Research on Crack Limit Dimension of Pressure Vessel Based on FAD Diagram

Pressure vessels are widely used in petrochemical, aerospace, transportation and other industries. In the process of processing, it will form surface opening defects, and these defects will threaten the production safety. In order to effectively avoid the occurrence of safety accidents and understand the service life of pressure vessels, it is necessary to predict and analyze the crack limit size. In response to the problem of complex stress and difficulty in theoretical calculation after cracks appear on the surface of pressure vessels, this article uses the ANSYS Workbench platform to simulate and analyze the pressure vessels and obtain relevant parameters such as stress intensity factor and stress. Through calculation, the toughness ratio and load ratio are obtained. Using the FAD Failure Assessment Diagram, the ultimate crack size of pressure vessels under safety conditions is obtained. This method provides a reference for crack analysis methods and safe use of pressure vessels.


Introduction
Pressure vessels are the most widely used equipment in industrial production control in China at present [1].During use, this equipment will cause various problems, especially cracks.This will affect the safety performance of pressure vessels and even lead to explosion accidents [2].To ensure the safety of pressure vessels, it is very important to find the allowable maximum crack size under the service load.Fan Kai et al. [3] proposed a safety evaluation method including restraint effect based on crack driving force method.Gao Yaodong et al. [4] studied the influence of initial crack size on the fatigue life of ultra-high pressure vessels in order to predict the service life of ultra-high pressure vessels more accurately.Yuan Shumeng et al. [5] compared the difference between GB/T 34019 standard and ASME Ⅷ -3 standard in calculating the critical crack growth life of pressure vessels, and concluded that fatigue crack growth analysis with stress intensity factor solution and dual parameter criterion of ASME Ⅷ -3 is relatively conservative.Liu Qi et al. [6] discussed the change rule of the nominal stress intensity factor of cracks in the presence of pits and cracks by using the finite element software.
To sum up, there are different methods to study the limit crack size of pressure vessels, and each method has its own characteristics.In this paper, ANSYS workbench software is used to analyze the static structure, and then the stress and stress intensity factor are obtained.Finally, the crack limit size is analyzed by FAD diagram.

Simulation Analysis of Pressure Vessels
To facilitate the analysis, the pressure vessel shown in figure 1 is taken as an example for research and analysis.The relevant parameters of pressure vessels are as follows: the pressure is 2.5MPa; The wall thickness of the cylinder is 18mm, the length of the cylinder is 7600mm, and the inner diameter is 2000mm; The material is 16MnR and the storage medium is nitrogen.

Pressure Vessel Crack Presetting
It can be known from the mechanical property [7] that the open type (type I) crack is easy to cause fatigue fracture.In addition, the crack defects of pressure vessels are mostly distributed on the inner surface.In the process of processing, the pressure vessel will form a surface opening defect, which extends along the axial direction of the vessel, and the crack shape is mostly semi-circular or semi-elliptical [8].Therefore, the preset crack is a semi elliptical opening type (Type I) crack.In severe cases, the deformation of pressure vessels poses a risk of safety accidents, so it is recommended to pre-install cracks at the location of the maximum deformation of the nitrogen storage tank.

Simulation Calculation
First, the parameters for prefab crack 1 are 1.6 mm depth and 3.2 mm long diameter.The crack of this size is preset on the inner wall of the nitrogen storage tank.Grid division shall be in the software default size.Stress intensity factor nephogram and equivalent stress nephogram of pressure vessel after prefab crack are obtained after simulation solution, as shown in figure 2 and figure 3. Figure 4 shows the corresponding stress intensity factor data curve of figure 2.   From figure 2, it can be concluded that the maximum stress intensity factor after the preset crack is 363.35 mm MPa • .From figure 4, the maximum stress is 653.37MPa.In this paper, the maximum stress intensity factor and maximum stress value of crack 2-7 are obtained successively by increasing the crack size at the same position and conducting the same analysis as that of crack 1.These results are presented in table 1.It can be seen from table 1 that, with the increase of crack size, the stress intensity factor obtained by simulation becomes bigger and bigger, but it never exceeds the fracture toughness of the material.

Failure Assessment Diagram
The two-criterion failure assessment diagram (FAD) is based on the elastoplastic fracture mechanics to determine the safety of crack defects.Two extreme failure cases are considered, namely elastic fracture and plastic instability.For the maximum allowable crack size, American ASME specifies to use the FAD (failure evaluation diagram) in API 579-1/ASME FFS-1 standard for calculation [9].
The failure assessment diagram is shown in figure 5.It has two main parameters: load ratio r L and toughness ratio r K .Their calculation formulas are shown in equations ( 1) -( 4) [10].p r L is the load ratio based on the principal stress, that is the ratio of the load corresponding to the principal stress to the plastic collapse load of the structure [11].Generally, the load ratio r L shall be less than the maximum allowable value max r L .
Failure Assessment Curve (FAC) is a function curve of load ratio and toughness ratio.Its function is shown in equation ( 3).FAC defines safe and unsafe zones.The FAD of several materials given in the API standard are shown in figure 5 [12].Based on the failure assessment diagram, the load ratio and the toughness ratio cannot be located at the upper part of the failure assessment curve.If they are located at the upper part, they will fail.

Calculation of Limit Size of Crack
The fracture toughness of 16MnR [13] is mm MPa 9 .3076 m 97.3MPaK Ic = = .Its yield strength and tensile strength can be obtained by looking up the table in Mechanical Design Manual [14].In order to obtain the toughness ratio and load ratio of each crack, the maximum stress and maximum stress intensity factor of crack 1-7 preset in Table 1 are put into equations ( 1) -( 4), as shown in table 2. The results are plotted on the FAD plot and compared as shown in figure 6.As shown in figure 6, when the crack depth is 2.1mm, it is within the failure assessment curve, belonging to the safe range.However, when the crack depth reaches 2.2 mm, the intersection of toughness ratio and load ratio is outside the failure assessment diagram, which is unsafe.So, 2.1 mm is taken as the limit depth of crack.

Conclusion
The evaluation of the limit size of cracks within the safety range of pressure vessels plays an important role in the design, manufacture, and repair of pressure vessels.Based on the fracture mechanics, this paper simulates the internal stress and stress intensity factor of pressure vessel after surface crack by

Figure 1 .
Figure 1.Three-dimensional model of nitrogen storage tank.

Figure 2 .
Figure 2. Simulation diagram of stress intensity factor.

Figure 4 .
Figure 4. Distribution of stress intensity factor.
Conference on Mechanical Engineering and Materials Journal of Physics: Conference Series 2694 (2024) 012058 IOP Publishing doi:10.1088/1742-6596/2694/1/0120585 Here, ys  is the yield strength of the material, uts  is the tensile strength of the material.

Table 1 .
Simulation Values of Different Crack Depth.

Table 2 .
Load ratio and toughness ratio of preconfigured crack.