Yang Hu，Jie Zhang，Jianlin Hu，Bo Xu
Keywords: CNG gas tank, ellipsoidal corrosion pit, mechanical behavior, stress, displacement
Abstract:
In this paper, mechanical behavior of CNG gas tank with single and multiple ellipsoidal
corrosion pit were investigated by finite element method. Effects of the length, depth,
number and arrangement of the corrosion pits and the internal pressure are discussed. The
results show that the high stress areas of the single axial and radial corrosion pits appear in
the axial direction. The Von Mises stress increases with the increasing of internal pressure
and depth. The stress of single radial corrosion pit decreases with the increasing of length.
With the increase of length and depth, the displacement of axial corrosion pit at the bottom
reduce. In the multiple corrosion pits, the more the number of corrosion pits, the more times
of stress fluctuation. When the number of corrosion pits exceeds 5, the high stress
concentration region moves to the radial outside of the corrosion pit. The vertical line
arrangement of corrosion pits has the greatest influence on the mechanical behavior of CNG
gas tank.
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Effect of Ellipsoidal Corrosion Pits on Mechanical Behaviour Behaviour of CNG Gas Tank Yang Hu1,2，Jie Zhang1,2*，Jianlin Hu1, Bo Xu2 1.Hebei Key Laboratory for Diagnosis, Reconstruction and Anti-disaster of Civil Engineering. Zhangjiakou, 075000, China 2. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China *Corresponding Author: Jie Zhang, E-mail: longmenshao@163.com Abstract In this paper, mechanical behavior of CNG gas tank with single and multiple ellipsoidal corrosion pit were investigated by finite element method. Effects of the length, depth, number and arrangement of the corrosion pits and the internal pressure are discussed. The results show that the high stress areas of the single axial and radial corrosion pits appear in the axial direction. The Von Mises stress increases with the increasing of internal pressure and depth. The stress of single radial corrosion pit decreases with the increasing of length. With the increase of length and depth, the displacement of axial corrosion pit at the bottom reduce. In the multiple corrosion pits, the more the number of corrosion pits, the more times of stress fluctuation. When the number of corrosion pits exceeds 5, the high stress concentration region moves to the radial outside of the corrosion pit. The vertical line arrangement of corrosion pits has the greatest influence on the mechanical behavior of CNG gas tank. Keywords: CNG gas tank, ellipsoidal corrosion pit, mechanical behavior, stress, displacement. Introduction Because environmental issues threaten the widespread use of fossil fuels, compressed natural gas (CNG) is considered to be a major alternative of conventional gasoline due to the characteristics of high performance and low pollution. As one of the main equipment for storing CNG, CNG gas tanks are susceptible to corrosion by chemical components such as hydrogen sulfide (H2S), causing corrosion defects. Corrosion defects can even cause leakage of compressed natural gas with the use time increases. Therefore, it is necessary to study the effect of corrosion defects on the mechanical behavior of CNG gas tank. CNG gas tank and pipeline are two common shell structures. At present, most of the research is mainly focused on the following: the influence of corrosion defects on the mechanical behavior of 1 pipeline. Siraj et al.[1] used the CSA and RSTRENG burst pressure capacity model to derived the probabilistic characteristics of defect geometry, and then promoted the application of CSA and RSTRENG models in reliability analysis. Sun and Cheng[2] established the models of steel pipelines that containing multiple corrosion defects with different geometries and orientations to determine the failure pressure. Benjamin et al.[3-4] presented the principle of pipeline corrosion defect interaction, and then compared the failure pressure that predicted by various evaluation methods. Chen et al.[5] Investigated the failure behavior and failure pressure of X80 pipeline with single corrosion defects and proposed an evaluation procedure for predicting the failure pressure. Nirbhay et al.[6] established the model of compressed natural gas (CNG) tank under different loading conditions. The effects of operating pressure, test pressure and burst pressure on behavior and failure were presented. Lie and Li[7] described two different assessment maps for predicting the failure pressure of compressed natural gas tank containing internal longitudinal surface cracks. Valsgard et al.[8] designed a new reliable method of CNG to meet the safety level and then explored the effects of welding length, manufacturing tolerances and manufacturing methods on fatigue performance. But few scholars combine the characteristics of the pipeline to study the effect of corrosion defects on the mechanical behavior of CNG gas tanks. In this paper, the research method of the corrosion defects of pipeline was adopted for the study of CNG gas tank. The model of CNG gas tank was established to investigate the mechanical behavior. The effect of internal pressure, length, depth, number and arrangement of corrosion defects on failure pressure were studied under internal pressure conditions. These results provide a theoretical basis for evaluating the safety and reliability of CNG gas tanks. Materials and Methods Material Model of Tank Material hardening has great influence on the blasting failure of shell. Therefore, the Ramberg-Osgood stress-strain rule is used in the model to reflect the hardening characteristics of the material after yielding[9]. σ ε σ = +α ε0 σ s σs Where n （1） ε 0 is the initial strain, ε 0 = σ s E . σ s is yield stress, MPa. E is elasticity modulus, MPa. α is the hardening coefficient. n is power hardening exponent. Failure Criteria of Tank There are three failure modes for numerical simulation of shells with corrosion defects. The first is 2 the elastic limit criterion[10]. If the stress in the Von Mises of corrosion region is greater than the yield stress of the material, the shell is liable to fail. The second is the failure criterion based on plastic limit state[11]. Failure of the shell with corrosion pits can be determined by the circumferential stress in the corrosion region. Material failure occurs when the circumferential stress reaches tensile strength. The third is the plastic failure theory caused by excessive local stress, which can be considered as the failure of the shell after the equivalent stress in the region of corrosion defect reaches the yield limit[12]. In this paper, to obtain the critical state of shell, the plastic failure theory is used to calculate the equivalent stress and Von Mises stress is considered to be the minimum equivalent, as shown in Eq.2: 1 2 2 2 2 1 σν = (σ 1 − σ 2 ) + (σ 1 − σ 3 ) + (σ 2 − σ 3 ) < [σ ] 2 Where, （2） σν is the Von Mises stress, MPa. σ 1 , σ 2 and σ 3 are three direction principal stresses, MPa. Refer to ASME B31G-2009[9], failure pressure is: d 1 − 0.85 2t t Pf = σ D 1 − 0.85 d ⋅ 1 t M （3） σ = σ s + 68.95 2 （4） 4 l l l2 M = 1 + 0.6275 − 0.00337 ≤ 50 , Dt Dt Dt M = 0.032 l2 l2 + 3.3, > 50 Dt Dt （5） （6） Where Pf is the failure pressure of shell, MPa. D is the outer diameter of the shell. t is the shell wall is thick, mm. d is the depth of the corrosion pit, mm. M is the Folias expansion coefficient. σ is the flow stress, MPa. σ s is the yield strength of the shell, MPa. l is the length of the corrosion pit, mm. Effect of Single Corrosion Pit Constitutive Model of Single Corrosion Pit 3 In this paper, the numerical simulation model of CNG406-100-20 high pressure tank is established by using finite element analysis software. The influence of the internal pressure, length, depth, number and arrangement of elliptical corrosion defects on the mechanical behavior is studied. As is shown in Fig.1, the elliptical corrosion pit is simulated in the middle of the CNG gas tank to simplify the calculation. According to the long axis direction, elliptical corrosion pits are divided into two categories: If the long axis direction of corrosion pits is the same as the axial direction of the gas tank, it is called axial corrosion pit. If the long axis direction is the same as the radial direction, it is called radial corrosion pit. The material of CNG406-100-20 high pressure gas tank is 30CrMo. the Yield stress is 720MPa, the Young’s modulus is 210×103MPa, and the Poisson’s ratio is 0.3. The internal pressure is applied to the inner wall of the gas tank. According to the actual situation, under different internal pressures, the effects of various factors on the mechanical behavior of the gas tank were considered. Such as the length, depth, number and arrangement of single and multiple corrosion pits. Fig.1 Finite element model of a single corrosion pit Internal Pressure of Gas Tank When the internal pressure is 20MPa, the different stress distribution of CNG tank with or without corrosion pits are shown in Fig.2. Under the action of internal pressure, the cylinder of CNG gas tank without corrosion pit is the region of high stress concentration, the two spherical shell on both sides are the stress transition area, and the mouth of bottle is a low stress region. When the tank produces a corrosion pit, the maximum stress is concentrated in the corrosion pit. The maximum stress of gas tank with corrosion pit is 1.3-1.6 times that of gas tank without corrosion pit. And the stress of axial corrosion pit is the greatest. Therefore, the corrosion pit has a great 4 influence on the mechanical behavior of CNG gas tank. Fig.2 The different stress distributions of CNG tank with or without corrosion pits When the length of single corrosion pit is 8mm, the depth is 4mm, the Von Mises stress of axial and radial corrosion pits under different internal pressure are shown in Fig.3. The stress is distributed symmetrically. A dumbbell-shaped high stress area appears in the axial direction of the corrosion pits, and a low stress area appears in the radial direction. The stress of radial corrosion pit is greater than that of axial corrosion pit. With the increasing of internal pressure, the Von Mises stress increases and the axial stress increases more than the radial stress. When the internal pressure is 20 MPa, the maximum Von Mises stress is less than the Yield stress, so the gas tank can be used safely. Under the same internal pressure condition, the maximum stress of the axial corrosion pit is greater than the radial corrosion pit. When the bottom wall thickness of the corrosion pit is the thinnest, but the Von Mises stress is the maximum. Therefore, material failure is more likely to occur in corrosion pits under higher internal pressure and longer working hours, and then lead to leakage. The corrosion pit has obvious influence on the stress of Y-axis. The radial cross section of ellipse corrosion pit is taken as the reference plane. The stress distribution of Y-axis in the range of reference plane ±0.04m are shown in Fig.4. The variation trend of Von Mises stress on both sides of the reference plane is similar. And the maximum stress increases with the increasing of internal pressure. When the internal pressure is the same, the Mises stress of radial corrosion pit increase first and then decrease, reaching the maximum at the reference plane. The maximum stress near the reference plane isn’t obvious change. But the Von Mises stress of axial corrosion pit increase to the maximum first, and then decrease. After passing the reference plane, the stress increases 5 to the maximum again and then decrease. With the increase of internal pressure, it is more obvious that stress decrease first and then increase under the maximum stress. The curve of axial corrosion pit is slower than that of the radial corrosion pit to get more accurate stress curve. When the internal pressure is 20MPa, stress at the reference plane has reached the limit and the stress has not decreased first and then increased. The reason for this is that the bottom of the corrosion pit is the thinnest and the Mises stress is limited by internal pressure. (a) Axial corrosion pit (b) Radial corrosion pit Fig.3 Von Mises stress of corrosion pit under different internal pressure (a) Axial corrosion pit (b) Radial corrosion pit Fig.4 Von Mises stress of corrosion pit in Y-axis under different internal pressure As the circumference of the gas tank is 160 times the long axis of the corrosion pit, the corrosion pit can be regarded as a plane to study the displacement of corrosion pit under different internal pressure. Displacement of corrosion pit in XZ plane under different internal pressure are shown in Fig.5. The displacement of corrosion pit increases with the increase of internal pressure. When the angles are 0° and 180°, the thickness of the wall is the largest, which is the same as in the no 6 corrosion pit. When the angle is 90°, the thickness of the wall is the thinnest. In the range of 0° to 90° and 180° to 90°, the displacement increases with the decrease of wall thickness. And the displacement decreases by a small margin at 90°. The greater the internal pressure, the more obvious the change in the thinnest of the wall thickness. This is due to the variation of radians at the bottom of the elliptical corrosion pit, which results in uneven wall thickness and uneven stress distribution. In the XZ plane, the curve of the radial corrosion pit is gentler than that of axial corrosion pit. So, the displacement of radial corrosion pit fluctuates less. Fig.5 Displacement of corrosion pit in XZ plane under different internal pressure Geometry of Single Corrosion Pit Pit Length and depth are the two most important geometric parameters of the corrosion pit. When the internal pressure is 20MPa, the Fig.6 shows the maximum Von Mises stress of corrosion pit under different length and depth. When the depth of the corrosion pit is 4mm, the axial and radial corrosion pit models with the length of 4, 6, 8, 10, 12mm were established respectively as shown in Fig.6(a). With the increasing of length, the stress of axial corrosion pit increases, but the stress of radial corrosion pit decreases. The difference between the stress of radial corrosion pit reducing is greater than that of axial corrosion pit increasing. As shown in Fig.6(b) when the length of corrosion pit is 8mm, the stress increases of radial corrosion pit is faster than that of axial corrosion pit with the increasing of depth. Therefore, the length and depth of corrosion pit have greater influence on radial corrosion pit. 7 (a) (b) Fig.6 Von Mises stress of corrosion pit under geometric parameters Fig.7 The stress distribution of CNG gas tank under different length The stress distribution of CNG gas tank under different length is shown in Fig.7. The high stress concentration region appears in the corrosion pit. The longer the length of axial corrosion pit is, the slender the high stress area is. With the increasing of length, the maximum stress of radial corrosion pit is concentrated in the bottom of the pit. And the radial sub-high stress area appears in the transition region between the cylinder and the spherical shell. As shown in Fig.8, the high stress area increases with depth increases. When the depth is 5mm, the sub-high stress area appears in the radial direction. Therefore, the effect of length and depth on radial stress is greater than axial stress. Displacement of corrosion pit in XZ plane under geometric parameters is shown in Fig.9. The displacement of different length is smaller than that of depth. When the wall thickness is the 8 thinnest at 90°, the displacement of radial corrosion pit under different length and depth is the maximum. But the displacement of axial corrosion pit fluctuations. At the thinnest wall thickness, the displacement is not the largest. As shown in Fig.8, the axial corrosion pit has the maximum stress at the two ends of the long axis. As the length of the long axis increases, the high stress region moves outward, the stress in the middle of the corrosion pit decreases, and the displacement decreases. Fig.8 The stress distribution of CNG gas tank under different depth (a) Length of corrosion pit (b) Depth of corrosion pit Fig.9 Displacement of corrosion pit in XZ plane under geometric parameters Effect of Multiple Corrosion Pits Constitutive Model of Multiple Corrosion Pits When the distance is 20mm, the length and depth of radial corrosion pits are 8mm and 4mm, respectively. The finite element model of multiple corrosion pits is shown in Fig.10. In actual working conditions, corrosion pits usually appear in the form of multiple pits. Therefore, the 9 multiple corrosion pits model can more accurately simulate the mechanical behavior of CNG gas tank. Fig.10 Finite element model of multiple corrosion pits The Number of Multiple Corrosion Pits The local stress distribution of CNG gas tank under different number of corrosion pit as shown in Fig.11. A dumbbell-shaped high stress area appears in the axial direction of the corrosion pits. And a spindle-shaped low stress area appears in the radial direction. The maximum Von Mises stress is concentrated at the bottom of the corrosion pit. With the increasing of the number of corrosion pits, the high stress region of the outside corrosion pit moves to the side with fewer corrosion pits. When the number of corrosion pits is small, the maximum stress occurs at the corrosion pit in the middle. When the number of corrosion pits exceeds 5, the maximum stress occurs in the outermost corrosion pit. The change of radians is the main cause of this phenomenon. The larger the number of radians corrosion pits, the larger the ratio of the corrosion range to the radians of the cylinder. Fig.11 The stress distribution under different number of corrosion pits 10 In order to further study the influence of the number of corrosion pits on the mechanical behavior of the CNG gas tank, the Von Mises stress on the cross section of the corrosion pit is considered. As shown in the Fig.12, the number of corrosion pits has little effect on the stress of the gas tank at a distance from the corrosion pit. And the stress fluctuates up and down near the corrosion pit. The number of corrosion pits affects the number of fluctuations. The greater the number of corrosion pits, the greater the stress fluctuation. As the number of corrosion pits increases, the average stress value increases. Fig.12 Von Mises stress under different number of corrosion pits Fig.13 Displacement in XZ plane under different number of corrosion pits In the range of 0 to 180°, the displacement in XY cross section of pits is shown in the Fig.13. Taking the YZ plane as the symmetric plane, the displacement of the gas tank is symmetrical. The 11 closer it is to the corrosion pit, the bigger the displacement of the gas tank is. In the initial range of 30°, the displacement of single corrosion pit is the smallest. The displacement of CNG gas tank increases with the number of corrosion pits. The displacement at the bottom of the corrosion pit is less than that on both sides of the corrosion pit. And the difference displacement of corrosion pit between bottom and sides decrease with the reducing of the number of corrosion pits. Therefore, the number of corrosion pit has great influence on the displacement. The Rank of Multiple Corrosion Pits Multi-corrosion pits are distributed in the inner wall of the gas tank in different arrangements. Taking three corrosion pits as an example, consider the four different arrangements to study the mechanical properties of gas cylinders. The stress distribution of CNG tank under different arrangement of corrosion pits as shown in Fig.14. When the corrosion pits are arranged in a vertical line, the stress is the maximum. When the corrosion pits are arranged in an inclined line, the stress is the minimum, and the interaction of corrosion pits is smaller. When the corrosion pits are arranged in an inclined line, the interaction between the corrosion pits is minimal. The stress difference between the spherical shell and the cylinder of CNG gas tank is small, when the corrosion pits are arranged in vertical line. This phenomenon is due to the axial stress is most affected by the arrangement of the vertical lines of the corrosion pit. Fig.14 The stress distribution of CNG tank under different arrangement of corrosion pits Von Mises stress under different arrangement of corrosion pits is shown in Fig.15. The stress fluctuates violently in the corrosion pit region. The maximum stress is in the corrosion pit and is 1.4 times that in the non-corrosion pit. When the corrosion pits are arranged in a vertical line, the maximum stress is appeared. The symmetrical triangle arrangement of corrosion pits affects each other and the stress fluctuation on the path is minimized. Therefore, the rank of multiple corrosion pits can change the stress distribution. 12 Fig.15 Von Mises stress under different arrangement of corrosion pits The displacement in XZ plane under different arrangement of corrosion pits is shown in Fig.16. The displacement of symmetrical triangle arrangement is least affected by a single corrosion pit. When the corrosion pits are arranged in an inclined line and a vertical line, the corrosion pit in the middle has the greatest influence on the displacement of the path. And the displacement of inclined line is larger than that of vertical line. When the corrosion pits are arranged in a horizontal line, the displacement of path affected by three corrosion pits. Fig.16 Displacement in XZ plane under different arrangement of corrosion pits 13 Conclusions Corrosion pits seriously threaten the safe use of CNG gas tanks. There are mainly two types of corrosion pits on the inner wall of the gas tank, axial corrosion pits and radial corrosion pits. Effects of the length, depth, number and arrangement of the corrosion pits and the internal pressure of the gas tank on the mechanical behavior of the CNG gas tank were discussed. The results are as follows: （1）In the single corrosion pit condition, the high stress areas of the axial and radial corrosion pits appear in the axial direction of the corrosion pit. The Von Mises stress increases with the increasing of internal pressure and depth. The stress of radial corrosion pit decreases with the increasing of length. With the increase of length and depth, the high stress area of the axial corrosion pit moves outward in the axial direction to decrease the stress of bottom, which reduce the displacement at the bottom. （2）In the multiple corrosion pits, the more the number of corrosion pits, the more times of stress fluctuation. When the number of corrosion pits exceeds 5, the high stress concentration region moves to the radial outside of the corrosion pit. The effect of multiple corrosion pits on displacement is similar to that of single corrosion pit. The vertical line arrangement of corrosion pits has the greatest influence on the mechanical behavior of CNG gas tank. Acknowledgments This work is supported by Hebei Key Laboratory for Diagnosis, Reconstruction and Anti-disaster of Civil Engineering, Nanchong science and technology program (NC17SY4018), Project of Sichuan education hall (17ZA0423), and State Key Laboratory for GeoMechanics and Deep Underground Engineering (China University of Mining & Technology , SKLGDUEK1729) . References [1] ‘Evaluation of statistics of metal-loss corrosion defect profile to facilitate reliability analysis of corroded pipelines’, T. Siraj, and W. X. Zhou, Journal of Pressure Vessels and Piping, 166, pp107-115, 2018. [2] ‘Assessment by finite element modeling of the interaction of multiple corrosion defects and the effect on failure pressure of corroded pipelines’, J. I. Sun, and Y. F. Cheng, Engineering Structures, 165, 15, pp278-286, 2018. [3] ‘Interaction of corrosion defects in pipelines– part 1: fundamentals’, A. C. Beniamin, J. L. F. Freire, and R. D. 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