹,我们最为关心的是自由表面处的应力强度因子的值。因为此类裂纹自由表面处应力强度因子会随着裂纹扩展迅速增长,自由表面处会轻易进入失稳扩展阶段,从而撕裂成整圈环形裂纹,导致容器端部有整体脱离的风险,失效后果严重。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.

为此,如图1所示,本发明采用的实施步骤如下:To this end, as shown in Figure 1, the implementation steps adopted by the present invention are as follows:

1、根据高压及超高压容器的结构及运行载荷条件,对盲底部位进行弹性应力分析。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.

具体操作时,高压及超高压容器盲底部位应力分布复杂,无法用解析法直接求得,可利用ANSYS或其他分析软件,采用数值计算方法进行线弹性应力分析得出。当然,分析结果需根据容器的结构及载荷,进行模型建立、网格划分、加载求解等步骤,此为常规流程,就不再赘述。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、根据应力分析的结果,提取出垂直于裂纹所在平面的应力分布数据。2. Based on the results of stress analysis, extract the stress distribution data perpendicular to the plane where the crack is located.

具体操作时,可在ANSYS分析软件中沿裂纹扩展方向定义路径,提取出沿该路径上的应力分布数据,就可得到所需的垂直于裂纹所在平面的应力分布数据。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、测量出盲底部位裂纹的形状参数,包括:椭圆形裂纹深度值、椭圆形裂纹长度值。将应力分布数据进行多段离散化,并进行各段离散化数据的求解。各段离散化数据分别进行多项式求解,每段函数之间应保持数值连续,不得有间断。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.

更具体包括:More specifically include:

3.1、考虑到计算过程的简洁性,又兼顾计算结果的准确度,该步骤优先考虑进行二次多项式求解,即每三组应力分布数据进行分段,每段离散化数据之间首尾连接,这样可保证各段数据之间的连续性,包括: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)以下式进行第i段离散化数据的应力分布函数y i (x)的求解:1) Use the following formula to solve the stress distribution function y i (x) of the i-th segment of discretized data:

式中:In the formula:

x为裂纹自由表面起所测得的距离,也即深度,为变量,,单位mm x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ;

n为离散化的总段数。 n is the total number of discretized segments.

2)第i段离散化数据的多项式系数a 0i 、a 1i 、a 2i 按下式计算: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:

式中:In the formula:

为应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

为应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

为应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data/> The corresponding stress value of the group, unit MPa ;

为应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data/> The depth value corresponding to the group, in mm ;

为应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data/> The depth value corresponding to the group, in mm ;

为应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data/> The depth value corresponding to the group, in mm .

4、按下式计算裂纹形状系数Q4. Calculate the crack shape coefficient Q according to the following formula:

式中:In the formula:

为椭圆形裂纹深度值,在本发明裂纹下是常量,单位mm 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 ;

为椭圆形裂纹长度值,单位mm is the length value of the elliptical crack, in mm ;

为椭圆形裂纹深度值与椭圆形裂纹长度值的比值。 is the ratio of the elliptical crack depth value to the elliptical crack length value.

5、以下式计算裂纹自由表面处应力强度因子5. Calculate the stress intensity factor at the free surface of the crack with the following formula :

式中:In the formula:

p i为容器的内压力,单位MPa p i is the internal pressure of the container, in MPa ;

Q为裂纹形状系数; Q is the crack shape coefficient;

K I,0 ~K I,4均为分应力强度因子,计算过程如下: K I,0 ~ K I,4 are all stress intensity factors. The calculation process is as follows:

M 1B ~M 4B均为中间系数,计算公式如下: M 1B ~ M 4B are all intermediate coefficients, and the calculation formula is as follows:

G 0 ~G 3均为裂纹自由表面处系数,按GB 34019—2017《超高压容器》中的表F.2取值,在表F.2所给出值之间的取插值。 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.

实施例1:Example 1:

假定某台超高压容器承受的内压为200MPa,温度为常温;筒体内半径为150mm,外半径为250mm,盲底厚度为140mm。在盲底部位有一椭圆形裂纹,椭圆形裂纹深度值为16mm,椭圆形裂纹长度值/>为48mm。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.

通过本发明所提计算方法进行此裂纹自由表面处应力强度因子的计算,具体实施步骤包括: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、按轴对称问题考虑,对盲底部位进行弹性应力分析。1. Considering the axial symmetry problem, conduct elastic stress analysis on the blind bottom position.

通过ANSYS软件进行模型建立、网格划分、加载求解等步骤得出的应力分析结果如图2所示。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、根据裂纹所在的平面定义路径,可提取出沿路径上的应力分布数据,即垂直于裂纹所在平面的应力分布数据,定义的路径如图3所示。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、按本发明的流程进行数据的多段离散化,根据各段离散化数据分别进行二次多项式求解,最终求解的函数绘制结果如图4所示。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.

从图4中可以明显看出,如果按传统方法对应力分布数据进行三次多项式拟合,拟合出来的结果与原始数据相差较大,拟合效果很差;而按本发明求解值与原始数据都能对逐一对应上,表征精度很高。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、计算出此裂纹形状系数Q=1.7496。4. Calculate the crack shape coefficient Q= 1.7496.

5、计算出此裂纹自由表面处应力强度因子5. Calculate the stress intensity factor at the free surface of this crack .

当然,按本发明的流程,也可继续求解出各个裂纹深度下自由表面处应力强度因子值。按椭圆形裂纹深度值与椭圆形裂纹长度值的比值为1/3考虑,本发明与传统方法求解出的结果如图5所示。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.

从图5中可以看出,本发明的计算结果与传统方法计算结果相差较大,相对误差最大可接近30%。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%.

实施例1表明,应用本发明中所提的计算方法,数据离散化形成的分段函数求解所表征的结果,明显比传统方法所拟合的计算结果更为精确,这也必然使得后续的自由表面处应力强度因子计算结果更为精确。应用本发明中所提的计算方法,不需要采用数值分析方法对含裂纹开孔结构进行专门的断裂力学分析,只需在弹性分析的基础之上进行代数运算便可得出计算结果,简洁快速,适合于工程中的应用。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.

该实施例1体现出了本发明在应力分布复杂的盲底部位计算的优越性。This Example 1 demonstrates the superiority of the present invention in calculating blind bottom locations with complex stress distribution.

实施例2:Example 2:

高压及超高压容器盲底部位应力分布复杂,因此传统方法力有不及。但是需承认的是,通常对于筒体部位的应力分布数据,传统方法中的三次多项式拟合结果可以很好地表征垂直于裂纹所在平面的应力分布,用传统的方法可得出精准的应力强度因子。即对于筒体部位的应力分布数据,用传统方法可得出精准的裂纹自由表面处应力强度因子值。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.

鉴于此,此处以一组沿筒体壁厚方向的应力分布数据为例,进行传统方法与本发明计算结果的对比,从而验证本发明的计算流程的可靠性。需注意,此处计算的对象并非为应力分布复杂的盲底部位,而是应力分布平缓的筒体部位: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:

假定某台超高压容器承受的内压为200MPa,温度为常温;筒体内半径为150mm,外半径为250mm,沿着壁厚方向存在椭圆形裂纹。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.

具体步骤包括:Specific steps include:

1、通过应力分析,根据裂纹所在的平面定义路径,可提取出沿路径上的应力分布数据,即垂直于裂纹所在平面的应力分布数据,定义的路径如图6所示。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、根据应力分布数据,按本发明的流程进行数据的多段离散化,根据各段的离散化数据分别进行二次多项式求解,最终求解的函数绘制结果如图7所示。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.

从图7中可以明显看出,本发明的计算结果与传统方法的计算结果几乎重合,两者之间的贴合度极高。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、按椭圆形裂纹深度值与椭圆形裂纹长度值的比值为1/3考虑时,通过本发明及传统方法分别求解出各个裂纹深度下自由表面处应力强度因子值,结果如图8所示。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 .

从图8中可以明显看出,就应力分布平缓的筒体部位而言,本发明的计算结果与传统方法计算结果几乎重合,相对误差基本稳定在0%左右。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%.

实施例2表明了本发明的计算流程具有极佳的可靠性。Example 2 shows that the calculation process of the present invention has excellent reliability.

当然,对于本领域技术人员而言,本发明不限于上述示范性实施例的细节,而还包括在不背离本发明的精神或基本特征的情况下,能够以其他的具体形式实现的相同或类似方式。因此,无论从哪一点来看,均应将实施例看作是示范性的,而且是非限制性的,本发明的范围由所附权利要求而不是上述说明限定,因此旨在将落在权利要求的等同要件的含义和范围内的所有变化囊括在本发明内。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.

此外,应当理解,虽然本说明书按照实施方式加以描述,但并非每个实施方式仅包含一个独立的技术方案,说明书的这种叙述方式仅仅是为清楚起见,本领域技术人员应当将说明书作为一个整体,各实施例中的技术方案也可以经适当组合,形成本领域技术人员可以理解的其他实施方式。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.

本发明未详细描述的技术部分均为公知技术。The technical parts not described in detail in the present invention are all known technologies.

Claims (6)

1.应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于包括以下步骤: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.根据容器结构及载荷参数,对应力集中部位进行弹性应力分析;S1. According to the container structure and load parameters, perform elastic stress analysis on the stress concentration parts; S2.根据分析的结果,提取出垂直于裂纹所在平面的应力分布数据;S2. Based on the analysis results, extract the stress distribution data perpendicular to the plane where the crack is located; S3.把应力分布数据进行离散化,获得离散化数据,各段离散化数据分别进行多项式求解,获得相应段离散化数据的应力分布函数;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.进行裂纹形状系数的计算;S4. Calculate the crack shape coefficient; S5.进行裂纹自由表面处应力强度因子的计算。S5. Calculate the stress intensity factor at the free surface of the crack. 2.根据权利要求1所述的应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于:步骤S3中,每三组彼此相邻的应力分布数据形成一段离散化数据,各相邻段离散化数据之间彼此衔接,以保证连续性;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; 具体包括以下子步骤:Specifically, it includes the following sub-steps: S31.按下式求取第i段离散化数据的多项式系数a 0i 、a 1i a 2i 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: 式中:In the formula: 为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; 为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; 为步骤S2中所提取的应力分布数据中第/>组对应的应力值,单位MPa is the stress distribution data extracted in step S2/> The corresponding stress value of the group, unit MPa ; 为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; 为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; 为步骤S2中所提取的应力分布数据中第/>组对应的深度值,单位mm is the stress distribution data extracted in step S2/> The depth value corresponding to the group, in mm ; S32.以下式进行第i段离散化数据的应力分布函数y i (x)的求解:S32. Solve the stress distribution function y i (x) of the i -th segment of discretized data using the following formula: 式中: In the formula: x为裂纹自由表面起所测得的距离,也即深度,为变量,,单位mm x is the measured distance from the free surface of the crack, that is, the depth, which is a variable, , unit mm ; n为离散化的总段数。 n is the total number of discretized segments. 3.根据权利要求2所述的应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于:步骤S5包括以下子步骤: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.进行分应力强度因子K I,0 ~K I,4的计算:S51. Calculate the component stress intensity factors K I,0 ~ K I,4 : 式中:In the formula: 为椭圆形裂纹深度值,为常量,单位mm is the depth value of the elliptical crack, which is a constant and the unit is mm ; S52.以下式计算裂纹自由表面处应力强度因子S52. Calculate the stress intensity factor at the free surface of the crack with the following formula : 式中: In the formula: p i为容器的内压力,单位MPa p i is the internal pressure of the container, in MPa ; Q为裂纹形状系数; Q is the crack shape coefficient; M 1B ~M 4B均为中间系数,计算公式如下: M 1B ~ M 4B are all intermediate coefficients, and the calculation formula is as follows: G 0 ~G 3均为裂纹自由表面处系数,按GB 34019—2017《超高压容器》中的表F.2取值,在表F.2所给出值之间的取插值。 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.根据权利要求3所述的应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于:步骤S4中,以下式计算裂纹形状系数Q4. 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: 式中: In the formula: 为椭圆形裂纹长度值,单位mm; is the length value of the elliptical crack, in mm; 为椭圆形裂纹深度值与椭圆形裂纹长度值的比值。 is the ratio of the elliptical crack depth value to the elliptical crack length value. 5.根据权利要求1或2或3或4所述的应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于:步骤S1中,对应力集中部位进行弹性应力分析时,通过ANSYS分析软件,采用数值计算方法进行线弹性应力分析得出。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.根据权利要求1或2或3或4所述的应力集中部位裂纹自由表面处应力强度因子的计算方法,其特征在于:步骤S2中,使用ANSYS分析软件沿裂纹扩展方向定义路径,提取出沿该路径上的应力分布数据,即得到所需的垂直于裂纹所在平面的应力分布数据。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.
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