CN118010621A - Method for calculating fatigue extension life of axial and radial crack based on outer wall of cylindrical longitudinal weld - Google Patents
Method for calculating fatigue extension life of axial and radial crack based on outer wall of cylindrical longitudinal weld Download PDFInfo
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Abstract
The invention belongs to the technical field of high-pressure container design development and failure assessment, and particularly relates to a shaft radial crack fatigue extension life calculation method based on a cylindrical longitudinal weld outer wall. The invention comprises the following steps: determining structural parameters and cyclic alternating load working conditions of a high-pressure thick-wall welding cylinder, and obtaining shape parameters of initial cracks of a longitudinal weld joint of the cylinder and the outer wall of a heat affected zone part; calculating a stress intensity factor of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition; and actually measuring the fracture toughness or stress corrosion fracture toughness of the test piece, establishing a crack expansion rate calculation model of the test piece under the driving action of cyclic alternating load and service medium environment, and carrying out crack expansion calculation to obtain the fatigue expansion life. The method synchronously considers the influence of the internal and external pressure load, the welding residual stress and the service medium environment of the container, has the advantages of high efficiency and simplicity in the calculation process and high accuracy of the calculation result, and has high practicability in engineering calculation.
Description
Technical Field
The invention belongs to the technical field of high-pressure container design development and failure assessment, and particularly relates to a shaft radial crack fatigue extension life calculation method based on a cylindrical longitudinal weld outer wall.
Background
In engineering application, most high-pressure containers are of a plate welding structure, namely, are formed by rolling and welding thick-wall plates. Welding is a metallurgical process with uneven heating (large temperature difference), the internal structure grains of a welding line and a heat affected zone are coarse, and the workpiece is influenced by the restraint degree, so that the workpiece can yield and deform in the welding process, and larger residual stress is generated in the welding line and the heat affected zone after welding and cooling. The welding residual stress is very destructive, because the welding residual stress can continuously overlap primary and secondary stress and the like in the container bearing process in the service process of the high-pressure container, so that very large overlapping stress is obtained, and the welding residual stress is also the reason that most of welding containers are easy to crack in welding seams and heat affected zones. Engineering practice shows that compared with the base material of the pressure vessel, the weld joint and the heat affected zone part are easier to initiate surface cracks, and further rapidly expand under the corrosive environment or fatigue working condition, thereby causing the vessel to crack and fail.
According to the plate shell theory, the circumferential stress of the cylinder is twice of the axial stress and is the first main stress, so that the longitudinal weld joint and the heat affected zone part of the cylinder are easier to initiate radial cracks of the shaft, and the method has more engineering significance for fatigue expansion research and safety evaluation. The radial crack of the outer wall shaft can be generally regarded as semi-elliptic, based on the theory of fracture mechanics, the calculation of the expansion of the cylindrical longitudinal weld joint containing the radial crack of the outer wall shaft under the corrosive environment or the fatigue working condition mainly comprises the following steps: ① Respectively calculating stress intensity factors of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition; ② Establishing a crack propagation rate calculation model of the crack under the driving action of the cyclic alternating load and the service medium environment; ③ And (3) carrying out cyclic iterative computation on the basis of the initial crack until the critical crack depth is reached.
For the fatigue extension life of cracks, researchers still mainly use a finite element method at present; however, because a very complex welding cold and hot process exists in the welding process of the cylindrical longitudinal weld, the input load and boundary conditions in the welding process are difficult to accurately simulate by a finite element method, so that the welding residual stress calculated by simulation often has a larger difference from the actual welding residual stress; in addition, in the process of calculating the fatigue extension life of the crack by using the finite element method, the crack-containing structure needs to be modeled, loaded, calculated and solved, the workload is very large, and the solving accuracy is greatly influenced by the finite element grid. Therefore, the calculation of fatigue extension life of cracks at the weld joint by adopting a finite element numerical calculation method is not suitable for the engineering field. Furthermore, for typical cracks in high pressure vessels, ASME BPVC. VIII.3-2023, another construction rule for high pressure vessels, and GB/T34019-2017, ultra high pressure vessels are all mentioned, but at the same time the effect of welding residual stresses is not considered, and neither is explicitly stated to be suitable for welded structures, since the two standards do not take into account the effect of welding residual stresses.
Therefore, for the calculation of fatigue extension life of cracks initiated at the weld and heat affected zone parts of the high pressure plate welded container, engineering personnel often do not consider the influence of welding residual stress. In addition, the existing method generally only considers that the high-pressure container bears the internal pressure load, but the actual engineering also encounters a pressure container which bears the internal pressure and the external pressure simultaneously or independently, for example: cylindrical containers operating in deep sea environments, etc., often have less consideration for cracking of the outer walls of such high pressure containers. In practical engineering application, the method for calculating the crack fatigue extension life is very important for radial cracks of the outer wall shaft of the cylindrical longitudinal welding seam, which is simple, efficient, comprehensive and accurate in calculation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a shaft radial crack fatigue extension life calculation method based on the outer wall of a cylindrical longitudinal weld. The method synchronously considers the influences of the internal and external pressure load, the welding residual stress and the service medium environment of the container, so that the method can be pertinently applied to the calculation flow of the crack fatigue extension life of the outer wall of the cylindrical longitudinal weld in the design and operation stages, and has the advantages of high efficiency and simplicity in the calculation process and high accuracy of the calculation result, and the method has high practicability in engineering calculation.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for calculating the fatigue extension life of the axial and radial crack based on the outer wall of the cylindrical longitudinal weld is characterized by comprising the following steps of:
s1, determining structural parameters and cyclic alternating load working conditions of a high-pressure thick-wall welding cylinder, and obtaining shape parameters of initial cracks of a longitudinal weld joint of the cylinder and the outer wall of a heat affected zone part;
s2, respectively calculating stress intensity factors of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition, wherein the method specifically comprises the following steps:
s2.1, preparing a cylindrical longitudinal weld welded joint test piece, and measuring the yield strength of the test piece at the working temperature in an actual measurement mode;
S2.2, selecting one of the initial working condition and the final working condition to calculate a reference fitting coefficient A i', wherein i is an integer, and i is more than or equal to 0 and less than or equal to 3:
① If the cylinder is not post-weld heat treated, then:
Wherein p i is the cylinder internal pressure load in MPa; k is the ratio of the outer diameter of the cylinder to the inner diameter of the cylinder; p o is the cylinder external pressure load in MPa; r t p0.2 is the actually measured yield strength of the test piece at the working temperature, and the unit is MPa;
② If the cylinder is post-weld heat treated, then:
Then, fitting stress distribution of a plane vertical to the radial crack of the outer wall shaft under the initial working condition and the final working condition by the A i' obtained by calculation;
S2.3, calculating an actual fitting coefficient A i under the initial working condition and the final working condition according to the following formula:
In the method, in the process of the invention,
A is the depth of a semi-elliptic crack, and the unit is mm;
t is the wall thickness of the cylinder, and the unit is mm;
Then, the calculated shape coefficient Q of the radial crack of the outer wall shaft is combined to obtain the stress intensity factors of the deepest point and the free surface of the radial initial crack of the outer wall shaft under the initial working condition and the final working condition;
S3, actually measuring the fracture toughness or stress corrosion fracture toughness of the test piece, establishing a crack growth rate calculation model of the test piece under the driving action of cyclic alternating load and service medium environment, and carrying out crack growth calculation to obtain the fatigue expansion life.
Preferably, in the step S2.2, stress distribution perpendicular to the plane of the radial crack of the outer wall shaft under the initial working condition and the final working conditionThe fitting formula of (2) is:
In the method, in the process of the invention,
X is the distance measured from the free surface of the crack, and is a variable, the unit mm, and x is more than or equal to 0 and less than or equal to t.
Preferably, in the step S2.3, a calculation formula of the shape coefficient Q of the radial crack of the outer wall shaft is:
In the method, in the process of the invention,
L is the length of the semi-elliptic crack, in mm.
Preferably, in step S2.3, the stress intensity factor K I at the deepest point and the free surface of the radial initial crack of the outer wall shaft under the initial working condition and the final working condition is:
wherein, G 0、G1、G2 and G 3 are stress intensity factor influence coefficients and have no dimension.
Preferably, in the step S1, determining structural parameters of the high-pressure thick-wall welding cylinder includes: the outer radius of the cylinder, the inner radius of the cylinder, the use materials of the base material and the welding material of the cylinder and the cylinder welding process; the cyclic alternating load working condition comprises a pressure load and a temperature load under the initial working condition and the final working condition of the cylinder; the shape parameters of the initial cracks of the cylindrical longitudinal weld joint and the outer wall of the heat affected zone part comprise semi-elliptical crack depth and semi-elliptical crack length, and the semi-elliptical crack depth and the semi-elliptical crack length are measured by adopting a nondestructive testing method.
Preferably, in the step S3, the fracture toughness or stress corrosion fracture toughness of the test piece is obtained by testing a three-point bending test piece or a CT test piece; and carrying out a pre-crack fatigue expansion test on the test piece in a service medium environment in a three-point bending test piece or CT test piece mode to obtain a crack expansion rate calculation model.
Preferably, in the step S3, when performing crack extension calculation, the critical crack depth is determined by using the fracture toughness K IC or the stress corrosion fracture toughness K ISCC of the test piece as a critical value, a semi-elliptical crack depth and a trend chart of the semi-elliptical crack length accumulated along with the cycle number in the extension process are obtained through the crack extension calculation, then a mode of gradually reducing the step length Δa is adopted to obtain the total cycle number N p of the crack extension to the critical crack depth and the total cycle number N c of the crack extension to 0.25 times of the critical crack depth, and the smaller value of N p/2 and N c is taken as the fatigue extension life.
Preferably, after the fatigue extension life is obtained, the half-elliptic crack depth and the half-elliptic crack length corresponding to the fatigue extension life are the finally allowable crack depth and crack length; in the service process of the high-pressure thick-wall welding cylinder, when the monitored actual crack depth and the monitored actual crack length do not exceed the finally allowable crack depth and the crack length, the actual crack is safe, otherwise, a risk alarm is triggered.
The invention has the beneficial effects that:
1) The calculation method provided by the invention not only considers the stress caused by the pressure load, but also considers important influencing factors such as residual stress generated in the welding cold and hot process, the service medium environment and the like, has high implementation feasibility, more accurate calculation results, provides a quantitative analysis method for fatigue extension life and safety evaluation of the cracks for engineering personnel, and solves the technical problems existing at present.
2) The calculation method provided by the invention does not need to use finite element calculation software and the like, has a perfect calculation flow suitable for the crack fatigue extension life of the outer wall of the cylindrical longitudinal weld in the design and operation stages, has strong calculation pertinence, quick and simple calculation process and high practicability in engineering calculation.
Drawings
FIG. 1 is a block diagram of a computational flow of the present invention;
FIG. 2 is a graph showing the distribution trend of stresses perpendicular to the plane of cracks caused by internal and external pressure loads and cold and hot deformation of welding in example 1;
FIG. 3 is a graph showing the comparison of the fitted curve and the original stress distribution data in example 1;
FIG. 4 is a graph showing the variation of stress intensity factors at the deepest point and the free surface during crack propagation in example 1;
FIG. 5 is a graph showing the depth and length trend of the semi-elliptical crack and the final allowable crack depth and crack length obtained during the crack propagation process of example 1;
Fig. 6 is a graph of safety versus risk profile for a semi-elliptical crack during crack propagation in example 1.
Detailed Description
For ease of understanding, the calculation method proposed in the present invention is further described herein with reference to fig.1 to 6:
For the high-pressure thick-wall welding cylinder with the inner wall and the outer wall bearing pressure load, the existence form and the stress structure of radial cracks of the outer wall shaft which are initiated at the longitudinal welding line and the heat affected zone part are provided. The calculation of fatigue extension life of the longitudinal weld joint of the cylinder with the crack and the heat affected zone part is mainly based on the theory of linear elastic fracture mechanics, and comprises the following processes:
① Respectively calculating stress intensity factors of the deepest point and the free surface of the cylindrical longitudinal weld joint and the initial crack of the heat affected zone under the cyclic alternating load working condition;
② Establishing a crack propagation rate calculation model of the crack under the driving action of the cyclic alternating load and the service medium environment;
③ And (3) carrying out cyclic iterative computation on the basis of the initial crack until the critical crack depth is reached.
Meanwhile, for a high-pressure thick-wall welding cylinder with inner and outer walls bearing pressure load, the stress of a plane where radial cracks of an outer wall shaft of the cylinder are located, namely hoop stress distribution, can be obtained through mathematical deduction, and the following functional formula is obtained:
In the method, in the process of the invention, The stress is vertical to the plane where the radial crack of the outer wall shaft of the cylinder is located, is the stress caused by internal and external pressure loads, belongs to the category of primary stress, and is in unit MPa; p i is the cylinder internal pressure load in MPa; p o is the cylinder external pressure load in MPa; r i is the inner radius of the cylinder, in mm; r o is the outer radius of the cylinder, in mm; k is the ratio of the outer diameter to the inner diameter of the cylinder; x is the distance in mm from the free surface of the crack.
As can be seen from the functional equation, as the value of x increases, the stress value increases.
At this time, the welding residual stress of the cylindrical longitudinal weld and the heat affected zone is divided into two cases:
① If the cylinder is not subjected to the post-welding heat treatment process, the welding residual stress perpendicular to the plane where the radial crack of the outer wall shaft of the cylinder is located can be obtained by the following formula:
In the method, in the process of the invention, The welding residual stress which is vertical to the plane where the radial crack (at the longitudinal weld joint and the heat affected zone) of the outer wall shaft of the cylinder is positioned is the residual stress caused by cold and hot deformation in the welding process, and belongs to the category of secondary stress, and the unit is MPa; r t p0.2 is the actually measured yield strength of the cylindrical longitudinal weld welded joint test piece at the working temperature, and the unit is MPa; t is the wall thickness of the cylinder, in mm.
② If the cylinder is subjected to a post-welding heat treatment process, the welding residual stress perpendicular to the plane of the radial crack of the outer wall shaft of the cylinder can be obtained according to the following formula:
For radial cracks of the outer wall shaft which occur at the longitudinal weld joint of the cylinder and the heat affected zone, the influence of primary stress and secondary stress (residual stress) should be comprehensively considered. The method for calculating the fatigue life of radial crack of the outer wall shaft, usually semi-elliptical crack, can be further described with reference to fig. 1, namely, the method comprises the following steps:
D1. Determining structural parameters of the cylinder, comprising: the outer radius of the cylinder, the inner radius of the cylinder, the used materials (including parent materials and welding materials) of the cylinder and the welding process of the cylinder.
D2. determining a cyclic alternating load condition of the cylinder, comprising: pressure load and temperature load under initial and final conditions.
D3. Measuring shape parameters of initial cracks of the cylindrical longitudinal weld joint and the outer wall of the heat affected zone part, wherein the shape parameters comprise the depth and the length of the cracks; the initial crack size may be measured using a non-destructive method.
D4. Stress intensity factors of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition are calculated respectively, and the method specifically comprises the following steps:
D4.1. preparing a cylindrical longitudinal weld welded joint test piece (hereinafter referred to as a test piece), and measuring the yield strength of the test piece at the working temperature.
The test pieces here should satisfy the following conditions: the test piece should be welded with the cylinder at the extension part of the longitudinal weld of the cylinder; the parent metal (including heat treatment state) of the test piece and the welding material are consistent with the manufacturing time of the product; the test piece is welded by a welder of the welding container under the same conditions, processes and welding processes as the welding container; the test piece should be heat treated by the same process as the high pressure vessel in which the cylinder is located.
D4.2. And respectively fitting stress distribution perpendicular to a plane where the radial crack of the outer wall shaft is located under the initial working condition and the final working condition according to the following steps:
whereas for thick-walled welded cylinders themselves, the following two cases are used:
① If the cylinder is not post-weld heat treated, then:
Wherein p i is the cylinder internal pressure load in MPa; k is the ratio of the outer diameter of the cylinder to the inner diameter of the cylinder; p o is the cylinder external pressure load in MPa; r t p0.2 is the actually measured yield strength of the test piece at the working temperature, and the unit is MPa;
② If the cylinder is post-weld heat treated, then:
D4.3. the actual fitting coefficient A i under the initial working condition and the final working condition is calculated according to the following steps:
In the method, in the process of the invention,
A is the depth of a semi-elliptic crack, and usually, each time the crack grows, the crack is calculated as an initial crack cycle and is measured in unit mm;
D4.4. The shape factor Q of the radial crack of the outer wall axis is calculated as follows:
wherein l is the length of a semi-elliptic crack, and the unit is mm;
D4.5. and respectively calculating stress intensity factors K I at the deepest point of the radial initial crack and the free surface of the outer wall shaft under the initial working condition and the final working condition according to the following steps:
wherein G i is a stress intensity factor influence coefficient, and is dimensionless.
D5. Test pieces were tested for fracture toughness or stress corrosion fracture toughness.
When the materials used for the cylinder are compatible with the medium, only the fracture toughness K IC at room temperature needs to be tested, otherwise the stress corrosion fracture toughness K ISCC in a corrosive environment should be tested. Typically, fracture toughness or stress corrosion fracture toughness can be obtained by three-point bending test pieces or CT test piece testing.
D6. and establishing a crack expansion rate calculation model under the driving action of the cyclic alternating load and the service medium environment.
The crack fatigue propagation rate calculation model is related to the materials used for the cylinder (including parent materials and welding materials), the welding process and the environment of the use medium, and particularly in a corrosive environment, the same materials can obviously accelerate to be propagated than in an air environment. In general, a crack growth rate calculation model of a test piece is obtained by performing a pre-crack fatigue growth test on a three-point bending test piece or a CT test piece in a specific medium environment. The crack growth rate calculation model for different material types can refer to published data, typically the classical Paris equation, and will not be described herein.
D7. Crack growth calculations were performed.
The crack propagation calculation is a cyclic iteration solution based on the stress intensity factor calculation step and the crack propagation rate calculation model; this is a dynamic calculation process, and each time a crack grows (i.e., the step size Δa is increased), the calculation is performed as an initial calculation condition for the next step until the critical crack depth is calculated. The critical crack depth can be determined by adopting a classical stress intensity factor criterion, namely taking the fracture toughness K IC or the stress corrosion fracture toughness K ISCC of a test piece as a critical value.
D8. And obtaining the fatigue extension life and the final allowable crack depth and crack length.
Through crack extension calculation, a semi-elliptical crack depth and a change trend graph of the semi-elliptical crack length accumulated along with the cycle times in the extension process can be obtained, then the total cycle times N p of corresponding cracks extending to the critical crack depth and the total cycle times N c.Np and N c of corresponding cracks extending to the critical crack depth which are 0.25 times can be respectively obtained, and trial calculation is repeatedly carried out by adopting a gradual reduction method until N p and N c have no obvious change or only change within a set threshold range. The smaller values of N p/2 and N c were taken as fatigue extension lives, which correspond to crack depths and crack lengths that were the final allowable crack depths and crack lengths.
D9. and establishing a crack safety and risk interval, and providing a basis for periodic monitoring.
During the service of the high-pressure container, the cracks should be tracked and monitored periodically in real time. When the monitored actual crack depth and the actual crack length do not exceed the allowable crack depth and crack length, the actual crack can be considered safe, otherwise, risks are considered to exist, and treatments such as alarming and the like can be performed.
In order to further understand the present invention, on the basis of the above scheme, the present invention also provides practical embodiments as follows:
Example 1
Assume that a certain high-pressure container is of a single-layer plate welding structure, wherein:
Assuming that a certain high-pressure container is of a single-layer plate welding structure, the inner radius r i of the cylinder is 600mm, and the outer radius r o of the cylinder is 900mm; the plate is a Q345R thick wall plate, the welding material is an E5015-N2 (J507 RH) high-toughness low-hydrogen welding rod, and the whole heat treatment is fully carried out after the welding; the bearing internal pressure load p i is 70MPa, the external pressure load p o is 20MPa, the working temperature is normal temperature, the outer wall contact medium is sea water, and the cyclic working is carried out within the range of 0-70 MPa of internal pressure and 0-20 MPa of external pressure. Through nondestructive testing on the longitudinal weld joint of the cylinder and the heat affected zone, the outer wall is found to have a radial crack of the shaft, namely a is 1mm, and l is 4mm.
The calculation method for calculating the fatigue extension life of the crack comprises the following specific implementation steps:
1. respectively calculating stress intensity factors of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition:
The initial working condition of the high-pressure container is that the internal pressure is 0MPa, the external pressure is 0MPa and the normal temperature is adopted; the final working condition is that the internal pressure is 70MPa, the external pressure is 20MPa and the normal temperature is adopted.
The specific refinement is calculated as follows:
1.1. And respectively calculating the stress distribution vertical to the plane where the crack is caused by the internal and external pressure load and the cold and hot deformation of the welding under the initial working condition and the final working condition, as shown in figure 2. Fig. 2 shows that the effect of the welding residual stress on the overall stress distribution trend is great, and especially the effect of the tensile stress caused at the near inner and outer surfaces on the cracks is hardly negligible.
1.2. And (3) preparing a cylindrical longitudinal weld welded joint test piece, wherein the yield strength R t p0.2 of the test piece at the working temperature is found to be 360MPa.
1.3. Calculating a reference fitting coefficient A i' required in a fitting formula under an initial working condition and a final working condition respectively:
The calculated A 0′～A3' under the initial working condition is as follows: 399.12, -11.88, -3002.0, 3117.62; a 0′～A3' under the end state working condition is as follows: 399.12, 16.19, -2995.9, 3133.38.
The fitting curve drawn according to the obtained reference fitting coefficient is shown in fig. 3. Fig. 3 shows that the fitting curves under the initial working condition and the final working condition are basically coincident with the trend of the original stress distribution data, and the determinable coefficient R 2 (the statistic for measuring the fitting goodness) of the fitting curves is 0.9999, which shows that the fitting precision is very high and the characterization effect is very good.
1.4. The actual fitting coefficient a i is calculated.
The calculated A 0～A3 under the initial working condition is as follows: 399.12, -0.040, -0.033, 0.00012; a 0～A3 under the end state working condition is as follows: 399.12, 0.054, -0.033, 0.00012.
1.5. The shape coefficients Q at the crack deepest point and the free surface were calculated to be 1.1366, 1.2732, respectively.
1.6. The stress intensity factors K I at the deepest point and the free surface of the crack under the initial working condition are respectively 18.03 MPa.m 1/2、13.44MPa·m1/2 through calculation; the stress intensity factors K I at the deepest point and the free surface of the crack under the end state working condition are 26.62MPa m 1/2、19.25MPa·m1/2 respectively.
2. The stress corrosion fracture toughness K IC of the welding joint under the normal-temperature seawater environment is tested to be 60 MPa.m 1/2.
3. Establishing a crack growth rate calculation model under the driving action of cyclic alternating load and service medium environment, wherein the crack growth rate calculation model comprises the following steps:
and (3) testing in a normal-temperature seawater environment to obtain a crack propagation rate calculation model of the Q345R cylindrical longitudinal weld joint test piece, wherein the crack propagation rate calculation model is tested according to a standard Paris equation as follows:
Wherein da/dN is the expansion rate in the crack depth direction, and the unit is m/times; dl/dN is the expansion rate in the crack length direction, and the unit is m/times; c is 10.25X10 -12, m/time (MPa.m 1/2)-m; m is 3.95, dimensionless; C and m are both characteristic coefficients; deltaK I is the stress intensity factor amplitude, unit MPa.m 1/2).
4. Crack growth calculations were performed.
The calculation process is iterated circularly, and each time a crack grows, the initial calculation condition is used as the next step to calculate until the critical crack depth. And judging the critical crack depth, and taking the corresponding crack depth at the time of K Imax=KIC= 60 MPa·m1/2. In the process of crack propagation, the variation trend of stress intensity factors at the deepest point and the free surface of the crack under the initial working condition and the final working condition is shown in fig. 4.
FIG. 4 shows that the critical crack depth is 9.8mm, at which point the stress intensity factor at the free surface of the crack reaches a critical value under end-state conditions.
5. And obtaining the fatigue extension life and the final allowable crack depth and crack length.
The depth and length trend of the semi-elliptical crack during crack propagation is shown in fig. 5. Figure 5 shows that the crack depth and crack length exhibit a tendency to grow slowly followed by significantly faster. And repeatedly performing trial calculation by adopting a method of gradually reducing delta a, and finally taking the total cycle number N p = 27542 times when the crack is expanded to the critical crack depth of 9.8mm when the step delta a = 0.005mm, and the total cycle number N c = 14902 times when the crack is expanded to the critical crack depth of 0.25 times, namely 2.45 mm.
Taking the smaller values of N p/2 and N c, 13771 times as fatigue life, the corresponding crack depth and crack length were the final allowable crack depth and crack length, i.e. the intersection point in FIG. 5, were 2.28mm and 5.71mm, respectively.
6. And establishing a crack safety and risk interval, and providing a basis for periodic monitoring.
During the service of the high-pressure vessel, actual cracks should be monitored periodically. When the crack depth and crack length of the actual crack monitored are not more than 2.28mm and 5.71mm, i.e. in the safety zone of fig. 6, the crack is considered safe, otherwise there is a risk.
The embodiment shows that the calculation method provided by the invention has feasibility for calculating the fatigue extension life of the radial crack of the outer wall shaft initiated at the longitudinal weld joint and the heat affected zone part of the cylinder of the high-pressure container, thereby providing a calculation method and a calculation basis for the fatigue extension life of the crack at the part for engineering personnel and solving the technical problems existing at present. The invention not only considers the stress caused by internal and external pressure loads, but also considers the residual stress generated in the welding process and the influence of the service medium environment, and the whole calculation process does not need to use other finite element calculation software, professional mathematical analysis software and the like, thereby ensuring the rapidness and conciseness of calculation, facilitating the application in engineering and having remarkable effect.
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 (8)
1. The method for calculating the fatigue extension life of the axial and radial crack based on the outer wall of the cylindrical longitudinal weld is characterized by comprising the following steps of:
s1, determining structural parameters and cyclic alternating load working conditions of a high-pressure thick-wall welding cylinder, and obtaining shape parameters of initial cracks of a longitudinal weld joint of the cylinder and the outer wall of a heat affected zone part;
s2, respectively calculating stress intensity factors of the deepest point and the free surface of the initial crack under the cyclic alternating load working condition, wherein the method specifically comprises the following steps:
s2.1, preparing a cylindrical longitudinal weld welded joint test piece, and measuring the yield strength of the test piece at the working temperature in an actual measurement mode;
S2.2, selecting one of the initial working condition and the final working condition to calculate a reference fitting coefficient A i', wherein i is an integer, and i is more than or equal to 0 and less than or equal to 3:
if the cylinder is not post-weld heat treated, then:
Wherein p i is the cylinder internal pressure load in MPa; k is the ratio of the outer diameter of the cylinder to the inner diameter of the cylinder; p o is the cylinder external pressure load in MPa; r t p0.2 is the actually measured yield strength of the test piece at the working temperature, and the unit is MPa;
② If the cylinder is post-weld heat treated, then:
Then, fitting stress distribution of a plane vertical to the radial crack of the outer wall shaft under the initial working condition and the final working condition by the A i' obtained by calculation;
S2.3, calculating an actual fitting coefficient A i under the initial working condition and the final working condition according to the following formula:
In the method, in the process of the invention,
A is the depth of a semi-elliptic crack, and the unit is mm;
t is the wall thickness of the cylinder, and the unit is mm;
Then, the calculated shape coefficient Q of the radial crack of the outer wall shaft is combined to obtain the stress intensity factors of the deepest point and the free surface of the radial initial crack of the outer wall shaft under the initial working condition and the final working condition;
S3, actually measuring the fracture toughness or stress corrosion fracture toughness of the test piece, establishing a crack growth rate calculation model of the test piece under the driving action of cyclic alternating load and service medium environment, and carrying out crack growth calculation to obtain the fatigue expansion life.
2. The method for calculating the fatigue life of the axial crack based on the outer wall of the cylindrical longitudinal weld according to claim 1, wherein: in the step S2.2, the stress distribution of the plane vertical to the radial crack of the outer wall shaft under the initial working condition and the final working condition is distributedThe fitting formula of (2) is:
In the method, in the process of the invention,
X is the distance measured from the free surface of the crack, and is a variable, the unit mm, and x is more than or equal to 0 and less than or equal to t.
3. The method for calculating the fatigue life of the axial crack based on the outer wall of the cylindrical longitudinal weld according to claim 2, wherein: in the step S2.3, the calculation formula of the shape coefficient Q of the radial crack of the outer wall shaft is:
In the method, in the process of the invention,
L is the length of the semi-elliptic crack, in mm.
4. A method of calculating the fatigue life of a radial crack of a shaft based on an outer wall of a cylindrical longitudinal weld according to claim 3, wherein: in the step S2.3, the stress intensity factor K I at the deepest point and the free surface of the radial initial crack of the outer wall shaft under the initial working condition and the final working condition is:
wherein, G 0、G1、G2 and G 3 are stress intensity factor influence coefficients and have no dimension.
5. The method for calculating the fatigue life of the axial crack propagation based on the outer wall of the cylindrical longitudinal weld according to claim 1 or 2 or 3 or 4, characterized in that: in the step S1, determining structural parameters of the high-pressure thick-wall welding cylinder includes: the outer radius of the cylinder, the inner radius of the cylinder, the use materials of the base material and the welding material of the cylinder and the cylinder welding process; the cyclic alternating load working condition comprises a pressure load and a temperature load under the initial working condition and the final working condition of the cylinder; the shape parameters of the initial cracks of the cylindrical longitudinal weld joint and the outer wall of the heat affected zone part comprise semi-elliptical crack depth and semi-elliptical crack length, and the semi-elliptical crack depth and the semi-elliptical crack length are measured by adopting a nondestructive testing method.
6. The method for calculating the fatigue life of the axial crack propagation based on the outer wall of the cylindrical longitudinal weld according to claim 1 or 2 or 3 or 4, characterized in that: in the step S3, the fracture toughness or stress corrosion fracture toughness of the test piece is obtained through testing a three-point bending test piece or a CT test piece; and carrying out a pre-crack fatigue expansion test on the test piece in a service medium environment in a three-point bending test piece or CT test piece mode to obtain a crack expansion rate calculation model.
7. The method for calculating the fatigue life of the axial crack based on the outer wall of the cylindrical longitudinal weld according to claim 6, wherein: in the step S3, when the crack extension calculation is performed, the critical crack depth is determined by using the fracture toughness K IC or the stress corrosion fracture toughness K ISCC of the test piece as a critical value, a semi-elliptical crack depth and a trend chart of the semi-elliptical crack length accumulated along with the cycle times in the extension process are obtained through the crack extension calculation, then a mode of gradually reducing the step length deltaa is adopted to obtain the total cycle times N p of the crack extension to the critical crack depth and the total cycle times N c of the crack extension to 0.25 times the critical crack depth, and the smaller value of N p/2 and N c is taken as the fatigue extension life.
8. The method for calculating the fatigue life of the axial crack based on the outer wall of the cylindrical longitudinal weld according to claim 7, wherein: after the fatigue extension life is obtained, the half-elliptic crack depth and the half-elliptic crack length corresponding to the fatigue extension life are the finally allowable crack depth and crack length; in the service process of the high-pressure thick-wall welding cylinder, when the monitored actual crack depth and the monitored actual crack length do not exceed the finally allowable crack depth and the crack length, the actual crack is safe, otherwise, a risk alarm is triggered.
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